Aspen Adsim

Aspen Adsim2004.1 Adsorption Reference Guide Who Should Read this Guide 2 Who Should Read this Guide This guide contains reference information for use by experienced users of the Aspen Adsim application. The guide also describes the following Aspen Adsim features: • Numerical methods for solving the partial differential equations. • Estimation module. • Cyclic Organizer. • Flowsheeting strategies. General Information 3 General Information This section provides Copyright details and lists any other documentation related to the Aspen Adsim 2004.1 release. Copyright Version: 2004.1 April 2005 Copyright © 1991-2005 Aspen Technology, Inc, and its applicable subsidiaries, affiliates, and suppliers. All rights reserved. This Software is a proprietary product of Aspen Technology, Inc., its applicable subsidiaries, affiliates and suppliers and may be used only under agreement with AspenTech. 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All other brand and product names are trademarks or registered trademarks of their respective companies. This document is intended as a guide to using AspenTech's software. This documentation contains AspenTech proprietary and confidential information and may not be disclosed, used, or copied without the prior consent of AspenTech or as set forth in the applicable license. Corporate Aspen Technology, Inc. Phone: (1) (617) 949-1000 Ten Canal Park Toll Free: (1) (888) 996-7001 General Information 5 Cambridge, MA 02141-2201 Fax: (1) (617) 949-1030 USA URL: http://www.aspentech.com General Information 6 Related Documentation In addition to this document, the following documents are provided to help users learn and use the Aspen Adsim applications. Title Content Aspen Adsim 2004.1 Library Reference Guide Describes the models, streams, procedures and submodels available in Aspen Adsim. AES 2004.1 Installation Guide Full installation procedures for both server and client. Aspen Engineering Suite 2004.1 What’s New Guide An overview of new features and functionality within this release. Technical Support 7 Technical Support Online Technical Support Center AspenTech customers with a valid license and software maintenance agreement can register to access the Online Technical Support Center at: http://support.aspentech.com You use the Online Technical Support Center to: • Access current product documentation. • Search for technical tips, solutions, and frequently asked questions (FAQs). • Search for and download application examples. • Search for and download service packs and product updates. • Submit and track technical issues. • Search for and review known limitations. • Send suggestions. Registered users can also subscribe to our Technical Support e-Bulletins. These e-Bulletins proactively alert you to important technical support information such as: • Technical advisories. • Product updates. • Service Pack announcements. • Product release announcements. Technical Support 8 Phone and E-mail Customer support is also available by phone, fax, and e-mail for customers who have a current support contract for their product(s). Toll-free charges are listed where available; otherwise local and international rates apply. For the most up-to-date phone listings; please see the Online Technical Support Center at: http://support.aspentech.com Support Centers Operating Hours North America 8:00 – 20:00 Eastern time South America 9:00 – 17:00 Local time Europe 8:30 – 18:00 Central European time Asia and Pacific Region 9:00 – 17:30 Local time Contents 9 Contents GENERAL INFORMATION................................................................................. 3 Copyright................................................................................................................ 3 Related Documentation............................................................................................. 6 TECHNICAL SUPPORT...................................................................................... 7 Online Technical Support Center ................................................................................ 7 Phone and E-mail ..................................................................................................... 8 INTRODUCING ASPEN ADSIM ....................................................................... 17 1 GAS ADSORPTION PROCESSES.................................................................. 18 About Gas Adsorption Processes............................................................................... 18 Bed Model Assumptions for Gas Adsorption Processes ................................................. 19 About Aspen Adsim's Bed Models ............................................................................. 20 Bed Model Ports................................................................................................ 20 Configure Form (Gas) ............................................................................................. 21 Configure Form (gas): Bed Type.......................................................................... 22 Configure Form (gas): Spatial Dimensions ............................................................ 24 Configure Form (gas): Internal Heat Exchanger..................................................... 25 Configure Layer Form (gas) ..................................................................................... 26 General Tab (gas) .................................................................................................. 26 General Tab (gas): Discretization Method to be used.............................................. 26 General Tab (gas): Number of Nodes ................................................................... 27 General Tab (gas): Number of Radial Nodes.......................................................... 27 General Tab (gas): Flux Limiter to be used ........................................................... 27 General Tab (gas): Gas Model Assumption............................................................ 27 Material/Momentum Balance Tab (gas) ..................................................................... 28 About Axial Dispersion in Gas Adsorption Processes ............................................... 28 Material/Momentum Balance Tab (gas): Material Balance Assumption....................... 29 Material/Momentum Balance Tab (gas): Momentum Balance Assumption .................. 31 Material/Momentum Balance Tab (gas): 2-D Dispersive Properties ........................... 33 Kinetic Model Tab (gas) .......................................................................................... 37 Kinetic Model Tab (gas): Film Model Assumption.................................................... 37 Kinetic Model Tab (gas): Kinetic Model Assumption ................................................ 37 Contents 10 Kinetic Model Tab (gas): Form of Lumped Resistance Model .................................... 50 Kinetic Model Tab (gas): Molecular Diffusivities ..................................................... 51 Kinetic Model Tab (gas): Form of Mass Transfer Coefficients.................................... 52 Kinetic Model Tab (gas): Apply Cyclic Correction.................................................... 55 Kinetic Model Tab (gas): Estimated Mass Transfer Coefficient Assumption ................. 56 Gas Adsorption Layer (gas): Particle Material Balance, Number of Nodes................... 56 Kinetic Model Tab (gas): Particle Material Balance, Effective Diffusivity ..................... 56 Isotherm Tab (gas) ................................................................................................ 57 About Adsorption Isotherms for Gas Adsorption Processes ...................................... 57 Guidelines for Choosing Aspen Adsim Isotherm Models (gas)................................... 58 About Multi-Component Mixture Isotherms (gas) ................................................... 58 Isotherm Tab (gas): Isotherm Assumed for Layer .................................................. 61 Isotherm Tab (gas): Adsorbed Solution Theory...................................................... 70 Isotherm Tab (gas): Isotherm Dependency........................................................... 70 Energy Balance Tab (gas)........................................................................................ 70 Energy Balance Tab (gas): Energy Balance Assumption .......................................... 70 Energy Balance Tab (gas): Consider Heat of Adsorbed Phase................................... 71 Energy Balance Tab (gas): Heat of Adsorption Assumption...................................... 72 Energy Balance Tab (gas): Form of Heat Transfer Coefficient................................... 73 Energy Balance Tab (gas): Form of Gas Thermal Conductivity ................................. 75 Energy Balance Tab (gas): Heat Transfer to Environment........................................ 76 Energy Balance Tab (gas): Form of Gas-Wall Heat Transfer Coefficient ..................... 78 Reaction Tab (gas) ................................................................................................. 79 About Gas Adsorption with Reaction Processes ...................................................... 79 Reaction Tab (gas): Reactions Present ................................................................. 80 Reaction Tab (gas): Homogeneous Rate Dependency ............................................. 80 Reaction Tab (gas): Number of Homogeneous Reactions......................................... 81 Reaction Tab (gas): Heterogeneous Rate Dependency ............................................ 81 Reaction Tab (gas): Number of Heterogeneous Reactions ....................................... 81 Reaction Tab (gas): Are Solid Reactants Present.................................................... 82 Reaction Tab (gas): Solid Reactant List ................................................................ 82 Procedures Tab (gas).............................................................................................. 82 Gas Adsorption: Summary of Mass and Energy Balance Equations................................. 82 Gas Adsorption: Mass Balance for Gas Phase......................................................... 83 Gas Adsorption: Mass Balance for Additional Solid Phase ........................................ 83 Gas Adsorption: Gas Phase Energy Balance........................................................... 84 Gas Adsorption: Solid Phase Energy Balance......................................................... 84 Gas Adsorption: Wall Energy Balance................................................................... 85 Gas Adsorption: Summary of Factors that affect the Mass Balance Equations............. 85 Gas Adsorption: Defining the Mass Balance for Additional Solid Phases ..................... 87 Gas Adsorption: Summary of Factors that affect the Energy Balance ........................ 87 Contents 11 Gas Adsorption: Defining the Energy Balance in the Gas Phase................................ 87 Gas Adsorption: Defining the Energy Balance for the Solid Phase ............................. 90 Gas Adsorption: Defining Energy Balance for the Wall ............................................ 92 Gas Adsorption: Explanation of Equation Symbols....................................................... 93 2 GAS CYCLIC STEADY STATE MODELING..................................................... 99 Introduction .......................................................................................................... 99 What is CSS Modeling…? ........................................................................................100 Discretization Techniques for Time and Space ...........................................................103 Connectivity between CSS Models ...........................................................................103 Bed Model Details .................................................................................................104 Material Balance ..............................................................................................104 Momentum Balance..........................................................................................105 Kinetic Model ...................................................................................................106 Energy Balance................................................................................................109 Adsorption Equilibrium Models ................................................................................112 Introduction ....................................................................................................112 Mathematical Equation Form for Extended Langmuir 1...........................................113 Mathematical Equation Form for Extended Langmuir 2...........................................113 Mathematical Equation Form for Extended Langmuir 3...........................................114 Mathematical Equation Form for Extended Langmuir 4...........................................115 Mathematical Equation Form for Extended Langmuir 5...........................................116 Mathematical Equation Form for Loading Ratio Correlation 1...................................117 Mathematical Equation Form for Loading Ratio Correlation 2...................................118 Mathematical Equation Form for Loading Ratio Correlation 3...................................119 Mathematical Equation Form for Loading Ratio Correlation 4...................................120 Mathematical Equation Form for Loading Ratio Correlation 5...................................121 Mathematical Equation Form for Extended Dual-Site Langmuir 1.............................122 Mathematical Equation Form for Extended Dual-Site Langmuir 2.............................123 I.A.S.T. (Ideal Adsorbed Solution Theory)............................................................123 Pure Isotherm List for the IAST Calculation of CSS................................................125 Langmuir 1 .....................................................................................................126 Langmuir 2 .....................................................................................................126 Langmuir 3 .....................................................................................................127 Langmuir 4 .....................................................................................................128 Langmuir 5 .....................................................................................................129 Dual-Site Langmuir 1........................................................................................130 Dual-Site Langmuir 2........................................................................................130 Sips (Langmuir-Freundlich) 1.............................................................................131 Sips (Langmuir-Freundlich) 2.............................................................................132 Sips (Langmuir-Freundlich) 3.............................................................................133 Contents 12 Sips (Langmuir-Freundlich) 4.............................................................................134 Sips (Langmuir-Freundlich) 5.............................................................................135 Henry 1 ..........................................................................................................136 Henry 2 ..........................................................................................................136 Henry 3 ..........................................................................................................137 Henry 4 ..........................................................................................................137 Freundlich 1 ....................................................................................................138 Toth 1 ............................................................................................................139 BET 1.............................................................................................................139 User Guidelines.....................................................................................................140 How to Create a CSS Simulation Flowsheet ..........................................................140 How to Create a Dynamic Simulation Flowsheet using CSS Models ..........................158 How to Convert a CSS Flowsheet to a Dynamic Flowsheet ......................................174 How to Convert a Dynamic Flowsheet into a CSS Flowsheet ...................................177 Developer’s Tips to Get Better Convergence Property in CSS Simulation...................180 3 ION-EXCHANGE PROCESSES.....................................................................184 About Ion-Exchange Processes...........................................................................184 Bed Model Assumptions for Ion-Exchange............................................................185 Configure Form (ionx).......................................................................................185 Configure Layer Form (ionx) ..............................................................................185 General Tab (ionx) ...........................................................................................186 General Tab (ionx): Discretization Method to be Used............................................186 General Tab (ionx): Number of Nodes .................................................................186 Material/Momentum Balance Tab (ionx)...............................................................186 Material/Momentum Balance Tab (ionx): Material Balance Assumption.....................186 About Axial Dispersion in Ion-Exchange Processes ................................................188 Deciding When to Use Axial Dispersion in Ion-Exchange Processes ..........................188 Kinetic Model Tab (ionx)....................................................................................189 Kinetic Model Tab (ionx): Film Model Assumption..................................................189 Kinetic Model Tab (ionx): Kinetic Model Assumption ..............................................190 Kinetic Model Tab (ionx): Form of Lumped Resistance ...........................................190 Kinetic Model Tab (ionx): Form of Mass Transfer Coefficient ...................................191 Isotherm Tab (ionx) .........................................................................................191 About Adsorption Isotherms for Ion-Exchange Processes .......................................191 Isotherm Tab (ionx): Isotherm Assumed for Layer ................................................192 Summary of Mass Balance Equations for Ion-Exchange Processes ...........................194 Explanation of Equation Symbols for Ion-Exchange Processes.................................195 4 LIQUID ADSORPTION PROCESSES ...........................................................197 About Liquid Adsorption Processes......................................................................197 Bed Model Assumptions for Liquid Adsorption.......................................................198 Contents 13 Configure Form (liq) .........................................................................................198 Configure Layer Form (liq).................................................................................198 General Tab (liq)..............................................................................................199 General Tab (liq): Discretization Method to be Used ..............................................199 General Tab (liq): Number of Nodes....................................................................199 Material/Momentum Balance (liq) .......................................................................199 Material/Momentum Balance Tab (liq): Material Balance Assumption .......................199 Material/Momentum Balance Tab (liq): Pressure Drop Assumption...........................201 Material/Momentum Balance Tab (liq): Velocity Assumption ...................................202 Material/Momentum Balance Tab (liq): Overall Material Balance Assumption.............202 Kinetic Model Tab (liq) ......................................................................................202 Kinetic Model Tab (liq): Film Model Assumption ....................................................203 Kinetic Model Tab (liq): Kinetic Model Assumption.................................................203 Kinetic Model Tab (liq): Form of Mass Transfer Coefficient......................................204 About Adsorption Isotherms for Liquid Adsorption.................................................205 Guidelines for Choosing Aspen Adsim Isotherm Models ..........................................205 The Ideal Adsorbed Solution Theory (IAS) ...........................................................206 Isotherm Tab (liq): Isotherm Assumed for Layer...................................................206 Energy Balance Tab (liq) ...................................................................................212 Energy Balance Tab (liq): Energy Balance Assumption...........................................212 Energy Balance Tab (liq): Consider Heat of Adsorbed Phase ...................................214 Energy Balance Tab (liq): Heat of Adsorption Assumption ......................................214 Energy Balance Tab (liq): Form of Heat Transfer Coefficient ...................................215 Energy Balance Tab (liq): Form of Fluid Thermal Conductivity.................................216 Energy Balance Tab (liq): Heat Transfer to Environment ........................................217 Procedures Tab (liq) .........................................................................................219 Liquid Adsorption: Summary of Mass and Energy Balance ......................................219 Liquid Adsorption: Mass Balance.........................................................................219 Liquid Adsorption: Solid Phase Energy Balance .....................................................220 Liquid Adsorption: Fluid Phase Energy Balance .....................................................220 Liquid Adsorption: Wall Energy Balance...............................................................220 Liquid Adsorption: Explanation of Equation Symbols..............................................221 5 NUMERICAL METHODS .............................................................................224 About Numerical Methods..................................................................................224 Choosing the Discretization Method ....................................................................225 About the Discretization Methods........................................................................225 Upwind Differencing Scheme 1...........................................................................227 Upwind Differencing Scheme 2...........................................................................228 Central Differencing Scheme 1...........................................................................228 Central Differencing Scheme 2...........................................................................229 Leonard Differencing Scheme.............................................................................229 Contents 14 Quadratic Upwind Differencing Scheme ...............................................................230 Mixed Differencing Scheme................................................................................232 Biased Upwind Differencing Scheme....................................................................233 Fromms’ scheme..............................................................................................234 Flux Limited Discretization Scheme.....................................................................235 6 ESTIMATION WITH ASPEN ADSIM............................................................236 Two Estimation Tools in Aspen Adsim 2004.1 .......................................................236 About the Estimation Module .............................................................................236 Defining Estimated Variables in the Estimation Module ..........................................238 Steady-State Estimation Using the Estimation Module ...........................................239 Manually Entering Steady-State Experimental Data...............................................239 Steady-State Experimental Data from the Clipboard..............................................240 Dynamic Estimation Using the Estimation Module .................................................242 Manually Entering Dynamic Experimental Data .....................................................243 Dynamic Experimental Data from the Clipboard....................................................244 Performing Estimation Using the Estimation Module ..............................................247 Converting Estimation Module Data ....................................................................247 Recommendations When Using the Estimation Module...........................................247 7 CYCLIC OPERATION .................................................................................249 Cyclic Operations in Aspen Adsim 2004.1.............................................................249 About the Cycle Organizer .................................................................................249 Opening the Cycle Organizer..............................................................................250 Cycle Organizer Window....................................................................................250 Step Control ....................................................................................................252 Time Driven Step .............................................................................................252 Discrete Event Driven Step................................................................................252 Step Variables .................................................................................................256 Adding Step Variables.......................................................................................256 Removing Step Variables...................................................................................257 Changing Step Variable Values...........................................................................257 Interaction Control ...........................................................................................258 Defining a Step Interaction................................................................................258 Deleting Interaction Steps .................................................................................259 Adding Extra Interaction Steps...........................................................................259 Interacting Steps and Time Controls ...................................................................259 Additional Cycle Controls...................................................................................260 Maximum Cycles Box........................................................................................260 Record Initial and Record Frequency Boxes..........................................................261 Take Snapshot Box...........................................................................................261 Cyclic Steady State Testing Box .........................................................................261 Contents 15 Additional Step Controls....................................................................................262 Execute End of Step Script Box ..........................................................................262 Take Snapshot at End of Step Box......................................................................262 Generating Cyclic Tasks ....................................................................................263 Activating and Deactivating Cyclic Tasks..............................................................263 Cyclic Reports..................................................................................................264 Preparing Aspen Adsim for Cyclic Reporting .........................................................264 Cyclic Stream Reports.......................................................................................265 Cyclic Recovery Reports ....................................................................................266 8 FLOWSHEETING .......................................................................................268 About Model Types ...........................................................................................268 General Model Types ........................................................................................269 Reversibility ....................................................................................................269 About Flowsheets in Aspen Adsim.......................................................................272 Connectivity on Flowsheets................................................................................273 Templates.......................................................................................................274 Demonstrations ...............................................................................................274 Types of Flowsheet in Aspen Adsim.....................................................................275 Types of Flowsheet: Simple Flowsheet ................................................................275 Intermediate Flowsheet.....................................................................................276 Full Flowsheet..................................................................................................277 Single Bed Approach.........................................................................................278 Pressure Interaction Diagram.............................................................................278 Interactions.....................................................................................................281 Specifications for Flowsheets .............................................................................283 Solver Options.................................................................................................283 Run Time Options.............................................................................................285 Model Specification...........................................................................................286 Consistency and Problem Definition Checks..........................................................287 Physical Properties ...........................................................................................288 Use of User Fortran ..........................................................................................289 Using a Physical Properties Application ................................................................290 Switching Between Methods...............................................................................290 Connecting to Aspen Dynamics Flowsheets ..........................................................291 Typical Workflows ............................................................................................291 Valid Flowsheet Combinations ............................................................................293 Connecting to a Single Bed Approach Flowsheet ...................................................296 9 REFERENCE LIST FOR ADSORPTION PROCESSES......................................298 INDEX ..........................................................................................................299 Contents 16 Introducing Aspen Adsim 17 Introducing Aspen Adsim Aspen Adsim simulates gas processes with adsorption only, or adsorptive reaction gas processes where both reaction and adsorption occur simultaneously. Gas-phase adsorption is widely used for the large-scale purification or bulk separation of air, natural gas, chemicals and petrochemicals. 1 Gas Adsorption Processes 18 1 Gas Adsorption Processes This chapter contains information on: • About Gas Adsorption Processes. • Bed Model Assumptions for Gas Adsorption Processes. • About Aspen Adsim Bed Models. • Configure Form. • Configure Layer Form. • General Tab. • Material/Momentum Balance Tab. • Kinetic Model Tab. • Isotherm Tab. • Energy Balance Tab. • Reaction Tab. • Procedure Tab. • Summary of Mass and Energy Balance Equations. • Explanation of Equation Symbols. About Gas Adsorption Processes Gas-phase adsorption is widely used for the large-scale purification or bulk separation of air, natural gas, chemicals and petrochemicals, where it is often better to use gas-phase adsorption rather than the older unit operations of distillation and absorption. Adsorbent attracts molecules from the gas, removing the molecules from the gas phase and concentrate on the surface of the adsorbent. Many process concepts have been developed to allow: • Efficient contact of feed gas mixtures with adsorbent to carry out desired separations. • Efficient regeneration of the adsorbent for subsequent reuse. 1 Gas Adsorption Processes 19 For gas phase applications, most commercial adsorbents are pellets, beads, or other granular shapes, typically about 1.5 to 3.2 mm in diameter. These adsorbents are usually packed into fixed beds through which the gaseous feed mixtures are passed. Normally, the process is cyclic. When the bed capacity is exhausted, the feed flow is stopped to finish the loading step of the process. The bed is then treated to remove the adsorbed molecules in separate regeneration steps, then the cycle is repeated. Gas phase adsorption processes have seen a growth in both variety and scale, especially since 1970. This is due mainly to improvements in adsorbents, for example the discovery of porous adsorbents with a large surface area, such as zeolites. These advances have encouraged parallel inventions of new process concepts. Increasingly, the development of new applications requires close cooperation in adsorbent design and process cycle development and optimization. Bed Model Assumptions for Gas Adsorption Processes Aspen Adsim simulates gas processes with adsorption only, or adsorptive reaction gas processes where both reaction and adsorption occur simultaneously. For gas processes, the bed model makes the following assumptions: • Isothermal or non-isothermal conditions apply. Terms in the energy balances include: − Thermal conductivity of gas and thermal conductivity of solid. − Compression. − Gas-solid heat transfer. − Heat of adsorption. − Enthalpy of adsorbed phase. − Heat exchange with environment. − Wall energy terms. − Enthalpy of mixing is negligible. • Plug flow or plug flow with axial dispersion occurs. • The system is fully mixed in the radial direction. Alternatively, radial dispersion and thermal conduction are used to account for radial material and temperature distributions. • The gas phase is ideal or non-ideal, the non-ideal behavior needing a compressibility factor. • Gas phase pressure is either constant (with velocity either constant, or varying according to mass balance and only applicable for breakthrough simulations), or the pressure varies according to a laminar or turbulent flow momentum balance. 1 Gas Adsorption Processes 20 • Mass transfer is described using a lumped overall resistance, or by a model that accounts separately for micropore and macropore effects. The driving force is based on a liquid or solid film, and is either linear, quadratic, or user-specified. Mass transfer coefficients are either constant, or vary with local conditions. A limited rigorous particle material balance functionality is provided. • Adsorption isotherms are either applicable for single or multi-component adsorption. IAS theory can be used for pure component isotherms. About Aspen Adsim's Bed Models The table shows the classifications of adsorption bed models: Name Type Model type Flow setter under compressible flow conditions. Flow type Reversible. Time dependency Dynamic. Reversible models handle forward or reverse flow in the bed. They contain dummy variables associated with the input and output streams. The adsorption bed models are usually flow setters, but within the bed they can be both flow setters and pressure setters. This is because they determine internal pressure profiles and gas velocity profiles, provided the general compressible flow model is used. The nature of the process and its operating conditions determine the type of model to use. For example, a bulk separation process such as producing oxygen-rich gas from air requires a different model to that for a purification process for removing trace impurities. The adsorption column models use a set of partial differential equations to represent the momentum, heat, and material balances across the column. You can add further relationships, which are specific to the various options. Bed Model Ports Bed models contain an input and an output port. Each port has associated variables that correspond to the material connection stream variables, and which allow for reversible flow. 1 Gas Adsorption Processes 21 Configure Form (Gas) On the Configure form of the bed model: 1 Enter the number of layers within the bed (one or more). 2 Enter the bed type: Vertical, Horizontal or Radial. See Configure Form for Gas Process Bed Model, later. 3 For vertical beds only, define the spatial dimensions of the bed model: 1-D or 2-D. See Configure Form for Gas Process Bed Model: Spatial Dimensions, later. 4 For vertical and horizontal beds, specify whether an internal heat exchanger is present. See Configure Form for Gas Process Bed Model: Internal Heat, and See Configure Form for Gas Process Bed Model: Spatial Dimensions, later. 5 In the Description box for each layer, type a brief name or description. 6 Click Configure to open the 1 Gas Adsorption Processes 22 Configure Layer Form (gas) dialog box. 7 Click Specify to open the Specify form for the layer model. Configure Form (gas): Bed Type To choose the bed type: • In the Bed Type box, choose vertical, horizontal or radial bed orientation. Vertical Bed Type Typically, you use a vertical orientation for an adsorption bed. Vertical columns prevent variation in flow width because the flow is along the column axis. Horizontal Bed Type Occasionally, you may need to choose horizontal orientation, for example, when a vertical bed may cause fluidization of the bed. Horizontal beds allow a much greater inflow area, keeping gas superficial velocities below the fluidization velocity. In the horizontal column orientation, the flow through the adsorbent packing is still vertical, but is now at right angles to the column axis so there is variation in the effective flow area of the column with height above the column base. The height of the start of the (first) adsorbent layer above the column base is the same thickness as the empty dead space and supporting grating. 1 Gas Adsorption Processes 23 L H 0,1 H B,1 H 0,2 H B,2 D B z W(z) Layer 1 Layer 2 The effective width W(z) of the bed is given as: ( ) | | 5 . 0 4 ) ( z D z z W B − = Where: B D = Column diameter z = Height of adsorbent above column base The effective cross-sectional flow area of the bed is the product of the width and the total horizontal length of the bed, that is, W(z)L. 1 Gas Adsorption Processes 24 Radial Bed Type Use a radial bed type when the flow through the bed is in the radial direction, from a central core to the outer circumference of the packed bed. Product Feed Adsorbent Layer 1 Inner Core Bed Shell Adsorbent Layer 2 The volumes of the central core and the bed shell are the dead volumes of the column. The positive radial co-ordinate runs from the center of the bed to the outer circumference. Configure Form (gas): Spatial Dimensions If you select a vertical bed type, you need to specify either one- or two- dimensional spatial discretization: • One-dimensional discretization — Spatial derivatives are evaluated in axial (flow) direction only. • Two dimensional discretization — Second order spatial derivatives are evaluated in both the axial and radial direction, allowing the calculation of radial composition and temperature distributions. 1 Gas Adsorption Processes 25 Configure Form (gas): Internal Heat Exchanger The adsorption columns used in some temperature swing adsorption processes are equipped with internal heat exchangers to improve adsorbent regeneration. Aspen Adsim¹ can simulate this configuration through the following sub-options: • None, that is, no heat exchanger • 1-Phase, internal • 1-Phase, jacket • Steam-Water, internal • Steam-Water, jacket The heat exchanger operates either as a jacket encircling the adsorption column or is integrated into the packed bed of the adsorbent. The heat exchange medium remains in the phase it is supplied in, or is condensed in order to use its heat of evaporation to heat the bed. Heat Exchange Jacket Internal Heat Exchanger 1 Gas Adsorption Processes 26 Configure Layer Form (gas) Use the options in the Configure Layer Form to specify the bed layers. The form has the following tabs: • General tab • Material/Momentum Balance tab • Kinetic Model tab • Isotherm Tab • Energy Balance tab • Reaction tab • Procedures tab General Tab (gas) Use the General tab to specify the numerical options for solving the partial differential equations, and to select the gas model assumption. General Tab (gas): Discretization Method to be used These discretization methods are available for gas phase adsorption processes: • UDS1 • UDS2 • CDS1 • CDS2 • LDS • QDS • MIXED • Flux Limiter • BUDS • FROMM 1 Gas Adsorption Processes 27 General Tab (gas): Number of Nodes In the Number of Nodes box, choose an appropriate number of axial nodes for your chosen discretization method. General Tab (gas): Number of Radial Nodes The Number of Radial Nodes option is available only if you selected a vertical bed with a 2-D spatial dimension. Choose an appropriate number of radial nodes. The derivatives in the component material balances and the gas phase energy balances are second order in radial co-ordinates, and are approximated by central differences. General Tab (gas): Flux Limiter to be used If flux limiter is your discretization method, choose from: • van Leer • OSPRE • SMART General Tab (gas): Gas Model Assumption Gas flowing through the packed bed can be ideal or non-ideal. The gas model defines the relationship between pressure, temperature and molar density: g g T R Z P ρ = (overall) or i g i c T R Z Py = (component) Where: P = Pressure Z = Compressibility factor R = Universal gas constant g T = Gas phase temperature g ρ = Molar gas phase density i y = Mole fraction of component i i c = Molar concentration of component i 1 Gas Adsorption Processes 28 In the Gas Model Assumption box, choose from: • Ideal Gas Law (where Z=1) • Fixed Compressibility (where Z is constant) • User Procedure Compressibility (where Z is supplied through a user Fortran subroutine interfaced by the procedure pUser_g_Compressibility, or calculated using a selected physical properties package) • User Submodel Compressibility (where Z is supplied through the user submodel gUserCompressibility) Material/Momentum Balance Tab (gas) Use the Material/Momentum Balance tab to specify the material and momentum balances, and the 2-D dispersive properties. About Axial Dispersion in Gas Adsorption Processes As a fluid flows through a packed column, axial mixing tends to occur. This reduces the efficiency of separation so should be minimized in column design. However, if axial dispersion occurs, the model must account for its effects. In gases, there are three main sources of axial dispersion: • From wall effects, due to non-uniformity of packing either at the wall (wall effects) or in the core section of the packing (channeling). You can avoid this type of dispersion by having a sufficiently large ratio of bed-to-particle diameters. • From molecular diffusion effects. • From turbulent mixing effects arising from the splitting and recombining of flows around the adsorbent particles. In general, the molecular diffusion and turbulent mixing effect are additive and proportional to the second order spatial concentration derivative, so they can be lumped together into a single effective dispersion coefficient, i E . The dispersion term in the material balance is typically expressed as: 2 2 z c E k zk i ∂ ∂ ε − Where: i ε = Interparticle voidage zk E = Axial dispersion coefficient of component k The type of flow determines whether this term is included or omitted in the material balance. 1 Gas Adsorption Processes 29 It is useful to work out the Peclet number Pe using a dispersion coefficient (effective bulk diffusivity z E ), typical bed velocities ( g ν ), and bed height ( b H ): Pe v H E g b z = The Peclet number quantifies the degree of dispersion introduced into the system. It is dimensionless so is more convenient to use for this purpose than the dispersion coefficient. The following table shows the effect of different values of Peclet number: If the Peclet number is The effect of axial dispersion on bed performance is 0 Infinite: the bulk gas is perfectly mixed and the gas is homogeneous through the entire bed. < 30 Significant. > 100 Very slight: The bed operates under near plug flow conditions. ∞ Zero: The bed operates under plug flow conditions. Note: The numerical methods used to model the spatial derivatives in the general equations can also introduce an artificial form of dispersion. Material/Momentum Balance Tab (gas): Material Balance Assumption The Material Balance Assumption option is available unless you previously chose vertical bed and two-dimensional bed discretization. Choose from these options: • Convection Only • Convection with Constant Dispersion • Convection with Estimated Dispersion • Convection with User Submodel Dispersion • Convection with User Procedure Dispersion Material Balance Assumption (gas): Convection Only The Convection Only option drops the dispersion term from the material balance, so the model represents plug flow with a zero dispersion coefficient (infinite Peclet number). Because the dispersion term is missing, you need not supply the dispersion coefficient. 1 Gas Adsorption Processes 30 Material Balance Assumption (gas): Convection with Constant Dispersion The Convection with Constant Dispersion option assumes that the dispersion coefficient is constant for all components throughout the bed. You supply its value. Material Balance Assumption (gas): Convection with Estimated Dispersion The Convection with Estimated Dispersion option assumes that the dispersion coefficient varies along the length of the bed. Aspen Adsim estimates the values during the simulation. Aspen Adsim estimates the components' dispersion coefficients using the following correlation, (Kast, 1988): | | . | \ | + + = p g mk i i p g mk zk r v D r v D E 2 49 . 9 1 73 . 0 ε ε Where: g ν = Gas velocity mk D = Molecular diffusivity zk E = Axial dispersion coefficient i ε = Interparticle voidage p r = Particle radius Material Balance Assumption (gas): Convection with User Submodel Dispersion If you choose Convection with User Submodel Dispersion, the (varying) dispersion coefficient is estimated using the user submodel gUserDispersion. Material Balance Assumption (gas): Convection with User Procedure Dispersion If you choose Convection with User Procedure Dispersion, the (varying) dispersion coefficient is estimated through a user-supplied Fortran subroutine, which Aspen Adsim interfaces through the procedure pUser_g_Dispersion. 1 Gas Adsorption Processes 31 Material/Momentum Balance Tab (gas): Momentum Balance Assumption Use the Momentum Balance Assumption box to specify how the adsorption bed layer model treats gas velocity and pressure. Base your choice on the plant operating conditions and the envisaged scope of the simulation (constant pressure models are only applicable for breakthrough investigations). Choose from: Constant pressure options—The bed is driven by gas superficial velocity and the pressure is assumed constant in the bed. The bed is velocity-driven, and no momentum balance is needed. These models are applicable only for breakthrough investigations. The constant pressure options are: • Constant Pressure and Velocity • Constant Pressure with Varying Velocity Pressure driven options—The velocity is related to the overall or internal pressure gradients. In such cases, velocity and pressure gradient are related through a momentum balance. The pressure-drop relationships apply to local conditions inside the bed, so the momentum equations for entire beds can be used to determine local pressure gradients. No simplifying assumptions are made regarding the gas densities, gas velocities, or pressures. The pressure driven options are: • Darcy's Law • Karman-Kozeny Equation • Burke-Plummer Equation • Ergun Equation Momentum Balance Assumption (gas): Constant Pressure and Velocity Use the Constant Pressure and Velocity option only when using a simple flowsheet to simulate the breakthrough behavior of an adsorption column. The gas velocity and pressure are constant along the bed, whilst the gas density is essentially constant along the bed. These assumptions are valid only when dealing with the removal of trace components from a bulk carrier gas. Momentum Balance Assumption (gas): Constant Pressure with Varying Velocity Use the Constant Pressure with Varying Velocity option only when using a simple flowsheet to simulate the breakthrough behavior of an adsorption column. Gas density is constant along the bed, so the pressure does not vary axially. Superficial velocity varies along the bed due to the rate at which the gas is adsorbed onto the solid, or desorbed from it. 1 Gas Adsorption Processes 32 This option is applicable to bulk separation applications, in which case the axial velocity profile is determined by an overall material balance rather than an axial pressure gradient. Momentum Balance Assumption (gas): Darcy's Law Use this option to apply a linear relationship between the gas superficial velocity and the pressure gradient at a particular point in a bed. Darcy's law states that pressure drop is directly proportional to flow rate. You have to set the proportionality constant. The relationship is given as: g p K z P ν ∂ ∂ − = Where: p K = Darcy’s law proportionality constant g ν = Gas velocity Momentum Balance Assumption (gas): Karman-Kozeny Equation Choose this option to use the Karman-Kozeny equation to relate velocity to pressure drop. This is the laminar component of the Ergun equation: ( ) g i p i v r z P 3 2 2 3 2 ) 1 ( 10 5 . 1 ε ψ ε u ∂ ∂ − × − = − For details of the Karman-Kozeny model see Bird et al. (1960). Where: ψ = Shape factor u = Dynamic gas viscosity Momentum Balance Assumption (gas): Burke-Plummer Equation This option uses the Burke-Plummer equation to relate velocity to pressure gradient: 2 3 5 2 ) 1 ( 10 75 . 1 g i p i g v r M z P ψε ε ρ ∂ ∂ − × − = − Where: M = Molecular weight The equation is valid for fully turbulent conditions when the particle Reynolds number Re is: 1000 2 > = u ρ g p g v r M Re For details of the Burke-Plummer model, see Bird et al. (1960). 1 Gas Adsorption Processes 33 Momentum Balance Assumption (gas): Ergun Equation This option uses the Ergun equation, which combines the description of pressure drops by the Karman-Kozeny equation for laminar flow and the Burke-Plummer equation for turbulent flow. ( ) | | . | \ | − × + − × − = − − 2 3 5 3 2 2 3 2 ) 1 ( 10 75 . 1 2 ) 1 ( 10 5 . 1 g i p i g g i p i v r M v r z P ψε ε ρ u ε ψ ε ∂ ∂ It is valid for both laminar and turbulent flow, and is the most popular option. For details of the Ergun model, see Bird et al. (1960). Set Variables for Pressure-Drop Options (gas) This table shows the variables you need to specify for the pressure drop options: Equation Symbol Variable Definition p K Kp Proportionality constant ψ Sfac Sphericity p r Rp Particle radius i ε Ei Interparticle voidage Material/Momentum Balance Tab (gas): 2-D Dispersive Properties The 2-D Dispersive Properties option is available only if you selected vertical bed and two-dimensional discretization. The axial dispersion is calculated from: 2 2 z c E k zk i ∂ ∂ ε − Additionally, a radial dispersion term is also evaluated: | . | \ | ∂ ∂ − r c r r r E k rk i ∂ ∂ ε 1 If you later specify the process as non-isothermal, equivalent dispersive terms are evaluated for the gas and solid phase energy balances. Namely: • Gas phase thermal conduction in axial direction: 2 2 z T k g gz i ∂ ∂ −ε • Gas phase thermal conduction in radial direction: | | . | \ | ∂ ∂ ∂ ∂ − r T r r r k g gr i 1 ε 1 Gas Adsorption Processes 34 • Solid phase thermal conduction in axial direction: 2 2 z T k s sz ∂ ∂ − • Solid phase thermal conduction in radial direction: | . | \ | ∂ ∂ ∂ ∂ − r T r r r k s sr 1 Choose from: • Fixed • Estimated 2-D Dispersive Properties (gas): Fixed Choose this option if the dispersive properties are constant throughout the packed bed. You must supply values for: • zk E : The dispersion coefficient of component k for the axial direction. • rk E : The dispersion coefficient of component k for the radial direction. For non-isothermal operation, you must give values for the following thermal conductivities: • g k : The effective thermal conductivity of the gas phase. • s k : The effective thermal conductivity of the solid phase. 2-D Dispersive Properties (gas): Estimated Choose this option when variables such as pressure, temperature and velocity are changing significantly through the column. These variables influence the values of dispersion coefficients and thermal conductivities. The axial dispersion coefficient is estimated using the following correlation, (Kast, 1988): | | . | \ | + + = p g mk i i p g mk zk r v D r v D E 2 49 . 9 1 73 . 0 ε ε Where: g ν = Gas Velocity mk D = Molecular diffusivity of component k zk E = Axial dispersion coefficient of component k i ε = Interparticle voidage p r = Particle radius 1 Gas Adsorption Processes 35 The radial dispersion coefficient is evaluated according to (Carberry, 1976): 4 g p rk v r E = Where: rk E = Radial dispersion coefficient of component k Assuming the analogy between mass and heat transfer is valid, the effective gas phase thermal conductivity in the axial direction is: ( ) ∑ = = nc i i i z pg g gz y E C k 1 , ρ Where: gz k = Effective gas phase thermal conductivity in axial direction g ρ = Molar gas density pg C = Molar specific heat capacity at constant volume The effective gas phase thermal conductivity in the radial direction comprises a static and a dynamic contribution (Froment and Bischoff, 1990). The two contributions are additive. Assuming the validity of the analogy between heat and mass transfer, the dynamic contribution to the effective radial gas phase thermal conductivity is: ( ) ∑ = = nc k k rk pg g i dyn gr y E C k 1 ρ ε Where: dyn gr k = Dynamic contribution to the effective gas phase thermal conductivity in radial direction As the adsorbent (a solid) is not in motion, it has no dynamic contribution to its effective thermal conductivity in the radial direction. 1 Gas Adsorption Processes 36 The static contribution of the gas phase effective thermal conductivity in the radial direction is: ( ) rg p g i stat gr r k k α β ε 2 + = Where: 0 . 1 = β = Factor ( ) 3 3 100 1 1 2 1 10 227 . 0 | . | \ | − − + × = − T p p rg ε ε α = Radiation contribution p = Emissivity g k = Thermal conductivity of the gas. The total effective radial gas phase thermal conductivity is now given by: stat gr dyn gr gr k k k + = The effective radial solid phase thermal conductivity comes from: ( ) s p rs g i stat sr sr k r k k k γ α φ ε β + + − = = 2 1 1 Where: 3 3 100 2 10 227 . 0 | . | \ | − × = − T p p rs α = Radiation contribution 28 . 0 = φ = Function of the packing density 3 2 = γ = Factor s k = Thermal conductivity of the solid Aspen Adsim assumes that the effective solid thermal conductivity in the axial direction is not a function of any process variables, so s k is constant through the simulation. 1 Gas Adsorption Processes 37 Kinetic Model Tab (gas) Use the Kinetic Model tab to specify the model kinetics, such as resistances, diffusivities and mass transfer coefficients. Kinetic Model Tab (gas): Film Model Assumption In the Film Model Assumption box, choose from: • Solid, where the mass transfer driving force is expressed as a function of the solid phase loading. • Fluid, where the mass transfer driving force is expressed as a function of the gas phase concentration. Kinetic Model Tab (gas): Kinetic Model Assumption Typically, several mass transfer resistances occur in gas phase adsorption processes: • Mass transfer resistance between the bulk gas phase and the gas-solid interface. • Mass transfer resistance due to the porous structure of the adsorbent. In cases where the adsorbent has two distinct pore size regions, such as macropores and micropores, the resistance can be subdivided to account separately for each region. You can consider mass transfer resistances in one these ways: • Lumped Resistance ÷ Separate mass transfer resistances are lumped as a single overall factor, or one resistance dominates all others. • Micro & Macro Pore ÷ The effects of the individual resistances to mass transfer in the micro- and macropores can be accounted for individually. • Particle MB ÷ Where all components are adsorbed and the adsorbent has a homogenous pore structure, you can use a rigorous particle material balance to determine the loading profile inside the adsorbent. • Particle MB 2 ÷ Where inert components are present, or the radial gas phase concentration profiles in the pores of the adsorbent particles are to be accounted for in addition to the loading profiles. The adsorbent should possess a homogenous pore structure. This option performs a rigorous particle material balance for both the adsorbed and the gas phases. 1 Gas Adsorption Processes 38 In the Kinetic Model Assumption box, choose from these options: • Lumped Resistance • Micro and Macro Pore Effects • Particle MB • Particle MB 2 • User Procedure • User Submodel Kinetic Model Assumption (gas): Lumped Resistance Here, the separate resistances to mass transfer is lumped as a single overall factor, or one mass transfer resistance dominates the others. Kinetic Model Assumption (gas): Micro and Macro Pore Effects Two concentration gradients greatly affect the diffusion rate: • Within the pores of the solid. • Within the void spaces between the particles (that is, within the crystallines). Under practical conditions in gas separation, pore diffusion limits the overall mass transfer rate between the bulk flow and the internal surface of a particle. This gives importance to the effect of pore diffusion on the dynamics of absorbers. The following table shows the difference between modeling macropore and micropore resistance in composite and uniform adsorbents: Pore structure Example(s) Micropore diffusional resistance Macropore diffusional resistance Uniform Activated carbon alumina silica molecular sieve carbon High Negligible Composite Zeolites High High When modeling adsorbents with uniform pore structure, you can usually discount any macropore diffusional resistance. However, when modeling composite adsorbents, both resistances can be significant and should be accounted for. Qualitatively, a higher pore diffusion rate results in a sharper and steeper concentration wave front, giving a better separation. Quantitative prediction of behavior requires the simultaneous solution of the mass balance within the particle, as well as for the bulk flow in the bed. Solving the mass balance equation within the particle is usually complex. However, you can simplify the mass balance equation in two ways: • Use expressions that relate the overall uptake rate to the bulk flow concentration: ( ) i s i ads c f t w J i = = ∂ ∂ ρ , 1 Gas Adsorption Processes 39 Where: s ρ = Adsorbent bulk density i w = Loading of component i due to adsorption i ads J , = Mass transfer rate of component i • If you know the concentration profile within the particle, you can make considerable savings in numerical computation because integration along the radial distance in the particle is no longer necessary. Several researchers have recently shown that profiles obtained by exact numerical solutions of both Pressure Swing and Thermal Swing Adsorption processes are usually parabolic in shape, so you can model pore diffusion by assuming a parabolic concentration profile within the particle. The model developed for particle diffusion accounts for both interparticle (macropore) and intraparticle (micorpore) diffusion effects. The model assumes that material flows first from the bulk gas to the macropores (crystallines), and then from the macropores to the solid surface via the micropores: r P 2r c Interpellet porosity Micropore Bulk Gas Macropore Solid Surface Bulk: c bk , ε B , w bk Macropores: w msk , c msk Interpellet Voidage: ε i Pellet (macroparticle) Intrapellet Porosity ε P Solid Microporous Particles: w k , c k c bk , ε B , w bk c msk , (1-ε i ) ε P , w msk ε i c k , w k * * * * * * The material balance model assumes that: • Radial concentration profile within the particle is parabolic. • Concentration profile within the particle is radially symmetric. • Radial dispersion is negligible. 1 Gas Adsorption Processes 40 Gas Phase The component balance in the bulk gas phase is of the form: ( ) ( ) ( ) 0 1 1 = ∂ ∂ − + ∂ ∂ − + ∂ ∂ + ∂ ∂ t c t w t c z v c msk p i k s p bk B g bk ε ε ρ ε ε [Convection] + [accumulation] + [mass transfer (accumulation) to micropore] + [mass transfer (accumulation) to macropore] In the given example, the gas phase material balance is written for a convection only situation in a vertical, one-dimensional adsorption layer. Macropore (Crystalline) The material balance in the macropore is given as: Fluid Film Model: ( ) ( ) ( ) msk bk mac k s p msk p i c c K t w t c − = ∂ ∂ − + ∂ ∂ − ρ ε ε ε 1 1 [accumulation] + [mass transfer to micropore] = [rate of mass transfer from bulk gas] Solid Film Model: ( ) ( ) ( ) ( ) * * 1 1 1 msk bk mac s p k s p msk p i w w K t w t c − − = ∂ ∂ − + ∂ ∂ − ρ ε ρ ε ε ε Micropore (Particle) Fluid Film Model: ( ) ( ) * 1 k msk mic k s p c c K t w − = ∂ ∂ − ρ ε [accumulation] = [rate of mass transfer from macropore] Solid Film Model: ( ) ( ) ( ) k sk mic s p k s p w w K t w − − = ∂ ∂ − * 1 1 ρ ε ρ ε [accumulation] = [rate of mass transfer from macropore] Specifying Particle Resistance Coefficients If you choose Micro & Macro Pore Effects, you must specify the values of the macropore and micropore resistances: mac K and mic K . The following options are available in the Form of Mass Transfer Coefficient field. 1 Gas Adsorption Processes 41 Constant This option forces the particle resistance coefficients to be constant throughout the bed. Set the coefficients in the variable arrays Kmac and Kmic. The macropore constant mac K is given by: 2 0 . 15 P efP mac r D K = Where: efP D = Component diffusivities in macropores p r = Particle radius The micropore constant mic K is given by: 2 0 . 15 c efc mic r D K = Where: efc D = Component diffusivities in micropores c r = Microparticle radius Estimated This option uses a submodel in which Aspen Adsim automatically estimates the coefficients. User Procedure If you choose this option, the bed model is written so that the component rates of mass transfer are related to local conditions in the bed through the procedure type pUser_g_Kinetic. ) , , , , , ( g i s i g i v w T c P T f t w = ∂ ∂ Note: Langmuir adsorption kinetics is quite a popular option, and can be applied with such a procedure. User Submodel The name of the submodel is gUserKinetic. 1 Gas Adsorption Processes 42 Kinetic Model Assumption (gas): Particle MB This option determines the loading and gas phase concentration profiles inside an adsorbent particle, by rigorously solving the particle material balance for both phases. For this to work, the following conditions must be met: • Adsorbent has a uniform pore structure. • Effective gas phase diffusion coefficient is calculated from the molecular and the Knudsen diffusion coefficients. • Effective diffusivities for the gas and adsorbed phase are independent of the location inside the particle. The Particle Material Balance option considers two mass transfer resistances: • The intraparticle mass transfer resistance, which is the diffusional resistance inside the particle pore structure, caused by both gas and adsorbed phase diffusion. • The interparticle mass transfer resistance, which is the resistance to mass transfer posed by the boundary layer between particle surface and bulk gas. The following figure illustrates these resistances: 1 Gas Adsorption Processes 43 r r p Bulk Gas Boundary Layer Adsorbent Particle (Uniform Pore Structure) c i c i * w i * w i (r) 0 0 = ∂ ∂ = r i r w J i p r r i r w = ∂ ∂ ( ) ( ) * i i f r r i ei s i c c k a r w D a J p − ε − = ∂ ∂ ρ = = 1 The particle material balance is expressed as: 0 2 2 2 = ∂ ∂ + ∂ ∂ − ∂ ∂ r w r w r D t w k k ek k Where: k w = Loading ek D = Effective adsorbed phase diffusion coefficient r = Radial particle co-ordinate The effective diffusion coefficient is assumed constant throughout the particle. It is calculated from the particle location inside the adsorber (axial and radial column co-ordinate) using the procedure pUser_g_De or submodel gUserEffDiff. 1 Gas Adsorption Processes 44 The boundary conditions for this partial differential equation come from both the symmetry condition at r=0: 0 0 = ∂ ∂ = r i r w and the material flux through the boundary layer at p r r = : ( ) ( ) * 1 k k fk i r r k ek s c c k a r w D a p − − = ∂ ∂ = ε ρ Where: a = Specific particle surface s ρ = Bulk density of solid i ε = Interparticle voidage fk k = Boundary layer mass transfer coefficient k c = Gas phase concentration * k c = Interface gas phase concentration The gas phase composition and the loading are coupled by the condition that thermodynamic equilibrium has been achieved at the interface between gas phase and particle: ( ) * * i eq r r i i c f w w p = = = Where: eq f = Isotherm equation * i w = Loading at p r r = The boundary layer mass transfer coefficient is expressed using the following Sherwood number correlation: 6 . 0 3 / 1 1 . 1 2 Re Sc Sh i i + = Where: mi p fi i D r k Sh 2 = = Sherwood number M D Sc g mi i ρ u = = Schmidt number u ρ g p g M r v Re 2 = = Reynolds number 1 Gas Adsorption Processes 45 mi D = Mean molecular diffusion coefficient u = Gas phase dynamic viscosity g ρ = Molar gas phase density M = Mean molecular weight g ν = Superficial velocity Kinetic Model Assumption (gas): Particle MB 2 This option determines the loading and gas phase concentration profiles inside an adsorbent particle, by rigorously solving the particle material balance for both phases. For this to work: • Adsorbent has a uniform pore structure. • Effective gas phase diffusion coefficient is calculated from the molecular and the Knudsen diffusion coefficients. • Effective diffusivities for gas and adsorbed phase are independent of the location inside the particle. The Particle Material Balance 2 option considers two mass transfer resistances: • The intraparticle mass transfer resistance, which is the diffusional resistance inside the particle pore structure, caused by both gas and adsorbed phase diffusion. • The interparticle mass transfer resistance, which is the resistance to mass transfer posed by the boundary layer between particle surface and bulk gas. The following figure illustrates these resistances: 1 Gas Adsorption Processes 46 r r p Bulk Gas Boundary Layer Adsorbent Particle (Uniform Pore Structure) c i c i * w i * w i (r) 0 0 = ∂ ∂ = r i r w J i p r r i r w = ∂ ∂ ( ) ( ) ( ) 3 0 2 3 0 2 * , 3 1 3 1 p r p i p p r i s i i i f r r p i i p r r i ei s r dr r t c r dr r t w J c c k r c D r w D p p p p ∫ ∫ ∂ ∂ − + ∂ ∂ = − = ∂ ∂ + ∂ ∂ − = = ε ε ρ ε ρ p r r p i r c = ∂ ∂ 0 = ∂ ∂ = p r r p i r c (r) c p i The particle material balance is given by: 0 2 1 2 1 2 2 2 2 = ∂ ∂ + ∂ ∂ − − ∂ ∂ + ∂ ∂ − ∂ ∂ − + ∂ ∂ r w r w r D r c r c r D t w t c k k s ek p k p k pk k s p k p ε ρ ε ρ ε Where: ε = Interparticle voidage p ε = Intraparticle voidage s ρ = Bulk density k w = Loading p k c = Gas phase concentration 1 Gas Adsorption Processes 47 ek D = Effective adsorbed phase diffusion coefficient pk D = Effective pore gas phase diffusion coefficient r = Radial particle co-ordinate The effective adsorbed phase diffusion coefficient is assumed constant through the particle. You calculate it from the particle location inside the adsorber (given by the axial and radial column co-ordinate), using the procedure pUser_g_De or the submodel gUserEffDiff. The effective pore gas diffusion coefficient is calculated from the molecular diffusion coefficient and the Knudsen diffusion coefficient: | | . | \ | + = mi Ki p pi D D Tort D 1 1 1 ε and 5 . 0 97 | | . | \ | = i Pore Ki M T r D Where: Tort = Tortuosity of adsorbent pi D = Effective pore gas diffusion coefficient Ki D = Knudsen diffusion coefficient mi D = Molecular diffusion coefficient of component i in the mixture Pore r = Pore radius in adsorbent T = Adsorbent temperature i M = Molecular weight of component i The boundary conditions for this partial differential equation come from both the symmetry condition at r=0: 0 0 = ∂ ∂ = r i r w and 0 0 = ∂ ∂ = r p i r c 1 Gas Adsorption Processes 48 and the material flux through the boundary layer at p r r = : ( ) ( ) ( ) 3 0 2 3 0 2 * , 3 1 3 1 p r p i p p r i s i i i fi r r p i i p r r i ei s r dr r t c r dr r t w J c c k r c D r w D p p p p ∫ ∫ ∂ ∂ − + ∂ ∂ = − = ∂ ∂ + ∂ ∂ − = = ε ε ρ ε ρ Where: s ρ = Bulk density of solid ε = Interparticle voidage p ε = Interparticle voidage fi k = Boundary layer mass transfer coefficient i c = Bulk gas phase concentration * i c = Interface gas phase concentration p i c = Pore gas phase concentration i w = Loading i J = Material flux p r = particle radius pi D = Effective gas phase pore diffusion coefficient ei D = Effective adsorbed phase diffusion coefficient The gas phase concentration and the loading are coupled by the condition that thermodynamic equilibrium has been at each radial location inside particle, so: ( ) p i eq i c f w = Where: eq f = Isotherm equation p i c = Pore gas phase concentration i w = Loading These calculations give the isotherm correlation at each radial node, which increases the computational effort. 1 Gas Adsorption Processes 49 The boundary layer mass transfer coefficient is given by the following Sherwood number correlation: 6 . 0 3 / 1 1 . 1 2 Re Sc Sh i i + = Where: mi p fi i D r k Sh 2 = = Sherwood number M D Sc g mi i ρ u = = Schmidt number u ρ g p g M r v Re 2 = = Reynolds number mi D = Mean molecular diffusion coefficient u = Gas phase dynamic viscosity g ρ = Molar gas phase density M = Mean molecular weight g ν = Superficial velocity Kinetic Model Assumption (gas): User Procedure With this option, the bed model relates component rates of mass transfer to local conditions in the bed through the procedure pUser_g_Kinetic. ) , , , , , ( g i s i g i v w T c P T f t w = ∂ ∂ Note: Langmuir adsorption kinetics is quite a popular option, and can be applied with such a procedure. Kinetic Model Assumption (gas): User Submodel With this option, the bed model relates component rates of mass transfer to local conditions in the bed through the submodel gUserKineticModel. ) , , , , , ( g i s i g i v w T c P T f t w = ∂ ∂ Note: Langmuir adsorption kinetics is quite a popular option, and can be applied with such a procedure. 1 Gas Adsorption Processes 50 Kinetic Model Tab (gas): Form of Lumped Resistance Model Use the Lumped Resistance option to select the overall form of the mass transfer rate model. This option determines how the model relates the mass transfer rate due to adsorption ( i ads J , ), to the local gas and solid states. The mass transfer rate is related to the adsorbent uptake, as follows: i ads i s J t w , = ∂ ∂ ρ If you chose Lumped Resistance as the kinetic model assumption, in the Form of the Lumped Resistance Model box, you need to choose between the following driving force expressions: • Linear • Quadratic Form of Lumped Resistance Model (gas): Linear The mass transfer driving force for component i is a linear function of the gas phase concentration (fluid film) or solid phase loading (solid film). Fluid: ( ) * i i gi i s c c MTC t w − = ∂ ∂ ρ Solid: ( ) i i si i w w MTC t w − = ∂ ∂ * Form of Lumped Resistance Model (gas): Quadratic The mass transfer driving force is a quadratic function of the fluid film concentration or solid film loading. Fluid: ( ) ( ) i i i gi i s c c c MTC t w 2 2 * 2 − = ∂ ∂ ρ Solid: ( ) ( ) i i i si i w w w MTC t w 2 2 2 * − = ∂ ∂ 1 Gas Adsorption Processes 51 Kinetic Model Tab (gas): Molecular Diffusivities This option applies if you previously selected one of the following options: • Particle MB as your kinetic model assumption. • Estimated as your form of mass transfer coefficient. In either case, mean gas phase molecular diffusivities are required for the calculation of film mass transfer coefficients. These mass transfer coefficients describe the resistance against mass transfer posed by the boundary layer surrounding the adsorbent particle. r P 2r c Interpellet porosity Micropore Bulk Gas Macropore Solid Surface Bulk: c bk , ε B , w bk Macropores: w msk , c msk Interpellet Voidage: ε i Pellet (macroparticle) Intrapellet Porosity ε P Solid Microporous Particles: w k , c k c bk , ε B , w bk c msk , (1-ε i ) ε P , w msk ε i c k , w k * * * * * * Typically, the mass transfer coefficients are evaluated from Sherwood or Colburn j-factor correlations. Values and estimation equations for diffusion coefficients for various gases are given by Bird et al. (1960) and Reid et al. (1977), for example. Molecular Diffusivities (gas): Fixed The mean molecular diffusion coefficients are fixed for each component. You supply a value for each component into the array Dm(*) of the adsorbent layer model. 1 Gas Adsorption Processes 52 Molecular Diffusivities (gas): User Procedure You supply the mean gas phase diffusion coefficients using a Fortran subroutine, which Aspen Adsim interfaces through the procedure pUser_g_Diffusivity. Kinetic Model Tab (gas): Form of Mass Transfer Coefficients If you selected either Lumped Resistance or Micro & Macropore for your kinetic model assumption then, in the Form of Mass Transfer Coefficients box, choose from these options: • Arrhenius • Constant • Estimated • Pressure Dependent Arrhenius • User Procedure • User Submodel Form of Mass Transfer Coefficients (gas): Arrhenius This option evaluates the mass transfer coefficient as a function of temperature from an Arrhenius type equation: | . | \ | − = RT E k MTC acti i i exp 0 To use this option, you must supply the pre-exponential factor i k 0 and the activation energy acti E for each component i, as fixed variables in the Specify table for the adsorbent layer. Form of Mass Transfer Coefficients (gas): Constant Here, the mass transfer coefficient for each component is constant throughout the bed. You must supply a constant value of mass transfer coefficient for each component in the Specify table for the adsorbent layer. Form of Mass Transfer Coefficients (gas): Estimated If you have selected Lumped Resistance as your kinetic model assumption, and Estimated in the Form of Mass Transfer Coefficients box, choose the Estimated Mass Transfer Coefficient Assumption from: • Micro and Macro Pores Considered • Macropore Only 1 Gas Adsorption Processes 53 Methods exist in the literature for estimating the mass transfer coefficient as a function of the supplied isotherm. One such method is based on the Henry's Coefficient. These methods rarely provide exact values; they are approximations that serve only as rough guides. They usually need to be fine- tuned. You can fine-tune the values by adjusting the estimated values until the timing and shape of the simulated breakthrough curves match the experimentally measured breakthrough curves. In general, the adsorption rate model for component i can be expressed as: ( ) ( ) * * i i Ki i i i i i c c K k w w k t w − = − = ∂ ∂ The effective mass transfer coefficient is given as a lumped term comprising the external film resistance term, the macropore diffusion term, and the micropore diffusion term: ci Ki c pi p p fi p i D K r K r k r k 15 15 3 1 2 2 + + = ε The Henry's coefficient Ki K is obtained from the isotherm as: i i i i Ki P w RT c w K ∂ ∂ = ∂ ∂ = * * The dimensionless Henry’s coefficient, Ki K , is obtained by: i s Ki Ki K K ε ρ = The film resistance coefficient fi k is obtained from the Sherwood number as: p mi i fi r D Sh k 2 = Where: i Sh = 6 . 0 3 / 1 1 . 1 0 . 2 Re Sc i + Re = Reynolds number i Sc = Schmidt number = ( ) s mi D ρ u The macropore diffusion coefficient pi K is obtained from: | | . | \ | + = mi Ki pi D D Tort K 1 1 1 1 Gas Adsorption Processes 54 The Knudsen diffusion coefficient Ki D is: 5 . 0 97 | | . | \ | = i Pore Ki M T r D Where: g ρ = Gas density ci D = Micropore diffusion coefficient Ki D = Knudsen diffusion coefficient mi D = Multi-component molecular diffusion coefficient p e = particle (macro) porosity i k = effective mass transfer coefficient Ki K = Henry's coefficient fi k = Film resistance coefficient pi K = Macropore diffusion coefficient w = Loading R = Universal Gas Constant c r = Radius of crystalline or primary micropore p r = Particle radius Tort = Tortuosity factor u = Dynamic viscosity To include the effect of the micropore resistance in the estimated values for the mass transfer coefficients: • Give values for the micropore diffusion coefficients and the radius of the primary micropore. To ignore the micropore effect: • In the Estimated Mass Transfer Coefficient Assumption box, select Macropore only. Form of Mass Transfer Coefficients (gas): Pressure Dependent Arrhenius This option is based on the Arrhenius model, but also accounts for changes in total pressure. As such it is especially suitable for PSA systems. The model was found to represent experimental data well. 1 Gas Adsorption Processes 55 | . | \ | − = RT E P k MTC acti Pi i exp 0 You have to supply the pre-exponential factor Pi k 0 and the activation energy acti E for each component i, as fixed variables in the Specify table for the adsorbent layer. Form of Mass Transfer Coefficients (gas): User Procedure Here, the mass transfer coefficients are estimated using a Fortran subroutine, which Aspen Adsim interfaces through the procedure pUser_g_MTC. Form of Mass Transfer Coefficients (gas): User Submodel If you choose this option, the mass transfer coefficients are estimated and then returned through the submodel gUserMTC. Kinetic Model Tab (gas): Apply Cyclic Correction This option is available only if you selected Lumped Resistance as your kinetic model assumption, and either Constant or Estimated in the Form Of Mass Transfer Coefficient box. Furthermore, this option applies only to cyclic processes and especially PSA systems. The Glueckauf (see Yang, 1987 for example) approximation of a lumped mass transfer coefficient states: 2 , P ei i s r D MTC Ω = with Ω=15. Nakao and Suzuki (1983) showed that the value of 15 underestimates the magnitude of the mass transfer coefficient for short adsorption times. Assuming that an adsorption column is in adsorbing mode for about half the total time of the adsorption cycle, the following time constant can be calculated: Cycle P e t r D 2 5 . 0 = θ The parameter Ω is a function of θ: 162.5 : 001 . 0 5.14 : 1 . 0 001 . 0 15 : 1 . 0 = ≤ = < ≤ = ≥ Ω θ θ Ω θ Ω θ The above equations are evaluated automatically by Aspen Adsim when you select this option. 1 Gas Adsorption Processes 56 Kinetic Model Tab (gas): Estimated Mass Transfer Coefficient Assumption This option is available only if you selected Estimated as your estimated mass transfer coefficient. Gas Adsorption Layer (gas): Particle Material Balance, Number of Nodes This option is available only if you selected Particle MB or Particle MB 2 as your kinetic model assumption. It determines how many nodes to use for the central finite difference discretization of the second order derivative in the particle material balance: ( ) ( ) 2 1 1 1 1 2 2 2 2 2 1 r w w w r w w r r w r r r k k k k k k ∆ ∆ − + − + + − + − ≈ | . | \ | ∂ ∂ ∂ ∂ Kinetic Model Tab (gas): Particle Material Balance, Effective Diffusivity This option is available only if you selcted Particle MB or Particle MB 2 as your Kinetic Model Assumption. With this option, the form of the effective adsorbed phase diffusion coefficient is determined. Choose one of three options: • Fixed • User Procedure • User Submodel Particle Material Balance, Effective Diffusivity (gas): Fixed With this option, the effective diffusion coefficients for each component in the adsorbed phase are given a constant value, which you supply through the array De(*) of the adsorbent layer model. Particle Material Balance, Effective Diffusivity (gas): User Procedure You supply the mean adsorbed phase diffusion coefficients using a Fortran subroutine, which Adsim interfaces through the procedure pUser_g_De. Particle Material Balance, Effective Diffusivity (gas): User Submodel You supply the mean adsorbed phase diffusion coefficients through the user submodel gUserEffDiff. 1 Gas Adsorption Processes 57 Isotherm Tab (gas) Use the Isotherm tab to define the adsorption isotherms to be used in your gas adsorption process. The Aspen Adsim isotherm models are expressed as functions of either partial pressures or concentrations. When you use Aspen Adsim isotherm models for pure components or for multi-component mixtures, you must supply isotherm parameters consistent with the functional form. It is imperative that you convert isotherm parameters to Aspen Adsim's base units of measurement, which are listed in the following table: Variable Unit of measurement Loading (w) kmol/kg Gas phase concentration (c) kmol/m 3 Pressure (P) bar Temperature (T) K About Adsorption Isotherms for Gas Adsorption Processes Adsorption is the tendency of molecules from an ambient fluid phase (gas or liquid) to stick to the surface of a solid. Most of the important industrial applications of adsorption depend on differences in the affinity of the solid surface for different components. Adsorption isotherms describe the tendency for the components to adsorb onto the solid; they describe the amount of each component adsorbed onto the solid at thermodynamic equilibrium. The driving force behind all adsorptive gas separation processes is the departure from adsorption equilibrium, so adsorption isotherms are crucially important data in the design of adsorbers. If you know the adsorption isotherms for the components of the feed, you can create a bed model to predict the performance of the adsorber bed for the specified operating conditions. Aspen Adsim has a comprehensive list of adsorption isotherms. You choose these isotherms from the Configurure Layer forms for the layers making up the bed model. This section explains these choices for pure component, multi- component, and user-supplied isotherms. For more information, see Chapters 2 through 4 in Ruthven, 1984, Chapters 2 and 3 in Yang, 1987, and Chapter 3 in Kast, 1988 (German language). 1 Gas Adsorption Processes 58 Guidelines for Choosing Aspen Adsim Isotherm Models (gas) Choose a model that is appropriate to the process you are investigating. The equilibrium specified by the isotherm model affects the driving force for mass transfer, so you can get significantly different simulation results when using different models, even if the model parameters are derived from exactly the same set of data. The isotherm model parameters are always set variables. You can estimate these parameters from experimental data, or use published literature values. Important: The expressions in this section are equilibrium equations. Depending on the mass transfer rate model you choose, the expressions compute either: • w*, the loading which would be at equilibrium with the actual gas phase composition - or - • c*, the gas phase composition which would be at equilibrium with the actual loading. The choice between w* and c* is automatically handled by Aspen Adsim. Aspen Adsim names the equilibrium variable arrays (of size n or n×m) either Ws or Cs. In bed models, these variables are distributed axially, or axially and radially, and have indices to identify their location in the bed. About Multi-Component Mixture Isotherms (gas) In adsorber design, you are usually interested in the adsorption equilibria of mixtures, rather than those of pure components. This is because adsorbed gas components interact on the solid surface, so individual gas components adsorb in a different fashion when mixed with other components. Mixture adsorption equilibria data are not readily available. Although measurements can be made, they are tedious and time-consuming to perform, so it is common practice to predict mixture isotherms from pure component isotherms. Several methods for predicting mixture isotherms from pure component data have been proposed recently, including: • Vacancy Solution • Extended Langmuir Approach • Ideal Adsorbed Solution • Real Adsorbed Solution Theory Most of the physical adsorption models contain two or three parameters, and the parameters for mixture isotherms are written as a function of the pure component parameters and the composition of the adsorbed phase. 1 Gas Adsorption Processes 59 Vacancy Solution (gas) The vacancy solution is the least popular of all the methods, but the approach has been developed in a limited number of cases for some single and multi- component systems. Extended Langmuir Approach (gas) This is an extension of the Langmuir isotherms for single components. Langmuir models use a weighting factor to account for the inter-species interaction in mixtures. The extended Langmuir approach takes a single component gas isotherm parameter and, depending on the components of the multi-component gas mixture, calculates a fitting parameter to account for the presence of other components. The values of the interaction parameters depend on all the species present. The value of the weighted inter-species interaction parameter is obtained from mixture experimental data. Ideal Adsorbed Solution (gas) Recently, the Ideal Adsorbed Solution Theory (IAS) has become popular for multi-component mixtures. The method enables you to predict adsorption equilibria for components in a gaseous mixture. It requires data only for the pure-component adsorption equilibria at the same temperature and on the same adsorbent. The model treats the mixed adsorbate phase as an ideal solution in equilibrium with the gas phase. The Gibbs approach is used for vapor-liquid equilibria, in which the fundamental equations of thermodynamic equilibrium are developed, and applies this to the gas-adsorbed phase equilibria. At first sight, ideal behavior in the adsorbed phase seems improbable. However, many systems have shown strong correlation between experimental data and predictions by IAS theory, including binary and ternary mixtures on activated carbons, zeolites, and silica gel. For a full description of the IAS approach, see Chapter 4 of Ruthven (1984) or Chapter 3 of Kast (1988) (German language). IAS is available in Aspen Adsim. To use it, choose the appropriate isotherm on the Isotherm Tab of the layer configuration form. The basic requirements for thermodynamic equilibrium between two phases are that the pressure, temperature and chemical potential of each component are equal in both phases. The chemical potential for an adsorbed phase can be written as (Kast, 1988): ( ) ( ) ( ) ( ) ( ) i i i i i i ads x RT P RT T x T γ Π u Π u ln ln , , 0 0 , + + = The chemical potential for an ideal gas phase is given by: ( ) ( ) P y RT T i i i gas ln 0 , + = u u The equilibrium condition is: i ads i gas , , u u = 1 Gas Adsorption Processes 60 Assuming ideal behavior in the adsorbed phase (that is, 1 = i γ ), an expression analogous to Raoult’s law can be derived: ( ) Π 0 i i i P x P y = The pressure 0 i P is a fictitious pure component gas phase pressure, which gives the same spread pressure in the adsorbed phase as the gas mixture at pressure P. The relationship between 0 i P and the spreading pressure 0 i Π is derived using the Gibbs-Duhem equation for a single adsorbed component: ( ) ( ) Π u Π 0 0 0 0 0 ln( i i i i i P RTd w d w Ad = = On integrating and using the pure component isotherm to replace 0 i w : ( ) dP P IP P T f RT A i P eq i ∫ = 0 0 0 , , Π The equation set is completed with the following conditions: ∑ = = n i i x 1 1 ∑ = = n i i y 1 1 ... 0 0 0 = = = k j i Π Π Π The total loading and component loadings are calculated from: ∑ = = n i tot i i w w x 1 0 1 and tot i i w x w = Real Adsorbed Solution Theory (gas) The derivation of the Ideal Adsorbed Solution Theory (see earlier) assumed ideal behavior in the adsorbed phase. This assumption resulted in the activity coefficient of each component being set to unity ( 1 = i γ ). Non-ideal behavior in the adsorbed phase can be accounted for by evaluating the activity coefficient using a suitable Gibbs excess enthalpy correlation (for example, Wilson or UNIQUAC). The binary parameters of the E g models have to be determined from suitable experiments (Costa et al., 1981). Once those parameters are known, AspenTech’s Aspen Properties system is used to supply the value of i γ so that: ( ) Π = 0 i i i i P x P y γ can be evaluated. 