Emirates Journal for Engineering Research, 17 (1), 9-16 (2012) (Regular Paper) MODELING AND CONTROL OF ACETYLENE HYDROGENATION PROCESS Salam Al-Dawery1, Haider M. Dakhil2 Department of Chemical Engineering, University of Nizwa, Oman, E-mail:
[email protected] 2 Department of Chemical Engineering, University of Baghdad, Baghdad, Iraq, E-mail:
[email protected] 1 (Received November 2010 and Accepted May 2011) ﻟﻘﺪ ﺗﻢ ﺗﻄﻮﺑﺮ.ﻟﻘﺪ ﺗﻢ اﻟﺤﺼﻮل ﻋﻠﻰ اﻟﻨﻤﻮذج اﻟﺮﻳﺎﺿﻲ ﻟﻌﻤﻠﻴﺔ هﺪرﺟﺔ اﻻﺳﺘﻴﻠﻴﻦ اﻟﺼﻨﺎﻋﻴﺔ و ﻣﻦ ﺛﻢ اﺳﺘﺨﺪاﻣﻬﺎ ﻻﻏﺮاض اﻟﺴﻴﻄﺮة ﻟﻔﺪ ﺗﻢ ﺗﻤﺜﻴﻞ اﻟﻤﻔﺎﻋﻞ.هﺬا اﻟﻨﻤﻮذج اﻟﺮﺑﺎﺿﻲ ﻟﻴﺸﻤﻞ ﺟﻤﻴﻊ وﺣﺪات اﻟﻌﻤﻠﻴﺔ اﻟﺼﻨﺎﻋﻴﺔ ﻣﺜﻞ اﻟﻤﻔﺎﻋﻞ واﻟﻤﺒﺎدﻻت اﻟﺤﺮارﻳﺔ وﻏﺒﺮهﺎ ﻻﻏﺮاض. ﺑﻴﻨﻤﺎ ﺗﻢ ﺗﻤﺜﺒﻞ اﻟﻤﺒﺎدﻻت اﻟﺤﺮارﻳﺔ ﺑﺪاﻟﺔ ﺗﺤﻮﻳﻞ ﻣﻦ اﻟﻤﺮﺗﺒﺔ اﻻوﻟﻰ,اﻟﺮﺋﻴﺴﻲ ﺑﺪاﻟﺔ ﺗﺤﻮﻳﻞ ﻣﺮﺗﺒﺔ ﺛﺎﻧﻴﺔ ﻣﻊ ﺗﺎﺧﻴﺮ زﻣﻨﻲ ﺟﻤﻴﻊ اﻟﻨﺘﺎﺋﺞ آﺎﻧﺖ ﺿﻤﻦ اﻟﻤﺴﺘﻮى اﻟﻤﻘﺒﻮل,(PID ) ﺗﻢ اﺳﺘﺨﺪام ﻧﻈﺎم ﺳﻴﻄﺮة ﻋﺎم,اﻟﺴﻴﻄﺮة ﻋﻠﻰ وﺣﺪات ﻋﻤﻠﻴﺔ اﻟﻬﺪرﺟﺔ Mathematical model for an industrial acetylene hydrogenation plant was developed and then used for control purposes. The developed model covers all individual units of the plant such as reactor, cooler, steam heater etc. The key reaction of the plant was modeled by a second order transfer function plus dead time, while the heating and cooling units are modeled by first order transfer function. A conventional PID controllers were applied to control the plant units, an acceptable results were obtained. 1. INTRODUCTION The cracking of petrochemical naphtha with vapor produces a stream composed mainly of ethylene and also of paraffins, diolefins, aromatics, and small amount of acetylene. The ethylene is mainly used in the production of polymers, especially polyethylene[1]. Small amounts of acetylene, on the order of parts per million, are harmful to the catalysts used in polymerization[2]. Therefore, the acetylene in the ethylene stream must be hydrogenated with a minimum loss of ethylene. Polyethylene has been key product for many industries since 1960's. The feed of the polymerization reactor, which comes from the olefin plant, is a mixture of hydrocarbons mainly consisting ethylene. An undesired impurity in the ethylene stream is acetylene at approximately 2% to 30% of the effluent of the olefin plant which may lead to undesirable polymer properties; the amount of acetylene in the feed of the ethylene polymerization reactor should not exceed 2-3 ppm[3]. It is harmful contaminant in polymer grade ethylene, so the removal of acetylene is a key step in the purification process. The most effective method for removing acetylene, down to typical levels of 2-3 ppm, is selective hydrogenation over palladium catalysts in multi-bed adiabatic reactor. The term selective is used as the conditions which promote the hydrogenation of acetylene to ethane. Cider[4] studied the hydrogenation of acetylene, ethylene and propylene at transient conditions caused by cross-desorption of carbon monoxide due to a pulse of acetylene. Mathematical modeling of the transient reaction system showed that a simple model is able to explain the competition for the active sites and the difference in reactivity Schbib[2] studied the kinetics of acetylene hydrogenation in the presence of large amounts of ethylene in a laboratory flow reactor. Experiments were carried out using a Pd/α-Al2O3 commercial catalyst and a simulated cracker gas mixture at varying temperature and pressure. Gobbo[5] discussed the modeling, simulation, and dynamic optimization of an industrial reaction system for acetylene hydrogenation. The process consists of three adiabatic fixed-bed reactors, in series, with interstage cooling. The model is able to satisfactorily predict the outlet temperature and concentrations of ethane, acetylene, methylacetylene, and propadiene in each reactor. The acetylene conversion and ethylene selectivity profiles were optimized for the reactors, taking into account catalyst deactivation and process constraints. Therefore, the removal of acetylene is a key in the purification process. The most