Dynamic Simulation and Optimization of a Dual-Type Methanol Reactor Using Genetic Algorithms

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<ul><li><p>Research Article</p><p>Dynamic Simulation and Optimizationof a Dual-Type Methanol Reactor UsingGenetic Algorithms</p><p>In this investigation, a dynamic simulation and optimization for an auto-thermaldual-type methanol synthesis reactor was developed in the presence of catalystdeactivation. Theoretical investigation was performed in order to evaluate theperformance, optimal operating conditions, and enhancement of methanol pro-duction in an auto-thermal dual-type methanol reactor. The proposed reactormodel was used to simulate, optimize, and compare the performance of a dual-type methanol reactor with a conventional methanol reactor. An auto-thermaldual-type methanol reactor is a shell-and-tube heat exchanger reactor in whichthe first reactor is cooled with cooling water and the second one is cooled withsynthesis gas. The proposed model was validated against daily process data mea-sured of a methanol plant recorded for a period of 4 years. Good agreement wasachieved. The optimization was achieve by use of genetic algorithms in two stepsand the results show there is a favorable profile of methanol production ratealong the dual-type reactor relative to the conventional-type reactor. Initially, theoptimal ratio of reactor lengths and temperature profiles along the reactor wereobtained. Then, the approach was followed to get an optimal temperature profileat three periods of operation to maximize production rate. These optimizationapproaches increased by 4.7% and 5.8% additional yield, respectively, through-out 4 years, as catalyst lifetime. Therefore, the performance of the methanol reac-tor system improves using optimized dual-type methanol reactor.</p><p>Keywords: Catalysts, Dynamic optimization, Genetic algorithms, Methanol, Modeling</p><p>Received: October 27, 2007; revised: December 28, 2007; accepted: January 13, 2008</p><p>DOI: 10.1002/ceat.200700408</p><p>1 Introduction</p><p>Methanol is a primary liquid petrochemical that is producedin large scale worldwide. It is used as fuel, as solvent and as abuilding block to produce chemical intermediates. It is pro-duced from synthesis gas in a large scale throughout the world.In the methanol synthesis process, synthesis gas (CO2, CO,and H2) converts to methanol in a tubular packed bed reactor.The synthesis gas is produced from natural gas in the reformersection. Such a reactor usually resembles a vertical shell andtube heat exchanger. A conventional type of methanol reactorincludes tubes that are packed with catalyst pellets. Boilingwater is circulating in the shell side to remove the heat of</p><p>exothermic reactions. Methanol synthesis reactions occur in aset of vertical tubes packed by Cu-based catalysts. The reactorthat is presented in this study is a Lurgi-type [1] which in-cludes a shell-and-tube heat exchanger that is installed verti-cally and operates at a pressure in the range of 7677 bar. Heatof exothermic reactions is removed from tubes by boilingwater, flowing in the shell of the reactor as coolant. The cata-lyst deactivates in the reactor mainly due to thermal sintering,in the course of the process. Thus, reactor operation is a dy-namic state.The parameters affecting the production rate in an indus-</p><p>trial methanol reactor are parameters such as temperature andcatalyst deactivation. In the case of reversible exothermic reac-tions such as methanol synthesis, selection of a relatively lowtemperature permits higher conversion but this must be bal-anced against a slower rate of reaction leading to a largeamount of catalyst. To the left of the point of maximum pro-duction rate, increasing temperature improves the rate of reac-tion, which leads to more methanol production. Nevertheless,</p><p> 2008 WILEY-VCH Verlag GmbH &amp; Co. KGaA, Weinheim http://www.cet-journal.com</p><p>Fatemeh Askari1</p><p>Mohammad Reza</p><p>Rahimpour1</p><p>Abdolhossein Jahanmiri1</p><p>Ali Khosravanipour</p><p>Mostafazadeh1</p><p>1Chemical and PetroleumEngineering Department,School of Engineering, ShirazUniversity, Shiraz 71345 Iran.