1 Gas Adsorption Processes 61 Isotherm Tab (gas): Isotherm Assumed for Layer Aspen Adsim enables you to use a number of pure component isotherms and multi-component isotherms. In the Isotherm Assumed for Layer box, select from: • Langmuir Models • Freundlich Models • Langmuir-Freundlich Model • Henry's Models • Toth Model • B.E.T. (Brunauer, Emmett & Teller) Models • B.E.T. Multilayer • Dubinin-Astakov Model • Linear Model • Volmer Model • Myers Model • Extended Langmuir Models • Extended Langmuir- Freundlich Model • Dual-Site Langmuir Model • Single Layer B.E.T • Dual Layer B.E.T • User Procedure • User Submodel • IAS Isotherm Assumed for Layer (gas): Langmuir Models Langmuir isotherm models typically apply to the adsorption of a single molecule layer on completely homogeneous surfaces, with negligible interaction between adsorbed molecules. There are three standard sub-options for the pure component Langmuir isotherms supported in Aspen Adsim: Langmuir 1. The isotherm is a function of a partial pressure or concentration: i i i P IP P IP w 2 1 1+ = (partial pressure) or i i i c IP c IP w 2 1 1+ = (concentration) 1 Gas Adsorption Processes 62 Langmuir 2. The isotherm is a function of temperature, and one of partial pressure or concentration: i Ts IP i Ts IP i P e IP P e IP w / 3 / 1 4 2 1+ = (partial pressure) or i Ts IP i Ts IP i c e IP c e IP w / 3 / 1 4 2 1+ = (concentration) Langmuir 3. The isotherm is a function of temperature, and one of partial pressure or concentration. Unlike Langmuir2, the maximum loading, expressed by ( ) s T IP IP 2 1 − , is a function of temperature, so reflects more accurately the physical reality of numerous adsorption processes: ( ) i T IP i T IP s i P e IP P e IP T IP IP w s s / 3 / 3 2 1 4 4 1+ − = (partial pressure) or ( ) i T IP i T IP s i c e IP c e IP T IP IP w s s / 3 / 3 2 1 4 4 1+ − = (concentration) Isotherm Assumed for Layer (gas): Freundlich Models Aspen Adsim has two sub-options for the pure component Freundlich isotherms: Freundlich 1. The isotherm is a function of partial pressure or concentration: 2 1 IP i i P IP w = (partial pressure) or 2 1 IP i i C IP w = (concentration) Freundlich 2. The isotherm is a function of temperature, and one of partial pressure or concentration: 2 3 / 1 IP i T IP i P e IP w s = (partial pressure) or 2 3 / 1 IP i T IP i c e IP w s = (concentration) 1 Gas Adsorption Processes 63 Isotherm Assumed for Layer (gas): Langmuir-Freundlich Model This isotherm is a function of temperature, and one of partial pressure or concentration: s s T IP IP i T IP IP i i e P IP e P IP IP w / 5 / 2 1 6 3 4 3 1+ = (partial pressure) or s s T IP IP i T IP IP i i e c IP e c IP IP w / 5 / 2 1 6 3 4 3 1+ = (concentration) Isotherm Assumed for Layer (gas): Henry's Models Aspen Adsim has two sub-options of the pure component Henry's isotherms: Henry 1. The isotherm is a function of partial pressure or concentration: i i P IP w 1 = (partial pressure) or i i c IP w 1 = (concentration) Henry 2. The isotherm is a function of temperature, and one of partial pressure or concentration: i T IP i P e IP w s / 1 2 = (partial pressure) or i T IP i c e IP w s / 1 2 = (concentration) Isotherm Assumed for Layer (gas): Toth Model The isotherm is a function of partial pressure or concentration: 2 1 2 2 ) ( 1 ) ( 3 1 IP IP i IP i i P IP P IP w + = (partial pressure) or 2 1 2 2 ) ( 1 ) ( 3 1 IP IP i IP i i c IP c IP w + = (concentration) 1 Gas Adsorption Processes 64 Isotherm Assumed for Layer (gas): B.E.T Use the B.E.T. (Brunauer, Emmett and Teller) type isotherm (or multilayer Langmuir relation) for gas-solid systems in which condensation is approached, and hence the number of adsorbed layers is extremely large. This isotherm is a function of temperature and one of partial pressure or concentration: | | . | \ | − | | . | \ | + | | . | \ | = s i s i s i i T IP P IP T IP P IP T IP P IP w 6 5 4 3 2 1 exp 1 exp 1 exp (partial pressure) or | | . | \ | − | | . | \ | + | | . | \ | = s i s i s i i T IP c IP T IP c IP T IP c IP w 6 5 4 3 2 1 exp 1 exp 1 exp (concentration) Isotherm Assumed for Layer (gas): BET Multilayer The BET Multilayer isotherm is similar to the BET isotherm, but has an additional parameter, 4 IP , stating the number of layers adsorbed. Physically, it fills the gap between the Langmuir isotherm (single layer BET) and the BET isotherm with an infinite number of layers. Use it only for systems where the operating temperature is below the critical temperature of the adsorbate. The isotherm is always evaluated as a function of the relative pressure: sat i i P P = φ If you selected concentration dependency, the following equation is used to calculate the partial pressure: g i i RT c P = The saturation pressure sat P is calculated according to a base 10 Antoine equation, using degrees Celsius or Kelvin as temperature units of measurement. The parameter 8 IP is then a conversion factor for calculating sat P in bar. s T IP IP IP sat IP P + − × = 7 6 5 10 8 1 Gas Adsorption Processes 65 The kinetic factor b is: | | . | \ | = s T IP IP b 3 2 exp The isotherm is: ( ) ( ) | | . | \ | − − + + + − | | . | \ | − = +1 4 4 1 4 4 4 1 1 1 1 1 IP IP IP i b b IP IP b IP w φ φ φ φ φ φ Isotherm Assumed for Layer (gas): Dubinin-Astakov Model This isotherm is a function of temperature, and one of partial pressure or concentration: | | | | 2 4 3 2 2 1 ) / ( exp ) / ( exp IP AA IP IP AA IP w i − + − = Where: | | . | \ | = sat i s P P RT AA ln (partial pressure) or | | . | \ | = sat s i s P RT c RT AA ln (concentration) and | | . | \ | − − = 7 6 5 10 8 IP T IP IP sat s IP P IP8 is a conversion factor to convert the resulting partial pressure predicted by the Log10 base Antoine Equation, into bar (Aspen Adsim's base unit of measurement for pressure). Isotherm Assumed for Layer (gas): Linear Model This isotherm is a function of partial pressure or concentration: 2 1 IP P IP w i i + = (partial pressure) or 2 1 IP c IP w i i + = (concentration) Isotherm Assumed for Layer (gas): Volmer Model The Volmer isotherm expresses concentration as a function of loading: | | . | \ | − − = i i i i i w IP IP w IP w IP IP w IP c 1 2 1 1 2 1 exp 1 Gas Adsorption Processes 66 Isotherm Assumed for Layer (gas): Myers Model TheMyers isotherm expresses concentration as a function of loading: | | . | \ | = 1 2 1 exp IP w IP IP c i i Isotherm Assumed for Layer (gas): Extended Langmuir Models There are three standard sub-options of the extended Langmuir isotherms supported in Aspen Adsim: Extended Langmuir 1. This isotherm is a function of partial pressure or concentration: ( ) ∑ + = k k k i i i P IP P IP w 2 1 1 (partial pressure) or ( ) ∑ + = k k k i i i c IP c IP w 2 1 1 (concentration) Extended Langmuir 2. This isotherm is a function of temperature, and one of partial pressure or concentration: ( ) ∑ + = k k T IP k i T IP i i P e IP P e IP w s k s i / 3 / 1 4 2 1 (partial pressure) or ( ) ∑ + = k k T IP k i T IP i i c e IP c e IP w s k s i / 3 / 1 4 2 1 (concentration) Extended Langmuir 3. This isotherm is a function of temperature, and one of partial pressure or concentration: ( ) ∑ + − = k k T IP k i T IP i s i i i P e IP P e IP T IP IP w s k s i / 3 / 3 2 1 4 4 1 ) ( (partial pressure) or ( ) ∑ + − = k k T IP k i T IP i s i i i c e IP c e IP T IP IP w s k s i / 3 / 3 2 1 4 4 1 ) ( (concentration) 1 Gas Adsorption Processes 67 Isotherm Assumed for Layer (gas): Extended Langmuir- Freundlich Model This isotherm is a function of temperature, and one of partial pressure or concentration: ( ) ∑ + = k T IP IP k k T IP IP i i i i s k k s i i e P IP e P IP IP w / 5 / 2 1 4 3 4 3 1 (partial pressure) or ( ) ∑ + = k T IP IP k k T IP IP i i i i s k k s i i e c IP e c IP IP w / 5 / 2 1 4 3 4 3 1 (concentration) Isotherm Assumed for Layer (gas): Dual-Site Langmuir Model This isotherm is a function of temperature, and one of partial pressure or concentration: ∑ ∑ + + + = k k T IP k i T IP i k k T IP k i T IP i i P e IP P e IP P e IP P e IP W s k s i s k s i ) ( 1 ) ( 1 / 7 / 5 / 3 / 1 8 6 4 2 (partial pressure) or ∑ ∑ + + + = k k T IP k i T IP i k k T IP k i T IP i i c e IP c e IP c e IP c e IP W k k s i s k s i ) ( 1 ) ( 1 / 7 / 5 / 3 / 1 8 6 4 2 (concentration) Isotherm Assumed for Layer (gas): Single Layer B.E.T. This isotherm is an extended B.E.T isotherm with a monolayer. It is equivalent to the extended Langmuir isotherm. The isotherm is a function of temperature, and one of partial pressure or concentration: ( ) ∑ + = k T IP k k T IP i i i i s k s i e P IP e P IP IP w / 2 / 2 1 3 3 1 (partial pressure) or ( ) ∑ + = k T IP k k T IP i i i i s k s i e c IP e c IP IP w / 2 / 2 1 3 3 1 (concentration) 1 Gas Adsorption Processes 68 Isotherm Assumed for Layer (gas): Dual Layer B.E.T. This isotherm is a function of temperature, and one of partial pressure or concentration: ( ) ( ) ( ) ( ) + + + + = ∑ ∑ ∑ ∑ k T IP k k k k T IP k k k T IP k k i T IP i k T IP k k T IP i i i i s k s k s k s i s k s i e P IP IP e P IP e P IP IP e IP e P IP e P IP IP w / 2 4 / 2 / 2 4 / 2 / 2 / 2 1 3 3 3 3 3 3 1 1 1 (partial pressure) or ( ) ( ) ( ) ( ) + + + + = ∑ ∑ ∑ ∑ k T IP k k k k T IP k k k T IP k k i T IP i k T k IP k k T IP i i i i s k s k s k s i s s i e c IP IP e c IP e c IP IP e IP e c IP e c IP IP w / 2 4 / 2 / 2 4 / 2 / 2 / 2 1 3 3 3 3 3 3 1 1 1 (concentration) Isotherm Assumed for Layer (gas): User Procedure You can supply your own proprietary isotherm relationships using a Fortran subroutine, which Aspen Adsim interfaces through either the procedure pUser_g_Isotherm_P (partial pressure dependent isotherm) or pUser_g_Isotherm_C (concentration dependent isotherm). The functional relationship is: ( ) IP y y P T f w nc eq i , ... , , 1 = (partial pressure) or ( ) IP c c T f w nc eq i , ... , 1 = (concentration) You can also supply pure component user-specified isotherms, for use as multi-component isotherms, using the IAS method. Here, you must supply two Fortran subroutines: • The first subroutine is interfaced by the procedure pUser_g_Isotherm_Poi. This procedure relates the fictitious pure component partial pressure 0 i P (resulting in the same spread pressure as the mixture at pressure P), to the loading 0 i w by means of a pure component isotherm: ( ) IP P T f w i eq i , , 0 0 = • The second subroutine integrates the Gibbs isotherm to give the spread pressure. It is interfaced by the procedure pUser_g_Gibbs. The relationship to be evaluated is: ( ) ( ) ∫ = = 0 0 0 0 , , , , i P eq i i dP P IP P T f g IP P T g RT A with Π 1 Gas Adsorption Processes 69 Isotherm Assumed for Layer (gas): User Submodel You can supply your own proprietary isotherm relationships using one of these two submodels: • gUserIsothermPp (partial pressure dependent isotherm) • gUserIsothermC (concentration dependent isotherm) The functional relationship is: ( ) IP y y P T f w nc eq i , ... , , 1 = (partial pressure) or ( ) IP c c T f w nc eq i , ... , 1 = (concentration) Pure component user specified isotherms may be supplied and used as multi- component isotherms using the IAS method, in which case you must supply two submodels: • The first submodel is gUserIsothermPoi. This relates the fictious pure component partial pressure 0 i P (resulting in the same spread pressure as the mixture at pressure P), to the loading 0 i w by means of a pure component isotherm: ( ) IP P T f w i eq i , , 0 0 = • The second submodel is gUserGibbs. This integrates the Gibbs isotherm to give the spread pressure. The relationship to be evaluated is: ( ) ( ) ∫ = = 0 0 0 0 , , , , i P eq i i dP P IP P T f g IP P T g RT A with Π Isotherm Assumed for Layer (gas): IAS The IAS facility in Aspen Adsim lets you calculate competitive, multicomponent adsorption behavior using pure component isotherms. Each pure component isotherm has the same expression as its pure component version. Aspen Adsim's standard pure component isotherms available with IAS are: • Langmuir models • Freundlich models • Langmuir-Freundlich models • Henry's models • BET multilayer • User-specified isotherms (user procedure or user submodel) 1 Gas Adsorption Processes 70 Isotherm Tab (gas): Adsorbed Solution Theory If you choose an IAS isotherm, you can then use either the ideal adsorbed solution theory (IAS) or the real adsorbed solution theory (RAST). The two options are: • IAS • RAST With RAST selected and with user procedures supplying the physical properties, you must write a Fortran procedure to supply the activity coefficients. The procedure is described by the type pUser_Act_Coeff. The procedure evaluates i γ as a function of temperature, pressure and the composition of the adsorbed phase: ( ) nc i x x p T f ,..., , , 1 = γ Isotherm Tab (gas): Isotherm Dependency In the isotherm dependency box, choose from: • Concentration — The adsorption isotherm model is a function of concentration. • Partial Pressure — The adsorption isotherm model is a function of partial pressure. Energy Balance Tab (gas) Use the Energy Balance tab to specify how the energy balance is incorporated into the model for your gas adsorption process. Energy Balance Tab (gas): Energy Balance Assumption In the Energy Balance Assumption box, choose your prefered type of energy balance, from: • Isothermal • Non-Isothermal with No Conduction • Non-Isothermal with Gas Conduction • Non-Isothermal with Solid Conduction • Non-Isothermal with Gas and Solid Conduction • None For a vertical bed type with 2-D spatial dimension, the conduction options are not available as conduction is automatically considered for all dimensions. 1 Gas Adsorption Processes 71 Energy Balance Assumption (gas): Isothermal The Isothermal option completely ignores the energy balance. The gas temperature g T and the solid temperature s T are held constant and equal. Energy Balance Assumption (gas): Non-Isothermal with No Conduction This option ignores the axial thermal conduction for the gas and solid phases. Energy Balance Assumption (gas): Non-Isothermal with Gas Conduction This option includes the thermal conduction (axial thermal dispersion) term in the gas energy balance: 2 2 z T k g gz i ∂ ∂ ε − You need to define the form of the gas thermal conductivity. Energy Balance Assumption (gas): Non-Isothermal with Solid Conduction This option includes the thermal conduction term in the solid energy balance: 2 2 z T k s sz ∂ ∂ − You must supply a value for sz k in the Specify table for the layer. Energy Balance Assumption (gas): Non-Isothermal with Gas and Solid Conduction This option includes the thermal conduction term for both gas and solid phases. You must define the form of the gas thermal conductivity. See Energy Balance Tab: Form of Gas Thermal Conductivity, later. Energy Balance Tab (gas): Consider Heat of Adsorbed Phase Aspen Adsim models also let you include the enthalpy content of the adsorbed phase in the solid-phase energy balance. The Enthalpy of Adsorbed Phase term is optional. If the enthalpy content of the adsorbed phase is significant for your process, choose this option to include it in the solid phase energy balance. The term for each component is a function of the loading and the temperature in the solid phase, the adsorbed phase heat capacity, and the solid density: t T w C H s i pai s i ∂ ∂ ρ = 1 Gas Adsorption Processes 72 The total contribution is the sum for all components: ( ) H i i ∑ This equation is quite rigorous, despite neglecting some second order terms such as enthalpy of mixing. In the Consider Heat of Adsorbed Phase box, choose from: • None • Constant • User Procedure • User Submodel Consider Heat of Adsorbed Phase(gas): None If you choose this option, the enthalpy of adsorbed phase term is ignored in the solid phase energy balance. Consider Heat of Adsorbed Phase(gas): Constant Here, the heat capacities of the adsorbed phase components pai C are constant. Consider Heat of Adsorbed Phase(gas): User Procedure With this option, the heat capacities of the adsorbed phase components pai C are calculated using a user-defined subroutine, which Aspen Adsim interfaces through the procedure pUser_g_Cpa. Consider Heat of Adsorbed Phase(gas): User Submodel The heat capacities of the adsorbed phase components pai C are calculated through the user-defined submodel gUserCpa. Energy Balance Tab (gas): Heat of Adsorption Assumption You must include the heat of adsorption in the solid-phase energy balance if it is significant for the process. The rate of heat generation by adsorption of each component i per unit mass of solid, depends on the local rate of mass transfer (the change in the amount of material adsorbed): i H t w HT i i ∆ ∂ ∂ = These rates are held in vectors, HT, and summed for all components to obtain the total rate of heat generation by adsorption per unit volume of solid: ∑ − i i HT s ) ( ρ 1 Gas Adsorption Processes 73 In the Heat of Adsorption Assumption box, choose from: • None • Constant • User Procedure • User Submodel Heat of Adsorption Assumption (gas): None The heat generation by adsorption term is omitted from the energy balance. Heat of Adsorption Assumption (gas): Constant With this option, the heat of adsorption is constant for each component i. Choose it to set the heat of adsorption to constant values, which you supply in the Specify table for the layer for each component. Heat of Adsorption Assumption (gas): User Procedure Here, the heat of adsorption is given by the Fortran procedure pUser_g_DH. You can vary the heat of adsorption and make it a function of, for example, local loading, temperature, and pressure. In general terms: ) , , ( ij j sj ij w P T f H = ∆ Where i designates the component and j designates the node. Heat of Adsorption Assumption (gas): User Submodel With this option, the heat of adsorption comes from the submodel gUserDH. You can vary the heat of adsorption and make it a function of, for example, local loading, temperature, and pressure. In general terms: ) , , ( ij j sj ij w P T f H = ∆ Where i designates the component and j designates the node. Energy Balance Tab (gas): Form of Heat Transfer Coefficient If you specify a non-isothermal energy balance, Aspen Adsim generates the solid and gas-phase energy balances with a film resistance to the heat transfer between the solid and the gas. Heat transfer is assumed to occur between the two phases according to the film resistance model: ) ( bed of m per ferred heat trans of rate 3 s g p T T a HTC − = If there is no such heat transfer resistance, the gas and solid temperatures are equal (lumped): sj gj T T = for all nodes j = 1, m To get this condition, set the heat transfer coefficient to a large value (such as 1). 1 Gas Adsorption Processes 74 In the Form of Heat Transfer Coefficient box, choose from: • Constant • Estimated • User Procedure • User Submodel Form of Heat Transfer Coefficient (gas): Constant Choose this option to make the heat transfer coefficient a constant value, which you set through the variable HTC in the Specify table for the layer. Form of Heat Transfer Coefficient (gas): Estimated The heat transfer coefficient is estimated as follows: 1 Calculate the Reynolds number: u ρ g g p v M r Re 2 = If the calculated value falls below 1E-10, it is reset to this value. 2 Calculate the Prandl number: M k C Pr g pg u = If the calculated value falls below 1E-10, it is reset to this value. 3 Calculate the j-factor: If Re < 190 then 51 . 0 66 . 1 − = Re j otherwise 41 . 0 983 . 0 − = Re j 4 Calculate the heat transfer coefficient: 3 2 Pr − = g g pg v C j HTC ρ If the calculated value falls below 1E-10, it is reset to a value of 1. Form of Heat Transfer Coefficient (gas): User Procedure With this option, the user procedure pUser_g_HTC relates the local heat transfer coefficient to the state of the bed at a particular point in the bed. This means you can interface your own Fortran code to calculate the coefficients. Note that the heat transfer coefficient becomes a distributed variable when you select this option. The values are held in the variables HTC(1), HTC(2)……HTC(n). In general terms: ) , , , ( gj j j gj j v c P T f HTC = Form of Heat Transfer Coefficient (gas): User Submodel Here, the local heat transfer coefficient is defined through the user submodel gUserHTC, using the same dependencies as in the User Procedure option. 1 Gas Adsorption Processes 75 Energy Balance Tab (gas): Form of Gas Thermal Conductivity If you selected non-isothermal with gas and/or solid conduction, you need to choose the form of gas thermal conductivity. In the Form of Gas Thermal Conductivity box, choose from: • Constant • Based on Axial Dispersion • User Procedure • User Submodel Form of Gas Thermal Conductivity (gas): Constant The thermal conductivity g k has a constant value, which you set in the layer Specify form. Form of Gas Thermal Conductivity (gas): Based on Axial Dispersion This option assumes that the analogy between heat transfer and mass transfer is valid. The effective thermal conductivity coefficient is calculated as the product of the heat capacity of the gas, the axial dispersion coefficient, and the density of the gas: gz k = (Heat capacity) x (Averaged Axial dispersion coefficient) x (Molar density) ( ) g k k zk pg gz y E C k ρ ∑ = Form of Gas Thermal Conductivity (gas): User Procedure The thermal conductivity varies axially along the bed. If you supply the necessary physical properties directly, Aspen Adsim¹ interfaces a Fortran subroutine through the procedure pUser_g_Kg. If the physical properties come from a package such as PROPERTIES PLUS, Aspen Adsim handles the required calls automatically. Form of Gas Thermal Conductivity (gas): User Submodel The thermal conductivity varies axially along the bed and is defined in the user submodel gUserKg. 1 Gas Adsorption Processes 76 Energy Balance Tab (gas): Heat Transfer to Environment In the Heat Transfer to Environment box, choose from: • Adiabatic • Thin Wall • Rigorous Model Heat Transfer to Environment (gas): Adiabatic No heat transfer occurs between the bed and the wall. Heat Transfer to Environment (gas): Thin Wall With this option, the heat exchange between the gas in the bed and the environment is included in the gas phase energy balance as: ) ( 4 amb g B w T T D H − The conductivity along the wall and the heat accumulation in the wall are neglected. w H combines the heat transfer resistances of: • Boundary layer between gas and wall, on the inside of the column. • Material of the column wall, including insulation material. • Boundary layer between the outer column wall and the surroundings. The following equation (Bird et al., 1960) calculates w H for the column cross section shown in the Heat Transfer to Environment figure (on the next page). 1 2 1 1 1 1 2 1 ln ln 2 1 2 − − + | . | \ | + | . | \ | + | . | \ | = wo o o i wi i i w H D k D D k D D H D D H 1 Gas Adsorption Processes 77 T g T amb H wi H wo k 1 k 2 D i D 1 D o 1 Gas Adsorption Processes 78 Heat Transfer to Environment (gas): Rigorous Model This option includes a wall energy balance equation that contains the following terms: • Heat transfer from the gas in the bed to the inner wall. • Heat transfer from the outer wall to the environment (including the influence of any insulating material). • Axial thermal conduction along the wall. • Heat accumulation within the wall material. The wall is assumed to be thin and conductive enough for the inner and outer wall temperatures to be equal. The adiabatic option, that is, ignoring the wall energy balance, is valid only when the wall is extremely thin and non- conductive. Energy Balance Tab (gas): Form of Gas-Wall Heat Transfer Coefficient There are two options available for the definition of the gas-wall heat transfer coefficient w H : • Constant • Estimated Form of Gas-Wall Heat Transfer Coefficient (gas): Constant In the Specify table for the layer, set the heat transfer coefficient w H to be a fixed variable. Form of Gas-Wall Heat Transfer Coefficient (gas): Estimated With this option, the gas-wall heat transfer coefficient is calculated from the local conditions inside the adsorbent layer. The correlation uses results from a graphical representation given by Kast, 1988: ( ) 11 . 22 0477 . 0 10 2 1 2 6 + + × − = | | . | \ | + − H H H B B sphere w Pe Pe Pe D H C Nu where: sphere C = 12 for a packed bed of spheres g char w w k x H Nu = = Nusselt number for gas-wall heat transfer g pg g g char H k MC v x Pe ρ = = Gas wall heat transfer Peclet number char x = 1.15(2 p r ) = Characteristic length for a sphere 1 Gas Adsorption Processes 79 Reaction Tab (gas) Use the Reaction tab to generate a layer model that combines adsorption with reaction (heterogeneous and/or homogeneous). The mass and energy balances must include the reaction terms as well as the mass and heat transfer rates caused by adsorption. Furthermore, the formation of additional solid phases, such as coke, must be accounted for. About Gas Adsorption with Reaction Processes Adsorptive reactors combine, into a single process unit, the unit operations of heterogeneous and/or homogeneous chemical reaction and adsorption. Such a hybrid process gives benefits over conventional catalytic reactors: • Higher conversions, for example, when the product in an equilibrium reaction is removed by adsorption from the gas phase. An example of higher conversion is the catalytic dehydrogenation of methyl-cyclohexane to produce toluene. Adsorption of toluene greatly enhances the conversion. • Higher selectivity, when the desired product of an equilibrium reaction scheme is adsorbed. Adsorptive reactors are also used in a number of gas purification processes: • Removing sulfur compounds from gases by first contacting them with α or γ-ferric oxide monohydrates (Iron Sponge) to adsorb sulfur in the form of ferric sulfide, then periodically reoxidizing the surface to form elemental sulfur and to refresh the ferric oxides. • Removing mercury from natural gas streams by treatment in an ex-situ TSA regenerative process. The process uses an activated carbon adsorbent that contains sulfur, and which allows the formation of mercuric sulfide. Adsorptive reactors are also useful in air purification processes. Careful selection of the adsorbent may allow one impurity to be adsorbed onto the adsorbent surface, while another impurity reacts on it. For example, modified activated carbon is used as an adsorbent for sulfur dioxide and a catalyst for NOx reduction. An important application of adsorptive reactors is the separation of radioactive wastes. Such applications usually require extremely high degrees of purification because of the high toxicity of many radioactive elements. Nuclear power plants generate radioactive xenon and krypton as products of the fission reactions, and these can leak out in small quantities into the coolant, to be released to the atmosphere with other gases. To prevent such release, off gases are treated in charcoal delay systems, which prevent the release of xenon and krypton until sufficient time has elapsed for the short- lived radioactivity to decay. Similarly, radioactive iodine from nuclear fuel reprocessing may be captured by chemisorption on molecular sieve zeolites containing silver. 1 Gas Adsorption Processes 80 Reaction Tab (gas): Reactions Present In the Reactions Present box, choose a reaction type from: • None • Homogeneous • Heterogeneous • Homogeneous and Heterogeneous Reactions Present (gas): None No reactions are present in the gas or solid phases. Reactions Present (gas): Homogeneous Reactions are present in the gas phase only. Reactions Present (gas): Heterogeneous Reactions are heterogeneously catalyzed by a solid. The catalyst and adsorbent are assumed to be different, giving rise to two distinct solid phases. Solid reaction participants can be considered. Reactions Present (gas): Homogeneous and Heterogeneous Reactions are present in both the gas phase and the solid phase. Reaction Tab (gas): Homogeneous Rate Dependency In the Homogeneous Rate Dependency box, select the type of expression for homogeneous reaction rate. Choose from these options: • Homogenous Rate Dependency: Partial Pressure • Homogenous Rate Dependency: Concentration Homogeneous Rate Dependency (gas): Partial Pressure The reaction rate for components in the gas phase is related to the partial pressure of the component and gas phase temperature through the procedure pUser_g_Gas_Rx_Rate_Pp, which requires the user to supply the appropriate Fortran subroutine. Homogeneous Rate Dependency (gas): Concentration The reaction rate for components in the gas phase is related to the concentration of the component and gas phase temperature through the procedure pUser_g_Gas_Rx_Rate_C, which requires the user to supply the appropriate Fortran subroutine. 1 Gas Adsorption Processes 81 Reaction Tab (gas): Number of Homogeneous Reactions In the Number of Homogeneous Reactions box, select the number of reactions that occur in the gas phase. Reaction Tab (gas): Heterogeneous Rate Dependency In the Heterogeneous Rate Dependency box, select the type of expression for heterogeneous reaction rate. Choose from: • Partial Pressure • Concentration Heterogeneous Rate Dependency (gas): Partial Pressure With this option, the reaction rate for components on the surface of the catalytic adsorbent is related to the gas phase partial pressure of the component and gas phase temperature, through one of these procedures: • pUser_g_Cat_Rx_Rate_Pp • pUser_g_Cat_Rx_Rate_Pp_Sol (for when solid reactants are present) Both procedures require you to supply the appropriate Fortran subroutine. Heterogeneous Rate Dependency (gas): Concentration With this option, the reaction rate for components on the surface of the catalytic adsorbent is related to the concentration of the component and gas phase temperature through one of these procedures: • pUser_g_Cat_Rx_Rate_C • pUser_g_Cat_Rx_Rate_C_Sol (for when solid reactants are present) Both procedures require you to supply the appropriate Fortran subroutine. Reaction Tab (gas): Number of Heterogeneous Reactions In the Number of Heterogeneous Reactions box, select the number of reactions that occur on the surface of the catalytic adsorbent. 1 Gas Adsorption Processes 82 Reaction Tab (gas): Are Solid Reactants Present This option is active only if heterogeneous reactions are present. Choose from: Yes. Here, solid reaction participants are present. The solids are formed either by the reaction (for example carbon in reaction networks that suffer from coking), or they represent catalytically active sites being deactivated or reactivated. You define, through Fortran subroutines, the way solid components interact with the gas phase. Aspen Adsim interfaces these subroutines through one of these two procedures: • pUser_g_Cat_Rx_Rate_Pp - or - • pUser_g_Cat_Rx_Rate_Pp_Sol No. Here, no solid reactants are present. Reaction Tab (gas): Solid Reactant List In the Solid Reactant List box, choose a default list or a user-defined list of solid reactants. Procedures Tab (gas) Use the Procedures tab to view a list of the user procedures in use within the current adsorption layer model. Gas Adsorption: Summary of Mass and Energy Balance Equations This section summarizes the equations for mass and energy balances used for gas adsorption processes in Aspen Adsim. 1 Gas Adsorption Processes 83 Gas Adsorption: Mass Balance for Gas Phase The overall mass balance for a multi-component gas phase accounts for the convection of material and mass transfer, from the gas to the solid phase. Aspen Adsim uses this equation only for constant pressure systems, and it is suitable only for simulating breakthrough curves at constant pressure and temperature. The governing partial differential equation is: ( ) 0 = ∑ + t w z v k k s g g ∂ ∂ ρ ∂ ρ ∂ For an explanation of the symbols used, see Explanation of Equation Symbols, later. Each component in the gas phase is governed by a similar equation, with extra terms for accumulation, and for axial and radial dispersion terms (if required): ( ) 0 + 1 2 2 = + + | . | \ | ∂ ∂ ∂ ∂ − − k k B k g k rk i k zk i J t c z c v r c r r r E z c E ∂ ∂ ε ∂ ∂ ε ∂ ∂ ε In general, axial and radial dispersion needs to be considered, but the dispersion coefficient can be difficult to measure. Aspen Adsim sets the dispersion coefficient either to a constant value, or calculates it as a function of local conditions (that is, a distributed parameter). Gas Adsorption: Mass Balance for Additional Solid Phase The concentration of each solid component i is calculated from its formation rate: 0 , , = − ∂ ∂ i sol i sol R t c 1 Gas Adsorption Processes 84 Gas Adsorption: Gas Phase Energy Balance The gas phase energy balance includes terms for: • Thermal conduction • Convection of energy, accumulation of heat • Compression • Heat transfer from gas to solid • Heat transfer from gas to the internal wall • Heat of reaction. The governing partial differential equation is: ( ) ( ) 0 4 + , , 2 2 = + + + − + − + + + − Hx Hx g cat p cat s r o g B w s g p g g g vg B g g g vg g i ga Q a t T C H T T D H T T HTCa z v P t T C z T v C z T k ∂ ∂ ρ ∂ ∂ ∂ ∂ ρ ε ∂ ∂ ρ ∂ ∂ ε The above equation is in its most complete form, including axial thermal conduction, heat transfer to the environment, and the effect of heterogeneous and homogenous chemical reactions. The only term missing is the radial thermal conduction term, which is included for 2-dimensional, vertical beds. However, in this geometry, heat transfer to the environment is a boundary condition so is not part of the energy balance (it is in the 1-dimensional case). Gas Adsorption: Solid Phase Energy Balance The solid phase energy balance includes terms for: • Thermal conduction • Accumulation of heat • Accumulation of enthalpy in the adsorbed phase • Heat of adsorption • Gas-solid heat transfer from gas to solid (expressed in terms of a film resistance, where the heat transfer area is proportional to the area of the adsorbent particles) The solid phase energy balance is: ( ) ∑ ∑ = = = − − | . | \ | + + + | . | \ | ∂ ∂ ∂ ∂ − − n i s g p i i s s n i i pai s s ps s s sr s sa T T HTCa t w H t T w C t T C r T r r r k z T k 1 1 2 2 0 ) ( 1 1 ∂ ∂ ∆ ρ ∂ ∂ ρ ∂ ∂ ρ ∂ ∂ 1 Gas Adsorption Processes 85 Gas Adsorption: Wall Energy Balance The wall energy balance includes terms for: • Axial thermal conduction along the wall • Heat accumulation within the wall material • Heat transfer from the bed to the inner wall • Heat transfer from the outer wall to the environment The governing equation is: ( ) ( ) ( ) ( ) ( ) 0 4 4 2 2 2 2 2 2 2 = − − + + + − − + − + − amb w B T B T B amb w g B T B B w w pw w w w T T D W D W D H T T D W D D H t T c z T k ∂ ∂ ρ ∂ ∂ For a 2-dimensional bed model, Aspen Adsim replaces the third term with the sum of the conductive energy fluxes in the radial direction, which come from the solid phase energy balances. These fluxes are the boundary conditions for 2-dimensional bed models. Gas Adsorption: Summary of Factors that affect the Mass Balance Equations This section lists the factors that affect the mass balance in the solid and gas phases. Gas Adsorption: Axial Dispersion Term The axial dispersion term is: 2 2 z c E k zk i ∂ ∂ ε − Gas Adsorption: Radial Dispersion Term This term is only active if you chose vertical bed and two-dimensional spatial discretization: | . | \ | ∂ ∂ ∂ ∂ − r c r r r E k rk i 1 ε Gas Adsorption: Convection Term The convection term is: ( ) z c v k g ∂ ∂ Gas Adsorption: Gas Phase Accumulation Term The accumulation term is: t c k B ∂ ∂ ε 1 Gas Adsorption Processes 86 Gas Adsorption: Rate of Flux to Solid Surface The rate of flux to the solid surface is given by: J w t S = −ρ ∂ ∂ Gas Adsorption: Rate of Adsorption The rate of adsorption is represented as an accumulation term in the gas phase mass balance. The linear driving force solid-film model is: ( ) s k ads k k k k J w w MTCs t w ρ ∂ ∂ , * = − = There are analogous expressions for gas films and quadratic driving forces. If a particle material balance was considered, t w k ∂ ∂ is taken to be the integral uptake of the particle as determined by the flux through the boundary layer. (See Also Particle MB.) Note: Procedure-defined expressions need adjusting accordingly. Gas Adsorption: Reaction Term The reaction term accounts for the removal or formation of components in the gas phase, due to reaction on the solid catalyst's surface. It is represented as: k reac gas i k reac cat J J , , , , ε + Where: k reac cat J , , = rate of consumption or production of k by heterogeneous (catalytic) reactions k reac gas J , , = rate of consumption or production of k by homogeneous (gas phase) reactions. j gas k j gas reacgas n j k reac gas R J , , , 1 , , ν ∑ = − = j cat k j cat reaccat n j cat s k reac cat R J , , , 1 , , , ν ρ ∑ = − = 1 Gas Adsorption Processes 87 You must define the rates of reaction in a user procedure, as a function of temperature, and one of partial pressure or component concentration. The total rate of flux to the surface per unit volume is then: k reac gas i k reac cat k ads k J J J J , , , , , ε + + = k reac gas i k reac cat k s k J J t w J , , , , ε ∂ ∂ ρ + + = Gas Adsorption: Defining the Mass Balance for Additional Solid Phases During the catalytic reaction, solid phases such as coke deposit sometimes form, or a metal oxide catalyst is oxidized and/or reduced. The concentration of each solid component i is calculated from its rate of formation: 0 , , = − ∂ ∂ i sol i sol R t c You must define the reaction rate of the solid components in a Fortran subroutine, as a function of temperature, pressure, and solid component concentrations. Aspen Adsim interfaces this subroutine through the procedure pUser_g_Cat_RX_Rate_Pp_Sol. Gas Adsorption: Summary of Factors that affect the Energy Balance This section lists the factors that affect the energy balance equations in the: • Gas phase energy balance. • Solid phase energy balance. • Wall energy balance. Gas Adsorption: Defining the Energy Balance in the Gas Phase This section lists the factors that affect the energy balance equations in the gas phase. Gas Adsorption: Effect of Compression The reversible rate of internal energy increase per unit volume by compression is: z v P g ∂ ∂ 1 Gas Adsorption Processes 88 Gas Adsorption: Convective Term The gas convective term is always included in the gas phase energy balance: z T v C g g g vg ∂ ∂ ρ Gas Adsorption: Accumulation in Gas Phase The enthalpy accumulation in the gas phase is represented as: t T C g g vg i ∂ ∂ ρ ε Gas Adsorption: Axial Thermal Conduction in Gas Phase The axial gas thermal conduction (axial thermal dispersion) term is given by: 2 2 z T k g gz i ∂ ∂ −ε Where gz k is evaluated based on your choices in: • Energy Balance tab for 1-dimesional models. • Material/Momentum Balance tab for two dimensional models. Gas Adsorption: Radial Thermal Conduction in Gas Phase The radial gas thermal conduction term (radial thermal dispersion) is represented as: | | . | \ | ∂ ∂ ∂ ∂ − r T r r r k g gr i 1 ε Where gr k is evaluated according to the options selected in the material and momentum balance tab for two-dimensional models. Gas Adsorption: Gas-Solid Heat Transfer Aspen Adsim uses a film resistance model to represent heat transfer between gases and solids: Rate of heat transferred per unit volume = ) ( s g p T T HTCa − with: ( ) p i p r a 3 1 ε − = This is for adsorption only. You set p a for adsorption and reaction. 1 Gas Adsorption Processes 89 Gas Adsorption: Heat Exchange between Gas and Internal Wall For one-dimensional vertical and horizontal bed models: ) ( 4 o g B w T T D H − Where: amb o T T = for adiabatic/thin walls and w o T T = for thick walls For other geometries, this term is missing because: • Radial bed models are always considered to be adiabatic. • For two dimensional vertical bed models, the heat transfer to the column wall is one of the thermal boundary conditions for the radial direction. Gas Adsorption: Rate of Heat Generation by Reaction The rate of heat generation by reaction is the sum of the contributions from individual reactions: ∑ ∑ = = + = cat nreac l l cat l Rcat cat s gas nreac k k gas k Rgas i R R H R H H , 1 , , , , 1 , , ρ ε Where: k = index for the set of homogenous reactions l = index for the set of heterogeneous reactions l Rcat k Rgas H H , , , = molar heats of reactions k and l, typically in MJ/kmol k gas R , = rate of homogenous reaction k, typically in kmol/(m 3 s) l cat R , = rate of heterogeneous reaction l, typically in kmol/(kg s) cat s, ρ = catalyst bulk density You must define the rates of reaction in a user procedure, as a function of temperature, and one of partial pressure or concentration. The heat of reaction must also be defined as a function of temperature and mole fraction. See the following procedures, described in the Adsim Library Reference guide: • pUser_g_Cat_RX_Rate_Pp_Sol • pUser_g_Cat_RX_Rate_C_Sol • pUser_g_Cat_RX_Rate_Pp • pUser_g_Cat_RX_Rate_C • pUser_g_Gas_RX_Rate_Pp • pUser_g_Gas_RX_Rate_C • pUser_g_Cat_RX_Heat • pUser_g_Gas_RX_Heat 1 Gas Adsorption Processes 90 Gas Adsorption: Heat Exchange between Gas and Internal Heat Exchanger The heat exchange between the gas phase and a heat exchanger (either as jacket around the packed bed or via tubes surrounded by adsorbents) is given by: Hx Hx Q a Where Hx a is the specific heat exchange area per unit bed volume and Hx Q the energy flux exchanged, given by: ( ) Hx g Hx Hx T T U Q − = for single phase exchange media, and ( ) ( ) St g St Hx Cw g Cw Hx Hx T T U T T U Q − + − = , , for two phase exchange media. See also Configure Form (gas) earlier in this chapter. Gas Adsorption: Defining the Energy Balance for the Solid Phase This section lists the factors that affect the energy balance equations in the solid phase. Gas Adsorption: Accumulation in Solid Phase The solid phase enthalpy accumulation is always included in the solid phase energy balance: t T C s ps s ∂ ∂ ρ Gas Adsorption: Axial Thermal Conductivity in Solid Phase The solid thermal conduction term is: 2 2 z T k s sz ∂ ∂ − Gas Adsorption: Radial Thermal Conductivity in Solid Phase This term is active only for vertical beds and two-dimensional spatial discretization: | . | \ | ∂ ∂ ∂ ∂ − r T r r r k s sr 1 1 Gas Adsorption Processes 91 Gas Adsorption: Heat of Adsorption The rate of heat generation by adsorption of each component i, per unit mass of solid, is a function of the local rate of mass transfer: t w H HT i i i ∂ ∂ = ∆ These rates are held in vectors i HT and summed for all components to give the total rate of heat generation by adsorption per unit volume of solid: ( ) ∑ − i i s HT ρ Gas Adsorption: Heat of Adsorbed Phase The term for each component is a function of the loading and the temperature in the solid phase: t T w C H s i pai s i ∂ ∂ ρ = The total contribution comes from the sum for all components: ( ) ∑ i i H You supply pai C (heat capacity of adsorbed component i) as either a fixed value for each component, or through a user procedure or submodel. Try these guidelines when deciding what specific heat capacity to use (Tien, 1994): For c T T << use pai C for liquid For T just below c T use system knowledge to specify pai C For c T T > use pai C for compressed gas Gas Adsorption: Gas-Solid Heat Transfer The gas-solid heat transfer term is the same as for the gas phase, but with the sign reversed: ) ( s g p T T a HTC − 1 Gas Adsorption Processes 92 Gas Adsorption: Defining Energy Balance for the Wall This is applicable only if you selected a rigorous model for the heat transfer to the environment. The following effects are considered: • Heat exchange between gas and wall. • Between wall and environment. • Axial thermal conductivity along wall. • Heat content of wall. Gas Adsorption: Heat Exchange between Gas and Wall When the rigorous wall energy balance is selected, Aspen Adsim includes, in the wall energy balance, the heat exchange between the gas in the bed and the inner surface of the wall. The term is represented as: ( ) ( ) w g B T B B w T T D W D D H − − + 2 2 4 Where B D = Internal diameter of layer T W = Width of column wall The supply of w H is defined by the Form of Gas-Wall Heat Transfer Coefficient option. It is either constant or estimated from a correlation. The heat exchange between gas and wall is also included in the gas phase energy balance. Note that the equation has a slightly different form, since the basis of the equation is per unit volume of gas phase: ( ) w g B w T T D H − 4 Gas Adsorption: Heat Exchange between Wall and Environment When you include a rigorous wall energy balance, the corresponding term in the wall energy balance gives the heat transfer between the outer wall and the environment: ( ) ( ) ) ( D D 4 2 2 B B amb w B T T amb T T D W W H − − + + Gas Adsorption: Axial Thermal Conductivity along Wall The axial thermal conduction along the wall is always part of the wall energy balance. The term is represented as: 1 Gas Adsorption Processes 93 2 2 z T k w w ∂ ∂ − You must specify the value of the wall thermal conductivity w k in the Specify table for the layer. Gas Adsorption: Heat Content of Wall The Heat Content of Wall term is always included in the wall energy balance: t T C w pw w ∂ ∂ ρ You must specify the value of the wall density w ρ and the specific heat capacity of the wall pw C in the Specify table for the layer. Gas Adsorption: Explanation of Equation Symbols Symbol Explanation Aspen Adsim base units a Specific particle surface. m 2 /m 3 Hx a Specific heat exchanger surface. m 2 (HX area)/m 3 (Bed) P a Specific particle surface per unit volume bed. m 2 (Particle area)/m 3 (Bed) A Area. m 2 AA Placeholder variable used for Dubinin- Astakhov isotherm evaluation. b Kinetic Langmuir factor. 1/bar bk c Bulk gas phase concentration. kmol/m 3 k c Molar concentration of component k. kmol/m 3 msk c Macropore gas phase concentration. kmol/m 3 sol c Concentration of solid phase reactant. kmol/kg pai c Specific heat capacity of adsorbed phase. MJ/kmol/K cat p c , Specific heat capacity of catalyst. MJ/kg/K pg c Specific gas phase heat capacity at constant pressure. MJ/kmol/K ps c Specific heat capacity of adsorbent. MJ/kmol/K pW c Specific heat capacity of column wall. MJ/kg/K 1 Gas Adsorption Processes 94 vg c Specific gas phase heat capacity at constant volume. MJ/kmol/K B D Bed diameter. m efc D Effective micropore diffusion coefficient. m 2 /s efP D Effective macropore diffusion coefficient. m 2 /s ek D Effective adsorbed phase diffusivity of component k. m 2 /s ki D Knudsen diffusion coefficient of component i. m 2 /s mk D Mean molecular diffusion coefficient of component k. m 2 /s k act E , Activation energy for Arrhenius relationship. MJ/kmol ik E Radial dispersion coefficient of component k. m 2 /s zk E Axial dispersion coefficient of component k. m 2 /s f Function. - eq f Equilibrium (isotherm) relationship. - amb H Wall-ambient heat transfer coefficient. MW/m 2 /K B H Height of adsorbent layer. m i H Rate of change of heat of adsorbed phase. MJ/m 3 /s R H Combined heats of homogenous and heterogeneous reactions. MJ/m 3 (Bed)/s Rcat H Heat of catalytic reaction. MJ/kmol Rgas H Gas phase heat of reaction. MJ/kmol Ti H Heat of adsorption contribution to solid phase energy balance. MJ/m 3 /s w H Gas-wall heat transfer coefficient. MJ/m 2 /s i H ∆ Heat of adsorption of component i. MJ/kmol HTC Gas-solid heat transfer coefficient. MJ/m 2 /s IP Isotherm parameter, units depend on isotherm. j Colburn j-factor for heat or mass transfer. - k ads J , Mass transfer rate of component k owing to adsorption. kmol/m 3 (Bed)/s k reac cat J , , Mass transfer rate of component k owing to heterogeneous catalytic reactions. kmol/m 3 (Bed)/s 1 Gas Adsorption Processes 95 reac gas J , Mass transfer rate of component k owing to homogenous, gas phase reactions. kmol/m 3 (Void)/s k J Mass transfer rate of component k to/from adsorbent. kmol/m 3 (Bed)/s k k 0 Pre-exponential factor for Arrhenius relationship. m/s Pk k 0 Pre-exponential factor for pressure dependent Arrhenius relationship. m/s fk k Film mass transfer coefficient of component k. m/s g k Gas phase thermal conductivity. MW/m/K gr k Effective radial gas phase thermal conductivity. MW/m/K dyn gr k Dynamic contribution to gr k . MW/m/K stat gr k Static contribution to sr k . MW/m/K i k Effective, lumped mass transfer coefficient of component i. 1/s s k Solid thermal conductivity. MW/m/K gz k Effective axial gas phase thermal conductivity. MW/m/K sr k Effective radial solid phase thermal conductivity. MW/m/K stat sr k Static contribution to gr k . MW/m/K sz k Effective axial solid phase thermal conductivity. MW/m/K W k Thermal conductivity of column wall. MW/m/K Ki K Isotherm slope of component i (Henry’s coefficient). m 3 /kg Ki K Dimensionless isotherm slope of component i (Henry’s coefficient). - mac K Macropore mass transfer coefficient. 1/s mic K Micropore mass transfer coefficient. 1/s p K Darcy’s constant. bar s/m 2 Pi K Macropore diffusion coefficient. m 2 /s L Length of horizontal bed. m M Molecular weight. kg/kmol g MTC Gas film mass transfer coefficient. 1/s s MTC Solid film mass transfer coefficient. 1/s 1 Gas Adsorption Processes 96 p Emissivity in calculation of effective thermal conductivities. P Pressure. bar 0 i P IAS vapor pressure. bar sat P Saturation pressure. bar Hx Q Heat transfer rate to internal heat exchanger. MJ/m 2 /s r Radial co-ordinate (in packed bed or particle). m c r Microparticle (crystal) radius. m p r Particle radius. m R Universal gas constant. bar m 3 /kmol/K cat R Catalytic reaction rate. kmol/kg/s gas R Gas phase reaction rate. kmol/m 3 /s sol R Solid phase reaction rate. kmol/kg/s t Time. s cycle t Adsorption cycle time. s T Temperature. K 0 T Equal to amb T or W T , depending on context used. K amb T Ambient temperature. K c T Critical temperature. K CW T Cooling water temperature. K s T Solid phase temperature. K g T Gas phase temperature. K Hx T Heat exchange medium temperature. K St T Steam temperature. K W T Wall temperature. K Tort Adsorbent tortuosity. - Hx U Overall heat transfer coefficient: gas to heat exchange medium. MW/m 2 /K cw Hx U , Overall heat transfer coefficient: gas to cooling water. MW/m 2 /K 1 Gas Adsorption Processes 97 St Hx U , Overall heat transfer coefficient: gas to steam. MW/m 2 /K g v Gas phase superficial velocity. m/s k w Loading. kmol/kg 0 k w Pure component loading of component k. kmol/kg W Width of horizontal bed. m T W Width of column wall. m char x Characteristic length. m k x Mole fraction of component k in the adsorbed phase. - k y Mole fraction of component k in the gas phase. - z Axial co-ordinate. m Z Gas compressibility factor. - Symbol Explanation Aspen Adsim base units rg α Radiation contribution to stat gr k . rs α Radiation contribution to stat sr k . β Factor used in stat gr k calculation. ∆r Radial discretization distance. m B ε Total bed voidage. m 3 (Void+Pore)/m 3 (Bed) i ε Interparticle voidage. m 3 (Void)/m 3 (Bed) P ε Intraparticle voidage. m 3 (Pore)/m 3 (Particle) φ Function of packing density, used in stat sr k calculation. φ Relative pressure: k sat k P P , / . - γ Factor used in stat sr k calculation. i γ Activity coefficient of component i. - u Dynamic viscosity. N s/m 2 i ads, u Chemical potential of component i in the adsorbed phase. MJ/kmol i gas, u Chemical potential of component i in the gas phase. MJ/kmol jk ν Stoichiometric coefficient of component k in reaction j. - 1 Gas Adsorption Processes 98 0 i Π Spreading pressure of component i. bar m θ Time constant for adsorption cycle. - g ρ Gas phase molar density. kmol/m 3 s ρ Adsorbent bulk density. kg/m 3 cat s, ρ Catalyst bulk density. kg/m 3 W ρ Wall density. kg/m 3 Ω Parameter in Glueckauf expression. - Ψ Particle shape factor. - Dimensionless number Defining expression Description W Nu g char w k x H Nusselt number for gas wall heat transfer. H Pe g pg g g char k MC v x ρ Gas-wall heat transfer Peclet number. K Pe z b g E H v Component Peclet number for mass transfer. Pr M k C g pg u Prandl number. k Sc M D g mi ρ u Component Schmidt number. k Sh mi p fi D r k 2 Component Sherwood number. Re u ρ g g p v M r 2 Particle Reynolds number. 2 Gas Cyclic Steady State Modeling 99 2 Gas Cyclic Steady State Modeling Introduction Aspen Adsim 2004.1 presents an innovative new modeling approach to maximize profitability in the design, simulation, and optimization of periodic adsorption processes for gas separation, processes, such as Pressure Swing Adsorption (PSA), Thermal Swing Adsorption (TSA), Vacuum Swing Adsorption (VSA), etc. Direct determination of the cyclic steady state, without carrying out a dynamic simulation over a large number of cycles, is now available using Aspen Adsim 2004.1. This powerful tool - Cyclic Steady State (CSS) modeling (the result of complete discretization of both time and space) presents a periodic adsorption process as a steady state problem. The Aspen Adsim 2004.1 CSS models offer an extremely efficient design tool that can be more readily used as an optimization package to determine optimal design and operating conditions for an adsorption process. The following sections outline CSS modeling tasks and include instructions on using CSS models for your engineering business: • What is CSS Modeling…? • Discretization Techniques for Time and Space • Connectivity Between CSS Models • Bed Model Details • Material Balance • Momentum Balance • Kinetic Model • Energy Balance • Adsorption Equilibrium Models • User Guidelines 2 Gas Cyclic Steady State Modeling 100 • How to Create a CSS Simulation Flowsheet • How to Create a Dynamic Simulation Flowsheet using CSS Models • How to Convert a CSS Flowsheet to a Dynamic Flowsheet • How to a Convert Dynamic Flowsheet to a CSS Flowsheet • Developer’s Tips to Get Better Convergence Property in CSS Simulation What is CSS Modeling…? A periodic adsorption process operates on sequential steps (for example, continuously repeated steps of Feed, Purge, Pressure equalization, Blow down, Production, etc.) with multiple adsorbers packed with single or multiple adsorbent layers. Although the operation of each bed is batchwise, the whole system is continuous because of the use of multi-beds that are ultimately operated in a cyclic steady state within a confined cycle time. Cyclic Steady State (CSS), which is the nature of periodic adsorption processes, implies a steady state in which the conditions at the end of each cycle are identical to those at the beginning. The traditional approach for CSS determination is to carry out a dynamic simulation of the system, beginning with a specified set of initial condition, over a large number of cycles until a CSS is eventually confirmed from a defined criteria, e.g., the cycle initial state at t 0 must be identical to the cycle end state at t N , as illustrated in Figure 1. Spatial Domain Time Domain Cycle end state(tN) S t e p 1 S t e p 2 S t e p N t1 t2 tN tN-1 t0 dynamic simulation C y c l e i n i t i a l s t a t e ( t 0 ) Figure 1 Illustration for traditional dynamic simulation of a periodic adsorption process 2 Gas Cyclic Steady State Modeling 101 t0 tN t1 t2 tN-1 Periodic Boundary State(tN) = State(t0) i.e. Cyclic Steady State Time domain (t) S p a t i a l d o m a i n ( x ) Figure 2 Illustration for the concept of CSS modeling system in Aspen Adsim From a mathematical point of view, the criterion for CSS is considered a unique characteristic of a periodic adsorption process, and has brought ideas to explore a better numerical method toward CSS in terms of cost-effective process simulation. The existence of periodic time boundary inspires to replace the initial condition by a periodicity condition requiring that the system state at the end of each cycle is identical to that at its beginning. As illustrated in Figure 2, the forced reformulation also constrains the system within a specified time domain length, from the starting point (t 0 ) to the ending point (t N ). This suggests a steady state simulation is feasible by complete discretization of space and time within a confined time length (i.e., cycle time). Based on the above concept, the CSS models in Aspen Adsim 2004.1 have been developed to determine CSS from purely steady state simulation. Direct determination of CSS will effectively save the costs for the optimization of periodic adsorption process since the technique could offer an extremely efficient design tool that can be more readily used as an optimization package to determine optimal design and operating conditions. Further benefits come from the fact that the graphic user interface of the freshly released CSS models from Aspen Adsim 2004.1 is the same as those of existing Aspen Adsim dynamic models. Therefore, existing Adsim users should find it easy to use this new feature. The high-level functionalities of CSS bed model (gCSS_Adsorber) in Aspen Adsim 2004.1 are listed in Table 1, compared with the original Aspen Adsim dynamic bed model (gas_bed). 2 Gas Cyclic Steady State Modeling 102 Table 1. Functional comparison of CSS and dynamic bed models in Aspen Adsim 2004.1 2 Gas Cyclic Steady State Modeling 103 Discretization Techniques for Time and Space Spatial derivatives of CSS bed model (gCSS_Adsorber) are discretized by one of the following numerical methods: • CFD4 – 4 th Order Central Finite Difference, equivalent to CDS2 in gas_bed • OCFE2 – 2 nd Order Orthogonal Collocation on Finite Elements • OCFE4 – 4 th Order Orthogonal Collocation on Finite Elements Time derivatives of CSS models are explained using 1 st Order Backward Finite Difference approximation: ( ) t x t u x t u t x t u j n j n j n ∆ − ≈ ∂ ∂ − ) , ( ) , ( , 1 Connectivity between CSS Models CSS models contain at least an input and an output port (gCSS_Port). Each port has associated variables that correspond to the material connection stream (gCSS_Material_Connection) that allows reversible flow. These are the available connections for CSS models: 2 Gas Cyclic Steady State Modeling 104 Bed Model Details Material Balance The CSS bed model (gCSS_Adsorber) uses the following material balance for the bulk gas adsorption: ( ) 0 2 2 = ∂ ∂ + ∂ ∂ + ∂ ∂ + ∂ ∂ − t Q t C x C v x C D i b i t i g i b Li ρ ε ε The physical meanings of each term are: 2 2 x C D i b Li ∂ ∂ − ε Axial dispersion contribution 1 ( ) x C v i g ∂ ∂ Convection t C i t ∂ ∂ ε Gas phase accumulation 2 t Q i b ∂ ∂ ρ Adsorbed phase accumulation 3 The following continuity equation is required to complete the material balance around the system,: g i i C ρ = ∑ Notation i C Gas phase concentration for component i, kmol/m 3 Li D Axial dispersion coefficient for component i, m 2 /s t Time, s i Q Amount adsorbed for component i, kmol/kg-adsorbent g v Superficial gas velocity, m/s x Axial distance coordinate, m b ε Bed (interparticle) voidage p ε Intraparticle voidage t ε Total voidage 2 Gas Cyclic Steady State Modeling 105 g ρ Gas density, kmol/m 3 b ρ Bed packing density, kg/m 3 p ρ Particle density (solid density, true density), kg/m 3 References 1 If a concentration gradient exists in a packed bed, a diffusive mass flux will occur. In addition, eddy (turbulent) diffusion due to the flow also contributes to the mass flux. The resultant flux is referred to as mass dispersion, which may be expressed mathematically in terms of Fick’s law, where the proportionality constant is called dispersion coefficient. Dispersion occurs in both radial and axial directions in the bed. The axial dispersed mixing often occurs when a fluid flows through a packed bed and may cause unfavorable separation efficiency as the separation factor is becoming smaller. In general, flow through a packed bed may be adequately represented with inclusion of the axial dispersed plug flow consideration. 2 Here, t ε is the total bed voidage, which is the combined interparticle and intraparticle voidages calculated from ( ) b p b t ε ε ε ε − + = 1 . 3 Here, b ρ is the bed (packing) density calculated from ( ) b p b ε ρ ρ − = 1 . Momentum Balance Gas flow through a packed bed can be described by a relevant pressure drop correlation. Within the CSS adsorber model (gCSS_Adsorber), one of the following pressure drop correlations may be chosen as the one. Note that there is no other option to assume an ideal flow regime, such as Constant Pressure and Velocity and Constant Pressure with Variable Velocity since the CSS models has been developed fundamentally for cyclic process for gas separation. (1) Darcy’s Law: g p v K x P − = ∂ ∂ (2) Blake-Kozeny: ( ) ( ) g b p b g v r x P 3 2 2 5 2 1 10 150 ε ψ ε u − × − = ∂ ∂ − 2 Gas Cyclic Steady State Modeling 106 (3) Burke-Plummer: ( ) ( ) 2 3 5 2 1 10 75 . 1 g b p b g w v r M x P ε ψ ε ρ − × − = ∂ ∂ − (4) Ergun Equation: ( ) ( ) ( ) ( ) | | . | \ | − × + − × − = ∂ ∂ − − 2 3 5 3 2 2 5 2 1 10 75 . 1 2 1 10 150 g b p b g w g b p b g v r M v r x P ε ψ ε ρ ε ψ ε u Notation p K Darcy Coefficient, bar.s/m 2 w M Molecular weight of gaseous mixture, kg/kmol P Gas pressure, bar p r Particle radius, m g v Superficial gas velocity, m/s x Axial distance coordinate, m b ε Bed voidage (void fraction) g u Gas mixture viscosity, cP g ρ Gas density, kmol/m 3 ψ Particle shape factor Kinetic Model Rigorous simulation of an adsorption process requires a reliable representation of the adsorption kinetics for the adsorbent used. In adsorption, the mass transfer mechanism consists of four steps: • Fluid film transfer • Pore diffusion • Adhesion on surface • Surface diffusion Because the surface adhesion rate approximates the order of the collision frequency of the gas molecule on the solid surface, (which is much greater than for the transport processes) the equilibrium is assumed instantaneously at the interfaces. Adsorptives initially transfer from the bulk gas phase through an external film to the external surface of the particles. The molecules are diffused into the 2 Gas Cyclic Steady State Modeling 107 pores of the particle, adsorbed on the active sites and then diffused along the surface. While fluid film transfer and pore diffusion are treated as sequential steps, pore diffusion and surface diffusion generally occur in parallel. Any combination of the three steps can constitute the rate-controlling mechanism. This mechanism definitely depends on the adsorption system and can vary with the operating conditions of the process. Typically, a film adjacent to the surface confines the mass transfer rate between solid and fluid phases and this external film mass transfer resistance may be determined by the hydrodynamic condition. It is in fact more convenient to depict film transfer rate in terms of an effective transfer coefficient or a lumped resistance coefficient rather than to use a diffusion equation to represent adsorption kinetics in a rigorous manner. The CSS adsorber model (gCSS_Adsorber) within Aspen Adsim 2004.1 limits two types of lumped kinetic models for application. They are: Linear Driving Force Approximation and Quadratic Driving Force Approximation. Both approximations have a lumped resistance coefficient that may be determined at either fluid or solid film where the mass transfer occurs: (1) Linear Driving Force Approximation (LDFA): ( ) * i i F i b C C k t Q i − = ∂ ∂ ρ at fluid film ( ) i i Si i Q Q k t Q − = ∂ ∂ * at solid film (2) Quadratic Driving Force Approximation (QDFA): ( ) ( ) i i i Fi i b C C C k t Q 2 2 * 2 − = ∂ ∂ ρ at fluid film ( ) ( ) i i i Si i Q Q Q k t Q 2 2 2 * − = ∂ ∂ at solid film The lumped mass transfer coefficient, Fi k or Si k , can be determined by a constant or by a certain relationship according to the dynamic conditions of adsorption system. The CSS adsorber model (gCSS_Adsorber) provides the following choices in determining the lumped mass transfer coefficient from the empirical assessment by Aspen Adsim users: • Constant LDFi i k k = • Arrhenius | | . | \ | − = s i i i RT E k k exp 0 2 Gas Cyclic Steady State Modeling 108 • Effective Diffusivity 2 15 p ei i r D k = Linear Driving Force Approximation 2 2 p ei i r D k π = Quadratic Driving Force Approximation • Pressure Dependent P k k Pi i = • Pressure Dependent Arrhenius | | . | \ | − = s i Pi i RT E P k k exp 0 Notation i C Gas phase concentration for component i, kmol/m 3 * i C Equilibrium gas phase concentration for component i, kmol/m 3 ei D Effective diffusivity for component i, m 2 /s i E Activation energy for component i, MJ/kmol i k Mass transfer coefficient (fluid or solid) for component i, 1/s i LDF k Mass transfer coefficient as a constant for component i, 1/s Pi k Pressure dependent mass transfer coefficient for component i, bar/s i k 0 Pre-exponent for component i, 1/s Pi k 0 Pre-exponent for component i, bar/s Fi k Fluid film mass transfer coefficient for component i, 1/s Si k Solid film mass transfer coefficient for component i, 1/s P Gas pressure, bar i Q Amount adsorbed for component i, kmol/kg-adsorbent * i Q Equilibrium amount adsorbed for component i, kmol/kg-adsorbent p r Particle radius, m 2 Gas Cyclic Steady State Modeling 109 t Time, s s T Solid temperature, K R Gas constant (8.31451e-3), MJ/kmol/K b ρ Bed packing density, kg/m 3 Energy Balance The CSS adsorber model (gCSS_Adsorber) uses the following energy balances to represent the heat transportations of non-isothermal system with compressible flow: (1) In Fluid Phase: ( ) ( ) 0 2 2 = − + − + ∂ ∂ + ∂ ∂ + ∂ ∂ + ∂ ∂ − w g Hi Hi w s g p s g t g Vg g g g g Vg g b g T T V A H T T a H t T C x v P x T v C x T k ε ρ ρ ε 2 2 x T k g b g ∂ ∂ − ε Axial thermal conduction x T v C g g g Vg ∂ ∂ ρ Convection x v P g ∂ ∂ P-V work compression t T C g t g Vg ∂ ∂ ε ρ Thermal accumulation in gas phase ( ) s g p s T T a H − Heat transfer between gas and solid (adsorbent particle) ( ) w g Hi Hi w T T V A H − Heat transfer between gas and the internal wall of adsorber 2 Gas Cyclic Steady State Modeling 110 (2) In Solid Phase: ( ) 0 2 2 = − − | . | \ | ∂ ∂ ∆ + ∂ ∂ + ∂ ∂ − ∑ s g p s i i i p s b Ps s s T T a H t Q H t T C x T k ρ ρ 2 2 x T k s s ∂ ∂ − Axial thermal conduction t T C s b Ps ∂ ∂ ρ Thermal accumulation in solid phase ∑ | . | \ | ∂ ∂ ∆ i i i p t Q H ρ Thermal accumulation by the enthalpy of adsorption ( ) s g p s T T a H − Heat transfer between gas and solid (3) In Wall phase: ( ) ( ) 0 2 2 = − + − − ∂ ∂ + ∂ ∂ − amb w Ho Ho amb w g Ho Hi w w w Pw w w T T V A H T T V A H t T C x T k ρ 2 2 x T k w w ∂ ∂ − Axial thermal conduction along the wall t T C w w Pw ∂ ∂ ρ Thermal accumulation in the wall material ( ) w g Ho Hi w T T V A H − Heat transfer between gas and wall ( ) amb w Ho Ho amb T T V A H − Heat transfer between wall and environment Notation p a Particle external surface area to particle volume ratio (=3/rp), m Hi A Internal wall heat transfer area, m Ho A External wall heat transfer area, m Vg C Gas mixture heat capacity, MJ/kmol/K Ps C Solid (=adsorbent particle) heat capacity, MJ/kg/K 2 Gas Cyclic Steady State Modeling 111 Pw C Adsorber material (e.g., stainless steel) specific heat capacity, MJ/kg/K s H Fluid/solid heat transfer coefficient, MW/m 2 /K w H Fluid/wall heat transfer coefficient, MW/m 2 /K amb H Wall/environment heat transfer coefficient, MW/m 2 /K g k Gas mixture thermal conductivity, MW/m/K s k Solid phase thermal conductivity, MW/m/K w k Wall phase thermal conductivity, MW/m/K P Gas pressure, bar i Q Amount adsorbed for component i, kmol/kg-adsorbent t Time, s g T Gas temperature, K s T Solid temperature, K w T Wall temperature, K g v Superficial gas velocity, m/s Hi V Internal wall element volume for heat transfer, m 2 Ho V External wall element volume for heat transfer, m 2 x Axial distance coordinate, m i H ∆ Enthalpy of adsorption for component i (i.e., heat of adsorption), MJ/kmol b ε Bed voidage (void fraction) t ε Total voidage g ρ Gas density, kmol/m 3 b ρ Bed packing density, kg/m 3 w ρ Wall material density, kg/m 3 2 Gas Cyclic Steady State Modeling 112 Adsorption Equilibrium Models Introduction Adsorption equilibrium established after the adsorptive has been in with the adsorbed surface for a long time, and can be represented in general form: 0 ) , , ( = T Q f i i ρ (Eqn 1) In this equation, Q i is the concentration for component i on adsorbed phase, i.e., amount adsorbed, ρ ι is the density for component i in fluid phase, and T is the temperature. For an isothermal condition, the Eqn1 can be represented by the adsorption isotherm: T i i f Q ) (ρ = and T i i Q f ) ( = ρ (Eqn 2) Eqn 2, which is commonly referred to as adsorption equilibrium isotherm, is most frequently used in researches including adsorption process simulation. For pure component adsorption, an equilibrium relationship could simply be represented by mathematical equation such as the Langmuir, the Freundlich, the Sips, the Toth, and so on. Eqn 1 can also take the following form and is called the adsorption isostere (see Ref. 1): i Q i T f ) ( = ρ (Eqn 3) However, the adsorption isostere cannot be measured directly because it is impractical to hold i Q constant. For multi-component system, the explanation of adsorption equilibrium relationship often causes considerable attention due to a unique and complex mixing rule that governing an adsorption system of interest. For many decades, numerous researchers have considered multi-component adsorption equilibria from thermodynamic perspective and developed a number of theories or models based on various assumptions concerning the nature of adsorbed phase. The CSS model in Aspen Adsim offers the following types of adsorption equilibrium models for multi-component system. Please note all equilibrium models only require pure equilibrium information in order to predict mixture equilibrium: References 1 D. M. Young and A. D. Crowell, Physical Adsorption of Gases, Butterworths, London (1962). 2 Gas Cyclic Steady State Modeling 113 Mathematical Equation Form for Extended Langmuir 1 { } ∑ + = k k k i i i i Py IP Py IP IP Q 2 2 1 1 (Pressure dependent equilibrium) { } ∑ + = k k k i i i i C IP C IP IP Q 2 2 1 1 (Concentration dependent equilibrium) i i IP IP 2 1 , Isotherm parameters for component i P Total gas pressure i y Gas phase mole fraction for component i i C Fluid phase concentration for component i i Q Adsorbed phase concentration (i.e., amount adsorbed) for component I Mathematical Equation Form for Extended Langmuir 2 | | ( ) | | ( ) { } ∑ + = k k s k k i s i i i i Py T IP IP Py T IP IP IP Q 3 2 3 2 1 exp 1 exp (Pressure dependent equilibrium) | | ( ) | | ( ) { } ∑ + = k k s k k i s i i i i C T IP IP C T IP IP IP Q 3 2 3 2 1 exp 1 exp (Concentration dependent equilibrium) i i i IP IP IP 3 2 1 , , Isotherm parameters for component i s T Adsorbent particle temperature in Kelvin P Total gas pressure 2 Gas Cyclic Steady State Modeling 114 i y Gas phase mole fraction for component i i C Fluid phase concentration for component i i Q Adsorbed phase concentration (i.e., amount adsorbed) for component I Mathematical Equation Form for Extended Langmuir 3 ( ) | | ( ) | | ( ) { } ∑ + + = k k s k k i s i i s i i i Py T IP IP Py T IP IP T IP IP Q 4 3 4 3 2 1 exp 1 exp (Pressure dependent equilibrium) ( ) | | ( ) | | ( ) { } ∑ + + = k k s k k i s i i s i i i C T IP IP C T IP IP T IP IP Q 4 3 4 3 2 1 exp 1 exp (Concentration dependent equilibrium) i i i i IP IP IP IP 4 3 2 1 , , , Isotherm parameters for component i s T Adsorbent particle temperature in Kelvin P Total gas pressure i y Gas phase mole fraction for component i i C Fluid phase concentration for component i i Q Adsorbed phase concentration (i.e., amount adsorbed) for component I 2 Gas Cyclic Steady State Modeling 115 Mathematical Equation Form for Extended Langmuir 4 ( ) | | ( ) | | ( ) { } ∑ + = k k s k k i s i i IP s i i Py T IP IP Py T IP IP T IP Q i 4 3 4 3 1 exp 1 exp 2 (Pressure dependent equilibrium) ( ) | | ( ) | | ( ) { } ∑ + = k k s k k i s i i IP s i i C T IP IP C T IP IP T IP Q i 4 3 4 3 1 exp 1 exp 2 (Concentration dependent equilibrium) i i i i IP IP IP IP 4 3 2 1 , , , Isotherm parameters for component i s T Adsorbent particle temperature in Kelvin P Total gas pressure i y Gas phase mole fraction for component i i C Fluid phase concentration for component i i Q Adsorbed phase concentration (i.e., amount adsorbed) for component I 2 Gas Cyclic Steady State Modeling 116 Mathematical Equation Form for Extended Langmuir 5 | | ( ) | | ( ) | | ( ) { } ∑ + = k k s k k i s i i s i i i Py T IP IP Py T IP IP T IP IP Q 4 3 4 3 2 1 exp 1 exp exp (Pressure dependent equilibrium) | | ( ) | | ( ) | | ( ) { } ∑ + = k k s k k i s i i s i i i C T IP IP C T IP IP T IP IP Q 4 3 4 3 2 1 exp 1 exp exp (Concentration dependent equilibrium) i i i i IP IP IP IP 4 3 2 1 , , , Isotherm parameters for component i s T Adsorbent particle temperature in Kelvin P Total gas pressure i y Gas phase mole fraction for component i i C Fluid phase concentration for component i i Q Adsorbed phase concentration (i.e., amount adsorbed) for component I 2 Gas Cyclic Steady State Modeling 117 Mathematical Equation Form for Loading Ratio Correlation 1 ( ) ( ) { } ∑ + = k IP k k IP i i i i k i Py IP Py IP IP Q 3 3 2 2 1 1 (Pressure dependent equilibrium) { } ∑ + = k IP k k IP i i i i k i C IP C IP IP Q 3 3 2 2 1 1 (Concentration dependent equilibrium) i IP ? Isotherm parameters for component i P Total gas pressure i y Gas phase mole fraction for component i i C Fluid phase concentration for component i i Q Adsorbed phase concentration (i.e., amount adsorbed) for component I 2 Gas Cyclic Steady State Modeling 118 Mathematical Equation Form for Loading Ratio Correlation 2 | | ( )( ) | | ( )( ) { } ∑ + + + = k T IP IP k s k k T IP IP i s i i i i s k k s i i Py T IP IP Py T IP IP IP Q 5 4 5 4 3 2 3 2 1 exp 1 exp (Pressure dependent equilibrium) | | ( ) | | ( ) { } ∑ + + + = k T IP IP k s k k T IP IP i s i i i i s k k s i i C T IP IP C T IP IP IP Q 5 4 5 4 3 2 3 2 1 exp 1 exp (Concentration dependent equilibrium) i IP ? Isotherm parameters for component i s T Adsorbent particle temperature in Kelvin P Total gas pressure i y Gas phase mole fraction for component i i C Fluid phase concentration for component i i Q Adsorbed phase concentration (i.e., amount adsorbed) for component I 2 Gas Cyclic Steady State Modeling 119 Mathematical Equation Form for Loading Ratio Correlation 3 ( ) | | ( )( ) | | ( )( ) { } ∑ + + + + = k T IP IP k s k k T IP IP i s i i s i i i s k k s i i Py T IP IP Py T IP IP T IP IP Q 6 5 6 5 4 3 4 3 2 1 exp 1 exp (Pressure dependent equilibrium) ( ) | | ( ) | | ( ) { } ∑ + + + + = k T IP IP i s k k T IP IP i s i i s i i i s k k s i i C T IP IP C T IP IP T IP IP Q 6 5 6 5 4 3 4 3 2 1 exp 1 exp (Concentration dependent equilibrium) i IP ? Isotherm parameters for component i s T Adsorbent particle temperature in Kelvin P Total gas pressure i y Gas phase mole fraction for component i i C Fluid phase concentration for component i i Q Adsorbed phase concentration (i.e., amount adsorbed) for component I 2 Gas Cyclic Steady State Modeling 120 Mathematical Equation Form for Loading Ratio Correlation 4 ( ) | | ( )( ) | | ( )( ) { } ∑ + + + = k T IP IP k s k k T IP IP i s i i IP s i i s k k s i i i Py T IP IP Py T IP IP T IP Q 6 5 6 5 2 4 3 4 3 1 exp 1 exp (Pressure dependent equilibrium) ( ) | | ( ) | | ( ) { } ∑ + + + = k T IP IP i s k k T IP IP i s i i IP s i i s k k s i i i C T IP IP C T IP IP T IP Q 6 5 6 5 2 4 3 4 3 1 exp 1 exp (Concentration dependent equilibrium) i IP ? Isotherm parameters for component i s T Adsorbent particle temperature in Kelvin P Total gas pressure i y Gas phase mole fraction for component i i C Fluid phase concentration for component i i Q Adsorbed phase concentration (i.e., amount adsorbed) for component I 2 Gas Cyclic Steady State Modeling 121 Mathematical Equation Form for Loading Ratio Correlation 5 | | ( ) | | ( )( ) | | ( )( ) { } ∑ + + + = k T IP IP k s k k T IP IP i s i i s i i i s k k s i i Py T IP IP Py T IP IP T IP IP Q 6 5 6 5 4 3 4 3 2 1 exp 1 exp exp (Pressure dependent equilibrium) | | ( ) | | ( ) | | ( ) { } ∑ + + + = k T IP IP i s k k T IP IP i s i i s i i i s k k s i i C T IP IP C T IP IP T IP IP Q 6 5 6 5 4 3 4 3 2 1 exp 1 exp exp (Concentration dependent equilibrium) i IP ? Isotherm parameters for component i s T Adsorbent particle temperature in Kelvin P Total gas pressure i y Gas phase mole fraction for component i i C Fluid phase concentration for component i i Q Adsorbed phase concentration (i.e., amount adsorbed) for component I 2 Gas Cyclic Steady State Modeling 122 Mathematical Equation Form for Extended Dual-Site Langmuir 1 { } { } ∑ ∑ + + + = k k k i i i k k k i i i i Py IP Py IP IP Py IP Py IP IP Q 4 4 3 2 2 1 1 1 (Pressure dependent equilibrium) { } { } ∑ ∑ + + + = k k k i i i k k k i i i i C IP C IP IP C IP C IP IP Q 4 4 3 2 2 1 1 1 (Concentration dependent equilibrium) i IP ? Isotherm parameters for component i P Total gas pressure i y Gas phase mole fraction for component i i C Fluid phase concentration for component i i Q Adsorbed phase concentration (i.e., amount adsorbed) for component I 2 Gas Cyclic Steady State Modeling 123 Mathematical Equation Form for Extended Dual-Site Langmuir 2 | | ( ) | | ( ) { } | | ( ) | | ( ) { } ∑ ∑ + + + = k k s k k i s i i i k k s k k i s i i i i Py T IP IP Py T IP IP IP Py T IP IP Py T IP IP IP Q 6 5 6 5 4 3 2 3 2 1 exp 1 exp exp 1 exp (Pressure dependent equilibrium) | | ( ) | | ( ) { } | | ( ) | | ( ) { } ∑ ∑ + + + = k k s k k i s i i i k k s k k i s i i i i C T IP IP C T IP IP IP C T IP IP C T IP IP IP Q 6 5 6 5 4 3 2 3 2 1 exp 1 exp exp 1 exp (Concentration dependent equilibrium) i IP ? Isotherm parameters for component i s T Adsorbent particle temperature in Kelvin P Total gas pressure i y Gas phase mole fraction for component i i C Fluid phase concentration for component i i Q Adsorbed phase concentration (i.e., amount adsorbed) for component I I.A.S.T. (Ideal Adsorbed Solution Theory) The IAST 1 is a widely used engineering thermodynamic method, analogues to Raoult’s law in vapor-liquid equilibrium. The inputs to the IAST calculation are the pure-component adsorption isotherms at the temperature of interest, and the output is a prediction of mixture equilibrium. It has been known that the deviations from IAST might result from the chemical dissimilarity of the adsorptive species (as for deviations from Raoult’s law in vapor-liquid equilibrium) or from the heterogeneity of the adsorbent. Adsorbent heterogeneity might be present in one of following forms 2 : chemical or structural heterogeneity of the adsorbent surface 3 , variation of pore size and shape (either along the axis of individual pores or among the pores), or due to connectivity effects 4,5 . Nonideal adsorption can be accommodated in the general framework of adsorbed solution theory by real adsorbed solution theory (RAST 1 ) , in which nonideal interactions between the adsorbates on the adsorbent surface are accounted for by activity coefficients, and by heterogeneous ideal adsorbed 2 Gas Cyclic Steady State Modeling 124 solution theory (HIAST 6 ), in which the energetic heterogeneity of the adsorbent is taken into account. Subject to the assumption of an ideal adsorbed phase, equality of chemical potential in the bulk gas and adsorbed phases implies: 0 i i i f x f = (Eqn 1) where i f is the fugacity of component i in the bulk gas phase and i x is the mole fraction of component i in the adsorbed phase; 0 i f is the standard- state fugacity, that is, the fugacity of pure component i at the mixture spreading pressure, π ,when the adsorbed and bulk gas phases are in equilibrium. Please note, Eqn 1 describes the ideal adsorbed phase contacting with real (i.e., nonideal) gas phase, which is accounted by introducing gas fugacity instead of gas pressure. When an assumption of ideal gas phase is invoked, then the basic equation of IAST can be written by: 0 i i i P x P y = (Eqn 1) where P is total gas pressure, i y is the gas mole fraction for component i and i x is the mole fraction of component i in the adsorbed phase; 0 i P is the standard-state pressure, that is, the pressure of pure component i at the mixture spreading pressure, π ,when the adsorbed and bulk gas phases are in equilibrium. The spreading pressure is obtained from the experimental adsorption isotherm, i.e., ( ) i i P Q or ( ) i i C Q , via the Gibbs adsorption isotherm: ∫ = 0 0 ln i f i i f d Q RT A π (nonideal gas phase assumption) (Eqn 3) ∫ = 0 0 ln i P i i P d Q RT A π (ideal gas phase assumption) (Eqn 4) where A is the surface area of the adsorbent (which is not required in practice, as the product A π need not be separated in the calculation), R is the gas constant, T is the temperature, i f and i P are the fugacity and the pressure for pure component i . The complete description of the IAST as a predictive tool for multicomponent adsorption equilibria requires an expression for total amount adsorbed, T Q : ∑ = i i i T Q x Q 0 1 (Eqn 5) and the stoichiometric constraint: 1 = ∑ i i x (Eqn 6) In Eqn 5, 0 i Q is the amount component i adsorbed at the standard-state pressure. 2 Gas Cyclic Steady State Modeling 125 The CSS model in Aspen Adsim supports a comprehensive tool in applying the IAST. The main benefits from the IAST application within the CSS model are: • Capability to account gas phase nonideality by considering the gas fugacity that may be evaluated by either Aspen Properties or User Procedure. • No restriction for the type of pure component isotherm in the IAST calculation (namely, isotherm type free IAST). For example, it is now available to assign the best-fit isotherm equation to each component (e.g., the Langmuir isotherm for 1 st component, the Freundlich isotherm for 2 nd component, the Sips isotherm for 3 rd component, so on.), instead of using a specific type isotherm for all adsorbates. The available pure isotherm equations for the IAST within CSS model may be found at: List of Pure Isotherms Available in IAST Calculation of CSS model References 1 Myers, A. L.; Prausnitz, J. M. AIChE J. 1965, 11, 121. 2 Yun, J.-H.; Düren, T.; Keil, F. J.; Seaton, N. A. Langmuir 2002, 18, in print. 3 Rudzinski, W.; Everett, D. M. Adsorption of Gases on Heterogeneous Surfaces; Academic Press: New York, 1992. 4 López-Ramon, M. V.; Jagiello, J.; Bandosz, T. J.; Seaton, N. A. Langmuir 1997, 13, 4435. 5 Davies, G. M.; Seaton, N. A. Langmuir 1999, 15, 6263. 6 Valenzuela, D.; Myers, A. L.; Talu, O.; Zwiebel, I. AIChE J. 1988, 34, 397. Pure Isotherm List for the IAST Calculation of CSS The following are the pure isotherm equations available in the IAST calculation by CSS bed model (gCSS_Adsorber) from Aspen Adsim 2004.1. In the application, any combination of the pure isotherm equations will be acceptable in representing mixture adsorption equilibria by means of IAST, as predictive equilibrium theory. Langmuir 1 - 2 parameters / isothermal assumption Langmuir 2 - 3 parameters / temperature correlation Langmuir 3 - 4 parameters / temperature correlation Langmuir 4 - 4 parameters / temperature correlation Langmuir 5 - 4 parameters / temperature correlation Dual Site Langmuir 1 - 4 parameters / isothermal assumption Dual Site Langmuir 2 - 6 parameters / temperature correlation Sips (Langmuir-Freundlich) 1 - 3 parameters / isothermal assumption 2 Gas Cyclic Steady State Modeling 126 Sips (Langmuir-Freundlich) 2 - 5 parameters / temperature correlation Sips (Langmuir-Freundlich) 3 - 6 parameters / temperature correlation Sips (Langmuir-Freundlich) 4 - 6 parameters / temperature correlation Sips (Langmuir-Freundlich) 5 - 6 parameters / temperature correlation Henry 1 - 1 parameters / isothermal assumption Henry 2 - 2 parameters / temperature correlation Henry 3 - 2 parameters / temperature correlation Henry 4 - 2 parameters / temperature correlation Freundlich 1 - 2 parameters / isothermal assumption Toth 1 - 3 parameters / isothermal assumption BET 1 - 1 parameters / Langmuir 1 Pressure dependent i i i i i i P IP P IP IP Q 2 2 1 1+ = i IP 1 Isotherm parameter of comp i [kmol/kg-adsorbent] i IP 2 Isotherm parameter of comp i [bar] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i P Equilibrium pressure of comp i [bar] Concentration dependent i i i i i i C IP C IP IP Q 2 2 1 1+ = i IP 1 Isotherm parameter of comp i [kmol/kg-adsorbent] i IP 2 Isotherm parameter of comp i [kmol/m3] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i C Equilibrium concentration of comp i [kmol/m3] Langmuir 2 Pressure dependent 2 Gas Cyclic Steady State Modeling 127 | | ( ) | | ( ) i i i i i i i i P T IP IP P T IP IP IP Q 3 2 3 2 1 exp 1 exp + = i IP 1 Isotherm parameter of comp i [kmol/kg-adsorbent] i IP 2 Isotherm parameter of comp i [bar] i IP 3 Isotherm parameter of comp i [K] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i P Equilibrium pressure of comp i [bar] T Temperature [K] Concentration dependent | | ( ) | | ( ) i i i i i i i i C T IP IP C T IP IP IP Q 3 2 3 2 1 exp 1 exp + = i IP 1 Isotherm parameter of comp i [kmol/kg-adsorbent] i IP 2 Isotherm parameter of comp i [kmol/m 3 ] i IP 3 Isotherm parameter of comp i [K] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i C Equilibrium concentration of comp i [kmol/m 3 ] T Temperature [K] Langmuir 3 Pressure dependent ( ) | | ( ) | | ( ) i i i i i i i i i P T IP IP P T IP IP T IP IP Q 4 3 4 3 2 1 exp 1 exp + + = i IP 1 Isotherm parameter of comp i [kmol/kg-adsorbent] i IP 2 Isotherm parameter of comp i [kmol/kg/ K] i IP 3 Isotherm parameter of comp i [bar] i IP 4 Isotherm parameter of comp i [K] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i P Equilibrium pressure of comp i [bar] T Temperature [K] 2 Gas Cyclic Steady State Modeling 128 Concentration dependent ( ) | | ( ) | | ( ) i i i i i i i i i C T IP IP C T IP IP T IP IP Q 4 3 4 3 2 1 exp 1 exp + + = i IP 1 Isotherm parameter of comp i [kmol/kg-adsorbent] i IP 2 Isotherm parameter of comp i [kmol/kg/K] i IP 3 Isotherm parameter of comp i [kmol/m 3 ] i IP 4 Isotherm parameter of comp i [K] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i C Equilibrium concentration of comp i [kmol/m 3 ] T Temperature [K] Langmuir 4 Pressure dependent ( ) | | ( ) | | ( ) i i i i i i IP i i P T IP IP P T IP IP T IP Q i 4 3 4 3 1 exp 1 exp 2 + = i IP 1 Isotherm parameter of comp i [kmol.K/kg- adsorbent] i IP 2 Isotherm parameter of comp i [-] i IP 3 Isotherm parameter of comp i [bar] i IP 4 Isotherm parameter of comp i [K] i Q Equilibrium loading of comp i [kmol/kg- adsorbent] i P Equilibrium pressure of comp i [bar] T Temperature [K] Concentration dependent ( ) | | ( ) | | ( ) i i i i i i IP i i C T IP IP C T IP IP T IP Q i 4 3 4 3 1 exp 1 exp 2 + = i IP 1 Isotherm parameter of comp i [kmol.K/kg-adsorbent] i IP 2 Isotherm parameter of comp i [-] 2 Gas Cyclic Steady State Modeling 129 i IP 3 Isotherm parameter of comp i [kmol/m 3 ] i IP 4 Isotherm parameter of comp i [K] i Q Equilibrium loading of comp i [kmol/kg- adsorbent] i C Equilibrium concentration of comp i [kmol/m 3 ] T Temperature [K] Langmuir 5 Pressure dependent | | ( ) | | ( ) | | ( ) i i i i i i i i i P T IP IP P T IP IP T IP IP Q 4 3 4 3 2 1 exp 1 exp exp + = i IP 1 Isotherm parameter of comp i [kmol/kg-adsorbent] i IP 2 Isotherm parameter of comp i [K] i IP 3 Isotherm parameter of comp i [bar] i IP 4 Isotherm parameter of comp i [K] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i P Equilibrium pressure of comp i [bar] T Temperature [K] Concentration dependent | | ( ) | | ( ) | | ( ) i i i i i i i i i C T IP IP C T IP IP T IP IP Q 4 3 4 3 2 1 exp 1 exp exp + = i IP 1 Isotherm parameter of comp i [kmol/kg-adsorbent] i IP 2 Isotherm parameter of comp i [K] i IP 3 Isotherm parameter of comp i [kmol/m3] i IP 4 Isotherm parameter of comp i [K] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i C Equilibrium concentration of comp i [kmol/m3] T Temperature [K] 2 Gas Cyclic Steady State Modeling 130 Dual-Site Langmuir 1 Pressure dependent i i i i i i i i i i i P IP P IP IP P IP P IP IP Q 4 4 3 2 2 1 1 1 + + + = i IP 1 Isotherm parameter of comp i [kmol/kg-adsorbent] i IP 2 Isotherm parameter of comp i [bar] i IP 3 Isotherm parameter of comp i [kmol/kg-adsorbent] i IP 4 Isotherm parameter of comp i [bar] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i P Equilibrium pressure of comp i [bar] Concentration dependent i i i i i i i i i i i C IP C IP IP C IP C IP IP Q 4 4 3 2 2 1 1 1 + + + = i IP 1 Isotherm parameter of comp i [kmol/kg-adsorbent] i IP 2 Isotherm parameter of comp i [kmol/m3] i IP 3 Isotherm parameter of comp i [kmol/kg-adsorbent] i IP 4 Isotherm parameter of comp i [kmol/m3] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i C Equilibrium concentration of comp i [kmol/m3] Dual-Site Langmuir 2 Pressure dependent | | ( ) | | ( ) | | ( ) | | ( ) i i i i i i i i i i i i i i i P T IP IP P T IP IP IP P T IP IP P T IP IP IP Q 6 5 6 5 4 3 2 3 2 1 exp 1 exp exp 1 exp + + + = i IP 1 Isotherm parameter of comp i [kmol/kg-adsorbent] i IP 2 Isotherm parameter of comp i [bar] i IP 3 Isotherm parameter of comp i [K] 2 Gas Cyclic Steady State Modeling 131 i IP 4 Isotherm parameter of comp i [kmol/kg-adsorbent] i IP 5 Isotherm parameter of comp i [bar] i IP 6 Isotherm parameter of comp i [K] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i P Equilibrium pressure of comp i [bar] T Temperature [K] Concentration dependent | | ( ) | | ( ) | | ( ) | | ( ) i i i i i i i i i i i i i i i C T IP IP C T IP IP IP C T IP IP C T IP IP IP Q 6 5 6 5 4 3 2 3 2 1 exp 1 exp exp 1 exp + + + = i IP 1 Isotherm parameter of comp i [kmol/kg-adsorbent] i IP 2 Isotherm parameter of comp i [kmol/m3] i IP 3 Isotherm parameter of comp i [K] i IP 4 Isotherm parameter of comp i [kmol/kg-adsorbent] i IP 5 Isotherm parameter of comp i [kmol/m3] i IP 6 Isotherm parameter of comp i [K] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i C Equilibrium concentration of comp i [kmol/m3] T Temperature [K] Sips (Langmuir-Freundlich) 1 Pressure dependent i i IP i i IP i i i i P IP P IP IP Q 3 3 2 2 1 1+ = i IP 1 Isotherm parameter of comp i [kmol/kg-adsorbent] i IP 2 Isotherm parameter of comp i [bar] i IP 3 Isotherm parameter of comp i [-] 2 Gas Cyclic Steady State Modeling 132 i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i P Equilibrium pressure of comp i [bar] Concentration dependent i i IP i i IP i i i i C IP C IP IP Q 3 3 2 2 1 1+ = i IP 1 Isotherm parameter of comp i [kmol/kg-adsorbent] i IP 2 Isotherm parameter of comp i [kmol/m3] i IP 3 Isotherm parameter of comp i [-] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i C Equilibrium concentration of comp i [kmol/m3] Sips (Langmuir-Freundlich) 2 Pressure dependent | | ( ) | | ( ) T IP IP i i i T IP IP i i i i i i i i i P T IP IP P T IP IP IP Q 5 4 5 4 3 2 3 2 1 exp 1 exp + + + = i IP 1 Isotherm parameter of comp i [kmol/kg-adsorbent] i IP 2 Isotherm parameter of comp i [bar] i IP 3 Isotherm parameter of comp i [K] i IP 4 Isotherm parameter of comp i [-] i IP 5 Isotherm parameter of comp i [K] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i P Equilibrium pressure of comp i [bar] T Temperature [K] Concentration dependent | | ( ) | | ( ) T IP IP i i i T IP IP i i i i i i i i i C T IP IP C T IP IP IP Q 5 4 5 4 3 2 3 2 1 exp 1 exp + + + = 2 Gas Cyclic Steady State Modeling 133 i IP 1 Isotherm parameter of comp i [kmol/kg-adsorbent] i IP 2 Isotherm parameter of comp i [kmol/m3] i IP 3 Isotherm parameter of comp i [K] i IP 4 Isotherm parameter of comp i [-] i IP 5 Isotherm parameter of comp i [K] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i C Equilibrium concentration of comp i [kmol/m3] T Temperature [K] Sips (Langmuir-Freundlich) 3 Pressure dependent ( ) | | ( ) | | ( ) T IP IP i i i T IP IP i i i i i i i i i i P T IP IP P T IP IP T IP IP Q 6 5 6 5 4 3 4 3 2 1 exp 1 exp + + + + = i IP 1 Isotherm parameter of comp i [kmol/kg-adsorbent] i IP 2 Isotherm parameter of comp i [kmol/kg/K] i IP 3 Isotherm parameter of comp i [bar] i IP 4 Isotherm parameter of comp i [K] i IP 5 Isotherm parameter of comp i [-] i IP 6 Isotherm parameter of comp i [K] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i P Equilibrium pressure of comp i [bar] T Temperature [K] Concentration dependent ( ) | | ( ) | | ( ) T IP IP i i i T IP IP i i i i i i i i i i C T IP IP C T IP IP T IP IP Q 6 5 6 5 4 3 4 3 2 1 exp 1 exp + + + + = i IP 1 Isotherm parameter of comp i [kmol/kg-adsorbent] 2 Gas Cyclic Steady State Modeling 134 i IP 2 Isotherm parameter of comp i [kmol/kg/K] i IP 3 Isotherm parameter of comp i [kmol/m3] i IP 4 Isotherm parameter of comp i [K] i IP 5 Isotherm parameter of comp i [-] i IP 6 Isotherm parameter of comp i [K] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i C Equilibrium concentration of comp i [kmol/m3] T Temperature [K] Sips (Langmuir-Freundlich) 4 Pressure dependent ( ) | | ( ) | | ( ) T IP IP i i i T IP IP i i i IP i i i i i i i P T IP IP P T IP IP T IP Q 6 5 6 5 2 4 3 4 3 1 exp 1 exp + + + = i IP 1 Isotherm parameter of comp i [kmol.K/kg-adsorbent] i IP 2 Isotherm parameter of comp i [-] i IP 3 Isotherm parameter of comp i [bar] i IP 4 Isotherm parameter of comp i [K] i IP 5 Isotherm parameter of comp i [-] i IP 6 Isotherm parameter of comp i [K] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i P Equilibrium pressure of comp i [bar] T Temperature [K] Concentration dependent ( ) | | ( ) | | ( ) T IP IP i i i T IP IP i i i IP i i i i i i i C T IP IP C T IP IP T IP Q 6 5 6 5 2 4 3 4 3 1 exp 1 exp + + + = i IP 1 Isotherm parameter of comp i [kmol.K/kg-adsorbent] i IP 2 Isotherm parameter of comp i [-] 2 Gas Cyclic Steady State Modeling 135 i IP 3 Isotherm parameter of comp i [kmol/m3] i IP 4 Isotherm parameter of comp i [K] i IP 5 Isotherm parameter of comp i [-] i IP 6 Isotherm parameter of comp i [K] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i C Equilibrium concentration of comp i [kmol/m3] T Temperature [K] Sips (Langmuir-Freundlich) 5 Pressure dependent | | ( ) | | ( ) | | ( ) T IP IP i i i T IP IP i i i i i i i i i i P T IP IP P T IP IP T IP IP Q 6 5 6 5 4 3 4 3 2 1 exp 1 exp exp + + + = i IP 1 Isotherm parameter of comp i [kmol/kg-adsorbent] i IP 2 Isotherm parameter of comp i [K] i IP 3 Isotherm parameter of comp i [bar] i IP 4 Isotherm parameter of comp i [K] i IP 5 Isotherm parameter of comp i [-] i IP 6 Isotherm parameter of comp i [K] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i P Equilibrium pressure of comp i [bar] T Temperature [K] Concentration dependent | | ( ) | | ( ) | | ( ) T IP IP i i i T IP IP i i i i i i i i i i C T IP IP C T IP IP T IP IP Q 6 5 6 5 4 3 4 3 2 1 exp 1 exp exp + + + = i IP 1 Isotherm parameter of comp i [kmol/kg-adsorbent] i IP 2 Isotherm parameter of comp i [K] 2 Gas Cyclic Steady State Modeling 136 i IP 3 Isotherm parameter of comp i [kmol/m3] i IP 4 Isotherm parameter of comp i [K] i IP 5 Isotherm parameter of comp i [-] i IP 6 Isotherm parameter of comp i [K] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i C Equilibrium concentration of comp i [kmol/m3] T Temperature [K] Henry 1 Pressure dependent i i i P IP Q 1 = i IP 1 Isotherm parameter of comp i [kmol/bar/kg-adsorbent] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i P Equilibrium pressure of comp i [bar] Concentration dependent i i i C IP Q 1 = i IP 1 Isotherm parameter of comp i [m3/kg-adsorbent] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i C Equilibrium concentration of comp i [kmol/m3] Henry 2 Pressure dependent ( ) i i i i P T IP IP Q 2 1 + = i IP 1 Isotherm parameter of comp i [kmol/bar/kg-adsorbent] i IP 2 Isotherm parameter of comp i [kmol/bar/K/kg-adsorbent] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i P Equilibrium pressure of comp i [bar] 2 Gas Cyclic Steady State Modeling 137 T Temperature [K] Concentration dependent ( ) i i i i C T IP IP Q 2 1 + = i IP 1 Isotherm parameter of comp i [m3/kg-adsorbent] i IP 2 Isotherm parameter of comp i [m3/K/kg-adsorbent] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i C Equilibrium concentration of comp i [kmol/m3] T Temperature [K] Henry 3 Pressure dependent ( ) i IP i i P T IP Q i 2 1 = i IP 1 Isotherm parameter of comp i [kmol.K/bar/kg-adsorbent] i IP 2 Isotherm parameter of comp i [-] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i P Equilibrium pressure of comp i [bar] T Temperature [K] Concentration dependent ( ) i IP i i C T IP Q i 2 1 = i IP 1 Isotherm parameter of comp i [K.m3/kg-adsorbent] i IP 2 Isotherm parameter of comp i [-] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i C Equilibrium concentration of comp i [kmol/m3] T Temperature [K] Henry 4 Pressure dependent 2 Gas Cyclic Steady State Modeling 138 | | ( ) i i i i P T IP IP Q 2 1 exp = i IP 1 Isotherm parameter of comp i [kmol/bar/kg-adsorbent] i IP 2 Isotherm parameter of comp i [K] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i P Equilibrium pressure of comp i [bar] T Temperature [K] Concentration dependent | | ( ) i i i i C T IP IP Q 2 1 exp = i IP 1 Isotherm parameter of comp i [m3/kg-adsorbent] i IP 2 Isotherm parameter of comp i [K] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i C Equilibrium concentration of comp i [kmol/m3] T Temperature [K] Freundlich 1 Pressure dependent i IP i i i P IP Q 2 1 = i IP 1 Isotherm parameter of comp i [kmol/bar/kg-adsorbent] i IP 2 Isotherm parameter of comp i [-] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i P Equilibrium pressure of comp i [bar] Concentration dependent i IP i i i C IP Q 2 1 = i IP 1 Isotherm parameter of comp i [m3/kg-adsorbent] i IP 2 Isotherm parameter of comp i [-] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] 2 Gas Cyclic Steady State Modeling 139 i C Equilibrium concentration of comp i [kmol/m3] Toth 1 Pressure dependent ( ) i i IP IP i i i i i P IP P IP Q 3 3 1 2 1 + = i IP 1 Isotherm parameter of comp i [kmol/kg-adsorbent] i IP 2 Isotherm parameter of comp i [bar] i IP 3 Isotherm parameter of comp i [-] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i P Equilibrium pressure of comp i [bar] Concentration dependent ( ) i i IP IP i i i i i C IP C IP Q 3 3 1 2 1 + = i IP 1 Isotherm parameter of comp i [kmol/kg-adsorbent] i IP 2 Isotherm parameter of comp i [kmol/m3] i IP 3 Isotherm parameter of comp i [-] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i C Equilibrium concentration of comp i [kmol/m3] BET 1 Pressure dependent | | . | \ | + − | | . | \ | − = s i i i s i i s i i s i i i i i P P IP P P P P P P IP IP Q 2 2 1 1 1 i IP 1 Isotherm parameter of comp i [kmol/kg-adsorbent] i IP 2 Isotherm parameter of comp i [-] 2 Gas Cyclic Steady State Modeling 140 i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i P Equilibrium pressure of comp i [bar] s i P Saturated vapour pressure of comp i [bar] Concentration dependent | | . | \ | + − | | . | \ | − = RT P C IP RT P C RT P C RT P C IP IP Q s i i i s i i s i i s i i i i i 2 2 1 1 1 i IP 1 Isotherm parameter of comp i [kmol/kg-adsorbent] i IP 2 Isotherm parameter of comp i [-] i Q Equilibrium loading of comp i [kmol/kg-adsorbent] i C Equilibrium concentration of comp i [kmol/m3] s i P Saturated vapour pressure of comp i [bar] R Gas constant, 8.31433e-2 [bar.m3/kmol/K] T Temperature [K] User Guidelines How to Create a CSS Simulation Flowsheet Preconditions: The user must hold the licenses for Aspen Adsim 2004.1 and Aspen Properties 2004.1 (or Aspen Plus 2004.1). The property file, named air.appdf, is used for component properties definition. 