Modeling of Fischer-Tropsch Synthesis in a Slurry Reactor with Water Permeable Membrane

Available online at www.sciencedirect.comScienceDirect骂PJournal of NaturnlGs CemistyJournal of Natural Gas Chemistry 16(2007)107- 114SCIENCE PRESSArticleModeling of Fischer- Tropsch Synthesis in a Slurry Reactorwith Water Permeable MembraneFabiano A. N. Fernandes*Universidade Federal do Ceara, Departamento de Engenharia Quimica, Campus Universitario do Pici,Bloco 709, 60455- 760 Fortaleza- CE, Brazil[ Manuscript received April 25, 2007; revised May 16, 2007 ]Abstract: Fischer -Tropsch synthesis is an important chemical process for the production of liquidfuels and olefins. In recent years, the abundant availability of natural gas and the increasing demandof olefins, diesel, and waxes have led to a high interest to further develop this process. A mathematicalmodel of a slurry membrane reactor used for syngas polymerization was developed to simulate and comparethe maximum yields and operating conditions in the reactor with that in a conventional slurry reactor.The carbon polymerization was studied from a modeling point of view in a slurry reactor with a waterpermeable membrane and a conventional slurry reactor. Simulation results show that different parametersaffect syngas conversion and carbon product distribution, such as the hydrogen to carbon monoxide ratio,and the membrane parameters such as merbrane permeance.Key words: slurry reactor; membrane reactor; Fischer-Tropsch; modeling1. Introductionter gas shift reaction (WGS):CO+H2O←→CO2+H2Fischer-Tropsch synthesis (FTS) was discoverednearly 80 years ago, but until now, its applicationThe WGS reaction consumes part of the carbonin producing liquid fuels and other chemicals has notmonoxide that can be used by the FTS reaction and isbeen fully explored mainly due to economical reasons.therefore undesired. To minimize the WGS reaction,In recent years, FTS has become a subject of renewedthe choices are to reduce the amount of water availableinterest particularly in the context of the conversionin the reactor or to work with an excess of hydrogenof remote natural gas to liquid transportation fuelsto shift the equilibrium towards the reagents. An ex-and due to an escalate in oil price.cess of hydrogen in the reactor is not desired becauseNatural gas can be converted to carbon monox-it directly influences the product distribution and itide and bydrogen (synthesis gas) via the existingwill be difficult to change the product distribution inprocesses, such as steam reforming, carbon dioxidefavor of lower or higher hydrocarbon chains by justreforming, partial oxidation, and catalytic partial ox-changing the H2:CO ratio. The best solution will beidation, followed by the FT synthesis reaction:to eliminate or reduce the amount of water availablein the reactor. thus reducing the amount of carbonCO+(1 + m/2n)H2-→1/nCnHm +H20 (1dioxi中国煤化工action, or in the bestcaseYHC N M H Gtion from ocurring.When iron catalysts are used, the carbon monox-In uls btuy, a lliieliaiucal model of a slurryide polymerization occurs in combination with the wa-membrane reactor used for syngas polymerization was* Corresponding author. E-mail: fabiano@efftech.eng.br108Fabiano A. N. Fernandes / Journal of Natural Gas Chemistry Vol. 16 No.2 2007developed and the carbon monoxide polymerizationvan der Laan et al. [5]， Maretto and Krishna [6]，was studied from a modeling point of view in a slurryand Krishna and Sie [7]. To this basic mathematicalreactor with a water permeable membrane and in a model, the equations for water permeation throughconventional slury reactor, comparing the maximumthe membrane were added and studied. The basicyields and operating conditions in both reactors.assumptions made for the reactor were: steady-stateoperation, isothermal conditions, large bubbles flow2. Membrane reactorin plug flow regime due to its velocity, constant slurryvelocity, hydrocarbon