effective method for 9 Salam Al-Dawery. steam heater etc. Reaction Rate and Mechanism The primary overall reactions taking place in the reactor are (several side reactions referred to green oil would be ignored[3]) C2H2 + H2 → C2H4 C2H4 + H2 → C2H6 reaction 1 reaction 2 The heat balance equation for the fluid (gas mixture) is presented in equation below Several side reactions which lead to formation of C4 hydrocarbons and the heavy oligomer referred to as green oil were ignored[2]. down to 2-3 ppm. Divided above equation by Δx and differentiated with limit Δx→ 0 yield the equation below However the heat balance in the reactor for both solid and fluid has to share volume provided by the dimensions of the reactor such as the voidage ε. is selective hydrogenation over palladium catalyst in a multi-bed adiabatic reactor[6. cooler.8]. each of the plant units was modeled and then simulated using MatLab for which all the transient responses were obtained. Vol. [x] denotes the concentration of the species.1. It was highly non-linear and had many states corresponding to points on the finite difference mesh used to solve the partial differential equations. Rc and Re are ratios between adsorption equilibrium constants as follows: 10 Emirates Journal for Engineering Research. Mass balance Looking at small volume of the reactor ΔV. No. ACETYLENE PLANT MATHEMATICAL MODEL The acetylene hydrogenation plant consists of many units such as converter. k2. gives CO acts as a temporary poison by depriving C2H2 and C2H4 of surface area. The heat balance will be as follow Assuming that transferring between the solid and the fluid is infinitely good such that Tf = Ts = T. The * refers to the concentration on the catalyst surface.7. 2. as shown in Figure 1. 2012 . The mechanism for reaction taking place in the acetylene hydrogenation reaction is complex as modeled by four consecutive steps. 17. It was possible to describe the rates of the two reactions using: The model outlined above provides considerable insight into the mechanism and the dynamic of the reactor.1 Acetylene Converter Model and Dynamics The material and energy dynamic models for acetylene converter as well as the reaction kinetic can be summarized as presented below. the heat balance can be expressed as in the expression below: 2. but it was unsuitable for controller design[6. k1. thereby reducing their concentrations in the adsorbed phase. EA1 and EA2 are the appropriate pre-exponential factors and activation energies. Haider Dakhil removing acetylene. The objective of this work is to develop a mathematical model that suitable for control purposes and to study the dynamic behaviors of the acetylene hydrogenation plant. 7]. the mass balance will follow the conservation law: Heat balance For the solid catalyst in a small element Δx of the reactor. 1. 2012 Figure 1 Acetylene Hydrogenation Plant Layout with operating conditions 11 . Vol. 17.Modeling and Control of Acetylene Hydrogenation Process Emirates Journal for Engineering Research. No. The same second.4 minutes.Time delay can be found 2. 3.14 0C/ (tone/hr). Thus.The time constant is fixed at 1. There was a gain (K) associated with each input.The input temperature gain for acetylene concentration model KCin which represents the relationship between outlet acetylene temperature and inlet acetylene concentration at study state condition and equal to 0. Inlet to outlet temperature gain versus temperature rise[7] Figure 3.order lag term was used for all inputs. flow rate (F) and carbon monoxide concentration (CO). then KF=. By substituting all numerical values regarding parameters in equations 1 and 2. 2012 . 7. feed flow rate and carbon monoxide concentration are shown in Figures 4 to 9. 