Cstr Startup

cstr_startup.book Page 1 Monday, December 8, 2008 10:34 AM ® Startup of a CSTR SOLVED WITH COMSOL REACTION ENGINEERING LAB 3.5a © COPYRIGHT 2008. All rights reserved. No part of this documentation may be photocopied or reproduced in any form without prior written consent from COMSOL AB. COMSOL, COMSOL Multiphysics, COMSOL Reaction Engineering Lab, and FEMLAB are registered trademarks of COMSOL AB. Other product or brand names are trademarks or registered trademarks of their respective holders. Model Description This model reproduces the results found in Ref. Propylene glycol (PrOH) is produced from the reaction of propylene oxide (PrO) with water (W) in the presence of an acid catalyst: O + H2O H2SO4 HO OH (1) The reaction rate (mol/(m3·s)) is first order with respect to propylene oxide: r 1 = – k 1 c PrO (2) where the rate constant is temperature dependent according to the expression E1 ⎞ k 1 = A 1 exp ⎛ – ----------⎝ RgT⎠ (3) The Arrhenius parameters in Equation 3 are A1 = 4. STARTUP OF A CSTR | 1 . In this example you model the startup phase of a continuous stirred tank reactor (CSTR) used to produce propylene glycol.cstr_startup.000 metric tons produced worldwide each year.358 (J/ mol). Propylene glycol finds wide application as a moisturizer in foods. 1. December 8.71·109 (1/s) and E1 = 75.book Page 1 Monday. The model highlights the use of the predefined CSTR reactor type and also shows how to enter the thermodynamic data needed for energy balances. and cosmetics. The nonisothermal process is described by a set of coupled mass and energy balances that you easily set up and solve in the Reaction Engineering Lab. pharmaceuticals. 2008 10:34 AM Startup of a CSTR Introduction The hydrolysis of propylene oxide into propylene glycol is an important chemical process with 400. i ------dt i = Q + Q ext + ∑ vf. and v is the volumetric flow rate (m3/s). Figure 1: A perfectly mixed CSTR for the production of propylene glycol. In this term. For an incompressible and ideally mixed reacting liquid. Q represents the heat due to chemical reaction (J/s). The species mass balances are d ( ciVr ) -------------------. Vr denotes the reactor volume (m3).= v f. i( hf. The last term signifies heat added as species flow through the reactor. and Qext denotes heat added to the system (J/s).cstr_startup. The time evolution of the nonisothermal reacting system is given by several coupled balance equations. ci is the species molar concentration (mol/m3). December 8. STARTUP OF A CSTR | 2 . represent an average over the temperature interval. hi is the species molar enthalpy (J/mol). Cp. This example assumes that the species heat capacities. for instance by a heat exchanger. the energy balance is Vr dT ∑ ci Cp. The CSTR is a predefined reactor type in the Reaction Engineering Lab. The associated species’ enthalpies are then given by hi = C p. Ri is the species rate expression (mol/(m3·s)). i – hi ) (5) i where Cp.book Page 2 Monday. and T is the temperature (K). 2008 10:34 AM The liquid phase reaction takes place in a continuous stirred tank reactor (CSTR) equipped with a heat-exchanger. i cf. i – vc i + R i Vr dt (4) In Equation 4.i. On the right-hand side. It is further assumed that the mixture density is constant over time.i is the species molar heat capacity (J/(mol·K)). i ( T – T ref ) + hi ( T ref ) (6) where hi(Tref) is the standard heat of formation at the reference temperature Tref. i c f. Methanol (MeOH) is added to the mixture but does not react. MeOH 81.89 m3 vf cf. x⎠ (8) where F is the molar flow rate (mol/s). U is the overall heat transfer coefficient (J/(K·m2·s)).PrOH 192.cstr_startup. and A represents the heat