Dynamic modeling of a H2O-permselective membrane reactor to enhance methanol synthesis from syngas c Dynamic modeling of a H2O-permselective membrane reactor to enhance methanol synthesis from syngas c

Dynamic modeling of a H2O-permselective membrane reactor to enhance methanol synthesis from syngas c

  • 期刊名字:天然气化学(英文版)
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  • 论文作者:M.Farsi,A.Jahanmiri
  • 作者单位:Department of Chemical Engineering
  • 更新时间:2020-07-08
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Available online at www.sciencedirect.comJOURNALOFScienceDirectNATURAL GASCHEMISTRYEL SEVIERJourmal of Natural Gas Chemistry 21(2012)407- 414www. elsevier.com/ocate/jngcDynamic modeling of a H2O-permselective membrane reactor to enhancemethanol synthesis from syngas considering catalyst deactivationM. Farsi,A. Jahanmiri*Department of Chemical Engineering, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz 71345, Iran[ Manuscript received October 26, 2011; revised December 12, 2011]AbstractIn this paper, the effect of water vapor removal on methanol synthesis capacity from syngas in a fixed-bed membrane reactor is studied con-sidering long-term catalyst deactivation. A dynamic heterogeneous one-dimensional mathematical model that is composed of two sides isdeveloped to predict the performance of this configuration. In this configuration, conventional methanol reactor is supprted by an alumina-silica composite membrane layer for water vapor removal from reaction zone. To verify the accuracy of the considered model and assumptions,simulation results of the conventional methanol reactor is compared with the industrial plant data under the same process condition. The mem-brane reactor improves catalyst life time and enhances CO2 conversion to methanol by overcoming the limitation imposed by thermodynamicequilibrium. This configuration has enhanced the methanol production capacity about 4.06% compared with the industrial methanol reactorduring the production time.Key wordsmembrane reactor; heterogeneous model; dynamic simulation; composite membrane1. Introductionliterature. Graaf et al. modeled a low pressure methanolsynthesis reactor considering mass transfer resistance inRecently, catalytic hydrogenation of carbon dioxide tocatalyst [1]. They showed that size of the commercialmethanol (MeOH) as a bydrogen rich fuel has atracted grow-CuO/ZnO/Al2O3 catalyst exhibits intraparticle diffusion lim-ing attention. Methanol as the simplest aliphatic alcohols, is aitations. Al-Fadli et al. developed a transient model for acolorless liquid, completely miscible with water and organicmulti bed adiabatic reactor and showed that the feed tem-solvents. It forms an explosive mixture with air and burns withperature is main disturbance in this process [2]. Jahanmiriand Eslamloueyan modeled an industrial methanol reactor andtrial petrochemical products that is used as a fuel, solvent andshowed that the difference between heterogeneous and ho-intermediate for other component production. A great amountmogenous modeling is negligible [3]. Velardi and Barresi pro-of the produced methanol is converted to formaldehyde, aceticposed a multi-stage reactor network with auto-thermal behav-acid and MTBE.ior to promote the methanol reactor performance [4]. Kord-Methanol can be produced from different sources suchabadi and Jahanmiri optimized a low pressure methanol re-as natural gas, coal and biomass. The traditional method foractor to enhance overall production under dynamic conditionmethanol production is based on the direct combination of car-considering different catalyst activity [5]. This optimizationbon monoxide, carbon dioxide and hydrogen gases in a cat-approach enhanced a 2.9% additional yield in