1 Start Aspen Adsim 2004.1. 2 Initialize component properties by loading a property definition. 2 Gas Cyclic Steady State Modeling 141 3 Choose target components from the component list. (Example. A user chooses N2 and O2 as the components for a simulation.) 4 Select CSS_Info from Structure Types folder by either pressing [Ctrl + I] or clicking the right mouse button and choosing Create Instance. 2 Gas Cyclic Steady State Modeling 142 5 A dialog box is displayed for the name of the structure instance, and user enters a name. (Example. Enter CSSInfo as the name of the structure instance.) 6 Aspen Adsim shows the instance in a folder of the same name below Flowsheet\Structures folder. 2 Gas Cyclic Steady State Modeling 143 7 Select the global non-isothermal/isothermal option by choosing TRUE or FALSE the logical parameter, NonIsothermal, from the Specify Table of the instanced structure. (Example. Switch the global NonIsothermal parameter to TRUE from the Specify Table of the instance structure CSSInfo.) 2 Gas Cyclic Steady State Modeling 144 8 Construct a simulation flowsheet using models from the CSS folder of Aspen Adsim Gas Library. (Example. Re-construct N2PSACSS - supplied as one of Aspen Adsim 2004.1 demonstrations.) 2 Gas Cyclic Steady State Modeling 145 9 The connect models using the stream, gCSS_Material_Connection, from the Stream Types folder of Aspen Adsim Library and rename each model, as shown in the picture. (Example. Re-construct N2PSACSS - supplied as one of Aspen Adsim 2004.1 demonstrations.) 10 Specify models by putting assumptions and parameter values that are required for process simulation. The following are typical items for the N2PSACSS example. i Bed1 (gCSS_Adsorber): Click the right mouse button and select Specify table from the Forms menu and specify the CSS bed model B1. Leave all items as default, except the following: Layer(1).xNodes 10 Layer(1).NonAdiabatic True Layer(1).RigorousWallBalance True 2 Gas Cyclic Steady State Modeling 146 ii Bed1 (gCSS_Adsorber): Use right mouse button and select Specify_ table from Forms and specify the CSS bed model B1. Leave all items as default, except the following: Layer(1).Hs 1e-007 Layer(1).Ta 298.15 Layer(1).IP("N2",1) 0.00267288 Layer(1).IP("N2",2) 0.136 Layer(1).IP("O2",1) 0.00267287 Layer(1).IP("O2",2) 0.1413 Layer(1).ksLDF("N2") 0.00760501 Layer(1).ksLDF("O2") 0.04476 Table - Specify 2 Gas Cyclic Steady State Modeling 147 Table - Specify_ 2 Gas Cyclic Steady State Modeling 148 iii TD1 and TD2 (gCSS_TankVoid): these two tank/void models have the same specification. The following items should be changed: Ta 298.15 NonAdiabaticTankVoid True Hamb 1.e-005 2 Gas Cyclic Steady State Modeling 149 Hw 6.e-005 TD1 TD2 iv. VP1 (gCSS_Valve): change CheckValve option to True VP1 11 Select the Cycle Organizer from the Tools menu. Aspen Adsim displays the icon, Cycle_Organizer, on the simulation flowsheet, with a dialog box from Cycle Organizer. 2 Gas Cyclic Steady State Modeling 150 12 Cyclic Steady State simulation mode can be chosen by selecting Cycle Options from the Cycle menu. To define a CSS simulation flowsheet, check the check box out, Cyclic Steady-State mode. 2 Gas Cyclic Steady State Modeling 151 13 Define process cycle/step information within the Step menu. For this example, N2PSACSS, we have four process steps, and the interaction and control details are as follows: 2 Gas Cyclic Steady State Modeling 152 STEP1 2 Gas Cyclic Steady State Modeling 153 STEP2 STEP3 STEP4 2 Gas Cyclic Steady State Modeling 154 14 Define the variable to be manipulated and the values within the Cycle Organizer. STEP1 STEP2 2 Gas Cyclic Steady State Modeling 155 STEP3 STEP4 2 Gas Cyclic Steady State Modeling 156 15 Generate a Cycle Task either by executing Generate Task from Cycle menu or by clicking Generate Cycle from the status bar of Cycle Organizer. Aspen Adsim displays a green check-shape icon on the status bar, indicating a Cycle Task has been created correctly. BEFORE AFTER 2 Gas Cyclic Steady State Modeling 157 16 Close the Cycle Organizer, then confirm Aspen Adsim shows a green square on the simulation status bar and that the simulation mode is now set Steady State. If so, the simulation is ready to be run in CSS mode. 2 Gas Cyclic Steady State Modeling 158 How to Create a Dynamic Simulation Flowsheet using CSS Models Preconditions: The user must be a the licensed user of Aspen Adsim 2004.1 and Aspen Properties 2004.1 (or Aspen Plus 2004.1). The property file, named air.appdf, is used for component properties definition. 1 Start Aspen Adsim 2004.1. 2 Initialize component properties by loading a property definition. 3 Choose target components from the component list. (Example. Choose N2 and O2 as the components for a simulation.) 2 Gas Cyclic Steady State Modeling 159 4 Select CSS_Info from the Structure Types folder by either pressing [Ctrl + I] or clicking right mouse button and choosing Create Instance. 2 Gas Cyclic Steady State Modeling 160 5 A dialog box is displayed to enter the name of the structure instance, and the user enters a name. (Example. Enter CSSInfo as the name of the structure instance.) 6 Aspen Adsim displays the instance in a folder of the same name below the Flowsheet\Structures folder. 2 Gas Cyclic Steady State Modeling 161 7 Select the global non-isothermal/isothermal option by choosing TRUE or FALSE the logical parameter, NonIsothermal, from the Specify Table of the instanced structure. (Example. Switch the global NonIsothermal parameter to TRUE from the Specify Table of the instance structure CSSInfo.) 2 Gas Cyclic Steady State Modeling 162 8 Construct a simulation flowsheet using models from the CSS folder of Aspen Adsim Gas Library. (Example. Re-construct N2PSACSS - supplied as one of Aspen Adsim 2004.1 demonstrations.) 9 Next, connect models using the stream, gCSS_Material_Connection, from the Stream Types folder of Aspen Adsim Library and rename each model, as shown in the picture. (Example. Re-construct N2PSACSS - supplied as one of Aspen Adsim 2004.1 demonstrations.) 2 Gas Cyclic Steady State Modeling 163 10 Specify models by putting assumptions and parameter values required for the process simulation. – the following are typical items for the N2PSACSS example. v. Bed1 (gCSS_Adsorber): Click the right mouse button and select Specify table from Forms menu, then specify the CSS bed model B1. – leave all items as default, except the following: Layer(1).xNodes 10 Layer(1).NonAdiabatic True Layer(1).RigorousWallBalance True vi. Bed1 (gCSS_Adsorber): Click the right mouse button and select Specify_ table from Forms and specify the CSS bed model B1 - leave all items as default, except the following: Layer(1).Hs 1e-007 Layer(1).Ta 298.15 Layer(1).IP("N2",1) 0.00267288 Layer(1).IP("N2",2) 0.136 Layer(1).IP("O2",1) . 00267287 Layer(1).IP("O2",2) 0.1413 Layer(1).ksLDF("N2") 0.00760501 2 Gas Cyclic Steady State Modeling 164 Layer(1).ksLDF("O2") 0.04476 Table - Specify 2 Gas Cyclic Steady State Modeling 165 Table - Specify_ 2 Gas Cyclic Steady State Modeling 166 vii. TD1 and TD2 (gCSS_TankVoid): these two tank/void models have the same specification. The following items should be changed: Ta 298.15 NonAdiabaticTankVoid True Hamb 1.e-005 Hw 6.e-005 TD1 TD2 viii. VP1 (gCSS_Valve): change CheckValve option to True. VP1 2 Gas Cyclic Steady State Modeling 167 11 Select Cycle Organizer from the Tools menu; Aspen Adsim displays the icon Cycle_Organizer, on the simulation flowsheet and the Cycle Organizer dialog box. 12 Non Cyclic Steady State simulation mode can be chosen from the Cycle Options in the Cycle menu. To define a dynamic simulation flowsheet, uncheck Cyclic Steady-State mode check box and enter the value of Maximum cycle for dynamic simulation. 13 Define process cycle/step information within the Step menu. For this example, N2PSACSS, we have four process steps, and the interaction and control details are as follows: 2 Gas Cyclic Steady State Modeling 168 STEP1 2 Gas Cyclic Steady State Modeling 169 STEP2 STEP3 STEP4 2 Gas Cyclic Steady State Modeling 170 14 Define the variable to be manipulated and the values within Cycle Organizer. STEP1 STEP2 2 Gas Cyclic Steady State Modeling 171 STEP3 STEP4 2 Gas Cyclic Steady State Modeling 172 15 Generate a Cycle Task either by executing Generate Task from Cycle menu or by clicking Generate Cycle from the status bar of Cycle Organizer. Aspen Adsim displays a green check-shape icon on the status bar, indicating the Cycle Task has been created correctly. BEFORE AFTER 2 Gas Cyclic Steady State Modeling 173 16 Close Cycle Organizer and confirm that Aspen Adsim displays a green square on the simulation status bar and that simulation mode is now set Dynamic. If so, the simulation is ready to be run in dynamic mode. 2 Gas Cyclic Steady State Modeling 174 How to Convert a CSS Flowsheet to a Dynamic Flowsheet Preconditions: There is an existing Aspen Adsim 2004.1 data file defined in CSS mode to convert the simulation mode from CSS to dynamic. If you are not sure which Aspen Adsim data file is defined in CSS mode, please refer to How to Create a CSS Simulation Flowsheet. 1 Open the existing Aspen Adsim flowsheet (defined in CSS simulation mode). 2 Activate the Cycle Organizer by double-clicking the icon and locate the Cyclic Steady-State mode check box on the Cyclic Options Tab. 3 Uncheck the check box to convert the flowsheet from CSS to dynamic. The Cyclic Organizer displays a dialog box to ask the Maximum Variable Steps option (recommended answer is Yes). 2 Gas Cyclic Steady State Modeling 175 4 Enter the maximum cycles value (e.g., 20) in the Cycle Options Tab and generate the Cycle Task either by executing Generate Task from Cycle menu or by clicking Generate Cycle from the status bar of Cycle Organizer. Aspen Adsim displays a green check-shape icon on the status bar, indicating the Cycle Task has been created correctly. BEFORE AFTER 2 Gas Cyclic Steady State Modeling 176 5 Close the Cycle Organizer and then confirm Aspen Adsim displays a green square on the simulation status bar and if simulation mode is now set Dynamic. If so, the simulation is ready to be run in dynamic mode. 2 Gas Cyclic Steady State Modeling 177 How to Convert a Dynamic Flowsheet into a CSS Flowsheet Preconditions: There is an existing Aspen Adsim 2004.1 dynamic flowsheet created using CSS models and the user wishes to convert the simulation mode from dynamic to CSS. If you are not sure which Aspen Adsim data file is defined in dynamic mode using CSS models, please refer to How to Create a Dynamic Simulation Flowsheet using CSS Models. 1 Open an existing Aspen Adsim flowsheet (defined in dynamic simulation mode). 2 Activate the Cycle Organizer by double-clicking the icon and locate the Cyclic Steady-State mode check box on the Cyclic Options Tab. Check the check box to re-define the simulation as CSS flowsheet. BEFORE 2 Gas Cyclic Steady State Modeling 178 AFTER 2 Gas Cyclic Steady State Modeling 179 3 After confirming (from the status bar of Cycle Organizer) the Cycle Task is active, close the Cycle Organizer. If the Task is not active, generate a Cycle Task either by executing Generate Task from Cycle menu or by clicking Generate Cycle from the status bar of Cycle Organizer. 4 Aspen Adsim displays a green square on the simulation status bar and the simulation mode is now set to Steady State. If so, the simulation is ready to be run in CSS mode. 2 Gas Cyclic Steady State Modeling 180 Developer’s Tips to Get Better Convergence Property in CSS Simulation 1 Careful consideration in setting Solver Property options is required to ensure convergence of CSS models. In the Non Linear Solver Tab, we recommend selecting the Newton Method for CSS simulation whilst the Fast Newton is normally recommendable in a dynamic simulation. 2 Convergence criterion is recommended to set Residual and Variable. 3 Max. step reductions value should be maximized as 20. 4 Recommended Max. iterations value is 5000. 5 The value of Maximum variable step is highly sensitive for the convergence property. For CSS simulation, a recommended default value is 200, and this may be adjusted (normally increase as problem is complex) but should not exceed 500. Note that the value of the Maximum variable step must be reduced if the flowsheet follows dynamic (not exceed 50). 2 Gas Cyclic Steady State Modeling 181 Recommended Non Linear Solver Property 6 A new check box, ‘Use transpose’, has been added to the Solver Properties dialog Linear Solver Tab. The recommended selection for this option is CSS simulation. 2 Gas Cyclic Steady State Modeling 182 7 The following dialog shows the recommended tolerance table for CSS simulation. 2 Gas Cyclic Steady State Modeling 183 3 Ion-Exchange Processes 184 3 Ion-Exchange Processes This chapter contains for information on: • About Ion-Exchange Processes • Bed Model Assumptions for Ion-Exchange Processes • Configure Form for Ion-Exchange Processes • Configure Layer Form for Ion-Exchange Processes • General Tab • Material/Momentum Balance Tab • About Axial Dispersion in Ion-Exchange Processes • Kinetic Model Tab • Isotherm Tab • Summary of Mass Balance Equations for Ion-Exchange Processes About Ion-Exchange Processes In ion-exchange processes, a fluid phase (such as an aqueous solution) containing cations and anions, is contacted with an ion-exchange resin. Typically, the ion-exchange resin is inside a packed bed adsorption column. The resin contains bound groups carrying a positive or negative ionic charge, which are accompanied by displaceable ions of opposite charge (counterions). The displaceable ions have the same charge as the ions of interest in the fluid phase: since the ions in the fluid phase have a greater affinity for the bound groups than those originally present, the latter are displaced by the former. Generally, the resin has a fixed total charge capacity, so one ionic solute is exchanged for another while maintaining charge neutrality. Ion-exchange processes have become an important separation technique for aqueous electrolyte solutions and are used in these applications: • Water softening, where monovalent cations replace multivalent cations. • Water purification, where hydrogen or hydroxide ions replace cations (usually monovalent). • Multi-component separation of ionic mixtures of different type and charge. Ion-exchange may be written as a reversible reaction involving charge equivalent quantities. For example, in a water-softening process, the cation- exchange process is written as: Ca NaR CaR Na 2+ + + ⇔ + 2 2 2 3 Ion-Exchange Processes 185 where R is a stationary, univalent, anionic group in the poly-electrolyte network of the exchange phase. Bed Model Assumptions for Ion- Exchange The bed model assumptions for ion-exchange are: • Overall and component material balances apply for the liquid phase. • Isothermal conditions apply. • Plug flow or plug flow with axial dispersion applies. • The liquid stream pressure is constant (no frictional pressure drop). • The superficial velocity and thus volumetric flow rate remain constant. (The ion components are dilute so the effect of adsorption on the overall mass balance is negligible.) • Ideal mixing occurs in the aqueous phase. Since the ionic components are very dilute, overall molar volume remains constant. • Changes in molar volume between distinct, sequentially fed fluids are allowed. • The total exchange capacity of the bed Q is constant. • A lumped mass-transfer rate applies, with a liquid- or solid-film resistance. This resistance is either linear, quadratic, or user-defined. • The mass-action equilibrium is one alternative model for ion-exchange behavior. Others include the extended Langmuir and extended Langmuir- Freundlich models. Configure Form (ionx) In the Configure Form of the Ion-exchange process bed model: • Enter the number of layers within the bed (1 or more). • Click in the Description box for each layer and type in a brief name or description. • Click Configure to open the Configure Layer dialog box. • Click Specify to open the specify form for the layer model. Configure Layer Form (ionx) Use the options in the Configure Layer form to specify the set of equations within each layer of the bed. For more information on choosing the options for your ion-exchange process, see these sections: • General tab • Material/Momentum Balance tab • Kinetic Model tab • Isotherm tab 3 Ion-Exchange Processes 186 General Tab (ionx) Use the General tab to specify these options for your ion-exchange process: • Discretization method • Number of nodes General Tab (ionx): Discretization Method to be Used These discretization methods are available for ion-exchange processes: • UDS1 • UDS2 • CDS1 • LDS • QDS • MIXED • BUDS General Tab (ionx): Number of Nodes In the Number of Nodes box, choose an appropriate number of nodes for your chosen discretization method. Material/Momentum Balance Tab (ionx) Use the Material/Momentum Balance tab to specify the basic assumptions about material dispersion in the liquid phase for ion-exchange processes. Material/Momentum Balance Tab (ionx): Material Balance Assumption In the Material Balance Assumption box, choose from one of the following options: • Convection Only • Convection with Constant Dispersion • Convection with Estimated Dispersion • Convection with User Procedure Dispersion • Convection with User Submodel Dispersion Material Balance Assumption (ionx): Convection Only This option omits the dispersion term from the material balance, so the model represents plug flow with a zero dispersion coefficient (infinite Peclet number). 3 Ion-Exchange Processes 187 Because the dispersion term is omitted, you do not need to supply the dispersion coefficient. Material Balance Assumption (ionx): Convection with Constant Dispersion The Convection with Constant Dispersion option includes the dispersion term in the material balance for the bed. You must then supply a fixed value for the dispersion coefficient, z E . With this option, the dispersion coefficient is constant for all components throughout the bed. Material Balance Assumption (ionx): Convection with Estimated Dispersion The Convection with Estimated dispersion option includes the dispersion term in the material balance for the bed. Here, the dispersion coefficient varies along the length of the bed. Aspen Adsim estimates the components' dispersion coefficients in an ion-exchange bed using this correlation (Slater, 1991): 48 . 0 011 . 0 2 . 0 | | . | \ | + = i z P l Re E d v ε where: z E = Axial dispersion coefficient l v = Liquid Velocity i ε = Interparticle voidage p d = Particle diameter u ρ l P l l v d M Re = = Reynolds number u = Liquid viscosity l ρ = Liquid molar density l M = Liquid molecular weight Material Balance Assumption (ionx): Convection with User Procedure Dispersion The Convection with User Procedure Dispersion option includes the dispersion term in the material balance for the bed. The dispersion coefficient varies with axial position according to a user- supplied Fortran subroutine, which Aspen Adsim interfaces using the procedure pUser_i_Dispersion. 3 Ion-Exchange Processes 188 Material Balance Assumption (ionx): Convection with User Submodel Dispersion The Convection with User Submodel Dispersion option includes the dispersion term in the material balance for the bed. The dispersion coefficient varies with axial position according to the user- supplied submodel iUserDispersion. About Axial Dispersion in Ion- Exchange Processes As a fluid flows through a packed column such as an ion-exchange bed, axial dispersion (mixing) tends to occur, which reduces the efficiency of separation. Axial dispersion should be minimized in bed design, but, if it occurs, then Aspen Adsim must account for its effects. There are several sources of axial dispersion in ion-exchange processes (Ruthven, 1984): • Channeling caused by non-uniform packing, for example where different sections of the packing have different voidages. • Dispersion from wall effects due to non-uniform packing at the wall. This can be avoided by packing the bed well, and having a sufficiently large ratio of bed-to-particle diameters. • Hold-up of liquid in the laminar boundary layer surrounding the particles combined with small random fluctuations in the flow. • Splitting and recombining of the flow around the particles. The molecular diffusivities of liquids are too small to contribute significantly to axial dispersion. In general, the mixing effects are additive and can be lumped together into a single effective dispersion coefficient, z E . The dispersion term in the material balance is usually expressed as: 2 2 z c E k z i ∂ ∂ ε − The type of flow determines whether this term is omitted or included in the material balance. Deciding When to Use Axial Dispersion in Ion-Exchange Processes In deciding whether to include axial dispersion in the bed model, it is useful to work out the Peclet number, given an effective dispersion coefficient ( z E ), a liquid superficial velocity ( l v ), and a bed height ( b H ): z b E H v Pe l = 3 Ion-Exchange Processes 189 The Peclet number quantifies the degree of dispersion introduced into the system. It is dimensionless so is more convenient than the dispersion coefficient for this purpose. The following table shows the effect of different values of Peclet number: If the Peclet number is The effect of axial dispersion on bed performance is 0 Infinite: the bulk liquid is perfectly mixed., so the liquid composition is homogeneous throughout the entire bed. < 30 Significant. > 100 Very slight: The bed operates under near plug flow conditions. ∞ Zero: The bed operates under plug flow conditions. Numerical methods used to discretize the spatial derivatives in the general equations can also introduce an artificial form of dispersion. Kinetic Model Tab (ionx) The overall mass transfer of ionic components between the bulk liquid phase and the adsorbed phase must overcome two resistances: • Mass transfer resistance located in the boundary layer surrounding the particle. • Mass transfer resistance inside the resin particle. Typically, the second resistance determines the overall mass transfer rate. Aspen Adsim lumps the overall resistance to mass transfer into a single overall factor. You select the type of resistance from: • Film Model Assumption • Kinetic Model Assumption • Form of Lumped Resistance • Form of Mass Transfer Coefficient Kinetic Model Tab (ionx): Film Model Assumption In the Film Model Assumption box, choose from: • Solid — The mass transfer driving force is expressed as a function of the solid phase loading (solid film). • Fluid — The mass transfer driving force is expressed as a function of the liquid phase concentration (liquid film). 3 Ion-Exchange Processes 190 Kinetic Model Tab (ionx): Kinetic Model Assumption In the Kinetic Model Assumption box, choose from: • Lumped Resistance • User Procedure • User Submodel Kinetic Model Assumption (ionx): Lumped Resistance Here, the mass transfer driving force for component k is expressed as a function of the liquid phase concentration (liquid film), or solid phase loading (solid film). This function is either linear or quadratic. See Form of Lumped Resistance, later. Kinetic Model Assumption (ionx): User Procedure With this option, the component rates of mass transfer are related to local conditions in the bed through a relationship you supply in a Fortran subroutine, which Aspen Adsim interfaces using the procedure pUser_i_Kinetic. Kinetic Model Assumption (ionx): User Submodel With User Submodel selected, the component rates of mass transfer are related to local conditions in the bed through the user submodel iUserKinetic. Kinetic Model Tab (ionx): Form of Lumped Resistance This option is active only if you selected Lumped Resistance as your Kinetic Model assumption. The following options are available: • Linear • Quadratic Form of Lumped Resistance (ionx): Linear The mass transfer driving force for component k is expressed as a linear function of the liquid phase concentration or solid phase loading. ) ( * k k k k c c MTCl t w − = ∂ ∂ (fluid film) ) ( * k k k k w w MTCs t w − = ∂ ∂ (solid film) 3 Ion-Exchange Processes 191 Form of Lumped Resistance (ionx): Quadratic The mass transfer driving force is expressed as a quadratic function of the liquid phase concentration (fluid film) or solid phase loading (solid film). k k k k k c c c MTCl t w 2 ) ) ( ( 2 * 2 − = ∂ ∂ (fluid film) k k k k k w w w MTCs t w 2 ) ) (( 2 2 * − = ∂ ∂ (solid film) Kinetic Model Tab (ionx): Form of Mass Transfer Coefficient Use this option to specify how to define the mass transfer coefficients. Choose from: • Constant • User Procedure • User Submodel Form of Mass Transfer Coefficient (ionx): Constant With this option, the mass transfer coefficient for each component is constant throughout the bed. You must supply a constant value of mass transfer coefficient for each component in the Specify table of the layer. Form of Mass Transfer Coefficient (ionx): User Procedure Here, the mass transfer coefficients are functions of local bed conditions. The function is implemented in a Fortran subroutine, which Aspen Adsim interfaces using the procedure pUser_i_MTC. Form of Mass Transfer Coefficient (ionx): User Submodel With User Submodel selected, the mass transfer coefficients are functions of local bed conditions, and are returned through the user submodel iUserMTC. Isotherm Tab (ionx) Use the Isotherm tab to specify the adsorption isotherms for use in your ion- exchange process. About Adsorption Isotherms for Ion- Exchange Processes The driving force behind an ion-exchange separation process is the departure from adsorption equilibrium between the aqueous and adsorbed phases. Consequently, adsorption isotherms (also known as ion-exchange equilibria) are important data in the design of ion-exchangers. Aspen Adsim has a list of commonly used, standard multi-component adsorption isotherms. 3 Ion-Exchange Processes 192 Important: The equations presented are for equilibrium conditions. Depending on the mass transfer rate model you choose, they are used to compute either: • w*, the loading that would be at equilibrium with the actual liquid phase composition -or- • c*, the liquid phase composition that would be at equilibrium with the actual loading. This choice is automatically handled by Aspen Adsim depending on your selection of kinetic model. The equilibrium variable arrays (of size number of nodes × number of components) are named either Ws or Cs. In bed models, these variables are distributed, so they have a qualifier 1, 2, … n (=number of nodes), depending on the bed location. Isotherm Tab (ionx): Isotherm Assumed for Layer In the Isotherm Assumed for Layer box, choose from: • Mass Action Equilibrium • Extended Langmuir • Extended Langmuir-Freundlich • User Procedure • User Submodel Isotherm Assumed for Layer (ionx): Mass Action Equilibrium R R B + B + A + + R R A + + B B The exchange reaction in the ion-exchange process is typically takes the form: mB AR mBR A m + ⇔ + where m is a stoichiometric coefficient. • m is an integer or a fraction. It is given by the valence ratio of A and B. • A refers to an ionic component in solution. • B refers to a counter-ion on the ion-exchanger surface. • R refers to a bound group (of opposite sign to B). The associated equilibrium relationship can be written as: 1 0 1 − | | . | \ | | | . | \ | | | . | \ | = m m B B A A AB c Q y x x y K 3 Ion-Exchange Processes 193 where: AB K = Equilibrium constant or selectivity coefficient. x = Equivalent mole fraction in the adsorbed phase. y = Equivalent mole fraction in the aqueous phase. 0 c = Total ionic concentration. Q = Ion-exchange resin capacity. In Aspen Adsim, the parameter 1 IP equals AB K , and the parameter m equals 2 IP . The equation now becomes: 0 . 1 1 0 1 2 2 = | | . | \ | | | . | \ | | | . | \ | − A A IP IP B B A A A c Q y x x y IP Isotherm Assumed for Layer (ionx): Extended Langmuir The extended Langmuir isotherm was found to represent some experimental data satisfactorily: ( ) b b k k k i i i c IP c IP c IP w 2 2 1 1 + + = ∑ where b refers to the (original) counter-ion. Isotherm Assumed for Layer (ionx): Extended Langmuir- Freundlich This isotherm is based on the Langmuir isotherm and expressed as: ( ) b k i IP b b k IP k k IP i i i c IP c IP c IP w 4 4 2 3 3 1 1 + + = ∑ where b refers to the (original) counter-ion. Isotherm Assumed for Layer (ionx): User Procedure You can supply your own, proprietary isotherm relationships through a Fortran subroutine, which Aspen Adsim interfaces using one of two procedures: • pUser_i_Isotherm_C for solid film kinetic model • pUser_i_Isotherm_W for liquid film kinetic model Isotherm Assumed for Layer (ionx): User Submodel With User Submodel selected, you supply the isotherm relationship through the user submodel iUserIsotherm. 3 Ion-Exchange Processes 194 Summary of Mass Balance Equations for Ion-Exchange Processes This section summarizes the mass balance equations used by Aspen Adsim to simulate ion-exchange processes. The overall material balance is expressed as: 0 = + t z v l i l l ∂ ∂ρ ε ∂ ∂ρ This equation accounts for the fact that, during an ion-exchange cycle, solvents of different densities are being used in the different production, purge and regeneration stages. Density remains unchanged as a result of the ion-exchange process itself. Each ionic species in the liquid phase, fed into the ion-exchange column, is governed by the following material balance equation: 0 2 2 = + + + − k k i k l k z i J t c z c v z c E ∂ ∂ ε ∂ ∂ ∂ ∂ ε The mass transfer rate k J between the bulk liquid and the resin is given by: ( ) t w J k i k ∂ ∂ ε − = 1 where the uptake rate t w k ∂ ∂ can, for example, be determined by a solid film linear driving force relationship, such as: ( ) k k sk k w w MTC t w − = ∂ ∂ * The number of counter ions being released from the resin and entering the liquid phase is determined from the number of ions exchanged from the liquid phase — the total charge of both liquid and resin must remain neutral: ∑ ≠ = = nc b k k k b J J 1 Hence the behavior of the exchanged counter ion in the liquid phase can be described by: 0 1 2 2 = − + + − ∑ ≠ = nc b k k k b i b l b z i J t c z c v z c E ∂ ∂ ε ∂ ∂ ∂ ∂ ε 3 Ion-Exchange Processes 195 Explanation of Equation Symbols for Ion-Exchange Processes The tables explain the equation symbols used in Aspen Adsim's ion-exchange mass balance equations. Symbol Explanation Aspen Adsim base units b c Counter ion concentration in liquid phase. eq/m 3 k c Ion concentration in liquid phase. eq/m 3 * k c Liquid phase ion concentration in equilibrium with resin phase. eq/m 3 0 c Total liquid phase ion concentration. eq/m 3 p d Resin particle diameter. m z E Axial dispersion coefficient. m 2 /s B H Bed height. m IP Isotherm parameter. b J Counter ion material transfer rate. eq/m 3 /s k J Ion material transfer rate. eq/m 3 /s AB K Mass action equilibrium constant. m Stoichiometric coefficient used in mass action equilibrium. l M Solvent molecular weight. kg/kmol l MTC Liquid film mass transfer coefficient. 1/s s MTC Solid film mass transfer coefficient. 1/s Q Total resin ion capacity. eq/m 3 t Time. s k w Ion loading on resin. eq/m 3 * k w Ion loading in equilibrium with liquid phase ion concentration. eq/m 3 k x Ion mole fraction in adsorbed (resin) phase. k y Ion mole fraction in liquid phase. z Axial co-ordinate. m 3 Ion-Exchange Processes 196 i ε Bed voidage. u Solvent viscosity. N/m 2 /s i ρ Solvent molar density. kmol/m 3 Dimensionless number Defining expression Description Pe z B l E H v Peclet number Re u ρ l P l l v d M Reynolds number 4 Liquid Adsorption Processes 197 4 Liquid Adsorption Processes This chapter contains information on liquid adsorption processes and how they are simulated in Aspen Adsim. For more information, see the following topics: • About Liquid Adsorption Processes • Bed Model Assumptions for Liquid Adsorption • Configure Form • Configure Layer Form • General Tab • Material/Momentum Balance Tab • Kinetic Model Tab • About Adsorption Isotherms for Liquid Adsorption • Guidelines for Choosing Aspen Adsim Isotherm Models • Energy Balance Tab • Procedures Tab • Summary of Mass and Energy Balance • Explanation of Equation Symbols About Liquid Adsorption Processes Liquid phase adsorption has long been used to remove contaminants present at low concentrations in process streams, such as organics from waste water. When contaminants are not well defined, liquid phase adsorption can improve feed quality, defined by color, taste, odor, and storage stability. Unlike trace impurity removal, using liquid phase adsorption for bulk separation on a commercial scale is a relatively recent development. The first commercial operation was in the 1960s, in hydrocarbon processing. Since then, bulk adsorptive separation of liquids has been used to solve a broad range of problems, including individual isomer separations and class separations. The commercial availability of synthetic molecular sieves and ion-exchange resins, and the development of novel process concepts have been the two significant factors in the success of these processes. 4 Liquid Adsorption Processes 198 Bed Model Assumptions for Liquid Adsorption For liquid adsorption, the bed model assumes: • Plug flow, or plug flow with axial dispersion. • The liquid phase pressure is either constant or varies according to a laminar-flow momentum balance (with the pressure drop assumed proportional to the flow velocity). • The superficial velocity is constant, or varies due to adsorption and according to total mass balance. • Molar concentrations are calculated from molar volumes. Ideal mixing is assumed to occur in the liquid phase, so molar volume is a linear function of composition. • A lumped mass-transfer rate applies, with a liquid or solid-film resistance. This resistance is either linear, quadratic or user-defined. • Mass transfer coefficients are either constant or user defined. • The adsorption isotherm is chosen from Aspen Adsim defined isotherms, or specified by you. • Isothermal or non-isothermal conditions apply. The energy balance includes terms for: − Thermal conductivity of gas and solid. − Liquid-solid heat transfer. − Heat of adsorption. − Enthalpy of adsorbed phase. − Heat exchange with environment. − Wall energy terms. Configure Form (liq) This section contains information on the Configure form for a liquid process bed model. The following options are available: • Enter the number of layers within the bed (one or more). • Type a brief name or description in the Description box. • Click the Configure button to open the Configure Layer dialog box. • Click the Specify button to open the Specify form for the layer model. Configure Layer Form (liq) Use the options in the Configure Layer form to define the set of equations for each layer of the adsorption bed. For information on choosing the options for your liquid adsorption process, see the following sections: • General Tab • Material/Momentum Balance Tab • Kinetic Model Tab 4 Liquid Adsorption Processes 199 • Isotherm Tab • Energy Balance Tab • Procedures Tab General Tab (liq) Use the General tab to specify the numerical options for your liquid adsorption process. General Tab (liq): Discretization Method to be Used These discretization methods are available for liquid adsorption processes: • UDS1 • UDS2 • CDS1 • LDS • QDS • MIXED • BUDS General Tab (liq): Number of Nodes In the Number of Nodes box, choose an appropriate number of nodes for your discretization method. Material/Momentum Balance (liq) Use the Material/Momentum Balance tab to: • Make basic assumptions about axial dispersion in the liquid phase. • Determine how to treat the pressure drop in the adsorption bed model. • Specify whether the velocity is constant or varies along the column. Material/Momentum Balance Tab (liq): Material Balance Assumption In the Material Balance Assumption box, choose the material balance option for your liquid adsorption process. Choose from: • Convection Only • Convection with Constant Dispersion • Convection with Estimated Dispersion • Convection with User Procedure Dispersion • Convection with User Submodel Dispersion 4 Liquid Adsorption Processes 200 Material Balance Assumption (liq): Convection Only The Convection Only option leaves out the dispersion term from the material balance for the bed. The model now represents plug flow with a zero dispersion coefficient (infinite Peclet number). Because the dispersion term is omitted, you need not supply the dispersion coefficient. Material Balance Assumption (liq): Convection with Constant Dispersion The Convection with Constant Dispersion option includes the dispersion term in the material balance for the bed. You need to supply a constant value for the dispersion coefficient, z E . With this option, the dispersion coefficient is constant for all components throughout the bed. Material Balance Assumption (liq): Convection with Estimated Dispersion The Convection with Estimated Dispersion option includes the dispersion term in the material balance for the bed. With this option, the dispersion coefficient varies along the length of the bed. Aspen Adsim estimates the values during the simulation, for each component, using this correlation (Slater, 1991): 48 . 0 011 . 0 2 . 0 | | . | \ | + = i i i z i Re E r v P l ε ε ε ε Where: z E = Axial dispersion coefficient l v = Liquid Velocity i ε = Interparticle voidage p r = Particle radius Re = Reynolds number Material Balance Assumption (liq): Convection with User Procedure Dispersion The Convection with User Procedure Dispersion option includes the dispersion term in the material balance for the bed. With this option, the dispersion coefficient varies according to a user supplied Fortran subroutine, which Aspen Adsim interfaces through the procedure type pUser_l_dispersion. 4 Liquid Adsorption Processes 201 Material Balance Assumption (liq): Convection with User Submodel Dispersion The Convection with User Submodel Dispersion option includes the dispersion term in the material balance for the bed. With this option, the dispersion coefficient varies according to the submodel lUserDispersion. Material/Momentum Balance Tab (liq): Pressure Drop Assumption Use the Pressure Drop Assumption box to specify how Aspen Adsim treats the pressure drop in the adsorption bed model. You should base your choice on your knowledge of the actual operating conditions in the plant. This option corresponds to how internal superficial velocities are related to local pressure gradients. It applies to laminar flow. You must choose an appropriate material balance model with a particular pressure-drop option. In the Pressure Drop Assumption box, choose from these options: • None • Darcy's Law • Karman-Kozeny Pressure Drop Assumption (liq): None With None selected, there is no pressure drop across the bed. Pressure Drop Assumption (liq): Darcy's Law Select the Darcy's Law option to apply a linear relationship between the liquid superficial velocity and the pressure gradient at a particular point in a bed. Darcy's law states that the pressure drop is directly proportional to flow rate: l P v K z p − = ∂ ∂ Where: p K = Proportionality constant Pressure Drop Assumption (liq): Karman-Kozeny Select the Karman-Kozeny option to relate velocity to pressure drop: ( ) ( ) ψ ε u ε ψε ∂ ∂ p i i l i p r v r z p 2 1 10 5 . 1 1 2 3 3 − × − = − − 4 Liquid Adsorption Processes 202 Material/Momentum Balance Tab (liq): Velocity Assumption In the Velocity Assumption box, choose from: • Constant Velocity • Varying Velocity Velocity Assumption (liq): Constant Velocity With Constant Velocity selected, the liquid velocity is constant along the bed, so adsorption from the liquid phase has a negligible effect on the material balance. These assumptions are valid only when modeling the removal of trace components from a bulk liquid. Velocity Assumption (liq): Varying Velocity With Varying Velocity selected, the superficial velocity varies along the bed according to the rate at which the liquid components are adsorbed onto the solid, or desorbed. The rate is determined from material balance. This option is applicable to bulk separation applications. If you select this option: • The velocity profile is determined through the total material balance, by the effect of the rate of adsorption. • The velocity profile is stored in the discrete variables Vl_in(1)…Vl_in(n), where n is the number of nodes used in the numerical method. Material/Momentum Balance Tab (liq): Overall Material Balance Assumption In the Overall Material Balance Assumption box, choose from: • Constant Density • Dynamic Density Overall Material Balance Assumption (liq): Constant Density With the Constant Density option, the mass density is constant along the bed. The velocity alone changes, and that according to the overall mass balance. Overall Material Balance Assumption (liq): Dynamic Density With Dynamic Density selected, mass density varies according to the material balance. Both mass density and velocity vary according to the overall mass balance. Kinetic Model Tab (liq) When a species is adsorbed from the bulk liquid phase onto an active surface site of the adsorbents, it typically experiences the following mass transfer resistances: 4 Liquid Adsorption Processes 203 • The resistance between the bulk liquid and the external adsorbents surface. • The resistance exerted by the adsorbents pore structure. For bi-disperse adsorbents (such as zeolites), this resistance can be further divided into: − Macropore resistance. − Micropore resistance. These resistances are typically lumped into a single, overall mass transfer coefficient. The following options are available from the Kinetic Model tab: • Film Model Assumption • Kinetic Model Assumption • Form of Mass Transfer Coefficient Kinetic Model Tab (liq): Film Model Assumption In the Film Model Assumption box, choose from: • Solid ÷ the mass transfer driving force is expressed as a function of the solid phase loading. • Fluid ÷ the mass transfer driving force is expressed as a function of the liquid phase concentration. Kinetic Model Tab (liq): Kinetic Model Assumption In the Kinetic Model Assumption box, choose from: • Linear lumped resistance. • Quadratic lumped resistance. • Micro and macropore. • User procedure. • User submodel. Kinetic Model Assumption (liq): Linear Lumped Resistance With Linear Lumped Resistance selected, the mass transfer driving force for component i is expressed as a linear function of the liquid phase concentration or solid phase loading. ( ) * i i li i S c c MTC t w − = ∂ ∂ ρ (fluid) ( ) i i si i w w MTC t w − = * ∂ ∂ (solid) 4 Liquid Adsorption Processes 204 Kinetic Model Assumption (liq): Quadratic Lumped Resistance With Quadratic Lumped Resistance selected, the mass transfer driving force is expressed as a quadratic function of the liquid phase concentration or solid phase loading. ( ) ( ) i i i li i S c c c MTC t w 2 2 * 2 − = ∂ ∂ ρ (fluid) ( ) ( ) i i i si i w w w MTC t w 2 2 2 * − = ∂ ∂ (solid) Kinetic Model Assumption (liq): Micro and Macropore Model Two concentration gradients greatly affect the diffusion rate: • Within the pores of the solid. • Within the void spaces between the particles, that is, within the crystallines. Under practical conditions in gas separation, pore diffusion limits the overall mass transfer rate between the bulk flow and the internal surface of a particle, so it is an important factor in the dynamics of adsorbers. For more information, see Micro and Macro Pore Effects in Chapter 1. Kinetic Model Assumption (liq): User Procedure The User Procedure option relates the component rates of mass transfer to the local bed conditions through a user-supplied Fortran subroutine, which Aspen Adsim interfaces through the procedure type pUser_l_Kinetic. Kinetic Model Assumption (liq): User Submodel With User Submodel selected, the bed model calls the submodel lUserKinetic. This submodel needs the relationship between the component rates of mass transfer and the local bed conditions. Kinetic Model Tab (liq): Form of Mass Transfer Coefficient In the Form of Mass Transfer Coefficient box, you choose how mass transfer coefficients are defined. Choose from: • Constant • User Procedure • User Submodel Form of Mass Transfer Coefficient (liq): Constant With Constant selected, the mass transfer coefficient for each component is constant through the bed. You must supply a constant value of mass transfer coefficient for each component. 4 Liquid Adsorption Processes 205 Form of Mass Transfer Coefficient (liq): User Procedure If you choose User Procedure, the mass transfer coefficients are returned by a Fortran subroutine you supply, which Aspen Adsim interfaces through the procedure pUser_l_MTC. Form of Mass Transfer Coefficient (liq): User Submodel With User Submodel selected, the mass transfer coefficients are defined in the user submodel lUserMTC. About Adsorption Isotherms for Liquid Adsorption The driving force behind all adsorptive liquid separation processes is the departure from adsorption equilibrium, so adsorption isotherms are important data in adsorber design. If you know the adsorption isotherms for the components of the feed, you can create a bed model to predict the performance of the adsorber bed for the specified operating conditions. Aspen Adsim has a comprehensive list of multicomponent adsorption isotherms. Guidelines for Choosing Aspen Adsim Isotherm Models Make sure you choose a model that is appropriate for the process you are investigating. The equilibrium specified by the isotherm model affects the driving force for mass transfer. Consequently, you can obtain significantly different simulation results when using different models, even if the model parameters come from the same set of data. The expressions in this section are equilibrium equations. Depending on the mass transfer rate model you choose (See also Kinetic Model Tab (liq) on page 4-202), the expressions are used to compute either: • w* ÷ The loading that would be at equilibrium with the actual liquid phase composition -or- • c* ÷ The liquid phase composition that would be at equilibrium with the actual loading. This choice is automatically handled by Aspen Adsim. The equilibrium variable arrays (of size n) are named either Ws or Cs. In bed models, these variables are distributed, so they have a qualifier 1, 2, ... n, to denote their location in the bed. 4 Liquid Adsorption Processes 206 The Ideal Adsorbed Solution Theory (IAS) Recently, the Ideal Adsorbed Solution Theory (IAS) has become popular for multicomponent mixtures. The method lets you predict adsorption equilibria for components in a mixture. It needs data only for the pure-component adsorption equilibria at the same temperature, and on the same adsorbent. The model treats the mixed adsorbate phase as an ideal solution in equilibrium with the liquid phase. The model follows the formal, thermodynamic approach for vapor-liquid equilibria, in which the fundamental equations of thermodynamic equilibrium are developed, and applies this to the liquid-adsorbed phase equilibria. At first sight, ideal behavior in the adsorbed phase seems improbable. However, many systems have shown strong correlation between experimental data and predictions by IAS theory, including binary and ternary mixtures on activated carbons and zeolites. IAS is available in Aspen Adsim. To use it, choose the appropriate isotherm on the Isotherm tab of the Configure Layer form. For a full description of the IAS approach, see Chapter 4 of Ruthven (1984) or Chapter 3 of Kast (1988) (German language). Isotherm Tab (liq): Isotherm Assumed for Layer Use the Isotherm tab to choose which adsorption isotherms are used in your liquid adsorption process. Choose from: • Langmuir models (1,2) • Dual-Site Langmuir models (1,2 • Extended Langmuir models (1,2) • Freundlich models (1,2) • Langmuir-Freundlich models (1,2) • Extended Langmuir-Freundlich models (1,2) • Stoichiometric Equilibrium models (1,2) • IAS Langmuir models (1,2) • IAS Freundlich models (1,2) • IAS Langmuir-Freundlich models (1,2) • User Multicomponent Procedure • User Multicomponent Submodel • User Multicomponent Procedure with IAS • User Multicomponent Submodel with IAS Isotherm Assumed for Layer (liq): Langmuir Models (1,2) There are two types of Langmuir model available in Aspen Adsim: • Langmuir 1, which is temperature independent. • Langmuir 2, which is temperature dependent. 4 Liquid Adsorption Processes 207 Langmuir 1 This isotherm is expressed as: i i i i i i c IP c IP IP w 2 2 1 1+ = Langmuir 2 This isotherm is expressed as: i s i i i s i i i i c T IP IP c T IP IP IP w | | . | \ | + | | . | \ | = 3 2 3 2 1 exp 1 exp Isotherm Assumed for Layer (liq): Dual-Site Langmuir Models (1,2) There are two types of Dual-Site Langmuir model available in Aspen Adsim: • Dual-Site Langmuir 1, which is temperature independent. • Dual-Site Langmuir 2, which is temperature dependent. Dual-Site Langmuir 1 This isotherm is expressed as: ∑ ∑ = = + + + = nc k k k i i i nc k k k i i i i c IP c IP IP c IP c IP IP w 1 4 4 3 1 2 2 1 1 1 Dual-Site Langmuir 2 This isotherm is expressed as: ∑ ∑ = = | | . | \ | + | | . | \ | + | | . | \ | + | | . | \ | = nc k k s k k i s i i i nc k k s k k i s i i i i c T IP IP c T IP IP IP c T IP IP c T IP IP IP w 1 6 5 6 5 4 1 3 2 3 2 1 exp 1 exp exp 1 exp Isotherm Assumed for Layer (liq): Extended Langmuir Models (1,2) Aspen Adsim has two types of Extended Langmuir model: • Extended Langmuir 1, which is temperature independent. • Extended Langmuir 2, which is temperature dependent. Extended Langmuir 1 This isotherm is expressed as: 4 Liquid Adsorption Processes 208 ∑ = + = nc k k k i i i i c IP c IP IP w 1 2 2 1 1 Extended Langmuir 2 This isotherm is expressed as: ∑ = | | . | \ | + | | . | \ | = nc k k s k k i s i i i i c T IP IP c T IP IP IP w 1 3 2 3 2 1 exp 1 exp Isotherm Assumed for Layer (liq): Freundlich Models (1,2) There are two types of Freundlich model available in Aspen Adsim: • Freundlich 1, which is temperature independent. • Freundlich 2, which is temperature dependent. Freundlich 1 This isotherm is expressed as: i IP i i i c IP w 2 1 = Freundlich 2 This isotherm is expressed as: | | . | \ | = s i IP i i i T IP c IP w i 3 1 exp 2 Isotherm Assumed for Layer (liq): Langmuir-Freundlich Models (1,2) There are two types of Langmuir-Freundlich model available in Aspen Adsim: • Langmuir-Freundlich 1, which is temperature independent. • Langmuir-Freundlich 2, which is temperature dependent. Langmuir-Freundlich 1 This isotherm is expressed as: i i IP i i IP i i i i c IP c IP IP w 3 3 2 2 1 1+ = Langmuir-Freundlich 2 This isotherm is expressed as: 4 Liquid Adsorption Processes 209 | | . | \ | + | | . | \ | = s i IP i i s i IP i i i i T IP c IP T IP c IP IP w i i 4 2 4 2 1 exp 1 exp 3 3 Isotherm Assumed for Layer (liq): Extended Langmuir- Freundlich Models (1,2) There are two types of Extended Langmuir-Freundlich model available in Aspen Adsim: • Extended Langmuir-Freundlich 1, which is temperature independent. • Extended Langmuir-Freundlich 2, which is temperature dependent. Extended Langmuir-Freundlich 1 This isotherm is expressed as: ( ) ∑ = + = n j IP j j IP i i i i j i c IP c IP IP w 1 2 2 1 3 3 1 Extended Langmuir-Freundlich 2 This isotherm is expressed as: ∑ = | | . | \ | | | . | \ | + | | . | \ | = n j s j IP j j s i IP i i i i T IP c IP T IP c IP IP w j i 1 4 2 4 2 1 exp 1 exp 3 3 Isotherm Assumed for Layer (liq): Stoichiometric Equilibrium Models (1,2) Aspen Adsim has two types of Stoichiometric Equilibrium model: • Stoichiometric Equilibrium 1, which is temperature independent. • Stoichiometric Equilibrium 2, which is temperature dependent. Stoichiometric Equilibrium 1 This isotherm is expressed as: ∑ = = nc k k k i i i i c IP c IP IP w 1 2 2 1 Stoichiometric Equilibrium 2 This isotherm is expressed as: 4 Liquid Adsorption Processes 210 ∑ = | | . | \ | | | . | \ | = nc k k s k k i s i i i i c T IP IP c T IP IP IP w 1 3 2 3 2 1 exp exp Isotherm Assumed for Layer (liq): IAS Langmuir Models (1,2) With IAS Langmuir Models selected, the multicomponent adsorption behavior is expressed using Ideal Adsorbed Solution theory in combination with pure component isotherms. Aspen Adsim has two versions of the pure component Langmuir model: • IAS Langmuir 1, which is temperature independent. • IAS Langmuir 2, which is temperature dependent. IAS Langmuir 1 This isotherm is expressed as: i i i i i i c IP c IP IP w 2 2 1 1+ = IAS Langmuir 2 This isotherm is expressed as: i s i i i s i i i i c T IP IP c T IP IP IP w | | . | \ | + | | . | \ | = 3 2 3 2 1 exp 1 exp Isotherm Assumed for Layer (liq): IAS Freundlich Models (1,2) With IAS Freundlich Models selected, the multicomponent adsorption behavior is expressed using the Ideal Adsorbed Solution Theory in combination with pure component isotherms. Aspen Adsim has two versions of the pure component Freundlich model: • IAS Freundlich 1, which is temperature independent. • IAS Freundlich 2, which is temperature dependent. IAS Freundlich 1 This isotherm is expressed as: i IP i i i c IP w 2 1 = IAS Freundlich 2 This isotherm is expressed as: 4 Liquid Adsorption Processes 211 | | . | \ | = s i IP i i i T IP c IP w i 3 1 exp 2 Isotherm Assumed for Layer (liq): IAS Langmuir-Freundlich Models (1,2) With IAS Langmuir-Freundlich selected, the multicomponent adsorption behavior is expressed using the Ideal Adsorbed Solution Theory in combination with pure component isotherms. Aspen Adsim has two versions of the pure component Langmuir-Freundlich model: • IAS Langmuir-Freundlich 1, which is temperature independent. • IAS Langmuir-Freundlich 2, which is temperature dependent. IAS Langmuir-Freundlich 1 This isotherm is expressed as: i i IP i i IP i i i i c IP c IP IP w 3 3 2 2 1 1+ = IAS Langmuir-Freundlich 2 This isotherm is expressed as: | | . | \ | + | | . | \ | = s i IP i i s i IP i i i i T IP c IP T IP c IP IP w i i 4 2 4 2 1 exp 1 exp 3 3 Isotherm Assumed for Layer (liq): User Multicomponent Procedure You can supply your own, proprietary isotherm relationships through a Fortran subroutine, which Aspen Adsim interfaces using one of two procedures: • pUser_l_Isotherm_C for solid film kinetic model • pUser_l_Isotherm_W for liquid film kinetic model The functional relationship is: ( ) IP c c T f w nc eq i , ... , 1 = Isotherm Assumed for Layer (liq): User Multicomponent Submodel You can supply your own, proprietary isotherm relationships using the submodel lUserIsotherm. The functional relationship is: ( ) IP c c T f w nc eq i , ... , 1 = 4 Liquid Adsorption Processes 212 Isotherm Assumed for Layer (liq): User Purecomponent Procedure with IAS Select the User Purecomponent Procedure with IAS option to supply pure component, user-specified isotherms, which may be used as multicomponent isotherms. In this case, two Fortran subroutines are needed: The first subroutine is interfaced by the procedure type pUser_l_Isotherm_W. This relates the fictitious pure component concentration 0 i c (resulting in the same spread pressure as the mixture at total concentration tot c ), to the loading 0 i w , using the pure component isotherm: ( ) IP c T f w i eq i , , 0 0 = The second Fortran subroutine evaluates the integral of the Gibbs isotherm to give the spread pressure. It is interfaced by the procedure type pUser_l_Gibbs. The relationship to be evaluated is: ( ) ( ) ∫ = = 0 0 0 0 , , , , i c eq i i dc c IP c T f g IP c T g RT A with Π Isotherm Assumed for Layer (liq): User Purecomponent Submodel with IAS Select this option to supply pure component, user-specified isotherms, which may be used as multicomponent isotherms. In this case, you must supply two submodels: The first submodel is lUserIsotherm. This relates the fictitious pure component concentration 0 i c (resulting in the same spread pressure as the mixture at total concentration tot c ), to the loading 0 i w , using a pure component isotherm: ( ) IP c T f w i eq i , , 0 0 = The second submodel, lUserGibbs, evaluates the integral of the Gibbs isotherm to give the spread pressure. The relationship to be evaluated is: ( ) ( ) ∫ = = 0 0 0 0 , , , , i c eq i i dc c IP c T f g IP c T g RT A with Π Energy Balance Tab (liq) Use the Energy Balance tab to specify how the energy balance is incorporated into the model. Energy Balance Tab (liq): Energy Balance Assumption In the Energy Balance Assumption box, choose from the following options: 4 Liquid Adsorption Processes 213 • Isothermal • Non-Isothermal with no Conduction • Non-Isothermal with Fluid Conduction • Non-Isothermal with Solid Conduction • Non-Isothermal with Fluid and Solid Conduction Energy Balance Assumption (liq): Isothermal The Isothermal option ignores the energy balance. Fluid and solid temperatures are set to the same, constant value. Energy Balance Assumption (liq): Non-Isothermal with No Conduction The Non-Isothermal with No Conduction option ignores the axial thermal conduction for the fluid and solid phases within the energy balance. Energy Balance Assumption (liq): Non-Isothermal with Fluid Conduction The Non-Isothermal with Fluid Conduction option includes the thermal conduction (axial thermal dispersion) term in the fluid energy balance. This term is represented as: 2 2 z T k l l ∂ ∂ − The liquid phase thermal conductivity can be supplied in different ways as specified in the section Form of Fluid Thermal Conductivity. Energy Balance Assumption (liq): Non-Isothermal with Solid Conduction The Non-Isothermal with Solid Conduction option includes the thermal conduction term in the solid energy balance. The solid thermal conduction term is represented as: 2 2 z T k S S ∂ ∂ − You must supply a value for s k . Energy Balance Assumption (liq): Non-Isothermal with Fluid and Solid Conduction The Non-Isothermal with Fluid and Solid Conduction option includes the thermal conduction term for both fluid and solid phases. The liquid phase thermal conductivity can be supplied in different ways, as specified in the section Form of Fluid Thermal Conductivity field. 4 Liquid Adsorption Processes 214 Energy Balance Tab (liq): Consider Heat of Adsorbed Phase Aspen Adsim models enable you to include the heat capacity of the adsorbed phase in the solid-phase energy balance. The Heat of Adsorbed Phase term is optional. In the Consider Heat of Adsorbed Phase box, select from No or Yes: • No — Choose this option to ignore the enthalpy of the adsorbed phase term in the solid phase energy balance. • Yes — Choose this option if the enthalpy content of the adsorbed phase is significant for your process, and you want to include it in the overall energy balance. The term for each component is a function of the loading and the temperature in the solid phase: t T w C H S i Pi p i ads ∂ ∂ = ρ , The total contribution is the sum for all components: ∑ = nc i i ads H 1 , Energy Balance Tab (liq): Heat of Adsorption Assumption If the solid-phase energy balance is significant for the process, you must include the heat of adsorption within the balance. The rate of heat generation by adsorption of each component i, per unit mass of solid, is a function of the local rate of mass transfer and the heat of adsorption: i i i H t w HT ∆ ∂ ∂ = These rates are held in vectors and summed for all components to obtain the total rate of heat generation, by adsorption, per unit volume of solid: ( ) ∑ = nc i i p HT 1 ρ In the Heat of Adsorption Assumption box, choose from: • None • Constant • User Procedure • User Submodel Heat of Adsorption Assumption (liq): None The heat generation by adsorption term is omitted from the energy balance. 4 Liquid Adsorption Processes 215 Heat of Adsorption Assumption (liq): Constant The Constant option assumes the heat of adsorption is constant for each component i. Choose this option to set the heat of adsorption to constant values. These are held in a vector called DH. You must provide the values of the elements of DH. Heat of Adsorption Assumption (liq): User Procedure With User Procedure selected, the heat of adsorption comes from a user- supplied Fortran subroutine, which Aspen Adsim interfaces using the procedure pUser_l_DH. You can vary the heat of adsorption and make it a function of, for example, local loading, temperature, and pressure. In general terms: ) , , ( w P T f H s = ∆ Heat of Adsorption Assumption (liq): User Submodel With User Submodel selected, the heat of adsorption comes from the user submodel lUserDH. You can vary the heat of adsorption and make it a function of, for example, local loading, temperature, and pressure. In general terms: ) , , ( w P T f H s = ∆ Energy Balance Tab (liq): Form of Heat Transfer Coefficient If you request a non-isothermal energy balance, Aspen Adsim generates the solid and fluid phase energy balances, using a film resistance due to heat transfer between the solid and the fluid. Heat transfer is assumed to occur between the two phases according to: Rate of heat transferred per unit volume of bed ( ) ( ) S l i P T T HTC a − − = ε 1 If there is no heat transfer resistance between the solid and fluid, the temperature of the fluid and solid are equal (“lumped”). To obtain this condition, set the heat transfer coefficient to a very large value (such as 1MW/m 2 /K). In the Form of Heat Transfer Coefficient box, choose from: • Constant • Estimated • User Procedure • User Submodel Form of Heat Transfer Coefficient (liq): Constant Choose Constant to ensure the heat transfer coefficient has a single value, which is held in a variable called HTC. 4 Liquid Adsorption Processes 216 Form of Heat Transfer Coefficient (liq): Estimated The heat transfer coefficient is estimated as follows: 1 Calculate the Reynolds number: u ρ l l p v M r Re 2 = If the calculated value falls below 1E-10, reset it to this value. 2 Calculate the Prandl number: M k C Pr l pl u = If the calculated value falls below 1E-10, reset it to this value. 3 Calculate the j-factor: If Re < 190 then 51 . 0 66 . 1 − = Re j otherwise 41 . 0 983 . 0 − = Re j 4 Calculate the heat transfer coefficient: 3 2 Pr − = l l pl v C j HTC ρ If the calculated value falls below 1E-10, reset it to a value of 1. Form of Heat Transfer Coefficient (liq): User Procedure With the User Procedure option, the user procedure pUser_l_HTC relates the local heat transfer coefficient to the state of the bed at a particular point in the bed. This means you can interface your own Fortran code to calculate the coefficients. In general terms: ( ) l l v C P T f HTC , , , = Form of Heat Transfer Coefficient (liq): User Submodel With User Submodel selected, the local heat transfer coefficient is defined through the user submodel lUserHTC. Energy Balance Tab (liq): Form of Fluid Thermal Conductivity If you selected Non-isothermal with Fluid and/or Solid Conduction, you need to choose the form of fluid thermal conductivity . In the Form of Fluid Thermal Conductivity box, choose from: • Constant • Based on Axial Dispersion • User Procedure • User Submodel 4 Liquid Adsorption Processes 217 Form of Fluid Thermal Conductivity (liq): Constant The thermal conductivity has a constant value, which you set. Form of Fluid Thermal Conductivity (liq): Based on Axial Dispersion With Based on Axial Dispersion selected, the thermal conductivity coefficient is calculated as the product of the molar heat capacity of the fluid, the axial dispersion coefficient and the molar density of the fluid: l z Pl l E C k ρ = This method applies the analogy between heat and mass transfer. Form of Fluid Thermal Conductivity (liq): User Procedure With User Procedure selected, thermal conductivity varies axially along the bed and is defined in a user-defined Fortran subroutine, which Aspen Adsim interfaces using the procedure pUser_l_Kl. Form of Fluid Thermal Conductivity (liq): User Submodel With User Submodel selected, thermal conductivity varies axially along the bed and is defined in the user submodel lUserKl. Energy Balance Tab (liq): Heat Transfer to Environment In the Heat Transfer to Environment box, choose from: • Adiabatic • Thin Wall • Rigorous Model • Heat Exchange between Fluid and Wall • Heat Exchange between Wall and Environment • Axial Conductivity along the Wall • Heat Content of Wall Heat Transfer to Environment (liq): Adiabatic With Adiabatic selected, there is no heat transfer between the bed and the wall. Heat Transfer to Environment (liq): Thin Wall With the Thin Wall option, the fluid phase energy balance includes the heat exchange between the fluid in the bed and the environment: ( ) amb l B w T T D H − 4 4 Liquid Adsorption Processes 218 Heat Transfer to Environment (liq): Rigorous Model With Rigorous Model selected, the bed model applies a wall energy balance equation that contains the following terms: • Heat transfer from the fluid in the bed to the inner wall. • Heat transfer from the outer wall to the environment. • Axial thermal conduction along the wall. • Heat accumulation within the wall material. The wall is assumed to be thin and conductive enough for the inner and outer wall temperatures to be equal. The adiabatic option (that is, ignoring the wall energy balance) is valid only when the wall is non-conductive, or there is an infinite heat transfer resistance between the liquid and the wall surface. Heat Transfer to Environment (liq): Heat Exchange Between Fluid and Wall When the rigorous wall energy balance is selected, the heat exchange between the fluid in the bed and the inner surface of the wall is included in the wall energy balance. The term is represented as: ( ) w l wi wo wi w T T D D D H − − 2 2 4 You must define the value of the liquid-to-wall heat transfer coefficient, w H . The heat exchange between fluid and wall is also included in the fluid phase energy balance. Note that the equation has a slightly different form, owing to the different cross-sectional areas of the balances: ( ) w l wi w T T D H − 4 Heat Transfer to Environment (liq): Heat Exchange Between Wall and Environment When a rigorous wall energy balance is included, the heat transfer between the outer wall and the environment is expressed as: ( ) amb w wi wo wo amb T T D D D H − − 2 2 4 You must define the value of the heat transfer coefficient to the environment amb H and the temperature of the environment, amb T . To ignore the effect of heat exchange with the environment in the energy balance, set the value of the heat transfer coefficient to zero. Heat Transfer to Environment (liq): Axial Thermal Conductivity Along Wall The axial thermal conduction along the wall is always included in the wall energy balance. The term is: 4 Liquid Adsorption Processes 219 2 2 z T k w w ∂ ∂ − You must specify the thermal conductivity of the wall material, w k . Heat Transfer to Environment (liq): Heat Content of Wall The heat accumulation of the wall is always included in the wall energy balance. The term is: t T C w pw w ∂ ∂ ρ You must specify the value of the wall density, w ρ , and the specific heat capacity of the wall, pw C . Procedures Tab (liq) Use the Procedures tab to view a list of the user procedures being used within the current adsorption layer model. Liquid Adsorption: Summary of Mass and Energy Balance For information on the equations used in Aspen Adsim for mass and energy balances in liquid adsorption processes, see: • Liquid Adsorption: Mass Balance • Liquid Adsorption: Solid Phase Energy Balance • Liquid Adsorption: Fluid Phase Energy Balance • Liquid Adsorption: Wall Energy Balance Liquid Adsorption: Mass Balance The overall mass balance for a multi-component liquid phase contains terms for: • Convection of material. • Accumulation of material in the liquid phase. • Mass transfer from the liquid to the solid phase. The governing partial differential equation is: ( ) 0 1 = | . | \ | ∂ ∂ + ∂ ∂ + ∂ ∂ ∑ = nc i i i s Ml l Ml i t w M v z t ρ ρ ρ ε Each component in the liquid phase is governed by a material balance: ( ) 0 2 2 = ∂ ∂ + ∂ ∂ + ∂ ∂ + ∂ ∂ − t w t c c v z z c E i s i i i l i z i ρ ε ε 4 Liquid Adsorption Processes 220 Liquid Adsorption: Solid Phase Energy Balance The solid phase energy balance includes terms for: • Thermal conduction. • Accumulation of heat. • Accumulation of heat in the adsorbed phase. • Heat of adsorption. • Gas-solid heat transfer (expressed in terms of a film resistance where the heat transfer area is proportional to the area of the adsorbent particles). The solid phase energy balance is given as: ( ) ( ) ∑ ∑ = = = − − | . | \ | + + + − nc i s l p i i p nc i i pli s p s ps p s s T T HTC a t w H w C t T t T C z T k 1 1 2 2 0 ∂ ∂ ∆ ρ ∂ ∂ ρ ∂ ∂ ρ ∂ ∂ Liquid Adsorption: Fluid Phase Energy Balance The fluid phase energy balance includes terms for: • Thermal conduction. • Convection of energy. • Accumulation of heat, heat transfer from fluid to solid. • Heat transfer from fluid to the internal wall. The governing partial differential equation is: ( ) ( ) ( ) 0 4 1 2 2 = − + − − + ∂ ∂ + ∂ ∂ + ∂ ∂ − w l wi w s l i p l l pl i l l l pl l i l T T D H T T HTC a t T C z T v C z T k ε ρ ε ρ ε Liquid Adsorption: Wall Energy Balance The wall energy balance includes terms for: • Axial thermal conduction along the wall. • Heat accumulation within the wall material. • Heat transfer from the bed to the inner wall. • Heat transfer from the outer wall to the environment. The governing partial differential equation is: ( ) ( ) 0 4 4 2 2 2 2 2 2 = − − + − − − ∂ ∂ + ∂ ∂ − amb w wi wo wo amb w l wi wo wi w w pw w w w T T D D D H T T D D D H t T C z T k ρ 4 Liquid Adsorption Processes 221 Liquid Adsorption: Explanation of Equation Symbols Symbol Explanation Aspen Adsim base units p a Specific particle surface. m 2 /m 3 A Area. m 2 k c Molar concentration of component k. kmol/m 3 0 i c IAS pure component concentration. kmol/m 3 pl C Specific liquid phase heat capacity. MJ/kmol/K ps C Specific heat capacity of adsorbent. MJ/kmol/K pW C Specific heat capacity of column wall. MJ/kg/K B D Bed diameter. m wi D Inner bed diameter. m wo D Outer bed diameter. m z E Axial dispersion coefficient. m 2 /s eq f Equilibrium (isotherm) relationship. - g Function. - i ads H , Heat of component i in adsorbed phase. MJ/m 3 /s amb H Wall-ambient heat transfer coefficient. MW/m 2 /K B H Height of adsorbent layer. m i HT Heat of adsorption contribution to solid phase energy balance. MJ/m 3 /s w H Gas-wall heat transfer coefficient. MJ/m 2 /s i H ∆ Heat of adsorption of component i. MJ/kmol HTC Liquid-solid heat transfer coefficient. MJ/m 2 /s IP Isotherm parameter, units depend on isotherm. j Colburn j-factor for heat or mass transfer. - l k Liquid phase thermal conductivity. MW/m/K s k Solid thermal conductivity. MW/m/K 4 Liquid Adsorption Processes 222 P K Darcy’s constant. bar s/m 2 M Molecular weight. kg/kmol l MTC Liquid film mass transfer coefficient. 1/s s MTC Solid film mass transfer coefficient. 1/s p Pressure. bar p r Particle radius. m R Universal gas constant. bar m 3 /kmol/K t Time. s T Temperature. K amb T Ambient temperature. K s T Solid phase temperature. K l T Liquid phase temperature. K W T Wall temperature. K l v Liquid phase superficial velocity. m/s k w Loading. kmol/kg 0 k w Pure component loading of component k. kmol/kg W Width of horizontal bed. m T W Width of column wall. m z Axial co-ordinate. m Symbol Explanation Aspen Adsim base units i ε Interparticle voidage. m 3 (Void)/m 3 (Bed) u Dynamic viscosity. N s/m 2 0 i Π Spreading pressure of component i. bar m I M, ρ Liquid phase mass density. kg/m 3 l ρ Liquid phase molar density. kmol/m 3 p ρ Adsorbent apparent density. kg/m 3 s ρ Adsorbent bulk density. kg/m 3 W ρ Wall density. kg/m 3 4 Liquid Adsorption Processes 223 Ψ Particle shape factor. - Dimensionless number Defining expression Description Pe z b l E H v Peclet number for mass transfer. Pr M k C l pl u Prandl number. Re u ρ l l M p v r , 2 Particle Reynolds number. 5 Numerical Methods 224 5 Numerical Methods This chapter describes the numerical methods available in Aspen Adsim to solve its partial differential equations. See these topics for more information: • About Numerical Methods • Choosing the Discretization Method • About the Discretization Methods About Numerical Methods Aspen Adsim uses a set of partial differential equations (PDEs), ordinary differential equations (ODEs) and algebraic equations, together with the appropriate initial and boundary conditions, to fully describe the adsorption or ion-exchange column. Spatial derivatives are discretized using algebraic approximations, and a set of ordinary differential equations and algebraic equations (DAEs) results. The spatial derivative terms within the partial differential equations are first- or second-order derivatives of some distributed variable, such as concentration, temperature or molar flux. The approximations are defined over a fixed, uniform grid of points (nodes); the distributed variables are defined for each node by means of variable sets. The resulting system of differential and algebraic equations must be solved simultaneously since they are coupled. In a sense, the dependent variables at each node ‘march in time’ along parallel lines perpendicular to the spatial axis, which explains the commonly-used name for this solution technique: the numerical method of lines. The first-order spatial derivatives present the greatest challenge in providing numerically accurate and stable approximations, particularly when the system of equations is highly nonlinear ÷ a common occurrence in adsorption process simulation. A typical problem is the propagation of steep discontinuities known as fronts or shocks. The failure of approximations to adequately represent the first order derivatives is manifested by two unwanted and spurious effects: • Numerical diffusion leading to excessive ‘smearing’ of the solution. • Numerical oscillations, leading to non-physical solutions and the violation of physical bounds. 5 Numerical Methods 225 This chapter describes the methods available in Aspen Adsim to approximate first-order spatial derivatives, showing where the methods come from and how they are evaluated. Choosing the Discretization Method Your choice of discretization method depends chiefly on the type of process you are simulating, and the level of accuracy, stability and speed you are looking for. Each of the numerical methods differ in: • Method of approximation of spatial derivatives. • Number of points. • Accuracy (including any tendency towards oscillatory behavior). • Stability. • Simulation time required. The three best standard methods, in terms of accuracy, stability, and simulation time are: • Upwind Differencing Scheme 1. • Quadratic Upwind Differencing Scheme. • Mixed Differencing Scheme. The Biased Upwind Differencing Scheme and the Flux Limiter are recommended in cases where the system is highly nonlinear and breakthrough curves are very steep ÷ features associated with highly nonlinear adsorption isotherms and near-equilibrium behavior. The Flux Limiter technique gives the accuracy of a higher order technique, but with no oscillations at small node counts. Note that all second-order derivatives are approximated by a second-order accurate central difference scheme, which is known to be accurate, stable, and fast for all cases of interest. For details on the integration of the resulting system of differential equations with time, see the Aspen Custom Modeler Solver Options help. About the Discretization Methods To specify a discretization method: • On the General tab, in the Discretization Method to Be Used box, select the method you require. 5 Numerical Methods 226 Choose from these options: • Upwind Differencing Scheme 1 (UDS1, first order) • Upwind Differencing Scheme 2 (UDS2, second order) • Central Differencing Scheme 1 (CDS1, second order) • Central Differencing Scheme 2 (CDS2, fourth order) • Leonard Differencing Scheme (LDS, third order) • Quadratic Upwind Differencing Scheme (QDS, third order) • Mixed Differencing Scheme (MDS, ~third order) • Biased Upwind Differencing Scheme (BUDS, fourth order) • Fromms’ scheme (FROMM, third order) • Flux limited discretization scheme (Flux limiter) If you choose the Flux limited discretization scheme, you need to select one of these suboptions: • OSPRE • SMART • van Leer With schemes of higher order than UDS1 (first order), the bounds for some variable types need modifying. This is because higher order methods that are not flux limited tend to oscillate, so may return negative values for variables types with a lower bound of zero. The typical changes required are: Variable type Action normally required g_Conc_Mol l_Conc_Mol i_Conc_Eq Set the lower bound to minus the upper bound. g_Loading l_Loading Set the lower bound to minus the upper bound. 5 Numerical Methods 227 i_Loading_Eq Molefraction Widen the upper bound to 2, and set the lower bound to minus the new upper bound. Fraction Widen the upper bound to 2, and set the lower bound to minus the new upper bound. Upwind Differencing Scheme 1 Upwind Differencing Scheme 1 (UDS1) is the preferred option because it is: • Good all-round performer. • Unconditionally non-oscillatory. • Unconditionally stable. • Cheapest user of simulation time. • Reasonably accurate. You increase accuracy by increasing the number of nodes. If you need greater accuracy with a minimal increase in simulation time, use the Quadratic Upwind Differencing Scheme. For Upwind Differencing Scheme 1 to achieve the same level of accuracy, the number of nodes has to be increased by a factor of two through four, leading to a similar increase in simulation time. In most cases, use Upwind Differencing Scheme 1 first. Derivation of Upwind Differencing Scheme 1 Upwind Differencing Scheme 1 is a first-order upwind differencing scheme, based on a first-order Taylor expansion. First-order (convection) term: z z i i i ∆ Γ Γ ∂ Γ ∂ 1 − − = Second-order (dispersion) term is approximated with a second-order accurate central differencing scheme: 2 1 1 2 2 2 z z i i i i ∆ Γ Γ Γ ∂ Γ ∂ − + + − = Evaluation of Upwind Differencing Scheme 1 Upwind Differencing Scheme 1 has the following advantages (+) and disadvantages (–): + Unconditionally stable (that is, it does not produce oscillations in the solution). + Least simulation time. – Only first-order accurate. – Gives a large amount of so-called “false” or numerical diffusion. (However, this problem decreases as the number of nodes is increased.) 5 Numerical Methods 228 Upwind Differencing Scheme 2 The Upwind Differencing Scheme 2 (UDS2) option predicts sharper fronts than Upwind Differencing Scheme 1, but the solution tends to oscillate. Derivation of Upwind Differencing Scheme 2 Upwind Differencing Scheme 2 is a second-order upwind differencing scheme. The first-order (convection) term: z z i i i i ∆ Γ Γ Γ ∂ Γ ∂ 2 4 3 2 1 − − + − = Second-order (dispersion) term is approximated with a second-order accurate central differencing scheme: 2 1 1 2 2 2 z z i i i i ∆ Γ Γ Γ ∂ Γ ∂ − + + − = Evaluation of Upwind Differencing Scheme 2 Upwind Differencing Scheme 2 has the following advantages (+)and disadvantages (–): + Second-order accuracy (because it includes a higher order derivative than first-order upwind schemes). – May produce some numerical oscillations. Central Differencing Scheme 1 Central Differencing Schemes 1 and 2 (CDS1 and 2) may be used if you choose to include axial dispersion in the problem. They give good accuracy with a reasonable CPU time requirement. In a series of test problems, Central Differencing Scheme 1 used less CPU time than Central Differencing Scheme 2, but produced greater oscillations. Derivation of Central Differencing Scheme 1 Central Differencing Scheme 1 is a second-order central differencing scheme and takes the form: First-order convective term: ∂Γ ∂z z i i = − + − Γ Γ ∆ 1 1 2 Second-order (dispersion) term is approximated with a second-order accurate central differencing scheme: 2 1 1 2 2 2 z z i i i i ∆ Γ Γ Γ ∂ Γ ∂ − + + − = 5 Numerical Methods 229 Evaluation of Central Differencing Scheme 1 Central Differencing Scheme 1 has the following advantages (+) and disadvantages (–): + Second-order accurate. – Numerical instabilities. To overcome these instabilities, include axial dispersion in the bed model. This may cause errors in simulation if there is little axial dispersion in the beds, but these errors are no more inconvenient than the false diffusion associated with upwind differencing. Using Central Differencing Scheme 1 with axial dispersion may reduce the number of nodes in the grid, allowing smaller simulation times. Central Differencing Scheme 2 Central Differencing Schemes 1 and 2 (CDS1 and 2) are useful if you choose to include axial dispersion in the problem. They can give good accuracy with a reasonable CPU time requirement. In a series of test problems, Central Differencing Scheme 2 produced smaller oscillations than Central Differencing Scheme 1, but used more CPU time. Derivation of Central Differencing Scheme 2 Central Differencing Scheme 2 is a second-order central differencing scheme and takes the form: First-order derivative: z z i i i i i ∆ Γ Γ Γ Γ ∂ Γ ∂ 12 8 8 1 1 1 2 − − + + + − + − = Second-order (dispersion) term is approximated with a second-order accurate central differencing scheme: 2 1 1 2 2 2 z z i i i i ∆ Γ Γ Γ ∂ Γ ∂ − + + − = Evaluation of Central Differencing Scheme 2 Central Differencing Scheme 2 has the following advantages (+)and disadvantages (–): + Third-order accurate. – Requires increased CPU time. Leonard Differencing Scheme The Leonard Differencing Scheme (LDS) is comparable with the Quadratic Upwind Differencing Scheme: • Gives the same instability problems. • Less accurate. 5 Numerical Methods 230 • Requires less CPU time. Derivation of Leonard Differencing Scheme The Leonard Differencing Scheme is a linear combination of the Central Differencing Scheme 1 scheme and a second-order, four point finite differencing scheme. This combination yields: First-order derivative: z z i i i i ∆ Γ Γ Γ Γ ∂ Γ ∂ 6 6 3 2 2 1 1 − − + + − + = Second-order (dispersion) term is approximated with a second-order accurate central differencing scheme: 2 1 1 2 2 2 z z i i i i ∆ Γ Γ Γ ∂ Γ ∂ − + + − = Evaluation of Leonard Differencing Scheme The Leonard Differencing Scheme has the following advantages (+) and disadvantages (–): + Accurate. – Known to produce oscillations under convective conditions. Quadratic Upwind Differencing Scheme If you need greater accuracy than the Leonard Differencing Scheme, with a minimal increase in simulation time, use the Quadratic Upwind Differencing Scheme (QDS). The Quadratic Upwind Differencing Scheme is the most accurate of all the methods for the same number of points. Derivation of Quadratic Upwind Differencing Scheme The Quadratic Upwind Differencing Scheme is based on quadratic interpolation, as opposed to the linear interpolation typical of many other schemes. First-order derivative: z z i i i i i ∆ Γ Γ Γ Γ ∂ Γ ∂ 8 7 3 3 2 1 1 − − + + − + = Second-order (dispersion) term is approximated with a second-order accurate central differencing scheme: 2 1 1 2 2 2 z z i i i i ∆ Γ Γ Γ ∂ Γ ∂ − + + − = The scheme is also referred to as QUICK (Quadratic Upstream Interpolation for Convective Kinematics). 5 Numerical Methods 231 Evaluation of Quadratic Upwind Differencing Scheme The Quadratic Upwind Differencing Scheme has the following advantages (+) and disadvantages (–): + Very accurate. + Little numerical dispersion. + Well suited to explicit (time) integration. – Oscillates under highly convective conditions. Advantages of Quadratic Differencing Scheme: Example Both the Quadratic Upwind Differencing Scheme and the Mixed Differencing Scheme are more accurate than Upwind Differencing Scheme 1. They both use about the same simulation time, which is typically about 25% more than Upwind Differencing Scheme 1. For Upwind Differencing Scheme 1 to achieve the same level of accuracy, you must increase the number of nodes for Upwind Differencing Scheme 1 by a factor of two through four, leading to an equivalent increase in simulation time. Aspen Adsim Breakthrough Plot 5 Numerical Methods 232 In this breakthrough plot, both the Quadratic Upwind Differencing Scheme and the Mixed Differencing Scheme have 20 nodes. Initially, Upwind Differencing Scheme 1 also had 20 nodes, which caused high numerical diffusion. The number of nodes in Upwind Differencing Scheme 1 is increased first to 50 and then to 100, to reduce this diffusion. The cost of this is increased simulation time for Upwind Differencing Scheme 1. Mixed Differencing Scheme The Mixed Differencing Scheme is more stable than the Quadratic Upwind Differencing Scheme, so may be the answer if the Quadratic scheme is unstable. Derivation of Mixed Differencing Scheme The Mixed Differencing Scheme is a combination of the Quadratic Upwind Differencing Scheme and the Upwind Differencing Scheme 1. First-order derivative: z z i i i i ∆ Γ Γ Γ Γ ∂ Γ ∂ 12 11 7 3 2 1 1 − − + + − + = Second-order (dispersion) term is approximated with a second-order accurate central differencing scheme: 2 1 1 2 2 2 z z i i i i ∆ Γ Γ Γ ∂ Γ ∂ − + + − = Evaluation of Mixed Differencing Scheme The Mixed Differencing Scheme has the following advantages (+)and disadvantages (–): + Accurate. Advantages of Mixed Differencing Scheme: Example The Mixed Differencing Scheme is a compromise between accuracy and stability. It uses slightly less simulation time than the Quadratic Upwind Differencing Scheme. 5 Numerical Methods 233 Axial Profile Plot This graph shows that Upwind Differencing Scheme 1 and Mixed Differencing Scheme are the most stable of all the methods, while Central Differencing Scheme 1 is the least stable. Note that, in cases with initially clean beds, problems can sometimes be more difficult to initialize with Mixed Differencing Scheme than with Upwind Differencing Scheme 1. Biased Upwind Differencing Scheme It is known that: • High-order central difference approximations tend to produce excessive oscillations upwind from a discontinuity. • Upwind difference schemes tend to produce excessive oscillations downwind of a discontinuity. Carver and Schiesser (1980) suggest that a correct combination of the two largely cancels out these upwind and downwind oscillations. From this, they developed a five-point biased upwind differencing scheme consisting of one point downwind and three grid points upwind. The approximation is a 5 Numerical Methods 234 combination of central and upwind difference approximations. Results suggest that the biased scheme performs better than classical approximations. Use Biased Upwind Differencing Scheme (BUDS) when the system is highly nonlinear, and where the presence of sharp fronts requires accurate solution. Because of its fourth-order accuracy, BUDS provides good accuracy for a smaller number of nodes than other lower-order approximations, while the extra CPU time is small. A potential drawback with BUDS is that, under certain circumstances, it also produces oscillatory behavior. If this happens, then all the other linear differencing schemes are also likely to suffer this problem, with the exception of UDS1. Derivation of Biased Upwind Differencing Scheme The fourth-order Biased Upwind Differencing Scheme is based on a fifth-order Taylor expansion. First order (convection) term: z z i i i i i i ∆ Γ Γ Γ Γ Γ ∂ Γ ∂ 1 1 2 3 3 10 18 6 + − − − + + − + − = Second order (dispersion) term is based on a second-order accurate central differencing scheme: 2 1 1 2 2 2 z z i i i i ∆ Γ Γ Γ ∂ Γ ∂ − + + − = Evaluation of Biased Upwind Differencing Scheme The Biased Upwind Differencing Scheme has the following advantages (+) and disadvantages (–): + Fourth-order accurate, so gives good accuracy for small node counts (so is especially suited to sharp fronts). + Simulation time only slightly larger than third-order schemes. + Good stability, and less likely to produce oscillations than other higher- order linear discretization techniques. – May produce oscillations under extreme conditions. Fromms’ scheme Fromms’ scheme is the sum of a first order and a second order scheme. It may produce instabilities for large ratios of time to spatial discretization step. Derivation of Fromms' Scheme First order (convection) term: ( ) { } { } ( ) z z i i i i i i i ∆ Γ Γ Γ Γ Γ Γ Γ 2 1 1 1 25 . 0 − − + − − − − + − = ∂ ∂ 5 Numerical Methods 235 Second order (dispersion) term is based on a second-order accurate central differencing scheme: 2 1 1 2 2 2 z z i i i i ∆ Γ Γ Γ ∂ Γ ∂ − + + − = Flux Limited Discretization Scheme Flux limited schemes combine the accuracy of higher order finite differencing schemes with the stability of the first order upwind differencing scheme (UDS1). Derivation of the Flux Limited Discretization Scheme The flux limited differencing scheme is: ( ) ( ) z r z r z z i i i i i i i i i ∆ Γ Γ Ψ ∆ Γ Γ Ψ ∆ Γ Γ Γ 2 1 1 1 1 2 1 2 1 − − − − − − − − + − = ∂ ∂ Here Ψ is the flux-limiter function and r the gradient ratio, calculated as: 1 1 − + − − = i i i i i r Γ Γ Γ Γ There are three versions of the flux-limiter function Ψ to choose from: • van Leer • OSPRE • SMART Second order (dispersion) term is based on a second-order accurate central differencing scheme: 2 1 1 2 2 2 z z i i i i ∆ Γ Γ Γ ∂ Γ ∂ − + + − = 6 Estimation with Aspen Adsim 236 6 Estimation with Aspen Adsim The chapter contains the following information about the Estimation Module: • Two Estimation Tools in Aspen Adsim 2004.1 • About the Estimation Module • Defining Estimated Variables in the Estimation Module • Steady State Estimation Using the Estimation Module • Dynamic Estimation Using the Estimation Module • Performing Estimation Using the Estimation Module • Converting Estimation Module Data • Recommendations when Using the Estimation Module Two Estimation Tools in Aspen Adsim 2004.1 Aspen Adsim 2004.1 has two estimation tools; one internal, and one external: • Estimation Module, which is the existing, internal estimation tool that has been available since Aspen Adsim 10.0 This chapter describes how to use the Estimation Module. • Estimation features built into Aspen Custom Modeler, which are now accessible from Aspen Adsim 2004.1: − Simulation engine data tables. − Automation (via any COM-compliant application). This new development links Aspen Adsim more tightly to the overall system. For more information, consult the Aspen Custom Modeler help files. To do this, first open the Aspen Adsim 2004.1 help file, navigate to the topic 'Two Estimation Tools in Aspen Adsim 2004.1', then use the available links. About the Estimation Module The Estimation Module has been in existence since Aspen Adsim 10.0, It provides an alternate estimation method to automation. The interface simplifies the entry of: • Estimated variables. 