exchange area (m2).6 J/(mol·K) Heat capacity of PrOH Cp.47·10 m /s 3 2903 mol/m Volumetric flow rate Concentration of PrO in feed stream 3 cf.6·10 J/mol Enthalpy of formation of PrOH at Tref href.W -286. x ( T x – T ) ⋅ 1 – exp ⎛ ------------------⎞ ⎝ F x C p. 2008 10:34 AM The heat of reaction is given by Q = – Vr ∑ Hj rj (7) j where Hj is the enthalpy of reaction (J/mol). which in this case is water.4 J/(mol·K) Heat capacity of heat exchanger medium 3 href.MeOH -238.W 75. The following table summarizes additional parameters describing the reactor setup and process conditions: PARAMETER VALUE Vr 1.1·103 J/mol Enthalpy of formation of W at Tref 3 href.W 36291 mol/m Concentration of W in feed stream cf.5·10 J/mol Enthalpy of formation of PrO at Tref href.4 J/(mol·K) Heat capacity of W Cp.6 J/mol Enthalpy of formation of MeOH at Tref Tf 297 K Feed stream temperature STARTUP OF A CSTR | 3 .PrO -153.book Page 3 Monday. and rj denotes the reaction rate (mol/(m3·s)).MeOH 3629 mol/m3 Concentration of MeOH in feed stream 3 c0. Tx is the inlet temperature of the heat exchanger medium.PrOH -525.6 J/(mol·K) Heat capacity of MeOH Cpx 75.W 55273 mol/m Initial concentration of W in the reactor Cp.PrO 146. The subscript x refers to the heat exchanger medium.5 J/(mol·K) Heat capacity of PrO Cp.PrO DESCRIPTION Reactor volume -3 3 3. The heat added by the heat exchanger is given by UA Q ext = Fx C p. December 8. Figure 2: Concentrations of reactant PrO (mol/m3) after 4 hours of operation (left) and reactor temperature (K) after 4 hours of operation (right). The same result STARTUP OF A CSTR | 4 . December 8.book Page 4 Monday. respectively). Initially both the reactant concentration and the temperature oscillate around their respective steady-state values (491 mol/m3 and 336 K. Results Figure 2 shows the concentration of PrO (mol/m3) and the reactor temperature (K) as a function of reaction time.cstr_startup. 2008 10:34 AM PARAMETER VALUE DESCRIPTION T0 297 K Initial reactor temperature Tref 293 K Reference temperature Tx 289 K Temperature of heat exchanger medium at inlet Fx 126 mol/s Heat exchanger medium molar flow UA 8441 J/(s·K) Heat exchange parameter The model described here is readily set up and solved using the predefined CSTR reactor type in the Reaction Engineering Lab. Figure 4 shows the concentration-temperature phase plane for three initial condition sets: (cPrO = 0. T0 = 340 K). STARTUP OF A CSTR | 5 . Figure 3: Trajectory in the concentration-temperature phase plane. In the process modeled here. The model predicts that the reactor temperature passes a maximum value higher than the steady-state temperature. From a safety perspective it is therefore relevant to look closer at possible sets of initial conditions to see if process operation limits are violated. (cPrO = 0. it is undesirable to exceed a reactor temperature of 355 K to avoid undesirable side reactions and not damage reactor equipment. 2008 10:34 AM can be illustrated by a trajectory in the concentration-temperature phase plane as presented in Figure 3.book Page 5 Monday. and (cPrO = 1400. Safety limit Figure 4: Trajectories in the concentration-temperature phase plane for three sets of initial conditions. T0 = 297 K).cstr_startup. December 8. T0 = 340 K). 2008 10:34 AM The plot shows that all investigated initial conditions converge to the same steady state. 553–559. Fogler. 1999. However. pp. Prentice Hall PTR. STARTUP OF A CSTR | 6 .cstr_startup.book Page 6 Monday.. Reference 1. Example 9-4. starting with cPrO = 1400 mol/m3 and T0 = 340 K leads to violation of the temperature safety limits. Elements of Chemical Reaction Engineering 3rd Ed. S. December 8. H.