methanol re-alytic packed bed reactor. The conventional methanol reactoractor. Recently, a dual-type reactor system instead of a con-is a shell and tube heat exchanger that tubes are packed withventional methanol reactor was proposed by Rahimpour andcatalyst pellets. Boiling water circulates through the shell sideAlizadehhesari [6].of the reactor to remove the generated reaction heat. Due toThe main factors affecting the production rate in the in-the equilibrium behavior of the reactions, methanol conver-dustrial methanol reactor are catalyst deactivation and thermo-sion in the conventional reactor is low and most of the unre-dynamic equilihrim limitatinns. Deray of catalyst activityacted syngas should be circulated in the process.is very com中国煤化_ L ochemical industries,There are several researches on methanol process in thewhich forceYHCN M H Gdy operation. In the* Corresponding author. Tel: +98-71 1-2303071; Fax: +98-711-6287294; E -mail: jahanmir@ shirazu.ac.ir (A. Jahanmiri)CopyrightO2012, Dalian Institute of Chemical Physics, Chinese Academy of Sciences. All rights reserved.doi: 10.1016/S 1003-9953(1 1)60383-6Journal of Natural Gas Chemistiy Vol. 21 No.42012409two concentric pipes. The wall of inner tube is water vapor-3. Reaction kineticspermsclective and in the annular space between inner andouter tubes, methanol synthesis reactions are placed. TheThe kinetic reaction system should be coupled with theouter tube surrounded by cooling water (saturated liquid) andmathematical model to complete simulation. The reactions ofthe heat of reactions is transferred to the cooling water andmethanol synthesis are mainly, CO and CO2 hydrogenationsweep gas stream.and the reversed water-gas shift reaction, as following:Table 1. Base case specifications of studied reactor, catalyst and feedCO+ 2H2 -→CH3OHValue(1)Feed composition (mole percentage)0H298 = -90.55 J. mol~H265.9co4.CO2 +3H2一+ CH3OH + H2OCO2(2)△H298 = -49.43 J. molN29.H2O0.04CHgOH0.5CO2 +H2-→ CO+ H2OCH410.3(3)AH298 = +41.12J. mol :Total molar flow per tube (mols- |)0.64Inlet temperature (K)503In this work, rate expressions have been selected fromInlet pressure (bar)76.98Graaf et al. [16,17]. The selected rate expressions for CO andCatalyst particleCO2 hydrogenation and the reversed water- gas shift reactionsDensity (kg.m~ 3)177re:Particle diameter (m)5.47x 10-3Specific surface area (m2.m -3)626.98Reactork1Kcofcofh2__ fci:OHTube number2962fi2KrzLength of reactor (m)7.022r1=;(1+ Kcofco + Kco,fco2)(H2 + K2/2 Knzoft2o)Bed void fraction0.39(4)Tube inner diameter (m)3.8x 10-2Tube outer diameter (m)4.3x10 2k2Kco2( fo2Jf6/2fH2ofCH3OHf2KBColing water(1 + Kcofco + Kco,fco,)(f2 + kKh2/Knoft2o)Feed -Reaction zone. c888Sweep gas→Ho2-pemsclecive side↑↑1k3Kco2 ( fo,fu2-fH2ofco)KBr3= 7(1 + Kcofco + Kco2fco)(fH2 + Kk=2/2Knofz2o)Figure 2. Schematic for an element of membrane reactor(6Partial pressure difference of water vapor between innerThe reaction rate constants, adsorption equilibriumtube and annular space permits the diffusion of water vaporconstants and reaction equilibrium constants are tabulatedthrough alumina/silica composite membrane layers. The basein Table 3.case specifications of dual-membrane reactor are tabulated inTable 3. Reaction rate constants, adsorption equilibrium constants andTable 2.reaction equilibriuim constantsTable 2. Base case specifications of membrane reactorABParametersk= Aexpk4.89- 63000.1.09- 87500Water membrane tube diameter (inner tube) (m)1.5x 10-2.64- 152900Inner diameter of outer tube (m)4.2x 10-2K= Aexp中国煤化工二:1646800Outer diameter of outer tube (m)4.8x10-MHCNMHG.os61700Sweep gasKr2o/Kx26.3784000Temperature (K)Kp= 104/T-B .513912.621Pressure (bar)74.98KPz306610.592Flow rate (mols-1)0.6-2.029410M. Farsi et al/ Jourmal