6 Estimation with Aspen Adsim 237 • Measured data. • Estimation solver options. The Estimation Module provides two main types of estimation: • Steady-state (fitting constant parameters to static data). • Dynamic (fitting constant parameters to time-dependent data). To access the Estimation Module: • On the Tools menu, click Estimation Module. This places an Estimation Module block on the flowsheet, provided one is not already there. The block opens to display the Estimation Module form. An indication is given if either previously defined data or results are available. The Estimation Module form contains: • Buttons for commonly performed tasks (these are on the right-hand side). • Tabs for different data types. This table lists the buttons on the Estimation Module form: Button name Description Store Store entered information in flowsheet block. Clear Clear all current data in the Estimation Module. Load Replace current data with data stored in flowsheet block. 6 Estimation with Aspen Adsim 238 Open Open version 10.0 estimation files. Run Execute estimation run. Help Open help page. Copy Table Copy currently visible table onto the clipboard. This table lists the tabs on the Estimation Module form: Tab name Description Estimated Variables Currently selected Fixed variables to be estimated and their results (if available). Experimental Data Measured experimental data. Estimation Solver Options Solver options associated with estimation. Defining Estimated Variables in the Estimation Module Use the Estimated Variables tab to define the variables that need to be fitted against experimental data. A list shows those variables that have a Fixed specification (assumed constant during the simulation), to a maximum of three levels of submodel hierarchy. The list shows only the valid variables that were available on opening. 6 Estimation with Aspen Adsim 239 To select a variable for estimation, select the adjacent box. All selected variables are added to the table. In the table, you can: • Modify the initial value (guess). • Change the units of measurement of the initial value. • View the result after a successful estimation run, along with other statistical information. Steady-State Estimation Using the Estimation Module Aspen Adsim typically uses steady-state estimation to fit isotherm parameters to static experimental data. For this purpose, the static_isotherm model is provided, which gives access to both the standard inbuilt isotherms and user defined isotherms. The standard flowsheet for static isotherm fitting contains only a static_isotherm block. You can add any number of experiments. Each experiment: • Can be included in the estimation run. • Has an individual experimental weighting (the default value being 1). Dynamic experimental data cannot used or entered. Manually Entering Steady-State Experimental Data To add steady-state experimental data: 1 In the Experimental Data tab, click the Add button. The New Experiment dialog box appears, where you select Steady-State experiment type. The dialog box looks different if experiments already exist in the Estimation Module. These must be of one type: steady-state or dynamic. So as an example, if you are adding to a set of steady-state experiments, then the dialog box only has the steady-state option. 2 Click OK to return to the Experimental Data tab. 6 Estimation with Aspen Adsim 240 This now has a list of the data sets, as well as extra tabs for adding experimental conditions and measurements. You can weight each experiment individually, the default being 1. 3 Define the experimental conditions using the variables added to the Fixed Variables list, for example the temperature, pressure and mixture composition. Only variables that are Fixed, and which are chosen for estimation, can be selected. The value of the Fixed variables can be modified. 4 Add measured data to the Measured Variables list. The following tips are useful: − You can add any Free, Initial or RateInitial variable to the list. − The units of measurement are those currently active. − Each experimental point can have an individual weighting applied, the default weighting being 1. − When additional experiments are added, the same variables can be copied from the currently active experiment. Steady-State Experimental Data from the Clipboard To import steady-state experimental data, for example from Microsoft ® Excel: 1 Create a new steady-state experiment, as described in Manually Entering Steady-State Experimental Data on page 6-239. The experimental name is used as the prefix for any copied experiment. 6 Estimation with Aspen Adsim 241 2 When creation is complete, you are prompted with a dialog box asking if you want to copy data from Microsoft ® Excel. Click the Yes button. 3 The Obtain Steady State Experiments From Clipboard dialog box appears, which requires copied data to function. Leave this dialog box untouched for now. 4 Open Microsoft ® Excel and copy the data set to the clipboard. The Estimation Module assumes that copied data takes this format: − Each row is a single experiment. − Columns represent experimental variables (normally, you list the manipulated variables first, followed by the measured variables). 6 Estimation with Aspen Adsim 242 5 Return to the Obtain Steady State Experiments From Clipboard dialog box, and click the Paste button. A populated table now appears in the dialog box. 6 For each column of data, mark whether it is a varied (manipulated) or measured variable. To do this, select the column and click either the Varied or Measured buttons. A list appears, from which you select the appropriate variable for the column. 7 Transfer the pasted data to the Estimation Module, either by clicking the Close button or the Process button. − The experiments created on processing the data are added to any other existing experiments in the Estimation Module. − If any bounds are exceeded, a further dialog box opens in which you can automatically readjust the bounds for all variables of a similar type in the simulation. Dynamic Estimation Using the Estimation Module Use dynamic estimation whenever the experimental data is time-dependent, for example the measured outlet composition over time. Aspen Adsim does not assume a specific flowsheet layout, or the use of specialized models. You can use a standard process flowsheet that includes any operational task. 6 Estimation with Aspen Adsim 243 Manually Entering Dynamic Experimental Data To add dynamic experimental data: 1 In the Experimental Data tab, click the Add button. The New Experiment dialog box appears, where you select the Dynamic experiment type. The New Experiment dialog box looks different if experiments already exist in the Estimation Module. These must be of one type: steady-state or dynamic. So as an example, if you are adding to a set of dynamic experiments, then the dialog box has only the dynamic option. 2 Click OK to return to the Experimental Data tab. 6 Estimation with Aspen Adsim 244 The Experimental Data tab now has a list of the data sets, as well as extra tabs for adding experimental conditions and measurements. You can weight each experiment individually, the default weighting being 1. 3 Define the experimental conditions using the variables added to the Fixed Variables and Initial Variables list, for example the temperature, pressure and mixture composition. Only variables that are Fixed, and which are chosen for estimation, can be selected. The value of the Fixed and Initial variables can be modified. 4 Add measured data to the Measured Variables list. − You can add any Free, Initial or RateInitial variable to the list. − A new tab is created for each measured variable, through which you define the time dependency. − When new variables are added to an experiment, it is possible to copy the same time points from the currently selected variable. − The units of measurement for any variable are those currently active. − Each experimental point can have an individual weighting applied (the default value is 1). Dynamic Experimental Data from the Clipboard To import dynamic experimental data, for example from Microsoft ® Excel: 1 Create a new dynamic experiment. When this is completed, the Paste Data button is enabled: 2 The Obtain Dynamic Measurements for Experiment DynExpt From Clipboard dialog box appears, which needs copied data to function. Leave this dialog box untouched for now. 6 Estimation with Aspen Adsim 245 3 Open Microsoft ® Excel and copy the data set to the clipboard. The Estimation Module assumes that copied data takes this format: − Each row represents a time point. − Columns represent experimental variables. 4 Return to the Obtain Dynamic Measurements for Experiment DynExpt from Clipboard dialog box and click the Paste button. A populated table now appears in the dialog box. 6 Estimation with Aspen Adsim 246 5 For each column of data, mark whether it is the time of measurement, or the measured variable. To do this, select the column and click either the Time or Measured buttons. For measured variables, a list appears, from which you select the appropriate variable for the column. 6 Transfer the pasted data to the Estimation Module, either by closing the dialog box, or by clicking the Process button. − The experiments created on processing the data are added to any other existing experiments in the Estimation Module. − If any bounds are exceeded, a further dialog box opens in which you can automatically readjust the bounds for all variables of a similar type in the simulation. 6 Estimation with Aspen Adsim 247 Performing Estimation Using the Estimation Module To perform an estimation using the Estimation Module, click the Run button and leave the module open during the run. You cannot interact with the module during a run. After a successful estimation run, the module retrieves the results and stores them in the Estimation Module block on the flowsheet. The following results are available: • Final estimated value • Standard deviations • Correlation matrix • Covariance matrix Converting Estimation Module Data To convert from using the (old) Estimation Module to the (new) estimation tools available in Aspen Custom Modeler, use the script Convert_EstMod located in the Aspen Adsim library Script folder. To use the script: 1 Open the input file you want to convert. 2 Double-click the script in the library. After the script has converted the data, the Estimation Module block disappears from the flowsheet. To view the experimental data, from the Tools menu click Estimation, which accesses the new estimation system. 3 Save the input file. Recommendations When Using the Estimation Module The following tips will help you get the best out of the Estimation Module: • To check that the initial values used for the variables to be estimated give a converged solution, complete these two steps: − Execute a steady-state run for steady-state estimation. − Execute an initialization run for steady-state estimation. These two steps are important as they ensure that the first iteration of the estimation solver will succeed. • Use estimation solver tolerances that are greater than the general solver options. • If simulation convergence gives rise to multiple solutions, try a different initial guess. • Try to measure variables that are sensitive to the estimated variables. Singular convergence normally indicates an insensitive measured variable. 6 Estimation with Aspen Adsim 248 • Check the bounds of the estimated variables. For example, ensure the lower bound of a strictly positive isotherm parameter is zero. • The fit is only as accurate as the range of data presented by the experiments, so include more than one set of experimental data. For example, with a single data set, the estimated value is useful only for the operating range of the data. 7 Cyclic Operation 249 7 Cyclic Operation Many adsorption processes operate in a cyclic manner. Each cycle is described by a series of single or multiple sequential steps or discrete events. When simulating a cyclic process, you must be able to specify when certain events are going to occur. Aspen Adsim contains a Cycle Organizer for you to define cyclic operations. This chapter contains information on the following topics: • Cyclic Operations in Aspen Adsim 2004.1 • About the Cycle Organizer • Opening the Cycle Organizer • Cycle Organizer Window • Step Control • Step Variables • Interaction Control • Additional Cycle Controls • Additional Step Controls • Generating Cyclic Tasks • Activating and Deactivating Tasks • Cyclic Reports Cyclic Operations in Aspen Adsim 2004.1 In Aspen Adsim 2004.1, the Configure form has been extensively modified to allow for many new features. Input files created in previous releases are still compatible. When you open the Cycle Organizer, the old cycle definitions are automatically converted to match the new system, and the old cyclic task is automatically deleted. You then need to regenerate the cyclic task. About the Cycle Organizer The Cycle Organizer lets you rapidly create the steps that define a cyclic process. Use it to: • Create any number of steps. • Define the step termination event. • Manipulate flowsheet variables for a given step. 7 Cyclic Operation 250 • Generate a cyclic task based on the Task Language. • Distribute cycle information to other flowsheet blocks through global variables. • Store multiple cycle definitions. • Control variable recording and automated snapshots. • Execute V(isual)B(asic) scripts for additional calculations and control. Here is some more information about the Cycle Organizer: • The main Configure form gives the status of the system and the active state of the cyclic task. • All entered data is stored in the block on the flowsheet. This allows the data to be saved with the flowsheet input file. • Only one Cycle Organizer block is allowed on the flowsheet. • When you configure the flowsheet for cyclic operation, it is advisable to configure it as if it is about to execute the first step of the cycle. • On adding a new step, you are asked two questions: − Is the new step to be placed before or after the currently selected step? − Is the information to be copied from the currently selected step into the newly created one (to act as a template). Opening the Cycle Organizer To access the Cycle Organizer: • From the Tools menu, click Cycle Organizer. If a Cycle Organizer block does not exist on the flowsheet, one is automatically placed on the flowsheet and the Cycle Organizer window appears. The block looks like this: To open Cycle Organizer block present on the flowsheet, use either the Tools menu or double-click the flowsheet block. Cycle Organizer Window The Cycle Organizer window looks like this: 7 Cyclic Operation 251 The Cycle Organizer toolbar gives access to the various fields and controls needed to define and generate a cyclic task. The table lists the main buttons on the toolbar, their purpose, and the options available on their drop-down menus. (The Print and Online button are not described.) Toolbar button Purpose Options Cycle Cycle controls, such as creating and activating cycles. Cycle Options New Cycle Generate Task Activate Cycle Delete Cycle Step Step controls, such as modifying and inserting steps. Control Manipulated Interactions Other Add/Insert Step Delete Step Variable (available only if you selected Manipulated from the Step menu) Adding or Deleting variables. Add Variable/s Delete Variable/s 7 Cyclic Operation 252 Step Control There are three ways to define the termination of a given step: • Explicit time, where termination is linked to elapsed time. • Discrete event, where termination is linked to an event, such as when a vessel has reached a given pressure. • Dependent on another step. If the step is the second half of an interaction, the step is controlled by the elapsed time for the interaction’s first half. This ensures step symmetry within the cycle. To access the step control panel: • In the Cycle Organizer window, click the Step toolbar button; or from the neighboring drop-down menu, click Control. Time Driven Step Time Driven Step is the most common step control method. Here, the step control is a fixed elapsed time; for example, the step is set to terminate after 60 seconds. The step time remains constant from cycle to cycle. To select a time-driven step control: • Enable the Time Driven radio button and give the step time in the specified units: When the cyclic task is generated, the value is automatically converted to the base time units assumed by the models. Likewise, should the time unit of measurement change, any variable that is ramped in the current step, and any dependent or interacting step, automatically have their times and time units modified. Discrete Event Driven Step Event-driven step controls are implicit events, for which the time of occurrence is unknown. For example, "the step will terminate when a vessel has reached a given pressure". To define the event, enable one of these three radio buttons: 7 Cyclic Operation 253 • Value ÷ a comparison between a Free variable and a value defines the event. • Variable ÷ a comparison between a Free variable and another variable defines the event. • Expression ÷ a complex expression defines the event. Discrete Event Driven Step: Variable/ValueComparison With Value as your choice of step control, a comparison between a Free variable and a value defines the event. To define the event: 1 Enable the Value radio button. 2 Specify the monitored variable, either by selecting it from a list of variables, or by typing the exact name. 3 Select a comparison operator from: == Equal to <> Not equal to <= Less than or equal to >= Greater than or equal to 4 Give the value for comparison, in the unit of measurement of the monitored variable. The unit of measurement can be modified. 7 Cyclic Operation 254 Discrete Event Driven Step: Variable/Variable Comparison With Variable as your choice of step control, a comparison between two variables defines the event. The procedure for this is similar to the Value option, described in the previous subsection, except that you must specify two variables: • Monitored variable. • Variable to make the comparison with. Discrete Event Driven Step: Complex Expression With Expression selected, a complex expression that is built up from logical operators defines the event. This is useful when the step termination depends on a true or false condition. To define the expression: 1 Enable the Expression radio button. 7 Cyclic Operation 255 2 Double-click in the Expression text box. The Expression Builder dialog box appears, where you create expressions: 3 Insert typical operations for the comparisons, using the buttons provided. A searchable list is provided to ensure that you insert only valid variables into the expression. Note: No error checking is provided for the expression entered, so take care to enter values that are within the valid bounds and in the compared variable's base unit of measurement. Discrete Event Driven Step: Step Dependent The final method of step control is to make the step dependent on a previous step. To use this option: 1 Enable the Step dependent radio button. 2 In the neighboring drop-down menu, specify the dependent step. Only steps that occur before the current step can be selected. Likewise, this option is not available for the first step in any given cycle. If the step for which a dependency is being defined, is the start of a chain of step interactions, all interacting steps assume the elapsed time and time unit 7 Cyclic Operation 256 of measurement of the dependent step. Likewise, all ramp times will be checked and converted to the new time unit of measurement. Step Variables Within each step of a cycle, different variables may be modified. These variables may control, for example: • Feed condition • Valve opening • Heater duty The variable change may be stepped or a gradual/ramped change. To access the list of manipulated variables: • From the Step button's drop-down list, click Manipulated. Adding Step Variables To add a new manipulated step variable: 1 Click the Variable button on the toolbar; or from its drop-down list, click Add Variable/s. The Variable Selector dialog box appears, which lists the available fixed and initial variables that have not already been selected in the current step. 2 Select a variable using one of these actions: − Double-click on the variable in the list. − Type the name of the variable in the text box at the top of the dialog box (a dynamic search takes place during typing). − Select multiple variables, using either the SHIFT or CTRL key. − Use wildcards in the text box to reduce the list size and then select. Valid wildcards are: * for any character combination. ? for a single character place holder. Note the following points: • There is no limit to the number of variables that can be manipulated in a given step. • You can access all variables in the flowsheet, except global variables. 7 Cyclic Operation 257 • Selected variables are listed alphabetically in the table. Removing Step Variables You remove step variables directly from the Cycle Organizer window. To remove a single manipulated variable: 1 Select the row of the required variable. 2 From the Variable button's drop-down menu, click Delete Variable/s. To remove a series of variables in contiguous rows, select the rows to be deleted. Changing Step Variable Values For each defined manipulated variable, the following fields are given: Field Description Value Value of the variable for the current step. A check is made to ensure the value is within the bounds for the variable in the current unit of measurement. If a bound is violated, you can automatically adjust bounds for all variables of the same type. Units Unit of measurement. To modify this, double-click the field and a drop-down menu appears. On changing the unit of measurement, any values provided for the Value and Target fields are automatically recalculated. Spec Specification of the variable. This cannot be modified. Ramped Variable to be ramped. Double-clicking this field displays a drop-down menu, where you choose between no ramping, linear ramping or S-shaped ramping. Target Target value of the ramp. This is visible only for ramped variables. For ramped variables, the number in the Value column is used as the initial starting point of the ramp. Time Elapsed time of a ramp. This is visible only for ramped variables. For time-driven steps, the value entered here cannot be greater than the step time. 7 Cyclic Operation 258 With discrete event-driven steps; if the event occurs before the ramp has completed, the step terminates when the ramp has completed. There is no limit to the number of variables that can be ramped in a given step. Interaction Control If the flowsheet contains interaction units (see Single Bed Approach in Chapter 7), the Step toolbar's drop-down menu contains an Interactions option: This option accesses the Interaction Control table, which lists the interaction units and the currently defined step interactions. Defining a Step Interaction To define a step interaction: • Double-click on the step containing the source material, and from the drop-down list, select the step in which the material is returned. Note the following points about step interactions: • Once you select an interacting step, the target cell updates automatically. • The last row also shows the root defining step for any interactions. This step defines the elapsed time for all associated interacting steps. • Interaction numbers are: − Positive for forward interactions, where material is accepted early in the cycle and returned later in the same cycle. − Negative for reverse interactions. • A single interaction unit is not restricted to a single set of interacting steps; it can be reused for any number of interacting step sets. However, only a single quantity of material can be accepted or returned for a given step. For this reason, if you want to transfer multiple amounts of material in a step, you must use more than one interaction. 7 Cyclic Operation 259 Deleting Interaction Steps To delete an interaction: • From the drop-down list, click None. Adding Extra Interaction Steps If you insert additional steps before or between existing interacting steps, the interaction numbers are renumbered automatically. For example, if you insert a step between the interacting steps 1 and 3 for unit D1, the new interacting steps are now 1 and 4. Interacting Steps and Time Controls Once you have defined an interacting pair of steps, the second half of the pair is forced to be time controlled. This ensures time symmetry and maintenance of the material balance between interacting steps. The time control is based on: • Fixed time for a time driven step. • Elapsed time for an event driven step. The Cycle Organizer continually checks the root defining steps of all interactions, to ensure time controls are in place. Explanation of Why Time Controls Are Imposed A single step cannot receive material from both a time driven step, and one that is event driven; nor from two similarly controlled steps that use different times or events. This is because the duration of an event driven step may change from cycle to cycle, so the elapsed time can vary. For example, in a five-step process using three interaction units, step 1 is time driven, and step 2 event driven. Interaction unit D1 has interactions 1→3 and 5→4; interaction unit D2 has a single interaction 2→4; interaction unit D3 has a single interaction, 3→5. The table suggests that step 3 is time driven, and step 4 is time driven based on the elapsed time of the event in step 2. In step 5, however, we have two 7 Cyclic Operation 260 interactions: one with step 4 (assumed event driven) and the other with step 3 (assumed time driven). In this instance, the step that occurs first is assumed as the root defining step. Thus steps 2 through 5 are all dependent on the elapsed time of step 1. Additional Cycle Controls To access additional cycle controls: • Click the Cycle toolbar button, or from the button’s drop-down menu, click Cycle Options. The additional controls provided for the overall cycle include: • Number of cycles to execute. • Record frequency. • End of cycle snapshots. • Cycle steady-state testing. Maximum Cycles Box Use the Maximum Cycles box to specify the maximum number of cycles to execute in a given run. It is coupled to the Record Initial and Record Frequency options. Assuming you have set the run options for indefinite running, the simulation automatically pauses once the given number of cycles has been performed. Click the Play button again to execute a further batch of cycles. 7 Cyclic Operation 261 Record Initial and Record Frequency Boxes Use the Record Initial box to specify the number of cycles at the start of the simulation for which the record attribute remains on. This applies only to variables that have it set to true and time equals zero. Use the Record Frequency box to specify the cycle at which the record attributes are switched off and then back on for a single cycle. • If you set these two options to 1, the variables are recorded for all cycles. • If you set Record Initial to 5, Record Frequency to 10, and the Maximum Cycles to 25, variables are recorded only for cycles 1, 2, 3, 4, 5, 15 and 25. This significantly reduces the size of the plot data file. When using these options, the maximum number of cycles is always automatically modified to ensure the last cycle executed is recorded. Take Snapshot Box To automatically take a snapshot at the end of every cycle (or cycles based on the settings for Record Initial and Record Frequency): • Select the Take Snapshot at End of Cycle box. Taking a snapshot at the end of each cycle is useful if you want a material balance at points during the run. The simulator uses the snapshots to rewind to a time point in history. Cyclic Steady State Testing Box Select the Cyclic Steady State Testing box to test when the dynamic cyclic simulation has reached a periodic, cyclic, steady state. You need to set a tolerance for this option to work. During the simulation, the total loading and total solid temperature at the end of a cycle are compared to the value of the previous cycle. When their relative difference is below the test tolerance, the simulation pauses. 7 Cyclic Operation 262 If the Record Initial and Record Frequency are not equal to 1, the simulation automatically pauses after the next recorded cycle. Additional Step Controls To access the additional step controls: • Click the Step toolbar button, or from the button’s drop-down menu, click Other. The additional controls provided for the overall cycle include: • Execution of a named script. • End of step snapshots. Execute End of Step Script Box Select this box to run a flowsheet level script at the end of a step, for every cycle. This is useful for executing external calculations or runtime logging. Specify the script in the Script Name box. If the script does not exist during cyclic task generation, a template script with the name provided is automatically created. Take Snapshot at End of Step Box To automatically take a snapshot at the end of step for every cycle (or cycles based on your settings for Record Initial and Record Frequency settings): • Select the Take a Snapshot at End of Step box. Taking a snapshot at the end of each cycle is useful if you want a material balance at points during the run. The simulator uses the snapshots to rewind back to a time point in history. 7 Cyclic Operation 263 Generating Cyclic Tasks Once a new cycle has been defined, or changes made to an existing definition, the cyclic task needs generating before the simulation can be run. This is indicated in the Cycle Organizer status bar, as follows: To generate the cyclic task: • From the Cycle button's drop-down menu, click Generate Task. View the Cycle Organizer status bar to see how the generation is progressing: • You see when the cyclic task has been successfully generated (should there be any errors, these will be given in the simulation messages window). • You see when there is another inactive cycle. Note the following points: • If any variable in a step is ramped, additional tasks are generated. The "callable" task contains a single ramp statement. The names of these additional tasks are prefixed by the main task name, followed by an index indicating the step and the manipulated variable. • Generated cyclic tasks are created using the Task Language. You can open and edit tasks using this language, but any changes you make are lost if you regenerate the task using the Cycle Organizer. • Only a single cycle definition can be active. If there is more than one cycle description stored within the Cycle Organizer, whenever it is opened it will always display the currently active cycle (or the first cycle definition should no cycle be active). Activating and Deactivating Cyclic Tasks Use the Cycle Organizer to activate and deactivate cyclic tasks. If cyclic tasks have been generated for all cycle definitions stored within the Cycle Organizer, you must not activate and deactivate the task by double- clicking the task in the Flowsheet section of Simulation Explorer. To activate a cycle: • With the cycle currently inactive , from the Cycle drop- down menu, click Activate Cycle. To deactivate a cycle: 7 Cyclic Operation 264 • With the cycle currently active , from the Cycle drop- down menu click Deactivate Cycle. This also deactivates any other currently active cycle definition. Cyclic Reports Cyclic reports are now available that provide information on the quantity and quality of material passing along a stream during any step, and any cycle. In overview, you are picking out information about particular steps and cycles, from the larger Block and Stream reports. Cyclic reports therefore require: • A Cycle Organizer on the flowsheet. • Block and Stream reporting enabled. There are two types of Cyclic report: • Cyclic Stream reports • Cyclic Recovery reports Preparing Aspen Adsim for Cyclic Reporting Before you start your simulation, you need to enable Block and Stream reporting, and specify when to stop recording information for the Cyclic report. To prepare for cyclic reporting: 1 From the Tools menu, point to Report and then click Reporting. The Flowsheet Reporting dialog box appears: 2 Select the Enable blocks/streams reports box, and underneath, state the number of recorded cycle histories. 3 Click OK. When you now run the simulation, step-by-step and cycle-by-cycle information is recorded, until the number of cycle histories is reached (this is 11 cycles in our example). 7 Cyclic Operation 265 Cyclic Stream Reports The Cyclic Stream report gives the following information, based on either a total cycle or on an individual step, for each direction of every Aspen Adsim stream on the flowsheet: • Total material passed. • Cycle or step averaged flowrate. • Total of component passed. • Cycle or step averaged component composition. • Total energy passed. • Cycle or step averaged enthalpy. It also gives the start time, end time and the elapsed time of the selected cycle or step. Creating Cyclic Stream Reports You create Cyclic Stream reports for either a cycle or a step. To create a Cyclic Stream report: 7 Cyclic Operation 266 1 From the Aspen Adsim Tools menu, point to Report and click Stream Report. The Cyclic Report dialog box opens. You now build the report to view it. 2 Enable either the Cycle radio button or Step radio button. 3 In the Cycle number list, select a cycle number. For a step report, you also need to select a step. 4 Click the Build button, or from its drop-down menu click Stream Report. This builds and then displays the Cyclic Stream report. Cyclic Stream reports can be: • Copied to the clipboard, where additional information is added, such as the date and time, and input file name. • Printed to the default printer, which prints only the currently visible columns of the report. The report can be resized. Cyclic Recovery Reports The Cyclic Recovery Report gives the following recovery information for every product stream with respect to every feed stream: • Total material • Individual component • Total energy 7 Cyclic Operation 267 Creating Cyclic Recovery Reports You create Cyclic Recovery reports for either a cycle or a step. To create a Cyclic Recovery report: 1 From the Aspen Adsim Tools menu, point to Report and click Stream Report. The Cyclic Report dialog box opens. You now build the report to view it. 2 Enable either the Cycle radio button or Step radio button. 3 In the Cycle number list, select a cycle number. For a step report, you also need to select a step. 4 From the Build button's drop-down menu, click Recovery Report. This builds and then displays the Cyclic Recovery report. 8 Flowsheeting 268 8 Flowsheeting This chapter contains information on: • About model types • General model types • Reversibility • About flowsheets in Aspen Adsim • Types of Flowsheet in Aspen Adsim • Single bed approach • Pressure interaction diagram • Interactions • Specifications for flowsheets • Physical properties • Connecting to Aspen Dynamics flowsheets About Model Types For reversible flow within an Aspen Adsim flowsheet, you need to make some modeling assumptions that define the type of flowsheet interactivity. These assumptions are broadly similar between gas, ion-exchange and liquid systems. The models in the Aspen Adsim library support these flow regimes: 8 Flowsheeting 269 General Model Types The general model types available in Aspen Adsim are: Model type Used in Description Typical models Non-Reversible Gas Ion-Exchange Liquid Assumes that there is no flow reversal in the model. Material flow is from Process_In to Process_Out. All models (except for adsorbent/resin beds) can be configured in this way. Reversible Flow Setter Gas Relates pressure drop across the model to the flowrate through the model. Able to specify the flowrate directly. The model does not contain any material holdup, but may contain a momentum balance. Typical models: gas_bed, gas_valve, gas_ramp. Reversible Pressure Setter Gas Accumulates material and energy (adsorbent beds are an exception). The pressure at each port is equated directly to the internal pressure. Able to specify the pressure directly. . gas_tank_void, gas_buffer_intera ction, gas_feed, gas_product. Non-Reversible Delay Gas Used as part of an interaction train. Stores stream information or passes downstream/upstream pressure information. gas_valve, gas_ramp, gas_interaction. Reversible Ion-Exchange Liquid Feed or product train to allow for reversible flow. Feeds, products, valves, tanks, distributors. Reversibility You get reversibility within the flowsheet by categorizing the models into certain types. Consider the gas phase system as a typical example: The usual modeling approach is to equate the outlet condition to either the internal condition (a tank for example) or inlet condition (a valve for example). 8 Flowsheeting 270 Y 1 T 1 P 1 H 1 Y 2 T 2 P 2 H 2 F = ƒ(P s1,out ,P s2,in ) Y s1,out = Y s2,in T s1,out = T s2,in H s1,out = H s2,in Y s1,in = Y 1 T s1,in = T 1 P s1,in = P 1 H s1,in = H 1 Tank1 Valve Tank2 Y s1,in = Y s1,out T s1,in = T s1,out P s1,in = P s1,out H s1,in = H s1,out Y s2,in = Y s2,out T s2,in = T s2,out P s2,in = P s2,out H s2,in = H s2,out S1 S2 This approach works if the pressure in tank 1 is greater than, or equal to the pressure in tank 2. To allow for a reversed pressure profile, the stream condition must not be directly related to the tank condition, otherwise the model becomes singular. This is where the model type is introduced. To allow for reverse flow between tanks 1 and 2, the stream condition needs to be determined not by the tanks, but by the unit in-between, the valve unit. The valve uses the following information to ensure the appropriate flow condition is selected: • Internal composition of the tanks, from the tank units. • Pressure difference across the valve itself. We now introduce the concept of flow setter models and pressure setter models: • As the valve model sets the stream conditions and determines the flow, the underlying model is described as a “flow setter”. • The tanks accumulate only material and energy, and relate their pressure to this accumulation, so the underlying model is described as a “pressure setter”. To finally accomplish this task, the streams must carry information, such as the internal condition of the pressure setters (the tanks), as well as the actual stream condition. 8 Flowsheeting 271 Y 1 T 1 P 1 H 1 Y 2 T 2 P 2 H 2 F = ƒ(P s1,out ,P s2,in ) Y s1,out = Y s2,in T s1,out = T s2,in H s1,out = H s2,in If P s1,out >= P s2,in Then Y s1,out = Y s1,out,r Else Y s2,in = Y s2,in,r If P s1,out >= P s2,in Then T s1,out = T s1,out,r Else T s2,in = T s2,in,r If P s1,out >= P s2,in Then H s1,out = H s1,out,r Else H s2,in = H s2,in,r Y s1,in,r = Y 1 T s1,in,r = T 1 P s1,in = P 1 H s1,in,r = H 1 Tank1 Valve Tank2 Y s1,in = Y s1,out Y s1,in,r = Y s1,out,r T s1,in = T s1,out T s1,in,r = T s1,out,r P s1,in = P s1,out H s1,in = H s1,out H s1,in,r = H s1,out,r S1 S2 Y s2,in = Y s2,out Y s2,in,r = Y s2,out,r T s2,in = T s2,out T s2,in,r = T s2,out,r P s2,in = P s2,out H s2,in = H s2,out H s2,in,r = H s2,out,r Y s2,out,r = Y 2 T s2,out,r = T 2 P s2,out = P 2 H s2,out,r = H 2 By using an alternating sequence of pressure and flow setters, you can model process trains where reversibility may occur, without causing singularities. For adsorbent and resin beds, it is important that the discretization scheme used to solve the partial differential equations can cope with flow reversal at either the inlet and outlet boundaries, or internally. 8 Flowsheeting 272 1 2 n-1 n 1 2 n-1 n 1 2 n-1 n Forward Direction Reverse Direction Discretization Nodes Outlet Boundaries Inlet Boundaries Process Out Process Out Process In Process In 1 2 n-1 n Outlet Boundaries 1 2 n-1 n Inlet Boundaries The scheme used within the adsorbent and resin models assumes a constant discretization mesh, with the boundaries evaluated at each local node with respect to the flow and/or pressure gradient. This approach allows for the chosen discretization method to automatically switch between forward and backward differencing. About Flowsheets in Aspen Adsim You create Aspen Adsim flowsheets either interactively through the graphical user interface, or from a prepared template. The available models are classified into three main phases or types: • Gas • Ion-exchange • Liquid You can mix these phase types on a flowsheet, subject to these restrictions: • Use a common global component list. 8 Flowsheeting 273 • Interconnect model blocks using only the appropriate stream type for the phase or model type. The only exception is a gas phase model block, which can contain a liquid outlet to remove any condensed material. The flowsheeting environment is very flexible, allowing you to create any process flowsheet subject to these restrictions: • Overall model size versus simulation speed. • Available models/process operation descriptions. • Hardware limitations. The flowsheet scope should ideally cover only the adsorbent columns and any immediate equipment required to operate the process. When creating new problems, it is good practice to start with a simple flowsheet to ensure the column model assumptions are correct. Once validated, you can then add further complexity, such as column deadspaces, interaction units, other columns and cyclic behavior. Connectivity on Flowsheets You must use the correct material connection (stream) when connecting model blocks on the flowsheet: Model prefix Stream type gas_ gas_Material_connection ionx_ ionx_Material_Connection liq_ liq_Material_Connection Create the connections by dragging and dropping from the library to the flowsheet. Connectivity is enforced by the port types used by each library model and material connection: Model prefix Port type gas_ g_Material_Port ionx_ i_Material_Port liq_ liq_Material_Port So, a model with the prefix 'gas_' accepts only connections made with a gas_Material_Connection. The ports and material connections pass the following information between model blocks (depending on phase or type): • Molar/Volumetric flowrate • Molefraction composition/Component concentration • Molar density • Absolute temperature • Pressure • Specific enthalpy 8 Flowsheeting 274 Controllers are not connected using material connections; they use a special stream type called ControlSignal instead. ControlSignal connects a single exposed variable from one model block to another single exposed variable in the same or another model block. Templates Predefined process templates are available through the Template Organizer. To access this: • From the File menu, click Templates. The Template Organizer appears: The available templates feature: • Recommended solver options. • Runtime options set to the appropriate time units. • Default component list configured for use with Fortran-based physical properties and populated with dummy components. • Flowsheet layouts based on standard descriptions. Before copying a template to the current working directory, a name is requested, which is then used for both the input file and the directory that houses all the files for the new problem. Demonstrations All of the examples in the Aspen Adsim casebook come as part of the standard installation. These casebook examples are a further source of process templates. 8 Flowsheeting 275 To access the example files: • From the File menu, click Demonstration Organizer. The Demonstration Organizer appears: To open a casebook example: • Select the problem of interest and click Open. You are told if a set of files will be copied, or if a copy of the example already exists. Types of Flowsheet in Aspen Adsim There are three types of flowsheet in Aspen Adsim: • Simple flowsheet • Intermediate flowsheet • Full flowsheet Types of Flowsheet: Simple Flowsheet The simple flowsheet is the smallest workable flowsheet to operate an adsorbent/resin bed. It is a recommended starting point for new simulations. Use it to: • Ensure the absorbent/resin bed works effectively. • Simplify testing of key parameters and configuration assumptions. The simple flowsheet typically includes the following unit operations for all phases or types: 8 Flowsheeting 276 • Feed boundary unit. • Adsorbent/resin bed (can contain any number of layers). • Product boundary unit. Adsorbent or Resin Bed Product Boundary Feed Boundary Intermediate Flowsheet The intermediate flowsheet is useful for simulating non-interacting adsorption cycles. It builds upon the simple flowsheet by including (except for ion- exchange): • Adsorbent bed deadspaces or voids. • Feed and product valves. 8 Flowsheeting 277 Adsorbent Bed Product Boundary Feed Boundary Top Deadspace (Tank) Bottom Deadspace (Tank) Product Valve Feed Valve Use the intermediate flowsheet to simulate: • Co-current or counter-current adsorption. • Repressurization and depressurization. • Purge using streams of different compositions. Full Flowsheet The full flowsheet is the final step in flowsheet complexity. It builds on either the simple or intermediate flowsheet by including: • Interactions with other adsorbent/resin beds. • Additional feed or product trains. • Intermediate buffer tanks or pressure receivers. • Feed and product pumps. To simulate interacting beds, there are two levels of overall model complexity: 8 Flowsheeting 278 • Single bed approach — this uses a single bed to simulate processes containing more than one bed. • Rigorous multi-bed — this simulates all adsorbent/resin beds with interconnecting units. Single Bed Approach An inherent problem when modeling an adsorption system is the number of equations to be solved, the majority of which are discretizations of the partial differential equations. One way of modeling adsorption systems that comprise multiple adsorbent/resin beds, is to use the single bed approach. For the method to be valid: • Each adsorbent/resin bed (or series bed train) must be identical. • Each adsorbent/resin bed must undergo the same steps in a given cycle. If these assumptions are met, then you can rigorously model a single “real” adsorbent/resin bed and store any information (material) that would normally be sent to an interacting bed. This stored information can then be replayed back to the real bed later in the cycle. The single bed approach retains the accuracy of the final results (see the spreadsheet included within the installation): • Same average purity. • Same number of cycles to achieve cyclic steady-state. Simulation speed is also improved: • Fewer equations (due to fewer beds). • Less data to be communicated between the client (GUI) and the server (simulation engine). Pressure Interaction Diagram Before creating a flowsheet, it is important to sketch out the pressure interaction diagram for your process. This diagram is a graph of pressure versus time, with material interactions overlaid. In the following example, a simple three step Oxygen VSA process is examined. The process uses three identical adsorbent beds, each undergoing the following steps in a cycle: • Production at high pressure with some product that counter-currently repressurizes another bed. • Evacuate to low pressure. The material is sent to waste. • Repressurize using product material. The Pressure-Interaction diagram for the process looks similar to this: 8 Flowsheeting 279 P t Bed 1 Bed 2 Bed 3 60 180 120 If the single bed approach is applied, using Bed 1 as the real bed, the interactions would look like this: 8 Flowsheeting 280 P t Bed 1 Bed 2 Bed 3 60 180 120 Record Replay Flowsheet Scope Material profile information from step 1 can be stored and then replayed back to Bed 1 during step 3. The final pressure-interaction diagram for the new single bed process looks like this: 8 Flowsheeting 281 P t Bed 1 60 180 120 Interactions When material from a step is used by another step, this is called an interaction. Aspen Adsim handles any number of interactions in an adsorption process cycle. Using the Oxygen VSA example, the pressure-interaction diagram was as follows: P t Bed 1 60 180 120 The three, 60 second duration steps were: • Step 1 — 0 through 60 seconds — there was production with some material used to repressurize another bed. • Step 2 — 60 through 120 seconds — there was counter-current evacuation to waste. • Step 3 — 120 through 180 seconds — there was counter-current repressurization with product material. In this example there is only one interaction, a top-to-top interaction between steps 1 and 3. To create this interaction when using the single bed approach, you must use an interaction model to simulate the bed that the real modeled bed is interacting with. In gas systems, for example, it is named gas_interaction. The interaction model records one or more of the following profiles (dependent on the phase of the system): • Flowrate • Composition or concentration • Density 8 Flowsheeting 282 • Temperature • Pressure • Specific enthalpy To use the gas_interaction model, for example: • The inlet stream must always be connected to a valve (configured as a non-reversible delay) whose inlet is connected to point on the flowsheet where material is withdrawn. The valve passes the interaction unit information about the upstream (or relative bed) pressure. Typically, the valve inlet is connected to a gas_tank_void model that is being used to simulate an adsorbent bed deadspace or void. • The outlet stream defines where material is returned to the flowsheet. No valve is required on the outlet stream. Real Bed Scope Store Profile Real Bed Scope Replay Profile Valve Present In Scope Valve Not Present In Scope Store Replay Use the withdrawal and return point for material, to define whether the interaction is: • Top-to-top • Top-to-bottom • Bottom-to-bottom • Bottom-to-top So, for the Oxygen VSA example, the following additions are needed to create a top-to-top interaction off the real adsorbent bed’s top void. 8 Flowsheeting 283 Tank Valve Interaction From bed To product Notes: o The interaction units use the Delay function. o The accuracy of the delay function is dependent on the communication interval, not the integration step size. It is recommended that you have at least four communication points within the shortest step. o If the simulation is closed or a snapshot re-used, the delay buffer is emptied and all historical profile information is lost. o The snapshot does not store delay information. Specifications for Flowsheets This section gives information on: • Solver Options • Run Time Options • Model Specification • Consistency and Model Definition Checks Solver Options If you create a flowsheet that is not based on a template, the following solver options are recommended as good initial starting points: General Tab: Solver Options The recommended solver options are: 8 Flowsheeting 284 Option Value Absolute Variable Tolerance 1e-5 Relative Variable Tolerance 1e-5 Absolute Equation Tolerance 1e-7 Variable Change Tolerance 1e-5 Numerical Derivative Absolute Tolerance 1e-6 Numerical Derivative Relative Tolerance 1e-6 Solver Scaling Disabled Eliminate Equivalence Equations Enabled, Standard Integrator Tab: Solver Options The recommended solver options are: Option Value Integrator Variable Step Implicit Euler Initial Integration Step 1 Minimum Integration Step 1 Maximum Integration Step 5 Step Reduction Factor 0.5 Maximum Step Increment Factor 1.5 Absolute Integration Error Tolerance 1e-5 Tear Integration Tolerance 1 Maximum Corrector Iterations 500 Show Highest Integration Errors 0 Use Interpolation Enabled Reconverge Torn Variables Disbaled Note: When running rapid cycles, the integration steps may need reducing. Linear Solver Tab: Solver Options The recommended solver options are: Option Value Name MA48 Drop Tolerance 0 Pivot Tolerance 0 Re-analyse Threshold 2 8 Flowsheeting 285 Re-analyze FLOPS Window Size 0 Re-pivot every 0 Solver searches 3 Non-Linear Solver Tab: Solver Options The recommended solver options are: Options Value Mode General Method Fast Newton Convergence Criterion Residual Maximum Divergent Steps 20 Maximum Step Reductions 20 Maximum Iterations 500 Maximum Fast Newton Steps 8 Dogleg Method Disabled Run Time Options To set the runtime options for Aspen Adsim: • From the Run menu, click Run Options. The following settings are recommended: Options Value Comments Solution Time Units Seconds Time unit assumed by library models. Display Update 2 Interval when data is communicated between client and server. Communication Problem dependent Resolution at which plot data and delay information is saved. Small values make the plot data file grow more rapidly. When using interactions, ensure this value is set to provide at least five communication points in the shortest interaction step. When studying rapid transients, set this to a small value. Pause at Problem dependent Uncheck when using the Cycle Organizer (run time controlled by maximum number of cycles). Check and provide a desired end time for other simulations. This value can also be modified using the Run menu Pause At option. Pause after Unchecked Number of communication intervals to execute. Real time synchronization Unchecked Real time to simulation time factor. A value of zero indicates run as fast as possible. 8 Flowsheeting 286 Model Specification Aspen Adsim library models may require one or more of the following types of specification: • Definition of model assumptions. • Specification of constant variables. • Initial and preset conditions. The normal approach is to first configure the model, then specify the constant variables exposed and finally, if required, specify the model initial condition. Defining Model Configurations The model configuration is the selectable assumptions a model may have. For example, with an adsorbent layer, you have the option to: • Include a dispersive term in the component material balance. • Specify whether the layer is isothermal or non-isothermal. You set these options in the model Configure form, which opens when you double-click a flowsheet model block. This form displays selection boxes for any available adjustable assumptions. On changing an assumption, the model automatically reconfigures, so there may be slight pause depending on the overall complexity of the change. Specification of Constant Variables All models in the Aspen Adsim library contain recommended fixed variables. This ensures that the overall degrees of freedom of a complete problem are always met. Therefore, there is no need to determine which values are required to be specified. Each model in the Aspen Adsim model library contains a Specify table. You access the Specify table in one of these three ways: • Using the Configure form for the model. • From the Flowsheet menu, clicking Forms options. • Using the model’s context sensitive menu (selecting and right-clicking a flowsheet model block). The recommended columns made visible in the Specify table are: • Value • Units • Derivative • Specification • Description Presets and Initialization If a model contains state variables (variables that are differentiated with respect to time), initial values are required. Adsorbent layer and tank models typically fall into this category. To define the preset and initial variables, click the button on the Configure form to open the Initials table, which shows the recommended variables to preset and initial. 8 Flowsheeting 287 For an adsorbent/resin bed: • Provide values for a single discretization node within a given layer. To propagate this value through the rest of the layer, either click the Initialize button on the model’s configure form, or select Check & Initial from the Flowsheet menu. • To specify a layer that is at saturated equilibrium with a given bulk phase composition, initialize the bulk phase values (molefraction or concentration) and for the loading, set the derivatives to zero with a specification of Rateinitial. • For a gas adsorbent layer that includes a pressure drop correlation (momentum balance), the standard specification is to initialize the superficial velocity and initial ncomps-1 bulk phase molefractions. For a gas phase tank or void: • Preset (provide free specified values for) the internal composition. • Preset (provide a free specified value for) the internal pressure. • Provide an initial value of the temperature. • From the above and using the internal volume, the initialize method calculates the material molar holdup. • A valid alternative specification is to initialize the temperature, pressure and ncomps-1 internal molefractions, and to free the internal molar holdup. If you modify initial or preset values solely in the Initials table (and not elsewhere), the Check & Initial option in the Flowsheet menu always ensures that the problem contains the correct number of initial variables. The recommended columns to made visible in the Initials table are: • Value • Units • Derivative • Specification • Description Consistency and Problem Definition Checks When creating and specifying a flowsheet, it is recommended that you make these checks: • For cyclic processes, configure the flowsheet with first step conditions. • Check the initial and preset pressure conditions throughout the flowsheet. Ensure the pressure gradient is correct for the direction of material travel, for example feed to product. • Allow cross-valve pressure drops of at least 1 mbar. • For gas adsorbent beds, for robust initialization assume a small initial superficial velocity, for example 3.55e-4 m/s. • Pay particular attention to the deadspaces connected to a gas adsorbent. Ensure the pressure profile between the two units are reasonable and in the correct direction, and that the deadspaces have been correctly 8 Flowsheeting 288 initialized. Unreasonable initial conditions for deadspace are the principal cause of full flowsheet convergence problems at the start of the simulation. • Make use of the Flowsheet menu Check & Initial option. It indicates unconnected and invalid streams, corrects interaction unit configurations, runs any model-based initialization methods, and correctly configures material stream source and destination unit types. • If the model has too many initial variables, use Variable Finder to find all Initial and Rateinitial variables. Set the specification of any found variables to Free and then use the Check & Initial option from the Flowsheet menu. The default initial condition is reconstructed. • Make use of the recommended Fixed variables. If any are set to a specification of Free, another variable needs to be Fixed and vice-versa. For example, using a simple gas flowsheet, the default specification is for it to be pressure driven. If forced feed is required, set the feed unit flowrate specification to Fixed and the product unit specification to Free. • The library models contain default specifications. Should the problem become over or underspecified, use either the specification analysis tool; or using Variable Finder, find all variables and from the properties page, set the specification to default values. • For flowsheets with interaction units, ensure the run time communication interval allows at least five communication points within the shortest interacting steps. • For processes that operate under rapid cyclic conditions, ensure the integrator step sizes are suitable. For example, when using the Variable Step Implicit Euler integrator, try setting the maximum integrator step to half the shortest step time, and the initial and minimum steps sizes to 1/5 through 1/10 of the maximum integrator step. • The default solution bounds for variables defined in the library are suitable for most problems. However, when operating with large pressure or temperature swings, or very rapid cycles, the default bounds may need readjusting. Use the Variable Finder for this. • If you receive messages stating that empty arrays are being passed to procedures, this usually indicates that the current component list is not defined. When flowsheeting, it is usual to first create the component list and then start placing models on the flowsheet. • If a spanner/wrench appears in the specification window when flowsheeting, ensure that a component list is defined and that all connections are in place. Physical Properties Various physical properties are required by the Aspen Adsim models. Typical properties required are: • Molecular weight • Viscosity • Density • Enthalpy Aspen Adsim supports two ways of supplying this physical property data: 8 Flowsheeting 289 • User Fortran subroutines. • External physical property application (Properties Plus, Aspen Properties). The component list created for the problem governs the method in which physical properties are called. • If you use a template, the default component list assumes that user Fortran subroutines are being used. • When starting a new problem (without a template), the default component list is configured for use with an external properties application. To modify it for use with user-Fortran, you must first convert it to a component set (to do this, right-click the list and select convert). • If a new component list is created, by default it is assumed an external properties application will be used. If you want the user Fortran option, select the Is ComponentSet box is on creation. Use of User Fortran Historically, Aspen Adsim assumed that any physical property calculations or data were supplied through user Fortran subroutines. The advantages of using user Fortran based calculations are: • Simulation speed. • When distributing a problem, only need to additionally supply the library. Disadvantages of using the user Fortran method are: • Inflexibility when changing component names. Arrays indexed by component name are passed to procedures in ASCII order, hence subroutines may need modifying in response to changing component order. • Addition and removal of components from the simulation. The user subroutines either need reworking after each change or a collection of different versions of subroutines (each assuming different numbers of components) will be required. When creating a component list: The interface between the subroutine and model is defined by the Procedure type. The procedure definition defines the calling arguments, subroutine name and library name. The subroutines created then need to be compiled into a library so that they link to the simulation during runtime. It is important that the compiled library is placed in the simulator engine’s working directory. The working directory has the same name as the current simulation, and is one level down from the default working directory. For example, if the name of the current problem is N2PSA.ada and the default working folder has been defined as C:\MySims, the simulation engine’s working folder for this problem is C:\MySims\N2PSA. This applies to both local PC and remote server implementations. 8 Flowsheeting 290 Using a Physical Properties Application The simplest way of incorporating physical property calculations and data, is to use an external physical properties application such as Properties Plus or Aspen Properties. The advantages of using an external physical properties application are: • Ability to create a single definition file containing all the components and physical property methods of interest, and only those required in the current problem. • Large collection of rigorous physical property methods. • Extensive component database. The disadvantages are: • Speed penalties. • Requires application on same machine. When using Properties Plus or Aspen Properties, for example, the steps required before using either application are: 1 Create an .appdf file. 2 In Aspen Adsim, within the Explorer window, right-click Component Lists and select Properties. Define where the .appdf is located. 3 Create or convert a component list and select the components required. Switching Between Methods To switch between using user Fortran and an external properties application for the supply of physical property calculations and data: 1 If converting from user Fortran to an external application, ensure the link to an .appdf file is already defined. (To do this, right-click the ComponentLists object in Explorer and browse for a previously created .appdf file.) 2 Select the currently active component list. 3 Right-click the list and select Convert. The component list switches to the other method it’s currently using. When switching from Fortran to application based properties, if the component names originally defined are present in the .appdf file, the same components will be present, otherwise mismatches will be discarded. 4 Open the Configure form for any library model of the flowsheet. The global variable that switches the two methods is automatically updated. 8 Flowsheeting 291 Connecting to Aspen Dynamics Flowsheets You can now connect Aspen Adsim flowsheet sections to Aspen Dynamics flowsheet sections (except for ion-exchange flowsheets). There are two new utilities models for this purpose: • Dynamics_Inlet_Connect • Dynamics_Outlet_Connect These models are in the Utilities folder of the Aspen Adsim library. The model link must be done from within Aspen Adsim; the link cannot be set up from Aspen Dynamics. Tip: If you are creating an Aspen Adsim flowsheet for connection with an Aspen Dynamics flowsheet, it is good practice to name the active component list as 'Type 1'. This simplifies later conversion. Typical Workflows When you want to connect Aspen Dynamics models to Aspen Adsim models, there are two possible situations: • Attach individual Aspen Dynamics models to an existing Aspen Adsim simulation. • Attach a complete Aspen Dynamics simulation to an existing Aspen Adsim simulation. Attaching Individual Aspen Dynamics Models To attach an individual Aspen Dynamics model (for example, a rigorous compressor model) to an existing Aspen Adsim simulation: 1 In Aspen Adsim, open the Aspen Adsim simulation. 2 Open the Aspen Dynamics library. To do this: From the File menu, click Open Library and navigate to the Lib folder of the AMSystem 2004.1 installation. 3 Place the required Aspen Dynamics model onto the Aspen Adsim flowsheet. 4 Attach the new Aspen Dynamics flowsheet block to an existing Aspen Adsim flowsheet block, as follows: Attach an Aspen Adsim material stream to the Aspen Adsim flowsheet block, and an Aspen Dynamics material stream to the newly placed Aspen Dynamics flowsheet block. Now connect these two streamsusing either a Dynamics_Inlet_Connect or Dynamics_Outlet_Connect model from the Utility folder of the Aspen Adsim library. Your choice depends on whether the Aspen Dynamics model is on the inlet or outlet side of the Aspen Adsim mode. 5 Repeat steps 3 and 4 until the flowsheet is complete. 8 Flowsheeting 292 6 Check and modify the global variables relating to Aspen Dynamics flow schemes. You do this in the Global variables table, or from the Configure form of a Dynamics_Inlet_Connect or Dynamics_Outlet_Connect block: Global variable Brief description Notes GlobalPDriven Is the flowsheet pressure driven? For gas systems, set to True. GlobalPropMode Property mode Default is Local. If property convergence is difficult, set to Rigorous. (Aspen Adsim uses only rigorous property calls.) GlobalRFlow Reverse flow? Set to True if the model is expected to operate reversibly. 7 Specify, and provide initial values for, the new Aspen Dynamics blocks. Attaching Complete Aspen Dynamics Flowsheet To attach a complete Aspen Dynamics simulation to an existing Aspen Adsim simulation (for example, an Aspen Dynamics based cryogenic distillation train to an Aspen Adsim TSA system for air dehumidification): 1 In Aspen Adsim, open the Aspen Adsim simulation. 2 Check the component lists being used: − Ensure matching component list names between the Aspen Adsim and Aspen Dynamics simulations. Typically, the Aspen Dynamics version is called “Type1”. If necessary, you must rename the Aspen Adsim component list name to match. If the Aspen Adsim component list name is Default, you cannot rename it through the GUI. Instead, open the input file (.ada extension) within a text editor and search and replace the original component name, to the new component name. − Ensure the same components are actively in use. − Ensure the same properties definition file, .appdf, is in use. 3 The type of Aspen Dynamics flowsheet that can be imported depends on the type of Aspen Adsim flowsheet: − For gas-based Adsim flowsheets, imported Aspen Dynamics flowsheets must be pressure driven. See Valid Flowsheet Combinations, later. − For liquid-based Aspen Adsim flowsheets, imported Aspen Dynamics flowsheets may be either pressure driven or flow driven. See Valid Flowsheet Combinations, later. − You must check the Globals table in Aspen Adsim and set the global parameters GlobalPDriven and GlobalRFlow to match those in the Aspen Dynamics flowsheet to be imported. 4 From the File menu, click Import Flowsheet. This imports the Aspen Dynamics simulation into Aspen Adsim. Note these points: − Aspen Adsim does not support flowsheet hierarchy, so all Aspen Adsim based blocks and streams must exist on the main flowsheet. 8 Flowsheeting 293 − Repeated blocks, streams, plots, tables and tasks names are flagged during the flowsheet import. You can rename or delete these repetitions, or import the flowsheet into a hierarchy block. − Aspen Adsim automatically opens the Aspen Dynamics model library during the import. − The Aspen Adsim simulation flowsheet is updated with the imported Aspen Dynamics simulation flowsheet. − For common global variables, Aspen Adsim retains the original settings from before the flowsheet was imported. 5 Repeat steps 2 through 4 until all the required flowsheet sections are present within Aspen Adsim. 6 Between each flowsheet section, connect the appropriate Aspen Adsim or Aspen Dynamics feed and product streams: − For an existing Aspen Adsim feed or product stream, remove the boundary termination block (unlike Aspen Dynamics, Aspen Adsim has no concept of using open ended streams to indicate flowsheet boundaries). Now connect these open-ended Aspen Adsim streams with their Aspen Dynamics counterparts, using either a Dynamics_Inlet_Connect or a Dynamics_Outlet_Connect from the Utilities folder of the Aspen Adsim library. (Your choice depends on whether the Aspen Dynamics model is on the inlet or outlet side of the Aspen Adsim flowsheet.) 7 Repeat step 6 until the flowsheet is complete. 8 In the Cycle Organizer, modify the cycle description to account for any cyclic operation of imported Aspen Dynamics blocks, then regenerate the cyclic task. Valid Flowsheet Combinations The valid combinations of Aspen Adsim and Aspen Dynamics flowsheets are: • Connect gas-based Aspen Adsim flowsheets to pressure driven Aspen Dynamics flowsheet sections. • Connect liquid-based Aspen Adsim flowsheets to flow driven Aspen Dynamics flowsheet sections. Further valid combinations are also possible, and these are listed in the following table. Some combinations have constraints: in the table, bracketed numbers mark where this happens and you should refer to the notes underneath for more details. Inlet side section (Aspen Dynamics) Outlet side section (Aspen Dynamics) Gas (Aspen Adsim) Liquid (Aspen Adsim) Pressure driven Pressure driven Supported (1) Not Supported Pressure driven Not present Supported (2) Supported (3) Not present Pressure driven Supported (4) Supported (5) Flow driven Flow driven Partial support (6) Supported Flow driven Not present Partial support (7) Supported 8 Flowsheeting 294 Not present Flow driven Partial support (8) Supported Reversible (pressure driven) Reversible (pressure driven) Supported (9) Not supported Reversible (pressure driven) Not present Supported (10) Supported Not present Reversible (pressure driven) Supported (11) Supported You cannot mix flow assumptions, for example a pressure driven inlet and a flow driven outlet. This is because a single set of global variables is used to control the Aspen Dynamics flowsheet assumption. The following notes relate to the bracketed numbers (denoting constraints) in the previous table: 1 Connect the Aspen Dynamics flowsheet sections on both the inlet and outlet sides to a pressure node (a gas_tank_void for example). 2 Connect the Aspen Dynamics flowsheet section on the inlet side to a pressure node (a gas_tank_void for example). 3 Fix a pressure at the Aspen Adsim flowsheet outlet. 4 Connect the Aspen Dynamics flowsheet sections on the outlet side to a pressure node (a gas_tank_void, for example). 5 Fix a pressure at the Aspen Adsim flowsheet inlet. 6 Connect both Aspen Dynamics flowsheet sections only to a gas_bed model. 7 Connect the Aspen Dynamics flowsheet only to an Aspen Adsim gas_bed inlet. 8 Connect the Aspen Dynamics flowsheet only to an Aspen Adsim gas_bed outlet. 9 Connect the Aspen Dynamics flowsheet sections on both the inlet and outlet sides to a pressure node (a gas_tank_void for example). The single bed approach is not recommended; use a full rigorous Aspen Adsim flowsheet instead. 10 Connect the Aspen Dynamics flowsheet section on the inlet side to a pressure node (a gas_tank_void for example). The single bed approach is not recommended; use a full rigorous Aspen Adsim flowsheet instead. 11 Connect the Aspen Dynamics flowsheet section on the outlet side to a pressure node (a gas_tank_void, for example). The single bed approach is not recommended; use a full rigorous Aspen Adsim flowsheet instead. Global Variables A number of global variables control the operation of both Aspen Adsim and Aspen Dynamics models. These variables can be found in the Globals table within the Simulation object in the Simulation Explorer. You can also access many of these global variables through the Configure form of the Dynamics_Inlet_Connect and Dynamics_Outlet_Connect model blocks. 8 Flowsheeting 295 The global variables used are as follows: Global variable Default value Description GlobalPropMode Local The global property mode. Aspen Dynamics models use GlobalPropMode to select between local or rigorous physical properties calculations: The Local option uses simplified functions whose parameters are updated from an external physical property package. This improves the simulation time. The rigorous option uses methods contained within the external physical properties package. Note: All Aspen Adsim models use rigorous property calls. GlobalPdriven False Is the simulation pressure driven? Aspen Dynamics models use GlobalPdriven to switch the overall flowsheet scheme between pressure-driven flow and flow-driven flow. In general, for Aspen Dynamics models used in conjunction with Aspen Adsim models: When the system is gas, set to True. When the system is liquid, set to False. Note: If you anticipate flow reversibility within Aspen Dynamics models, the flowsheet must be pressure driven (so set the parameter to True). GlobalRFlow False Does the simulation support reverse flow? Aspen Dynamics uses GlabalRFlow to switch between uni-directional and bi-directional flow. For bi-directional flow, you must also set GlobalPdriven to True, otherwise the Aspen Dynamics models will default to uni- directional, flow-driven flow. GlobalTimeScaler 1 Seconds per model time unit. Aspen Dynamics models assume time units of hours, whereas Aspen Adsim models assume seconds. When models from both products exist on the same flowsheet, a common time unit needs to be adopted to successfully calculate time derivatives and delay times. Aspen Dynamics uses GlobalTimeScaler to rescale time derivatives and calculated delay times, from hours to seconds. IsSingleBed False Is the single bed approach being used? IsSingleBed indicates to Aspen Adsim’s Dynamics_Inlet_Connect and Dynamics_Outlet_Connect models, whether the Aspen Adsim flowsheet is using the Single-Bed approach to simulate a multi-bed flowsheet using a single column. When set to True, a set of equations is enabled that generate pseudo continuous flow from an inherently discontinuous flow. 8 Flowsheeting 296 Connecting to a Single Bed Approach Flowsheet The single bed approach to modeling a cyclic adsorption process is an abstract representation of the real process, so it suffers from the inherent behavior of discontinuous flow at the flowsheet boundaries. For example, a product stream from an Aspen Adsim flowsheet may be active (producing material) only during one step in the cycle. time Flowrate Cycle This behavior can disrupt Aspen Dynamics flowsheets that are connected to this same outlet boundary, as they may be expecting to continuously receive material. For example, a discontinuous supply of material may cause adverse effects to downstream units such as distillation columns or compressors. To counter this problem, the Dynamics_Inlet_Connect and Dynamics_Outlet_Connect models have been developed, which contain a series of expressions to generate a pseudo continuous flow of material. They use a similar set of expressions to the gas_interaction model. The flow, composition, temperature, pressure and enthalpy profiles are recorded during the flow of actual material, whilst a delay function is used to reproduce the same profile, periodically throughout the rest of the cycle. time Flowrate Cycle Delayed Profiles DT 2 x DT 3 x DT 4 x DT The two models use a variable that switches/toggles to indicate when flow of real material occurs. When set to 1 (that is On, for real flow), the inlet and outlet port variables are mapped together and the time at which the switch 8 Flowsheeting 297 was set to 1 is recorded. When no real flow is occurring, the variable switches to 0 (that is Off, for pseudo flow); and the time at which the switch occurred is recorded, and a delay time is calculated. The Aspen Dynamics port variables are then mapped to the appropriate Aspen Adsim port variables, but through the delay function. When the elapsed time from the switch off exceeds the calculated delay time, the delay time is incremented by the original delay time. DelayTime Time Seconds 0 10 20 30 40 50 60 70 80 90 100 B 1 . T o g g l e B 1 . D e l a y T i m e 1 2 3 4 5 6 7 8 9 1 0 - 5 0 5 1 0 1 5 2 0 2 5 3 0 The result of this procedure is a continuously variable delay time that produces a profile with a repeating pattern. Output_Values Time Seconds 0 10 20 30 40 50 60 70 80 90 100 B 1 . C a l c O u t p u t B 1 . R e a l O u t p u t 0 . 5 1 1 . 5 2 - 1 - 0 . 5 0 0 . 5 1 This method is applicable only if the assumption that the flow profile expected at the inlet and/or outlet side of the Aspen Adsim flowsheet is consistent within a given cycle. The delay function is used to replicate flow profiles. This, coupled with the fact that it uses interpolation of historical data, explains why you may see a slight degradation in the overall material balance. 9 Reference List for Adsorption Processes 298 9 Reference List for Adsorption Processes Bird, R.B., Stewart, W.E., Lightfoot, E.N., Transport Phenomena, John Wiley and Sons, New York, 1960. Carberry, J.J., Chemical and Catalytic Reaction Engineering, McGraw-Hill, New York, 1976. Carver, M.B., Scheisser, W.E., American Institute of Chemical Engineers, Annual Meeting, November 16-18, 1980. Costa, E., Sotelo, J.L., Calleja, G., Marron, C., Adsorption of Binary and Ternary Hydrocarbon Gas Mixtures on Activated Carbon: Experimental Determination and Theoretical Prediction of the Ternary Equilibrium Data, AIChE Journal, Vol. 27, No. 1, 1981. Froment, G.F. and Bischoff, K.B., Chemical Reactor Analysis and Design, John Wiley and Sons, New York, 1990. Kast, W., Adsorption aus der Gasphase, VCH, Weinheim, 1988. Nakao, S.I., Suzuki, M.U., Mass Transfer Coefficient in Cyclic Adsorption and Desorption, Journal of Chem. Eng. of Japan, Vol 16, No 2, 1983. Reid, C.R., Prausnitz, J.M., Sherwood, T.K., The Properties of Gases and Liquids, McGraw-Hill, New York, 1977. Ruthven, D.M., Principles of Adsorption and Adsorptive Processes, John Wiley and Sons, 1984. Slater, M.J., The Principles of Ion Exchange Technology, Butterworth, Heinemann, Boston, 1991. Tien, Chi, Adsorption Calculations and Modeling, Butterworth-Heinemann, 1994. Wakoo, N., Chem Eng Sci, 31, pp 11-15, 1976. Yang, R.T., Gas Separation by Adsorption Processes, Butterworth, 1987. Index 299 Index A Activating cyclic tasks 257 Adsorbed solution theory (gas) 64 Adsorption isotherms (gas) about 51 choosing 52 list 55 multicomponent mixture isotherms 52 Aspen Custom Modeler™ 230 Aspen Properties™ 284 available 299 Axial dispersion (gas) 22 Axial dispersion (ionx) 182 Axial dispersion (use for differencing schemes) 223 B B.E.T isotherm (gas) 58 B.E.T. Multilayer isotherm (gas) 58 Bed model assumptions (gas) 11, 13 Bed model assumptions (ionx) 179 Bed model assumptions (liq) 192 Bed model ports (gas) 14 Bed models (gas) 14 Biased Upwind Differencing Scheme 227 Brunaur, Emmet and Teller See B.E.T Burke-Plummer equation (gas) 26 C Central differencing schemes 222, 223 Complex expression step control 248 Compressiblity (gas) 21 Conduction (gas) 65 Conduction (liq) 207, 210 Configure form (gas) about 15 bed types 16 internal heat exchanger 19 spatial dimensions of beds 18 Configure form (ionx) 179 Configure form (liq) 192 Configure form tabs (gas) Energy Balance 64 General 20 Isotherm 51 Kinetic Model 31 Material/Momentum Balance 22 Procedures 76 Reaction 73 Configure form tabs (ionx) General 180 Isotherm 185 Kinetic Model 183 Material/Momentum Balance 180 Configure form tabs (liq) Energy Balance 206 General 193 Isotherm 200 Kinetic Model 196 Material/Momentum Balance 193 Procedures 213 Index 300 Configure Layer form (gas) 20 Configure Layer form (ionx) 179 Configure Layer form (liq) 192 Connecting controllers 268 Connectivity in flowsheets 267 Consistency checks for flowsheets 281 Constant variables (specifying) 280 Controllers 268 ControlSignal stream 268 Convection (gas) 23 Convection (ionx) 180 Convection (liq) 193 Convert_EstMod script 241 Cycle controls 254 Cycle Organizer about 243 cycle controls 254 Cycle Organizer window 244 cyclic reports 258 cyclic tasks 257 interaction control 252 opening 244 step controls 246, 256 step variables 250 Cycle Organizer block 244 Cycle Organizer window 244 cycle controls 254 cyclic reports 258 cyclic tasks 257 interaction controls 252 step controls 256 step variables 250 Cycle snapshots 255 Cyclic corrections (gas) 49 Cyclic operations 243 Cyclic Recovery report 260 Cyclic reports 258 Cyclic Recovery reports 260 Cyclic Stream reports 259 preparing 258 Cyclic Stream report 259 Cyclic tasks 257 D Darcy's Law (gas) 26 Darcy's law (liq) 195 Deactivating cyclic tasks 257 Demonstration Organizer 269 Demonstrations 268 Density (liq) 196 Discretization methods about 218 choosing 219 list 219 recommended 219 Discretization methods (gas) 20 Discretization methods (ionx) 180 Discretization methods (liq) 193 Dispersion (gas) 23 Dispersion (ionx) 180, 182 Dispersion (liq) 193 Dispersion coefficient (ionx) 180 Dispersion coefficient (liq) 193 Dispersive properties (gas) 27 documentation 297 Dual Layer B.E.T isotherm (gas) 62 Dual-Site Langmuir isotherm (gas) 61 Dual-Site Langmuir isotherms (liq) 201 Dubinin-Astakov isotherm (gas) 59 Dynamic estimation about 236 entering data manually 237 importing data from clipboard 238 E Effective diffusivity (gas) 36, 39, 50 Energy balance assumption (gas) 64 Energy balance assumption (liq) 206 Index 301 Energy balance equations (gas) factors affecting equations 81 gas phase 78, 81 solid phase 78, 84 wall 79, 86 Energy balance equations (liq) 213 Energy Balance tab (gas) 64 Energy Balance tab (liq) 206 Enthalpy (gas) 65 Enthalpy (liq) 208 Equation symbols (gas) 87 Equation symbols (ionx) 189 Ergun equation (gas) 27 Estimated mass transfer coefficient (gas) 50 Estimated Variables tab 232 Estimation converting Estimation Module data 241 dynamic 236 estimated variables 232 Estimation Module 230 methods available 230 performing using Estimation Module 241 recommendations 241 steady-state 233 Estimation methods 241 Estimation Module about 230 converting to Aspen Custom Modeler™ methods 241 defining estimated variables 232 dynamic estimation 236 recommendations 241 steady-state estimation 233 using 241 Estimation Module block 231 Estimation Module form 231 Event-driven step controls 246 Experimental Data tab 233, 237 Expression Builder dialog box 249 Extended Langmuir isotherm (ionx) 187 Extended Langmuir isotherms (gas) 60 Extended Langmuir isotherms (liq) 201 Extended Langmuir-Freundlich isotherm (gas) 61 Extended Langmuir-Freundlich isotherm (ionx) 187 Extended Langmuir-Freundlich isotherms (liq) 203 F Film model assumption (gas) 31 Film model assumption (ionx) 183 Film model assumption (liq) 197 Flow reversibility 263 Flowsheet specifications See Specifying flowsheets Flowsheet types 269 full 271 intermediate 270 simple 269 Flowsheets about 266 Connectivity 267 Cycle Organizer block 244 demonstrations 268 interactions 275 model types 263 physical property calculations 282 Pressure Interaction diagram 272 reversibility of flow 263 single bed approach 272 specifications 277 templates 268 types 269 Fluid phase energy balance (liq) 214 Fluid thermal conductivity (liq) 210 Flux Limited Differencing Scheme 229 Flux Limiter method? (gas) 21 Freundlich isotherms (gas) 56 Index 302 Freundlich isotherms (liq) 202 Fromm's Scheme 228 Full flowsheet 271 G g_Material_Port 267 Gas adsorption processes (overview) 11, 12 Gas model assumption (gas) 21 Gas thermal conductivity (gas) 69 gas_Material_connection 267 Gas-Wall heat transfer coefficient (gas) 72 General tab (gas) 20 General tab (ionx) 180 General tab (liq) 193 Generating cyclic tasks 257 Glueckauf approximation (gas) 49 gUserCompressibility submodel 22 gUserCpa submodel 66 gUserDH submodel 67 gUserDispersion submodel 24 gUserEffDiff submodel 37, 41, 50 gUserGibbs submodel 63 gUserHTC submodel 68 gUserIsothermC submodel 63 gUserIsothermPoi submodel 63 gUserIsothermPp submodel 63 gUserKg submodel 69 gUserKinetic submodel 35 gUserKineticModel submodel 43 gUserMTC submodel 49 H Heat capacity (gas) 66 Heat capacity (liq) 208 Heat exchanger (gas) 19 Heat of adsorbed phase (gas) 65 Heat of adsorbed phase (liq) 208 Heat of adsorption (gas) 66 Heat of adsorption (liq) 208 Heat transfer coefficient (gas) 67 Heat transfer coefficient (liq) 209 Heat transfer to environment (gas) 70 Heat transfer to environment (liq) 211 Henry isotherms (gas) 57 Henry's coefficient (gas) 47 Heterogeneous rate dependency (gas) 75 Heterogeneous reactions (gas) 74 Homogeneous rate dependency (gas) 74 Homogeneous reactions (gas) 74 Horizontal beds (gas) 16 I i_Material_Port 267 IAS (gas) 53, 64 IAS (liq) about 200 IAS Freundlich isotherms 204 IAS Langmuir isotherms 204 IAS Langmuir-Freundlich isotherms 205 Purecomponent procedure with IAS isotherm 206 Purecomponent submodel with IAS isotherm 206 IAS Freundlich isotherms (liq) 204 IAS isotherm (gas) 63 IAS Langmuir isotherms (liq) 204 IAS Langmuir-Freundlich isotherms (liq) 205 Ideal Adsorbed Solution theory See IAS Ideal gas (gas) 21 Importing data from Microsoft® Excel dynamic 239 steady-state 235 Initialization for models 280 Interaction control 252 Interactions 252 Interactions between steps 275 Interactions example 275 Intermediate flowsheet 270 Index 303 Internal heat exchanger (gas) 19 Ion-exchange adsorption processes (overview) 178 Ion-exchange equilibria 185 Ion-exchange resins 178 ionx_Material_connection 267 Isotherm assumed for layer (gas) 55 Isotherm assumed for layer (ionx) 186 Isotherm assumed for layer (liq) 200 Isotherm dependency (gas) 64 Isotherm list (gas) 55 Isotherm list (ionx) 186 Isotherm list (liq) 200 Isotherm tab (gas) 51 Isotherm tab (ionx) 185 Isotherm tab (liq) 200 Isothermal conditions (gas) 65 Isothermal conditions (liq) 207 Isotherms (gas) 55 Isotherms (ionx) 185 Isotherms (liq) 199 iUserDispersion submodel 182 iUserIsotherm submodel 187 iUserKinetic submodel 184 iUserMTC submodel 185 K Karman-Kozeny equation (gas) 26 Karman-Kozeny equation (liq) 195 Kinetic model assumption (gas) 31 Kinetic model assumption (ionx) 184 Kinetic model assumption (liq) 197 Kinetic Model tab (gas) 31 Kinetic Model tab (ionx) 183 Kinetic Model tab (liq) 196 Knudson diffusion coefficient (gas) 48 L Langmuir isotherms (gas) 55 Langmuir isotherms (liq) 200 Langmuir-Freundlich isotherm (gas) 57 Langmuir-Freundlich isotherms (liq) 202 Leonard Differencing Scheme 223 Linear isotherm (gas) 59 liq_Material_connection 267 liq_Material_Port 267 Liquid adsorption processes (overview) 191 Lumped resistance (gas) 32, 44, 46 Lumped resistance (ionx) 184 Lumped resistance (liq) 197 lUserDH submodel 209 lUserDispersion submodel 195 lUserGibbs submodel 206 lUserHTC submodel 210 lUserIsotherm submodel 205, 206 lUserKinetic submodel 198 lUserKl submodel 211 lUserMTC submodel 199 M Mass action equilibrium isotherm (ionx) 186 Mass balance equations (gas) additional solid phase 77, 81 factors affecting equations 79 gas phase 77 Mass balance equations (ionx) 188 Mass balance equations (liq) 213 Mass transfer (gas) about 31 lumped resistance 32, 44 micro and macropore effects 32 molecular diffusivities 45 particle material balance 36, 39 procedures 43 submodels 43 Mass transfer (ionx) 183 Mass transfer (liq) 196 Mass transfer coefficient (gas) 46, 50 Index 304 Mass transfer coefficient (ionx) 185 Mass transfer coefficient (liq) 198 Mass transfer driving force (gas) 31 Mass transfer driving force (ionx) 183 Mass transfer driving force (liq) 197 Material balance assumption (gas) 23 Material balance assumption (ionx) 180 Material balance assumption (liq) 193 Material/Momentum Balance tab (gas) 22 Material/Momentum Balance tab (ionx) 180 Material/Momentum Balance tab (liq) 193 Maximum number of cycles 254 Micro and macropore effects (gas) 32, 34, 46 Micro and macropore effects (liq) 198 Microsoft® Excel 235, 239 Mixed Differencing Scheme 226 Model configuration (defining) 280 Model specifications 280 Model types 262 Models list of types 263 reversibility 263 types 262 Molecular diffusivities (gas) 45 Molecular diffusivity (ionx) 182 Momentum balance assumption (gas) about 25 constant pressure options 25 pressure driven options 26 Multicomponent mixture isotherms (gas) 52 Myers isotherm (gas) 60 N New Experiment dialog box dynamic 237 steady-state 233 Nodes (gas) 21 Non-ideal gas (gas) 21 Non-isothermal conditions (gas) 65 Non-isothermal conditions (liq) 209, 210 Non-Isothermal conditions (liq) 207 Nonlinearity and numerical methods 218 Non-Reversible Delay models 263 Non-Reversible models 263 Number of heterogeneous reactions (gas) 75 Number of homogeneous reactions (gas) 75 Number of nodes (gas) 21 Number of nodes (ionx) 180 Number of nodes (liq) 193 Numerical methods about 218 Biased Upwind Differencing Scheme 227 Central Differencing Schemes 222, 223 Flux Limited Differencing Scheme 229 Fromm's Scheme 228 Leonard Differencing Scheme 223 Mixed Differencing Scheme 226 Quadratic Upwind Differencing Scheme 224 recommended 219 selecting 219 Upwind differencing schemes 221 Upwind Differencing Schemes 222 O Obtain Dynamic Measurements for Experiment DynExpt From Clipboard dialog box 238 Obtain Steady State Experiments From Clipboard dialog box 235 Overall material balance assumption (liq) 196 P Particle material balance See Particle MB options Particle MB 2 option (gas) 39, 50 Particle MB option (gas) 36, 50 Particle resistance coefficients (gas) 34 PDE differencing schemes Biased Upwind 227 Central 222, 223 Index 305 Flux Limited 229 Fromm's 228 Leonard 223 Mixed 226 Quadratic Upwind 224 Upwind 221, 222 Peclet number (gas) 23 Peclet number (ionx) 183 Physical property calculations about 282 external applications 284 switching between methods 284 user Fortran 283 Port types 267 Prandl number (gas) 68 Prandl number (liq) 210 Presets for models 280 Pressure (gas) 25 Pressure (liq) 195 Pressure drop assumption (liq) 195 Pressure drop options (gas) 27 Pressure Interaction diagram 272 Pressure Interaction diagram example 272 Problem definition checks for flowsheets 281 Procedures (used in) effective diffusivity 50 fluid thermal conductivity 211 gas thermal conductivity 69 heat of adsorbed phase 66 heat of adsorption 67, 209 heat transfer coefficient 68, 210 isotherms 62, 187, 205 kinetic model 43, 184, 198 mass transfer coefficient 49, 185, 199 material balance 24, 181, 194 molecular diffusivities 46 purecomponent isotherms 206 Procedures tab (gas) 76 Procedures tab (liq) 213 Properties Plus™ 284 pUser_Act_Coeff procedure 64 pUser_g_Cat_Rx_Heat procedure 83 pUser_g_Cat_Rx_Rate_C procedure 75, 83 pUser_g_Cat_Rx_Rate_C_Sol procedure 75, 83 pUser_g_Cat_Rx_Rate_Pp procedure 75, 76, 83 pUser_g_Cat_Rx_Rate_Pp_Sol procedure 75, 76, 81, 83 pUser_g_Compressibility procedure 22 pUser_g_Cpa procedure 66 pUser_g_De procedure 37, 41, 50 pUser_g_DH procedure 67 pUser_g_Diffusivity procedure 46 pUser_g_Dispersion procedure 24 pUser_g_Gas_Rx_Heat procedure 83 pUser_g_Gas_Rx_Rate_C procedure 74, 83 pUser_g_Gas_Rx_Rate_Pp procedure 74, 83 pUser_g_Gibbs procedure 62 pUser_g_HTC procedure 68 pUser_g_Isotherm_C procedure 62 pUser_g_Isotherm_P procedure 62 pUser_g_Isotherm_Poi procedure 62 pUser_g_Kg procedure 69 pUser_g_Kinetic procedure 35, 43 pUser_g_MTC procedure 49 pUser_i_Dispersion procedure 181 pUser_i_Isotherm_C procedure 187 pUser_i_Isotherm_W procedure 187 pUser_i_Kinetic procedure 184 pUser_i_MTC procedure 185 pUser_l_DH procedure 209 pUser_l_Dispersion procedure 194 pUser_l_Gibbs procedure 206 pUser_l_HTC procedure 210 pUser_l_Isotherm_C procedure 205 pUser_l_Isotherm_W procedure 205, 206 pUser_l_Kinetic procedure 198 pUser_l_Kl procedure 211 Index 306 pUser_l_MTC procedure 199 Q Quadratic Upwind Differencing Scheme 224 R Radial beds (gas) 18 Radial nodes (gas) 21 Rate dependency (gas) 74, 75 Reaction processes (gas) 73 Reaction tab (gas) 73 Reactions present? (gas) 74 Reactions type (gas) 74 Real Adsorbed Solution theory (gas) 64 Real Adsorbed Solution Theory (gas) 54 Recommended numerical methods 219 Recording cycle information 255 Reference list 292 Reversibility example 264 Reversibility of flow 263 Reversible Flow Setter models 263 Reversible models 263 Reversible Pressure Setter models 263 Rigorous multiple bed approach 272 Run time options (specifying) 279 Running end-of-step scripts 256 S Sherwood number (gas) 47 Simple flowsheet 269 Simulation Messages window 254, 255 Single bed approach 252, 272 Single Layer B.E.T isotherm (gas) 61 Snapshots 255, 256 Solid phase energy balance (liq) 214 Solid reactant list (gas) 76 Solid reactants present? (gas) 76 Solver options (specifying) 277 Spatial dimensions of beds (gas) 18 Specifying flowsheets checks 281 list of options 277 model specification 280 run time options 279 solver options 277 Static_isotherm model 233 Steady state testing (cyclic) 255 Steady-state estimation about 233 entering data manually 233 importing data from clipboard 234 Step controls 256 Step dependent step control 249 Step interaction control 252 Step interactions 252, 275 Step variables 250 Stoichiometric Equilibrium isotherms (liq) 203 Submodels (used in) component isotherms 206 effective diffusivity 50 fluid thermal conductivity 211 gas thermal conductivity 69 heat of adsorbed phase 66 heat of adsorption 67, 209 heat transfer coefficient 68, 210 isotherms 63, 187, 205 kinetic model 43, 184, 198 mass transfer coefficient 49, 185, 199 material balance 24, 182, 195 T Task Language 257 Template Organizer 268 Templates 268 Time controls (reason for) 253 Time-driven step controls 246 Toth isotherm (gas) 57 Index 307 U Upwind differencing schemes 221, 222 User Multicomponent Procedure isotherm (liq) 205 User Multicomponent Submodel isotherm (liq) 205 User Purecomponent Procedure with IAS isotherm (liq) 206 User Purecomponent Submodel with IAS isotherm (liq) 206 V Variable fields 251 Variable Selector dialog box 250 Velocity (gas) 25 Velocity assumption (liq) 196 Vertical beds (gas) 16, 18, 27 Volmer isotherm (gas) 59 W Wall energy balance (liq) 214 Water softening and purification (ionx) 178 Who Should Read this Guide This guide contains reference information for use by experienced users of the Aspen Adsim application. The guide also describes the following Aspen Adsim features: • • • • Numerical methods for solving the partial differential equations. Estimation module. Cyclic Organizer. Flowsheeting strategies. Who Should Read this Guide 2 General Information This section provides Copyright details and lists any other documentation related to the Aspen Adsim 2004.1 release. Copyright Version: 2004.1 April 2005 Copyright © 1991-2005 Aspen Technology, Inc, and its applicable subsidiaries, affiliates, and suppliers. All rights reserved. This Software is a proprietary product of Aspen Technology, Inc., its applicable subsidiaries, affiliates and suppliers and may be used only under agreement with AspenTech. 