4.5 minutes as calculated from Figure 3. Whilst the dynamic model have been subjected to some of linearization following by model order reduction. Therefore the Acetylene concentration model can be described by the following equation: The dynamic responses of the converter (outlet temperature and concentration) to step changes in feed temperature. the energy linearized model for the converter can be represented by the following transfer function: Where.Assuming the feed flow rate of gases mixture is equal to 52630 kg/hr.015 oC/ppm 5. KTine(−τ DS ) K KF Tin + F + CO 2 CO (2) 2 2 (τs +1) (τs +1) (τs +1) The numerical values for parameters of the above two equations can be determined based on the followings: CC2H 2out = 1. Time delay versus inverse of flow[7] 12 Emirates Journal for Engineering Research.the ratio between gains (KF/KTin) was -0. 8.The carbon monoxide concentration gain is constant and equal to -0. the converter material and energy balances can be modeled by the following matrix: Figure 2. in addition the effect of a change in the inlet temperature is delayed by dead time τD. 17.assuming temperature rise across the converter bed equal to 20 oC 2.0. the resultant linear model would contain all the uncertainty of the full model plus the additional errors due to linearization and model order reduction. Haider Dakhil A linear low order model was needed.3 oC/oC as calculated from Figure 2.001 oC/ppm 6. No. Vol.Salam Al-Dawery. Tout = K Tin e ( −τ D S ) (τ s + 1) 2 Tin + KF (τ s + 1) 2 F+ K CO (τ s + 1) 2 CO (1) This model predicted the outlet temperature (Tout) as a function of the inlet temperature (Tin).322.the value of the input temperature gain KTin equal to 2. Composition dynamics are assumed to be similar to that of temperature dynamics.1. 0098 F (S ) S +1) Figure 7 Acetylene concentration response to a step change in the feed flow rate 1.098S+1) 0.0032 ( 0.Modeling and Control of Acetylene Hydrogenation Process Figure 4 Temperature response of acetylene converter to a step change in inlet temperature Figure 8 Temperature response of acetylene converter to a step change in carbon monoxide concentration Figure 5 Acetylene concentration response to a step change in the inlet temperature Figure 9 Acetylene concentration response of acetylene converter to a step change in carbon monoxide concentration 2. 2012 13 . No.3 Intercooler and Aftercooler Dynamic Model The mathematical model for this shell and tube exchanger type (see Figure 1) was derived based on unsteady-state energy balance and represented by the following transfer function: Tout ( S ) = − 0. 17.098 S +1) .2 Steam Heater Dynamic Model The mathematical model for the shell and tube exchanger (see Figure 1) was derived based on unsteady-state energy balance and represented by the following transfer function: (3) Figure 6 Temperature response of acetylene converter to a step change in the feed flow rate This model predicted the outlet temperature (Tout) as a function of the inlet temperature (Tin).997 FW (S) + (0. There was a gain (K) associated with each input.417 (0. 2.0043 Tin ( S ) + ( 0. Vol. steam flow rate (Fs) and feed flow rate (F). The steam heater responses to different step changes are shown in Figures 10 to 12.098 T (S ) S+1) W (4) Emirates Journal for Engineering Research. 1. 2012 .1. Haider Dakhil Figure 10 Temperature response of steam heater to a step change in inlet temperature Figure 13 Temperature response of intercooler to a step change in inlet temperature Figure 11 Temperature response of steam heater to a step change in steam feed flow rate Figure 14 Temperature response of intercooler to a step change in feed flow rate Figure 12 Temperature response of steam heater to a step change in feed flow rate This model predicted the outlet temperature (Tout) as a function of the inlet temperature (Tin). The cooler responses to different step changes are shown in Figures 13 to 16. No.Salam Al-Dawery. Vol. 17. cooling water flow rate (Fw). cooling water temperature (Tw) and feed flow rate (F). Figure 15 Temperature response of intercooler to a step change in cooling water flow rate 14 Emirates Journal for Engineering Research. There was a gain (K) associated with each input. 