of Natural Gas Chemistry Vol. 21 No. 420124. Mathematical modeling4.2. Deactivation model4.1. Reaction sideThe loss of catalyst activity, which means the loss of ac-tive surface area, is due to thermal sintering in commercialA one-dimensional heterogeneous mathematical model,low-pressure methanol catalysts. Thus, to get a more practi-based on mass and energy conservation laws, has been devel-cal simulation, deactivation of catalyst has been considered inoped to simulate the membrane reactor under dynamic condi-the mathematical model. The presented deactivation modelstion. In this model the following assumptions are considered:in the literature for commercial methanol catalysts are tem-●Radial dispersion of mass and energy is negligible.perature dependent without considering components effect on●The gas mixture is an ideal gas.sintering and deactivation. In this research, a proper deactiva-, Due to high gas velocity, axial diffusion of mass andtion model for the commercial catalyst has been adopted fromheat are negligible.Hanken [19].●Bed void fraction is assumed constant.dc= - Kdexp「一Ea(13)●Plug flow pattern is considered in the reaction tube.dR(一Tr。●Heat transfer to surrounding is neglected.●The homogenous reactions are neglected.4.3. Membrane sideSubject to these mentioned assumptions, mass and energybalances for the gas phase in reaction zone are expressed by:To remove produced water vapor from reaction zone andshift thermodynamic equilibrium limitations, permeability ofd(Cty)1 d(Fzy)+acCrke(u: -喝)一the membrane for water vapor should be at least as large asdtAc dthe water production. Lee et al. studied the efficiency andstability of alumina/silica composite membranes to permeateπD1A.rw.(P.2- P.I)water vapor in a membrane reactor experimentally [20]. Theycalculated permeation rate for this composite membrane. Thepermit H2O flux across the membrane is obtained from:d(T号)C唱d(F2T2)pCpdt=-Aa-+aohy(TR -项)-Qi=π(P,- P,2)(14)The flux of permeated water vapor through the compos-TDru. 2(理-T1)- TD2u-3(I理-Tsen)- (8)ite membrane depends on the water partial pressure differenceAcbetween two sides and membrane permeability. Mass and en-rD1 [_"ewC,dTergy balance equations for water vapor permselective side (in-Ac Jτ。ner tube) are as follows:The integral term considered in the energy balance is si-d(Cy)1 d(F1y). πD]multaneous heat and mass transfer during water vapor perme-Am dz2+ Arw,;(P.2- P,1)ation through the membrane layer. Mass and energy balances(15)for the solid phase are expressed by:ρCp1qp(OET) + D-2(7-79+。 d(Ciu)AmPdzAm= anCtkgi2(uf -蹈) + nar,Pb(9)TDI [_"QwC,dTAm Jr。c d(T))P- dt=arhr(TE -T)+Ponar:(-0Hq,i) (10)(16)In above equations ni is the effectiveness factor, which is4.4. Auxiliary equationdefined as actual reaction rate per particle to theoretical re-To complete simulation, auxiliary correlations should beaction rate in the absence of intermal mass transfer. This pa-added to the considered model. In the heterogeneous model,rameters in calculated from dusty gas model along the reactorheat and mass transfer coefficients between gas and solid[1]. The pressure drop through the catalytic packed bed hasphases, physical properties of chemical species and overallbeen calculated from Tallmadge equation that is feasible forheat transfer coefficient should be estimated from proper cor-wide range of Reynolds number [18]. The related equationrelations. The used correlations for calculation of physicalfor tubular reactors is: .properties,中国煤化工ricient are summarizedf=150(1-g)2、4.2 (1-e)1.66(11)in Table 4.YHCNMHGε3Re16 ε35. Numerical solutionOP_ξ=f。