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All other brand and product names are trademarks or registered trademarks of their respective companies. This document is intended as a guide to using AspenTech's software. This documentation contains AspenTech proprietary and confidential information and may not be disclosed, used, or copied without the prior consent of AspenTech or as set forth in the applicable license. Corporate Aspen Technology, Inc. Ten Canal Park Phone: (1) (617) 949-1000 Toll Free: (1) (888) 996-7001 General Information 4 Cambridge, MA 02141-2201 USA Fax: (1) (617) 949-1030 URL: http://www.aspentech.com General Information 5 Related Documentation In addition to this document, the following documents are provided to help users learn and use the Aspen Adsim applications. Title Aspen Adsim 2004.1 Library Reference Guide Content Describes the models, streams, procedures and submodels available in Aspen Adsim. Full installation procedures for both server and client. An overview of new features and functionality within this release. AES 2004.1 Installation Guide Aspen Engineering Suite 2004.1 What’s New Guide General Information 6 Technical Support 7 . Search for technical tips. Search for and download application examples. Search for and review known limitations.com You use the Online Technical Support Center to: • • • • • • • Access current product documentation. Registered users can also subscribe to our Technical Support e-Bulletins.Technical Support Online Technical Support Center AspenTech customers with a valid license and software maintenance agreement can register to access the Online Technical Support Center at: http://support. Send suggestions. These e-Bulletins proactively alert you to important technical support information such as: • • • • Technical advisories. Submit and track technical issues.aspentech. and frequently asked questions (FAQs). Search for and download service packs and product updates. solutions. Product updates. 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Toll-free charges are listed where available. please see the Online Technical Support Center at: http://support. and e-mail for customers who have a current support contract for their product(s). fax. ......................................................................... 29 Material/Momentum Balance Tab (gas): Momentum Balance Assumption ................................................................................................................................................................................................................ 3 Related Documentation.... 26 General Tab (gas) ....... 20 Configure Form (Gas) ............. 21 Configure Form (gas): Bed Type.................................................. 17 1 GAS ADSORPTION PROCESSES........................... 27 Material/Momentum Balance Tab (gas) .......................................... 27 General Tab (gas): Number of Radial Nodes........................................................................................ 37 Contents 9 ..................... 25 Configure Layer Form (gas) ................................................. 18 Bed Model Assumptions for Gas Adsorption Processes ............................................................ 31 Material/Momentum Balance Tab (gas): 2-D Dispersive Properties ......... 28 About Axial Dispersion in Gas Adsorption Processes ..................................... 19 About Aspen Adsim's Bed Models ................................................................................ 20 Bed Model Ports .................... 28 Material/Momentum Balance Tab (gas): Material Balance Assumption........................................... 8 INTRODUCING ASPEN ADSIM ................................................................................................ 27 General Tab (gas): Gas Model Assumption ...............................................................................................................................................................................................Contents GENERAL INFORMATION.............................................. 3 Copyright............................................... 7 Online Technical Support Center ....... 26 General Tab (gas): Discretization Method to be used ................................................................................................................................................................................................................................................... 6 TECHNICAL SUPPORT.............................................................................................................. 26 General Tab (gas): Number of Nodes ................. 33 Kinetic Model Tab (gas) . 7 Phone and E-mail......... 37 Kinetic Model Tab (gas): Kinetic Model Assumption ................................................................................................................................. 18 About Gas Adsorption Processes...................................... 37 Kinetic Model Tab (gas): Film Model Assumption................................................................................................................................................................................................................. 24 Configure Form (gas): Internal Heat Exchanger .... 22 Configure Form (gas): Spatial Dimensions ....................................................................................................... 27 General Tab (gas): Flux Limiter to be used ...................................... .... 58 About Multi-Component Mixture Isotherms (gas) ...................................................................................................................... 81 Reaction Tab (gas): Heterogeneous Rate Dependency ..................................... 84 Gas Adsorption: Solid Phase Energy Balance .............................. 87 Gas Adsorption: Summary of Factors that affect the Energy Balance ........................................... 70 Energy Balance Tab (gas)................... 58 Isotherm Tab (gas): Isotherm Assumed for Layer .......Kinetic Model Tab (gas): Form of Lumped Resistance Model .................. 76 Energy Balance Tab (gas): Form of Gas-Wall Heat Transfer Coefficient ............ 84 Gas Adsorption: Wall Energy Balance ............................. 75 Energy Balance Tab (gas): Heat Transfer to Environment..... 55 Kinetic Model Tab (gas): Estimated Mass Transfer Coefficient Assumption ................ 56 Isotherm Tab (gas) ........................................................... 81 Reaction Tab (gas): Number of Heterogeneous Reactions ................................. 50 Kinetic Model Tab (gas): Molecular Diffusivities ......... 83 Gas Adsorption: Gas Phase Energy Balance................................... 57 Guidelines for Choosing Aspen Adsim Isotherm Models (gas).. 57 About Adsorption Isotherms for Gas Adsorption Processes . 79 Reaction Tab (gas): Reactions Present ................................................................................................................................................................................................................ 80 Reaction Tab (gas): Homogeneous Rate Dependency ................................ 70 Energy Balance Tab (gas): Energy Balance Assumption .. 83 Gas Adsorption: Mass Balance for Additional Solid Phase ................................................................................................................. Number of Nodes.......................................... 56 Gas Adsorption Layer (gas): Particle Material Balance............................ 79 About Gas Adsorption with Reaction Processes ......................... 72 Energy Balance Tab (gas): Form of Heat Transfer Coefficient.......... 80 Reaction Tab (gas): Number of Homogeneous Reactions........................................................................................................................ 61 Isotherm Tab (gas): Adsorbed Solution Theory................. 81 Reaction Tab (gas): Are Solid Reactants Present........................................................................................................................................................................................................................ 51 Kinetic Model Tab (gas): Form of Mass Transfer Coefficients.... 82 Gas Adsorption: Mass Balance for Gas Phase........................ 56 Kinetic Model Tab (gas): Particle Material Balance...... 85 Gas Adsorption: Defining the Mass Balance for Additional Solid Phases ............................................... 70 Isotherm Tab (gas): Isotherm Dependency............................................................................................................................... 52 Kinetic Model Tab (gas): Apply Cyclic Correction................ 87 Contents 10 ............. 82 Gas Adsorption: Summary of Mass and Energy Balance Equations.................................................. 85 Gas Adsorption: Summary of Factors that affect the Mass Balance Equations.................................... 82 Procedures Tab (gas)................................................... 71 Energy Balance Tab (gas): Heat of Adsorption Assumption........................................ 82 Reaction Tab (gas): Solid Reactant List ............................................. Effective Diffusivity .. 78 Reaction Tab (gas) ............................................................... 70 Energy Balance Tab (gas): Consider Heat of Adsorbed Phase............................ 73 Energy Balance Tab (gas): Form of Gas Thermal Conductivity ............................................................................ .......127 Langmuir 4 .........................123 I...............................................114 Mathematical Equation Form for Extended Langmuir 4... 92 Gas Adsorption: Explanation of Equation Symbols....................................................................................................120 Mathematical Equation Form for Loading Ratio Correlation 5......................................113 Mathematical Equation Form for Extended Langmuir 2.........123 Pure Isotherm List for the IAST Calculation of CSS............................................................... 93 2 GAS CYCLIC STEADY STATE MODELING.............128 Langmuir 5 .................133 Contents 11 ....126 Langmuir 2 ....................................................................................................................................................................................103 Connectivity between CSS Models ....................................................104 Material Balance ...............................................................................................................................S.............................................................A............................................................. 99 Introduction ...........................................................................116 Mathematical Equation Form for Loading Ratio Correlation 1.............................................................130 Dual-Site Langmuir 2.............. 87 Gas Adsorption: Defining the Energy Balance for the Solid Phase ................................................................................................................125 Langmuir 1 .. 99 What is CSS Modeling…? ...................... 90 Gas Adsorption: Defining Energy Balance for the Wall ...........................................126 Langmuir 3 ................................................................T................................. (Ideal Adsorbed Solution Theory)...112 Introduction .......................................................................112 Mathematical Equation Form for Extended Langmuir 1...............................................132 Sips (Langmuir-Freundlich) 3 ...........................................................................................................100 Discretization Techniques for Time and Space ..........................................................................................................Gas Adsorption: Defining the Energy Balance in the Gas Phase .........................................................................................................................................106 Energy Balance....103 Bed Model Details ...................121 Mathematical Equation Form for Extended Dual-Site Langmuir 1 ........................................................................................129 Dual-Site Langmuir 1.................................................................................................................................104 Momentum Balance .......................................................................................................................................................................................................................................................................................................118 Mathematical Equation Form for Loading Ratio Correlation 3........................................................................105 Kinetic Model.....................................115 Mathematical Equation Form for Extended Langmuir 5.....117 Mathematical Equation Form for Loading Ratio Correlation 2...............119 Mathematical Equation Form for Loading Ratio Correlation 4...................................................113 Mathematical Equation Form for Extended Langmuir 3............................109 Adsorption Equilibrium Models ....122 Mathematical Equation Form for Extended Dual-Site Langmuir 2 ........................130 Sips (Langmuir-Freundlich) 1 .............................................................................................................................................................................131 Sips (Langmuir-Freundlich) 2 ...................... ...................................................................134 Sips (Langmuir-Freundlich) 5 ...................................................................................................................135 Henry 1 ..........................195 4 LIQUID ADSORPTION PROCESSES ..........................184 About Ion-Exchange Processes......136 Henry 3 ..............191 About Adsorption Isotherms for Ion-Exchange Processes ...........................................................................................................................................................................................................................................................................................186 General Tab (ionx): Number of Nodes ..........................................................186 General Tab (ionx): Discretization Method to be Used.............188 Kinetic Model Tab (ionx)......188 Deciding When to Use Axial Dispersion in Ion-Exchange Processes ..191 Isotherm Tab (ionx) ..............................185 Configure Form (ionx)............................197 About Liquid Adsorption Processes.....................................................................................136 Henry 2 ..186 About Axial Dispersion in Ion-Exchange Processes ...........................................................................................................................................................185 Configure Layer Form (ionx) ................................................180 3 ION-EXCHANGE PROCESSES.......................................................139 User Guidelines..........................................189 Kinetic Model Tab (ionx): Film Model Assumption.............................................................................................................................137 Freundlich 1 .................................................................................................................158 How to Convert a CSS Flowsheet to a Dynamic Flowsheet .....194 Explanation of Equation Symbols for Ion-Exchange Processes...........................................................................................................................................................................................................................................................................................................................................................................................................................................197 Bed Model Assumptions for Liquid Adsorption ......................................................................................140 How to Create a Dynamic Simulation Flowsheet using CSS Models .............................140 How to Create a CSS Simulation Flowsheet .................................................................................198 Contents 12 ..190 Kinetic Model Tab (ionx): Form of Mass Transfer Coefficient ...................................................................174 How to Convert a Dynamic Flowsheet into a CSS Flowsheet ....................................................Sips (Langmuir-Freundlich) 4 ..............................189 Kinetic Model Tab (ionx): Kinetic Model Assumption ..............191 Isotherm Tab (ionx): Isotherm Assumed for Layer ..............................................186 Material/Momentum Balance Tab (ionx): Material Balance Assumption..................192 Summary of Mass Balance Equations for Ion-Exchange Processes ...............186 Material/Momentum Balance Tab (ionx)............184 Bed Model Assumptions for Ion-Exchange............190 Kinetic Model Tab (ionx): Form of Lumped Resistance .............................................................................................................................138 Toth 1 ...................139 BET 1 ....................................................................185 General Tab (ionx) ................177 Developer’s Tips to Get Better Convergence Property in CSS Simulation................................137 Henry 4 ........................................................................................................................... ....................................................220 Liquid Adsorption: Wall Energy Balance .............................................................................198 General Tab (liq)....Configure Form (liq) ........................220 Liquid Adsorption: Fluid Phase Energy Balance ..199 Material/Momentum Balance Tab (liq): Material Balance Assumption ...........................................................................................................................205 The Ideal Adsorbed Solution Theory (IAS) ................................................................201 Material/Momentum Balance Tab (liq): Velocity Assumption ................................................................................................................212 Energy Balance Tab (liq): Energy Balance Assumption.................................................................................................219 Liquid Adsorption: Summary of Mass and Energy Balance .........................................212 Energy Balance Tab (liq): Consider Heat of Adsorbed Phase ................199 General Tab (liq): Number of Nodes...................................................................................202 Kinetic Model Tab (liq) ........................205 Guidelines for Choosing Aspen Adsim Isotherm Models ...........202 Material/Momentum Balance Tab (liq): Overall Material Balance Assumption......................................................................................................................................................................................224 Choosing the Discretization Method .......227 Upwind Differencing Scheme 2 ......................................................................217 Procedures Tab (liq) ...........................199 General Tab (liq): Discretization Method to be Used ...................................................................................219 Liquid Adsorption: Solid Phase Energy Balance ..................................206 Isotherm Tab (liq): Isotherm Assumed for Layer.................................215 Energy Balance Tab (liq): Form of Fluid Thermal Conductivity..................................221 5 NUMERICAL METHODS ......199 Material/Momentum Balance (liq) ..............206 Energy Balance Tab (liq) .........................................................229 Leonard Differencing Scheme.225 Upwind Differencing Scheme 1 ...................................................203 Kinetic Model Tab (liq): Kinetic Model Assumption.............216 Energy Balance Tab (liq): Heat Transfer to Environment .........................214 Energy Balance Tab (liq): Heat of Adsorption Assumption ............................................................................................................................................203 Kinetic Model Tab (liq): Form of Mass Transfer Coefficient..220 Liquid Adsorption: Explanation of Equation Symbols............................................................................................224 About Numerical Methods.......................................................219 Liquid Adsorption: Mass Balance...204 About Adsorption Isotherms for Liquid Adsorption ...................................................................................................................................................................................225 About the Discretization Methods............228 Central Differencing Scheme 1 .........202 Kinetic Model Tab (liq): Film Model Assumption ..........................................................................................................................198 Configure Layer Form (liq).....................................................................214 Energy Balance Tab (liq): Form of Heat Transfer Coefficient .................................................................................228 Central Differencing Scheme 2 ........199 Material/Momentum Balance Tab (liq): Pressure Drop Assumption........................................................................................................................................................................................................................................229 Contents 13 . ............238 Steady-State Estimation Using the Estimation Module ..................................................................................................242 Manually Entering Dynamic Experimental Data ..................................................................Quadratic Upwind Differencing Scheme .....................................................................................................................252 Discrete Event Driven Step .................................................................................................................240 Dynamic Estimation Using the Estimation Module .........249 Opening the Cycle Organizer..................................................236 Two Estimation Tools in Aspen Adsim 2004.....................................................................233 Fromms’ scheme.......247 Converting Estimation Module Data ..............................................259 Additional Cycle Controls........................244 Performing Estimation Using the Estimation Module .................................................................247 Recommendations When Using the Estimation Module ........................................................................261 Take Snapshot Box......................................................................................261 Contents 14 ................1 ..............................................................................239 Manually Entering Steady-State Experimental Data .......................................................................249 About the Cycle Organizer ....................................................................................................................................................236 Defining Estimated Variables in the Estimation Module ......................................................................261 Cyclic Steady State Testing Box ......259 Interacting Steps and Time Controls ..............................................234 Flux Limited Discretization Scheme .....................................................................250 Step Control .......................................................................................236 About the Estimation Module ................................................................................................230 Mixed Differencing Scheme.......................................................................................................................235 6 ESTIMATION WITH ASPEN ADSIM.256 Removing Step Variables..............................................................................................260 Maximum Cycles Box ...............258 Deleting Interaction Steps ................................................1.......................................................................................................................................................260 Record Initial and Record Frequency Boxes .......................257 Interaction Control ..249 Cyclic Operations in Aspen Adsim 2004...................................................243 Dynamic Experimental Data from the Clipboard ....................................................................................................256 Adding Step Variables ...........................................................................................................................................................................259 Adding Extra Interaction Steps.......................................................................................252 Step Variables ...........................................................................247 7 CYCLIC OPERATION ..............................................................................................................239 Steady-State Experimental Data from the Clipboard..........258 Defining a Step Interaction ............................................................................257 Changing Step Variable Values..................252 Time Driven Step .......................................................232 Biased Upwind Differencing Scheme................250 Cycle Organizer Window...................................................................................................... .................................................264 Cyclic Stream Reports........................................................262 Execute End of Step Script Box ..............................281 Specifications for Flowsheets ....274 Types of Flowsheet in Aspen Adsim.....277 Single Bed Approach.......................................................273 Templates ............................................................................291 Valid Flowsheet Combinations ....................286 Consistency and Problem Definition Checks................................................................................................276 Full Flowsheet....................................................................................................................................................................275 Intermediate Flowsheet..269 Reversibility ...........................................263 Cyclic Reports...................................................................................290 Connecting to Aspen Dynamics Flowsheets .....264 Preparing Aspen Adsim for Cyclic Reporting .................................................................275 Types of Flowsheet: Simple Flowsheet ............................................................................................................................274 Demonstrations .............................................................283 Solver Options ........................269 About Flowsheets in Aspen Adsim..................................................................................................289 Using a Physical Properties Application .....................................................................................................296 9 REFERENCE LIST FOR ADSORPTION PROCESSES...................................................287 Physical Properties .265 Cyclic Recovery Reports ..........................................................................................................................291 Typical Workflows .........262 Generating Cyclic Tasks ...................298 INDEX .............................................................Additional Step Controls ......................272 Connectivity on Flowsheets.........285 Model Specification.................................................................................................................................................................................................................................................................................................................................................266 8 FLOWSHEETING .........................................................................................................................................................................................299 Contents 15 ................................................................................262 Take Snapshot at End of Step Box ..................................................................................................................................268 About Model Types ....................283 Run Time Options........290 Switching Between Methods...................................................288 Use of User Fortran ................................................................................................................................................................263 Activating and Deactivating Cyclic Tasks....................................................................................................................................................................................................................................................268 General Model Types ..........................................................................................................................................................278 Interactions......................................................................................................................293 Connecting to a Single Bed Approach Flowsheet .................................................278 Pressure Interaction Diagram......................................................................................................................................................................... Contents 16 . Introducing Aspen Adsim Aspen Adsim simulates gas processes with adsorption only. or adsorptive reaction gas processes where both reaction and adsorption occur simultaneously. chemicals and petrochemicals. natural gas. Gas-phase adsorption is widely used for the large-scale purification or bulk separation of air. Introducing Aspen Adsim 17 . 1 Gas Adsorption Processes 18 . General Tab. natural gas. Reaction Tab. Configure Form. Energy Balance Tab. Material/Momentum Balance Tab. About Gas Adsorption Processes Gas-phase adsorption is widely used for the large-scale purification or bulk separation of air. Many process concepts have been developed to allow: • • Efficient contact of feed gas mixtures with adsorbent to carry out desired separations. Adsorbent attracts molecules from the gas. Procedure Tab. Efficient regeneration of the adsorbent for subsequent reuse. Bed Model Assumptions for Gas Adsorption Processes. Isotherm Tab. Kinetic Model Tab. chemicals and petrochemicals. Configure Layer Form. where it is often better to use gas-phase adsorption rather than the older unit operations of distillation and absorption. About Aspen Adsim Bed Models. removing the molecules from the gas phase and concentrate on the surface of the adsorbent.1 Gas Adsorption Processes This chapter contains information on: • • • • • • • • • • • • • • About Gas Adsorption Processes. Explanation of Equation Symbols. Summary of Mass and Energy Balance Equations. such as zeolites. for example the discovery of porous adsorbents with a large surface area. most commercial adsorbents are pellets.For gas phase applications. the non-ideal behavior needing a compressibility factor. These adsorbents are usually packed into fixed beds through which the gaseous feed mixtures are passed. radial dispersion and thermal conduction are used to account for radial material and temperature distributions. Increasingly. Alternatively. The bed is then treated to remove the adsorbed molecules in separate regeneration steps. For gas processes. Normally. the development of new applications requires close cooperation in adsorbent design and process cycle development and optimization. − Gas-solid heat transfer. Terms in the energy balances include: − Thermal conductivity of gas and thermal conductivity of solid. Gas phase adsorption processes have seen a growth in both variety and scale. The system is fully mixed in the radial direction. the bed model makes the following assumptions: • Isothermal or non-isothermal conditions apply. the feed flow is stopped to finish the loading step of the process.2 mm in diameter. − Enthalpy of mixing is negligible. • • • • 1 Gas Adsorption Processes 19 . then the cycle is repeated. − Wall energy terms. or adsorptive reaction gas processes where both reaction and adsorption occur simultaneously. − Compression. the process is cyclic. − Heat exchange with environment. − Heat of adsorption. These advances have encouraged parallel inventions of new process concepts. This is due mainly to improvements in adsorbents. Plug flow or plug flow with axial dispersion occurs. The gas phase is ideal or non-ideal. beads. Bed Model Assumptions for Gas Adsorption Processes Aspen Adsim simulates gas processes with adsorption only. or the pressure varies according to a laminar or turbulent flow momentum balance. Gas phase pressure is either constant (with velocity either constant. − Enthalpy of adsorbed phase. especially since 1970.5 to 3. or other granular shapes. or varying according to mass balance and only applicable for breakthrough simulations). typically about 1. When the bed capacity is exhausted. The nature of the process and its operating conditions determine the type of model to use. You can add further relationships. Bed Model Ports Bed models contain an input and an output port. quadratic.• Mass transfer is described using a lumped overall resistance. • About Aspen Adsim's Bed Models The table shows the classifications of adsorption bed models: Name Model type Flow type Time dependency Type Flow setter under compressible flow conditions. The driving force is based on a liquid or solid film. or vary with local conditions. or by a model that accounts separately for micropore and macropore effects. The adsorption bed models are usually flow setters. and is either linear. Reversible. For example. provided the general compressible flow model is used. and which allow for reversible flow. heat. Dynamic. or user-specified. Mass transfer coefficients are either constant. IAS theory can be used for pure component isotherms. A limited rigorous particle material balance functionality is provided. This is because they determine internal pressure profiles and gas velocity profiles. a bulk separation process such as producing oxygen-rich gas from air requires a different model to that for a purification process for removing trace impurities. Adsorption isotherms are either applicable for single or multi-component adsorption. 1 Gas Adsorption Processes 20 . but within the bed they can be both flow setters and pressure setters. which are specific to the various options. Each port has associated variables that correspond to the material connection stream variables. They contain dummy variables associated with the input and output streams. The adsorption column models use a set of partial differential equations to represent the momentum. and material balances across the column. Reversible models handle forward or reverse flow in the bed. For vertical and horizontal beds. See Configure Form for Gas Process Bed Model: Internal Heat. specify whether an internal heat exchanger is present. later. later. For vertical beds only. define the spatial dimensions of the bed model: 1-D or 2-D.Configure Form (Gas) On the Configure form of the bed model: 1 2 3 Enter the number of layers within the bed (one or more). type a brief name or description. Enter the bed type: Vertical. and See Configure Form for Gas Process Bed Model: Spatial Dimensions. later. See Configure Form for Gas Process Bed Model. Horizontal or Radial. In the Description box for each layer. Click Configure to open the 4 5 6 1 Gas Adsorption Processes 21 . See Configure Form for Gas Process Bed Model: Spatial Dimensions. In the horizontal column orientation. Horizontal beds allow a much greater inflow area. Horizontal Bed Type Occasionally. you may need to choose horizontal orientation. keeping gas superficial velocities below the fluidization velocity. Vertical Bed Type Typically. 1 Gas Adsorption Processes 22 .Configure Layer Form (gas) dialog box. 7 Click Specify to open the Specify form for the layer model. choose vertical. when a vertical bed may cause fluidization of the bed. but is now at right angles to the column axis so there is variation in the effective flow area of the column with height above the column base. horizontal or radial bed orientation. Configure Form (gas): Bed Type To choose the bed type: • In the Bed Type box. the flow through the adsorbent packing is still vertical. The height of the start of the (first) adsorbent layer above the column base is the same thickness as the empty dead space and supporting grating. Vertical columns prevent variation in flow width because the flow is along the column axis. you use a vertical orientation for an adsorption bed. for example. 1 W ( z ) = [4 z (DB − z )] Where: 0.2 HB.1 Layer 2 Layer 1 z W(z) The effective width W(z) of the bed is given as: DB H0. 1 Gas Adsorption Processes 23 .2 H0. that is. W(z)L.L HB.5 DB z = = Column diameter Height of adsorbent above column base The effective cross-sectional flow area of the bed is the product of the width and the total horizontal length of the bed. Radial Bed Type Use a radial bed type when the flow through the bed is in the radial direction. you need to specify either one. from a central core to the outer circumference of the packed bed. Configure Form (gas): Spatial Dimensions If you select a vertical bed type. The positive radial co-ordinate runs from the center of the bed to the outer circumference. 1 Gas Adsorption Processes 24 .or twodimensional spatial discretization: • • One-dimensional discretization — Spatial derivatives are evaluated in axial (flow) direction only. Two dimensional discretization — Second order spatial derivatives are evaluated in both the axial and radial direction. allowing the calculation of radial composition and temperature distributions. Product Inner Core Adsorbent Layer 1 Adsorbent Layer 2 Bed Shell Feed The volumes of the central core and the bed shell are the dead volumes of the column. The heat exchange medium remains in the phase it is supplied in. internal Steam-Water. or is condensed in order to use its heat of evaporation to heat the bed. no heat exchanger 1-Phase. jacket Steam-Water.Configure Form (gas): Internal Heat Exchanger The adsorption columns used in some temperature swing adsorption processes are equipped with internal heat exchangers to improve adsorbent regeneration. jacket The heat exchanger operates either as a jacket encircling the adsorption column or is integrated into the packed bed of the adsorbent. internal 1-Phase. Aspen Adsim can simulate this configuration through the following sub-options: • • • • • None. that is. Internal Heat Exchanger Heat Exchange Jacket 1 Gas Adsorption Processes 25 . and to select the gas model assumption.Configure Layer Form (gas) Use the options in the Configure Layer Form to specify the bed layers. The form has the following tabs: • • • • • • • General tab Material/Momentum Balance tab Kinetic Model tab Isotherm Tab Energy Balance tab Reaction tab Procedures tab General Tab (gas) Use the General tab to specify the numerical options for solving the partial differential equations. General Tab (gas): Discretization Method to be used These discretization methods are available for gas phase adsorption processes: • • • • • • • • • • UDS1 UDS2 CDS1 CDS2 LDS QDS MIXED Flux Limiter BUDS FROMM 1 Gas Adsorption Processes 26 . temperature and molar density: P = Z RTg ρ g (overall) or Pyi = Z RTg ci (component) Where: P Z R = = = = = = = Pressure Compressibility factor Universal gas constant Gas phase temperature Molar gas phase density Mole fraction of component i Molar concentration of component i Tg ρg yi ci 1 Gas Adsorption Processes 27 . General Tab (gas): Flux Limiter to be used If flux limiter is your discretization method. The derivatives in the component material balances and the gas phase energy balances are second order in radial co-ordinates.General Tab (gas): Number of Nodes In the Number of Nodes box. and are approximated by central differences. choose an appropriate number of axial nodes for your chosen discretization method. Choose an appropriate number of radial nodes. General Tab (gas): Number of Radial Nodes The Number of Radial Nodes option is available only if you selected a vertical bed with a 2-D spatial dimension. choose from: • • • van Leer OSPRE SMART General Tab (gas): Gas Model Assumption Gas flowing through the packed bed can be ideal or non-ideal. The gas model defines the relationship between pressure. The dispersion term in the material balance is typically expressed as: − ε i E zk Where: ∂ 2 ck ∂z 2 = = Interparticle voidage Axial dispersion coefficient of component k εi E zk The type of flow determines whether this term is included or omitted in the material balance. • • In general. or calculated using a selected physical properties package) User Submodel Compressibility (where Z is supplied through the user submodel gUserCompressibility) • Material/Momentum Balance Tab (gas) Use the Material/Momentum Balance tab to specify the material and momentum balances. choose from: • • • Ideal Gas Law (where Z=1) Fixed Compressibility (where Z is constant) User Procedure Compressibility (where Z is supplied through a user Fortran subroutine interfaced by the procedure pUser_g_Compressibility. This reduces the efficiency of separation so should be minimized in column design. the molecular diffusion and turbulent mixing effect are additive and proportional to the second order spatial concentration derivative. the model must account for its effects. so they can be lumped together into a single effective dispersion coefficient. there are three main sources of axial dispersion: • From wall effects. You can avoid this type of dispersion by having a sufficiently large ratio of bed-to-particle diameters. However. In gases. 1 Gas Adsorption Processes 28 . E i . About Axial Dispersion in Gas Adsorption Processes As a fluid flows through a packed column. due to non-uniformity of packing either at the wall (wall effects) or in the core section of the packing (channeling). and the 2-D dispersive properties. From turbulent mixing effects arising from the splitting and recombining of flows around the adsorbent particles. axial mixing tends to occur.In the Gas Model Assumption box. if axial dispersion occurs. From molecular diffusion effects. Zero: The bed operates under plug flow conditions. you need not supply the dispersion coefficient. Note: The numerical methods used to model the spatial derivatives in the general equations can also introduce an artificial form of dispersion. The following table shows the effect of different values of Peclet number: If the Peclet number is 0 < 30 > 100 ∞ The effect of axial dispersion on bed performance is Infinite: the bulk gas is perfectly mixed and the gas is homogeneous through the entire bed. and bed height ( H b ): Pe = vgH b Ez The Peclet number quantifies the degree of dispersion introduced into the system. Significant. so the model represents plug flow with a zero dispersion coefficient (infinite Peclet number). Very slight: The bed operates under near plug flow conditions.It is useful to work out the Peclet number Pe using a dispersion coefficient (effective bulk diffusivity E z ). Choose from these options: • • • • • Convection Only Convection with Constant Dispersion Convection with Estimated Dispersion Convection with User Submodel Dispersion Convection with User Procedure Dispersion Material Balance Assumption (gas): Convection Only The Convection Only option drops the dispersion term from the material balance. It is dimensionless so is more convenient to use for this purpose than the dispersion coefficient. typical bed velocities (ν g ). 1 Gas Adsorption Processes 29 . Material/Momentum Balance Tab (gas): Material Balance Assumption The Material Balance Assumption option is available unless you previously chose vertical bed and two-dimensional bed discretization. Because the dispersion term is missing. the (varying) dispersion coefficient is estimated through a user-supplied Fortran subroutine. You supply its value. Aspen Adsim estimates the components' dispersion coefficients using the following correlation.73Dmk + v g rp ε i 1 + 9. which Aspen Adsim interfaces through the procedure pUser_g_Dispersion. the (varying) dispersion coefficient is estimated using the user submodel gUserDispersion.49   Where:  ε i Dmk   2v g rp   νg Dmk E zk = = = = = Gas velocity Molecular diffusivity Axial dispersion coefficient Interparticle voidage Particle radius εi rp Material Balance Assumption (gas): Convection with User Submodel Dispersion If you choose Convection with User Submodel Dispersion. Material Balance Assumption (gas): Convection with Estimated Dispersion The Convection with Estimated Dispersion option assumes that the dispersion coefficient varies along the length of the bed. (Kast. 1 Gas Adsorption Processes 30 . Material Balance Assumption (gas): Convection with User Procedure Dispersion If you choose Convection with User Procedure Dispersion.Material Balance Assumption (gas): Convection with Constant Dispersion The Convection with Constant Dispersion option assumes that the dispersion coefficient is constant for all components throughout the bed. 1988): E zk = 0. Aspen Adsim estimates the values during the simulation. Gas density is constant along the bed. or pressures. Choose from: Constant pressure options—The bed is driven by gas superficial velocity and the pressure is assumed constant in the bed.Material/Momentum Balance Tab (gas): Momentum Balance Assumption Use the Momentum Balance Assumption box to specify how the adsorption bed layer model treats gas velocity and pressure. Superficial velocity varies along the bed due to the rate at which the gas is adsorbed onto the solid. so the pressure does not vary axially. These assumptions are valid only when dealing with the removal of trace components from a bulk carrier gas. No simplifying assumptions are made regarding the gas densities. Momentum Balance Assumption (gas): Constant Pressure with Varying Velocity Use the Constant Pressure with Varying Velocity option only when using a simple flowsheet to simulate the breakthrough behavior of an adsorption column. In such cases. velocity and pressure gradient are related through a momentum balance. The gas velocity and pressure are constant along the bed. These models are applicable only for breakthrough investigations. The constant pressure options are: • • Constant Pressure and Velocity Constant Pressure with Varying Velocity Pressure driven options—The velocity is related to the overall or internal pressure gradients. The pressure driven options are: • • • • Darcy's Law Karman-Kozeny Equation Burke-Plummer Equation Ergun Equation Momentum Balance Assumption (gas): Constant Pressure and Velocity Use the Constant Pressure and Velocity option only when using a simple flowsheet to simulate the breakthrough behavior of an adsorption column. The pressure-drop relationships apply to local conditions inside the bed. so the momentum equations for entire beds can be used to determine local pressure gradients. 1 Gas Adsorption Processes 31 . Base your choice on the plant operating conditions and the envisaged scope of the simulation (constant pressure models are only applicable for breakthrough investigations). and no momentum balance is needed. or desorbed from it. whilst the gas density is essentially constant along the bed. The bed is velocity-driven. gas velocities. 75 × 10 −5 vg ∂z 2rpψε i3 Where: M = Molecular weight The equation is valid for fully turbulent conditions when the particle Reynolds number Re is: Re = Mρ g 2rp v g µ > 1000 For details of the Burke-Plummer model.This option is applicable to bulk separation applications.5 × 10 −3 µ (1 − ε i ) 2 = vg ∂z (2 rpψ )2 ε i3 For details of the Karman-Kozeny model see Bird et al. in which case the axial velocity profile is determined by an overall material balance rather than an axial pressure gradient. Momentum Balance Assumption (gas): Darcy's Law Use this option to apply a linear relationship between the gas superficial velocity and the pressure gradient at a particular point in a bed. (1960). 1 Gas Adsorption Processes 32 . You have to set the proportionality constant. Darcy's law states that pressure drop is directly proportional to flow rate. see Bird et al. The relationship is given as: ∂P = − Kpνg ∂z Where: Kp = = Darcy’s law proportionality constant Gas velocity νg Momentum Balance Assumption (gas): Karman-Kozeny Equation Choose this option to use the Karman-Kozeny equation to relate velocity to pressure drop. Where: ψ µ = = Shape factor Dynamic gas viscosity Momentum Balance Assumption (gas): Burke-Plummer Equation This option uses the Burke-Plummer equation to relate velocity to pressure gradient: Mρ g (1 − ε i ) 2 ∂P = −1. (1960). This is the laminar component of the Ergun equation: ∂P − 1. which combines the description of pressure drops by the Karman-Kozeny equation for laminar flow and the Burke-Plummer equation for turbulent flow. Set Variables for Pressure-Drop Options (gas) This table shows the variables you need to specify for the pressure drop options: Equation Symbol Variable Kp Sfac Rp Ei Definition Proportionality constant Sphericity Particle radius Interparticle voidage Kp ψ rp εi Material/Momentum Balance Tab (gas): 2-D Dispersive Properties The 2-D Dispersive Properties option is available only if you selected vertical bed and two-dimensional discretization.5 × 10 −3 (1 − ε i ) 2 (1 − ε i ) 2  ∂P µv g + 1.Momentum Balance Assumption (gas): Ergun Equation This option uses the Ergun equation.75 × 10 −5 Mρ g vg  = −  ∂z 2rp ψε i3  (2rp ψ )2 ε i3   It is valid for both laminar and turbulent flow. (1960). The axial dispersion is calculated from: − ε i E zk ∂ 2 ck ∂z 2 1 ∂  ∂c k  r  r ∂r  ∂r  Additionally. Namely: • • Gas phase thermal conduction in axial direction: − ε i k gz Gas phase thermal conduction in radial direction: − ε i k gr ∂ 2Tg ∂z 2 1 ∂  ∂Tg r r ∂r  ∂r      1 Gas Adsorption Processes 33 . see Bird et al. equivalent dispersive terms are evaluated for the gas and solid phase energy balances. a radial dispersion term is also evaluated: − ε i E rk If you later specify the process as non-isothermal.  1. For details of the Ergun model. and is the most popular option. For non-isothermal operation. These variables influence the values of dispersion coefficients and thermal conductivities. You must supply values for: • • E zk : The dispersion coefficient of component k for the axial direction.49   Where:  ε i Dmk   2v g rp   νg Dmk E zk = = = = = Gas Velocity Molecular diffusivity of component k Axial dispersion coefficient of component k Interparticle voidage Particle radius εi rp 1 Gas Adsorption Processes 34 . k s : The effective thermal conductivity of the solid phase.73Dmk + v g rp ε i 1 + 9. Erk : The dispersion coefficient of component k for the radial direction. The axial dispersion coefficient is estimated using the following correlation. (Kast. 2-D Dispersive Properties (gas): Estimated Choose this option when variables such as pressure. 1988): E zk = 0.• • ∂ 2Ts Solid phase thermal conduction in axial direction: − k sz ∂z 2 Solid phase thermal conduction in radial direction: − k sr 1 ∂  ∂Ts   r r ∂r  ∂r  Choose from: • • Fixed Estimated 2-D Dispersive Properties (gas): Fixed Choose this option if the dispersive properties are constant throughout the packed bed. you must give values for the following thermal conductivities: • • k g : The effective thermal conductivity of the gas phase. temperature and velocity are changing significantly through the column. The radial dispersion coefficient is evaluated according to (Carberry. the effective gas phase thermal conductivity in the axial direction is: k gz = ρ g C pg ∑ (Ez . 1976): E rk = rp v g 4 = Radial dispersion coefficient of component k Where: Erk Assuming the analogy between mass and heat transfer is valid. it has no dynamic contribution to its effective thermal conductivity in the radial direction. the dynamic contribution to the effective radial gas phase thermal conductivity is: dyn k gr = ε i ρ g C pg ∑ (Erk yk ) k =1 nc Where: dyn k gr = Dynamic contribution to the effective gas phase thermal conductivity in radial direction As the adsorbent (a solid) is not in motion. The two contributions are additive. Assuming the validity of the analogy between heat and mass transfer. 1990).i yi ) i =1 nc Where: k gz = = = Effective gas phase thermal conductivity in axial direction Molar gas density Molar specific heat capacity at constant volume ρg C pg The effective gas phase thermal conductivity in the radial direction comprises a static and a dynamic contribution (Froment and Bischoff. 1 Gas Adsorption Processes 35 . 227 × 10 −3  T  =   ε 1 − p  100  1+ 2(1 − ε ) p = = = Radiation contribution Emissivity Thermal conductivity of the gas. so k s is constant through the simulation. 1 Gas Adsorption Processes 36 .0 α rg p = Factor 3 0.The static contribution of the gas phase effective thermal conductivity in the radial direction is: stat k gr = ε i (k g + β 2rpα rg ) Where: β = 1.227 ×10 −3 φ = 0. kg The total effective radial gas phase thermal conductivity is now given by: dyn stat k gr = k gr + k gr The effective radial solid phase thermal conductivity comes from: stat k sr = k sr = β (1 − ε i ) 1 kg + + α rs 2rp γ ks φ Where: α rs = 0.28 γ = ks p  T    2 − p  100  3 = Radiation contribution = Function of the packing density = Factor = Thermal conductivity of the solid 2 3 Aspen Adsim assumes that the effective solid thermal conductivity in the axial direction is not a function of any process variables. Fluid. or the radial gas phase concentration profiles in the pores of the adsorbent particles are to be accounted for in addition to the loading profiles. you can use a rigorous particle material balance to determine the loading profile inside the adsorbent. such as resistances.and macropores can be accounted for individually. The adsorbent should possess a homogenous pore structure. Kinetic Model Tab (gas): Film Model Assumption In the Film Model Assumption box. Particle MB  Where all components are adsorbed and the adsorbent has a homogenous pore structure. diffusivities and mass transfer coefficients. several mass transfer resistances occur in gas phase adsorption processes: • • Mass transfer resistance between the bulk gas phase and the gas-solid interface. where the mass transfer driving force is expressed as a function of the gas phase concentration. You can consider mass transfer resistances in one these ways: • • • • 1 Gas Adsorption Processes 37 . or one resistance dominates all others. This option performs a rigorous particle material balance for both the adsorbed and the gas phases. such as macropores and micropores. where the mass transfer driving force is expressed as a function of the solid phase loading.Kinetic Model Tab (gas) Use the Kinetic Model tab to specify the model kinetics. Particle MB 2  Where inert components are present. choose from: • • Solid. Micro & Macro Pore  The effects of the individual resistances to mass transfer in the micro. Kinetic Model Tab (gas): Kinetic Model Assumption Typically. In cases where the adsorbent has two distinct pore size regions. Mass transfer resistance due to the porous structure of the adsorbent. Lumped Resistance  Separate mass transfer resistances are lumped as a single overall factor. the resistance can be subdivided to account separately for each region. Within the void spaces between the particles (that is.i ρ s = ∂w = f (ci ) ∂t i 1 Gas Adsorption Processes 38 . Under practical conditions in gas separation. However. when modeling composite adsorbents. Solving the mass balance equation within the particle is usually complex.In the Kinetic Model Assumption box. the separate resistances to mass transfer is lumped as a single overall factor. you can usually discount any macropore diffusional resistance. as well as for the bulk flow in the bed. a higher pore diffusion rate results in a sharper and steeper concentration wave front. within the crystallines). both resistances can be significant and should be accounted for. you can simplify the mass balance equation in two ways: • Use expressions that relate the overall uptake rate to the bulk flow concentration: J ads . pore diffusion limits the overall mass transfer rate between the bulk flow and the internal surface of a particle. This gives importance to the effect of pore diffusion on the dynamics of absorbers. However. giving a better separation. The following table shows the difference between modeling macropore and micropore resistance in composite and uniform adsorbents: Pore structure Example(s) Micropore diffusional resistance High Macropore diffusional resistance Negligible Uniform Activated carbon alumina silica molecular sieve carbon Zeolites Composite High High When modeling adsorbents with uniform pore structure. Quantitative prediction of behavior requires the simultaneous solution of the mass balance within the particle. or one mass transfer resistance dominates the others. choose from these options: • • • • • • Lumped Resistance Micro and Macro Pore Effects Particle MB Particle MB 2 User Procedure User Submodel Kinetic Model Assumption (gas): Lumped Resistance Here. Kinetic Model Assumption (gas): Micro and Macro Pore Effects Two concentration gradients greatly affect the diffusion rate: • • Within the pores of the solid. Qualitatively. εB.i • If you know the concentration profile within the particle. wmsk εi Interpellet porosity Macropore c*. The model developed for particle diffusion accounts for both interparticle (macropore) and intraparticle (micorpore) diffusion effects. Concentration profile within the particle is radially symmetric. Radial dispersion is negligible. wk k Solid Surface Micropore The material balance model assumes that: • • • Radial concentration profile within the particle is parabolic. Several researchers have recently shown that profiles obtained by exact numerical solutions of both Pressure Swing and Thermal Swing Adsorption processes are usually parabolic in shape. w* bk Bulk Gas Intrapellet Porosity εP * cmsk. you can make considerable savings in numerical computation because integration along the radial distance in the particle is no longer necessary. w* bk Macropores: w* . cmsk msk Interpellet Voidage: εi Pellet (macroparticle) rP 2rc Solid Microporous Particles: wk. εB. ck * cbk. (1-εi) εP. and then from the macropores to the solid surface via the micropores: Bulk: cbk. so you can model pore diffusion by assuming a parabolic concentration profile within the particle. The model assumes that material flows first from the bulk gas to the macropores (crystallines). 1 Gas Adsorption Processes 39 .Where: ρs = = = Adsorbent bulk density Loading of component i due to adsorption Mass transfer rate of component i wi J ads . one-dimensional adsorption layer. The following options are available in the Form of Mass Transfer Coefficient field. you must specify the values of the macropore and micropore resistances: K mac and K mic . the gas phase material balance is written for a convection only situation in a vertical.Gas Phase The component balance in the bulk gas phase is of the form: ∂ (cbk vg ) ∂z + εB ∂cbk ∂w ∂c + (1 − ε p )ρ s k + (1 − ε i )ε p msk = 0 ∂t ∂t ∂t [Convection] + [accumulation] + [mass transfer (accumulation) to micropore] + [mass transfer (accumulation) to macropore] In the given example. Macropore (Crystalline) The material balance in the macropore is given as: Fluid Film Model: (1 − ε i )ε p ∂cmsk + (1 − ε p )ρ s ∂wk ∂t ∂t = K mac (cbk − cmsk ) [accumulation] + [mass transfer to micropore] = [rate of mass transfer from bulk gas] Solid Film Model: (1 − ε i )ε p ∂wk ∂c msk * * + (1 − ε p )ρ s = (1 − ε p )ρ s K mac wbk − wmsk ∂t ∂t ( ) Micropore (Particle) Fluid Film Model: (1 − ε )ρ p s ∂wk * = K mic c msk − c k ∂t ( ) [accumulation] = [rate of mass transfer from macropore] Solid Film Model: (1 − ε )ρ p s ∂wk * = (1 − ε p )ρ s K mic wsk − wk ∂t ( ) [accumulation] = [rate of mass transfer from macropore] Specifying Particle Resistance Coefficients If you choose Micro & Macro Pore Effects. 1 Gas Adsorption Processes 40 . 0 Where: Defc rc2 Component diffusivities in micropores Microparticle radius Defc rc = = Estimated This option uses a submodel in which Aspen Adsim automatically estimates the coefficients. Set the coefficients in the variable arrays Kmac and Kmic. the bed model is written so that the component rates of mass transfer are related to local conditions in the bed through the procedure type pUser_g_Kinetic. User Submodel The name of the submodel is gUserKinetic. wi . P. v g ) ∂t Note: Langmuir adsorption kinetics is quite a popular option.Constant This option forces the particle resistance coefficients to be constant throughout the bed. ci . 1 Gas Adsorption Processes 41 . and can be applied with such a procedure. ∂wi = f (Tg . User Procedure If you choose this option. Ts .0 Where: DefP rP2 Component diffusivities in macropores Particle radius DefP rp = = The micropore constant K mic is given by: K mic = 15. The macropore constant K mac is given by: K mac = 15. The Particle Material Balance option considers two mass transfer resistances: • • The following figure illustrates these resistances: 1 Gas Adsorption Processes 42 . Effective diffusivities for the gas and adsorbed phase are independent of the location inside the particle. caused by both gas and adsorbed phase diffusion. by rigorously solving the particle material balance for both phases.Kinetic Model Assumption (gas): Particle MB This option determines the loading and gas phase concentration profiles inside an adsorbent particle. For this to work. which is the resistance to mass transfer posed by the boundary layer between particle surface and bulk gas. the following conditions must be met: • • • Adsorbent has a uniform pore structure. which is the diffusional resistance inside the particle pore structure. Effective gas phase diffusion coefficient is calculated from the molecular and the Knudsen diffusion coefficients. The interparticle mass transfer resistance. The intraparticle mass transfer resistance. It is calculated from the particle location inside the adsorber (axial and radial column co-ordinate) using the procedure pUser_g_De or submodel gUserEffDiff. 1 Gas Adsorption Processes 43 .Boundary Layer Adsorbent Particle (Uniform Pore Structure) Bulk Gas ∂w i wi* ∂r r =rp Ji = aρsDei ∂w i ∂r wi(r) ci Ji c* i r rp =0 r =0 ∂w i ∂r = a(1 − ε )k f c i − c i* r =rp ( ) The particle material balance is expressed as:  2 ∂wk ∂ 2 wk  ∂wk − Dek  + =0 ∂t ∂r 2   r ∂r Where: wk Dek r = = = Loading Effective adsorbed phase diffusion coefficient Radial particle co-ordinate The effective diffusion coefficient is assumed constant throughout the particle. 6 Where: Shi = Sci = Re = k fi 2rp Dmi = Sherwood number µ Dmi ρ g M v g 2rp Mρ g = Schmidt number µ = Reynolds number 1 Gas Adsorption Processes 44 .1Sci1 / 3 Re 0.The boundary conditions for this partial differential equation come from both the symmetry condition at r=0: ∂wi ∂r =0 r =0 and the material flux through the boundary layer at r = rp : aρ s Dek Where: a ∂wk ∂r = = = = = = * = a(1 − ε i )k fk c k − c k r = rp ( ) Specific particle surface Bulk density of solid Interparticle voidage Boundary layer mass transfer coefficient Gas phase concentration Interface gas phase concentration ρs εi k fk ck * ck The gas phase composition and the loading are coupled by the condition that thermodynamic equilibrium has been achieved at the interface between gas phase and particle: wi* = wi Where: r = rp = f eq ci* ( ) f eq wi* = = Isotherm equation Loading at r = rp The boundary layer mass transfer coefficient is expressed using the following Sherwood number correlation: Shi = 2 + 1. which is the diffusional resistance inside the particle pore structure. Effective diffusivities for gas and adsorbed phase are independent of the location inside the particle.Dmi µ = = = = = Mean molecular diffusion coefficient Gas phase dynamic viscosity Molar gas phase density Mean molecular weight Superficial velocity ρg M νg Kinetic Model Assumption (gas): Particle MB 2 This option determines the loading and gas phase concentration profiles inside an adsorbent particle. which is the resistance to mass transfer posed by the boundary layer between particle surface and bulk gas. For this to work: • • • Adsorbent has a uniform pore structure. The Particle Material Balance 2 option considers two mass transfer resistances: • The intraparticle mass transfer resistance. • The following figure illustrates these resistances: 1 Gas Adsorption Processes 45 . The interparticle mass transfer resistance. caused by both gas and adsorbed phase diffusion. Effective gas phase diffusion coefficient is calculated from the molecular and the Knudsen diffusion coefficients. by rigorously solving the particle material balance for both phases. Boundary Layer Adsorbent Particle (Uniform Pore Structure) Bulk Gas ∂w i wi* ∂r ρs ∂w Dei i (1 − ε ) ∂r rp r =rp + D p .i r = rp ∂cip ∂r = k f ci − ci* r = rp rp ( ) wi(r) ci Ji ∂c c* ∂r i p i r = rp ∂c p ∂w 3 ∫ i r 2 dr 3 ∫ i r 2 dr ∂t ∂t + (1 − ε )ε p 0 3 Ji = ρs 0 3 rp rp ∂w i ∂r =0 r =0 r c p (r) i rp εp ∂cip ∂r =0 r = rp The particle material balance is given by:  2 ∂ckp ∂ 2 ckp  ρ ∂wk ρ ∂ckp + − Dek s + s − D pk  2  1− ε ∂t 1 − ε ∂t ∂r   r ∂r = = = = = Interparticle voidage Intraparticle voidage Bulk density Loading Gas phase concentration  2 ∂wk ∂ 2 wk  +  =0 ∂r 2   r ∂r Where: ε εp ρs wk ckp 1 Gas Adsorption Processes 46 . Dek D pk r = = = Effective adsorbed phase diffusion coefficient Effective pore gas phase diffusion coefficient Radial particle co-ordinate The effective adsorbed phase diffusion coefficient is assumed constant through the particle. The effective pore gas diffusion coefficient is calculated from the molecular diffusion coefficient and the Knudsen diffusion coefficient: 1 1  Tort  1  =  D + D  D pi ε p  Ki mi  and  T DKi = 97rPore  M  i Where: Tort = = = = = = =     0. using the procedure pUser_g_De or the submodel gUserEffDiff. You calculate it from the particle location inside the adsorber (given by the axial and radial column co-ordinate).5 Tortuosity of adsorbent Effective pore gas diffusion coefficient Knudsen diffusion coefficient Molecular diffusion coefficient of component i in the mixture Pore radius in adsorbent Adsorbent temperature Molecular weight of component i D pi DKi Dmi rPore T Mi The boundary conditions for this partial differential equation come from both the symmetry condition at r=0: ∂wi ∂r and =0 r =0 ∂cip ∂r =0 r =0 1 Gas Adsorption Processes 47 . and the material flux through the boundary layer at r = rp : ρs ∂w Dei i (1 − ε ) ∂r rp + D p . 1 Gas Adsorption Processes 48 . which increases the computational effort. so: wi = f eq cip Where: ( ) f eq cip wi = = = Isotherm equation Pore gas phase concentration Loading These calculations give the isotherm correlation at each radial node.i r = rp ∂cip ∂r = k fi ci − ci* r = rp rp ( ) ∂wi 2 ∂cip 2 r dr r dr 3∫ 3∫ ∂t ∂t 0 0 + (1 − ε )ε p Ji = ρs 3 3 rp rp Where: ρs ε = = = = = = = = = = = = Bulk density of solid Interparticle voidage Interparticle voidage Boundary layer mass transfer coefficient Bulk gas phase concentration Interface gas phase concentration Pore gas phase concentration Loading Material flux particle radius Effective gas phase pore diffusion coefficient Effective adsorbed phase diffusion coefficient εp k fi ci ci* cip wi Ji rp D pi Dei The gas phase concentration and the loading are coupled by the condition that thermodynamic equilibrium has been at each radial location inside particle. ci . P. v g ) ∂t Note: Langmuir adsorption kinetics is quite a popular option. the bed model relates component rates of mass transfer to local conditions in the bed through the submodel gUserKineticModel. wi . ∂wi = f (Tg . Ts . Kinetic Model Assumption (gas): User Submodel With this option. and can be applied with such a procedure.6 Where: Shi = Sci = Re = k fi 2rp Dmi = Sherwood number µ Dmi ρ g M v g 2rp Mρ g = Schmidt number µ = = = = = = Reynolds number Dmi µ Mean molecular diffusion coefficient Gas phase dynamic viscosity Molar gas phase density Mean molecular weight Superficial velocity ρg M νg Kinetic Model Assumption (gas): User Procedure With this option. the bed model relates component rates of mass transfer to local conditions in the bed through the procedure pUser_g_Kinetic. Ts .The boundary layer mass transfer coefficient is given by the following Sherwood number correlation: Shi = 2 + 1. 1 Gas Adsorption Processes 49 . ∂wi = f (Tg . wi . v g ) ∂t Note: Langmuir adsorption kinetics is quite a popular option. ci .1Sci1 / 3 Re 0. P. and can be applied with such a procedure. Kinetic Model Tab (gas): Form of Lumped Resistance Model Use the Lumped Resistance option to select the overall form of the mass transfer rate model. Fluid: (c ) − ci* ∂w ρ s i = MTC gi i ∂t 2ci 2 ( ) 2 2 Solid: ∂wi wi* − (wi ) = MTC si ∂t 2 wi 2 ( ) 1 Gas Adsorption Processes 50 . This option determines how the model relates the mass transfer rate due to adsorption ( J ads . you need to choose between the following driving force expressions: • • Linear Quadratic Form of Lumped Resistance Model (gas): Linear The mass transfer driving force for component i is a linear function of the gas phase concentration (fluid film) or solid phase loading (solid film).i ∂t If you chose Lumped Resistance as the kinetic model assumption. The mass transfer rate is related to the adsorbent uptake. in the Form of the Lumped Resistance Model box. to the local gas and solid states. Fluid: ρs ∂wi = MTC gi ci − ci* ∂t ( ) Solid: ∂wi = MTC si wi* − wi ∂t ( ) Form of Lumped Resistance Model (gas): Quadratic The mass transfer driving force is a quadratic function of the fluid film concentration or solid film loading.i ). as follows: ρs ∂wi = J ads . Estimated as your form of mass transfer coefficient. In either case. cmsk msk Interpellet Voidage: εi Pellet (macroparticle) rP 2rc Solid Microporous * Particles: wk. εB. wk k Solid Surface Micropore Typically. These mass transfer coefficients describe the resistance against mass transfer posed by the boundary layer surrounding the adsorbent particle. the mass transfer coefficients are evaluated from Sherwood or Colburn j-factor correlations.Kinetic Model Tab (gas): Molecular Diffusivities This option applies if you previously selected one of the following options: • • Particle MB as your kinetic model assumption. ck cbk. (1-εi) εP. Molecular Diffusivities (gas): Fixed The mean molecular diffusion coefficients are fixed for each component. for example. (1960) and Reid et al. Bulk: cbk. (1977). 1 Gas Adsorption Processes 51 . w* bk Macropores: w* . wmsk εi Interpellet porosity Macropore c*. mean gas phase molecular diffusivities are required for the calculation of film mass transfer coefficients. w* bk Bulk Gas Intrapellet Porosity εP * cmsk. You supply a value for each component into the array Dm(*) of the adsorbent layer model. εB. Values and estimation equations for diffusion coefficients for various gases are given by Bird et al. and Estimated in the Form of Mass Transfer Coefficients box. in the Form of Mass Transfer Coefficients box. You must supply a constant value of mass transfer coefficient for each component in the Specify table for the adsorbent layer. Kinetic Model Tab (gas): Form of Mass Transfer Coefficients If you selected either Lumped Resistance or Micro & Macropore for your kinetic model assumption then. choose from these options: • • • • • • Arrhenius Constant Estimated Pressure Dependent Arrhenius User Procedure User Submodel Form of Mass Transfer Coefficients (gas): Arrhenius This option evaluates the mass transfer coefficient as a function of temperature from an Arrhenius type equation:  − E acti  MTC i = k 0i exp   RT  To use this option. you must supply the pre-exponential factor k 0i and the activation energy E acti for each component i.Molecular Diffusivities (gas): User Procedure You supply the mean gas phase diffusion coefficients using a Fortran subroutine. the mass transfer coefficient for each component is constant throughout the bed. which Aspen Adsim interfaces through the procedure pUser_g_Diffusivity. Form of Mass Transfer Coefficients (gas): Estimated If you have selected Lumped Resistance as your kinetic model assumption. as fixed variables in the Specify table for the adsorbent layer. Form of Mass Transfer Coefficients (gas): Constant Here. choose the Estimated Mass Transfer Coefficient Assumption from: • • Micro and Macro Pores Considered Macropore Only 1 Gas Adsorption Processes 52 . is obtained by: K Ki = K Ki ρs εi The film resistance coefficient k fi is obtained from the Sherwood number as: k fi = Shi Where: Dmi 2r p Shi = 2. they are approximations that serve only as rough guides.0 + 1.6 Re = = Reynolds number Schmidt number = Sci µ (Dmi ρ s ) The macropore diffusion coefficient K pi is obtained from:  1 1 1  = Tort   D + D  K pi mi   Ki 1 Gas Adsorption Processes 53 . K Ki . One such method is based on the Henry's Coefficient.Methods exist in the literature for estimating the mass transfer coefficient as a function of the supplied isotherm. You can fine-tune the values by adjusting the estimated values until the timing and shape of the simulated breakthrough curves match the experimentally measured breakthrough curves. the adsorption rate model for component i can be expressed as: ∂wi = k i wi* − wi = k i K Ki ci − ci* ∂t ( ) ( ) The effective mass transfer coefficient is given as a lumped term comprising the external film resistance term. the macropore diffusion term.1Sci1 / 3 Re 0. They usually need to be finetuned. In general. These methods rarely provide exact values. and the micropore diffusion term: rp rp2 rc2 1 = + + k i 3k fi 15ε p K pi 15 K Ki Dci The Henry's coefficient K Ki is obtained from the isotherm as: K Ki = ∂w* ∂wi* = RT i ∂ci ∂Pi The dimensionless Henry’s coefficient. In the Estimated Mass Transfer Coefficient Assumption box. As such it is especially suitable for PSA systems. 1 Gas Adsorption Processes 54 .5 ρg Dci DKi Dmi ep ki K Ki k fi K pi w R = = = = = = = = = = = = = = = Gas density Micropore diffusion coefficient Knudsen diffusion coefficient Multi-component molecular diffusion coefficient particle (macro) porosity effective mass transfer coefficient Henry's coefficient Film resistance coefficient Macropore diffusion coefficient Loading Universal Gas Constant Radius of crystalline or primary micropore Particle radius Tortuosity factor Dynamic viscosity rc rp Tort µ To include the effect of the micropore resistance in the estimated values for the mass transfer coefficients: • Give values for the micropore diffusion coefficients and the radius of the primary micropore. The model was found to represent experimental data well.The Knudsen diffusion coefficient D Ki is:  T DKi = 97rPore  M  i Where:     0. but also accounts for changes in total pressure. select Macropore only. To ignore the micropore effect: • Form of Mass Transfer Coefficients (gas): Pressure Dependent Arrhenius This option is based on the Arrhenius model. 5 The above equations are evaluated automatically by Aspen Adsim when you select this option.MTC i = k 0 Pi  − E acti  exp  P  RT  You have to supply the pre-exponential factor k 0 Pi and the activation energy E acti for each component i. 1987 for example) approximation of a lumped mass transfer coefficient states: MTC s .5 De t Cycle rP2 : Ω = 15 5. 1 Gas Adsorption Processes 55 . Nakao and Suzuki (1983) showed that the value of 15 underestimates the magnitude of the mass transfer coefficient for short adsorption times. the mass transfer coefficients are estimated and then returned through the submodel gUserMTC. as fixed variables in the Specify table for the adsorbent layer. Furthermore. Form of Mass Transfer Coefficients (gas): User Submodel If you choose this option.1 : Ω = θ θ ≤ 0.i = ΩDei rP2 with Ω=15. and either Constant or Estimated in the Form Of Mass Transfer Coefficient box.1 0. this option applies only to cyclic processes and especially PSA systems. the mass transfer coefficients are estimated using a Fortran subroutine. the following time constant can be calculated: θ = 0.001 : Ω = 162.001 ≤ θ < 0. Kinetic Model Tab (gas): Apply Cyclic Correction This option is available only if you selected Lumped Resistance as your kinetic model assumption. Form of Mass Transfer Coefficients (gas): User Procedure Here. Assuming that an adsorption column is in adsorbing mode for about half the total time of the adsorption cycle.14 The parameter Ω is a function of θ: θ ≥ 0 . The Glueckauf (see Yang. which Aspen Adsim interfaces through the procedure pUser_g_MTC. the form of the effective adsorbed phase diffusion coefficient is determined. Effective Diffusivity (gas): User Procedure You supply the mean adsorbed phase diffusion coefficients using a Fortran subroutine. With this option. Choose one of three options: • • • Fixed User Procedure User Submodel Particle Material Balance. Gas Adsorption Layer (gas): Particle Material Balance. Number of Nodes This option is available only if you selected Particle MB or Particle MB 2 as your kinetic model assumption. Effective Diffusivity This option is available only if you selcted Particle MB or Particle MB 2 as your Kinetic Model Assumption. which Adsim interfaces through the procedure pUser_g_De. Effective Diffusivity (gas): Fixed With this option. the effective diffusion coefficients for each component in the adsorbed phase are given a constant value. which you supply through the array De(*) of the adsorbent layer model. It determines how many nodes to use for the central finite difference discretization of the second order derivative in the particle material balance: 1 ∂  2 ∂w  2 wk +1 − wk −1 wk +1 − 2 wk + wk −1 + r ≈ 2(∆r ) r 2 ∂r  ∂r  rk (∆r )2 Kinetic Model Tab (gas): Particle Material Balance. 1 Gas Adsorption Processes 56 . Particle Material Balance. Particle Material Balance. Effective Diffusivity (gas): User Submodel You supply the mean adsorbed phase diffusion coefficients through the user submodel gUserEffDiff.Kinetic Model Tab (gas): Estimated Mass Transfer Coefficient Assumption This option is available only if you selected Estimated as your estimated mass transfer coefficient. 1984. If you know the adsorption isotherms for the components of the feed. You choose these isotherms from the Configurure Layer forms for the layers making up the bed model. 1987. so adsorption isotherms are crucially important data in the design of adsorbers. When you use Aspen Adsim isotherm models for pure components or for multi-component mixtures. which are listed in the following table: Variable Loading (w) Gas phase concentration (c) Pressure (P) Temperature (T) Unit of measurement kmol/kg kmol/m3 bar K About Adsorption Isotherms for Gas Adsorption Processes Adsorption is the tendency of molecules from an ambient fluid phase (gas or liquid) to stick to the surface of a solid. you must supply isotherm parameters consistent with the functional form.Isotherm Tab (gas) Use the Isotherm tab to define the adsorption isotherms to be used in your gas adsorption process. The Aspen Adsim isotherm models are expressed as functions of either partial pressures or concentrations. you can create a bed model to predict the performance of the adsorber bed for the specified operating conditions. Adsorption isotherms describe the tendency for the components to adsorb onto the solid. and user-supplied isotherms. 1 Gas Adsorption Processes 57 . see Chapters 2 through 4 in Ruthven. For more information. The driving force behind all adsorptive gas separation processes is the departure from adsorption equilibrium. they describe the amount of each component adsorbed onto the solid at thermodynamic equilibrium. It is imperative that you convert isotherm parameters to Aspen Adsim's base units of measurement. This section explains these choices for pure component. multicomponent. 1988 (German language). Most of the important industrial applications of adsorption depend on differences in the affinity of the solid surface for different components. Chapters 2 and 3 in Yang. and Chapter 3 in Kast. Aspen Adsim has a comprehensive list of adsorption isotherms. including: • • • • Vacancy Solution Extended Langmuir Approach Ideal Adsorbed Solution Real Adsorbed Solution Theory Most of the physical adsorption models contain two or three parameters. or use published literature values. Mixture adsorption equilibria data are not readily available. The equilibrium specified by the isotherm model affects the driving force for mass transfer. This is because adsorbed gas components interact on the solid surface. Although measurements can be made. 1 Gas Adsorption Processes 58 . so individual gas components adsorb in a different fashion when mixed with other components. Important: The expressions in this section are equilibrium equations. Several methods for predicting mixture isotherms from pure component data have been proposed recently. Aspen Adsim names the equilibrium variable arrays (of size n or n×m) either Ws or Cs. the expressions compute either: • w*. The choice between w* and c* is automatically handled by Aspen Adsim.or • c*. so it is common practice to predict mixture isotherms from pure component isotherms. About Multi-Component Mixture Isotherms (gas) In adsorber design. rather than those of pure components. You can estimate these parameters from experimental data. and the parameters for mixture isotherms are written as a function of the pure component parameters and the composition of the adsorbed phase. you are usually interested in the adsorption equilibria of mixtures. the loading which would be at equilibrium with the actual gas phase composition . even if the model parameters are derived from exactly the same set of data. so you can get significantly different simulation results when using different models.Guidelines for Choosing Aspen Adsim Isotherm Models (gas) Choose a model that is appropriate to the process you are investigating. or axially and radially. Depending on the mass transfer rate model you choose. The isotherm model parameters are always set variables. the gas phase composition which would be at equilibrium with the actual loading. In bed models. these variables are distributed axially. they are tedious and time-consuming to perform. and have indices to identify their location in the bed. The Gibbs approach is used for vapor-liquid equilibria. The extended Langmuir approach takes a single component gas isotherm parameter and.i = µ i0 (T ) + RT ln ( yi P ) The chemical potential for an ideal gas phase is given by: The equilibrium condition is: µ gas . The method enables you to predict adsorption equilibria for components in a gaseous mixture. calculates a fitting parameter to account for the presence of other components. The model treats the mixed adsorbate phase as an ideal solution in equilibrium with the gas phase. IAS is available in Aspen Adsim. The basic requirements for thermodynamic equilibrium between two phases are that the pressure.Vacancy Solution (gas) The vacancy solution is the least popular of all the methods. in which the fundamental equations of thermodynamic equilibrium are developed. Langmuir models use a weighting factor to account for the inter-species interaction in mixtures. The values of the interaction parameters depend on all the species present.i = µ ads . ideal behavior in the adsorbed phase seems improbable. zeolites. The value of the weighted inter-species interaction parameter is obtained from mixture experimental data. To use it. choose the appropriate isotherm on the Isotherm Tab of the layer configuration form. xi ) = µ i0 (T ) + RT ln (Pi 0 (Π )) + RT ln (γ i xi ) µ gas .i (T . The chemical potential for an adsorbed phase can be written as (Kast. many systems have shown strong correlation between experimental data and predictions by IAS theory. Π . For a full description of the IAS approach. the Ideal Adsorbed Solution Theory (IAS) has become popular for multi-component mixtures. Extended Langmuir Approach (gas) This is an extension of the Langmuir isotherms for single components.i 1 Gas Adsorption Processes 59 . see Chapter 4 of Ruthven (1984) or Chapter 3 of Kast (1988) (German language). temperature and chemical potential of each component are equal in both phases. However. and silica gel. but the approach has been developed in a limited number of cases for some single and multicomponent systems. including binary and ternary mixtures on activated carbons. Ideal Adsorbed Solution (gas) Recently. At first sight. It requires data only for the pure-component adsorption equilibria at the same temperature and on the same adsorbent. and applies this to the gas-adsorbed phase equilibria. 1988): µ ads . depending on the components of the multi-component gas mixture. P. 1 Gas Adsorption Processes 60 . analogous to Raoult’s law can be derived: γ i = 1 ). Non-ideal behavior in the adsorbed phase can be accounted for by evaluating the activity coefficient using a suitable Gibbs excess enthalpy correlation (for example.Assuming ideal behavior in the adsorbed phase (that is.. AspenTech’s Aspen Properties system is used to supply the value of γ i so that: E yi P = γ i xi Pi 0 (Π ) can be evaluated.. Once those parameters are known. which gives the same spread pressure in the adsorbed phase as the gas mixture at pressure P. IP ) dP P The equation set is completed with the following conditions: ∑x i =1 n i =1 i =1 =1 ∑y i Π i0 = Π 0 = Π k0 = . Wilson or UNIQUAC). The relationship between Pi and the spreading pressure 0 0 Π i0 is derived using the Gibbs-Duhem equation for a single adsorbed component: AdΠ i0 = wi0 dµ i0 = wi0 RTd ln( Pi 0 (Π ) ( ) On integrating and using the pure component isotherm to replace wi : 0 AΠ i0 = RT n Pi0 ∫ 0 f eq (T . 