products in the gas and in theThe bubble column slurry reactor consists of aliquid phases assumed to be in equilibrium at the re-tower where the synthesis gas and liquid phase (liq-actor outlet, negligible mass and heat transfer resis-uid+catalyst) are fed through the bottom of the col-tances between the catalyst and the liquid, the gas-umnn. The liquid phase is fed at very low velocitiesliquid mass transfer limitation located in the liquidso that the liquid products can be continuously with-phase, intrinsic kinetics for Fischer-Tropsch synthesisdrawn. The synthesis gas goes through the reactor asand water-gas shift reactions.bubbles and exchanges mass with the liquid phase. InThe kinetic model for the FTS reaction on an irona commercial process, the velocity of the gas is highcatalyst and for the WGS reaction are given as:enough to produce large and small bubbles, and thereactor operates at a heterogeneous regime or churn-Rprs =k.Pco. PR:5(3)turbulent flow regime. The slurry reactor is also pro-(1 +a. Pco +b. Poo2)2vided with thousands of cooling tubes or cooling coils,with a heat exchange surface that can be as high asPco2 : Pr20 m2 per m3 of the reactor [1]. The cooling tubeshwes. ( Pco : Pr2oK()are used to remove the heat released by the FTS reac-RwGs =.(Pco + K2. PH2o)2tion and to control the reactor temperature, ensuringthe isothermal conditions inside the reactor, in spiteThe gas-phase mass balance for component i inof the high heat of reaction (△H=- 170 kJ/mol CO)the large bubbles and the gas phase balance for com-[2-5].ponent i in the small bubbles are:Water permeable membrane tubes can also be in-serted in the reactor to remove the water produced bythe FTS reaction and to prevent the WGS reactiond(Uc - Upr).C,c+ (kL .a).Cic=(from occurring. A dry sweep gas flows continuouslydH|mei -C.inside the membrane tube and water permeates to the(5)inner tube through the membrane. A schematic rep-resentation of the membrane is provided in Figure 1.UpF「C%.cH(Ct,G -Ci,c)=(kx.a)片mgt -Ci,L(6)The mass balance for component i in the com-pletely mixed liquid phase is:HH2CH (kr.a),c .HI( mGLMembraneFigure 1. Schematic representation of the mem-brane reactor(mgL-Ciu)| +EL.EP:PP .EvyR=13. Mathematical model中国煤化工(7)wher.MYHCNMH Gs, 2-WGSThe mathematical model of the bubble columnThe mass balance for water in the completelyslurry reactor was based on the model presented bymixed liquid phase is (i=H2O):Journal of Natural Gas Chemistry Vol. 16 No.22007109bubbles, followed by solving the algebraic set of equa-tions of the mass balance for the small bubbles and1H(m o),.(9( Clc-Ci,L)dH+(kt.a),cthe liquid phase. To solve the mathematical model, .first, initial estimates were provided for the gas con-Ci,Gcentration in the liquid phase and in the small bubblesnc -Ciu)-β. AM. (Ci,L - Ci,m)+(step 1). These values were used to numerically inte-Us.grate Equation 5 (step 2), and subsequently to solveEL.EP.P° Evi-RjCi,L=0algebraic Equations 6 and 7 (step 3), thus obtaining(8)new values for gas concentration in the liquid and theThe boundary conditions at the reactor entrance:small bubble phases. An iterative procedure was cre-H=0→C',c = CiG = CitG. The mass transferated to run steps 2 and 3 until the concentrations incoefficient of component i for large and small bub-all phases converged. The numerical integration wasbles are given by the correlations:carried out using a 5th order Runge _Kutta method.A program written in Fortran was developed to solve\ 0.(k:.a) = (kxa)ea.(品)“(9the model. The kinetic parameters for the reactionare presented in Table 1 and the simulated operatingconditions are presented in Table 2.(k.a) = (hn . o)a.(品)(10)Table 1. Kinetic parameters for Fischer-Tropschwhere，Drer: -2x109 m2/s， (kLa)er =0.5 εB, andsynthesis in iron catalyst and for water gas shift(kr.a)gef=EDF. .ParameterPre- exponential factorThe molar flow rate of the gas phase will changekpTs (mol/ikg-s-MPa1.5)0.0339because of reaction. The superficial velocity was as-a (MPa-1)1.185sumed to be a linear function of the overall carbonb (MPa-1)0.656monoxide conversion (Xco).kwGs (mol/kg.s)0.0292K13.07Uc=[1 + ac . Xco] .