</p><p>Correspondence: Prof. M. R. Rahimpour (rahimpor@shirazu.ac.ir),Chemical and Petroleum Engineering Department, School of Engineer-ing, Shiraz University, Shiraz 71345 Iran.</p><p>Chem. Eng. Technol. 2008, 31, No. 4, 513524 513</p></li><li><p>as the temperature increases, the deterio-rating effect of equilibrium conversionemerges and decreases methanol produc-tion [2].There are several studies on methanol</p><p>process in the literature. Lange presented areview of methanol synthesis technologies[3]. Rahimpour et al. investigated enhance-ment of methanol production using opti-mized Pd-Ag membrane in a methanolsynthesis reactor [4]. Kordabadi and Ja-hanmiri [5, 6] performed a study on theoptimization of a methanol synthesis reac-tor to enhance overall production and anoptimization investigation on the metha-nol synthesis reactor in the face of catalystdeactivation using multi-objective geneticalgorithms. Recently, Rahimpour and Lot-finejad presented a dynamic model for aPd-Ag membrane dual-type methanol syn-thesis reactor [7].In this study, an auto-thermal dual-type</p><p>reactor where the first reactor is cooled by saturated water andthe second reactor is cooled by feed gas has been developed.The dynamic heterogeneous one-dimensional model was con-sidered. The basic structure of the model is composed of heatand mass balance conservation equations coupled throughthermodynamic and kinetic relations, as well as auxiliary cor-relations for predicting physical properties. Due to stark tem-perature effects on methanol synthesis kinetics and catalyst de-activation, optimal temperature is an important factor foroptimal operations of the methanol reactor. The purpose ofthis study is to optimize the methanol synthesis reactor whichconsists of two procedures. An optimization program was de-veloped to obtain more methanol production during a periodof operation. The first approach is to find the optimal ratio ofreactor lengths and optimal cooling temperature profiles alongthe dual-type methanol synthesis reactor to enhance methanolproduction during 1400 days of operation. In second proce-dure, the optimal temperature profiles at three periods of op-eration were performed to reach the maximum methanol pro-duction rate. Optimization tasks were investigated using noveloptimization tools, genetic algorithms. Genetic algorithms areimitations of natural evolution and are believed to be the mostpowerful optimization technique amongst the stochastic meth-ods.</p><p>2 Process Description</p><p>2.1 Conventional Methanol Reactor (CMR)</p><p>Fig. 1 shows the scheme of a single-type methanol reactor[8]. Methanol synthesis is performed by passing a synthesisgas containing hydrogen, carbon dioxide, carbon oxide, andany inert gases at an elevated temperature and pressurethrough several beds of methanol synthesis catalyst. A single-</p><p>type (conventional-type and real plant) methanol reactor isbasically a vertical shell-and-tube heat exchanger. The synthe-sis gas is fed to the tube side of the reactor and the coolingwater flows into the shell side in co-current mode. The cata-lyst is packed in vertical tubes and surrounded by boilingwater. The methanol synthesis reactions are carried out overthe commercial CuO/ZnO/Al2O3 catalyst. The heat ofexothermic reactions is transferred to the boiling water andsteam is produced. The product goes to a heat exchangerand its heat transfers to the feed stream. Finally, the coldproduct is transported to the distillation section. In fact,methanol is recovered by cooling the product gas stream tobelow the dew point of the methanol and separation of theproduct as a liquid.The technical design data of the catalyst pellet and input</p><p>data of the conventional-type methanol reactor are summa-rized in Tabs. 1 and 2.