1981).. This assumption resulted in the activity coefficient of each component being set to unity ( γ i = 1 ). j The total loading and component loadings are calculated from: ∑w i =1 n xi 0 i = 1 wtot and wi = xi wtot Real Adsorbed Solution Theory (gas) The derivation of the Ideal Adsorbed Solution Theory (see earlier) assumed ideal behavior in the adsorbed phase. an expression yi P = xi Pi 0 (Π ) The pressure Pi is a fictitious pure component gas phase pressure. The binary parameters of the g models have to be determined from suitable experiments (Costa et al. E. The isotherm is a function of a partial pressure or concentration: wi = or IP1 Pi 1 + IP2 Pi IP1ci 1 + IP2 ci (partial pressure) wi = (concentration) 1 Gas Adsorption Processes 61 . In the Isotherm Assumed for Layer box. There are three standard sub-options for the pure component Langmuir isotherms supported in Aspen Adsim: Langmuir 1. Multilayer Dubinin-Astakov Model Linear Model Volmer Model Myers Model Extended Langmuir Models Extended Langmuir. with negligible interaction between adsorbed molecules.Freundlich Model Dual-Site Langmuir Model Single Layer B.T User Procedure User Submodel IAS Isotherm Assumed for Layer (gas): Langmuir Models Langmuir isotherm models typically apply to the adsorption of a single molecule layer on completely homogeneous surfaces. Emmett & Teller) Models B.E.T. (Brunauer. select from: • • • • • • • • • • • • • • • • • • • Langmuir Models Freundlich Models Langmuir-Freundlich Model Henry's Models Toth Model B.E.Isotherm Tab (gas): Isotherm Assumed for Layer Aspen Adsim enables you to use a number of pure component isotherms and multi-component isotherms.T Dual Layer B.E.T. and one of partial pressure or concentration: wi = IP1e IP3 / Ts Pi IP2 or (partial pressure) wi = IP1e IP3 / Ts ciIP2 (concentration) 1 Gas Adsorption Processes 62 . Unlike Langmuir2. so reflects more 1 accurately the physical reality of numerous adsorption processes: wi = or (IP1 − IP2Ts )IP3 e IP / T Pi 4 s 1 + IP3 e IP4 / Ts Pi (partial pressure) wi = (IP1 − IP2Ts )IP3 e IP / T ci 4 s 1 + IP3 e IP4 / Ts ci (concentration) Isotherm Assumed for Layer (gas): Freundlich Models Aspen Adsim has two sub-options for the pure component Freundlich isotherms: Freundlich 1. the maximum loading. The isotherm is a function of partial pressure or concentration: wi = IP1 Pi IP2 or (partial pressure) wi = IP1C iIP2 (concentration) Freundlich 2. The isotherm is a function of temperature. and one of partial pressure or concentration. The isotherm is a function of temperature.Langmuir 2. and one of partial pressure or concentration: IP1e IP2 / Ts Pi wi = 1 + IP3 e IP4 / Ts Pi or (partial pressure) IP1e IP2 / Ts ci wi = 1 + IP3 e IP4 / Ts ci (concentration) Langmuir 3. is a function of temperature. The isotherm is a function of temperature. expressed by (IP − IP2Ts ) . Isotherm Assumed for Layer (gas): Langmuir-Freundlich Model This isotherm is a function of temperature. and one of partial pressure or concentration: IP1 IP2 PiIP3 e IP4 / Ts wi = 1 + IP5 PiIP3 e IP6 / Ts or (partial pressure) IP1 IP2 ciIP3 e IP4 / Ts wi = 1 + IP5 ciIP3 e IP6 / Ts (concentration) Isotherm Assumed for Layer (gas): Henry's Models Aspen Adsim has two sub-options of the pure component Henry's isotherms: Henry 1. and one of partial pressure or concentration: wi = IP1e IP2 / Ts Pi or (partial pressure) wi = IP1e IP2 / Ts ci (concentration) Isotherm Assumed for Layer (gas): Toth Model The isotherm is a function of partial pressure or concentration: 1  ( IP1 Pi )  wi =  IP2  1 + ( IP3 Pi )  IP2 IP2 (partial pressure) or 1  ( IP1ci ) IP2  IP2 wi =  IP2  1 + ( IP3 ci )  (concentration) 1 Gas Adsorption Processes 63 . The isotherm is a function of partial pressure or concentration: wi = IP Pi 1 or (partial pressure) wi = IP ci 1 (concentration) Henry 2. The isotherm is a function of temperature. IP4 .E. and hence the number of adsorbed layers is extremely large. it fills the gap between the Langmuir isotherm (single layer BET) and the BET isotherm with an infinite number of layers. The isotherm is always evaluated as a function of the relative pressure: φi = Pi Psat If you selected concentration dependency. using degrees Celsius or Kelvin as temperature units of measurement. Physically.E. The parameter IP is then a conversion factor for calculating 8 Psat in bar. but has an additional parameter. stating the number of layers adsorbed.Isotherm Assumed for Layer (gas): B. Emmett and Teller) type isotherm (or multilayer Langmuir relation) for gas-solid systems in which condensation is approached. Psat = IP8 × 10 IP5 − IP6 IP7 + Ts 1 Gas Adsorption Processes 64 . (Brunauer. Use it only for systems where the operating temperature is below the critical temperature of the adsorbate. This isotherm is a function of temperature and one of partial pressure or concentration:  IP  IP1 Pi exp 2  T   s  wi =   IP4    IP6  1 + IP3 Pi exp  T  1 − IP5 Pi exp T      s   s    or (partial pressure)  IP  IP1ci exp 2  T   s  wi =   IP4    IP   1 − IP5 ci exp 6  1 + IP3 ci exp T  T   s    s   (concentration) Isotherm Assumed for Layer (gas): BET Multilayer The BET Multilayer isotherm is similar to the BET isotherm. the following equation is used to calculate the partial pressure: Pi = ci RTg The saturation pressure Psat is calculated according to a base 10 Antoine equation.T.T Use the B. and one of partial pressure or concentration: wi = IP1 exp − ( AA / IP2 ) 2 + IP3 exp − ( AA / IP4 ) 2 Where: [ ] [ ]  P AA = RTs ln i P  sat or             (partial pressure)  c RT AA = RTs ln i s  P  sat and  IP6  IP5 −  Ts − IP7  (concentration) Psat = IP8 10 IP8 is a conversion factor to convert the resulting partial pressure predicted by the Log10 base Antoine Equation. Isotherm Assumed for Layer (gas): Linear Model This isotherm is a function of partial pressure or concentration: wi = IP1 Pi + IP2 or (partial pressure) wi = IP1ci + IP2 (concentration) Isotherm Assumed for Layer (gas): Volmer Model The Volmer isotherm expresses concentration as a function of loading: ci =  IP1 wi IP1 wi exp  IP − IP w IP2 − IP1 wi 1 i  2     1 Gas Adsorption Processes 65 .The kinetic factor b is:  IP  b = IP2 exp 3  T   s  The isotherm is:  IP bφ  1 − (IP4 + 1)φ IP4 + IP4φ IP4 wi =  1   1 − φ  1 + (b − 1)φ − bφ IP4 +1       Isotherm Assumed for Layer (gas): Dubinin-Astakov Model This isotherm is a function of temperature. into bar (Aspen Adsim's base unit of measurement for pressure). This isotherm is a function of partial pressure or concentration: wi = or IP1i Pi 1 + ∑ (IP2 k Pk ) k (partial pressure) wi = IP1i ci 1 + ∑ (IP2 k c k ) k (concentration) Extended Langmuir 2. and one of partial pressure or concentration: wi = or IP1i e IP2 i / Ts Pi 1 + ∑ IP3k e IP4 k / Ts Pk ( ( ) ) (partial pressure) k IP1i e IP2 i / Ts ci wi = 1 + ∑ IP3k e IP4 k / Ts c k k (concentration) Extended Langmuir 3. and one of partial pressure or concentration: ( IP1i − IP2i Ts ) IP3i e IP4 i / Ts Pi wi = 1 + ∑ IP3k e IP4 k / Ts Pk ( ) (partial pressure) k or wi = ( IP1i − IP2i Ts ) IP3i e IP4 i / Ts ci 1 + ∑ IP3k e IP4 k / Ts c k ( ) (concentration) k 1 Gas Adsorption Processes 66 . This isotherm is a function of temperature.Isotherm Assumed for Layer (gas): Myers Model TheMyers isotherm expresses concentration as a function of loading:  w  ci = IP1 exp IP2 i   IP1    Isotherm Assumed for Layer (gas): Extended Langmuir Models There are three standard sub-options of the extended Langmuir isotherms supported in Aspen Adsim: Extended Langmuir 1. This isotherm is a function of temperature. E. and one of partial pressure or concentration: IP i e IP2 i / Ts Pi IP5i e IP6 i / Ts Pi 1 Wi = + 1 + ∑ ( IP3k e IP4 k / Ts Pk ) 1 + ∑ ( IP7 k e IP8 k / Ts Pk ) k k (partial pressure) or IP i e IP2 i / Ts ci IP5i e IP6 i / Ts ci 1 Wi = + 1 + ∑ ( IP3k e IP4 k / Ts ck ) 1 + ∑ ( IP7 k e IP8 k / Tk ck ) k k (concentration) Isotherm Assumed for Layer (gas): Single Layer B.E. and one of partial pressure or concentration: IP i IP2i Pi e IP3i / Ts 1 wi = 1 + ∑ IP2 k Pk e IP3 k / Ts ( ( ) ) (partial pressure) k or IP i IP2i ci e IP3i / Ts 1 wi = 1 + ∑ IP2 k ck e IP3 k / Ts k (concentration) 1 Gas Adsorption Processes 67 . and one of partial pressure or concentration: wi = or IP1i IP2i Pi IP3i e IP4 i / Ts 1 + ∑ IP5 k PkIP3 k e IP4 k / Ts ( ( ) ) (partial pressure) k wi = IP1i IP2i ciIP3i e IP4 i / Ts 1 + ∑ IP5 k c kIP3 k e IP4 k / Ts k (concentration) Isotherm Assumed for Layer (gas): Dual-Site Langmuir Model This isotherm is a function of temperature.Isotherm Assumed for Layer (gas): Extended LangmuirFreundlich Model This isotherm is a function of temperature.T isotherm with a monolayer. This isotherm is an extended B. The isotherm is a function of temperature.T. It is equivalent to the extended Langmuir isotherm. for use as multi-component isotherms. P. IP • ( ) The second subroutine integrates the Gibbs isotherm to give the spread pressure. IP ) or (partial pressure) wi = f eq (T . IP ) (concentration) You can also supply pure component user-specified isotherms. to wi0 = f eq T . The relationship to be evaluated is: AΠ i0 = g T . and one of partial pressure or concentration: IP i IP2i Pi e 1 k + wi = 1 + ∑ IP2 k Pk e IP3 k / Ts   IP3 k / Ts IP3 k / Ts  k 1 + ∑ IP2 k Pk e  1 + IP4 k ∑ IP2 k Pk e  k k    ( IP3 i / Ts ) IP2i e IP3i / Ts IP4i ∑ IP2 k Pk e IP3 k / Ts ( ) ( ) ( ) (partial pressure) or IP2i e IP3i / Ts IP4i ∑ IP2 k ck e IP3 k / Ts IP i IP2i ci e IP3i / Ts 1 k + wi = 1 + ∑ IP2 k ck e IP3 k / Ts   IP3 k / Ts IP3 k / Ts  k 1 + ∑ IP2 k ck e  1 + IP4 k ∑ IP2 k ck e  k k    ( ) ( ) ( ) ( ) (concentration) Isotherm Assumed for Layer (gas): User Procedure You can supply your own proprietary isotherm relationships using a Fortran subroutine. c1 .. The functional relationship is: wi = f eq (T .E. IP ) P dP 1 Gas Adsorption Processes 68 . P.Isotherm Assumed for Layer (gas): Dual Layer B. using the IAS method. This procedure relates the fictitious pure component partial pressure Pi the loading wi by means of a pure component isotherm: 0 0 (resulting in the same spread pressure as the mixture at pressure P). y nc . Pi 0 .T. you must supply two Fortran subroutines: • The first subroutine is interfaced by the procedure pUser_g_Isotherm_Poi.. IP with g = RT ( ) Pi0 ∫ 0 f eq (T . It is interfaced by the procedure pUser_g_Gibbs... Here.cnc . which Aspen Adsim interfaces through either the procedure pUser_g_Isotherm_P (partial pressure dependent isotherm) or pUser_g_Isotherm_C (concentration dependent isotherm). This isotherm is a function of temperature. Pi 0 . y1 . to the loading wi by means of a pure component isotherm: 0 0 wi0 = f eq T . This relates the fictious pure component partial pressure Pi (resulting in the same spread pressure as the mixture at pressure P). multicomponent adsorption behavior using pure component isotherms. IP ) or (partial pressure) wi = f eq (T . Pi 0 .. y1 .. c1 . IP with g = RT ( ) Pi0 ∫ 0 f eq (T . Each pure component isotherm has the same expression as its pure component version. IP ) (concentration) Pure component user specified isotherms may be supplied and used as multicomponent isotherms using the IAS method..cnc .Isotherm Assumed for Layer (gas): User Submodel You can supply your own proprietary isotherm relationships using one of these two submodels: • • gUserIsothermPp (partial pressure dependent isotherm) gUserIsothermC (concentration dependent isotherm) The functional relationship is: wi = f eq (T . This integrates the Gibbs isotherm to give the spread pressure. Aspen Adsim's standard pure component isotherms available with IAS are: • • • • • • Langmuir models Freundlich models Langmuir-Freundlich models Henry's models BET multilayer User-specified isotherms (user procedure or user submodel) 1 Gas Adsorption Processes 69 . P. y nc . IP ) P dP Isotherm Assumed for Layer (gas): IAS The IAS facility in Aspen Adsim lets you calculate competitive. IP • ( ) The second submodel is gUserGibbs.. P. Pi 0 . in which case you must supply two submodels: • The first submodel is gUserIsothermPoi. The relationship to be evaluated is: AΠ i0 = g T . The procedure is described by the type pUser_Act_Coeff. The two options are: • • IAS RAST With RAST selected and with user procedures supplying the physical properties. from: • • • • • • Isothermal Non-Isothermal with No Conduction Non-Isothermal with Gas Conduction Non-Isothermal with Solid Conduction Non-Isothermal with Gas and Solid Conduction None For a vertical bed type with 2-D spatial dimension. you can then use either the ideal adsorbed solution theory (IAS) or the real adsorbed solution theory (RAST).Isotherm Tab (gas): Adsorbed Solution Theory If you choose an IAS isotherm. The procedure evaluates γ i as a function of temperature. you must write a Fortran procedure to supply the activity coefficients. choose your prefered type of energy balance. choose from: • • Concentration — The adsorption isotherm model is a function of concentration.. xnc ) Isotherm Tab (gas): Isotherm Dependency In the isotherm dependency box. p. Partial Pressure — The adsorption isotherm model is a function of partial pressure. Energy Balance Tab (gas): Energy Balance Assumption In the Energy Balance Assumption box. pressure and the composition of the adsorbed phase: γ i = f (T . 1 Gas Adsorption Processes 70 . x1 . Energy Balance Tab (gas) Use the Energy Balance tab to specify how the energy balance is incorporated into the model for your gas adsorption process.... the conduction options are not available as conduction is automatically considered for all dimensions. the adsorbed phase heat capacity.Energy Balance Assumption (gas): Isothermal The Isothermal option completely ignores the energy balance. Energy Balance Assumption (gas): Non-Isothermal with Gas and Solid Conduction This option includes the thermal conduction term for both gas and solid phases. and the solid density: H i = ρ s C pai wi ∂Ts ∂t 1 Gas Adsorption Processes 71 . Energy Balance Assumption (gas): Non-Isothermal with No Conduction This option ignores the axial thermal conduction for the gas and solid phases. If the enthalpy content of the adsorbed phase is significant for your process. later. The term for each component is a function of the loading and the temperature in the solid phase. Energy Balance Tab (gas): Consider Heat of Adsorbed Phase Aspen Adsim models also let you include the enthalpy content of the adsorbed phase in the solid-phase energy balance. Energy Balance Assumption (gas): Non-Isothermal with Gas Conduction This option includes the thermal conduction (axial thermal dispersion) term in the gas energy balance: ∂ 2T − εi k ∂z 2 gz g You need to define the form of the gas thermal conductivity. choose this option to include it in the solid phase energy balance. Energy Balance Assumption (gas): Non-Isothermal with Solid Conduction This option includes the thermal conduction term in the solid energy balance: − k sz ∂ 2Ts ∂z 2 You must supply a value for k sz in the Specify table for the layer. The Enthalpy of Adsorbed Phase term is optional. See Energy Balance Tab: Form of Gas Thermal Conductivity. The gas temperature Tg and the solid temperature Ts are held constant and equal. You must define the form of the gas thermal conductivity. the heat capacities of the adsorbed phase components C pai are constant. HT.The total contribution is the sum for all components: ∑(H ) i i This equation is quite rigorous. the heat capacities of the adsorbed phase components C pai are calculated using a user-defined subroutine. depends on the local rate of mass transfer (the change in the amount of material adsorbed): HTi = ∂w ∆H i ∂t i These rates are held in vectors. The rate of heat generation by adsorption of each component i per unit mass of solid. choose from: • • • • None Constant User Procedure User Submodel Consider Heat of Adsorbed Phase(gas): None If you choose this option. Consider Heat of Adsorbed Phase(gas): Constant Here. and summed for all components to obtain the total rate of heat generation by adsorption per unit volume of solid: ρ s ∑ (− HT ) i i 1 Gas Adsorption Processes 72 . Energy Balance Tab (gas): Heat of Adsorption Assumption You must include the heat of adsorption in the solid-phase energy balance if it is significant for the process. Consider Heat of Adsorbed Phase(gas): User Submodel The heat capacities of the adsorbed phase components C pai are calculated through the user-defined submodel gUserCpa. In the Consider Heat of Adsorbed Phase box. the enthalpy of adsorbed phase term is ignored in the solid phase energy balance. despite neglecting some second order terms such as enthalpy of mixing. Consider Heat of Adsorbed Phase(gas): User Procedure With this option. which Aspen Adsim interfaces through the procedure pUser_g_Cpa. In the Heat of Adsorption Assumption box, choose from: • • • • None Constant User Procedure User Submodel Heat of Adsorption Assumption (gas): None The heat generation by adsorption term is omitted from the energy balance. Heat of Adsorption Assumption (gas): Constant With this option, the heat of adsorption is constant for each component i. Choose it to set the heat of adsorption to constant values, which you supply in the Specify table for the layer for each component. Heat of Adsorption Assumption (gas): User Procedure Here, the heat of adsorption is given by the Fortran procedure pUser_g_DH. You can vary the heat of adsorption and make it a function of, for example, local loading, temperature, and pressure. In general terms: ∆H ij = f (Tsj , Pj , wij ) Where i designates the component and j designates the node. Heat of Adsorption Assumption (gas): User Submodel With this option, the heat of adsorption comes from the submodel gUserDH. You can vary the heat of adsorption and make it a function of, for example, local loading, temperature, and pressure. In general terms: ∆H ij = f (Tsj , Pj , wij ) Where i designates the component and j designates the node. Energy Balance Tab (gas): Form of Heat Transfer Coefficient If you specify a non-isothermal energy balance, Aspen Adsim generates the solid and gas-phase energy balances with a film resistance to the heat transfer between the solid and the gas. Heat transfer is assumed to occur between the two phases according to the film resistance model: rate of heat transferred per m 3 of bed = HTC a p (Tg − Ts ) If there is no such heat transfer resistance, the gas and solid temperatures are equal (lumped): Tgj = Tsj for all nodes j = 1, m To get this condition, set the heat transfer coefficient to a large value (such as 1). 1 Gas Adsorption Processes 73 In the Form of Heat Transfer Coefficient box, choose from: • • • • Constant Estimated User Procedure User Submodel Form of Heat Transfer Coefficient (gas): Constant Choose this option to make the heat transfer coefficient a constant value, which you set through the variable HTC in the Specify table for the layer. Form of Heat Transfer Coefficient (gas): Estimated The heat transfer coefficient is estimated as follows: 1 Calculate the Reynolds number: Re = 2rp M ρ g v g µ If the calculated value falls below 1E-10, it is reset to this value. 2 Calculate the Prandl number: Pr = µ C pg kg M If the calculated value falls below 1E-10, it is reset to this value. 3 Calculate the j-factor: If Re < 190 then j = 1.66 Re 4 −0.51 −0.41 otherwise j = 0.983Re Calculate the heat transfer coefficient: HTC = jC pg v g ρ g Pr −2 3 If the calculated value falls below 1E-10, it is reset to a value of 1. Form of Heat Transfer Coefficient (gas): User Procedure With this option, the user procedure pUser_g_HTC relates the local heat transfer coefficient to the state of the bed at a particular point in the bed. This means you can interface your own Fortran code to calculate the coefficients. Note that the heat transfer coefficient becomes a distributed variable when you select this option. The values are held in the variables HTC(1), HTC(2)……HTC(n). In general terms: HTC j = f (Tgj , Pj , c j , vgj ) Form of Heat Transfer Coefficient (gas): User Submodel Here, the local heat transfer coefficient is defined through the user submodel gUserHTC, using the same dependencies as in the User Procedure option. 1 Gas Adsorption Processes 74 Energy Balance Tab (gas): Form of Gas Thermal Conductivity If you selected non-isothermal with gas and/or solid conduction, you need to choose the form of gas thermal conductivity. In the Form of Gas Thermal Conductivity box, choose from: • • • • Constant Based on Axial Dispersion User Procedure User Submodel Form of Gas Thermal Conductivity (gas): Constant The thermal conductivity k g has a constant value, which you set in the layer Specify form. Form of Gas Thermal Conductivity (gas): Based on Axial Dispersion This option assumes that the analogy between heat transfer and mass transfer is valid. The effective thermal conductivity coefficient is calculated as the product of the heat capacity of the gas, the axial dispersion coefficient, and the density of the gas: k gz = (Heat capacity) x (Averaged Axial dispersion coefficient) x (Molar density) k gz = C pg ∑ (Ezk yk )ρ g k Form of Gas Thermal Conductivity (gas): User Procedure The thermal conductivity varies axially along the bed. If you supply the necessary physical properties directly, Aspen Adsim interfaces a Fortran subroutine through the procedure pUser_g_Kg. If the physical properties come from a package such as PROPERTIES PLUS, Aspen Adsim handles the required calls automatically. Form of Gas Thermal Conductivity (gas): User Submodel The thermal conductivity varies axially along the bed and is defined in the user submodel gUserKg. 1 Gas Adsorption Processes 75 Energy Balance Tab (gas): Heat Transfer to Environment In the Heat Transfer to Environment box, choose from: • • • Adiabatic Thin Wall Rigorous Model Heat Transfer to Environment (gas): Adiabatic No heat transfer occurs between the bed and the wall. Heat Transfer to Environment (gas): Thin Wall With this option, the heat exchange between the gas in the bed and the environment is included in the gas phase energy balance as: 4H w (Tg − Tamb ) DB The conductivity along the wall and the heat accumulation in the wall are neglected. H w combines the heat transfer resistances of: • • • Boundary layer between gas and wall, on the inside of the column. Material of the column wall, including insulation material. Boundary layer between the outer column wall and the surroundings. The following equation (Bird et al., 1960) calculates H w for the column cross section shown in the Heat Transfer to Environment figure (on the next page).   D ln D1  ln o   D  D 1   Di   1 i 1 +  +  + Hw =     Do k2 2   Di H k1  H wo   2 wi  2   −1 −1 1 Gas Adsorption Processes 76 Do D1 Di Tg Tamb Hwi k1 k2 Hwo 1 Gas Adsorption Processes 77 Heat Transfer to Environment (gas): Rigorous Model This option includes a wall energy balance equation that contains the following terms: • • • • Heat transfer from the gas in the bed to the inner wall. Heat transfer from the outer wall to the environment (including the influence of any insulating material). Axial thermal conduction along the wall. Heat accumulation within the wall material. The wall is assumed to be thin and conductive enough for the inner and outer wall temperatures to be equal. The adiabatic option, that is, ignoring the wall energy balance, is valid only when the wall is extremely thin and nonconductive. Energy Balance Tab (gas): Form of Gas-Wall Heat Transfer Coefficient There are two options available for the definition of the gas-wall heat transfer coefficient H w : • • Constant Estimated Form of Gas-Wall Heat Transfer Coefficient (gas): Constant In the Specify table for the layer, set the heat transfer coefficient H w to be a fixed variable. Form of Gas-Wall Heat Transfer Coefficient (gas): Estimated With this option, the gas-wall heat transfer coefficient is calculated from the local conditions inside the adsorbent layer. The correlation uses results from a graphical representation given by Kast, 1988:  C sphere H B Nu w 1 +  DB Pe H  where:   = −2 × 10 −6 (Pe H )2 + 0.0477 Pe H + 22.11   C sphere = Nu w = Pe H = xchar 12 for a packed bed of spheres = Nusselt number for gas-wall heat transfer H w xchar kg x char v g ρ g MC pg kg = 1.15(2 r p ) = Gas wall heat transfer Peclet number = Characteristic length for a sphere 1 Gas Adsorption Processes 78 and which allows the formation of mercuric sulfide. • Adsorptive reactors are also used in a number of gas purification processes: • • Adsorptive reactors are also useful in air purification processes. must be accounted for. To prevent such release. into a single process unit. the formation of additional solid phases. Removing sulfur compounds from gases by first contacting them with α or γ-ferric oxide monohydrates (Iron Sponge) to adsorb sulfur in the form of ferric sulfide. Nuclear power plants generate radioactive xenon and krypton as products of the fission reactions. off gases are treated in charcoal delay systems. Such applications usually require extremely high degrees of purification because of the high toxicity of many radioactive elements. then periodically reoxidizing the surface to form elemental sulfur and to refresh the ferric oxides. Removing mercury from natural gas streams by treatment in an ex-situ TSA regenerative process. An important application of adsorptive reactors is the separation of radioactive wastes. which prevent the release of xenon and krypton until sufficient time has elapsed for the shortlived radioactivity to decay. Adsorption of toluene greatly enhances the conversion. Such a hybrid process gives benefits over conventional catalytic reactors: • Higher conversions. when the desired product of an equilibrium reaction scheme is adsorbed. Higher selectivity. the unit operations of heterogeneous and/or homogeneous chemical reaction and adsorption. The process uses an activated carbon adsorbent that contains sulfur. to be released to the atmosphere with other gases. modified activated carbon is used as an adsorbent for sulfur dioxide and a catalyst for NOx reduction. For example. The mass and energy balances must include the reaction terms as well as the mass and heat transfer rates caused by adsorption. An example of higher conversion is the catalytic dehydrogenation of methyl-cyclohexane to produce toluene. About Gas Adsorption with Reaction Processes Adsorptive reactors combine. Careful selection of the adsorbent may allow one impurity to be adsorbed onto the adsorbent surface. Furthermore. 1 Gas Adsorption Processes 79 . while another impurity reacts on it. radioactive iodine from nuclear fuel reprocessing may be captured by chemisorption on molecular sieve zeolites containing silver. Similarly. such as coke. when the product in an equilibrium reaction is removed by adsorption from the gas phase.Reaction Tab (gas) Use the Reaction tab to generate a layer model that combines adsorption with reaction (heterogeneous and/or homogeneous). for example. and these can leak out in small quantities into the coolant. Reactions Present (gas): Heterogeneous Reactions are heterogeneously catalyzed by a solid. Reactions Present (gas): Homogeneous Reactions are present in the gas phase only. choose a reaction type from: • • • • None Homogeneous Heterogeneous Homogeneous and Heterogeneous Reactions Present (gas): None No reactions are present in the gas or solid phases. Reactions Present (gas): Homogeneous and Heterogeneous Reactions are present in both the gas phase and the solid phase. select the type of expression for homogeneous reaction rate. which requires the user to supply the appropriate Fortran subroutine. Homogeneous Rate Dependency (gas): Concentration The reaction rate for components in the gas phase is related to the concentration of the component and gas phase temperature through the procedure pUser_g_Gas_Rx_Rate_C. Reaction Tab (gas): Homogeneous Rate Dependency In the Homogeneous Rate Dependency box. The catalyst and adsorbent are assumed to be different.Reaction Tab (gas): Reactions Present In the Reactions Present box. Choose from these options: • • Homogenous Rate Dependency: Partial Pressure Homogenous Rate Dependency: Concentration Homogeneous Rate Dependency (gas): Partial Pressure The reaction rate for components in the gas phase is related to the partial pressure of the component and gas phase temperature through the procedure pUser_g_Gas_Rx_Rate_Pp. which requires the user to supply the appropriate Fortran subroutine. giving rise to two distinct solid phases. Solid reaction participants can be considered. 1 Gas Adsorption Processes 80 . Reaction Tab (gas): Heterogeneous Rate Dependency In the Heterogeneous Rate Dependency box. select the number of reactions that occur on the surface of the catalytic adsorbent. Reaction Tab (gas): Number of Heterogeneous Reactions In the Number of Heterogeneous Reactions box. Heterogeneous Rate Dependency (gas): Concentration With this option. select the number of reactions that occur in the gas phase. Choose from: • • Partial Pressure Concentration Heterogeneous Rate Dependency (gas): Partial Pressure With this option. select the type of expression for heterogeneous reaction rate.Reaction Tab (gas): Number of Homogeneous Reactions In the Number of Homogeneous Reactions box. the reaction rate for components on the surface of the catalytic adsorbent is related to the gas phase partial pressure of the component and gas phase temperature. the reaction rate for components on the surface of the catalytic adsorbent is related to the concentration of the component and gas phase temperature through one of these procedures: • • pUser_g_Cat_Rx_Rate_C pUser_g_Cat_Rx_Rate_C_Sol (for when solid reactants are present) Both procedures require you to supply the appropriate Fortran subroutine. through one of these procedures: • • pUser_g_Cat_Rx_Rate_Pp pUser_g_Cat_Rx_Rate_Pp_Sol (for when solid reactants are present) Both procedures require you to supply the appropriate Fortran subroutine. 1 Gas Adsorption Processes 81 . You define. solid reaction participants are present. no solid reactants are present.Reaction Tab (gas): Are Solid Reactants Present This option is active only if heterogeneous reactions are present. through Fortran subroutines. or they represent catalytically active sites being deactivated or reactivated. Here. The solids are formed either by the reaction (for example carbon in reaction networks that suffer from coking). the way solid components interact with the gas phase. Aspen Adsim interfaces these subroutines through one of these two procedures: • • pUser_g_Cat_Rx_Rate_Pp . Procedures Tab (gas) Use the Procedures tab to view a list of the user procedures in use within the current adsorption layer model. Gas Adsorption: Summary of Mass and Energy Balance Equations This section summarizes the equations for mass and energy balances used for gas adsorption processes in Aspen Adsim. 1 Gas Adsorption Processes 82 . Choose from: Yes.or pUser_g_Cat_Rx_Rate_Pp_Sol No. choose a default list or a user-defined list of solid reactants. Reaction Tab (gas): Solid Reactant List In the Solid Reactant List box. Here. axial and radial dispersion needs to be considered. with extra terms for accumulation. a distributed parameter). Each component in the gas phase is governed by a similar equation. Gas Adsorption: Mass Balance for Additional Solid Phase The concentration of each solid component i is calculated from its formation rate: ∂c sol .Gas Adsorption: Mass Balance for Gas Phase The overall mass balance for a multi-component gas phase accounts for the convection of material and mass transfer.i ∂t − Rsol . but the dispersion coefficient can be difficult to measure.i = 0 1 Gas Adsorption Processes 83 . from the gas to the solid phase. The governing partial differential equation is: ∂ (v g ρ g ) ∂w + ρs ∑ k = 0 k ∂t ∂z For an explanation of the symbols used. and it is suitable only for simulating breakthrough curves at constant pressure and temperature. see Explanation of Equation Symbols. later. or calculates it as a function of local conditions (that is. Aspen Adsim sets the dispersion coefficient either to a constant value. Aspen Adsim uses this equation only for constant pressure systems. and for axial and radial dispersion terms (if required): − ε i E zk ∂ 2 ck 1 ∂  ∂c k − ε i E rk r r ∂r  ∂r ∂z 2 ∂c  ∂ (v g c k ) + εB k + Jk = 0 + ∂z ∂t  In general. including axial thermal conduction.cat ∂Tg + a Hx QHx = 0 ∂t DB The above equation is in its most complete form. and the effect of heterogeneous and homogenous chemical reactions. which is included for 2-dimensional. vertical beds. The governing partial differential equation is: − k ga ε i ∂ 2Tg ∂T g ∂T g ∂v g + Cvg v g ρ g + ε B C vg ρ g +P 2 ∂z ∂t ∂z ∂z + HTCa p (Tg − Ts ) + 4H w (Tg − To ) + H r + ρ s. However. The only term missing is the radial thermal conduction term.Gas Adsorption: Gas Phase Energy Balance The gas phase energy balance includes terms for: • • • • • • Thermal conduction Convection of energy. Gas Adsorption: Solid Phase Energy Balance The solid phase energy balance includes terms for: • • • • • Thermal conduction Accumulation of heat Accumulation of enthalpy in the adsorbed phase Heat of adsorption Gas-solid heat transfer from gas to solid (expressed in terms of a film resistance. where the heat transfer area is proportional to the area of the adsorbent particles) The solid phase energy balance is: n ∂T ∂ 2Ts ∂T 1 ∂  1 ∂Ts  − k sr + ρ sC ps s + ρ s ∑ (C pai wi ) s   2 ∂z ∂t ∂t r ∂r  r ∂r  i =1 n ∂w   + ρ s ∑  ∆H i i  − HTCa p (Tg − Ts ) = 0 ∂t  i =1  − k sa 1 Gas Adsorption Processes 84 . heat transfer to the environment is a boundary condition so is not part of the energy balance (it is in the 1-dimensional case). accumulation of heat Compression Heat transfer from gas to solid Heat transfer from gas to the internal wall Heat of reaction. heat transfer to the environment.cat C p. in this geometry. Aspen Adsim replaces the third term with the sum of the conductive energy fluxes in the radial direction. which come from the solid phase energy balances.Gas Adsorption: Wall Energy Balance The wall energy balance includes terms for: • • • • Axial thermal conduction along the wall Heat accumulation within the wall material Heat transfer from the bed to the inner wall Heat transfer from the outer wall to the environment The governing equation is: 2 ∂ 2Tw ∂Tw 4 DB 4(DB + WT ) (T − T ) + H amb (T − T ) = 0 − kw + ρ w c pw − Hw 2 2 ∂t ∂z 2 (DB + WT )2 − DB w amb (DB + WT )2 − DB g w For a 2-dimensional bed model. Gas Adsorption: Summary of Factors that affect the Mass Balance Equations This section lists the factors that affect the mass balance in the solid and gas phases. These fluxes are the boundary conditions for 2-dimensional bed models. Gas Adsorption: Axial Dispersion Term The axial dispersion term is: ∂ 2 ck − ε i E zk ∂z 2 Gas Adsorption: Radial Dispersion Term This term is only active if you chose vertical bed and two-dimensional spatial discretization: − ε i E rk 1 ∂  ∂c k  r  r ∂r  ∂r  Gas Adsorption: Convection Term The convection term is: ∂ (v g c k ) ∂z Gas Adsorption: Gas Phase Accumulation Term The accumulation term is: εB ∂ck ∂t 1 Gas Adsorption Processes 85 . Gas Adsorption: Reaction Term The reaction term accounts for the removal or formation of components in the gas phase.reac . j J cat .cat n reaccat ∑ j =1 ν cat .k Where: J cat .Gas Adsorption: Rate of Flux to Solid Surface The rate of flux to the solid surface is given by: J = −ρS ∂w ∂t Gas Adsorption: Rate of Adsorption The rate of adsorption is represented as an accumulation term in the gas phase mass balance. The linear driving force solid-film model is: J ∂wk * = MTCs k (wk − wk ) = ads .k J gas .k = − = = n reacgas rate of consumption or production of k by heterogeneous (catalytic) reactions rate of consumption or production of k by homogeneous (gas phase) reactions.reac . If a particle material balance was considered. It is represented as: J cat .reac . (See Also Particle MB.k + ε i J gas . ∑ j =1 ν gas .k R gas .) Note: Procedure-defined expressions need adjusting accordingly. ∂wk is taken to be the integral ∂t uptake of the particle as determined by the flux through the boundary layer. due to reaction on the solid catalyst's surface.reac .k J gas .k ∂t ρs There are analogous expressions for gas films and quadratic driving forces. j .reac .reac . j . j 1 Gas Adsorption Processes 86 .k Rcat .k = − ρ s. and one of partial pressure or component concentration.i ∂t − Rsol .reac .k ∂t Gas Adsorption: Defining the Mass Balance for Additional Solid Phases During the catalytic reaction. The concentration of each solid component i is calculated from its rate of formation: ∂c sol . The total rate of flux to the surface per unit volume is then: J k = J ads . and solid component concentrations. Gas Adsorption: Summary of Factors that affect the Energy Balance This section lists the factors that affect the energy balance equations in the: • • • Gas phase energy balance.k Jk = ρs ∂ wk + J cat .reac .reac . Gas Adsorption: Effect of Compression The reversible rate of internal energy increase per unit volume by compression is: P ∂v g ∂z 1 Gas Adsorption Processes 87 . or a metal oxide catalyst is oxidized and/or reduced.You must define the rates of reaction in a user procedure. solid phases such as coke deposit sometimes form.i = 0 You must define the reaction rate of the solid components in a Fortran subroutine.k + ε i J gas . Gas Adsorption: Defining the Energy Balance in the Gas Phase This section lists the factors that affect the energy balance equations in the gas phase. Aspen Adsim interfaces this subroutine through the procedure pUser_g_Cat_RX_Rate_Pp_Sol. as a function of temperature.reac . pressure. Solid phase energy balance. Wall energy balance.k + ε i J gas .k + J cat . as a function of temperature. You set a p for adsorption and reaction.Gas Adsorption: Convective Term The gas convective term is always included in the gas phase energy balance: C vg v g ρ g ∂T g ∂z Gas Adsorption: Accumulation in Gas Phase The enthalpy accumulation in the gas phase is represented as: ε i C vg ρ g ∂T g ∂t Gas Adsorption: Axial Thermal Conduction in Gas Phase The axial gas thermal conduction (axial thermal dispersion) term is given by: − ε i k gz ∂ 2Tg ∂z 2 Where k gz is evaluated based on your choices in: • • Energy Balance tab for 1-dimesional models. Gas Adsorption: Gas-Solid Heat Transfer Aspen Adsim uses a film resistance model to represent heat transfer between gases and solids: Rate of heat transferred per unit volume = HTCa p (Tg − Ts ) with: a p = (1 − ε i ) 3 rp This is for adsorption only. 1 Gas Adsorption Processes 88 . Material/Momentum Balance tab for two dimensional models. Gas Adsorption: Radial Thermal Conduction in Gas Phase The radial gas thermal conduction term (radial thermal dispersion) is represented as: − ε i k gr 1 ∂  ∂Tg r r ∂r  ∂r      Where k gr is evaluated according to the options selected in the material and momentum balance tab for two-dimensional models. the heat transfer to the column wall is one of the thermal boundary conditions for the radial direction.cat nreac .l = = index for the set of homogenous reactions index for the set of heterogeneous reactions molar heats of reactions k and l. this term is missing because: • • Radial bed models are always considered to be adiabatic. k R gas . Gas Adsorption: Rate of Heat Generation by Reaction The rate of heat generation by reaction is the sum of the contributions from individual reactions: H R = εi Where: k l nreac .l Rcat .k + ρ s . and one of partial pressure or concentration. typically in kmol/(m3 s) rate of heterogeneous reaction l.cat l =1 ∑H Rcat .k Rcat . The heat of reaction must also be defined as a function of temperature and mole fraction.Gas Adsorption: Heat Exchange between Gas and Internal Wall For one-dimensional vertical and horizontal bed models: 4 Hw (Tg − To) DB Where: To = Tamb for adiabatic/thin walls and To = Tw for thick walls For other geometries. typically in kmol/(kg s) catalyst bulk density H Rgas . See the following procedures.cat You must define the rates of reaction in a user procedure.k . For two dimensional vertical bed models. described in the Adsim Library Reference guide: • • • • • • • • pUser_g_Cat_RX_Rate_Pp_Sol pUser_g_Cat_RX_Rate_C_Sol pUser_g_Cat_RX_Rate_Pp pUser_g_Cat_RX_Rate_C pUser_g_Gas_RX_Rate_Pp pUser_g_Gas_RX_Rate_C pUser_g_Cat_RX_Heat pUser_g_Gas_RX_Heat 1 Gas Adsorption Processes 89 . gas k =1 ∑H Rgas . H Rcat . typically in MJ/kmol rate of homogenous reaction k.l = = = ρ s.l = Rgas . as a function of temperature. See also Configure Form (gas) earlier in this chapter.St (Tg − TSt ) for two phase exchange media. and QHx = U Hx .Cw (Tg − TCw ) + U Hx . given by: QHx = U Hx (Tg − THx ) for single phase exchange media.Gas Adsorption: Heat Exchange between Gas and Internal Heat Exchanger The heat exchange between the gas phase and a heat exchanger (either as jacket around the packed bed or via tubes surrounded by adsorbents) is given by: a Hx QHx Where a Hx is the specific heat exchange area per unit bed volume and Q Hx the energy flux exchanged. Gas Adsorption: Accumulation in Solid Phase The solid phase enthalpy accumulation is always included in the solid phase energy balance: ρ s C ps ∂Ts ∂t Gas Adsorption: Axial Thermal Conductivity in Solid Phase The solid thermal conduction term is: − k sz ∂ 2Ts ∂z 2 Gas Adsorption: Radial Thermal Conductivity in Solid Phase This term is active only for vertical beds and two-dimensional spatial discretization: − k sr 1 ∂  ∂Ts  r  r ∂r  ∂r  1 Gas Adsorption Processes 90 . Gas Adsorption: Defining the Energy Balance for the Solid Phase This section lists the factors that affect the energy balance equations in the solid phase. but with the sign reversed: HTC a p (Tg − Ts ) 1 Gas Adsorption Processes 91 . or through a user procedure or submodel. is a function of the local rate of mass transfer: HTi = ∆H i ∂wi ∂t These rates are held in vectors HTi and summed for all components to give the total rate of heat generation by adsorption per unit volume of solid: ρ s ∑ (− HTi ) i Gas Adsorption: Heat of Adsorbed Phase The term for each component is a function of the loading and the temperature in the solid phase: H i = ρ s C pai wi ∂Ts ∂t The total contribution comes from the sum for all components: ∑ (H ) i i You supply C pai (heat capacity of adsorbed component i) as either a fixed value for each component. Try these guidelines when deciding what specific heat capacity to use (Tien. 1994): For T << Tc use C pai for liquid For T just below Tc use system knowledge to specify C pai For T > Tc use C pai for compressed gas Gas Adsorption: Gas-Solid Heat Transfer The gas-solid heat transfer term is the same as for the gas phase. per unit mass of solid.Gas Adsorption: Heat of Adsorption The rate of heat generation by adsorption of each component i. The term is represented as: 1 Gas Adsorption Processes 92 . It is either constant or estimated from a correlation. Gas Adsorption: Heat Exchange between Gas and Wall When the rigorous wall energy balance is selected. in the wall energy balance. Aspen Adsim includes. the heat exchange between the gas in the bed and the inner surface of the wall. The following effects are considered: • • • • Heat exchange between gas and wall. The term is represented as: Hw 2 (DB + WT )2 − DB 4 DB (T g − Tw ) Where DB WT = = Internal diameter of layer Width of column wall The supply of H w is defined by the Form of Gas-Wall Heat Transfer Coefficient option. since the basis of the equation is per unit volume of gas phase: 4 Hw (Tg − Tw ) DB Gas Adsorption: Heat Exchange between Wall and Environment When you include a rigorous wall energy balance. Note that the equation has a slightly different form. Heat content of wall. the corresponding term in the wall energy balance gives the heat transfer between the outer wall and the environment: 2 (D B + WT )2 − DB 4 Hamb (D B + WT ) (Tw − Tamb) Gas Adsorption: Axial Thermal Conductivity along Wall The axial thermal conduction along the wall is always part of the wall energy balance. The heat exchange between gas and wall is also included in the gas phase energy balance.Gas Adsorption: Defining Energy Balance for the Wall This is applicable only if you selected a rigorous model for the heat transfer to the environment. Axial thermal conductivity along wall. Between wall and environment. Specific heat capacity of adsorbed phase. Specific heat exchanger surface. Specific heat capacity of column wall. Specific particle surface per unit volume bed. Kinetic Langmuir factor. Macropore gas phase concentration. Gas Adsorption: Explanation of Equation Symbols Symbol a Explanation Specific particle surface. Bulk gas phase concentration.∂ 2Tw − kw ∂z 2 You must specify the value of the wall thermal conductivity k w in the Specify table for the layer. Aspen Adsim base units m2/m3 m2(HX area)/m3(Bed) m2(Particle area)/m3(Bed) m2 aHx aP A AA b 1/bar kmol/m3 kmol/m3 kmol/m3 kmol/kg MJ/kmol/K MJ/kg/K MJ/kmol/K MJ/kmol/K MJ/kg/K cbk ck cmsk csol c pai c p .cat c pg c ps c pW 1 Gas Adsorption Processes 93 . Placeholder variable used for DubininAstakhov isotherm evaluation. Specific heat capacity of adsorbent. Area. Gas Adsorption: Heat Content of Wall The Heat Content of Wall term is always included in the wall energy balance: ρ w C pw ∂Tw ∂t You must specify the value of the wall density ρw and the specific heat capacity of the wall C pw in the Specify table for the layer. Specific gas phase heat capacity at constant pressure. Specific heat capacity of catalyst. Molar concentration of component k. Concentration of solid phase reactant. Function.k Eik E zk f f eq H amb HB Hi HR H Rcat H Rgas H Ti Hw ∆H i HTC IP j kmol/m3 (Bed)/s kmol/m3 (Bed)/s J ads . Height of adsorbent layer. units depend on isotherm. Heat of catalytic reaction. Activation energy for Arrhenius relationship. Heat of adsorption of component i. Bed diameter. Effective micropore diffusion coefficient. Equilibrium (isotherm) relationship. Effective adsorbed phase diffusivity of component k. Combined heats of homogenous and heterogeneous reactions. Mass transfer rate of component k owing to adsorption. Colburn j-factor for heat or mass transfer. Heat of adsorption contribution to solid phase energy balance.k J cat . MJ/kmol/K m m2/s m2/s m2/s m2/s m2/s MJ/kmol m2/s m2/s MW/m2/K m MJ/m3/s MJ/m3 (Bed)/s MJ/kmol MJ/kmol MJ/m3/s MJ/m2/s MJ/kmol MJ/m2/s Defc DefP Dek Dki Dmk Eact .reac . Axial dispersion coefficient of component k. Gas phase heat of reaction. Knudsen diffusion coefficient of component i. Rate of change of heat of adsorbed phase. Radial dispersion coefficient of component k. Effective macropore diffusion coefficient. Gas-wall heat transfer coefficient. Isotherm parameter. Mass transfer rate of component k owing to heterogeneous catalytic reactions. Mean molecular diffusion coefficient of component k. Gas-solid heat transfer coefficient. Wall-ambient heat transfer coefficient.k 1 Gas Adsorption Processes 94 .cvg DB Specific gas phase heat capacity at constant volume. reac Jk k0 k k 0 Pk k fk kg k gr dyn k gr stat k gr Mass transfer rate of component k owing to homogenous. gas phase reactions. Static contribution to k gr . Dimensionless isotherm slope of component i (Henry’s coefficient). Thermal conductivity of column wall. Mass transfer rate of component k to/from adsorbent. lumped mass transfer coefficient of component i. Solid film mass transfer coefficient. k sz kW K Ki K Ki K mac K mic Kp K Pi L M Effective axial solid phase thermal conductivity.J gas . ki ks k gz k sr stat k sr Effective. MTC g MTCs 1 Gas Adsorption Processes 95 . Effective axial gas phase thermal conductivity. Micropore mass transfer coefficient. Macropore mass transfer coefficient. Gas phase thermal conductivity. Dynamic contribution to Static contribution to kmol/m3 (Void)/s kmol/m3 (Bed)/s m/s m/s m/s MW/m/K MW/m/K MW/m/K MW/m/K 1/s MW/m/K MW/m/K MW/m/K MW/m/K MW/m/K MW/m/K m3/kg 1/s 1/s bar s/m2 m2/s m kg/kmol 1/s 1/s k gr . Effective radial solid phase thermal conductivity. Isotherm slope of component i (Henry’s coefficient). Molecular weight. Film mass transfer coefficient of component k. Darcy’s constant. Solid thermal conductivity. Pre-exponential factor for pressure dependent Arrhenius relationship. Gas film mass transfer coefficient. Effective radial gas phase thermal conductivity. Macropore diffusion coefficient. k sr . Pre-exponential factor for Arrhenius relationship. Length of horizontal bed. Gas phase temperature. depending on K context used. Gas phase reaction rate. Heat exchange medium temperature. Radial co-ordinate (in packed bed or particle). Equal to bar bar bar MJ/m2/s m m m bar m3/kmol/K kmol/kg/s kmol/m3/s kmol/kg/s s s K or Pi 0 Psat QHx r rc rp R Rcat Rgas Rsol t tcycle T T0 Tamb Tc TCW Ts Tg THx TSt TW Tort Tamb TW . Catalytic reaction rate. K K K K K K K K MW/m2/K MW/m2/K U Hx U Hx . IAS vapor pressure. Overall heat transfer coefficient: gas to heat exchange medium. Solid phase reaction rate. Microparticle (crystal) radius. Saturation pressure.cw 1 Gas Adsorption Processes 96 . Adsorption cycle time. Steam temperature. Particle radius. Ambient temperature. Critical temperature. Pressure. Time. Solid phase temperature. Overall heat transfer coefficient: gas to cooling water.p P Emissivity in calculation of effective thermal conductivities. Temperature. Wall temperature. Adsorbent tortuosity. Cooling water temperature. Heat transfer rate to internal heat exchanger. Universal gas constant. Gas compressibility factor. Mole fraction of component k in the gas phase. Chemical potential of component i in the adsorbed phase.i µ gas.U Hx . - stat k sr calculation. Total bed voidage. Characteristic length. Aspen Adsim base units α rg α rs β stat k gr calculation. Function of packing density. Axial co-ordinate. γi µ Activity coefficient of component i. Width of column wall. Chemical potential of component i in the gas phase. used in calculation. St vg wk 0 wk Overall heat transfer coefficient: gas to steam. Width of horizontal bed. Stoichiometric coefficient of component k in reaction j. stat k sr . MW/m2/K m/s kmol/kg kmol/kg m m m m - W WT xchar xk yk z Z Symbol Explanation Radiation contribution to Radiation contribution to Factor used in stat k gr . Intraparticle voidage. Dynamic viscosity. ∆r Radial discretization distance. Interparticle voidage. stat k sr m m3 (Void+Pore)/m3 (Bed) m3 (Void)/m3 (Bed) m3 (Pore)/m3 (Particle) εB εi εP φ φ γ Relative pressure: Factor used in Pk / Psat . Loading. Gas phase superficial velocity.k . Pure component loading of component k. Mole fraction of component k in the adsorbed phase.i ν jk 1 Gas Adsorption Processes 97 . N s/m2 MJ/kmol MJ/kmol - µ ads. Adsorbent bulk density. Sck Shk Re µ Dmi ρ g M k fi 2rp Dmi 2rp M ρ g vg Component Schmidt number. Prandl number. Parameter in Glueckauf expression. Component Sherwood number. Particle shape factor. NuW PeH PeK Pr H w xchar kg xchar vg ρ g MC pg kg Gas-wall heat transfer Peclet number. µ 1 Gas Adsorption Processes 98 .cat ρW Ω Ψ Dimensionless number Defining expression Description Nusselt number for gas wall heat transfer. Wall density. Particle Reynolds number. Catalyst bulk density. Time constant for adsorption cycle. Gas phase molar density. bar m kmol/m3 kg/m3 kg/m3 kg/m3 - ρg ρs ρ s. vgH b Ez µ C pg kg M Component Peclet number for mass transfer.Π i0 θ Spreading pressure of component i. without carrying out a dynamic simulation over a large number of cycles. and optimization of periodic adsorption processes for gas separation.1. such as Pressure Swing Adsorption (PSA). Vacuum Swing Adsorption (VSA). Direct determination of the cyclic steady state. is now available using Aspen Adsim 2004. etc.2 Gas Cyclic Steady State Modeling Introduction Aspen Adsim 2004. The Aspen Adsim 2004. This powerful tool . Thermal Swing Adsorption (TSA).1 CSS models offer an extremely efficient design tool that can be more readily used as an optimization package to determine optimal design and operating conditions for an adsorption process.Cyclic Steady State (CSS) modeling (the result of complete discretization of both time and space) presents a periodic adsorption process as a steady state problem. processes. simulation. The following sections outline CSS modeling tasks and include instructions on using CSS models for your engineering business: • • • • • • • • • • What is CSS Modeling…? Discretization Techniques for Time and Space Connectivity Between CSS Models Bed Model Details Material Balance Momentum Balance Kinetic Model Energy Balance Adsorption Equilibrium Models User Guidelines 2 Gas Cyclic Steady State Modeling 99 .1 presents an innovative new modeling approach to maximize profitability in the design. etc.. Purge. Cyclic Steady State (CSS). implies a steady state in which the conditions at the end of each cycle are identical to those at the beginning. continuously repeated steps of Feed. e. Pressure equalization. the whole system is continuous because of the use of multi-beds that are ultimately operated in a cyclic steady state within a confined cycle time.) with multiple adsorbers packed with single or multiple adsorbent layers. Blow down.• • • • • How to Create a CSS Simulation Flowsheet How to Create a Dynamic Simulation Flowsheet using CSS Models How to Convert a CSS Flowsheet to a Dynamic Flowsheet How to a Convert Dynamic Flowsheet to a CSS Flowsheet Developer’s Tips to Get Better Convergence Property in CSS Simulation What is CSS Modeling…? A periodic adsorption process operates on sequential steps (for example.g. as illustrated in Figure 1. n dynamic simulatio Cycle end state(t N) tN N ep St tN-1 Spatial Domain Figure 1 Illustration for traditional dynamic simulation of a periodic adsorption process cle Cy in ) (t 0 te ta ls itia p Ste 2 t2 Time Domain p1 Ste t1 t0 2 Gas Cyclic Steady State Modeling 100 . the cycle initial state at t0 must be identical to the cycle end state at tN. over a large number of cycles until a CSS is eventually confirmed from a defined criteria. which is the nature of periodic adsorption processes. Although the operation of each bed is batchwise. The traditional approach for CSS determination is to carry out a dynamic simulation of the system. beginning with a specified set of initial condition. Production. Cyclic Steady State Figure 2 Illustration for the concept of CSS modeling system in Aspen Adsim From a mathematical point of view.e. As illustrated in Figure 2. compared with the original Aspen Adsim dynamic bed model (gas_bed).1 is the same as those of existing Aspen Adsim dynamic models. the CSS models in Aspen Adsim 2004. the forced reformulation also constrains the system within a specified time domain length. existing Adsim users should find it easy to use this new feature. 2 Gas Cyclic Steady State Modeling 101 . cycle time).1 are listed in Table 1. This suggests a steady state simulation is feasible by complete discretization of space and time within a confined time length (i..Time domain (t) ia Spat t2 l dom x) ain ( tN-1 t1 tN t0 Periodic Boundary State(tN) = State(t0) i. and has brought ideas to explore a better numerical method toward CSS in terms of cost-effective process simulation. Further benefits come from the fact that the graphic user interface of the freshly released CSS models from Aspen Adsim 2004. Based on the above concept.1 have been developed to determine CSS from purely steady state simulation. The high-level functionalities of CSS bed model (gCSS_Adsorber) in Aspen Adsim 2004. Therefore. the criterion for CSS is considered a unique characteristic of a periodic adsorption process. Direct determination of CSS will effectively save the costs for the optimization of periodic adsorption process since the technique could offer an extremely efficient design tool that can be more readily used as an optimization package to determine optimal design and operating conditions. from the starting point (t0) to the ending point (tN).e. The existence of periodic time boundary inspires to replace the initial condition by a periodicity condition requiring that the system state at the end of each cycle is identical to that at its beginning. Table 1. Functional comparison of CSS and dynamic bed models in Aspen Adsim 2004.1 2 Gas Cyclic Steady State Modeling 102 . Each port has associated variables that correspond to the material connection stream (gCSS_Material_Connection) that allows reversible flow. x j ) − u (tn −1 . equivalent to CDS2 in gas_bed OCFE2 – 2nd Order Orthogonal Collocation on Finite Elements OCFE4 – 4 th Order Orthogonal Collocation on Finite Elements Time derivatives of CSS models are explained using 1st Order Backward Finite Difference approximation: ∂u (tn . x j ) ∆t Connectivity between CSS Models CSS models contain at least an input and an output port (gCSS_Port). These are the available connections for CSS models: 2 Gas Cyclic Steady State Modeling 103 . x j ) ∂t ≈ u (tn .Discretization Techniques for Time and Space Spatial derivatives of CSS bed model (gCSS_Adsorber) are discretized by one of the following numerical methods: • • • CFD4 – 4th Order Central Finite Difference. m/s Axial distance coordinate. m Bed (interparticle) voidage Intraparticle voidage Total voidage εb εp εt 2 Gas Cyclic Steady State Modeling 104 .: ∑C i i = ρg Notation Ci DLi t Qi vg x Gas phase concentration for component i. kmol/kg-adsorbent Superficial gas velocity. m2/s Time. kmol/m3 Axial dispersion coefficient for component i. s Amount adsorbed for component i.Bed Model Details Material Balance The CSS bed model (gCSS_Adsorber) uses the following material balance for the bulk gas adsorption: − DLi ε b ∂Ci ∂Qi ∂ 2Ci ∂ (v g Ci ) + + εt + ρb =0 2 ∂x ∂x ∂t ∂t The physical meanings of each term are: ∂ 2 Ci − DLi ε b Axial dispersion contribution1 2 ∂x ∂ (v g Ci ) ∂x ∂Ci ∂t ∂Qi ∂t Convection Gas phase accumulation2 Adsorbed phase accumulation3 εt ρb The following continuity equation is required to complete the material balance around the system. 3 Here. Within the CSS adsorber model (gCSS_Adsorber). kmol/m3 Bed packing density. where the proportionality constant is called dispersion coefficient. kg/m3 References If a concentration gradient exists in a packed bed. one of the following pressure drop correlations may be chosen as the one. Dispersion occurs in both radial and axial directions in the bed. which may be expressed mathematically in terms of Fick’s law. kg/m3 Particle density (solid density. The resultant flux is referred to as mass dispersion. Momentum Balance Gas flow through a packed bed can be described by a relevant pressure drop correlation.ρg ρb ρp 1 Gas density. ε t is the total bed voidage. which is the combined interparticle and intraparticle voidages calculated from 2 ε t = ε b + ε p (1 − ε b ) . ρb is the bed (packing) density calculated from ρ b = ρ p (1 − ε b ) . In addition. eddy (turbulent) diffusion due to the flow also contributes to the mass flux. Here. a diffusive mass flux will occur. flow through a packed bed may be adequately represented with inclusion of the axial dispersed plug flow consideration. In general. The axial dispersed mixing often occurs when a fluid flows through a packed bed and may cause unfavorable separation efficiency as the separation factor is becoming smaller. Note that there is no other option to assume an ideal flow regime. such as Constant Pressure and Velocity and Constant Pressure with Variable Velocity since the CSS models has been developed fundamentally for cyclic process for gas separation. (1) Darcy’s Law: ∂P = − K p vg ∂x (2) Blake-Kozeny: −5 ∂P − 150 × 10 µ g (1 − ε b ) vg = ∂x (2rpψ )2 ε b3 2 2 Gas Cyclic Steady State Modeling 105 . true density). the mass transfer mechanism consists of four steps: • • • • Fluid film transfer Pore diffusion Adhesion on surface Surface diffusion Because the surface adhesion rate approximates the order of the collision frequency of the gas molecule on the solid surface. In adsorption. bar Particle radius. cP Gas density.75 × 10 M w ρ g (1 − ε b ) 2 = vg (2rpψ )ε b3 ∂x (4) Ergun Equation:  150 × 10 −5 µ g (1 − ε b )2 1. kg/kmol Gas pressure. m/s Axial distance coordinate. m Superficial gas velocity. m Bed voidage (void fraction) Gas mixture viscosity. kmol/m3 Particle shape factor P rp vg x εb µg ρg ψ Kinetic Model Rigorous simulation of an adsorption process requires a reliable representation of the adsorption kinetics for the adsorbent used.75 × 10 −5 M w ρ g (1 − ε b ) 2  ∂P vg + vg  = −   (2rpψ )ε b3 ∂x (2rpψ )2 ε b3   Notation Kp Mw Darcy Coefficient. (which is much greater than for the transport processes) the equilibrium is assumed instantaneously at the interfaces.(3) Burke-Plummer: −5 ∂P − 1. bar.s/m2 Molecular weight of gaseous mixture. Adsorptives initially transfer from the bulk gas phase through an external film to the external surface of the particles. The molecules are diffused into the 2 Gas Cyclic Steady State Modeling 106 . Any combination of the three steps can constitute the rate-controlling mechanism. The CSS adsorber model (gCSS_Adsorber) within Aspen Adsim 2004. pore diffusion and surface diffusion generally occur in parallel. This mechanism definitely depends on the adsorption system and can vary with the operating conditions of the process. Typically. While fluid film transfer and pore diffusion are treated as sequential steps. can be determined by a constant or by a certain relationship according to the dynamic conditions of adsorption system. The CSS adsorber model (gCSS_Adsorber) provides the following choices in determining the lumped mass transfer coefficient from the empirical assessment by Aspen Adsim users: • • Constant ki = k LDFi  E  k i = k 0i exp − i   RT  s   Arrhenius 2 Gas Cyclic Steady State Modeling 107 . It is in fact more convenient to depict film transfer rate in terms of an effective transfer coefficient or a lumped resistance coefficient rather than to use a diffusion equation to represent adsorption kinetics in a rigorous manner. Both approximations have a lumped resistance coefficient that may be determined at either fluid or solid film where the mass transfer occurs: (1) Linear Driving Force Approximation (LDFA): ρb ∂Qi = k Fi Ci − Ci* ∂t ( ) at fluid film at solid film ∂Qi = k Si Qi* − Qi ∂t ( ) ( ) 2 (2) Quadratic Driving Force Approximation (QDFA): (C ) − Ci* ∂Q ρ b i = k Fi i ∂t 2Ci 2 2 at fluid film ∂Qi Q * − (Qi ) = k Si i ∂t 2Qi 2 ( ) at solid film The lumped mass transfer coefficient. k Fi or k Si . adsorbed on the active sites and then diffused along the surface.pores of the particle. They are: Linear Driving Force Approximation and Quadratic Driving Force Approximation. a film adjacent to the surface confines the mass transfer rate between solid and fluid phases and this external film mass transfer resistance may be determined by the hydrodynamic condition.1 limits two types of lumped kinetic models for application. Effective diffusivity for component i. m2/s Activation energy for component i. 1/s Gas pressure. bar/s Pre-exponent for component i. kmol/kg-adsorbent Equilibrium amount adsorbed for component i.• Effective Diffusivity ki = 15 Dei rp2 Linear Driving Force Approximation Quadratic Driving Force Approximation ki = • π 2 Dei rp2 k Pi P Pressure Dependent ki = • Pressure Dependent Arrhenius ki =  E  k 0 Pi exp − i   RT  P s   Notation Ci Ci* Dei Ei ki k LDFi k Pi k 0i k 0 Pi k Fi k Si P Qi Qi* rp Gas phase concentration for component i. 1/s Mass transfer coefficient as a constant for component i. kmol/m3 Equilibrium gas phase concentration for component i. bar/s Fluid film mass transfer coefficient for component i. m kmol/m3 2 Gas Cyclic Steady State Modeling 108 . 1/s Solid film mass transfer coefficient for component i. bar Amount adsorbed for component i. 1/s Pre-exponent for component i. MJ/kmol Mass transfer coefficient (fluid or solid) for component i. kmol/kg-adsorbent Particle radius. 1/s Pressure dependent mass transfer coefficient for component i. MJ/kmol/K Bed packing density. K Gas constant (8. s Solid temperature. kg/m3 ρb Energy Balance The CSS adsorber model (gCSS_Adsorber) uses the following energy balances to represent the heat transportations of non-isothermal system with compressible flow: (1) In Fluid Phase: − kgε b ∂ 2Tg ∂x 2 + CVg v g ρ g ∂Tg ∂x ∂t A + H s a p (Tg − Ts ) + H w Hi (Tg − Tw ) = 0 VHi ∂x +P ∂v g + CVg ρ g ε t ∂Tg − kgε b ∂ 2Tg ∂x 2 ∂Tg ∂x Axial thermal conduction CVg v g ρ g P ∂v g ∂x Convection P-V work compression CVg ρ g ε t ∂Tg ∂t Thermal accumulation in gas phase Heat transfer between gas and solid (adsorbent particle) H s a p (Tg − Ts ) Hw AHi (Tg − Tw ) VHi Heat transfer between gas and the internal wall of adsorber 2 Gas Cyclic Steady State Modeling 109 .31451e-3).t Ts R Time. MJ/kmol/K Solid (=adsorbent particle) heat capacity. m External wall heat transfer area. m Internal wall heat transfer area.(2) In Solid Phase: ∂ 2Ts ∂T ∂Qi   − ks + C Ps ρ b s + ρ p ∑  ∆H i  − H s a p (Tg − Ts ) = 0 2 ∂t ∂t  ∂x i  − ks ∂ 2Ts ∂x 2 ∂Ts ∂t   ∂Qi   ∂t  Axial thermal conduction Thermal accumulation in solid phase C Ps ρ b ρ p ∑  ∆H i i Thermal accumulation by the enthalpy of adsorption Heat transfer between gas and solid H s a p (Tg − Ts ) (3) In Wall phase: − kw − kw A A ∂ 2Tw ∂T + C Pw ρ w w − H w Hi (Tg − Tw ) + H amb Ho (Tw − Tamb ) = 0 2 VHo VHo ∂x ∂t ∂ 2Tw ∂x 2 ∂Tw ∂t Axial thermal conduction along the wall Thermal accumulation in the wall material Heat transfer between gas and wall C Pw ρ w Hw A Hi (Tg − Tw ) VHo H amb AHo (Tw − Tamb ) Heat transfer between wall and VHo environment Notation ap AHi AHo CVg C Ps Particle external surface area to particle volume ratio (=3/rp). m Gas mixture heat capacity. MJ/kg/K 2 Gas Cyclic Steady State Modeling 110 . m/s Internal wall element volume for heat transfer. MW/m2/K H amb Wall/environment heat transfer coefficient. kmol/m3 Bed packing density. MW/m/K Wall phase thermal conductivity. m2 External wall element volume for heat transfer. m Enthalpy of adsorption for component i (i. K Superficial gas velocity.g. MW/m2/K Fluid/wall heat transfer coefficient. MJ/kg/K Fluid/solid heat transfer coefficient. K Wall temperature. s Gas temperature.. stainless steel) specific heat capacity. MW/m/K Gas pressure.e. MW/m/K Solid phase thermal conductivity. K Solid temperature.. MJ/kmol Bed voidage (void fraction) Total voidage Gas density. heat of adsorption). m2 Axial distance coordinate. bar Amount adsorbed for component i. kg/m3 Wall material density. MW/m2/K kg ks kw P Qi t Tg Ts Tw vg VHi VHo x ∆H i Gas mixture thermal conductivity. kmol/kg-adsorbent Time.C Pw Hs Hw Adsorber material (e. kg/m3 εb εt ρg ρb ρw 2 Gas Cyclic Steady State Modeling 111 . the Sips. an equilibrium relationship could simply be represented by mathematical equation such as the Langmuir. numerous researchers have considered multi-component adsorption equilibria from thermodynamic perspective and developed a number of theories or models based on various assumptions concerning the nature of adsorbed phase. For an isothermal condition. 1): ρi = f (T )Q i (Eqn 3) However. Please note all equilibrium models only require pure equilibrium information in order to predict mixture equilibrium: References 1 D. the Eqn1 can be represented by the adsorption isotherm: Qi = f ( ρ i ) T and ρ i = f (Qi ) T (Eqn 2) Eqn 2.. Young and A. Crowell. Butterworths. M. and so on. which is commonly referred to as adsorption equilibrium isotherm. the adsorption isostere cannot be measured directly because it is impractical to hold Qi constant. For pure component adsorption.e. For multi-component system. ρ i . T ) = 0 (Eqn 1) In this equation. and T is the temperature. For many decades. the Freundlich. and can be represented in general form: f (Qi . D. ρι is the density for component i in fluid phase. amount adsorbed. Eqn 1 can also take the following form and is called the adsorption isostere (see Ref. is most frequently used in researches including adsorption process simulation. Qi is the concentration for component i on adsorbed phase. London (1962). The CSS model in Aspen Adsim offers the following types of adsorption equilibrium models for multi-component system. the Toth. i.Adsorption Equilibrium Models Introduction Adsorption equilibrium established after the adsorptive has been in with the adsorbed surface for a long time. Physical Adsorption of Gases. 2 Gas Cyclic Steady State Modeling 112 . the explanation of adsorption equilibrium relationship often causes considerable attention due to a unique and complex mixing rule that governing an adsorption system of interest. IP2i .e. amount adsorbed) for component I Mathematical Equation Form for Extended Langmuir 2 Qi = IP1i (IP2i exp[IP3i Ts ])Py i 1 + ∑ {(IP2 k exp[IP3k Ts ])Py k } k (Pressure dependent equilibrium) Qi = IP1i (IP2i exp[IP3i Ts ])C i 1 + ∑ {(IP2 k exp[IP3k Ts ])C k } k (Concentration dependent equilibrium) IP1i . IP2i P yi Ci Qi Isotherm parameters for component i Total gas pressure Gas phase mole fraction for component i Fluid phase concentration for component i Adsorbed phase concentration (i.. IP3i Isotherm parameters for component i Ts P Adsorbent particle temperature in Kelvin Total gas pressure 2 Gas Cyclic Steady State Modeling 113 .Mathematical Equation Form for Extended Langmuir 1 Qi = IP1i IP2i Py i 1 + ∑ {IP2 k Py k } k (Pressure dependent equilibrium) Qi = IP1i IP2i C i 1 + ∑ {IP2 k C k } k (Concentration dependent equilibrium) IP1i . IP3i . IP2i . IP4i Ts P yi Ci Qi Isotherm parameters for component i Adsorbent particle temperature in Kelvin Total gas pressure Gas phase mole fraction for component i Fluid phase concentration for component i Adsorbed phase concentration (i. amount adsorbed) for component I Mathematical Equation Form for Extended Langmuir 3 Qi = (IP1i + IP2iTs ) (IP3i exp[IP4i Ts ])Pyi 1 + ∑ {(IP3k exp[IP4 k Ts ])Py k } k (Pressure dependent equilibrium) Qi = (IP1i + IP2iTs ) (IP3i exp[IP4i Ts ])Ci 1 + ∑ {(IP3k exp[IP4 k Ts ])C k } k (Concentration dependent equilibrium) IP1i .e. amount adsorbed) for component I 2 Gas Cyclic Steady State Modeling 114 ...e.yi Ci Qi Gas phase mole fraction for component i Fluid phase concentration for component i Adsorbed phase concentration (i. . IP3i . IP4i Ts P yi Ci Qi Isotherm parameters for component i Adsorbent particle temperature in Kelvin Total gas pressure Gas phase mole fraction for component i Fluid phase concentration for component i Adsorbed phase concentration (i.Mathematical Equation Form for Extended Langmuir 4 Qi (IP = TsIP2 i (IP3i exp[IP4i Ts ])Py i 1 + ∑ {(IP3k exp[IP4 k Ts ])Py k } 1i k ) (Pressure dependent equilibrium) Qi = (IP TsIP2 i (IP3i exp[IP4i Ts ])C i 1 + ∑ {(IP3k exp[IP4 k Ts ])C k } 1i k ) (Concentration dependent equilibrium) IP1i . IP2i . amount adsorbed) for component I 2 Gas Cyclic Steady State Modeling 115 .e. IP4i Ts P yi Ci Qi Isotherm parameters for component i Adsorbent particle temperature in Kelvin Total gas pressure Gas phase mole fraction for component i Fluid phase concentration for component i Adsorbed phase concentration (i. IP2i . amount adsorbed) for component I 2 Gas Cyclic Steady State Modeling 116 .e. IP3i ..Mathematical Equation Form for Extended Langmuir 5 Qi = (IP1i exp[IP2i Ts ]) (IP3i exp[IP4i Ts ])Pyi 1 + ∑ {(IP3k exp[IP4 k Ts ])Py k } k (Pressure dependent equilibrium) Qi = (IP1i exp[IP2i Ts ]) (IP3i exp[IP4i Ts ])Ci 1 + ∑ {(IP3k exp[IP4 k Ts ])C k } k (Concentration dependent equilibrium) IP1i . . amount adsorbed) for component I 2 Gas Cyclic Steady State Modeling 117 .Mathematical Equation Form for Loading Ratio Correlation 1 IP i IP2i (Pyi ) 3i 1 Qi = IP 1 + ∑ IP2 k (Pyk ) 3 k IP { } k (Pressure dependent equilibrium) Qi = IP i IP2i Ci 3i 1 IP 1 + ∑ IP2 k Ck 3 k IP { } k (Concentration dependent equilibrium) IP? i P yi Ci Qi Isotherm parameters for component i Total gas pressure Gas phase mole fraction for component i Fluid phase concentration for component i Adsorbed phase concentration (i.e. e. amount adsorbed) for component I 2 Gas Cyclic Steady State Modeling 118 .Mathematical Equation Form for Loading Ratio Correlation 2 IP i (IP2i exp[IP3i Ts ])(Pyi ) 4 i 5 i s 1 Qi = IP + IP 1 + ∑ (IP2 k exp[IP3k Ts ])(Pyk ) 4 k 5 k IP + IP T { Ts } k (Pressure dependent equilibrium) IP i (IP2i exp[IP3i Ts ])Ci 4 i 5 i s 1 Qi = IP + IP 1 + ∑ (IP2 k exp[IP3k Ts ])Ck 4 k 5 k IP + IP T { Ts } k (Concentration dependent equilibrium) IP? i Ts P yi Ci Qi Isotherm parameters for component i Adsorbent particle temperature in Kelvin Total gas pressure Gas phase mole fraction for component i Fluid phase concentration for component i Adsorbed phase concentration (i.. e..Mathematical Equation Form for Loading Ratio Correlation 3 (IP1i + IP2iTs )(IP3i exp[IP4i Ts ])(Pyi )IP + IP T Qi = IP + IP T } ( 1 + ∑ { IP3k exp[IP4 k Ts ])(Pyk ) 5i 6i s 5k 6k s k (Pressure dependent equilibrium) (IP1i + IP2iTs )(IP3i exp[IP4i Ts ])Ci IP + IP T Qi = IP + IP T } ( 1 + ∑ { IP3k exp[IP4 k Ts ])Ci 5i 6i 5k 6k s s k (Concentration dependent equilibrium) IP? i Ts P yi Ci Qi Isotherm parameters for component i Adsorbent particle temperature in Kelvin Total gas pressure Gas phase mole fraction for component i Fluid phase concentration for component i Adsorbed phase concentration (i. amount adsorbed) for component I 2 Gas Cyclic Steady State Modeling 119 . e..Mathematical Equation Form for Loading Ratio Correlation 4 (IP Q = i TsIP2 i (IP3i exp[IP4i Ts ])(Pyi ) 5 i 6 i IP + IP T 1 + ∑ (IP3k exp[IP4 k Ts ])(Pyk ) 5 k 6 k s IP + IP 1i { ) Ts } k (Pressure dependent equilibrium) Qi = (IP TsIP2 i (IP3i exp[IP4i Ts ])Ci 5 i 6 i IP + IP T 1 + ∑ (IP3k exp[IP4 k Ts ])Ci 5 k 6 k s IP + IP 1i { ) Ts } k (Concentration dependent equilibrium) IP? i Ts P yi Ci Qi Isotherm parameters for component i Adsorbent particle temperature in Kelvin Total gas pressure Gas phase mole fraction for component i Fluid phase concentration for component i Adsorbed phase concentration (i. amount adsorbed) for component I 2 Gas Cyclic Steady State Modeling 120 . .Mathematical Equation Form for Loading Ratio Correlation 5 (IP1i exp[IP2i Ts ])(IP3i exp[IP4i Ts ])(Pyi )IP + IP Qi = IP + IP T } ( 1 + ∑ { IP3k exp[IP4 k Ts ])(Pyk ) 5i 5k 6k s 6i Ts k (Pressure dependent equilibrium) Qi = (IP1i exp[IP2i Ts ])(IP3i exp[IP4i Ts ])Ci IP + IP IP + IP T } ( 1 + ∑ { IP3k exp[IP4 k Ts ])Ci 5i 5k 6k s 6i Ts k (Concentration dependent equilibrium) IP? i Ts P yi Ci Qi Isotherm parameters for component i Adsorbent particle temperature in Kelvin Total gas pressure Gas phase mole fraction for component i Fluid phase concentration for component i Adsorbed phase concentration (i.e. amount adsorbed) for component I 2 Gas Cyclic Steady State Modeling 121 . Mathematical Equation Form for Extended Dual-Site Langmuir 1 Qi = IP1i IP2i Py i IP3i IP4i Py i + 1 + ∑ {IP2 k Py k } 1 + ∑ {IP4 k Py k } k k (Pressure dependent equilibrium) Qi = IP1i IP2i C i IP3i IP4i C i + 1 + ∑ {IP2 k C k } 1 + ∑ {IP4 k C k } k k (Concentration dependent equilibrium) IP? i P yi Ci Qi Isotherm parameters for component i Total gas pressure Gas phase mole fraction for component i Fluid phase concentration for component i Adsorbed phase concentration (i..e. amount adsorbed) for component I 2 Gas Cyclic Steady State Modeling 122 . or due to connectivity effects4.. Adsorbent heterogeneity might be present in one of following forms2: chemical or structural heterogeneity of the adsorbent surface3.T.5.e.Mathematical Equation Form for Extended Dual-Site Langmuir 2 Qi = IP1i (IP2i exp[IP3i Ts ]) Py i IP4i (IP5i exp[IP6i Ts ]) Py i + 1 + ∑ {(IP2 k exp[IP3k Ts ]) Py k } 1 + ∑ {(IP5 k exp[IP6 k Ts ]) Py k } k k (Pressure dependent equilibrium) Qi = IP1i (IP2i exp[IP3i Ts ])C i IP4i (IP5i exp[IP6i Ts ])C i + 1 + ∑ {(IP2 k exp[IP3k Ts ])C k } 1 + ∑ {(IP5 k exp[IP6 k Ts ])C k } k k (Concentration dependent equilibrium) IP? i Ts P yi Ci Qi Isotherm parameters for component i Adsorbent particle temperature in Kelvin Total gas pressure Gas phase mole fraction for component i Fluid phase concentration for component i Adsorbed phase concentration (i. and the output is a prediction of mixture equilibrium. The inputs to the IAST calculation are the pure-component adsorption isotherms at the temperature of interest. analogues to Raoult’s law in vapor-liquid equilibrium.A. variation of pore size and shape (either along the axis of individual pores or among the pores). in which nonideal interactions between the adsorbates on the adsorbent surface are accounted for by activity coefficients. and by heterogeneous ideal adsorbed 2 Gas Cyclic Steady State Modeling 123 . amount adsorbed) for component I I. It has been known that the deviations from IAST might result from the chemical dissimilarity of the adsorptive species (as for deviations from Raoult’s law in vapor-liquid equilibrium) or from the heterogeneity of the adsorbent.S. (Ideal Adsorbed Solution Theory) The IAST1 is a widely used engineering thermodynamic method. Nonideal adsorption can be accommodated in the general framework of adsorbed solution theory by real adsorbed solution theory (RAST1) . Qi is the amount component i adsorbed at the standard-state pressure.. the pressure of pure component i at the mixture spreading pressure. the fugacity of pure component i at the mixture spreading pressure. Please note. The spreading pressure is obtained from the experimental adsorption isotherm. which is accounted by introducing gas fugacity instead of gas pressure. that is. via the Gibbs adsorption isotherm: 0 πA RT = ∫ Qi d ln f i 0 f i0 (nonideal gas phase assumption) (ideal gas phase assumption) (Eqn 3) (Eqn 4) πA RT = ∫ Qi d ln Pi 0 Pi0 where A is the surface area of the adsorbent (which is not required in practice. T is the temperature. π . R is the gas constant. i. in which the energetic heterogeneity of the adsorbent is taken into account.when the adsorbed and bulk gas phases are in equilibrium.e.when the adsorbed and bulk gas phases are in equilibrium. equality of chemical potential in the bulk gas and adsorbed phases implies: f i = xi f i 0 (Eqn 1) where f i is the fugacity of component i in the bulk gas phase and xi is the mole fraction of component i in the adsorbed phase. Eqn 1 describes the ideal adsorbed phase contacting with real (i. that is. π . nonideal) gas phase. Qi (Pi ) or Qi (C i ) . When an assumption of ideal gas phase is invoked. y i is the gas mole fraction for component i and xi is the mole fraction of component i in the adsorbed phase. f i and Pi are the fugacity and the pressure for pure component i . The complete description of the IAST as a predictive tool for multicomponent adsorption equilibria requires an expression for total amount adsorbed. QT : x 1 = ∑ i0 QT i Qi (Eqn 5) and the stoichiometric constraint: ∑x i i =1 0 (Eqn 6) In Eqn 5.solution theory (HIAST6). then the basic equation of IAST can be written by: y i P = xi Pi 0 (Eqn 1) where P is total gas pressure. Subject to the assumption of an ideal adsorbed phase..e. as the product πA need not be separated in the calculation). 2 Gas Cyclic Steady State Modeling 124 . Pi is the standard-state pressure. f i 0 is the standard- state fugacity. 1992. Keil. The available pure isotherm equations for the IAST within CSS model may be found at: • List of Pure Isotherms Available in IAST Calculation of CSS model References 1 2 3 4 5 6 Myers. J. Rudzinski.1. 15. Langmuir 2002. T.2 parameters / isothermal assumption . M. For example. D. instead of using a specific type isotherm for all adsorbates. Düren.3 parameters / temperature correlation . so on. Pure Isotherm List for the IAST Calculation of CSS The following are the pure isotherm equations available in the IAST calculation by CSS bed model (gCSS_Adsorber) from Aspen Adsim 2004. the Langmuir isotherm for 1st component. V. A. Langmuir 1 Langmuir 2 Langmuir 3 Langmuir 4 Langmuir 5 Dual Site Langmuir 1 Dual Site Langmuir 2 . 1988. J. Valenzuela. Jagiello.. López-Ramon. F. Myers.).4 parameters / isothermal assumption . Seaton. Academic Press: New York. 34.. W. 11. 121. 18.. I. Yun. A. AIChE J. M. N.4 parameters / temperature correlation . Seaton. J.-H. No restriction for the type of pure component isotherm in the IAST calculation (namely. 4435.6 parameters / temperature correlation Sips (Langmuir-Freundlich) 1 . N. Everett. 397... Bandosz. The main benefits from the IAST application within the CSS model are: • Capability to account gas phase nonideality by considering the gas fugacity that may be evaluated by either Aspen Properties or User Procedure. M. Prausnitz. Davies. the Freundlich isotherm for 2nd component. in print. J. G.. Adsorption of Gases on Heterogeneous Surfaces. AIChE J.4 parameters / temperature correlation . M. T. Talu.g. as predictive equilibrium theory. 6263. Langmuir 1997. the Sips isotherm for 3rd component. L. any combination of the pure isotherm equations will be acceptable in representing mixture adsorption equilibria by means of IAST.. isotherm type free IAST). A.4 parameters / temperature correlation ..3 parameters / isothermal assumption 2 Gas Cyclic Steady State Modeling 125 .. A. Zwiebel. Seaton...The CSS model in Aspen Adsim supports a comprehensive tool in applying the IAST.. 1965. it is now available to assign the best-fit isotherm equation to each component (e. N.. L. In the application. A. D. 13. Langmuir 1999. O. J. 6 parameters / temperature correlation Sips (Langmuir-Freundlich) 4 .3 parameters / isothermal assumption .5 parameters / temperature correlation Sips (Langmuir-Freundlich) 3 .6 parameters / temperature correlation Sips (Langmuir-Freundlich) 5 .6 parameters / temperature correlation Henry 1 Henry 2 Henry 3 Henry 4 Freundlich 1 Toth 1 BET 1 .1 parameters / isothermal assumption .2 parameters / temperature correlation .Sips (Langmuir-Freundlich) 2 .2 parameters / isothermal assumption .2 parameters / temperature correlation .1 parameters / Langmuir 1 Pressure dependent Qi = IP1i IP2i Pi 1 + IP2i Pi Isotherm parameter of comp i [kmol/kg-adsorbent] Isotherm parameter of comp i [bar] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium pressure of comp i [bar] IP1i IP2i Qi Pi Concentration dependent Qi = IP1i IP2i C i 1 + IP2i C i Isotherm parameter of comp i [kmol/kg-adsorbent] Isotherm parameter of comp i [kmol/m3] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium concentration of comp i [kmol/m3] IP1i IP2i Qi Ci Langmuir 2 Pressure dependent 2 Gas Cyclic Steady State Modeling 126 .2 parameters / temperature correlation . Qi = IP1i (IP2i exp[IP3i T ])Pi 1 + (IP2i exp[IP3i T ])Pi Isotherm parameter of comp i [kmol/kg-adsorbent] Isotherm parameter of comp i [bar] Isotherm parameter of comp i [K] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium pressure of comp i [bar] Temperature [K] IP1i IP2i IP3i Qi Pi T Concentration dependent Qi = IP1i (IP2i exp[IP3i T ])C i 1 + (IP2i exp[IP3i T ])C i Isotherm parameter of comp i [kmol/kg-adsorbent] Isotherm parameter of comp i [kmol/m3] Isotherm parameter of comp i [K] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium concentration of comp i [kmol/m3] Temperature [K] IP1i IP2i IP3i Qi Ci T Langmuir 3 Pressure dependent Qi = (IP1i + IP2iT ) (IP3i exp[IP4i T ])Pi 1 + (IP3i exp[IP4i T ])Pi Isotherm parameter of comp i [kmol/kg-adsorbent] Isotherm parameter of comp i [kmol/kg/ K] Isotherm parameter of comp i [bar] Isotherm parameter of comp i [K] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium pressure of comp i [bar] Temperature [K] IP1i IP2i IP3i IP4i Qi Pi T 2 Gas Cyclic Steady State Modeling 127 . K/kg-adsorbent] Isotherm parameter of comp i [-] 2 Gas Cyclic Steady State Modeling 128 .K/kgIsotherm parameter of comp i [-] Isotherm parameter of comp i [bar] Isotherm parameter of comp i [K] Equilibrium loading of comp i [kmol/kgadsorbent] Equilibrium pressure of comp i [bar] Temperature [K] Concentration dependent Qi = (IP 1i 1 + (IP3i exp[IP4i T ])C i T IP2 i ) (IP 3i exp[IP4i T ])C i IP1i IP2i Isotherm parameter of comp i [kmol.Concentration dependent Qi = (IP1i + IP2iT ) (IP3i exp[IP4i T ])Ci 1 + (IP3i exp[IP4i T ])C i Isotherm parameter of comp i [kmol/kg-adsorbent] Isotherm parameter of comp i [kmol/kg/K] Isotherm parameter of comp i [kmol/m3] Isotherm parameter of comp i [K] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium concentration of comp i [kmol/m3] Temperature [K] IP1i IP2i IP3i IP4i Qi Ci T Langmuir 4 Pressure dependent Qi (IP = 1i 1 + (IP3i exp[IP4i T ])Pi adsorbent] T IP2 i ) (IP 3i exp[IP4i T ])Pi IP1i IP2i IP3i IP4i Qi Pi T Isotherm parameter of comp i [kmol. IP3i IP4i Qi Ci T Isotherm parameter of comp i [kmol/m3] Isotherm parameter of comp i [K] Equilibrium loading of comp i [kmol/kgadsorbent] Equilibrium concentration of comp i [kmol/m3] Temperature [K] Langmuir 5 Pressure dependent Qi = (IP1i exp[IP2i T ]) (IP3i exp[IP4i T ])Pi 1 + (IP3i exp[IP4i T ])Pi Isotherm parameter of comp i [kmol/kg-adsorbent] Isotherm parameter of comp i [K] Isotherm parameter of comp i [bar] Isotherm parameter of comp i [K] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium pressure of comp i [bar] Temperature [K] IP1i IP2i IP3i IP4i Qi Pi T Concentration dependent Qi = (IP1i exp[IP2i T ])(IP3i exp[IP4i T ])Ci 1 + (IP3i exp[IP4i T ])C i Isotherm parameter of comp i [kmol/kg-adsorbent] Isotherm parameter of comp i [K] Isotherm parameter of comp i [kmol/m3] Isotherm parameter of comp i [K] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium concentration of comp i [kmol/m3] Temperature [K] IP1i IP2i IP3i IP4i Qi Ci T 2 Gas Cyclic Steady State Modeling 129 . Dual-Site Langmuir 1 Pressure dependent Qi = IP1i IP2i Pi IP3i IP4i Pi + 1 + IP2i Pi 1 + IP4i Pi Isotherm parameter of comp i [kmol/kg-adsorbent] Isotherm parameter of comp i [bar] Isotherm parameter of comp i [kmol/kg-adsorbent] Isotherm parameter of comp i [bar] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium pressure of comp i [bar] IP1i IP2i IP3i IP4i Qi Pi Concentration dependent Qi = IP1i IP2i C i IP3i IP4i C i + 1 + IP2i C i 1 + IP4i C i Isotherm parameter of comp i [kmol/kg-adsorbent] Isotherm parameter of comp i [kmol/m3] Isotherm parameter of comp i [kmol/kg-adsorbent] Isotherm parameter of comp i [kmol/m3] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium concentration of comp i [kmol/m3] IP1i IP2i IP3i IP4i Qi Ci Dual-Site Langmuir 2 Pressure dependent Qi = IP1i (IP2i exp[IP3i T ]) Pi IP4i (IP5i exp[IP6i T ]) Pi + 1 + (IP2i exp[IP3i T ]) Pi 1 + (IP5i exp[IP6i T ]) Pi Isotherm parameter of comp i [kmol/kg-adsorbent] Isotherm parameter of comp i [bar] Isotherm parameter of comp i [K] IP1i IP2i IP3i 2 Gas Cyclic Steady State Modeling 130 . IP4i IP5i IP6i Qi Pi T Isotherm parameter of comp i [kmol/kg-adsorbent] Isotherm parameter of comp i [bar] Isotherm parameter of comp i [K] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium pressure of comp i [bar] Temperature [K] Concentration dependent Qi = IP1i (IP2i exp[IP3i T ])C i IP4i (IP5i exp[IP6i T ])C i + 1 + (IP2i exp[IP3i T ])C i 1 + (IP5i exp[IP6i T ])C i Isotherm parameter of comp i [kmol/kg-adsorbent] Isotherm parameter of comp i [kmol/m3] Isotherm parameter of comp i [K] Isotherm parameter of comp i [kmol/kg-adsorbent] Isotherm parameter of comp i [kmol/m3] Isotherm parameter of comp i [K] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium concentration of comp i [kmol/m3] Temperature [K] IP1i IP2i IP3i IP4i IP5i IP6i Qi Ci T Sips (Langmuir-Freundlich) 1 Pressure dependent Qi = IP1i IP2i Pi IP3 i IP3 i 1 + IP2i Pi IP1i IP2i IP3i Isotherm parameter of comp i [kmol/kg-adsorbent] Isotherm parameter of comp i [bar] Isotherm parameter of comp i [-] 2 Gas Cyclic Steady State Modeling 131 . Qi Pi Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium pressure of comp i [bar] Concentration dependent Qi = IP1i IP2i C i IP3 i IP3 i 1 + IP2i C i IP1i IP2i IP3i Qi Ci Isotherm parameter of comp i [kmol/kg-adsorbent] Isotherm parameter of comp i [kmol/m3] Isotherm parameter of comp i [-] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium concentration of comp i [kmol/m3] Sips (Langmuir-Freundlich) 2 Pressure dependent IP (IP exp[IP3i T ]) Pi 4 i 5 i Qi = 1i 2i IP + IP T 1 + (IP2i exp[IP3i T ]) Pi 4 i 5 i IP + IP T IP1i IP2i IP3i IP4i IP5i Qi Pi T Isotherm parameter of comp i [kmol/kg-adsorbent] Isotherm parameter of comp i [bar] Isotherm parameter of comp i [K] Isotherm parameter of comp i [-] Isotherm parameter of comp i [K] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium pressure of comp i [bar] Temperature [K] Concentration dependent IP (IP exp[IP3i T ])Ci 4 i 5 i Qi = 1i 2i IP + IP 1 + (IP2i exp[IP3i T ])Ci 4 i 5 i IP + IP T T 2 Gas Cyclic Steady State Modeling 132 . IP1i IP2i IP3i IP4i IP5i Qi Ci T Isotherm parameter of comp i [kmol/kg-adsorbent] Isotherm parameter of comp i [kmol/m3] Isotherm parameter of comp i [K] Isotherm parameter of comp i [-] Isotherm parameter of comp i [K] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium concentration of comp i [kmol/m3] Temperature [K] Sips (Langmuir-Freundlich) 3 Pressure dependent (IP1i + IP2iT )(IP3i exp[IP4i T ]) Pi IP + IP Qi = IP + IP T 1 + (IP3i exp[IP4i T ]) Pi 5i 5i 6i 6i T IP1i IP2i IP3i IP4i IP5i IP6i Qi Pi T Isotherm parameter of comp i [kmol/kg-adsorbent] Isotherm parameter of comp i [kmol/kg/K] Isotherm parameter of comp i [bar] Isotherm parameter of comp i [K] Isotherm parameter of comp i [-] Isotherm parameter of comp i [K] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium pressure of comp i [bar] Temperature [K] Concentration dependent Qi = IP1i (IP1i + IP2iT )(IP3i exp[IP4i T ])Ci IP + IP IP + IP T 1 + (IP3i exp[IP4i T ])Ci 5i 5i 6i 6i T Isotherm parameter of comp i [kmol/kg-adsorbent] 2 Gas Cyclic Steady State Modeling 133 . IP2i IP3i IP4i IP5i IP6i Qi Ci T Isotherm parameter of comp i [kmol/kg/K] Isotherm parameter of comp i [kmol/m3] Isotherm parameter of comp i [K] Isotherm parameter of comp i [-] Isotherm parameter of comp i [K] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium concentration of comp i [kmol/m3] Temperature [K] Sips (Langmuir-Freundlich) 4 Pressure dependent (IP Q = i 1i 1 + (IP3i exp[IP4i T ]) Pi T IP2 i (IP3i exp[IP4i T ]) Pi ) IP5 i + IP6 i T IP5 i + IP6 i T IP1i IP2i IP3i IP4i IP5i IP6i Qi Pi T Isotherm parameter of comp i [kmol.K/kg-adsorbent] Isotherm parameter of comp i [-] Isotherm parameter of comp i [bar] Isotherm parameter of comp i [K] Isotherm parameter of comp i [-] Isotherm parameter of comp i [K] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium pressure of comp i [bar] Temperature [K] Concentration dependent (IP Q = i 1i 1 + (IP3i exp[IP4i T ])Ci T IP2 i (IP3i exp[IP4i T ])Ci ) IP5 i + IP6 i T IP5 i + IP6 i T IP1i IP2i Isotherm parameter of comp i [kmol.K/kg-adsorbent] Isotherm parameter of comp i [-] 2 Gas Cyclic Steady State Modeling 134 . IP3i IP4i IP5i IP6i Qi Ci T Isotherm parameter of comp i [kmol/m3] Isotherm parameter of comp i [K] Isotherm parameter of comp i [-] Isotherm parameter of comp i [K] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium concentration of comp i [kmol/m3] Temperature [K] Sips (Langmuir-Freundlich) 5 Pressure dependent Qi = IP1i IP2i IP3i IP4i IP5i IP6i Qi Pi T (IP1i exp[IP2i T ])(IP3i exp[IP4i T ]) Pi IP IP + IP T 1 + (IP3i exp[IP4i T ]) Pi 5i 6i 5i + IP6 i T Isotherm parameter of comp i [kmol/kg-adsorbent] Isotherm parameter of comp i [K] Isotherm parameter of comp i [bar] Isotherm parameter of comp i [K] Isotherm parameter of comp i [-] Isotherm parameter of comp i [K] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium pressure of comp i [bar] Temperature [K] Concentration dependent Qi = IP1i IP2i (IP1i exp[IP2i T ])(IP3i exp[IP4i T ])Ci IP IP + IP T 1 + (IP3i exp[IP4i T ])Ci 5i 6i 5i + IP6 i T Isotherm parameter of comp i [kmol/kg-adsorbent] Isotherm parameter of comp i [K] 2 Gas Cyclic Steady State Modeling 135 . IP3i IP4i IP5i IP6i Qi Ci T Isotherm parameter of comp i [kmol/m3] Isotherm parameter of comp i [K] Isotherm parameter of comp i [-] Isotherm parameter of comp i [K] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium concentration of comp i [kmol/m3] Temperature [K] Henry 1 Pressure dependent Qi = IP i Pi 1 IP1i Qi Pi Isotherm parameter of comp i [kmol/bar/kg-adsorbent] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium pressure of comp i [bar] Concentration dependent Qi = IP iCi 1 IP1i Qi Ci Isotherm parameter of comp i [m3/kg-adsorbent] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium concentration of comp i [kmol/m3] Henry 2 Pressure dependent Qi = (IP i + IP2iT ) Pi 1 IP1i IP2i Qi Pi Isotherm parameter of comp i [kmol/bar/kg-adsorbent] Isotherm parameter of comp i [kmol/bar/K/kg-adsorbent] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium pressure of comp i [bar] 2 Gas Cyclic Steady State Modeling 136 . T Temperature [K] Concentration dependent Qi = (IP i + IP2iT )Ci 1 IP1i IP2i Qi Ci T Isotherm parameter of comp i [m3/kg-adsorbent] Isotherm parameter of comp i [m3/K/kg-adsorbent] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium concentration of comp i [kmol/m3] Temperature [K] Henry 3 Pressure dependent Qi = IP i T IP2 i Pi 1 ( ) IP1i IP2i Qi Pi T Isotherm parameter of comp i [kmol.m3/kg-adsorbent] Isotherm parameter of comp i [-] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium concentration of comp i [kmol/m3] Temperature [K] Henry 4 Pressure dependent 2 Gas Cyclic Steady State Modeling 137 .K/bar/kg-adsorbent] Isotherm parameter of comp i [-] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium pressure of comp i [bar] Temperature [K] Concentration dependent Qi = IP i T IP2 i Ci 1 ( ) IP1i IP2i Qi Ci T Isotherm parameter of comp i [K. Qi = (IP i exp[IP2i T ]) Pi 1 IP1i IP2i Qi Pi T Isotherm parameter of comp i [kmol/bar/kg-adsorbent] Isotherm parameter of comp i [K] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium pressure of comp i [bar] Temperature [K] Concentration dependent Qi = (IP i exp[IP2i T ])Ci 1 IP1i IP2i Qi Ci T Isotherm parameter of comp i [m3/kg-adsorbent] Isotherm parameter of comp i [K] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium concentration of comp i [kmol/m3] Temperature [K] Freundlich 1 Pressure dependent Qi = IP1i Pi IP2 i IP1i IP2i Qi Pi Isotherm parameter of comp i [kmol/bar/kg-adsorbent] Isotherm parameter of comp i [-] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium pressure of comp i [bar] Concentration dependent Qi = IP iCiIP2 i 1 IP1i IP2i Qi Isotherm parameter of comp i [m3/kg-adsorbent] Isotherm parameter of comp i [-] Equilibrium loading of comp i [kmol/kg-adsorbent] 2 Gas Cyclic Steady State Modeling 138 . Ci Equilibrium concentration of comp i [kmol/m3] Toth 1 Pressure dependent Qi = (IP IP i Pi 1 + Pi IP3i 2i ) 1 IP3 i IP1i IP2i IP3i Qi Pi Isotherm parameter of comp i [kmol/kg-adsorbent] Isotherm parameter of comp i [bar] Isotherm parameter of comp i [-] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium pressure of comp i [bar] Concentration dependent Qi = (IP IP iCi 1 + CiIP3i 2i ) 1 IP3 i IP1i IP2i IP3i Qi Ci Isotherm parameter of comp i [kmol/kg-adsorbent] Isotherm parameter of comp i [kmol/m3] Isotherm parameter of comp i [-] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium concentration of comp i [kmol/m3] BET 1 Pressure dependent IP1i IP2i Qi =  P 1 − is  P i  Pi Pi s  P P   1 − is + IP2i is   P Pi  i   IP1i IP2i Isotherm parameter of comp i [kmol/kg-adsorbent] Isotherm parameter of comp i [-] 2 Gas Cyclic Steady State Modeling 139 . m3/kmol/K] Temperature [K] IP1i IP2i Qi Ci Pi s R T User Guidelines How to Create a CSS Simulation Flowsheet Preconditions: The user must hold the licenses for Aspen Adsim 2004.appdf. is used for component properties definition. named air. 2 Gas Cyclic Steady State Modeling 140 .Qi Pi Pi s Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium pressure of comp i [bar] Saturated vapour pressure of comp i [bar] Concentration dependent IP1i IP2i Qi = Ci Pi s RT  C  C C  1 − s i  1 − s i + IP2i s i   P RT   P RT Pi RT  i i    Isotherm parameter of comp i [kmol/kg-adsorbent] Isotherm parameter of comp i [-] Equilibrium loading of comp i [kmol/kg-adsorbent] Equilibrium concentration of comp i [kmol/m3] Saturated vapour pressure of comp i [bar] Gas constant.1. 