唱(11)Kz85.81where, ac= -0.67The liquid, total gas and small bubbles holdup, asTable 2. Operating conditions and reactorwell as the small bubbles velocity are calculated as:parametersGas superficial velocity (m/s)0.25Liquid velocity (m/s)0.010.8.EpUpr=EDP.Vsref.(12)Total pressure (bar)30.0(1+VsrefSolids holdupReactor height (m)0.7.Ep \EDF = EDFret.( 1 +EDFref(13)Reactor diameter (m)7.0Membrane bheight (m)25.0Membrane external diameter (m)0.10EG=εB +EDF.(1-εp)(14)Number of membrane tubes270εL=1-εG一印p(15)The kinetic model used to simulate the CO poly-where, Vsref=0.095 m/s; EDFref=0.27.merization and product distribution assumes that theOwing to the assumption of isothermal conditionsalkyl and alkenyl mechanisms act together in the FTSin the reactor, which can be considered based on thesynthesis.academic and patent reports [1- 5], only the mass bal-The alkyl mechanism can be represented by theances and the population balances for the hydrocar-following reactions:bon species were considered in this study. As such,中国煤化Iinitiationall heat produced by the reaction is considered to beremoved by the cooling tubes of the reactor.YHCNMHGpropagationThe mathematical model is solved by numericalR(n) +●H P，P(n)reduction by surfaceintegration of the mass balance equations for the largehydride giving an alkane (termination)110Fabiano A. N. Fernandes / Journal of Natural Gas Chermistry Vol. 16 No.2 2007R(n) Koler P=(n)B-hydride eliminationreaction rate, and the concentration of hydrogen ingiving an olefin (termination)the polymerization site is proportional to the partialThe alkenyl mechanism can be represented by thepressure of hydrogen in the reaction media.following reactions:The kinetic parameters for the CO polymeriza-●CH2 +●CH 2 R"(2)initiationtion are presented in Table 3. The model has beenvalidated using the data reported by Raje & Davis [9]R"(m) +●CH 52, R"(n+1)propagationand Donnelly & Satterfield [10] and has provided aR"(n)kolef12 ,. P=(n)reduction giving ansatisfactory ftting. Further information on the ki-olefin (termination)netic model development can be found in FernandesMethane can be formed through the coupling of[11,12].one surface methyl species with one surface hydrideTable 3. Kinetic parameters for Co polymerizationspecies, followed by desorption from the surface.in iron catalyst (at 270。C) [10]●CH3+ H kemost, CH4ki (MPa-1)0.4963Ethylene can be formed through the coupling ofhiz (mol/h)8.054two surface methylene species, followed by desorptionkp (h/mol)0.3530from the surface. This reaction was demonstrated ex-kp2 (h/mol)0.4206perimentally by Brady & Pettit [8].kpar (MPa-1.h-1)0.02314●CH2 +●CH2 k02, CH2=CH2kolet (h-1)0.003487The mass balance for the FTS is given by the fol-kolef2 (h- 1)0.04792lowing set of equations:kmet (MPa-1h-1)0.06386ket (MPa-1.h-1)0.02421R(1)= k:Pa2.(16)ko2 (h/mol)0.09994R"(2)= kz.RrTs(17)4. Results and discussionkp2In conventional bubble slurry reactors， theR(n)=;kp.RFTs+kipar.PH2+kolet.. oReprs,. R(n-1)Fischer-Tropsch reaction has to compete with the(18)WGS reaction for the CO available in the reactionmedia. The conversion of CO into hydrocarbons isreduced and only about half of the CO is transformedKp2 : RrrsR"(n)=的2. Rrs + kole: R'"(n-1) (19)into paraffin and olefins. The remaining is convertedinto the undesired CO2 (Figure 2a). As the H2:CO ra-dP(1)= kimet' PH2. R(1)(20)tio increases, the conversion also increases up to a ra-ditio of about 2.0; after this point, the total conversionincreases but the FTS conversion tends to decreasedP(2)= ket.PH2. R(2)(21)slightly.dtHigher H2 concentrations can shift the WGS equi-dP=(2)librium towards the reactants (CO and H2O) but even: ko2. REHrS(22)dso this shift is not enough to enhance FTS