(12)To solve the set of nonlinear partial differential equationsJoural of Natural Gas Chemistry'Vol. 21 No. 42012411(PDE) obtained from dynamic modeling, the reactor lengththe system should be obtained through solving the governingis divided into equal discrete intervals, and using finitesteady state equations considering the activity to be unity. Thedifference method the PDEs are converted into a set of or-subject of steady state simulation of the membrane reactor isdinary differential equations in time domain. The set of equa-to determine the concentration and temperature profiles alongtions are solved by 4th order Runge-Kutta method [28]. Be-the reactor at normal operation. These steady state profiles arefore carrying out dynamic simulation, the initial condition ofused as the initial conditions of the unsteady state PDEs.Table 4. Considered correlations for calculation of physical properties, mass and heat transfer coftcientParametersEquationGas conductivityLindsay and Bromley [21]Mixture heat capacityIdeal [2]Viscosity of reaction mixturesLucas [22]Mass transfer cofficient between gas and solid phasesCussler [23]Mixture diffusion mass transfer cofficientHirschfelder et al. [24]Binary diffusion mass transfer cefficientWilke et al. [25]Heat transfer cofficient between gas phase and reactor wall[26]Permeation-exothermic side heat transfer cofficient[27]_6. Results and discussionhancement in the methanol production rate compared with theconventional reactor. According to Le Chatelier's principle,6.1. Model validationwhen an independent variable of a system at equilibrium, suchas temperature, pressure and concentration, is changed, theThe mathematical model involves a set of partialequilibrium shifts to reduce the effect of the change. The com-differential equations system that is solved numerically unparison of the methanol mole flow rate in the membrane andder dynamic condition. The steady state model of methanolconventional reactors shows that the methanol mole flow insynthesis reactor is validated against industrial methanol re-the membrane reactor is increased about 5.0% and 3.5% foractor [29]. The comparison between steady state simulation1st and 1200th days of operation, respectively.results and plant data for industrial case is shown in Table 5.The simulation results under steady state condition show thatTable 6. Methanol production rate in the conventionalthe considered model has a good agreement with the observedand membrane reactorsplant data under the same process condition.ConventionalMembrane reactorDayImprovementreactor (ton-day-l)(tonday~ 1)Table 5. Comparison between steady state simulation286.83025.0%results and plant data300278.12904.3%Composition ReactorReactor outletAbsolute600270.93.9%(mol%)simulation plant dateerror900262.73.6%CO22.0481.0511.032.8257.23.5%CO3.1180.9530.932.3H277.8775.875.12).5CH3OH0.4074.064.008Figure 3(a) shows methanol mole fraction profile in theannular space versus time. At the last part of the conven-tional reactor, the slope of methanol mole fraction decreases6.2. Dynamic simulationas a result of approaching the methanol mole fraction to theequilibrium value. The comparison of methanol mole frac-Mainly, the dynamic simulation has been carried out totion along the membrane and conventional reactors for lst andinvestigate the effect of catalyst activity on production rate1200th days of operation is presented in Figure 3(b). Out-considering position dependent catalyst activity rate. In thislet methanol mole fraction in the membrane reactor has beenpaper, the dynamic condition of membrane reactor such asincreased about 6.2% and 4.5% for 1st and 1200th days oftemperature, catalyst activity, methanol mole fraction and pro-operation, respectively. In the membrane reactor, water va-duction rate has been analyzed. Table 6 presents methanolpor removal decreases total mole flow rate along the reac-production