1 2 Start Aspen Adsim 2004. 8.1 (or Aspen Plus 2004. Initialize component properties by loading a property definition.1). The property file.1 and Aspen Properties 2004.31433e-2 [bar. ) 4 Select CSS_Info from Structure Types folder by either pressing [Ctrl + I] or clicking the right mouse button and choosing Create Instance.3 Choose target components from the component list. 2 Gas Cyclic Steady State Modeling 141 . (Example. A user chooses N2 and O2 as the components for a simulation. (Example. 2 Gas Cyclic Steady State Modeling 142 . and user enters a name.) 6 Aspen Adsim shows the instance in a folder of the same name below Flowsheet\Structures folder. Enter CSSInfo as the name of the structure instance.5 A dialog box is displayed for the name of the structure instance. Switch the global NonIsothermal parameter to TRUE from the Specify Table of the instance structure CSSInfo. (Example. NonIsothermal. from the Specify Table of the instanced structure.7 Select the global non-isothermal/isothermal option by choosing TRUE or FALSE the logical parameter.) 2 Gas Cyclic Steady State Modeling 143 . ) 2 Gas Cyclic Steady State Modeling 144 . Re-construct N2PSACSS .supplied as one of Aspen Adsim 2004.8 Construct a simulation flowsheet using models from the CSS folder of Aspen Adsim Gas Library.1 demonstrations. (Example. gCSS_Material_Connection. Re-construct N2PSACSS . from the Stream Types folder of Aspen Adsim Library and rename each model.RigorousWallBalance 10 True True 2 Gas Cyclic Steady State Modeling 145 .1 demonstrations. except the following: Layer(1).9 The connect models using the stream. as shown in the picture.supplied as one of Aspen Adsim 2004.xNodes Layer(1). Leave all items as default.NonAdiabatic Layer(1). (Example. i Bed1 (gCSS_Adsorber): Click the right mouse button and select Specify table from the Forms menu and specify the CSS bed model B1. The following are typical items for the N2PSACSS example.) 10 Specify models by putting assumptions and parameter values that are required for process simulation. Hs Layer(1).Specify 2 Gas Cyclic Steady State Modeling 146 .IP("N2".00760501 0.00267287 0.1) Layer(1).00267288 0.ksLDF("N2") Layer(1).Ta Layer(1).1413 0. Leave all items as default.ii Bed1 (gCSS_Adsorber): Use right mouse button and select Specify_ table from Forms and specify the CSS bed model B1.2) Layer(1).1) Layer(1).IP("N2".IP("O2".IP("O2".15 0.04476 Table .136 0. except the following: Layer(1).ksLDF("O2") 1e-007 298.2) Layer(1). Specify_ 2 Gas Cyclic Steady State Modeling 147 .Table . 15 True 1. The following items should be changed: Ta NonAdiabaticTankVoid Hamb 298.iii TD1 and TD2 (gCSS_TankVoid): these two tank/void models have the same specification.e-005 2 Gas Cyclic Steady State Modeling 148 . Cycle_Organizer.e-005 TD2 iv.Hw TD1 6. Aspen Adsim displays the icon. on the simulation flowsheet. VP1 (gCSS_Valve): change CheckValve option to True VP1 11 Select the Cycle Organizer from the Tools menu. with a dialog box from Cycle Organizer. 2 Gas Cyclic Steady State Modeling 149 . 12 Cyclic Steady State simulation mode can be chosen by selecting Cycle Options from the Cycle menu. To define a CSS simulation flowsheet. 2 Gas Cyclic Steady State Modeling 150 . Cyclic Steady-State mode. check the check box out. 13 Define process cycle/step information within the Step menu. N2PSACSS. For this example. and the interaction and control details are as follows: 2 Gas Cyclic Steady State Modeling 151 . we have four process steps. STEP1 2 Gas Cyclic Steady State Modeling 152 . STEP2 STEP3 STEP4 2 Gas Cyclic Steady State Modeling 153 . 14 Define the variable to be manipulated and the values within the Cycle Organizer. STEP1 STEP2 2 Gas Cyclic Steady State Modeling 154 . STEP3 STEP4 2 Gas Cyclic Steady State Modeling 155 . indicating a Cycle Task has been created correctly.15 Generate a Cycle Task either by executing Generate Task from Cycle menu or by clicking Generate Cycle from the status bar of Cycle Organizer. Aspen Adsim displays a green check-shape icon on the status bar. BEFORE AFTER 2 Gas Cyclic Steady State Modeling 156 . then confirm Aspen Adsim shows a green square on the simulation status bar and that the simulation mode is now set Steady State.16 Close the Cycle Organizer. If so. 2 Gas Cyclic Steady State Modeling 157 . the simulation is ready to be run in CSS mode. How to Create a Dynamic Simulation Flowsheet using CSS Models Preconditions: The user must be a the licensed user of Aspen Adsim 2004.1 and Aspen Properties 2004.1 (or Aspen Plus 2004.1). The property file, named air.appdf, is used for component properties definition. 1 2 Start Aspen Adsim 2004.1. Initialize component properties by loading a property definition. 3 Choose target components from the component list. (Example. Choose N2 and O2 as the components for a simulation.) 2 Gas Cyclic Steady State Modeling 158 4 Select CSS_Info from the Structure Types folder by either pressing [Ctrl + I] or clicking right mouse button and choosing Create Instance. 2 Gas Cyclic Steady State Modeling 159 5 A dialog box is displayed to enter the name of the structure instance, and the user enters a name. (Example. Enter CSSInfo as the name of the structure instance.) 6 Aspen Adsim displays the instance in a folder of the same name below the Flowsheet\Structures folder. 2 Gas Cyclic Steady State Modeling 160 7 Select the global non-isothermal/isothermal option by choosing TRUE or FALSE the logical parameter, NonIsothermal, from the Specify Table of the instanced structure. (Example. Switch the global NonIsothermal parameter to TRUE from the Specify Table of the instance structure CSSInfo.) 2 Gas Cyclic Steady State Modeling 161 8 Construct a simulation flowsheet using models from the CSS folder of Aspen Adsim Gas Library. (Example. Re-construct N2PSACSS - supplied as one of Aspen Adsim 2004.1 demonstrations.) 9 Next, connect models using the stream, gCSS_Material_Connection, from the Stream Types folder of Aspen Adsim Library and rename each model, as shown in the picture. (Example. Re-construct N2PSACSS - supplied as one of Aspen Adsim 2004.1 demonstrations.) 2 Gas Cyclic Steady State Modeling 162 10 Specify models by putting assumptions and parameter values required for the process simulation. – the following are typical items for the N2PSACSS example. v. Bed1 (gCSS_Adsorber): Click the right mouse button and select Specify table from Forms menu, then specify the CSS bed model B1. – leave all items as default, except the following: Layer(1).xNodes Layer(1).NonAdiabatic Layer(1).RigorousWallBalance 10 True True vi. Bed1 (gCSS_Adsorber): Click the right mouse button and select Specify_ table from Forms and specify the CSS bed model B1 - leave all items as default, except the following: Layer(1).Hs Layer(1).Ta Layer(1).IP("N2",1) Layer(1).IP("N2",2) Layer(1).IP("O2",1) Layer(1).IP("O2",2) Layer(1).ksLDF("N2") . 1e-007 298.15 0.00267288 0.136 00267287 0.1413 0.00760501 2 Gas Cyclic Steady State Modeling 163 ksLDF("O2") Table .Layer(1).04476 2 Gas Cyclic Steady State Modeling 164 .Specify 0. Specify_ 2 Gas Cyclic Steady State Modeling 165 .Table . e-005 6. VP1 VP1 (gCSS_Valve): change CheckValve option to True.15 True 1. TD1 and TD2 (gCSS_TankVoid): these two tank/void models have the same specification.vii. The following items should be changed: Ta NonAdiabaticTankVoid Hamb Hw TD1 298.e-005 TD2 viii. 2 Gas Cyclic Steady State Modeling 166 . Aspen Adsim displays the icon Cycle_Organizer. and the interaction and control details are as follows: 2 Gas Cyclic Steady State Modeling 167 . on the simulation flowsheet and the Cycle Organizer dialog box. For this example. we have four process steps. N2PSACSS. 12 Non Cyclic Steady State simulation mode can be chosen from the Cycle Options in the Cycle menu. 13 Define process cycle/step information within the Step menu. uncheck Cyclic Steady-State mode check box and enter the value of Maximum cycle for dynamic simulation.11 Select Cycle Organizer from the Tools menu. To define a dynamic simulation flowsheet. STEP1 2 Gas Cyclic Steady State Modeling 168 . STEP2 STEP3 STEP4 2 Gas Cyclic Steady State Modeling 169 . 14 Define the variable to be manipulated and the values within Cycle Organizer. STEP1 STEP2 2 Gas Cyclic Steady State Modeling 170 . STEP3 STEP4 2 Gas Cyclic Steady State Modeling 171 . 15 Generate a Cycle Task either by executing Generate Task from Cycle menu or by clicking Generate Cycle from the status bar of Cycle Organizer. BEFORE AFTER 2 Gas Cyclic Steady State Modeling 172 . indicating the Cycle Task has been created correctly. Aspen Adsim displays a green check-shape icon on the status bar. 16 Close Cycle Organizer and confirm that Aspen Adsim displays a green square on the simulation status bar and that simulation mode is now set Dynamic. 2 Gas Cyclic Steady State Modeling 173 . the simulation is ready to be run in dynamic mode. If so. 2 Gas Cyclic Steady State Modeling 174 . 3 Uncheck the check box to convert the flowsheet from CSS to dynamic. If you are not sure which Aspen Adsim data file is defined in CSS mode. Activate the Cycle Organizer by double-clicking the icon and locate the Cyclic Steady-State mode check box on the Cyclic Options Tab.1 data file defined in CSS mode to convert the simulation mode from CSS to dynamic. 1 2 Open the existing Aspen Adsim flowsheet (defined in CSS simulation mode).How to Convert a CSS Flowsheet to a Dynamic Flowsheet Preconditions: There is an existing Aspen Adsim 2004. The Cyclic Organizer displays a dialog box to ask the Maximum Variable Steps option (recommended answer is Yes). please refer to How to Create a CSS Simulation Flowsheet. indicating the Cycle Task has been created correctly. BEFORE AFTER 2 Gas Cyclic Steady State Modeling 175 .4 Enter the maximum cycles value (e. 20) in the Cycle Options Tab and generate the Cycle Task either by executing Generate Task from Cycle menu or by clicking Generate Cycle from the status bar of Cycle Organizer. Aspen Adsim displays a green check-shape icon on the status bar.g.. the simulation is ready to be run in dynamic mode. 2 Gas Cyclic Steady State Modeling 176 . If so.5 Close the Cycle Organizer and then confirm Aspen Adsim displays a green square on the simulation status bar and if simulation mode is now set Dynamic. How to Convert a Dynamic Flowsheet into a CSS Flowsheet Preconditions: There is an existing Aspen Adsim 2004. 1 2 Open an existing Aspen Adsim flowsheet (defined in dynamic simulation mode). If you are not sure which Aspen Adsim data file is defined in dynamic mode using CSS models. Activate the Cycle Organizer by double-clicking the icon and locate the Cyclic Steady-State mode check box on the Cyclic Options Tab. Check the check box to re-define the simulation as CSS flowsheet. please refer to How to Create a Dynamic Simulation Flowsheet using CSS Models.1 dynamic flowsheet created using CSS models and the user wishes to convert the simulation mode from dynamic to CSS. BEFORE 2 Gas Cyclic Steady State Modeling 177 . AFTER 2 Gas Cyclic Steady State Modeling 178 . If the Task is not active. If so.3 After confirming (from the status bar of Cycle Organizer) the Cycle Task is active. close the Cycle Organizer. Aspen Adsim displays a green square on the simulation status bar and the simulation mode is now set to Steady State. generate a Cycle Task either by executing Generate Task from Cycle menu or by clicking Generate Cycle from the status bar of Cycle Organizer. the simulation is ready to be run in CSS mode. 4 2 Gas Cyclic Steady State Modeling 179 . Note that the value of the Maximum variable step must be reduced if the flowsheet follows dynamic (not exceed 50).Developer’s Tips to Get Better Convergence Property in CSS Simulation 1 Careful consideration in setting Solver Property options is required to ensure convergence of CSS models. 2 3 4 5 2 Gas Cyclic Steady State Modeling 180 . The value of Maximum variable step is highly sensitive for the convergence property. iterations value is 5000. step reductions value should be maximized as 20. For CSS simulation. we recommend selecting the Newton Method for CSS simulation whilst the Fast Newton is normally recommendable in a dynamic simulation. In the Non Linear Solver Tab. and this may be adjusted (normally increase as problem is complex) but should not exceed 500. a recommended default value is 200. Convergence criterion is recommended to set Residual and Variable. Recommended Max. Max. 2 Gas Cyclic Steady State Modeling 181 . The recommended selection for this option is CSS simulation. ‘Use transpose’. has been added to the Solver Properties dialog Linear Solver Tab.Recommended Non Linear Solver Property 6 A new check box. 7 The following dialog shows the recommended tolerance table for CSS simulation. 2 Gas Cyclic Steady State Modeling 182 . 2 Gas Cyclic Steady State Modeling 183 . 3 Ion-Exchange Processes This chapter contains for information on: • • • • • • • • • • About Ion-Exchange Processes Bed Model Assumptions for Ion-Exchange Processes Configure Form for Ion-Exchange Processes Configure Layer Form for Ion-Exchange Processes General Tab Material/Momentum Balance Tab About Axial Dispersion in Ion-Exchange Processes Kinetic Model Tab Isotherm Tab Summary of Mass Balance Equations for Ion-Exchange Processes About Ion-Exchange Processes In ion-exchange processes, a fluid phase (such as an aqueous solution) containing cations and anions, is contacted with an ion-exchange resin. Typically, the ion-exchange resin is inside a packed bed adsorption column. The resin contains bound groups carrying a positive or negative ionic charge, which are accompanied by displaceable ions of opposite charge (counterions). The displaceable ions have the same charge as the ions of interest in the fluid phase: since the ions in the fluid phase have a greater affinity for the bound groups than those originally present, the latter are displaced by the former. Generally, the resin has a fixed total charge capacity, so one ionic solute is exchanged for another while maintaining charge neutrality. Ion-exchange processes have become an important separation technique for aqueous electrolyte solutions and are used in these applications: • • • Water softening, where monovalent cations replace multivalent cations. Water purification, where hydrogen or hydroxide ions replace cations (usually monovalent). Multi-component separation of ionic mixtures of different type and charge. Ion-exchange may be written as a reversible reaction involving charge equivalent quantities. For example, in a water-softening process, the cationexchange process is written as: Ca 2 + + 2 NaR ⇔ CaR2 + 2 Na + 3 Ion-Exchange Processes 184 where R is a stationary, univalent, anionic group in the poly-electrolyte network of the exchange phase. Bed Model Assumptions for IonExchange The bed model assumptions for ion-exchange are: • • • • • Overall and component material balances apply for the liquid phase. Isothermal conditions apply. Plug flow or plug flow with axial dispersion applies. The liquid stream pressure is constant (no frictional pressure drop). The superficial velocity and thus volumetric flow rate remain constant. (The ion components are dilute so the effect of adsorption on the overall mass balance is negligible.) Ideal mixing occurs in the aqueous phase. Since the ionic components are very dilute, overall molar volume remains constant. Changes in molar volume between distinct, sequentially fed fluids are allowed. The total exchange capacity of the bed Q is constant. A lumped mass-transfer rate applies, with a liquid- or solid-film resistance. This resistance is either linear, quadratic, or user-defined. The mass-action equilibrium is one alternative model for ion-exchange behavior. Others include the extended Langmuir and extended LangmuirFreundlich models. • • • • • Configure Form (ionx) In the Configure Form of the Ion-exchange process bed model: • • • • Enter the number of layers within the bed (1 or more). Click in the Description box for each layer and type in a brief name or description. Click Configure to open the Configure Layer dialog box. Click Specify to open the specify form for the layer model. Configure Layer Form (ionx) Use the options in the Configure Layer form to specify the set of equations within each layer of the bed. For more information on choosing the options for your ion-exchange process, see these sections: • • • • General tab Material/Momentum Balance tab Kinetic Model tab Isotherm tab 3 Ion-Exchange Processes 185 General Tab (ionx) Use the General tab to specify these options for your ion-exchange process: • • Discretization method Number of nodes General Tab (ionx): Discretization Method to be Used These discretization methods are available for ion-exchange processes: • • • • • • • UDS1 UDS2 CDS1 LDS QDS MIXED BUDS General Tab (ionx): Number of Nodes In the Number of Nodes box, choose an appropriate number of nodes for your chosen discretization method. Material/Momentum Balance Tab (ionx) Use the Material/Momentum Balance tab to specify the basic assumptions about material dispersion in the liquid phase for ion-exchange processes. Material/Momentum Balance Tab (ionx): Material Balance Assumption In the Material Balance Assumption box, choose from one of the following options: • • • • • Convection Only Convection with Constant Dispersion Convection with Estimated Dispersion Convection with User Procedure Dispersion Convection with User Submodel Dispersion Material Balance Assumption (ionx): Convection Only This option omits the dispersion term from the material balance, so the model represents plug flow with a zero dispersion coefficient (infinite Peclet number). 3 Ion-Exchange Processes 186 Because the dispersion term is omitted, you do not need to supply the dispersion coefficient. Material Balance Assumption (ionx): Convection with Constant Dispersion The Convection with Constant Dispersion option includes the dispersion term in the material balance for the bed. You must then supply a fixed value for the dispersion coefficient, E z . With this option, the dispersion coefficient is constant for all components throughout the bed. Material Balance Assumption (ionx): Convection with Estimated Dispersion The Convection with Estimated dispersion option includes the dispersion term in the material balance for the bed. Here, the dispersion coefficient varies along the length of the bed. Aspen Adsim estimates the components' dispersion coefficients in an ion-exchange bed using this correlation (Slater, 1991):  Re  vl d P = 0.2 + 0.011  ε  Ez  i  where: 0.48 Ez = = = = Axial dispersion coefficient Liquid Velocity Interparticle voidage Particle diameter Reynolds number Liquid viscosity Liquid molar density Liquid molecular weight vl εi dp Re = µ ρ l M l d P vl µ = = = = ρl Ml Material Balance Assumption (ionx): Convection with User Procedure Dispersion The Convection with User Procedure Dispersion option includes the dispersion term in the material balance for the bed. The dispersion coefficient varies with axial position according to a usersupplied Fortran subroutine, which Aspen Adsim interfaces using the procedure pUser_i_Dispersion. 3 Ion-Exchange Processes 187 Material Balance Assumption (ionx): Convection with User Submodel Dispersion The Convection with User Submodel Dispersion option includes the dispersion term in the material balance for the bed. The dispersion coefficient varies with axial position according to the usersupplied submodel iUserDispersion. About Axial Dispersion in IonExchange Processes As a fluid flows through a packed column such as an ion-exchange bed, axial dispersion (mixing) tends to occur, which reduces the efficiency of separation. Axial dispersion should be minimized in bed design, but, if it occurs, then Aspen Adsim must account for its effects. There are several sources of axial dispersion in ion-exchange processes (Ruthven, 1984): • • Channeling caused by non-uniform packing, for example where different sections of the packing have different voidages. Dispersion from wall effects due to non-uniform packing at the wall. This can be avoided by packing the bed well, and having a sufficiently large ratio of bed-to-particle diameters. Hold-up of liquid in the laminar boundary layer surrounding the particles combined with small random fluctuations in the flow. Splitting and recombining of the flow around the particles. • • The molecular diffusivities of liquids are too small to contribute significantly to axial dispersion. In general, the mixing effects are additive and can be lumped together into a single effective dispersion coefficient, E z . The dispersion term in the material balance is usually expressed as: ∂ 2 ck − ε i Ez ∂z 2 The type of flow determines whether this term is omitted or included in the material balance. Deciding When to Use Axial Dispersion in Ion-Exchange Processes In deciding whether to include axial dispersion in the bed model, it is useful to work out the Peclet number, given an effective dispersion coefficient ( E z ), a liquid superficial velocity ( vl ), and a bed height ( H b ): Pe = vl H b Ez 3 Ion-Exchange Processes 188 The Peclet number quantifies the degree of dispersion introduced into the system. It is dimensionless so is more convenient than the dispersion coefficient for this purpose. The following table shows the effect of different values of Peclet number: If the Peclet number is 0 The effect of axial dispersion on bed performance is Infinite: the bulk liquid is perfectly mixed., so the liquid composition is homogeneous throughout the entire bed. Significant. Very slight: The bed operates under near plug flow conditions. Zero: The bed operates under plug flow conditions. < 30 > 100 ∞ Numerical methods used to discretize the spatial derivatives in the general equations can also introduce an artificial form of dispersion. Kinetic Model Tab (ionx) The overall mass transfer of ionic components between the bulk liquid phase and the adsorbed phase must overcome two resistances: • • Mass transfer resistance located in the boundary layer surrounding the particle. Mass transfer resistance inside the resin particle. Typically, the second resistance determines the overall mass transfer rate. Aspen Adsim lumps the overall resistance to mass transfer into a single overall factor. You select the type of resistance from: • • • • Film Model Assumption Kinetic Model Assumption Form of Lumped Resistance Form of Mass Transfer Coefficient Kinetic Model Tab (ionx): Film Model Assumption In the Film Model Assumption box, choose from: • • Solid — The mass transfer driving force is expressed as a function of the solid phase loading (solid film). Fluid — The mass transfer driving force is expressed as a function of the liquid phase concentration (liquid film). 3 Ion-Exchange Processes 189 Kinetic Model Tab (ionx): Form of Lumped Resistance This option is active only if you selected Lumped Resistance as your Kinetic Model assumption. This function is either linear or quadratic. The following options are available: • • Linear Quadratic Form of Lumped Resistance (ionx): Linear The mass transfer driving force for component k is expressed as a linear function of the liquid phase concentration or solid phase loading. Kinetic Model Assumption (ionx): User Procedure With this option. which Aspen Adsim interfaces using the procedure pUser_i_Kinetic. ∂wk * = MTCl k (c k − c k ) ∂t ∂wk * = MTCs k ( wk − wk ) ∂t (fluid film) (solid film) 3 Ion-Exchange Processes 190 .Kinetic Model Tab (ionx): Kinetic Model Assumption In the Kinetic Model Assumption box. the mass transfer driving force for component k is expressed as a function of the liquid phase concentration (liquid film). or solid phase loading (solid film). See Form of Lumped Resistance. later. the component rates of mass transfer are related to local conditions in the bed through a relationship you supply in a Fortran subroutine. the component rates of mass transfer are related to local conditions in the bed through the user submodel iUserKinetic. Kinetic Model Assumption (ionx): User Submodel With User Submodel selected. choose from: • • • Lumped Resistance User Procedure User Submodel Kinetic Model Assumption (ionx): Lumped Resistance Here. * (c 2 − (c k ) 2 ) ∂wk = MTCl k k ∂t 2c k * (( wk ) 2 − wk2 ) ∂wk = MTCs k ∂t 2 wk (fluid film) (solid film) Kinetic Model Tab (ionx): Form of Mass Transfer Coefficient Use this option to specify how to define the mass transfer coefficients. Aspen Adsim has a list of commonly used. and are returned through the user submodel iUserMTC. Form of Mass Transfer Coefficient (ionx): User Procedure Here. The function is implemented in a Fortran subroutine. the mass transfer coefficients are functions of local bed conditions. You must supply a constant value of mass transfer coefficient for each component in the Specify table of the layer. which Aspen Adsim interfaces using the procedure pUser_i_MTC. Form of Mass Transfer Coefficient (ionx): User Submodel With User Submodel selected. Choose from: • • • Constant User Procedure User Submodel Form of Mass Transfer Coefficient (ionx): Constant With this option. 3 Ion-Exchange Processes 191 . the mass transfer coefficient for each component is constant throughout the bed.Form of Lumped Resistance (ionx): Quadratic The mass transfer driving force is expressed as a quadratic function of the liquid phase concentration (fluid film) or solid phase loading (solid film). About Adsorption Isotherms for IonExchange Processes The driving force behind an ion-exchange separation process is the departure from adsorption equilibrium between the aqueous and adsorbed phases. adsorption isotherms (also known as ion-exchange equilibria) are important data in the design of ion-exchangers. Consequently. Isotherm Tab (ionx) Use the Isotherm tab to specify the adsorption isotherms for use in your ionexchange process. the mass transfer coefficients are functions of local bed conditions. standard multi-component adsorption isotherms. • • • • m is an integer or a fraction. … n (=number of nodes). the loading that would be at equilibrium with the actual liquid phase composition -or• c*. the liquid phase composition that would be at equilibrium with the actual loading. they are used to compute either: • w*. depending on the bed location. these variables are distributed. In bed models. B refers to a counter-ion on the ion-exchanger surface. 2. This choice is automatically handled by Aspen Adsim depending on your selection of kinetic model.Important: The equations presented are for equilibrium conditions. Depending on the mass transfer rate model you choose. choose from: • • • • • Mass Action Equilibrium Extended Langmuir Extended Langmuir-Freundlich User Procedure User Submodel Isotherm Assumed for Layer (ionx): Mass Action Equilibrium A B R + ++ B + R B B + + A R R The exchange reaction in the ion-exchange process is typically takes the form: A + mBR ⇔ ARm + mB where m is a stoichiometric coefficient. so they have a qualifier 1. It is given by the valence ratio of A and B. The equilibrium variable arrays (of size number of nodes × number of components) are named either Ws or Cs. m m −1 The associated equilibrium relationship can be written as:  y  x 1 =  A  B K AB  x A  y B       Q   c   0 3 Ion-Exchange Processes 192 . Isotherm Tab (ionx): Isotherm Assumed for Layer In the Isotherm Assumed for Layer box. A refers to an ionic component in solution. R refers to a bound group (of opposite sign to B). and the parameter m equals 1 IP2 . 3 Ion-Exchange Processes 193 . Isotherm Assumed for Layer (ionx): User Procedure You can supply your own. the parameter IP equals K AB . Total ionic concentration. Isotherm Assumed for Layer (ionx): Extended LangmuirFreundlich This isotherm is based on the Langmuir isotherm and expressed as: wi = 1+ ∑ k ( IP1i ciIP2 i IP IP3k c kIP4 k + IP3b cb 4 b ) where b refers to the (original) counter-ion. you supply the isotherm relationship through the user submodel iUserIsotherm. which Aspen Adsim interfaces using one of two procedures: • • pUser_i_Isotherm_C for solid film kinetic model pUser_i_Isotherm_W for liquid film kinetic model Isotherm Assumed for Layer (ionx): User Submodel With User Submodel selected. Ion-exchange resin capacity.0 Isotherm Assumed for Layer (ionx): Extended Langmuir The extended Langmuir isotherm was found to represent some experimental data satisfactorily: wi = IP1i ci 1 + ∑ (IP2 k c k ) + IP2b cb k where b refers to the (original) counter-ion. Equivalent mole fraction in the aqueous phase. Equivalent mole fraction in the adsorbed phase.where: K AB x y = = = = = Equilibrium constant or selectivity coefficient. c0 Q In Aspen Adsim. The equation now becomes:  y  x IP1 A  A  B  x  y  A  B     IP2 A Q      c0  IP2 A −1 = 1. proprietary isotherm relationships through a Fortran subroutine. Density remains unchanged as a result of the ion-exchange process itself. such as: ∂wk * = MTC sk wk − wk ∂t ( ) The number of counter ions being released from the resin and entering the liquid phase is determined from the number of ions exchanged from the liquid phase — the total charge of both liquid and resin must remain neutral: Jb = ∑ Jk k =1 k ≠b nc Hence the behavior of the exchanged counter ion in the liquid phase can be described by: − ε i Ez nc ∂ 2 cb ∂c ∂c + vl b + ε i b − ∑ J k = 0 ∂z 2 ∂z ∂t k =1 k ≠b 3 Ion-Exchange Processes 194 . is governed by the following material balance equation: − ε i Ez ∂ 2 ck ∂c ∂c + vl k + ε i k + J k = 0 2 ∂z ∂z ∂t ∂wk ∂t ∂wk can. fed into the ion-exchange column.Summary of Mass Balance Equations for Ion-Exchange Processes This section summarizes the mass balance equations used by Aspen Adsim to simulate ion-exchange processes. Each ionic species in the liquid phase. during an ion-exchange cycle. for example. The overall material balance is expressed as: vl ∂ρ l ∂ρ + εi l = 0 ∂t ∂z This equation accounts for the fact that. solvents of different densities are being used in the different production. purge and regeneration stages. be determined by a solid film ∂t The mass transfer rate J k between the bulk liquid and the resin is given by: J k = (1 − ε i ) where the uptake rate linear driving force relationship. Ion mole fraction in adsorbed (resin) phase. Time. Isotherm parameter. Axial dispersion coefficient. Liquid film mass transfer coefficient.Explanation of Equation Symbols for Ion-Exchange Processes The tables explain the equation symbols used in Aspen Adsim's ion-exchange mass balance equations. Ion concentration in liquid phase. Ion material transfer rate. Mass action equilibrium constant. Liquid phase ion concentration in equilibrium with resin phase. Ion mole fraction in liquid phase. Symbol Explanation Counter ion concentration in liquid phase. m kg/kmol 1/s 1/s eq/m3 s eq/m3 eq/m3 eq/m3/s eq/m3/s Aspen Adsim base units eq/m3 eq/m3 eq/m3 eq/m3 m m2/s m cb ck * ck c0 dp Ez HB IP Jb Jk K AB m Ml MTCl MTCs Q t wk * wk xk yk z 3 Ion-Exchange Processes 195 . Ion loading on resin. Solvent molecular weight. Stoichiometric coefficient used in mass action equilibrium. Total resin ion capacity. Ion loading in equilibrium with liquid phase ion concentration. Solid film mass transfer coefficient. Resin particle diameter. Total liquid phase ion concentration. Bed height. Axial co-ordinate. Counter ion material transfer rate. N/m2/s kmol/m3 ρi Dimensionless number Pe Defining expression Description Peclet number vl H B Ez M l ρ l d P vl Re Reynolds number µ 3 Ion-Exchange Processes 196 . Solvent viscosity.εi µ Bed voidage. Solvent molar density. The commercial availability of synthetic molecular sieves and ion-exchange resins. defined by color. liquid phase adsorption can improve feed quality. using liquid phase adsorption for bulk separation on a commercial scale is a relatively recent development. odor. For more information.4 Liquid Adsorption Processes This chapter contains information on liquid adsorption processes and how they are simulated in Aspen Adsim. bulk adsorptive separation of liquids has been used to solve a broad range of problems. and the development of novel process concepts have been the two significant factors in the success of these processes. 4 Liquid Adsorption Processes 197 . Since then. including individual isomer separations and class separations. When contaminants are not well defined. see the following topics: • • • • • • • • • • • • • About Liquid Adsorption Processes Bed Model Assumptions for Liquid Adsorption Configure Form Configure Layer Form General Tab Material/Momentum Balance Tab Kinetic Model Tab About Adsorption Isotherms for Liquid Adsorption Guidelines for Choosing Aspen Adsim Isotherm Models Energy Balance Tab Procedures Tab Summary of Mass and Energy Balance Explanation of Equation Symbols About Liquid Adsorption Processes Liquid phase adsorption has long been used to remove contaminants present at low concentrations in process streams. taste. The first commercial operation was in the 1960s. in hydrocarbon processing. Unlike trace impurity removal. such as organics from waste water. and storage stability. − Wall energy terms. − Enthalpy of adsorbed phase. or varies due to adsorption and according to total mass balance. The adsorption isotherm is chosen from Aspen Adsim defined isotherms. with a liquid or solid-film resistance. Click the Specify button to open the Specify form for the layer model. The superficial velocity is constant. This resistance is either linear. see the following sections: • • • General Tab Material/Momentum Balance Tab Kinetic Model Tab 4 Liquid Adsorption Processes 198 . A lumped mass-transfer rate applies. The following options are available: • • • • Enter the number of layers within the bed (one or more). the bed model assumes: • • Plug flow. Molar concentrations are calculated from molar volumes. − Heat exchange with environment.Bed Model Assumptions for Liquid Adsorption For liquid adsorption. Isothermal or non-isothermal conditions apply. Type a brief name or description in the Description box. − Liquid-solid heat transfer. Click the Configure button to open the Configure Layer dialog box. The liquid phase pressure is either constant or varies according to a laminar-flow momentum balance (with the pressure drop assumed proportional to the flow velocity). so molar volume is a linear function of composition. Configure Layer Form (liq) Use the options in the Configure Layer form to define the set of equations for each layer of the adsorption bed. quadratic or user-defined. Mass transfer coefficients are either constant or user defined. For information on choosing the options for your liquid adsorption process. or plug flow with axial dispersion. The energy balance includes terms for: − Thermal conductivity of gas and solid. − Heat of adsorption. Ideal mixing is assumed to occur in the liquid phase. • • • • • • Configure Form (liq) This section contains information on the Configure form for a liquid process bed model. or specified by you. choose an appropriate number of nodes for your discretization method. Material/Momentum Balance Tab (liq): Material Balance Assumption In the Material Balance Assumption box. Determine how to treat the pressure drop in the adsorption bed model. choose the material balance option for your liquid adsorption process. Specify whether the velocity is constant or varies along the column.• • • Isotherm Tab Energy Balance Tab Procedures Tab General Tab (liq) Use the General tab to specify the numerical options for your liquid adsorption process. Material/Momentum Balance (liq) Use the Material/Momentum Balance tab to: • • • Make basic assumptions about axial dispersion in the liquid phase. Choose from: • • • • • Convection Only Convection with Constant Dispersion Convection with Estimated Dispersion Convection with User Procedure Dispersion Convection with User Submodel Dispersion 4 Liquid Adsorption Processes 199 . General Tab (liq): Discretization Method to be Used These discretization methods are available for liquid adsorption processes: • • • • • • • UDS1 UDS2 CDS1 LDS QDS MIXED BUDS General Tab (liq): Number of Nodes In the Number of Nodes box. The model now represents plug flow with a zero dispersion coefficient (infinite Peclet number). With this option.011  Re    = + ε i Ez ε i εi  εi    Where: 0. Material Balance Assumption (liq): Convection with Estimated Dispersion The Convection with Estimated Dispersion option includes the dispersion term in the material balance for the bed. you need not supply the dispersion coefficient. 4 Liquid Adsorption Processes 200 . Material Balance Assumption (liq): Convection with Constant Dispersion The Convection with Constant Dispersion option includes the dispersion term in the material balance for the bed. With this option. 1991): vl rP 0. using this correlation (Slater.Material Balance Assumption (liq): Convection Only The Convection Only option leaves out the dispersion term from the material balance for the bed. the dispersion coefficient varies according to a user supplied Fortran subroutine. Aspen Adsim estimates the values during the simulation. You need to supply a constant value for the dispersion coefficient. E z . the dispersion coefficient varies along the length of the bed.2 0. which Aspen Adsim interfaces through the procedure type pUser_l_dispersion. for each component. With this option.48 Ez = = = = = Axial dispersion coefficient Liquid Velocity Interparticle voidage Particle radius Reynolds number vl εi rp Re Material Balance Assumption (liq): Convection with User Procedure Dispersion The Convection with User Procedure Dispersion option includes the dispersion term in the material balance for the bed. the dispersion coefficient is constant for all components throughout the bed. Because the dispersion term is omitted. Material Balance Assumption (liq): Convection with User Submodel Dispersion The Convection with User Submodel Dispersion option includes the dispersion term in the material balance for the bed. the dispersion coefficient varies according to the submodel lUserDispersion.5 × 10 −3 µ (1 − ε i ) ∂p 2rpψε i = ∂z vl (1 − ε i ) 2rpψ 4 Liquid Adsorption Processes 201 . In the Pressure Drop Assumption box. With this option. It applies to laminar flow. Material/Momentum Balance Tab (liq): Pressure Drop Assumption Use the Pressure Drop Assumption box to specify how Aspen Adsim treats the pressure drop in the adsorption bed model. This option corresponds to how internal superficial velocities are related to local pressure gradients. Pressure Drop Assumption (liq): Darcy's Law Select the Darcy's Law option to apply a linear relationship between the liquid superficial velocity and the pressure gradient at a particular point in a bed. You should base your choice on your knowledge of the actual operating conditions in the plant. Darcy's law states that the pressure drop is directly proportional to flow rate: ∂p = − K P vl ∂z Where: Kp = Proportionality constant Pressure Drop Assumption (liq): Karman-Kozeny Select the Karman-Kozeny option to relate velocity to pressure drop: 3 − 1. You must choose an appropriate material balance model with a particular pressure-drop option. there is no pressure drop across the bed. choose from these options: • • • None Darcy's Law Karman-Kozeny Pressure Drop Assumption (liq): None With None selected. mass density varies according to the material balance. Velocity Assumption (liq): Varying Velocity With Varying Velocity selected. the mass density is constant along the bed. choose from: • • Constant Density Dynamic Density Overall Material Balance Assumption (liq): Constant Density With the Constant Density option. choose from: • • Constant Velocity Varying Velocity Velocity Assumption (liq): Constant Velocity With Constant Velocity selected. by the effect of the rate of adsorption. Material/Momentum Balance Tab (liq): Overall Material Balance Assumption In the Overall Material Balance Assumption box.Material/Momentum Balance Tab (liq): Velocity Assumption In the Velocity Assumption box. If you select this option: • • The velocity profile is determined through the total material balance. The velocity alone changes. the liquid velocity is constant along the bed. it typically experiences the following mass transfer resistances: 4 Liquid Adsorption Processes 202 . Both mass density and velocity vary according to the overall mass balance. This option is applicable to bulk separation applications. The velocity profile is stored in the discrete variables Vl_in(1)…Vl_in(n). The rate is determined from material balance. Overall Material Balance Assumption (liq): Dynamic Density With Dynamic Density selected. and that according to the overall mass balance. the superficial velocity varies along the bed according to the rate at which the liquid components are adsorbed onto the solid. so adsorption from the liquid phase has a negligible effect on the material balance. Kinetic Model Tab (liq) When a species is adsorbed from the bulk liquid phase onto an active surface site of the adsorbents. or desorbed. These assumptions are valid only when modeling the removal of trace components from a bulk liquid. where n is the number of nodes used in the numerical method. The resistance exerted by the adsorbents pore structure.• • The resistance between the bulk liquid and the external adsorbents surface. For bi-disperse adsorbents (such as zeolites). Quadratic lumped resistance. the mass transfer driving force for component i is expressed as a linear function of the liquid phase concentration or solid phase loading. Kinetic Model Tab (liq): Kinetic Model Assumption In the Kinetic Model Assumption box. Micro and macropore. User procedure. The following options are available from the Kinetic Model tab: • • • Film Model Assumption Kinetic Model Assumption Form of Mass Transfer Coefficient Kinetic Model Tab (liq): Film Model Assumption In the Film Model Assumption box. this resistance can be further divided into: − Macropore resistance. − Micropore resistance. ρS ∂wi = MTCli (ci − ci* ) ∂t (fluid) (solid) ∂wi = MTC si (wi* − wi ) ∂t 4 Liquid Adsorption Processes 203 . choose from: • • • • • Linear lumped resistance. Fluid  the mass transfer driving force is expressed as a function of the liquid phase concentration. choose from: • • Solid  the mass transfer driving force is expressed as a function of the solid phase loading. These resistances are typically lumped into a single. User submodel. Kinetic Model Assumption (liq): Linear Lumped Resistance With Linear Lumped Resistance selected. overall mass transfer coefficient. so it is an important factor in the dynamics of adsorbers. within the crystallines. ∂wi MTCli ci2 − (ci* ) ρS = ∂t 2c i ( 2 ) (fluid) (wi* ) − wi2 ∂wi = MTC si ∂t 2 wi 2 ( ) (solid) Kinetic Model Assumption (liq): Micro and Macropore Model Two concentration gradients greatly affect the diffusion rate: • • Within the pores of the solid. that is. Kinetic Model Assumption (liq): User Submodel With User Submodel selected. the mass transfer driving force is expressed as a quadratic function of the liquid phase concentration or solid phase loading. 4 Liquid Adsorption Processes 204 .Kinetic Model Assumption (liq): Quadratic Lumped Resistance With Quadratic Lumped Resistance selected. For more information. which Aspen Adsim interfaces through the procedure type pUser_l_Kinetic. the mass transfer coefficient for each component is constant through the bed. the bed model calls the submodel lUserKinetic. Within the void spaces between the particles. see Micro and Macro Pore Effects in Chapter 1. Kinetic Model Assumption (liq): User Procedure The User Procedure option relates the component rates of mass transfer to the local bed conditions through a user-supplied Fortran subroutine. Under practical conditions in gas separation. pore diffusion limits the overall mass transfer rate between the bulk flow and the internal surface of a particle. You must supply a constant value of mass transfer coefficient for each component. you choose how mass transfer coefficients are defined. Choose from: • • • Constant User Procedure User Submodel Form of Mass Transfer Coefficient (liq): Constant With Constant selected. Kinetic Model Tab (liq): Form of Mass Transfer Coefficient In the Form of Mass Transfer Coefficient box. This submodel needs the relationship between the component rates of mass transfer and the local bed conditions. so they have a qualifier 1. you can obtain significantly different simulation results when using different models. 2.Form of Mass Transfer Coefficient (liq): User Procedure If you choose User Procedure. Depending on the mass transfer rate model you choose (See also Kinetic Model Tab (liq) on page 4-202). to denote their location in the bed. The equilibrium variable arrays (of size n) are named either Ws or Cs. you can create a bed model to predict the performance of the adsorber bed for the specified operating conditions. Guidelines for Choosing Aspen Adsim Isotherm Models Make sure you choose a model that is appropriate for the process you are investigating. In bed models. Consequently. which Aspen Adsim interfaces through the procedure pUser_l_MTC. 4 Liquid Adsorption Processes 205 . these variables are distributed. This choice is automatically handled by Aspen Adsim. About Adsorption Isotherms for Liquid Adsorption The driving force behind all adsorptive liquid separation processes is the departure from adsorption equilibrium.. Form of Mass Transfer Coefficient (liq): User Submodel With User Submodel selected. The equilibrium specified by the isotherm model affects the driving force for mass transfer. The expressions in this section are equilibrium equations.. . the mass transfer coefficients are defined in the user submodel lUserMTC. If you know the adsorption isotherms for the components of the feed. the mass transfer coefficients are returned by a Fortran subroutine you supply. even if the model parameters come from the same set of data. so adsorption isotherms are important data in adsorber design. n. the expressions are used to compute either: • w*  The loading that would be at equilibrium with the actual liquid phase composition -or• c*  The liquid phase composition that would be at equilibrium with the actual loading. Aspen Adsim has a comprehensive list of multicomponent adsorption isotherms. see Chapter 4 of Ruthven (1984) or Chapter 3 of Kast (1988) (German language).The Ideal Adsorbed Solution Theory (IAS) Recently. many systems have shown strong correlation between experimental data and predictions by IAS theory. IAS is available in Aspen Adsim. 4 Liquid Adsorption Processes 206 . which is temperature independent. in which the fundamental equations of thermodynamic equilibrium are developed. which is temperature dependent. It needs data only for the pure-component adsorption equilibria at the same temperature.2) There are two types of Langmuir model available in Aspen Adsim: • • Langmuir 1. Langmuir 2. However. the Ideal Adsorbed Solution Theory (IAS) has become popular for multicomponent mixtures.2) Langmuir-Freundlich models (1. To use it. Choose from: • • • • • • • • • • • • • • Langmuir models (1.2) User Multicomponent Procedure User Multicomponent Submodel User Multicomponent Procedure with IAS User Multicomponent Submodel with IAS Isotherm Assumed for Layer (liq): Langmuir Models (1. including binary and ternary mixtures on activated carbons and zeolites. The model follows the formal.2) Stoichiometric Equilibrium models (1. thermodynamic approach for vapor-liquid equilibria.2) IAS Langmuir models (1.2) Dual-Site Langmuir models (1.2) IAS Freundlich models (1. The model treats the mixed adsorbate phase as an ideal solution in equilibrium with the liquid phase. At first sight.2) IAS Langmuir-Freundlich models (1. The method lets you predict adsorption equilibria for components in a mixture.2 Extended Langmuir models (1.2) Extended Langmuir-Freundlich models (1. For a full description of the IAS approach.2) Freundlich models (1. choose the appropriate isotherm on the Isotherm tab of the Configure Layer form. Isotherm Tab (liq): Isotherm Assumed for Layer Use the Isotherm tab to choose which adsorption isotherms are used in your liquid adsorption process. and applies this to the liquid-adsorbed phase equilibria. ideal behavior in the adsorbed phase seems improbable. and on the same adsorbent. Extended Langmuir 1 This isotherm is expressed as: 4 Liquid Adsorption Processes 207 . Extended Langmuir 2.2) Aspen Adsim has two types of Extended Langmuir model: • • Extended Langmuir 1. which is temperature dependent. which is temperature independent. which is temperature independent. which is temperature dependent. Dual-Site Langmuir 2. Dual-Site Langmuir 1 This isotherm is expressed as: wi = IP1i IP2i ci 1 + ∑ IP2 k ck k =1 nc + IP3i IP4i ci 1 + ∑ IP4 k ck k =1 nc Dual-Site Langmuir 2 This isotherm is expressed as:  IP   IP  IP1i IP2i exp 3i ci IP4i IP5i exp 6i ci  T   T   s   s  + wi = nc nc  IP   IP  1 + ∑ IP2 k exp 3k ck 1 + ∑ IP5 k exp 6 k ck  T   T  k =1 k =1  s   s  Isotherm Assumed for Layer (liq): Extended Langmuir Models (1.2) There are two types of Dual-Site Langmuir model available in Aspen Adsim: • • Dual-Site Langmuir 1.Langmuir 1 This isotherm is expressed as: wi = IP1i IP2i ci 1 + IP2i ci Langmuir 2 This isotherm is expressed as:  IP  IP1i IP2i exp 3i ci  T   s  wi =  IP  1 + IP2i exp 3i ci  T   s  Isotherm Assumed for Layer (liq): Dual-Site Langmuir Models (1. Freundlich 1 This isotherm is expressed as: wi = IP1i ciIP2 i Freundlich 2 This isotherm is expressed as:  IP wi = IP1i ciIP2 i exp 3i  T  s     Isotherm Assumed for Layer (liq): Langmuir-Freundlich Models (1. which is temperature independent. which is temperature dependent.wi = IP1i IP2i ci 1 + ∑ IP2 k ck k =1 nc Extended Langmuir 2 This isotherm is expressed as:  IP  IP i IP2i exp 3i ci 1  T   s  wi = nc  IP  1 + ∑ IP2 k exp 3k ck  T  k =1  s  Isotherm Assumed for Layer (liq): Freundlich Models (1. Freundlich 2. which is temperature dependent. Langmuir-Freundlich 1 This isotherm is expressed as: wi = IP1i IP2i ciIP3i 1 + IP2i ciIP3i Langmuir-Freundlich 2 This isotherm is expressed as: 4 Liquid Adsorption Processes 208 . Langmuir-Freundlich 2.2) There are two types of Freundlich model available in Aspen Adsim: • • Freundlich 1.2) There are two types of Langmuir-Freundlich model available in Aspen Adsim: • • Langmuir-Freundlich 1. which is temperature independent. 2) Aspen Adsim has two types of Stoichiometric Equilibrium model: • • Stoichiometric Equilibrium 1. which is temperature dependent. Stoichiometric Equilibrium 1 This isotherm is expressed as: wi = IP i IP2i ci 1 ∑ IP k =1 nc 2k k c Stoichiometric Equilibrium 2 This isotherm is expressed as: 4 Liquid Adsorption Processes 209 .2) There are two types of Extended Langmuir-Freundlich model available in Aspen Adsim: • • Extended Langmuir-Freundlich 1. which is temperature independent. Extended Langmuir-Freundlich 2. IP  IP1i IP2i ciIP3i exp 4i   T   s  wi =  IP  1 + IP2i ciIP3i exp 4i   T   s  Isotherm Assumed for Layer (liq): Extended LangmuirFreundlich Models (1. which is temperature dependent. Stoichiometric Equilibrium 2. which is temperature independent. Extended Langmuir-Freundlich 1 This isotherm is expressed as: wi = IP i IP2i ciIP3i 1 1 + ∑ IP2 j c j 3 j IP j =1 n ( ) Extended Langmuir-Freundlich 2 This isotherm is expressed as:  IP  IP i IP2i ciIP3i exp 4i  1  T   s  wi = n   IP   IP 1 + ∑  IP2 j c j 3 j exp 4 j    T   j =1   s  Isotherm Assumed for Layer (liq): Stoichiometric Equilibrium Models (1. 2) With IAS Freundlich Models selected. which is temperature dependent. which is temperature independent. Aspen Adsim has two versions of the pure component Freundlich model: • • IAS Freundlich 1. IP  IP1i IP2i exp 3i ci  T   s  wi = nc  IP  ∑ IP2k exp T3k ck   k =1  s  Isotherm Assumed for Layer (liq): IAS Langmuir Models (1. IAS Langmuir 2. the multicomponent adsorption behavior is expressed using Ideal Adsorbed Solution theory in combination with pure component isotherms. which is temperature independent. which is temperature dependent. IAS Freundlich 2. the multicomponent adsorption behavior is expressed using the Ideal Adsorbed Solution Theory in combination with pure component isotherms. IAS Freundlich 1 This isotherm is expressed as: wi = IP1i ciIP2 i IAS Freundlich 2 This isotherm is expressed as: 4 Liquid Adsorption Processes 210 . Aspen Adsim has two versions of the pure component Langmuir model: • • IAS Langmuir 1.2) With IAS Langmuir Models selected. IAS Langmuir 1 This isotherm is expressed as: wi = IP i IP2i ci 1 1 + IP2i ci IAS Langmuir 2 This isotherm is expressed as:  IP  IP1i IP2i exp 3i ci  T   s  wi =  IP  1 + IP2i exp 3i ci  T   s  Isotherm Assumed for Layer (liq): IAS Freundlich Models (1. . which Aspen Adsim interfaces using one of two procedures: • • pUser_l_Isotherm_C for solid film kinetic model pUser_l_Isotherm_W for liquid film kinetic model The functional relationship is: wi = f eq (T . IP wi = IP1i ciIP2 i exp 3i  T  s     Isotherm Assumed for Layer (liq): IAS Langmuir-Freundlich Models (1. IAS Langmuir-Freundlich 1 This isotherm is expressed as: wi = IP i IP2i ciIP3i 1 1+ IP2i ciIP3i IAS Langmuir-Freundlich 2 This isotherm is expressed as:  IP  IP i IP2i ciIP3i exp 4i  1  T   s  wi =  IP  1 + IP2i ciIP3i exp 4i   T   s  Isotherm Assumed for Layer (liq): User Multicomponent Procedure You can supply your own.. proprietary isotherm relationships using the submodel lUserIsotherm. IP ) Isotherm Assumed for Layer (liq): User Multicomponent Submodel You can supply your own.2) With IAS Langmuir-Freundlich selected. IP ) 4 Liquid Adsorption Processes 211 . proprietary isotherm relationships through a Fortran subroutine. IAS Langmuir-Freundlich 2. the multicomponent adsorption behavior is expressed using the Ideal Adsorbed Solution Theory in combination with pure component isotherms.cnc . The functional relationship is: wi = f eq (T . c1 ...cnc . which is temperature dependent. Aspen Adsim has two versions of the pure component Langmuir-Freundlich model: • • IAS Langmuir-Freundlich 1. c1 . which is temperature independent. The relationship to be evaluated is: AΠ i0 = g T . In this case. to the loading wi . user-specified isotherms. IP ) c dc Isotherm Assumed for Layer (liq): User Purecomponent Submodel with IAS Select this option to supply pure component. c.Isotherm Assumed for Layer (liq): User Purecomponent Procedure with IAS Select the User Purecomponent Procedure with IAS option to supply pure component. using a pure component isotherm: 0 0 wi0 = f eq T . IP ) c dc Energy Balance Tab (liq) Use the Energy Balance tab to specify how the energy balance is incorporated into the model. ci0 . IP ( ) The second Fortran subroutine evaluates the integral of the Gibbs isotherm to give the spread pressure. It is interfaced by the procedure type pUser_l_Gibbs. two Fortran subroutines are needed: The first subroutine is interfaced by the procedure type pUser_l_Isotherm_W. IP ( ) The second submodel. c. evaluates the integral of the Gibbs isotherm to give the spread pressure. This relates the fictitious pure component concentration ci (resulting in the same spread pressure as the mixture at total concentration ctot ). Energy Balance Tab (liq): Energy Balance Assumption In the Energy Balance Assumption box. which may be used as multicomponent isotherms. ci0 . IP with g = RT ( ) ci0 ∫ 0 f eq (T . user-specified isotherms. which may be used as multicomponent isotherms. In this case. you must supply two submodels: The first submodel is lUserIsotherm. This relates the fictitious pure component concentration ci (resulting in the same spread pressure as the mixture at total concentration ctot ). choose from the following options: 4 Liquid Adsorption Processes 212 . The relationship to be evaluated is: AΠ i0 = g T . lUserGibbs. ci0 . IP with g = RT ( ) ci0 ∫ 0 f eq (T . ci0 . using the pure component isotherm: 0 0 wi0 = f eq T . to the loading wi . The liquid phase thermal conductivity can be supplied in different ways. as specified in the section Form of Fluid Thermal Conductivity field. Energy Balance Assumption (liq): Non-Isothermal with No Conduction The Non-Isothermal with No Conduction option ignores the axial thermal conduction for the fluid and solid phases within the energy balance. Fluid and solid temperatures are set to the same. Energy Balance Assumption (liq): Non-Isothermal with Solid Conduction The Non-Isothermal with Solid Conduction option includes the thermal conduction term in the solid energy balance. constant value. This term is represented as: − kl ∂ 2T ∂z 2 l The liquid phase thermal conductivity can be supplied in different ways as specified in the section Form of Fluid Thermal Conductivity. Energy Balance Assumption (liq): Non-Isothermal with Fluid and Solid Conduction The Non-Isothermal with Fluid and Solid Conduction option includes the thermal conduction term for both fluid and solid phases. The solid thermal conduction term is represented as: ∂ 2TS − kS ∂z 2 You must supply a value for k s .• • • • • Isothermal Non-Isothermal with no Conduction Non-Isothermal with Fluid Conduction Non-Isothermal with Solid Conduction Non-Isothermal with Fluid and Solid Conduction Energy Balance Assumption (liq): Isothermal The Isothermal option ignores the energy balance. 4 Liquid Adsorption Processes 213 . Energy Balance Assumption (liq): Non-Isothermal with Fluid Conduction The Non-Isothermal with Fluid Conduction option includes the thermal conduction (axial thermal dispersion) term in the fluid energy balance. choose from: • • • • None Constant User Procedure User Submodel Heat of Adsorption Assumption (liq): None The heat generation by adsorption term is omitted from the energy balance. select from No or Yes: • • No — Choose this option to ignore the enthalpy of the adsorbed phase term in the solid phase energy balance. The term for each component is a function of the loading and the temperature in the solid phase: H ads .Energy Balance Tab (liq): Consider Heat of Adsorbed Phase Aspen Adsim models enable you to include the heat capacity of the adsorbed phase in the solid-phase energy balance.i = ρ p C Pi wi ∂TS ∂t The total contribution is the sum for all components: ∑H i =1 nc ads . per unit volume of solid: ρ p ∑ (HTi ) i =1 nc In the Heat of Adsorption Assumption box. per unit mass of solid. and you want to include it in the overall energy balance. The Heat of Adsorbed Phase term is optional. Yes — Choose this option if the enthalpy content of the adsorbed phase is significant for your process. you must include the heat of adsorption within the balance.i Energy Balance Tab (liq): Heat of Adsorption Assumption If the solid-phase energy balance is significant for the process. is a function of the local rate of mass transfer and the heat of adsorption: HTi = ∂wi ∆H i ∂t These rates are held in vectors and summed for all components to obtain the total rate of heat generation. 4 Liquid Adsorption Processes 214 . by adsorption. In the Consider Heat of Adsorbed Phase box. The rate of heat generation by adsorption of each component i. P. and pressure. local loading. w) Heat of Adsorption Assumption (liq): User Submodel With User Submodel selected. the temperature of the fluid and solid are equal (“lumped”). Aspen Adsim generates the solid and fluid phase energy balances. the heat of adsorption comes from a usersupplied Fortran subroutine. for example. You can vary the heat of adsorption and make it a function of. which is held in a variable called HTC. the heat of adsorption comes from the user submodel lUserDH. temperature. To obtain this condition. set the heat transfer coefficient to a very large value (such as 1MW/m2/K). You must provide the values of the elements of DH. and pressure. Heat of Adsorption Assumption (liq): User Procedure With User Procedure selected. temperature. choose from: • • • • Constant Estimated User Procedure User Submodel Form of Heat Transfer Coefficient (liq): Constant Choose Constant to ensure the heat transfer coefficient has a single value. which Aspen Adsim interfaces using the procedure pUser_l_DH. using a film resistance due to heat transfer between the solid and the fluid. local loading. for example. 4 Liquid Adsorption Processes 215 . These are held in a vector called DH.Heat of Adsorption Assumption (liq): Constant The Constant option assumes the heat of adsorption is constant for each component i. Choose this option to set the heat of adsorption to constant values. w) Energy Balance Tab (liq): Form of Heat Transfer Coefficient If you request a non-isothermal energy balance. Heat transfer is assumed to occur between the two phases according to: Rate of heat transferred per unit volume of bed = a P (1 − ε i )HTC (Tl − TS ) If there is no heat transfer resistance between the solid and fluid. You can vary the heat of adsorption and make it a function of. In general terms: ∆H = f (Ts . In general terms: ∆H = f (Ts . P. In the Form of Heat Transfer Coefficient box. reset it to a value of 1. In the Form of Fluid Thermal Conductivity box. vl ) Form of Heat Transfer Coefficient (liq): User Submodel With User Submodel selected. reset it to this value. In general terms: HTC = f (Tl . Energy Balance Tab (liq): Form of Fluid Thermal Conductivity If you selected Non-isothermal with Fluid and/or Solid Conduction. the local heat transfer coefficient is defined through the user submodel lUserHTC.Form of Heat Transfer Coefficient (liq): Estimated The heat transfer coefficient is estimated as follows: 1 Calculate the Reynolds number: Re = 2 rp M ρ l vl µ If the calculated value falls below 1E-10.983Re Calculate the heat transfer coefficient: HTC = jC pl vl ρ l Pr −2 3 If the calculated value falls below 1E-10. 3 Calculate the j-factor: If Re < 190 then j = 1. choose from: • • • • Constant Based on Axial Dispersion User Procedure User Submodel 4 Liquid Adsorption Processes 216 .41 otherwise j = 0. reset it to this value. you need to choose the form of fluid thermal conductivity . C . Form of Heat Transfer Coefficient (liq): User Procedure With the User Procedure option. P.66 Re 4 −0. the user procedure pUser_l_HTC relates the local heat transfer coefficient to the state of the bed at a particular point in the bed. 2 Calculate the Prandl number: Pr = µ C pl kl M If the calculated value falls below 1E-10. This means you can interface your own Fortran code to calculate the coefficients.51 −0. Form of Fluid Thermal Conductivity (liq): Based on Axial Dispersion With Based on Axial Dispersion selected. thermal conductivity varies axially along the bed and is defined in the user submodel lUserKl. Form of Fluid Thermal Conductivity (liq): User Submodel With User Submodel selected. choose from: • • • • • • • Adiabatic Thin Wall Rigorous Model Heat Exchange between Fluid and Wall Heat Exchange between Wall and Environment Axial Conductivity along the Wall Heat Content of Wall Heat Transfer to Environment (liq): Adiabatic With Adiabatic selected. thermal conductivity varies axially along the bed and is defined in a user-defined Fortran subroutine.Form of Fluid Thermal Conductivity (liq): Constant The thermal conductivity has a constant value. the axial dispersion coefficient and the molar density of the fluid: k l = C Pl E z ρ l This method applies the analogy between heat and mass transfer. Energy Balance Tab (liq): Heat Transfer to Environment In the Heat Transfer to Environment box. Form of Fluid Thermal Conductivity (liq): User Procedure With User Procedure selected. the thermal conductivity coefficient is calculated as the product of the molar heat capacity of the fluid. Heat Transfer to Environment (liq): Thin Wall With the Thin Wall option. there is no heat transfer between the bed and the wall. the fluid phase energy balance includes the heat exchange between the fluid in the bed and the environment: 4H w (Tl − Tamb ) DB 4 Liquid Adsorption Processes 217 . which you set. which Aspen Adsim interfaces using the procedure pUser_l_Kl. Tamb . The term is: 4 Liquid Adsorption Processes 218 . The wall is assumed to be thin and conductive enough for the inner and outer wall temperatures to be equal. the bed model applies a wall energy balance equation that contains the following terms: • • • • Heat transfer from the fluid in the bed to the inner wall. Heat transfer from the outer wall to the environment. Axial thermal conduction along the wall. owing to the different cross-sectional areas of the balances: Hw 4 (Tl − Tw ) Dwi Heat Transfer to Environment (liq): Heat Exchange Between Wall and Environment When a rigorous wall energy balance is included. H w . The heat exchange between fluid and wall is also included in the fluid phase energy balance. set the value of the heat transfer coefficient to zero. the heat transfer between the outer wall and the environment is expressed as: H amb 4 Dwo (Tw − Tamb ) 2 D − Dwi 2 wo You must define the value of the heat transfer coefficient to the environment H amb and the temperature of the environment. ignoring the wall energy balance) is valid only when the wall is non-conductive.Heat Transfer to Environment (liq): Rigorous Model With Rigorous Model selected. Note that the equation has a slightly different form. The term is represented as: Hw 4 Dwi (Tl − Tw ) 2 D − Dwi 2 wo You must define the value of the liquid-to-wall heat transfer coefficient. To ignore the effect of heat exchange with the environment in the energy balance. The adiabatic option (that is. Heat accumulation within the wall material. the heat exchange between the fluid in the bed and the inner surface of the wall is included in the wall energy balance. Heat Transfer to Environment (liq): Axial Thermal Conductivity Along Wall The axial thermal conduction along the wall is always included in the wall energy balance. or there is an infinite heat transfer resistance between the liquid and the wall surface. Heat Transfer to Environment (liq): Heat Exchange Between Fluid and Wall When the rigorous wall energy balance is selected. The term is: ρ wC pw ∂Tw ∂t You must specify the value of the wall density. Mass transfer from the liquid to the solid phase. k w . Liquid Adsorption: Summary of Mass and Energy Balance For information on the equations used in Aspen Adsim for mass and energy balances in liquid adsorption processes. capacity of the wall. Accumulation of material in the liquid phase. Heat Transfer to Environment (liq): Heat Content of Wall The heat accumulation of the wall is always included in the wall energy balance. and the specific heat Procedures Tab (liq) Use the Procedures tab to view a list of the user procedures being used within the current adsorption layer model. C pw . see: • • • • Liquid Adsorption: Mass Balance Liquid Adsorption: Solid Phase Energy Balance Liquid Adsorption: Fluid Phase Energy Balance Liquid Adsorption: Wall Energy Balance Liquid Adsorption: Mass Balance The overall mass balance for a multi-component liquid phase contains terms for: • • • Convection of material. ρ w . The governing partial differential equation is: nc ∂ρ Ml ∂ (vl ρ Ml ) + ρ s ∑  M i ∂wi  = 0 εi +   ∂t ∂z ∂t  i =1  Each component in the liquid phase is governed by a material balance: − ε i Ez ∂w ∂ 2 ci ∂ ∂c + (vl ci ) + ε i i + ρ s i = 0 2 ∂z ∂z ∂t ∂t 4 Liquid Adsorption Processes 219 .∂ 2Tw − kw ∂z 2 You must specify the thermal conductivity of the wall material. The solid phase energy balance is given as: − ks ∂ 2Ts ∂T ∂T + ρ p C ps s + ρ p s 2 ∂z ∂t ∂t ∑ (C nc i =1 nc ∂w   wi ) + ρ p ∑  ∆H i i  − a p HTC (Tl − Ts ) = 0 pli ∂t  i =1  Liquid Adsorption: Fluid Phase Energy Balance The fluid phase energy balance includes terms for: • • • • Thermal conduction. Heat transfer from fluid to the internal wall. Heat transfer from the outer wall to the environment. heat transfer from fluid to solid. Heat of adsorption.Liquid Adsorption: Solid Phase Energy Balance The solid phase energy balance includes terms for: • • • • • Thermal conduction. Heat transfer from the bed to the inner wall. Convection of energy. The governing partial differential equation is: − kw ∂ 2Tw ∂T 4D 4D + ρ wC pw w − H w 2 wi 2 (Tl − Tw ) + H amb 2 wo 2 (Tw − Tamb ) = 0 2 ∂z ∂t Dwo − Dwi Dwo − Dwi 4 Liquid Adsorption Processes 220 . Accumulation of heat in the adsorbed phase. Accumulation of heat. The governing partial differential equation is: − kl ε i ∂ 2Tl ∂T ∂T 4H w (Tl − Tw ) = 0 + C pl ρ l vl l + ε i C pl ρ l l + a p (1 − ε i )HTC (Tl − Ts ) + 2 ∂z ∂t Dwi ∂z Liquid Adsorption: Wall Energy Balance The wall energy balance includes terms for: • • • • Axial thermal conduction along the wall. Heat accumulation within the wall material. Gas-solid heat transfer (expressed in terms of a film resistance where the heat transfer area is proportional to the area of the adsorbent particles). Accumulation of heat. units depend on isotherm.i H amb HB HTi Hw ∆H i HTC IP j kl ks 4 Liquid Adsorption Processes 221 . Heat of adsorption of component i. Specific heat capacity of column wall. Height of adsorbent layer. Area. Function. Solid thermal conductivity. Axial dispersion coefficient. Heat of adsorption contribution to solid phase energy balance. Molar concentration of component k. Wall-ambient heat transfer coefficient. Colburn j-factor for heat or mass transfer. Liquid-solid heat transfer coefficient.Liquid Adsorption: Explanation of Equation Symbols Symbol Explanation Specific particle surface. Liquid phase thermal conductivity. Heat of component i in adsorbed phase. Isotherm parameter. Bed diameter. IAS pure component concentration. Inner bed diameter. Specific liquid phase heat capacity. Equilibrium (isotherm) relationship. Specific heat capacity of adsorbent. Gas-wall heat transfer coefficient. MW/m/K MW/m/K Aspen Adsim base units m2/m3 m2 kmol/m3 kmol/m3 MJ/kmol/K MJ/kmol/K MJ/kg/K m m m m2/s MJ/m3/s MW/m2/K m MJ/m3/s MJ/m2/s MJ/kmol MJ/m2/s ap A ck ci0 C pl C ps C pW DB Dwi Dwo Ez f eq g H ads . Outer bed diameter. KP M Darcy’s constant. Adsorbent bulk density. Width of column wall. Liquid phase mass density. Wall density. Molecular weight. Particle radius. Solid phase temperature. Aspen Adsim base units m3 (Void)/m3 (Bed) N s/m2 bar m kg/m3 kmol/m3 kg/m3 kg/m3 kg/m3 εi µ Π i0 ρ M. Liquid phase temperature. Dynamic viscosity. Ambient temperature. Liquid phase superficial velocity. Solid film mass transfer coefficient. Pure component loading of component k. Liquid film mass transfer coefficient. Universal gas constant. Spreading pressure of component i. Adsorbent apparent density. Temperature. Axial co-ordinate. Loading. Pressure. I ρl ρp ρs ρW 4 Liquid Adsorption Processes 222 . Width of horizontal bed. bar s/m2 kg/kmol 1/s 1/s bar m bar m3/kmol/K s K K K K K m/s kmol/kg kmol/kg m m m MTCl MTCs p rp R t T Tamb Ts Tl TW vl wk 0 wk W WT z Symbol Explanation Interparticle voidage. Wall temperature. Time. Liquid phase molar density. - Dimensionless number Pe Defining expression Description Peclet number for mass transfer.l v l Pr Re Particle Reynolds number. vl H b Ez µ C pl kl M 2 r p ρ M .Ψ Particle shape factor. Prandl number. µ 4 Liquid Adsorption Processes 223 . uniform grid of points (nodes).5 Numerical Methods This chapter describes the numerical methods available in Aspen Adsim to solve its partial differential equations. The approximations are defined over a fixed. The first-order spatial derivatives present the greatest challenge in providing numerically accurate and stable approximations. the dependent variables at each node ‘march in time’ along parallel lines perpendicular to the spatial axis. The resulting system of differential and algebraic equations must be solved simultaneously since they are coupled. The failure of approximations to adequately represent the first order derivatives is manifested by two unwanted and spurious effects: • • Numerical diffusion leading to excessive ‘smearing’ of the solution. particularly when the system of equations is highly nonlinear  a common occurrence in adsorption process simulation. 5 Numerical Methods 224 . In a sense. such as concentration. temperature or molar flux. The spatial derivative terms within the partial differential equations are firstor second-order derivatives of some distributed variable. ordinary differential equations (ODEs) and algebraic equations. which explains the commonly-used name for this solution technique: the numerical method of lines. together with the appropriate initial and boundary conditions. the distributed variables are defined for each node by means of variable sets. Numerical oscillations. Spatial derivatives are discretized using algebraic approximations. and a set of ordinary differential equations and algebraic equations (DAEs) results. to fully describe the adsorption or ion-exchange column. See these topics for more information: • • • About Numerical Methods Choosing the Discretization Method About the Discretization Methods About Numerical Methods Aspen Adsim uses a set of partial differential equations (PDEs). A typical problem is the propagation of steep discontinuities known as fronts or shocks. leading to non-physical solutions and the violation of physical bounds. Accuracy (including any tendency towards oscillatory behavior). Quadratic Upwind Differencing Scheme. The Biased Upwind Differencing Scheme and the Flux Limiter are recommended in cases where the system is highly nonlinear and breakthrough curves are very steep  features associated with highly nonlinear adsorption isotherms and near-equilibrium behavior. About the Discretization Methods To specify a discretization method: • On the General tab. For details on the integration of the resulting system of differential equations with time. The Flux Limiter technique gives the accuracy of a higher order technique. The three best standard methods. but with no oscillations at small node counts. and fast for all cases of interest. which is known to be accurate. in the Discretization Method to Be Used box. select the method you require. Simulation time required. Note that all second-order derivatives are approximated by a second-order accurate central difference scheme. Choosing the Discretization Method Your choice of discretization method depends chiefly on the type of process you are simulating. stability and speed you are looking for. in terms of accuracy. and simulation time are: • • • Upwind Differencing Scheme 1. stability. Stability. Each of the numerical methods differ in: • • • • • Method of approximation of spatial derivatives. and the level of accuracy. showing where the methods come from and how they are evaluated. 5 Numerical Methods 225 . Mixed Differencing Scheme.This chapter describes the methods available in Aspen Adsim to approximate first-order spatial derivatives. Number of points. see the Aspen Custom Modeler Solver Options help. stable. fourth order) Fromms’ scheme (FROMM. third order) Quadratic Upwind Differencing Scheme (QDS. fourth order) Leonard Differencing Scheme (LDS. This is because higher order methods that are not flux limited tend to oscillate. the bounds for some variable types need modifying. you need to select one of these suboptions: • • • OSPRE SMART van Leer With schemes of higher order than UDS1 (first order). second order) Central Differencing Scheme 1 (CDS1. The typical changes required are: Variable type g_Conc_Mol l_Conc_Mol i_Conc_Eq g_Loading l_Loading Action normally required Set the lower bound to minus the upper bound. third order) Mixed Differencing Scheme (MDS. ~third order) Biased Upwind Differencing Scheme (BUDS. first order) Upwind Differencing Scheme 2 (UDS2.Choose from these options: • • • • • • • • • • Upwind Differencing Scheme 1 (UDS1. second order) Central Differencing Scheme 2 (CDS2. so may return negative values for variables types with a lower bound of zero. third order) Flux limited discretization scheme (Flux limiter) If you choose the Flux limited discretization scheme. 5 Numerical Methods 226 . Set the lower bound to minus the upper bound. Unconditionally stable. leading to a similar increase in simulation time.i_Loading_Eq Molefraction Fraction Widen the upper bound to 2. You increase accuracy by increasing the number of nodes. this problem decreases as the number of nodes is increased. In most cases. use the Quadratic Upwind Differencing Scheme. Upwind Differencing Scheme 1 Upwind Differencing Scheme 1 (UDS1) is the preferred option because it is: • • • • • Good all-round performer. Widen the upper bound to 2. If you need greater accuracy with a minimal increase in simulation time. (However. Least simulation time. Reasonably accurate.) 5 Numerical Methods 227 . it does not produce oscillations in the solution). Gives a large amount of so-called “false” or numerical diffusion. and set the lower bound to minus the new upper bound. Derivation of Upwind Differencing Scheme 1 Upwind Differencing Scheme 1 is a first-order upwind differencing scheme. First-order (convection) term: ∂Γ i Γ i − Γ i −1 = ∂z ∆z Second-order (dispersion) term is approximated with a second-order accurate central differencing scheme: ∂ 2 Γ i Γ i +1 − 2Γ i + Γ i −1 = ∂z 2 ∆z 2 Evaluation of Upwind Differencing Scheme 1 Upwind Differencing Scheme 1 has the following advantages (+) and disadvantages (–): + + – – Unconditionally stable (that is. For Upwind Differencing Scheme 1 to achieve the same level of accuracy. and set the lower bound to minus the new upper bound. Only first-order accurate. Unconditionally non-oscillatory. the number of nodes has to be increased by a factor of two through four. use Upwind Differencing Scheme 1 first. based on a first-order Taylor expansion. Cheapest user of simulation time. Central Differencing Scheme 1 Central Differencing Schemes 1 and 2 (CDS1 and 2) may be used if you choose to include axial dispersion in the problem. Central Differencing Scheme 1 used less CPU time than Central Differencing Scheme 2. Derivation of Central Differencing Scheme 1 Central Differencing Scheme 1 is a second-order central differencing scheme and takes the form: First-order convective term: ∂Γ Γi +1 − Γi −1 = 2 ∆z ∂z Second-order (dispersion) term is approximated with a second-order accurate central differencing scheme: ∂ 2 Γ i Γ i +1 − 2Γ i + Γ i −1 = ∂z 2 ∆z 2 5 Numerical Methods 228 . They give good accuracy with a reasonable CPU time requirement. Derivation of Upwind Differencing Scheme 2 Upwind Differencing Scheme 2 is a second-order upwind differencing scheme. The first-order (convection) term: ∂Γ i 3Γ i − 4Γ i −1 + Γ i − 2 = 2∆z ∂z Second-order (dispersion) term is approximated with a second-order accurate central differencing scheme: ∂ 2 Γ i Γ i +1 − 2Γ i + Γ i −1 = ∂z 2 ∆z 2 Evaluation of Upwind Differencing Scheme 2 Upwind Differencing Scheme 2 has the following advantages (+)and disadvantages (–): + – Second-order accuracy (because it includes a higher order derivative than first-order upwind schemes). but the solution tends to oscillate. but produced greater oscillations.Upwind Differencing Scheme 2 The Upwind Differencing Scheme 2 (UDS2) option predicts sharper fronts than Upwind Differencing Scheme 1. May produce some numerical oscillations. In a series of test problems. Central Differencing Scheme 2 produced smaller oscillations than Central Differencing Scheme 1. but used more CPU time. This may cause errors in simulation if there is little axial dispersion in the beds. In a series of test problems. They can give good accuracy with a reasonable CPU time requirement. include axial dispersion in the bed model.Evaluation of Central Differencing Scheme 1 Central Differencing Scheme 1 has the following advantages (+) and disadvantages (–): + – Second-order accurate. Requires increased CPU time. Leonard Differencing Scheme The Leonard Differencing Scheme (LDS) is comparable with the Quadratic Upwind Differencing Scheme: • • Gives the same instability problems. Using Central Differencing Scheme 1 with axial dispersion may reduce the number of nodes in the grid. 5 Numerical Methods 229 . To overcome these instabilities. but these errors are no more inconvenient than the false diffusion associated with upwind differencing. allowing smaller simulation times. Numerical instabilities. Derivation of Central Differencing Scheme 2 Central Differencing Scheme 2 is a second-order central differencing scheme and takes the form: First-order derivative: ∂Γ i − Γ i + 2 + 8Γ i +1 − 8Γ i −1 + Γ i −1 = 12∆z ∂z Second-order (dispersion) term is approximated with a second-order accurate central differencing scheme: ∂ 2 Γ i Γ i +1 − 2Γ i + Γ i −1 = ∂z 2 ∆z 2 Evaluation of Central Differencing Scheme 2 Central Differencing Scheme 2 has the following advantages (+)and disadvantages (–): + – Third-order accurate. Less accurate. Central Differencing Scheme 2 Central Differencing Schemes 1 and 2 (CDS1 and 2) are useful if you choose to include axial dispersion in the problem. 5 Numerical Methods 230 . use the Quadratic Upwind Differencing Scheme (QDS). four point finite differencing scheme. Derivation of Leonard Differencing Scheme The Leonard Differencing Scheme is a linear combination of the Central Differencing Scheme 1 scheme and a second-order.• Requires less CPU time. with a minimal increase in simulation time. Known to produce oscillations under convective conditions. Quadratic Upwind Differencing Scheme If you need greater accuracy than the Leonard Differencing Scheme. First-order derivative: ∂Γ i 3Γ i +1 + 3Γ i − 7Γ i −1 + Γ i −2 = 8∆z ∂z Second-order (dispersion) term is approximated with a second-order accurate central differencing scheme: ∂ 2 Γ i Γ i +1 − 2Γ i + Γ i −1 = ∂z 2 ∆z 2 The scheme is also referred to as QUICK (Quadratic Upstream Interpolation for Convective Kinematics). Derivation of Quadratic Upwind Differencing Scheme The Quadratic Upwind Differencing Scheme is based on quadratic interpolation. The Quadratic Upwind Differencing Scheme is the most accurate of all the methods for the same number of points. This combination yields: First-order derivative: ∂Γ 2Γ i +1 + 3Γ i − 6Γ i −1 + Γ i − 2 = 6∆z ∂z Second-order (dispersion) term is approximated with a second-order accurate central differencing scheme: ∂ 2 Γ i Γ i +1 − 2Γ i + Γ i −1 = ∂z 2 ∆z 2 Evaluation of Leonard Differencing Scheme The Leonard Differencing Scheme has the following advantages (+) and disadvantages (–): + – Accurate. as opposed to the linear interpolation typical of many other schemes. Oscillates under highly convective conditions. leading to an equivalent increase in simulation time. Aspen Adsim Breakthrough Plot 5 Numerical Methods 231 . Advantages of Quadratic Differencing Scheme: Example Both the Quadratic Upwind Differencing Scheme and the Mixed Differencing Scheme are more accurate than Upwind Differencing Scheme 1. For Upwind Differencing Scheme 1 to achieve the same level of accuracy. They both use about the same simulation time. Little numerical dispersion.Evaluation of Quadratic Upwind Differencing Scheme The Quadratic Upwind Differencing Scheme has the following advantages (+) and disadvantages (–): + + + – Very accurate. you must increase the number of nodes for Upwind Differencing Scheme 1 by a factor of two through four. Well suited to explicit (time) integration. which is typically about 25% more than Upwind Differencing Scheme 1. Mixed Differencing Scheme The Mixed Differencing Scheme is more stable than the Quadratic Upwind Differencing Scheme. First-order derivative: ∂Γ 3Γ i +1 + 7Γ i − 11Γ i −1 + Γ i − 2 = 12∆z ∂z Second-order (dispersion) term is approximated with a second-order accurate central differencing scheme: ∂ 2 Γ i Γ i +1 − 2Γ i + Γ i −1 = ∂z 2 ∆z 2 Evaluation of Mixed Differencing Scheme The Mixed Differencing Scheme has the following advantages (+)and disadvantages (–): + Accurate. Derivation of Mixed Differencing Scheme The Mixed Differencing Scheme is a combination of the Quadratic Upwind Differencing Scheme and the Upwind Differencing Scheme 1. The cost of this is increased simulation time for Upwind Differencing Scheme 1. 5 Numerical Methods 232 . to reduce this diffusion. Upwind Differencing Scheme 1 also had 20 nodes. both the Quadratic Upwind Differencing Scheme and the Mixed Differencing Scheme have 20 nodes. Initially.In this breakthrough plot. Advantages of Mixed Differencing Scheme: Example The Mixed Differencing Scheme is a compromise between accuracy and stability. which caused high numerical diffusion. It uses slightly less simulation time than the Quadratic Upwind Differencing Scheme. so may be the answer if the Quadratic scheme is unstable. The number of nodes in Upwind Differencing Scheme 1 is increased first to 50 and then to 100. Biased Upwind Differencing Scheme It is known that: • • High-order central difference approximations tend to produce excessive oscillations upwind from a discontinuity.Axial Profile Plot This graph shows that Upwind Differencing Scheme 1 and Mixed Differencing Scheme are the most stable of all the methods. Carver and Schiesser (1980) suggest that a correct combination of the two largely cancels out these upwind and downwind oscillations. in cases with initially clean beds. From this. Note that. they developed a five-point biased upwind differencing scheme consisting of one point downwind and three grid points upwind. problems can sometimes be more difficult to initialize with Mixed Differencing Scheme than with Upwind Differencing Scheme 1. while Central Differencing Scheme 1 is the least stable. Upwind difference schemes tend to produce excessive oscillations downwind of a discontinuity. The approximation is a 5 Numerical Methods 233 . under certain circumstances. then all the other linear differencing schemes are also likely to suffer this problem. Derivation of Fromms' Scheme First order (convection) term: ∂Γ i (Γ i − Γ i −1 ) + 0. First order (convection) term: ∂Γ i − Γ i −3 + 6Γ i − 2 − 18Γ i −1 + 10Γ i + 3Γ i +1 = ∆z ∂z Second order (dispersion) term is based on a second-order accurate central differencing scheme: ∂ 2 Γ i Γ i +1 − 2Γ i + Γ i −1 = ∂z 2 ∆z 2 Evaluation of Biased Upwind Differencing Scheme The Biased Upwind Differencing Scheme has the following advantages (+) and disadvantages (–): + + + – Fourth-order accurate. Results suggest that the biased scheme performs better than classical approximations. BUDS provides good accuracy for a smaller number of nodes than other lower-order approximations. Use Biased Upwind Differencing Scheme (BUDS) when the system is highly nonlinear. so gives good accuracy for small node counts (so is especially suited to sharp fronts). while the extra CPU time is small. Good stability. Fromms’ scheme Fromms’ scheme is the sum of a first order and a second order scheme.combination of central and upwind difference approximations. Simulation time only slightly larger than third-order schemes. Because of its fourth-order accuracy. and where the presence of sharp fronts requires accurate solution. If this happens. Derivation of Biased Upwind Differencing Scheme The fourth-order Biased Upwind Differencing Scheme is based on a fifth-order Taylor expansion. A potential drawback with BUDS is that. and less likely to produce oscillations than other higherorder linear discretization techniques. it also produces oscillatory behavior. It may produce instabilities for large ratios of time to spatial discretization step. with the exception of UDS1.25({Γ i +1 − Γ i } − {Γ i −1 − Γ i − 2 }) = ∆z ∂z 5 Numerical Methods 234 . May produce oscillations under extreme conditions. calculated as: ri = Γ i +1 − Γ i Γ i − Γ i −1 There are three versions of the flux-limiter function Ψ to choose from: • • • van Leer OSPRE SMART Second order (dispersion) term is based on a second-order accurate central differencing scheme: ∂ 2 Γ i Γ i +1 − 2Γ i + Γ i −1 = ∂z 2 ∆z 2 5 Numerical Methods 235 . Derivation of the Flux Limited Discretization Scheme The flux limited differencing scheme is: ∂Γ i Γ i − Γ i −1 1 Γ − Γ i −1 1 Γ − Γ i −2 = + Ψ (ri ) i − Ψ (ri −1 ) i −1 ∂z 2 2 ∆z ∆z ∆z Here Ψ is the flux-limiter function and r the gradient ratio.Second order (dispersion) term is based on a second-order accurate central differencing scheme: ∂ 2 Γ i Γ i +1 − 2Γ i + Γ i −1 = ∂z 2 ∆z 2 Flux Limited Discretization Scheme Flux limited schemes combine the accuracy of higher order finite differencing schemes with the stability of the first order upwind differencing scheme (UDS1). About the Estimation Module The Estimation Module has been in existence since Aspen Adsim 10. which are now accessible from Aspen Adsim 2004.1 Aspen Adsim 2004. one internal. first open the Aspen Adsim 2004. consult the Aspen Custom Modeler help files. and one external: • Estimation Module.1 help file. For more information.0. • Estimation features built into Aspen Custom Modeler. internal estimation tool that has been available since Aspen Adsim 10.6 Estimation with Aspen Adsim The chapter contains the following information about the Estimation Module: • • • • • • • • Two Estimation Tools in Aspen Adsim 2004. which is the existing. 6 Estimation with Aspen Adsim 236 .1 About the Estimation Module Defining Estimated Variables in the Estimation Module Steady State Estimation Using the Estimation Module Dynamic Estimation Using the Estimation Module Performing Estimation Using the Estimation Module Converting Estimation Module Data Recommendations when Using the Estimation Module Two Estimation Tools in Aspen Adsim 2004. To do this. navigate to the topic 'Two Estimation Tools in Aspen Adsim 2004. The interface simplifies the entry of: • Estimated variables.0 This chapter describes how to use the Estimation Module.1'. − Automation (via any COM-compliant application).1: − Simulation engine data tables. then use the available links. This new development links Aspen Adsim more tightly to the overall system. It provides an alternate estimation method to automation.1 has two estimation tools. The Estimation Module form contains: • • Buttons for commonly performed tasks (these are on the right-hand side).• • • • • Measured data. Steady-state (fitting constant parameters to static data). provided one is not already there. On the Tools menu. This table lists the buttons on the Estimation Module form: Button name Store Clear Load Description Store entered information in flowsheet block. Clear all current data in the Estimation Module. click Estimation Module. Dynamic (fitting constant parameters to time-dependent data). Replace current data with data stored in flowsheet block. Estimation solver options. 6 Estimation with Aspen Adsim 237 . An indication is given if either previously defined data or results are available. The block opens to display the Estimation Module form. Tabs for different data types. The Estimation Module provides two main types of estimation: To access the Estimation Module: This places an Estimation Module block on the flowsheet. Solver options associated with estimation. A list shows those variables that have a Fixed specification (assumed constant during the simulation). This table lists the tabs on the Estimation Module form: Tab name Estimated Variables Experimental Data Estimation Solver Options Description Currently selected Fixed variables to be estimated and their results (if available). Copy currently visible table onto the clipboard. 6 Estimation with Aspen Adsim 238 . to a maximum of three levels of submodel hierarchy. Defining Estimated Variables in the Estimation Module Use the Estimated Variables tab to define the variables that need to be fitted against experimental data. Open help page. The list shows only the valid variables that were available on opening. Measured experimental data. Execute estimation run.Open Run Help Copy Table Open version 10.0 estimation files. The New Experiment dialog box appears. the static_isotherm model is provided. For this purpose. select the adjacent box. Manually Entering Steady-State Experimental Data To add steady-state experimental data: 1 In the Experimental Data tab. You can add any number of experiments. Dynamic experimental data cannot used or entered. Steady-State Estimation Using the Estimation Module Aspen Adsim typically uses steady-state estimation to fit isotherm parameters to static experimental data. 2 Click OK to return to the Experimental Data tab. So as an example. Each experiment: • • Can be included in the estimation run. along with other statistical information. Has an individual experimental weighting (the default value being 1). These must be of one type: steady-state or dynamic. you can: • • • Modify the initial value (guess). Change the units of measurement of the initial value.To select a variable for estimation. All selected variables are added to the table. 