8 Figure 18 Responses of outlet temperature and acetylene of the converter under PID controller. 1. it appears that the real process was highly non-linear. Also. 17. 4. the implementation of control system was shows a reliable and stable responses which agreed to that of process behavior. Vol. ACETYLENE PLANT CONTROL To study the dynamic behaviors of the acetylene hydrogenation plant under control. No. for the case of steam heater and intercooler.5 0. The parameters of all controllers were determined by using the Cohen and Coon method. DISCUSSION AND CONCLUSIONS Figure 16 Temperature response of intercooler to a step change in cooling water temperature From the mathematical model of the converter in acetylene process. 2012 15 .5 Controller Parameters T1 TD 2. a conventional PID controller was used to control each units of the plant based on their derived models. The best controller settings are presented in the Table below. and thus. Kc -2. Also. the closed loop responses of outlet temperatures under PID controller are shown in Figures 19 and 20 respectively. in which inlet temperature was chosen as manipulated variables and outlet temperature is the controlled variable. Similarly. The temperature dynamic responses of both systems were at an acceptable level. The dynamic behaviors of steam heater and intercooler and aftercooler exchangers were both described by first order lag model. The construction of block diagram for temperature control of the converter is shown Figure 17. Figure 17 Closed loop block diagram for Acetylene converter 3. many dynamic responses (both outlet temperature and acetylene concentration) were obtained and all gave a reliable and acceptable level of accuracy. PID Emirates Journal for Engineering Research. it can be recommended that the derived model for the Acetylene plant can be considered for applying advanced control strategies such as feedforward and or plant wide control for the overall plant control improvements. a linearized model has been derived and represented by second order lag with dead time. From above. To test the acceptability of the model.Modeling and Control of Acetylene Hydrogenation Process The responses of outlet temperature and acetylene concentration of the converter under PID controller are shown in Figure 18. and similarly for responses under control systems. J. Secchi. Vol. P. and Errazu.3. M. R. vol. Int. Figure 19 Temperature response of Steam Heater to a negative 100% step change in feed flow rate Figure 20 Temperature response of the Intercooler to a negative 100% step change in feed flow rate 16 Emirates Journal for Engineering Research. Vol.Sc. Industrial Process Control...Ind. AIChE Workshop. Ghoorchian. P.. H. 5. and optimization of afront-end system for acetylene hydrogenation reactors" . E. Chem. 7. 1437-1443.4 Oct. Hobbs. Chem. 2. H.. and Ferreira. Hydrogenation of Acetylene: Kinetic Studies and Reactor Modeling". Chem. M. Proc. 3. A. C. 715.. Inc. University of Baghdad..Salam Al-Dawery. W. Gobbo. L. A. A. N.. 7. N.M. pp. Cont. Eng. React. 1496-1505.1. 17. N.21 no. Schbib. Haider Dakhil REFERENCES 1. New York. G. Soares. M. (2004) "Modeling. 30 . 6. (2005). J./Dec. Thesis. Peacock. "(1996) Kinetics of Front-End Acetylene Hydrogenation in Ethylene Production". S. Weiss. vol. M. Gigola. 6.. pp.35 pp. (2000) "Handbook of Polyethylene". No. 2012 .. 1. J. Basel. R. Chem. Res. Garcia. Mostoufi. (2007) "Integrated multi-unit controller design for chemical process plant". vol.. (1979) "Computer control of Acetylene Hydrogenation Process". R. (1996) "Modeling and control of an acetylene converter". Ind. A.. Eng. 8. Marcel Dekker. simulation. Dakhil. J. Vol.. 4. Iraq. No. A. J.. R. A. Mandarin. . Eng. Res. G. and Sotudeh-Gharebagh.Braz. (1993) "Hydrogenation of Acetylene at Transient Conditions in the Presence of Olefins and Carbon Monoxide over Palladium/Alumina". J. Schoon. Eng... Cider.