conversionby lowering the CO2 concentration (Figure 2).dP(n)it=kpar.Pr2.R(n)(23)In an ideal membrane reactor where the mem-brane is able to remove all H2O from the reactor,thereby preventing the WGS reaction from occurring,dP=(n)= koler . R(m) + kole2. R'"(n)(24)the conversion of CO used is entirely towards hydro-carbons production and no CO2 will be generatedThe development of the mass balances assumes(Figu中国煤化工fCO in a membranethat the quasi-steady state is applied to the concen-reactE that in conventionaltration of the propagating species (as assumed for theYHc N M H Gnto hydrocarbons iszero order moment of live polymers), the consump-almost twice the conversion expected for a conven-tion of methylene units is proportional to the globaltional reactor (Figure 3a)Journal of Natural Gas Chemistry Vol. 16 No.2 200711112.0 (a)曼(bc)0.鱼0.8-.50.6E 0.6- CO---- H.... CO2B 0.4---- H,00.50.2into Hydrocarbonates冒0.21.2.02.1.0H2:CO (feed)H;:CO (eed)Figure 2. Carbon monoxide conversion (a), and partial pressure profiles for liquid (b) and gas phase (c) forconventional slurry reactor operating at isothermal conditions as function of Hz:CO feed ratioe)-----H, .----H20.8.虽0.8-.8 t” 0.6喜0.6-易0.4-).4 tWith membrane骨0.2F8hantmemthraw ithout membrane.0H:CO (feed)H;:CO (ee)Figure 3. Carbon monoxide conversion (a), and partial pressure profiles for liquid (b) and gas phase (c) forslurry reactor with water permeable membrane operating at isothermal conditions as function ofH2:CO feed ratioThe partial pressure of the components changesure 4a) and the rate of the WGS reaction decreasesdramatically when comparing the conventional reac-because of the lower partial pressure of water. Astor with the membrane reactors. In conventional re-seen in Figure 4, the partial pressure of CO2 (unde-actors, the H2:CO ratio in the reaction media is verysired product) decreases as H2O permeation increases.high even when the feed ratio is low (<1.5), becauseThe excess of H2 produced by the WGS reaction is ;of the production of more H2 by the WGS reaction.also minimized and the H2:CO ratio tends towardsTo ensure a H2:CO ratio of 2.0 at the liquid phase, a2.0.feed ratio of 1.0 or lower has to be used, while in anZeolite based and silicate based membranes are .ideal membrane reactor, the H2:CO feed ratio reflectsnowadays one of the most suitable membranes to sep-itself in the H2:CO ratio at the liquid phase where thearate water from hydrocarbon mixtures even thoughreaction actually takes place.he membrane selectivity is not perfect and a per-Membrane permeability is directly related to thecentage of low molecular weight hydrocarbons (up toflow rate of water from the reaction media to the per-Cs) can pass through the membrane [13], and mustmeation zone, controlling the concentration of waterbe recovered from the sweep gas (usually nitrogen).in the reaction zone and thus the rate of the WGSnt中国煤- the Fischer-Tropschreaction.As the membrane permeability to waterreactve an average molarincreases, the reactor behavior changes from a con-permYHCNMHGo,H2O/COof19.8,ventional reactor towards an ideal membrane reactor.H2O/CO2 of 34.2, being highly selective towards theThe CO conversion into hydrocarbons increases (Fig-permeation of water. Silicate based membranes have112Fabiano A. N. Fernandes / Journal of Natural Gas Chemistry Vol. 16 No.2 2007an average molar permeation ratio H2O/H2 of 22.0,tration alters the product distribution and also theH2O/CO of 4.8, H2O/CO2 of 44.0, having a lowerconversion and productivity of the reactor. Satisfac-selectivity for CO when compared to ZSM-5 mem-tory membranes must maintain the concentration ofbranes. Mordenite based membranes have lower sereagents in the gas phase near the feed concentration,lectivity and have an average molar permeation ratiootherwise, the excess of a specific reagent (hydrogenH2O/H2 of 0.8, H2O/CO of 3.7, H2O/CO2 of 1.0.or carbon monoxide) must be fed into the