6 Estimation with Aspen Adsim 239 . which gives access to both the standard inbuilt isotherms and user defined isotherms. if you are adding to a set of steady-state experiments. click the Add button. The dialog box looks different if experiments already exist in the Estimation Module. In the table. where you select Steady-State experiment type. View the result after a successful estimation run. The standard flowsheet for static isotherm fitting contains only a static_isotherm block. then the dialog box only has the steady-state option. the same variables can be copied from the currently active experiment. the default being 1. as described in Manually Entering Steady-State Experimental Data on page 6-239. 3 Define the experimental conditions using the variables added to the Fixed Variables list. 4 Add measured data to the Measured Variables list. The value of the Fixed variables can be modified. You can weight each experiment individually. pressure and mixture composition. as well as extra tabs for adding experimental conditions and measurements. can be selected. the default weighting being 1. Only variables that are Fixed. The experimental name is used as the prefix for any copied experiment. Each experimental point can have an individual weighting applied.This now has a list of the data sets. for example the temperature. for example from Microsoft® Excel: 1 Create a new steady-state experiment. When additional experiments are added. Initial or RateInitial variable to the list. Steady-State Experimental Data from the Clipboard To import steady-state experimental data. The following tips are useful: − − − − You can add any Free. 6 Estimation with Aspen Adsim 240 . The units of measurement are those currently active. and which are chosen for estimation. you list the manipulated variables first.2 When creation is complete. which requires copied data to function. Columns represent experimental variables (normally. Click the Yes button. 6 Estimation with Aspen Adsim 241 . 3 The Obtain Steady State Experiments From Clipboard dialog box appears. followed by the measured variables). The Estimation Module assumes that copied data takes this format: − − Each row is a single experiment. 4 Open Microsoft® Excel and copy the data set to the clipboard. you are prompted with a dialog box asking if you want to copy data from Microsoft® Excel. Leave this dialog box untouched for now. Aspen Adsim does not assume a specific flowsheet layout. from which you select the appropriate variable for the column. 7 Transfer the pasted data to the Estimation Module. and click the Paste button. 6 Estimation with Aspen Adsim 242 . select the column and click either the Varied or Measured buttons. a further dialog box opens in which you can automatically readjust the bounds for all variables of a similar type in the simulation. 6 For each column of data. mark whether it is a varied (manipulated) or measured variable.5 Return to the Obtain Steady State Experiments From Clipboard dialog box. either by clicking the Close button or the Process button. or the use of specialized models. for example the measured outlet composition over time. Dynamic Estimation Using the Estimation Module Use dynamic estimation whenever the experimental data is time-dependent. If any bounds are exceeded. − − The experiments created on processing the data are added to any other existing experiments in the Estimation Module. To do this. A list appears. You can use a standard process flowsheet that includes any operational task. A populated table now appears in the dialog box. Manually Entering Dynamic Experimental Data To add dynamic experimental data: 1 In the Experimental Data tab. 2 Click OK to return to the Experimental Data tab. click the Add button. So as an example. if you are adding to a set of dynamic experiments. The New Experiment dialog box looks different if experiments already exist in the Estimation Module. These must be of one type: steady-state or dynamic. then the dialog box has only the dynamic option. The New Experiment dialog box appears. 6 Estimation with Aspen Adsim 243 . where you select the Dynamic experiment type. The Experimental Data tab now has a list of the data sets, as well as extra tabs for adding experimental conditions and measurements. You can weight each experiment individually, the default weighting being 1. 3 Define the experimental conditions using the variables added to the Fixed Variables and Initial Variables list, for example the temperature, pressure and mixture composition. Only variables that are Fixed, and which are chosen for estimation, can be selected. The value of the Fixed and Initial variables can be modified. 4 Add measured data to the Measured Variables list. − − − − − You can add any Free, Initial or RateInitial variable to the list. A new tab is created for each measured variable, through which you define the time dependency. When new variables are added to an experiment, it is possible to copy the same time points from the currently selected variable. The units of measurement for any variable are those currently active. Each experimental point can have an individual weighting applied (the default value is 1). Dynamic Experimental Data from the Clipboard To import dynamic experimental data, for example from Microsoft® Excel: 1 Create a new dynamic experiment. When this is completed, the Paste Data button is enabled: 2 The Obtain Dynamic Measurements for Experiment DynExpt From Clipboard dialog box appears, which needs copied data to function. Leave this dialog box untouched for now. 6 Estimation with Aspen Adsim 244 3 Open Microsoft® Excel and copy the data set to the clipboard. The Estimation Module assumes that copied data takes this format: − − Each row represents a time point. Columns represent experimental variables. 4 Return to the Obtain Dynamic Measurements for Experiment DynExpt from Clipboard dialog box and click the Paste button. A populated table now appears in the dialog box. 6 Estimation with Aspen Adsim 245 5 For each column of data, mark whether it is the time of measurement, or the measured variable. To do this, select the column and click either the Time or Measured buttons. For measured variables, a list appears, from which you select the appropriate variable for the column. 6 Transfer the pasted data to the Estimation Module, either by closing the dialog box, or by clicking the Process button. − − The experiments created on processing the data are added to any other existing experiments in the Estimation Module. If any bounds are exceeded, a further dialog box opens in which you can automatically readjust the bounds for all variables of a similar type in the simulation. 6 Estimation with Aspen Adsim 246 Performing Estimation Using the Estimation Module To perform an estimation using the Estimation Module, click the Run button and leave the module open during the run. You cannot interact with the module during a run. After a successful estimation run, the module retrieves the results and stores them in the Estimation Module block on the flowsheet. The following results are available: • • • • Final estimated value Standard deviations Correlation matrix Covariance matrix Converting Estimation Module Data To convert from using the (old) Estimation Module to the (new) estimation tools available in Aspen Custom Modeler, use the script Convert_EstMod located in the Aspen Adsim library Script folder. To use the script: 1 2 Open the input file you want to convert. Double-click the script in the library. After the script has converted the data, the Estimation Module block disappears from the flowsheet. To view the experimental data, from the Tools menu click Estimation, which accesses the new estimation system. 3 Save the input file. Recommendations When Using the Estimation Module The following tips will help you get the best out of the Estimation Module: • To check that the initial values used for the variables to be estimated give a converged solution, complete these two steps: − Execute a steady-state run for steady-state estimation. − Execute an initialization run for steady-state estimation. These two steps are important as they ensure that the first iteration of the estimation solver will succeed. • • • Use estimation solver tolerances that are greater than the general solver options. If simulation convergence gives rise to multiple solutions, try a different initial guess. Try to measure variables that are sensitive to the estimated variables. Singular convergence normally indicates an insensitive measured variable. 6 Estimation with Aspen Adsim 247 • • Check the bounds of the estimated variables. For example, ensure the lower bound of a strictly positive isotherm parameter is zero. The fit is only as accurate as the range of data presented by the experiments, so include more than one set of experimental data. For example, with a single data set, the estimated value is useful only for the operating range of the data. 6 Estimation with Aspen Adsim 248 7 Cyclic Operation Many adsorption processes operate in a cyclic manner. Each cycle is described by a series of single or multiple sequential steps or discrete events. When simulating a cyclic process, you must be able to specify when certain events are going to occur. Aspen Adsim contains a Cycle Organizer for you to define cyclic operations. This chapter contains information on the following topics: • • • • • • • • • • • • Cyclic Operations in Aspen Adsim 2004.1 About the Cycle Organizer Opening the Cycle Organizer Cycle Organizer Window Step Control Step Variables Interaction Control Additional Cycle Controls Additional Step Controls Generating Cyclic Tasks Activating and Deactivating Tasks Cyclic Reports Cyclic Operations in Aspen Adsim 2004.1 In Aspen Adsim 2004.1, the Configure form has been extensively modified to allow for many new features. Input files created in previous releases are still compatible. When you open the Cycle Organizer, the old cycle definitions are automatically converted to match the new system, and the old cyclic task is automatically deleted. You then need to regenerate the cyclic task. About the Cycle Organizer The Cycle Organizer lets you rapidly create the steps that define a cyclic process. Use it to: • • • Create any number of steps. Define the step termination event. Manipulate flowsheet variables for a given step. 7 Cyclic Operation 249 All entered data is stored in the block on the flowsheet. one is automatically placed on the flowsheet and the Cycle Organizer window appears. use either the Tools menu or double-click the flowsheet block. you are asked two questions: − Is the new step to be placed before or after the currently selected step? − Is the information to be copied from the currently selected step into the newly created one (to act as a template).• • • • • • • • • • Generate a cyclic task based on the Task Language. it is advisable to configure it as if it is about to execute the first step of the cycle. The block looks like this: To open Cycle Organizer block present on the flowsheet. Execute V(isual)B(asic) scripts for additional calculations and control. click Cycle Organizer. Store multiple cycle definitions. If a Cycle Organizer block does not exist on the flowsheet. Here is some more information about the Cycle Organizer: Opening the Cycle Organizer To access the Cycle Organizer: • From the Tools menu. This allows the data to be saved with the flowsheet input file. On adding a new step. Distribute cycle information to other flowsheet blocks through global variables. Control variable recording and automated snapshots. Cycle Organizer Window The Cycle Organizer window looks like this: 7 Cyclic Operation 250 . Only one Cycle Organizer block is allowed on the flowsheet. When you configure the flowsheet for cyclic operation. The main Configure form gives the status of the system and the active state of the cyclic task. ) Toolbar button Cycle Purpose Cycle controls. The table lists the main buttons on the toolbar. and the options available on their drop-down menus. Add Variable/s Delete Variable/s 7 Cyclic Operation 251 . (The Print and Online button are not described. their purpose. Options Cycle Options New Cycle Generate Task Activate Cycle Delete Cycle Step Step controls. Control Manipulated Interactions Other Add/Insert Step Delete Step Variable (available only if you selected Manipulated from the Step menu) Adding or Deleting variables.The Cycle Organizer toolbar gives access to the various fields and controls needed to define and generate a cyclic task. such as modifying and inserting steps. such as creating and activating cycles. "the step will terminate when a vessel has reached a given pressure". automatically have their times and time units modified. To select a time-driven step control: • Enable the Time Driven radio button and give the step time in the specified units: When the cyclic task is generated. Likewise. Discrete Event Driven Step Event-driven step controls are implicit events. Dependent on another step. The step time remains constant from cycle to cycle. where termination is linked to elapsed time. click Control. To define the event. If the step is the second half of an interaction. where termination is linked to an event. Discrete event. the step control is a fixed elapsed time. Here. for which the time of occurrence is unknown. the value is automatically converted to the base time units assumed by the models. This ensures step symmetry within the cycle.Step Control There are three ways to define the termination of a given step: • • • Explicit time. or from the neighboring drop-down menu. the step is controlled by the elapsed time for the interaction’s first half. for example. any variable that is ramped in the current step. Time Driven Step Time Driven Step is the most common step control method. should the time unit of measurement change. and any dependent or interacting step. To access the step control panel: • In the Cycle Organizer window. For example. click the Step toolbar button. such as when a vessel has reached a given pressure. the step is set to terminate after 60 seconds. enable one of these three radio buttons: 7 Cyclic Operation 252 . • • • Value  a comparison between a Free variable and a value defines the event. Expression  a complex expression defines the event. in the unit of measurement of the monitored variable. To define the event: 1 2 3 Enable the Value radio button. The unit of measurement can be modified. 7 Cyclic Operation 253 . Variable  a comparison between a Free variable and another variable defines the event. Select a comparison operator from: == Equal to <> Not equal to <= Less than or equal to >= Greater than or equal to 4 Give the value for comparison. a comparison between a Free variable and a value defines the event. either by selecting it from a list of variables. Discrete Event Driven Step: Variable/ValueComparison With Value as your choice of step control. or by typing the exact name. Specify the monitored variable. This is useful when the step termination depends on a true or false condition. Discrete Event Driven Step: Complex Expression With Expression selected. 7 Cyclic Operation 254 . a comparison between two variables defines the event. To define the expression: 1 Enable the Expression radio button. The procedure for this is similar to the Value option. described in the previous subsection. a complex expression that is built up from logical operators defines the event. except that you must specify two variables: • • Monitored variable. Variable to make the comparison with.Discrete Event Driven Step: Variable/Variable Comparison With Variable as your choice of step control. where you create expressions: 3 Insert typical operations for the comparisons. this option is not available for the first step in any given cycle. so take care to enter values that are within the valid bounds and in the compared variable's base unit of measurement. using the buttons provided. Discrete Event Driven Step: Step Dependent The final method of step control is to make the step dependent on a previous step. To use this option: 1 2 Enable the Step dependent radio button. all interacting steps assume the elapsed time and time unit 7 Cyclic Operation 255 . is the start of a chain of step interactions.2 Double-click in the Expression text box. The Expression Builder dialog box appears. In the neighboring drop-down menu. If the step for which a dependency is being defined. specify the dependent step. Note: No error checking is provided for the expression entered. Likewise. A searchable list is provided to ensure that you insert only valid variables into the expression. Only steps that occur before the current step can be selected. Likewise. click Add Variable/s. To access the list of manipulated variables: • From the Step button's drop-down list. The Variable Selector dialog box appears. Valid wildcards are: * for any character combination. Note the following points: • • There is no limit to the number of variables that can be manipulated in a given step. except global variables. different variables may be modified. or from its drop-down list. You can access all variables in the flowsheet. ? for a single character place holder. These variables may control. Type the name of the variable in the text box at the top of the dialog box (a dynamic search takes place during typing). using either the SHIFT or CTRL key. 7 Cyclic Operation 256 . Select multiple variables. Step Variables Within each step of a cycle. Adding Step Variables To add a new manipulated step variable: 1 Click the Variable button on the toolbar. click Manipulated. 2 Select a variable using one of these actions: − − − − Double-click on the variable in the list.of measurement of the dependent step. all ramp times will be checked and converted to the new time unit of measurement. for example: • • • Feed condition Valve opening Heater duty The variable change may be stepped or a gradual/ramped change. which lists the available fixed and initial variables that have not already been selected in the current step. Use wildcards in the text box to reduce the list size and then select. any values provided for the Value and Target fields are automatically recalculated. Elapsed time of a ramp. Target value of the ramp. Unit of measurement. linear ramping or S-shaped ramping. On changing the unit of measurement. To modify this. A check is made to ensure the value is within the bounds for the variable in the current unit of measurement. the number in the Value column is used as the initial starting point of the ramp. From the Variable button's drop-down menu. you can automatically adjust bounds for all variables of the same type. This is visible only for ramped variables. double-click the field and a drop-down menu appears. Units Spec Ramped Target Time 7 Cyclic Operation 257 . This cannot be modified. Variable to be ramped. To remove a series of variables in contiguous rows. If a bound is violated. click Delete Variable/s. select the rows to be deleted. Removing Step Variables You remove step variables directly from the Cycle Organizer window. For ramped variables.• Selected variables are listed alphabetically in the table. Double-clicking this field displays a drop-down menu. the value entered here cannot be greater than the step time. where you choose between no ramping. For time-driven steps. To remove a single manipulated variable: 1 2 Select the row of the required variable. This is visible only for ramped variables. Changing Step Variable Values For each defined manipulated variable. the following fields are given: Field Value Description Value of the variable for the current step. Specification of the variable. where material is accepted early in the cycle and returned later in the same cycle. which lists the interaction units and the currently defined step interactions. Note the following points about step interactions: • • • Once you select an interacting step. you must use more than one interaction. A single interaction unit is not restricted to a single set of interacting steps. select the step in which the material is returned. This step defines the elapsed time for all associated interacting steps. it can be reused for any number of interacting step sets. only a single quantity of material can be accepted or returned for a given step. For this reason. if you want to transfer multiple amounts of material in a step. − Negative for reverse interactions. the Step toolbar's drop-down menu contains an Interactions option: This option accesses the Interaction Control table. There is no limit to the number of variables that can be ramped in a given step. The last row also shows the root defining step for any interactions. the step terminates when the ramp has completed. the target cell updates automatically. Interaction numbers are: − Positive for forward interactions. and from the drop-down list. • 7 Cyclic Operation 258 .With discrete event-driven steps. Interaction Control If the flowsheet contains interaction units (see Single Bed Approach in Chapter 7). if the event occurs before the ramp has completed. Defining a Step Interaction To define a step interaction: • Double-click on the step containing the source material. However. In step 5. For example. Elapsed time for an event driven step. Interaction unit D1 has interactions 1→ 3 and 5→ 4. interaction unit D3 has a single interaction. and step 2 event driven. to ensure time controls are in place. The table suggests that step 3 is time driven.Deleting Interaction Steps To delete an interaction: • From the drop-down list. This ensures time symmetry and maintenance of the material balance between interacting steps. the second half of the pair is forced to be time controlled. nor from two similarly controlled steps that use different times or events. click None. 3→ 5. however. step 1 is time driven. This is because the duration of an event driven step may change from cycle to cycle. Adding Extra Interaction Steps If you insert additional steps before or between existing interacting steps. and step 4 is time driven based on the elapsed time of the event in step 2. interaction unit D2 has a single interaction 2→ 4. in a five-step process using three interaction units. For example. the interaction numbers are renumbered automatically. Explanation of Why Time Controls Are Imposed A single step cannot receive material from both a time driven step. The time control is based on: • • Fixed time for a time driven step. if you insert a step between the interacting steps 1 and 3 for unit D1. so the elapsed time can vary. and one that is event driven. Interacting Steps and Time Controls Once you have defined an interacting pair of steps. we have two 7 Cyclic Operation 259 . the new interacting steps are now 1 and 4. The Cycle Organizer continually checks the root defining steps of all interactions. the step that occurs first is assumed as the root defining step. Additional Cycle Controls To access additional cycle controls: • Click the Cycle toolbar button. or from the button’s drop-down menu. Record frequency. The additional controls provided for the overall cycle include: • • • • Maximum Cycles Box Use the Maximum Cycles box to specify the maximum number of cycles to execute in a given run. Number of cycles to execute. Cycle steady-state testing. Assuming you have set the run options for indefinite running.interactions: one with step 4 (assumed event driven) and the other with step 3 (assumed time driven). It is coupled to the Record Initial and Record Frequency options. End of cycle snapshots. Click the Play button again to execute a further batch of cycles. Thus steps 2 through 5 are all dependent on the elapsed time of step 1. In this instance. 7 Cyclic Operation 260 . the simulation automatically pauses once the given number of cycles has been performed. click Cycle Options. 7 Cyclic Operation 261 . the simulation pauses. You need to set a tolerance for this option to work. When their relative difference is below the test tolerance. Use the Record Frequency box to specify the cycle at which the record attributes are switched off and then back on for a single cycle. the total loading and total solid temperature at the end of a cycle are compared to the value of the previous cycle. variables are recorded only for cycles 1. The simulator uses the snapshots to rewind to a time point in history. 5. 15 and 25. cyclic. Cyclic Steady State Testing Box Select the Cyclic Steady State Testing box to test when the dynamic cyclic simulation has reached a periodic. • • If you set these two options to 1. Take Snapshot Box To automatically take a snapshot at the end of every cycle (or cycles based on the settings for Record Initial and Record Frequency): • Select the Take Snapshot at End of Cycle box. 4. the variables are recorded for all cycles. the maximum number of cycles is always automatically modified to ensure the last cycle executed is recorded. 2. If you set Record Initial to 5. This applies only to variables that have it set to true and time equals zero. During the simulation.Record Initial and Record Frequency Boxes Use the Record Initial box to specify the number of cycles at the start of the simulation for which the record attribute remains on. When using these options. This significantly reduces the size of the plot data file. Record Frequency to 10. steady state. Taking a snapshot at the end of each cycle is useful if you want a material balance at points during the run. and the Maximum Cycles to 25. 3. 7 Cyclic Operation 262 . Specify the script in the Script Name box. End of step snapshots. a template script with the name provided is automatically created. Additional Step Controls To access the additional step controls: • Click the Step toolbar button.If the Record Initial and Record Frequency are not equal to 1. Taking a snapshot at the end of each cycle is useful if you want a material balance at points during the run. the simulation automatically pauses after the next recorded cycle. The simulator uses the snapshots to rewind back to a time point in history. click Other. This is useful for executing external calculations or runtime logging. Execution of a named script. The additional controls provided for the overall cycle include: • • Execute End of Step Script Box Select this box to run a flowsheet level script at the end of a step. Take Snapshot at End of Step Box To automatically take a snapshot at the end of step for every cycle (or cycles based on your settings for Record Initial and Record Frequency settings): • Select the Take a Snapshot at End of Step box. or from the button’s drop-down menu. If the script does not exist during cyclic task generation. for every cycle. click Activate Cycle. You can open and edit tasks using this language. Only a single cycle definition can be active. You see when there is another inactive cycle. whenever it is opened it will always display the currently active cycle (or the first cycle definition should no cycle be active).Generating Cyclic Tasks Once a new cycle has been defined. This is indicated in the Cycle Organizer status bar. Generated cyclic tasks are created using the Task Language. but any changes you make are lost if you regenerate the task using the Cycle Organizer. If cyclic tasks have been generated for all cycle definitions stored within the Cycle Organizer. the cyclic task needs generating before the simulation can be run. To activate a cycle: • With the cycle currently inactive down menu. from the Cycle drop- To deactivate a cycle: 7 Cyclic Operation 263 . . View the Cycle Organizer status bar to see how the generation is progressing: • You see when the cyclic task has been successfully generated (should there be any errors. followed by an index indicating the step and the manipulated variable. The "callable" task contains a single ramp statement. these will be given in the simulation messages window). If there is more than one cycle description stored within the Cycle Organizer. additional tasks are generated. The names of these additional tasks are prefixed by the main task name. click Generate Task. • • Note the following points: If any variable in a step is ramped. or changes made to an existing definition. you must not activate and deactivate the task by doubleclicking the task in the Flowsheet section of Simulation Explorer. as follows: To generate the cyclic task: • From the Cycle button's drop-down menu. • • Activating and Deactivating Cyclic Tasks Use the Cycle Organizer to activate and deactivate cyclic tasks. • With the cycle currently active . Click OK. you need to enable Block and Stream reporting. from the Cycle dropdown menu click Deactivate Cycle. from the larger Block and Stream reports. When you now run the simulation. Block and Stream reporting enabled. Cyclic Reports Cyclic reports are now available that provide information on the quantity and quality of material passing along a stream during any step. To prepare for cyclic reporting: 1 From the Tools menu. and any cycle. Cyclic Stream reports Cyclic Recovery reports There are two types of Cyclic report: Preparing Aspen Adsim for Cyclic Reporting Before you start your simulation. In overview. you are picking out information about particular steps and cycles. 7 Cyclic Operation 264 . Cyclic reports therefore require: • • • • A Cycle Organizer on the flowsheet. and specify when to stop recording information for the Cyclic report. step-by-step and cycle-by-cycle information is recorded. until the number of cycle histories is reached (this is 11 cycles in our example). state the number of recorded cycle histories. and underneath. point to Report and then click Reporting. The Flowsheet Reporting dialog box appears: 2 3 Select the Enable blocks/streams reports box. This also deactivates any other currently active cycle definition. Total of component passed. It also gives the start time.Cyclic Stream Reports The Cyclic Stream report gives the following information. Creating Cyclic Stream Reports You create Cyclic Stream reports for either a cycle or a step. end time and the elapsed time of the selected cycle or step. Total energy passed. Cycle or step averaged enthalpy. Cycle or step averaged flowrate. for each direction of every Aspen Adsim stream on the flowsheet: • • • • • • Total material passed. Cycle or step averaged component composition. based on either a total cycle or on an individual step. To create a Cyclic Stream report: 7 Cyclic Operation 265 . you also need to select a step. where additional information is added. select a cycle number. Cyclic Stream reports can be: • • Cyclic Recovery Reports The Cyclic Recovery Report gives the following recovery information for every product stream with respect to every feed stream: • • • Total material Individual component Total energy 7 Cyclic Operation 266 . such as the date and time. point to Report and click Stream Report. The Cyclic Report dialog box opens. and input file name. Printed to the default printer. The report can be resized. In the Cycle number list. or from its drop-down menu click Stream Report. Click the Build button. which prints only the currently visible columns of the report. This builds and then displays the Cyclic Stream report. You now build the report to view it. For a step report. 2 3 4 Enable either the Cycle radio button or Step radio button. Copied to the clipboard.1 From the Aspen Adsim Tools menu. you also need to select a step. click Recovery Report. 2 3 4 Enable either the Cycle radio button or Step radio button. select a cycle number. The Cyclic Report dialog box opens. This builds and then displays the Cyclic Recovery report. In the Cycle number list. 7 Cyclic Operation 267 . You now build the report to view it. From the Build button's drop-down menu. To create a Cyclic Recovery report: 1 From the Aspen Adsim Tools menu.Creating Cyclic Recovery Reports You create Cyclic Recovery reports for either a cycle or a step. point to Report and click Stream Report. For a step report. The models in the Aspen Adsim library support these flow regimes: 8 Flowsheeting 268 . These assumptions are broadly similar between gas. ion-exchange and liquid systems. you need to make some modeling assumptions that define the type of flowsheet interactivity.8 Flowsheeting This chapter contains information on: • • • • • • • • • • • About model types General model types Reversibility About flowsheets in Aspen Adsim Types of Flowsheet in Aspen Adsim Single bed approach Pressure interaction diagram Interactions Specifications for flowsheets Physical properties Connecting to Aspen Dynamics flowsheets About Model Types For reversible flow within an Aspen Adsim flowsheet. gas_feed. Stores stream information or passes downstream/upstream pressure information. gas_valve. Reversible Flow Setter Gas Relates pressure drop across the model to the flowrate through the model. Consider the gas phase system as a typical example: The usual modeling approach is to equate the outlet condition to either the internal condition (a tank for example) or inlet condition (a valve for example). The model does not contain any material holdup. gas_ramp. . products. gas_interaction. gas_product. but may contain a momentum balance. Material flow is from Process_In to Process_Out. Typical models: gas_bed. Typical models All models (except for adsorbent/resin beds) can be configured in this way. valves. Feeds. gas_buffer_intera ction. gas_tank_void. Reversible Ion-Exchange Liquid Feed or product train to allow for reversible flow. Non-Reversible Delay Gas Used as part of an interaction train.General Model Types The general model types available in Aspen Adsim are: Model type Non-Reversible Used in Gas Ion-Exchange Liquid Description Assumes that there is no flow reversal in the model. The pressure at each port is equated directly to the internal pressure. distributors. Reversible Pressure Setter Gas Accumulates material and energy (adsorbent beds are an exception). tanks. Able to specify the pressure directly. gas_ramp. 8 Flowsheeting 269 . Able to specify the flowrate directly. gas_valve. Reversibility You get reversibility within the flowsheet by categorizing the models into certain types. the streams must carry information. the underlying model is described as a “flow setter”.out S2 Tank2 Ys1.in = Ts1. The tanks accumulate only material and energy. otherwise the model becomes singular. such as the internal condition of the pressure setters (the tanks).out = Ts2.out Ps2.in = Ys2.in) Ys1. To allow for a reversed pressure profile. the stream condition must not be directly related to the tank condition.in Hs1. so the underlying model is described as a “pressure setter”.in = Ys1.in = Ps1.in = Ps2. the valve unit.out S1 Valve Ys2. from the tank units. the stream condition needs to be determined not by the tanks.out Ts2.in = P1 Hs1.in Ts1. To finally accomplish this task.in = Y1 Ts1. but by the unit in-between.in = H1 F = ƒ(Ps1. This is where the model type is introduced.out Hs2.out Ts1.in = Hs2.in = T1 Ps1. The valve uses the following information to ensure the appropriate flow condition is selected: • • Internal composition of the tanks.in = Ts2. We now introduce the concept of flow setter models and pressure setter models: • • As the valve model sets the stream conditions and determines the flow.Tank1 Y1 T1 P1 H1 Ys1. or equal to the pressure in tank 2.Ps2.in = Hs1.out Hs1.in Y2 T2 P2 H2 This approach works if the pressure in tank 1 is greater than. To allow for reverse flow between tanks 1 and 2. Pressure difference across the valve itself. and relate their pressure to this accumulation. as well as the actual stream condition.out = Hs2. 8 Flowsheeting 270 .out Ps1.out.out = Ys2. out.r Else Ys2.out.out >= Ps2.out = Ys1.in.r = H1 F = ƒ(Ps1.in.out Ts2.r S1 Valve Ys2.in = Ys2.out Hs1. For adsorbent and resin beds.out.out.in = Hs2. it is important that the discretization scheme used to solve the partial differential equations can cope with flow reversal at either the inlet and outlet boundaries.in = Hs2.in.out.in.r = T2 Ps2.out = Hs1.r Ts1.r = Ts2.r Else Hs2.out = Hs2.in.in = Ts2.in Hs1.Ps2.in.out Ys1.in = Ts2.out. you can model process trains where reversibility may occur.out = P2 Hs2.in) Ys1.out Ys2.out = Ts1.out.out Ts1.out = Ys2.r Else Ts2.r = Ys1.out >= Ps2.in.out.in.in Then Ts1.r = H2 Y2 T2 P2 H2 If Ps1.out >= Ps2.r = Ys2.r Ps2.in = Ys1.in = Ts1. 8 Flowsheeting 271 .out Hs2.in.in = Ps2.r If Ps1.r S2 Tank2 Ys1. without causing singularities.r = Y2 Ts2.r If Ps1.out Hs2.Tank1 Y1 T1 P1 H1 Ys1.in = Ys2.out.r Ts2.in Ys2.out.out.r Ps1.out = Ts2.r = Ts1.in.in = Hs1.out Hs1.in Then Hs1.r By using an alternating sequence of pressure and flow setters.out.in = Ps1.out. or internally.in Then Ys1.r = Hs1.in Ts1.in = P1 Hs1.in.in.r = Y1 Ts1.r = Hs2.r = T1 Ps1. or from a prepared template. This approach allows for the chosen discretization method to automatically switch between forward and backward differencing.Forward Direction 1 2 Outlet Boundaries n-1 n Process Out Process In 1 2 Inlet Boundaries n-1 n 1 2 Discretization Nodes n-1 n 1 2 Outlet Boundaries n-1 n Process Out Process In 1 2 Inlet Boundaries Reverse Direction n-1 n The scheme used within the adsorbent and resin models assumes a constant discretization mesh. with the boundaries evaluated at each local node with respect to the flow and/or pressure gradient. About Flowsheets in Aspen Adsim You create Aspen Adsim flowsheets either interactively through the graphical user interface. The available models are classified into three main phases or types: • • • • Gas Ion-exchange Liquid Use a common global component list. You can mix these phase types on a flowsheet. subject to these restrictions: 8 Flowsheeting 272 . other columns and cyclic behavior. interaction units. it is good practice to start with a simple flowsheet to ensure the column model assumptions are correct. Connectivity on Flowsheets You must use the correct material connection (stream) when connecting model blocks on the flowsheet: Model prefix gas_ ionx_ liq_ Stream type gas_Material_connection ionx_Material_Connection liq_Material_Connection Create the connections by dragging and dropping from the library to the flowsheet. you can then add further complexity. Available models/process operation descriptions.• Interconnect model blocks using only the appropriate stream type for the phase or model type. which can contain a liquid outlet to remove any condensed material. The only exception is a gas phase model block. Hardware limitations. When creating new problems. The flowsheet scope should ideally cover only the adsorbent columns and any immediate equipment required to operate the process. a model with the prefix 'gas_' accepts only connections made with a gas_Material_Connection. The ports and material connections pass the following information between model blocks (depending on phase or type): • • • • • • Molar/Volumetric flowrate Molefraction composition/Component concentration Molar density Absolute temperature Pressure Specific enthalpy 8 Flowsheeting 273 . such as column deadspaces. allowing you to create any process flowsheet subject to these restrictions: • • • Overall model size versus simulation speed. Connectivity is enforced by the port types used by each library model and material connection: Model prefix gas_ ionx_ liq_ Port type g_Material_Port i_Material_Port liq_Material_Port So. Once validated. The flowsheeting environment is very flexible. These casebook examples are a further source of process templates. click Templates. The Template Organizer appears: The available templates feature: • • • • Recommended solver options. Before copying a template to the current working directory. which is then used for both the input file and the directory that houses all the files for the new problem.Controllers are not connected using material connections. Demonstrations All of the examples in the Aspen Adsim casebook come as part of the standard installation. ControlSignal connects a single exposed variable from one model block to another single exposed variable in the same or another model block. To access this: • From the File menu. Flowsheet layouts based on standard descriptions. a name is requested. Templates Predefined process templates are available through the Template Organizer. 8 Flowsheeting 274 . they use a special stream type called ControlSignal instead. Runtime options set to the appropriate time units. Default component list configured for use with Fortran-based physical properties and populated with dummy components. click Demonstration Organizer.To access the example files: • From the File menu. The simple flowsheet typically includes the following unit operations for all phases or types: 8 Flowsheeting 275 . You are told if a set of files will be copied. Use it to: • • Ensure the absorbent/resin bed works effectively. Types of Flowsheet in Aspen Adsim There are three types of flowsheet in Aspen Adsim: • • • Simple flowsheet Intermediate flowsheet Full flowsheet Types of Flowsheet: Simple Flowsheet The simple flowsheet is the smallest workable flowsheet to operate an adsorbent/resin bed. or if a copy of the example already exists. It is a recommended starting point for new simulations. Simplify testing of key parameters and configuration assumptions. The Demonstration Organizer appears: To open a casebook example: • Select the problem of interest and click Open. It builds upon the simple flowsheet by including (except for ionexchange): • • Adsorbent bed deadspaces or voids. Adsorbent/resin bed (can contain any number of layers).• • • Feed boundary unit. Product Boundary Adsorbent or Resin Bed Feed Boundary Intermediate Flowsheet The intermediate flowsheet is useful for simulating non-interacting adsorption cycles. Feed and product valves. Product boundary unit. 8 Flowsheeting 276 . Intermediate buffer tanks or pressure receivers. there are two levels of overall model complexity: 8 Flowsheeting 277 . Full Flowsheet The full flowsheet is the final step in flowsheet complexity. Feed and product pumps. Additional feed or product trains.Product Valve Product Boundary Top Deadspace (Tank) Adsorbent Bed Feed Boundary Feed Valve Use the intermediate flowsheet to simulate: • • • Co-current or counter-current adsorption. To simulate interacting beds. Repressurization and depressurization. Bottom Deadspace (Tank) Purge using streams of different compositions. It builds on either the simple or intermediate flowsheet by including: • • • • Interactions with other adsorbent/resin beds. it is important to sketch out the pressure interaction diagram for your process. Same number of cycles to achieve cyclic steady-state. each undergoing the following steps in a cycle: • • • Production at high pressure with some product that counter-currently repressurizes another bed. Fewer equations (due to fewer beds). with material interactions overlaid. For the method to be valid: • • Each adsorbent/resin bed (or series bed train) must be identical. a simple three step Oxygen VSA process is examined. If these assumptions are met. the majority of which are discretizations of the partial differential equations. This diagram is a graph of pressure versus time. Repressurize using product material. The single bed approach retains the accuracy of the final results (see the spreadsheet included within the installation): • • • • Same average purity. One way of modeling adsorption systems that comprise multiple adsorbent/resin beds. Single Bed Approach An inherent problem when modeling an adsorption system is the number of equations to be solved. Less data to be communicated between the client (GUI) and the server (simulation engine). This stored information can then be replayed back to the real bed later in the cycle. In the following example. The Pressure-Interaction diagram for the process looks similar to this: 8 Flowsheeting 278 . is to use the single bed approach. The material is sent to waste. Simulation speed is also improved: Pressure Interaction Diagram Before creating a flowsheet. Each adsorbent/resin bed must undergo the same steps in a given cycle. Evacuate to low pressure.• • Single bed approach — this uses a single bed to simulate processes containing more than one bed. Rigorous multi-bed — this simulates all adsorbent/resin beds with interconnecting units. then you can rigorously model a single “real” adsorbent/resin bed and store any information (material) that would normally be sent to an interacting bed. The process uses three identical adsorbent beds. the interactions would look like this: 8 Flowsheeting 279 .P Bed 1 Bed 2 Bed 3 t 60 120 180 If the single bed approach is applied. using Bed 1 as the real bed. Flowsheet Scope Record P Replay Bed 1 Bed 2 Bed 3 t 60 120 180 Material profile information from step 1 can be stored and then replayed back to Bed 1 during step 3. The final pressure-interaction diagram for the new single bed process looks like this: 8 Flowsheeting 280 . you must use an interaction model to simulate the bed that the real modeled bed is interacting with. this is called an interaction. In gas systems. Step 3 — 120 through 180 seconds — there was counter-current repressurization with product material. Step 2 — 60 through 120 seconds — there was counter-current evacuation to waste. Using the Oxygen VSA example. the pressure-interaction diagram was as follows: P Bed 1 t 60 The three. In this example there is only one interaction. it is named gas_interaction. To create this interaction when using the single bed approach. Aspen Adsim handles any number of interactions in an adsorption process cycle.P Bed 1 t 60 120 180 Interactions When material from a step is used by another step. The interaction model records one or more of the following profiles (dependent on the phase of the system): • • • Flowrate Composition or concentration Density 8 Flowsheeting 281 . for example. 60 second duration steps were: • • • 120 180 Step 1 — 0 through 60 seconds — there was production with some material used to repressurize another bed. a top-to-top interaction between steps 1 and 3. • • • • Temperature Pressure Specific enthalpy The inlet stream must always be connected to a valve (configured as a non-reversible delay) whose inlet is connected to point on the flowsheet where material is withdrawn. for example: • Valve Present In Scope Real Bed Scope Store Real Bed Scope Valve Not Present In Scope Replay Store Profile • • • • Top-to-top Top-to-bottom Bottom-to-bottom Bottom-to-top Replay Profile Use the withdrawal and return point for material. to define whether the interaction is: So. To use the gas_interaction model. the following additions are needed to create a top-to-top interaction off the real adsorbent bed’s top void. Typically. the valve inlet is connected to a gas_tank_void model that is being used to simulate an adsorbent bed deadspace or void. The outlet stream defines where material is returned to the flowsheet. No valve is required on the outlet stream. The valve passes the interaction unit information about the upstream (or relative bed) pressure. for the Oxygen VSA example. 8 Flowsheeting 282 . The accuracy of the delay function is dependent on the communication interval. If the simulation is closed or a snapshot re-used. The snapshot does not store delay information. the delay buffer is emptied and all historical profile information is lost. the following solver options are recommended as good initial starting points: General Tab: Solver Options The recommended solver options are: 8 Flowsheeting 283 .To product Valve Tank Interaction From bed Notes: o o The interaction units use the Delay function. It is recommended that you have at least four communication points within the shortest step. o o Specifications for Flowsheets This section gives information on: • • • • Solver Options Run Time Options Model Specification Consistency and Model Definition Checks Solver Options If you create a flowsheet that is not based on a template. not the integration step size. Option Absolute Variable Tolerance Relative Variable Tolerance Absolute Equation Tolerance Variable Change Tolerance Numerical Derivative Absolute Tolerance Numerical Derivative Relative Tolerance Solver Scaling Eliminate Equivalence Equations Value 1e-5 1e-5 1e-7 1e-5 1e-6 1e-6 Disabled Enabled. the integration steps may need reducing.5 1e-5 1 500 0 Enabled Disbaled Note: When running rapid cycles.5 1. Linear Solver Tab: Solver Options The recommended solver options are: Option Name Drop Tolerance Pivot Tolerance Re-analyse Threshold Value MA48 0 0 2 8 Flowsheeting 284 . Standard Integrator Tab: Solver Options The recommended solver options are: Option Integrator Initial Integration Step Minimum Integration Step Maximum Integration Step Step Reduction Factor Maximum Step Increment Factor Absolute Integration Error Tolerance Tear Integration Tolerance Maximum Corrector Iterations Show Highest Integration Errors Use Interpolation Reconverge Torn Variables Value Variable Step Implicit Euler 1 1 5 0. The following settings are recommended: Options Solution Time Units Display Update Communication Value Seconds 2 Problem dependent Comments Time unit assumed by library models. Pause at Problem dependent Uncheck when using the Cycle Organizer (run time controlled by maximum number of cycles). A value of zero indicates run as fast as possible. Number of communication intervals to execute. When studying rapid transients. Interval when data is communicated between client and server. Resolution at which plot data and delay information is saved. click Run Options. This value can also be modified using the Run menu Pause At option.Re-analyze FLOPS Window Size Re-pivot every Solver searches 0 0 3 Non-Linear Solver Tab: Solver Options The recommended solver options are: Options Mode Method Convergence Criterion Maximum Divergent Steps Maximum Step Reductions Maximum Iterations Maximum Fast Newton Steps Dogleg Method Value General Fast Newton Residual 20 20 500 8 Disabled Run Time Options To set the runtime options for Aspen Adsim: • From the Run menu. When using interactions. Real time to simulation time factor. Check and provide a desired end time for other simulations. set this to a small value. Pause after Real time synchronization Unchecked Unchecked 8 Flowsheeting 285 . ensure this value is set to provide at least five communication points in the shortest interaction step. Small values make the plot data file grow more rapidly. clicking Forms options. The normal approach is to first configure the model.Model Specification Aspen Adsim library models may require one or more of the following types of specification: • • • Definition of model assumptions. if required. 8 Flowsheeting 286 . Specify whether the layer is isothermal or non-isothermal. then specify the constant variables exposed and finally. the model automatically reconfigures. On changing an assumption. which shows the recommended variables to preset and initial. there is no need to determine which values are required to be specified. For example. You set these options in the model Configure form. Each model in the Aspen Adsim model library contains a Specify table. This ensures that the overall degrees of freedom of a complete problem are always met. click the button on the Configure form to open the Initials table. You access the Specify table in one of these three ways: • • • Using the Configure form for the model. you have the option to: • • Include a dispersive term in the component material balance. Adsorbent layer and tank models typically fall into this category. initial values are required. Specification of Constant Variables All models in the Aspen Adsim library contain recommended fixed variables. To define the preset and initial variables. so there may be slight pause depending on the overall complexity of the change. Specification of constant variables. which opens when you double-click a flowsheet model block. Using the model’s context sensitive menu (selecting and right-clicking a flowsheet model block). specify the model initial condition. From the Flowsheet menu. Value Units Derivative Specification Description The recommended columns made visible in the Specify table are: • • • • • Presets and Initialization If a model contains state variables (variables that are differentiated with respect to time). Therefore. with an adsorbent layer. This form displays selection boxes for any available adjustable assumptions. Defining Model Configurations The model configuration is the selectable assumptions a model may have. Initial and preset conditions. pressure and ncomps-1 internal molefractions. or select Check & Initial from the Flowsheet menu. Preset (provide free specified values for) the internal composition. Pay particular attention to the deadspaces connected to a gas adsorbent. and that the deadspaces have been correctly • • • 8 Flowsheeting 287 . configure the flowsheet with first step conditions. the Check & Initial option in the Flowsheet menu always ensures that the problem contains the correct number of initial variables. Allow cross-valve pressure drops of at least 1 mbar. set the derivatives to zero with a specification of Rateinitial. the initialize method calculates the material molar holdup. Preset (provide a free specified value for) the internal pressure. To specify a layer that is at saturated equilibrium with a given bulk phase composition. • • For a gas phase tank or void: • • • • • If you modify initial or preset values solely in the Initials table (and not elsewhere). From the above and using the internal volume. For a gas adsorbent layer that includes a pressure drop correlation (momentum balance).55e-4 m/s. To propagate this value through the rest of the layer.For an adsorbent/resin bed: • Provide values for a single discretization node within a given layer. it is recommended that you make these checks: • • For cyclic processes. either click the Initialize button on the model’s configure form. Ensure the pressure profile between the two units are reasonable and in the correct direction. for example 3. A valid alternative specification is to initialize the temperature. and to free the internal molar holdup. Check the initial and preset pressure conditions throughout the flowsheet. initialize the bulk phase values (molefraction or concentration) and for the loading. the standard specification is to initialize the superficial velocity and initial ncomps-1 bulk phase molefractions. Provide an initial value of the temperature. for example feed to product. for robust initialization assume a small initial superficial velocity. The recommended columns to made visible in the Initials table are: • • • • • Value Units Derivative Specification Description Consistency and Problem Definition Checks When creating and specifying a flowsheet. Ensure the pressure gradient is correct for the direction of material travel. For gas adsorbent beds. • Make use of the Flowsheet menu Check & Initial option. The default solution bounds for variables defined in the library are suitable for most problems. or very rapid cycles. The library models contain default specifications. If forced feed is required. Typical properties required are: • • • • Molecular weight Viscosity Density Enthalpy Aspen Adsim supports two ways of supplying this physical property data: 8 Flowsheeting 288 . For flowsheets with interaction units. Make use of the recommended Fixed variables. If any are set to a specification of Free. and correctly configures material stream source and destination unit types. If a spanner/wrench appears in the specification window when flowsheeting.initialized. when using the Variable Step Implicit Euler integrator. when operating with large pressure or temperature swings. • • • • • • • • Physical Properties Various physical properties are required by the Aspen Adsim models. or using Variable Finder. set the feed unit flowrate specification to Fixed and the product unit specification to Free. use Variable Finder to find all Initial and Rateinitial variables. use either the specification analysis tool. runs any model-based initialization methods. Unreasonable initial conditions for deadspace are the principal cause of full flowsheet convergence problems at the start of the simulation. When flowsheeting. try setting the maximum integrator step to half the shortest step time. Use the Variable Finder for this. However. Should the problem become over or underspecified. It indicates unconnected and invalid streams. If the model has too many initial variables. Set the specification of any found variables to Free and then use the Check & Initial option from the Flowsheet menu. The default initial condition is reconstructed. the default bounds may need readjusting. ensure that a component list is defined and that all connections are in place. using a simple gas flowsheet. the default specification is for it to be pressure driven. find all variables and from the properties page. another variable needs to be Fixed and vice-versa. For example. ensure the integrator step sizes are suitable. this usually indicates that the current component list is not defined. If you receive messages stating that empty arrays are being passed to procedures. set the specification to default values. ensure the run time communication interval allows at least five communication points within the shortest interacting steps. For processes that operate under rapid cyclic conditions. For example. corrects interaction unit configurations. and the initial and minimum steps sizes to 1/5 through 1/10 of the maximum integrator step. it is usual to first create the component list and then start placing models on the flowsheet. Arrays indexed by component name are passed to procedures in ASCII order. When distributing a problem. 8 Flowsheeting 289 . The subroutines created then need to be compiled into a library so that they link to the simulation during runtime. hence subroutines may need modifying in response to changing component order.• • User Fortran subroutines. The advantages of using user Fortran based calculations are: • • • Simulation speed. the default component list is configured for use with an external properties application. you must first convert it to a component set (to do this. and is one level down from the default working directory. the simulation engine’s working folder for this problem is C:\MySims\N2PSA. the default component list assumes that user Fortran subroutines are being used. The component list created for the problem governs the method in which physical properties are called. If a new component list is created.ada and the default working folder has been defined as C:\MySims. The procedure definition defines the calling arguments. It is important that the compiled library is placed in the simulator engine’s working directory. • • If you use a template. • Use of User Fortran Historically. Aspen Adsim assumed that any physical property calculations or data were supplied through user Fortran subroutines. right-click the list and select convert). Inflexibility when changing component names. External physical property application (Properties Plus. For example. The user subroutines either need reworking after each change or a collection of different versions of subroutines (each assuming different numbers of components) will be required. Disadvantages of using the user Fortran method are: • When creating a component list: The interface between the subroutine and model is defined by the Procedure type. This applies to both local PC and remote server implementations. if the name of the current problem is N2PSA. The working directory has the same name as the current simulation. When starting a new problem (without a template). subroutine name and library name. Addition and removal of components from the simulation. only need to additionally supply the library. select the Is ComponentSet box is on creation. Aspen Properties). If you want the user Fortran option. by default it is assumed an external properties application will be used. To modify it for use with user-Fortran. The global variable that switches the two methods is automatically updated. The component list switches to the other method it’s currently using. • • • • The disadvantages are: When using Properties Plus or Aspen Properties.Using a Physical Properties Application The simplest way of incorporating physical property calculations and data. 2 3 8 Flowsheeting 290 . (To do this. 4 Open the Configure form for any library model of the flowsheet. within the Explorer window.appdf file. Switching Between Methods To switch between using user Fortran and an external properties application for the supply of physical property calculations and data: 1 If converting from user Fortran to an external application. the steps required before using either application are: 1 2 3 Create an . Speed penalties.) Select the currently active component list. Right-click the list and select Convert.appdf is located. Extensive component database. the same components will be present. Define where the . otherwise mismatches will be discarded. ensure the link to an . right-click the ComponentLists object in Explorer and browse for a previously created . Requires application on same machine. right-click Component Lists and select Properties. if the component names originally defined are present in the . Create or convert a component list and select the components required. Large collection of rigorous physical property methods. The advantages of using an external physical properties application are: • Ability to create a single definition file containing all the components and physical property methods of interest.appdf file is already defined.appdf file. When switching from Fortran to application based properties. for example. is to use an external physical properties application such as Properties Plus or Aspen Properties.appdf file. and only those required in the current problem. In Aspen Adsim. Open the Aspen Dynamics library. there are two possible situations: • • Attach individual Aspen Dynamics models to an existing Aspen Adsim simulation. as follows: Attach an Aspen Adsim material stream to the Aspen Adsim flowsheet block. There are two new utilities models for this purpose: • • Dynamics_Inlet_Connect Dynamics_Outlet_Connect These models are in the Utilities folder of the Aspen Adsim library. The model link must be done from within Aspen Adsim. the link cannot be set up from Aspen Dynamics. This simplifies later conversion. Attaching Individual Aspen Dynamics Models To attach an individual Aspen Dynamics model (for example. Attach the new Aspen Dynamics flowsheet block to an existing Aspen Adsim flowsheet block. a rigorous compressor model) to an existing Aspen Adsim simulation: 1 2 In Aspen Adsim.1 installation. Attach a complete Aspen Dynamics simulation to an existing Aspen Adsim simulation. Your choice depends on whether the Aspen Dynamics model is on the inlet or outlet side of the Aspen Adsim mode. Now connect these two streamsusing either a Dynamics_Inlet_Connect or Dynamics_Outlet_Connect model from the Utility folder of the Aspen Adsim library. it is good practice to name the active component list as 'Type 1'.Connecting to Aspen Dynamics Flowsheets You can now connect Aspen Adsim flowsheet sections to Aspen Dynamics flowsheet sections (except for ion-exchange flowsheets). Tip: If you are creating an Aspen Adsim flowsheet for connection with an Aspen Dynamics flowsheet. 5 Repeat steps 3 and 4 until the flowsheet is complete. click Open Library and navigate to the Lib folder of the AMSystem 2004. Typical Workflows When you want to connect Aspen Dynamics models to Aspen Adsim models. To do this: From the File menu. open the Aspen Adsim simulation. Place the required Aspen Dynamics model onto the Aspen Adsim flowsheet. 3 4 8 Flowsheeting 291 . and an Aspen Dynamics material stream to the newly placed Aspen Dynamics flowsheet block. See Valid Flowsheet Combinations. the Aspen Dynamics version is called “Type1”. (Aspen Adsim uses only rigorous property calls. open the input file (. you cannot rename it through the GUI. set to Rigorous. For liquid-based Aspen Adsim flowsheets. Note these points: − Aspen Adsim does not support flowsheet hierarchy. . imported Aspen Dynamics flowsheets may be either pressure driven or flow driven. This imports the Aspen Dynamics simulation into Aspen Adsim. If property convergence is difficult. or from the Configure form of a Dynamics_Inlet_Connect or Dynamics_Outlet_Connect block: Global variable GlobalPDriven GlobalPropMode Brief description Is the flowsheet pressure driven? Property mode Notes For gas systems. imported Aspen Dynamics flowsheets must be pressure driven.) Set to True if the model is expected to operate reversibly. later. You do this in the Global variables table.6 Check and modify the global variables relating to Aspen Dynamics flow schemes. Instead. GlobalRFlow Reverse flow? 7 Specify. − − 3 The type of Aspen Dynamics flowsheet that can be imported depends on the type of Aspen Adsim flowsheet: − − For gas-based Adsim flowsheets. Check the component lists being used: − Ensure matching component list names between the Aspen Adsim and Aspen Dynamics simulations. If the Aspen Adsim component list name is Default. If necessary. is in use. Default is Local. so all Aspen Adsim based blocks and streams must exist on the main flowsheet. click Import Flowsheet. an Aspen Dynamics based cryogenic distillation train to an Aspen Adsim TSA system for air dehumidification): 1 2 In Aspen Adsim. 8 Flowsheeting 292 . set to True. and provide initial values for. the new Aspen Dynamics blocks.ada extension) within a text editor and search and replace the original component name. open the Aspen Adsim simulation. − 4 From the File menu. See Valid Flowsheet Combinations.appdf. Ensure the same components are actively in use. Attaching Complete Aspen Dynamics Flowsheet To attach a complete Aspen Dynamics simulation to an existing Aspen Adsim simulation (for example. Typically. Ensure the same properties definition file. you must rename the Aspen Adsim component list name to match. later. to the new component name. You must check the Globals table in Aspen Adsim and set the global parameters GlobalPDriven and GlobalRFlow to match those in the Aspen Dynamics flowsheet to be imported. In the Cycle Organizer. Aspen Adsim retains the original settings from before the flowsheet was imported. Aspen Adsim automatically opens the Aspen Dynamics model library during the import. remove the boundary termination block (unlike Aspen Dynamics. Between each flowsheet section.) 7 8 Repeat step 6 until the flowsheet is complete. plots. and these are listed in the following table. Connect liquid-based Aspen Adsim flowsheets to flow driven Aspen Dynamics flowsheet sections. Repeat steps 2 through 4 until all the required flowsheet sections are present within Aspen Adsim. Inlet side section (Aspen Dynamics) Pressure driven Pressure driven Not present Flow driven Flow driven Outlet side section (Aspen Dynamics) Pressure driven Not present Pressure driven Flow driven Not present Gas (Aspen Adsim) Supported (1) Supported (2) Supported (4) Partial support (6) Partial support (7) Liquid (Aspen Adsim) Not Supported Supported (3) Supported (5) Supported Supported 8 Flowsheeting 293 . bracketed numbers mark where this happens and you should refer to the notes underneath for more details. You can rename or delete these repetitions. tables and tasks names are flagged during the flowsheet import. modify the cycle description to account for any cyclic operation of imported Aspen Dynamics blocks. Some combinations have constraints: in the table. Now connect these open-ended Aspen Adsim streams with their Aspen Dynamics counterparts. connect the appropriate Aspen Adsim or Aspen Dynamics feed and product streams: − For an existing Aspen Adsim feed or product stream. streams. then regenerate the cyclic task. The Aspen Adsim simulation flowsheet is updated with the imported Aspen Dynamics simulation flowsheet. or import the flowsheet into a hierarchy block. Valid Flowsheet Combinations The valid combinations of Aspen Adsim and Aspen Dynamics flowsheets are: • • Connect gas-based Aspen Adsim flowsheets to pressure driven Aspen Dynamics flowsheet sections. Aspen Adsim has no concept of using open ended streams to indicate flowsheet boundaries). using either a Dynamics_Inlet_Connect or a Dynamics_Outlet_Connect from the Utilities folder of the Aspen Adsim library.− − − − 5 6 Repeated blocks. For common global variables. (Your choice depends on whether the Aspen Dynamics model is on the inlet or outlet side of the Aspen Adsim flowsheet. Further valid combinations are also possible. Fix a pressure at the Aspen Adsim flowsheet outlet. The single bed approach is not recommended. Connect the Aspen Dynamics flowsheet section on the inlet side to a pressure node (a gas_tank_void for example).Not present Reversible (pressure driven) Reversible (pressure driven) Not present Flow driven Reversible (pressure driven) Not present Partial support (8) Supported (9) Supported Not supported Supported (10) Supported Reversible (pressure driven) Supported (11) Supported You cannot mix flow assumptions. for example a pressure driven inlet and a flow driven outlet. for example). Connect the Aspen Dynamics flowsheet sections on the outlet side to a pressure node (a gas_tank_void. use a full rigorous Aspen Adsim flowsheet instead. for example). Connect both Aspen Dynamics flowsheet sections only to a gas_bed model. use a full rigorous Aspen Adsim flowsheet instead. Connect the Aspen Dynamics flowsheet only to an Aspen Adsim gas_bed outlet. You can also access many of these global variables through the Configure form of the Dynamics_Inlet_Connect and Dynamics_Outlet_Connect model blocks. 10 Connect the Aspen Dynamics flowsheet section on the inlet side to a pressure node (a gas_tank_void for example). 11 Connect the Aspen Dynamics flowsheet section on the outlet side to a pressure node (a gas_tank_void. Connect the Aspen Dynamics flowsheet only to an Aspen Adsim gas_bed inlet. Global Variables A number of global variables control the operation of both Aspen Adsim and Aspen Dynamics models. use a full rigorous Aspen Adsim flowsheet instead. This is because a single set of global variables is used to control the Aspen Dynamics flowsheet assumption. Connect the Aspen Dynamics flowsheet sections on both the inlet and outlet sides to a pressure node (a gas_tank_void for example). The following notes relate to the bracketed numbers (denoting constraints) in the previous table: 1 2 3 4 5 6 7 8 9 Connect the Aspen Dynamics flowsheet sections on both the inlet and outlet sides to a pressure node (a gas_tank_void for example). 8 Flowsheeting 294 . The single bed approach is not recommended. These variables can be found in the Globals table within the Simulation object in the Simulation Explorer. Fix a pressure at the Aspen Adsim flowsheet inlet. The single bed approach is not recommended. For bi-directional flow. the flowsheet must be pressure driven (so set the parameter to True). 8 Flowsheeting 295 . In general. set to True. whether the Aspen Adsim flowsheet is using the Single-Bed approach to simulate a multi-bed flowsheet using a single column. Aspen Dynamics models assume time units of hours. a common time unit needs to be adopted to successfully calculate time derivatives and delay times. Aspen Dynamics models use GlobalPropMode to select between local or rigorous physical properties calculations: The Local option uses simplified functions whose parameters are updated from an external physical property package. set to False. The rigorous option uses methods contained within the external physical properties package. When set to True.The global variables used are as follows: Global variable GlobalPropMode Default value Local Description The global property mode. When models from both products exist on the same flowsheet. Aspen Dynamics uses GlobalTimeScaler to rescale time derivatives and calculated delay times. This improves the simulation time. a set of equations is enabled that generate pseudo continuous flow from an inherently discontinuous flow. GlobalPdriven False Is the simulation pressure driven? Aspen Dynamics models use GlobalPdriven to switch the overall flowsheet scheme between pressure-driven flow and flow-driven flow. whereas Aspen Adsim models assume seconds. IsSingleBed False Is the single bed approach being used? IsSingleBed indicates to Aspen Adsim’s Dynamics_Inlet_Connect and Dynamics_Outlet_Connect models. otherwise the Aspen Dynamics models will default to unidirectional. When the system is liquid. GlobalTimeScaler 1 Seconds per model time unit. Note: If you anticipate flow reversibility within Aspen Dynamics models. GlobalRFlow False Does the simulation support reverse flow? Aspen Dynamics uses GlabalRFlow to switch between uni-directional and bi-directional flow. flow-driven flow. for Aspen Dynamics models used in conjunction with Aspen Adsim models: When the system is gas. from hours to seconds. you must also set GlobalPdriven to True. Note: All Aspen Adsim models use rigorous property calls. the inlet and outlet port variables are mapped together and the time at which the switch 8 Flowsheeting 296 . as they may be expecting to continuously receive material. temperature. a discontinuous supply of material may cause adverse effects to downstream units such as distillation columns or compressors. which contain a series of expressions to generate a pseudo continuous flow of material. For example. Flowrate Delayed Profiles 4 x DT 3 x DT 2 x DT DT Cycle time The two models use a variable that switches/toggles to indicate when flow of real material occurs. For example. When set to 1 (that is On. They use a similar set of expressions to the gas_interaction model. a product stream from an Aspen Adsim flowsheet may be active (producing material) only during one step in the cycle. To counter this problem. Flowrate Cycle time This behavior can disrupt Aspen Dynamics flowsheets that are connected to this same outlet boundary. pressure and enthalpy profiles are recorded during the flow of actual material. so it suffers from the inherent behavior of discontinuous flow at the flowsheet boundaries. for real flow).Connecting to a Single Bed Approach Flowsheet The single bed approach to modeling a cyclic adsorption process is an abstract representation of the real process. the Dynamics_Inlet_Connect and Dynamics_Outlet_Connect models have been developed. composition. The flow. whilst a delay function is used to reproduce the same profile. periodically throughout the rest of the cycle. and the time at which the switch occurred is recorded. The Aspen Dynamics port variables are then mapped to the appropriate Aspen Adsim port variables. This.CalcOutput 1 1. for pseudo flow). but through the delay function.5 B1. When the elapsed time from the switch off exceeds the calculated delay time. -5 B1.5 -1 0. 1 -0. explains why you may see a slight degradation in the overall material balance. 8 Flowsheeting 297 .DelayTime 10 15 20 25 30 DelayTime 0 10 20 30 40 50 60 70 80 90 100 Time Seconds The result of this procedure is a continuously variable delay time that produces a profile with a repeating pattern.RealOutput 0 0. and a delay time is calculated. the variable switches to 0 (that is Off.Toggle 1 2 3 4 5 6 7 8 9 10 0 5 B1.5 B1.was set to 1 is recorded. coupled with the fact that it uses interpolation of historical data.5 2 Output_Values 0 10 20 30 40 50 60 70 80 90 100 Time Seconds This method is applicable only if the assumption that the flow profile expected at the inlet and/or outlet side of the Aspen Adsim flowsheet is consistent within a given cycle. When no real flow is occurring. The delay function is used to replicate flow profiles. the delay time is incremented by the original delay time. I. John Wiley and Sons. T. R. 1981. 1991.T. R. S. M.B... Butterworth.. Tien.J. McGraw-Hill. M. McGraw-Hill.. Prausnitz.U. 1984. M. Sherwood. Kast.. C. G.F. Butterworth-Heinemann.B. Wakoo. AIChE Journal.E. New York. Chem Eng Sci. Mass Transfer Coefficient in Cyclic Adsorption and Desorption. 31. N.. and Bischoff. J. W.. 1976.E... No 2. Gas Separation by Adsorption Processes. New York. 27. November 16-18.M. G. Costa. Ruthven. Vol. Chemical and Catalytic Reaction Engineering. 1990. VCH... Scheisser.. The Properties of Gases and Liquids.. Reid. Weinheim. pp 11-15. Carver. C. Chi. of Japan. Adsorption aus der Gasphase. 1988.N.9 Reference List for Adsorption Processes Bird. Transport Phenomena. American Institute of Chemical Engineers. D. Suzuki. Yang. 1976. J.. 9 Reference List for Adsorption Processes 298 . Adsorption Calculations and Modeling. Adsorption of Binary and Ternary Hydrocarbon Gas Mixtures on Activated Carbon: Experimental Determination and Theoretical Prediction of the Ternary Equilibrium Data. John Wiley and Sons.B. Boston. Slater. Annual Meeting. 1980. Heinemann.L.. Eng. Lightfoot. New York.. Froment. John Wiley and Sons. E. K.. Stewart.. 1977..M.. Marron. 1.J. W. Butterworth. New York. Carberry. J. 1994. The Principles of Ion Exchange Technology.K. Sotelo. W. 1983. Journal of Chem.. 1960. Calleja. 1987. Principles of Adsorption and Adsorptive Processes.R. E. Vol 16. Nakao. Chemical Reactor Analysis and Design. No. T. 13 Bed model assumptions (ionx) 179 Bed model assumptions (liq) 192 Bed model ports (gas) 14 Bed models (gas) 14 Biased Upwind Differencing Scheme 227 Brunaur.Index A Activating cyclic tasks 257 Adsorbed solution theory (gas) 64 Adsorption isotherms (gas) about 51 choosing 52 list 55 multicomponent mixture isotherms 52 Aspen Custom Modeler™ 230 Aspen Properties™ 284 available 299 Axial dispersion (gas) 22 Axial dispersion (ionx) 182 Axial dispersion (use for differencing schemes) 223 Complex expression step control 248 Compressiblity (gas) 21 Conduction (gas) 65 Conduction (liq) 207. 223 Index 299 .E. 210 Configure form (gas) about 15 bed types 16 internal heat exchanger 19 spatial dimensions of beds 18 Configure form (ionx) 179 Configure form (liq) 192 Configure form tabs (gas) Energy Balance 64 General 20 Isotherm 51 Kinetic Model 31 Material/Momentum Balance 22 Procedures 76 Reaction 73 Configure form tabs (ionx) General 180 Isotherm 185 Kinetic Model 183 Material/Momentum Balance 180 Configure form tabs (liq) Energy Balance 206 General 193 Isotherm 200 Kinetic Model 196 Material/Momentum Balance 193 Procedures 213 B B.E.T isotherm (gas) 58 B. Emmet and Teller See B.T Burke-Plummer equation (gas) 26 C Central differencing schemes 222.E. Multilayer isotherm (gas) 58 Bed model assumptions (gas) 11. E. 182 Dispersion (liq) 193 Dispersion coefficient (ionx) 180 Dispersion coefficient (liq) 193 Dispersive properties (gas) 27 documentation 297 Dual Layer B. 50 Energy balance assumption (gas) 64 Energy balance assumption (liq) 206 Index 300 . 256 step variables 250 Cycle Organizer block 244 Cycle Organizer window 244 cycle controls 254 cyclic reports 258 cyclic tasks 257 interaction controls 252 step controls 256 step variables 250 Cycle snapshots 255 Cyclic corrections (gas) 49 Cyclic operations 243 Cyclic Recovery report 260 Cyclic reports 258 Cyclic Recovery reports 260 Cyclic Stream reports 259 preparing 258 Cyclic Stream report 259 Cyclic tasks 257 D Darcy's Law (gas) 26 Darcy's law (liq) 195 Deactivating cyclic tasks 257 Demonstration Organizer 269 Demonstrations 268 Density (liq) 196 Discretization methods about 218 choosing 219 list 219 recommended 219 Discretization methods (gas) 20 Discretization methods (ionx) 180 Discretization methods (liq) 193 Dispersion (gas) 23 Dispersion (ionx) 180. 39.T isotherm (gas) 62 Dual-Site Langmuir isotherm (gas) 61 Dual-Site Langmuir isotherms (liq) 201 Dubinin-Astakov isotherm (gas) 59 Dynamic estimation about 236 entering data manually 237 importing data from clipboard 238 E Effective diffusivity (gas) 36.Configure Layer form (gas) 20 Configure Layer form (ionx) 179 Configure Layer form (liq) 192 Connecting controllers 268 Connectivity in flowsheets 267 Consistency checks for flowsheets 281 Constant variables (specifying) 280 Controllers 268 ControlSignal stream 268 Convection (gas) 23 Convection (ionx) 180 Convection (liq) 193 Convert_EstMod script 241 Cycle controls 254 Cycle Organizer about 243 cycle controls 254 Cycle Organizer window 244 cyclic reports 258 cyclic tasks 257 interaction control 252 opening 244 step controls 246. 86 Energy balance equations (liq) 213 Energy Balance tab (gas) 64 Energy Balance tab (liq) 206 Enthalpy (gas) 65 Enthalpy (liq) 208 Equation symbols (gas) 87 Equation symbols (ionx) 189 Ergun equation (gas) 27 Estimated mass transfer coefficient (gas) 50 Estimated Variables tab 232 Estimation converting Estimation Module data 241 dynamic 236 estimated variables 232 Estimation Module 230 methods available 230 performing using Estimation Module 241 recommendations 241 steady-state 233 Estimation methods 241 Estimation Module about 230 converting to Aspen Custom Modeler™ methods 241 defining estimated variables 232 dynamic estimation 236 recommendations 241 steady-state estimation 233 using 241 Estimation Module block 231 Estimation Module form 231 Event-driven step controls 246 Experimental Data tab 233. 81 solid phase 78. 237 Expression Builder dialog box 249 Extended Langmuir isotherm (ionx) 187 Extended Langmuir isotherms (gas) 60 Extended Langmuir isotherms (liq) 201 Extended Langmuir-Freundlich isotherm (gas) 61 Extended Langmuir-Freundlich isotherm (ionx) 187 Extended Langmuir-Freundlich isotherms (liq) 203 F Film model assumption (gas) 31 Film model assumption (ionx) 183 Film model assumption (liq) 197 Flow reversibility 263 Flowsheet specifications See Specifying flowsheets Flowsheet types 269 full 271 intermediate 270 simple 269 Flowsheets about 266 Connectivity 267 Cycle Organizer block 244 demonstrations 268 interactions 275 model types 263 physical property calculations 282 Pressure Interaction diagram 272 reversibility of flow 263 single bed approach 272 specifications 277 templates 268 types 269 Fluid phase energy balance (liq) 214 Fluid thermal conductivity (liq) 210 Flux Limited Differencing Scheme 229 Flux Limiter method? (gas) 21 Freundlich isotherms (gas) 56 Index 301 .Energy balance equations (gas) factors affecting equations 81 gas phase 78. 84 wall 79. 50 gUserGibbs submodel 63 gUserHTC submodel 68 gUserIsothermC submodel 63 gUserIsothermPoi submodel 63 gUserIsothermPp submodel 63 gUserKg submodel 69 gUserKinetic submodel 35 gUserKineticModel submodel 43 gUserMTC submodel 49 I i_Material_Port 267 IAS (gas) 53. 41. 12 Gas model assumption (gas) 21 Gas thermal conductivity (gas) 69 gas_Material_connection 267 Gas-Wall heat transfer coefficient (gas) 72 General tab (gas) 20 General tab (ionx) 180 General tab (liq) 193 Generating cyclic tasks 257 Glueckauf approximation (gas) 49 gUserCompressibility submodel 22 gUserCpa submodel 66 gUserDH submodel 67 gUserDispersion submodel 24 gUserEffDiff submodel 37. 64 IAS (liq) about 200 IAS Freundlich isotherms 204 IAS Langmuir isotherms 204 IAS Langmuir-Freundlich isotherms 205 Purecomponent procedure with IAS isotherm 206 Purecomponent submodel with IAS isotherm 206 IAS Freundlich isotherms (liq) 204 IAS isotherm (gas) 63 IAS Langmuir isotherms (liq) 204 IAS Langmuir-Freundlich isotherms (liq) 205 Ideal Adsorbed Solution theory See IAS Ideal gas (gas) 21 Importing data from Microsoft® Excel dynamic 239 steady-state 235 Initialization for models 280 Interaction control 252 Interactions 252 Interactions between steps 275 Interactions example 275 Intermediate flowsheet 270 H Heat capacity (gas) 66 Heat capacity (liq) 208 Heat exchanger (gas) 19 Heat of adsorbed phase (gas) 65 Heat of adsorbed phase (liq) 208 Heat of adsorption (gas) 66 Heat of adsorption (liq) 208 Index 302 .Freundlich isotherms (liq) 202 Fromm's Scheme 228 Full flowsheet 271 Heat transfer coefficient (gas) 67 Heat transfer coefficient (liq) 209 Heat transfer to environment (gas) 70 Heat transfer to environment (liq) 211 Henry isotherms (gas) 57 Henry's coefficient (gas) 47 Heterogeneous rate dependency (gas) 75 Heterogeneous reactions (gas) 74 Homogeneous rate dependency (gas) 74 Homogeneous reactions (gas) 74 Horizontal beds (gas) 16 G g_Material_Port 267 Gas adsorption processes (overview) 11. 206 lUserKinetic submodel 198 lUserKl submodel 211 lUserMTC submodel 199 M Mass action equilibrium isotherm (ionx) 186 Mass balance equations (gas) additional solid phase 77. 46 Lumped resistance (ionx) 184 Lumped resistance (liq) 197 lUserDH submodel 209 lUserDispersion submodel 195 lUserGibbs submodel 206 lUserHTC submodel 210 lUserIsotherm submodel 205. 44 micro and macropore effects 32 molecular diffusivities 45 particle material balance 36. 44.Internal heat exchanger (gas) 19 Ion-exchange adsorption processes (overview) 178 Ion-exchange equilibria 185 Ion-exchange resins 178 ionx_Material_connection 267 Isotherm assumed for layer (gas) 55 Isotherm assumed for layer (ionx) 186 Isotherm assumed for layer (liq) 200 Isotherm dependency (gas) 64 Isotherm list (gas) 55 Isotherm list (ionx) 186 Isotherm list (liq) 200 Isotherm tab (gas) 51 Isotherm tab (ionx) 185 Isotherm tab (liq) 200 Isothermal conditions (gas) 65 Isothermal conditions (liq) 207 Isotherms (gas) 55 Isotherms (ionx) 185 Isotherms (liq) 199 iUserDispersion submodel 182 iUserIsotherm submodel 187 iUserKinetic submodel 184 iUserMTC submodel 185 Langmuir isotherms (liq) 200 Langmuir-Freundlich isotherm (gas) 57 Langmuir-Freundlich isotherms (liq) 202 Leonard Differencing Scheme 223 Linear isotherm (gas) 59 liq_Material_connection 267 liq_Material_Port 267 Liquid adsorption processes (overview) 191 Lumped resistance (gas) 32. 39 procedures 43 submodels 43 Mass transfer (ionx) 183 Mass transfer (liq) 196 Mass transfer coefficient (gas) 46. 81 factors affecting equations 79 gas phase 77 Mass balance equations (ionx) 188 Mass balance equations (liq) 213 Mass transfer (gas) about 31 lumped resistance 32. 50 K Karman-Kozeny equation (gas) 26 Karman-Kozeny equation (liq) 195 Kinetic model assumption (gas) 31 Kinetic model assumption (ionx) 184 Kinetic model assumption (liq) 197 Kinetic Model tab (gas) 31 Kinetic Model tab (ionx) 183 Kinetic Model tab (liq) 196 Knudson diffusion coefficient (gas) 48 L Langmuir isotherms (gas) 55 Index 303 . 46 Micro and macropore effects (liq) 198 Microsoft® Excel 235.Mass transfer coefficient (ionx) 185 Mass transfer coefficient (liq) 198 Mass transfer driving force (gas) 31 Mass transfer driving force (ionx) 183 Mass transfer driving force (liq) 197 Material balance assumption (gas) 23 Material balance assumption (ionx) 180 Material balance assumption (liq) 193 Material/Momentum Balance tab (gas) 22 Material/Momentum Balance tab (ionx) 180 Material/Momentum Balance tab (liq) 193 Maximum number of cycles 254 Micro and macropore effects (gas) 32. 210 Non-Isothermal conditions (liq) 207 Nonlinearity and numerical methods 218 Non-Reversible Delay models 263 Non-Reversible models 263 Number of heterogeneous reactions (gas) 75 Number of homogeneous reactions (gas) 75 Number of nodes (gas) 21 Number of nodes (ionx) 180 Number of nodes (liq) 193 Numerical methods about 218 Biased Upwind Differencing Scheme 227 Central Differencing Schemes 222. 34. 239 Mixed Differencing Scheme 226 Model configuration (defining) 280 Model specifications 280 Model types 262 Models list of types 263 reversibility 263 types 262 Molecular diffusivities (gas) 45 Molecular diffusivity (ionx) 182 Momentum balance assumption (gas) about 25 constant pressure options 25 pressure driven options 26 Multicomponent mixture isotherms (gas) 52 Myers isotherm (gas) 60 Non-isothermal conditions (liq) 209. 223 Flux Limited Differencing Scheme 229 Fromm's Scheme 228 Leonard Differencing Scheme 223 Mixed Differencing Scheme 226 Quadratic Upwind Differencing Scheme 224 recommended 219 selecting 219 Upwind differencing schemes 221 Upwind Differencing Schemes 222 O Obtain Dynamic Measurements for Experiment DynExpt From Clipboard dialog box 238 Obtain Steady State Experiments From Clipboard dialog box 235 Overall material balance assumption (liq) 196 P Particle material balance See Particle MB options Particle MB 2 option (gas) 39. 50 Particle MB option (gas) 36. 50 Particle resistance coefficients (gas) 34 PDE differencing schemes Biased Upwind 227 Central 222. 223 N New Experiment dialog box dynamic 237 steady-state 233 Nodes (gas) 21 Non-ideal gas (gas) 21 Non-isothermal conditions (gas) 65 Index 304 . Flux Limited 229 Fromm's 228 Leonard 223 Mixed 226 Quadratic Upwind 224 Upwind 221. 76. 184. 187. 83 pUser_g_Cat_Rx_Rate_Pp procedure 75. 206 pUser_l_Kinetic procedure 198 pUser_l_Kl procedure 211 Index 305 . 198 mass transfer coefficient 49. 76. 83 pUser_g_Gibbs procedure 62 pUser_g_HTC procedure 68 pUser_g_Isotherm_C procedure 62 pUser_g_Isotherm_P procedure 62 pUser_g_Isotherm_Poi procedure 62 pUser_g_Kg procedure 69 pUser_g_Kinetic procedure 35. 210 isotherms 62. 222 Peclet number (gas) 23 Peclet number (ionx) 183 Physical property calculations about 282 external applications 284 switching between methods 284 user Fortran 283 Port types 267 Prandl number (gas) 68 Prandl number (liq) 210 Presets for models 280 Pressure (gas) 25 Pressure (liq) 195 Pressure drop assumption (liq) 195 Pressure drop options (gas) 27 Pressure Interaction diagram 272 Pressure Interaction diagram example 272 Problem definition checks for flowsheets 281 Procedures (used in) effective diffusivity 50 fluid thermal conductivity 211 gas thermal conductivity 69 heat of adsorbed phase 66 heat of adsorption 67. 194 molecular diffusivities 46 purecomponent isotherms 206 Procedures tab (gas) 76 Procedures tab (liq) 213 Properties Plus™ 284 pUser_Act_Coeff procedure 64 pUser_g_Cat_Rx_Heat procedure 83 pUser_g_Cat_Rx_Rate_C procedure 75. 81. 43 pUser_g_MTC procedure 49 pUser_i_Dispersion procedure 181 pUser_i_Isotherm_C procedure 187 pUser_i_Isotherm_W procedure 187 pUser_i_Kinetic procedure 184 pUser_i_MTC procedure 185 pUser_l_DH procedure 209 pUser_l_Dispersion procedure 194 pUser_l_Gibbs procedure 206 pUser_l_HTC procedure 210 pUser_l_Isotherm_C procedure 205 pUser_l_Isotherm_W procedure 205. 83 pUser_g_Cat_Rx_Rate_Pp_Sol procedure 75. 83 pUser_g_Gas_Rx_Rate_Pp procedure 74. 83 pUser_g_Compressibility procedure 22 pUser_g_Cpa procedure 66 pUser_g_De procedure 37. 50 pUser_g_DH procedure 67 pUser_g_Diffusivity procedure 46 pUser_g_Dispersion procedure 24 pUser_g_Gas_Rx_Heat procedure 83 pUser_g_Gas_Rx_Rate_C procedure 74. 205 kinetic model 43. 83 pUser_g_Cat_Rx_Rate_C_Sol procedure 75. 41. 199 material balance 24. 209 heat transfer coefficient 68. 181. 185. 210 isotherms 63.T isotherm (gas) 61 Snapshots 255. 182. 184. 187. 209 heat transfer coefficient 68. 255 Single bed approach 252. 198 mass transfer coefficient 49. 272 Single Layer B.pUser_l_MTC procedure 199 Spatial dimensions of beds (gas) 18 Specifying flowsheets checks 281 list of options 277 model specification 280 run time options 279 solver options 277 Static_isotherm model 233 Steady state testing (cyclic) 255 Steady-state estimation about 233 entering data manually 233 importing data from clipboard 234 Step controls 256 Step dependent step control 249 Step interaction control 252 Step interactions 252.E. 275 Step variables 250 Stoichiometric Equilibrium isotherms (liq) 203 Submodels (used in) component isotherms 206 effective diffusivity 50 fluid thermal conductivity 211 gas thermal conductivity 69 heat of adsorbed phase 66 heat of adsorption 67. 185. 199 material balance 24. 205 kinetic model 43. 256 Solid phase energy balance (liq) 214 Solid reactant list (gas) 76 Solid reactants present? (gas) 76 Solver options (specifying) 277 T Task Language 257 Template Organizer 268 Templates 268 Time controls (reason for) 253 Time-driven step controls 246 Toth isotherm (gas) 57 Index 306 . 75 Reaction processes (gas) 73 Reaction tab (gas) 73 Reactions present? (gas) 74 Reactions type (gas) 74 Real Adsorbed Solution theory (gas) 64 Real Adsorbed Solution Theory (gas) 54 Recommended numerical methods 219 Recording cycle information 255 Reference list 292 Reversibility example 264 Reversibility of flow 263 Reversible Flow Setter models 263 Reversible models 263 Reversible Pressure Setter models 263 Rigorous multiple bed approach 272 Run time options (specifying) 279 Running end-of-step scripts 256 S Sherwood number (gas) 47 Simple flowsheet 269 Simulation Messages window 254. 195 Q Quadratic Upwind Differencing Scheme 224 R Radial beds (gas) 18 Radial nodes (gas) 21 Rate dependency (gas) 74. 27 Volmer isotherm (gas) 59 W Wall energy balance (liq) 214 Water softening and purification (ionx) 178 Index 307 . 222 User Multicomponent Procedure isotherm (liq) 205 User Multicomponent Submodel isotherm (liq) 205 User Purecomponent Procedure with IAS isotherm (liq) 206 User Purecomponent Submodel with IAS isotherm (liq) 206 V Variable fields 251 Variable Selector dialog box 250 Velocity (gas) 25 Velocity assumption (liq) 196 Vertical beds (gas) 16. 18.U Upwind differencing schemes 221.