rate in the conventional and membrane reactorstor and shifts thermodvnamic eauilibrium, which enhancesunder the process conditions of Shiraz Petroleum Complex inoutlet methar中国煤化工of catalyst deacti-Iran [15]. As seen from this table, performance of methanolvation, meth;YHC N M H Gtion decreases withreactor has been improved and higher amount of methanolpassage of timic, WuICI ICsuIls luwer waler vapor removal andcould be produced in the membrane reactor. Due to overcomemethanol improvement. Figure 3(c) shows methanol molethe thermodynamic equilibrium limitations using permselec-fraction profiles along the reactor during the production timetive membrane, this configuration presents a considerable en-(about 4 years)..412M. Parsi et al./ Joumnal of Natural Gas Chemistry Vol. 21 No.4 2012is at maximum and the deactivation rate is low at lower CO20.065concentration [30,31]. This is usually explained by copper(a)一Membrane reactoroxidation caused by reversible reduction and oxidation reac-0.060---- Conventional reactortions. Thus, lower CO2 content over the catalyst surface in theannular space can improve catalyst activity and catalyst lifetime in the methanol process. Higher catalyst activity and cat-0.055alyst life time improve methanol production rate and increaseoperational time of the methanol process in this system. Fig-ure 4(b) shows CO2 mole fraction profiles along the reactor0.050during the production time.).0860.045200 400 600800 1000 1200a)Time (day)0.0840.06元0.082(b0.0800.0480.078Membrane reactorConventional reactor0.02Day conventional reactor---- 1500 Day conventional reacton200 400 600 800 1000 1200---- 1 Day mermbrane reactor-一- 1200 Day membrane reactorb)Length (m)0.1150.105(C0.063 :0.095.052-0.085正0.0390.0260.01 200900~只0.013.00~n 3000,6”ength'1200Figure 4. CO2 mole fraction profiles versus time in the annular space (a) and900600along the reactor (b)“300 TimeFigure 5 (a) and (b) shows the average catalyst activityFigure 3. (a) Methanol mole fraction profiles in the annular space versusversus time and water vapor mole fraction along the conven-ime, (b) comparison of methanol mole fraction in the membrane and conven-tional and membrane reactors for 1st and 1200th days of op-tional reactors, (C) methanol mole fraction profiles along the reactor versustimeeration. In the 1st day of operation and at the last part ofmembrane reactor, rate of water vapor removal is higher com-Figure 4 shows CO2 mole fraction profile for 1lst andpared with water vapor production, which leads to negative1200th days of operation in the conventional and membrane slope of water mole fraction versus length. Catalyst deacti-reactors. As shown in this figure, outlet CO2 mole fractionvation restricts methanol and water synthesis with passage offrom the membrane reactor is lower compared with the con-time and results lower partial pressure of water vapor in theventional reactor during the production time. Water vapor re-reactor and中国煤化工resented correlationsmoval changes reactions to CO2 consumption, increases ratefor industria;YHCNM H(Gr from lack of H2Oof CO2 hydrogenation and reveres water-gas shift reactions,and CO2 corwhich lead higher CO2 conversion to methanol. Because ofagents. In this study, a temperature dependent function hascatalyst deactivation, CO2 content in both reactors increasesbeen considered as deactivation model and effect of H2O andwith passage of time. It was known that the catalyst activityCO2 on deactivation has been explained typically consideringJoumal of Natural Gas Chemistry Vol. 21 No. 42012413in the membrane reactor is higher compared with the con-1.0ventional process under the same operating conditions. Fig-(aure 5(c) shows H2O mole fraction profiles along the reactorlength versus