</p><p> 2008 WILEY-VCH Verlag GmbH &amp; Co. KGaA, Weinheim http://www.cet-journal.com</p><p>Figure 1. Schematic of a conventional type methanol reactor [8].</p><p>Table 1. Catalyst and reactor specifications [8].</p><p>Parameter Value Unit</p><p>qs 1770 [kg m3]</p><p>dp 5.47103 [m]</p><p>cps 5.0 [kJ kg1 K1]</p><p>kc 0.004 [Wm1 K1]</p><p>av 626.98 [m2 m3]</p><p>ess</p><p>0.123 []</p><p>Number of tubes 2962 []</p><p>Tube length 7.022 [m]</p><p>514 F. Askari et al. Chem. Eng. Technol. 2008, 31, No. 4, 513524</p></li><li><p>2.2 Auto-Thermal Dual-Type Methanol Reactor(ADMR)</p><p>Fig. 2 shows the schematic diagram of an auto-thermal dual-type methanol reactor configuration. This process is mainlybased on two-stage reactors consisting of water-cooled andgas-cooled reactors. The synthesis gas is fed to the tube side ofthe gas-cooled reactor (the second reactor). The cold feed syn-thesis gas for the first reactor is routed through tubes of thesecond reactor in a counter-current flow with reacting gas andthen heated by heat of reaction produced in the shell. The out-let synthesis gas from the second reactor is fed to the shell ofthe first reactor (water-cooled) and the chemical reaction isinitiated by the catalyst. The heat of reaction is transferred tothe cooling water inside the tubes of the reactor. At this stage,the synthesis gas is partly converted to methanol in a singlewater-cooled reactor. The methanol-containing gas leaving the</p><p>first reactor is directed into the shell of the second reactor. Fi-nally, the product is removed from the downstream of the sec-ond reactor. The large inlet gas pre-heater normally requiredfor synthesis by a single water-cooled reactor is replaced by arelatively small trim pre-heater. As fresh synthesis gas is onlyfed to the first reactor, no catalyst poisons reach the second re-actor. The poison-free operation and the low operating tem-perature results in a virtually unlimited catalyst service life forthe gas-cooled reactor. In addition, reaction control also pro-longs the service life of the catalyst in the water-cooled reactor.If the methanol yields in the water-cooled reactor decreases asa result of declining catalyst activity, the temperature in the in-let section of the gas-cooled reactor will rise with a resultantimprovement in the reaction kinetics and hence, an increasedyield in the second reactor.</p><p>3 Mathematical Model of the Reactors</p><p>3.1 First Reactor</p><p>The reactor simulation includes steady state and dynamicmodels. The steady state simulation illustrates reactor perfor-mance with a fresh catalyst in the absence of catalyst deactiva-tion. Methanol reactors are modelled by a dynamic heteroge-neous model, which is a conventional model for a catalyticreactor with heat and mass transfer resistances. The balancestypically account for accumulation, convection, and transportto the solid phase. In this model, the following assumptionswere considered: one-dimensional plug flow in the shell andtube sides, the non-ideality of gas is neglected, the axial disper-sion is neglected here, and the heat loss by a coolant is consid-ered. The mass and energy balances for the solid phase are ex-pressed by:</p><p>i = 1,2,...,N1 (1)</p><p>esctyist kgictavyi yis g riqBa</p><p>qBcpsesdTsdt</p><p> avhf T Ts qBaNi1</p><p>g riDHf i 2</p><p>where yis and Ts are the solid-phase mole fraction and temper-ature, respectively.1) The following two conservation equationsare written for the fluid phase:</p><p>i = 1,2,...,N1</p><p>eBctyit </p><p>FtAc</p><p>yiz avctkgiyis yi 3</p><p>eBctcpgTt </p><p>FtAc</p><p>cpgTz avhf Ts T</p><p>pDiAc</p><p>UcTcT (4)</p><p> 2008 WILEY-VCH Verlag GmbH &amp; Co. KGaA, Weinheim http://www.cet-journal.com</p><p>Table 2. Input data of the reactor [8].</p><p>Feed conditions Value Unit</p><p>Composition (mol %)</p><p>CH3OH 0.50 []</p><p>CO2 9.40 []</p><p>CO 4.60 []</p><p>H2O 0.04 []</p><p>H2 65.90 []</p><p>N2 9.30 []</p><p>CH4 10.26 []</p><p>Total molar flow rate per tube 0.64 [mol s1]</p><p>Inlet temperature 503 [K]</p><p>Temperature of coolant 524 [K]</p><p>Pressure 76.98 [bar]</p><p>Figure 2. Schematic of an auto-thermal dual-type methanol reac-tor.