time.0.8Figure 6 shows the temperature profiles for reaction andwater vapor permeation side of the membrane reactor for 1st0.7and 1200th days of operation, respectively.In the mem-brane configuration, the reaction side has been placed between0.6sweep gas and cooling water sides. Thus, the generated heatof reaction can be transferred to boiling water and sweep gas.0.In the entrance of membrane reactor, the reaction tends to havehigher temperature that improves the kinetics constant and re-2000801001200sults higher reaction rate and conversion. Also, according toTime (day)Le Chatelier s principle, temperature reduction increases ther-0.03modynamics equilibrium and leads to a shift of the exothermicand reversible reactions in the exothermic direction. In the 1st(bday of operation, high temperature in the reactor entrance andlow temperature in the upper section of the reactor increase0.02kinetic constant and shift equilibrium limitation, respectively.However, decreasing temperature in the entrance zone reduceskinetic constant, which leads to lower reaction rate with pas-sage of time.三0.01- 1 Day conventional reactor--- 1200 Day conventional reactor.... I Day membrane reactor5301200 Day membrane reactor25上0.0005Length (m)区520E15 t(c10日0.024- 1 Day reaction side05 t---- 1200 Day reaction side0.018.... I Day sweep gas side一1200 Day sweep gas side0.01200 t45670.006Figure 6. Temperature profiles for reaction and water vapor permeation sideof the membrane reactor10007. Conclusionsso0me (day)Figure 5. (a) Average catalyst activity versus time, (b) H2O mole fractionPerformance of the methanol synthesis coupled with wa-profles in the annular space versus time, (C) H2O mole fraction profiles alongter vapor permeation through a catalytic membrane reactorthe reactor versus timeis studied by a mathematical heterogeneous model under dy-presented researches. It was mentioned that, the catalyst sin-namic condition. The simulation results for an industrial casetering is a solid state transformation which occurs at high tem-are compared with the plant data and the accuracy of theperatures and is promoted by water. In the methanol catalyst,proposed model and the considered assumptions are proved.H2O destroys the matrix material and decreases the copperMethanol production could be promoted beyond thermody-surface tension, leading to sintering. Also, Kung reported thatnamic equilibrium by water vapor removal from reaction sidehigh partial pressure of H2O leads to sintering [32]. Thus,as a product. This configuration enhances simultaneous CO2water vapor removal from reaction zone can improve catalystconversionantalyst life time andlife time in methanol synthesis process. Water mole fractionmethanol F中国煤化I'ater vapor promotesin output of membrane reactor is decreased about 21% dur-catalyst deaMHC N M H G vapor removal froming the production time. Therefore, membrane reactor pro-reaction zone decreases catalyst sintering. The simulationvides favorable catalyst activity compared with the conven-results show that methanol production capacity is improvedtional reactor and subsequently the methanol production rate about 4.06% in the proposed membrane reactor during the414M. Farsi et al./ Jourmal of Natural Gas Chemistry Vol. 21 No.42012production time (about 4 years). Methanol mole fraction inAt surface catalystthe output of membrane reactor is enhanced about 5.35%, in0 Inlet conditionsthis configuration. Generally, the obtained results suggest thatChemical speciesthe water vapor-permselective reactor could be feasible and1 Water membrane sidebeneficial.2 Reaction sideNomenclaturesCatalyst activityReferencesSpecific surface area of catalyst pellet (m?.m~ -3)Ac Cross section area of each tube (m2)[1] Graf G H, Scholtens H, Stamhuis E J, Beenackers A A C M.Am Membrane cross section area (m2)Chem Eng Sci, 1990, 45: 773Molar concentration of component i (mol:m- 3)[2] Al-Fadli A M, Soliman M A. Froment G F 4th Saudi Engineer-ing Conference. 199Cp Specific heat of the gas at constant pressure (J-mol 1.K- 1)[3] Jahanmiri A, Eslamloueyan R. Chem Eng Commun, 2002, 189:Total concentration (mol-m-3)Tube diameter (m)[4] Velardi S A, Barresi A A. Chem Eng Sci, 2002, 57: 2995Dp Catalyst particle diameter (m)[5] Kordabadi H, Jahanmini A. Chem Eng J, 2005, 108: 249Ed Activation energy of deactivation rate constant (j-mol- )[6] Rahimpour M R, Alizadehhesani K. Int J Hydrogen Energy,2009, 34: 1349Total molar flow rate (mols-1)[7]JungKD,JooOs,HanSH,UhmSJ,Chung1L.CatalLett,Friction factor1995, 35: 303Partial fugacity of component i (bar)[8] Sahibzada M, Chadwick D, Metcalfe I s. Stud Surf Sci Catal,△H Heat of reaction (J :mol- 11997, 107: 29ht Gas-solid heat transfer cofficient (W.m-2.K-)9] Wu J G, Saito M, Takeuchi M, Watanabe T. Appl Catal A, 2001,218: 235kq Reaction rate constant for the lst rate equation[10] Quinn R, Dahl T A, Toseland B A. Appl Catal A, 2004, 272: 61(mol-kg-1.s- l.bar-1/2)[11] Rahimpour M R, Ghader S. Chem Eng Technol, 2003, 26: 902Reaction rate constant for the 2rd rate equation[12] Sea B, Lee K H. React Kinet Catal Lett, 2003, 80: 33(mol:kg-'.s-1 .bar~ 1/2)[13] Gallucci F, Paturzo L, Basile A. Chem Eng Process, 2004, 43:Reaction rate constant for the 3nd rate equation1029(molkg-.s-1.bar-1/2)[14] liuta I, Larachi F, Fongarland P. Ind Eng Chem Res, 2010, 49:6870Kg Deactivation constant (s-1 )15] Shiraz petrochemical Company. Methanol Reactor Long Sheet,kig Mass transfer cofficient (m-s- 12002L Reactor lengh (m)[16] Graaf G H, Sitsema P JJ M, Stamhuis E J, Joosten G E. ChemTotal pressure (bar)Eng Sci, 1986, 41: 2883PPartial pressure of component i (bar)[17] Graf G H, Stamhuis EJ, Beenackers A A C M. Chem Eng Sci,1988, 43: 3185Qw Permeated water through membrane tube (molm 2)[18] Tallmadge J A. AIChE J, 1970, 16: 10921Rate of reaction for hydrogenation of CO (mol.kg19] Hanken L. Master thesis In Norwegian University of Sciencer2 Rate of reaction for hydrogenation of CO2 (mol.kg~ 1.s~ )and Technology. 1995r3Reversed water-gas shift reaction (mol-kg-1.s-l)20] Lee K H, Youn M Y, Sea B. Desalination, 2006, 191: 296R Universal gas constant (J.mol-'.K-1)[21] Lindsay A L, Bromley L A. Ind Eng Chem, 1950, 42: 1508Re Reynolds number[2] Poling B E, Prausnitz J M, O'Connell J P. The Properties ofGases & Liquids. New York: McGraw-Hill, 2001T Temperature (K)[23] Cussler E L. Diffusion: Mass Transfer in Fluid Systems. Cam-TR Reference temperature (K)bridge: Cambridge University Press, 1984uSuperficial velocity of fluid phase (m-s- )[24] Hirschfelder J 0, Cutiss C F, Bird R B. Molecular Theory ofU Overall heat transfer coffcient (W.m-2.K 1)Gases and Liquids. New York: John Wiley and Sons, 1952yi Mole fraction of component i (mol-mol 1)[25] Wilke CR. Chem Eng Prog, 1949, 45: 218z Axial reactor coordinate (m)[26] Dwivedi P N, Upadhyay S N. Ind Eng Chem Process Des Dev,1977, 16: 157Greek letters[27] Dittus F W, Boelter L M K. Heat Transfer in Automobile Radi-μ Viscosity of fluid phase (kg.m -1.s 1)ators of the Tubular Type. California: University of Californiaρ Density of fluid phase (kg:m 3)Publications in Engineering, 1930PB Bulk density (kg:m- 3)[28] Dormand中国煤化工! Math, 1980,6: 19πw Water vapor permeation rate constant (mol:m-2.s-1 .Pa~1)[29] Hartig FF993, 32: 424ε Bed void fraction[30] SkrzypelYHC N M H Gloczynski j, NowakP.Chem Eng J, 1995, 58: 101Superscripts[31] Ladebeck J. Hydrocarb Process, 1993, 72: 89g In bulk gas phase[32] Kung H H Catal Today, 1992, 11: 443

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