</p><p>1) List of symbols at the end of the paper.</p><p>Chem. Eng. Technol. 2008, 31, No. 4, 513524 Dynamic optimization 515</p></li><li><p>where yi and T are the fluid-phase mole fraction and tempera-ture, respectively.For heterogeneous models, several extra correlations for esti-</p><p>mation of mass and heat transfer coefficients are used.</p><p>3.2 Second Reactor</p><p>The mass balance for the gas phase, and mass and heat balancefor the solid phase are the same as for the first reactor but withdifferent initial conditions. The energy balance for the gasphase in the second reactor is as follows:</p><p>CtCpgTtube</p><p>t FtubeAtube</p><p>CPtubeTtube</p><p>z pDiAtube</p><p>UtubeTTtube (5)</p><p>The boundary conditions are as follows:</p><p>z = 0; yi = yis, T = T0 (6)</p><p>while the initial conditions are:</p><p>t = 0; yi = yiSS, yis = yis</p><p>SS, T = TSS, TS = TSSS, a = 1 (7)</p><p>4 Reaction Kinetics</p><p>The three main reactions that occur in the methanol reactorare: the hydrogenation of CO, the hydrogenation of CO2, andthe reversed water-gas shift reaction:</p><p>CO + 2 H2 CH3OH DH298 = 90.55 kJmol1 (8)</p><p>CO2 + 3 H2 CH3OH + H2O DH298 = 49.43 kJmol1 (9)</p><p>CO2 + H2 CO + H2O DH298 = +41.12 kJmol1 (10)</p><p>Reactions (8)(10) are not independent, so that one is a lin-ear combination of the other ones. Kinetics of the low-pressuremethanol synthesis over commercial CuO/ZnO/Al2O3 catalystshas been widely investigated. In this current study, the rate ex-pressions have been adopted from Graaf et al. [9]. The rateequations combined with the equilibrium rate constants [10]provide enough information about the kinetics of methanolsynthesis. The correspondent rate expressions due to the hy-drogenation of CO, CO2, and the reversed water-gas shift reac-tions are:</p><p>r1 k1KCOfCOf 32H2 fCH3OHf</p><p>12H2 KP1</p><p>1 KCOfCO KCO2 fCO2f 12H2 KH2OK12H2</p><p>fH2O(11)</p><p>r2 k2KCO2fCO2f 32H2 fCH3OHfH2Of</p><p>32H2</p><p>Kp21 KCOfCO KCO2 fCO2f 12H2 KH2OK</p><p>12H2</p><p>fH2O(12)</p><p>r3 k3KCO2 fCO2 fH2 fH2OfCOKP3</p><p>1 KCOfCO KCO2 fCO2f 12H2 KH2OK12H2</p><p>fH2O(13)</p><p>The reaction rate constants, adsorption equilibrium con-stants, and reaction equilibrium constants which occur in theformulation of kinetic expressions are tabulated in Tabs. 35,respectively.</p><p>5 Catalyst Deactivation Model</p><p>The catalyst deactivation model for the commercial methanolsynthesis (CuO/ZnO/Al2O3) was presented by Hanken [11].</p><p>da</p><p>dt Kd exp</p><p>EdR</p><p>1</p><p>T 1</p><p>TR</p><p> a5 14</p><p>whereTR, Ed, andKd are the reference temperature, activation en-ergy, and deactivation constant of the catalyst, respectively. Thenumerical value of TR is 513 K, of Ed is 91270 Jmol</p><p>1 and ofKd is0.00439 h1 [12]. Although other deactivationmodels were inves-tigated by other authors, the above model was fitted with indus-trial operating conditions; that is, the model is the only candidatefor the simulation andmodeling of such industrial plants.</p><p>6 Numerical Solution</p><p>The governing equations of the model form a system ofcoupled equations comprising algebraic, partial differential,and ordinary differential equations. This system of equationsis solved using a two-stage approach consisting of a steady-state identification stage followed by a dynamic solution stage.</p><p> 2008 WILEY-VCH Verlag GmbH &amp; Co. KGaA, Weinheim http://www.cet-journal.com</p><p>Table 3. Reaction rate constants [10].</p><p>k AexpB</p><p>RT</p><p> A B</p><p>k1 (4.89 0.29) 107 113000 300</p><p>k2 (1.09 0.07) 105 87500 300</p><p>k3 (9.64 7.30) 1011 152900 11800</p><p>Table 4. Adsorption equilibrium constants [10].</p><p>K AexpB</p><p>RT</p><p> A B</p><p>KCO (2.16 0.44) 105 46800 800</p><p>KCO2 (7.05 1.39) 107 61700 800</p><p>(KH2O/KH21/2) (6.37 2.88) 109 84000 1400</p><p>Table 5. Reaction equil...</p></li></ul>


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