reactor toFigure 5 shows the conversion of syngas into hydro-compensate for the loss through the membrane.carbons for three membranes at different permeationIn Figure 4, water permeation was based on fourrates. The different selectivity towards hydrogen andmembrane tubes described in Table 2. Membranescarbon monoxide affects the concentration of thesewith lower permeability can also be used but at the ex-reagents in the gas and liquid phase within the reaC-pense of having a greater number of membranes tubestion and consequently affects the conversion of syngasinside the reactor, to increase the total surface areainto hydrocarbons. A decrease in the reagents concen-for permeation..0-:0-coa)b)(c).8 F.81.5下CO2---- H,OH2O.6-1.0-0.4-。0..2 t- into Hydrocarbonates0,102(1520H2O permeation (mol/mrs)H2O permeation (mol/m-s)HO permeation (mo/ms)Figure 4. Carbon monoxide conversion (a), and partial pressure profiles for liquid (b) and gas phase (c) forslurry reactor with water permeable membrane operating at isothermal conditions as function ofmembrane permeability (Hg:CO feed ratio=2:1)Tropsch synthesis. As the membrane permeability0.affects the partial pressure of components, it alsoMembraneaffects the product distribution. Conventional reac-. ZSM-5名0.5----- Mordenite basedtors will produce a large quantity of light hydrocar-...... Silicate basedbon products ranging mainly from methane to gaso-line (Figure 6a).0.4When an ideal membrane reactor is used, and allwater is removed from the reactor media, the productdistribution will consist of light and heavy hydrocar-bons ranging from light gases to waxes with a goodamount of gasoline and diesel (transportation fuels).The production of olefins is equivalent to the produc-0.2.tion of paraffins, which can be suited to the produc-H2O permeation (mo/ms)tion of olefins for the polymer industry (Figure 6).Figure 5. Carbon monoxide conversion into hydro-As the permeability of the mermbrane increases,carbons for slurry reactor with water per-meable membrane operating at isother-the amount of light hydrocarbons decreases and themal conditions as function of membraneamc中国煤化工increases. The in-permeability (H2:CO feed ratio= =1:2)creaso enbances the pro-ducMYHC N M H Gvy olefins).The partial pressure of CO， H2，and H2ORegarding the allocation of the membrane tubesinfluences the product distribution of the Fischer-inside the reactor, zeolyte membranes such as ZSM5-1Journal of Natural Gas Chemistry Vol. 16 No.22007113have water permeability around 0.80 mol/m2.s (at the(5270 tubes). This tube spacing shows that there is ,conditions applied for the slurry reactor), a value thatenough room available for insertion of the membranewould require approximately 270 membrane tubes oftubes without compromising the reactor fluid dynam-50 mm diameter (same diameter as the cooling tubes)cs.for total water removal. This number is well belowThe average pore diameter reported in the liter-the number of cooling tubes required for heat removalature is below 0.5 micrometers [13], while a typical(more than 5000). Considering 270 membrane tubesFTS catalyst used in slurry reactor has an averageand 5000 cooling tubes, if a 19 cm tube spacing will bediameter of about 50 micrometers with narrow sizeused for the cooling tubes (FTS industry standard),distribution; therefore, few particles will fall belowthe insertion of the membrane tubes will infer in a;he 10 micrometers range, and thus the possibility of18.5 cm tube spacing for membrane+ cooling tubesmembrane tube clogging is minimal.1.0E+0(a)b)c)(d)1.0E-11.0E-21.0E-3 I1.0E-4103(Carbon numberFigure 6. Product distribution for different membrane permeability (H2:CO feed ratio= =2:1)Solid lines refer to parfins and dashed lines refer to olefins(a) Conventional reactor (no membrane), (b) Membrane permeability 9.42 mol/(m-s),(c) Membrane permeability 18.85 mol/(ms), (d) Total removal of water5. Conclusionssupport of the Brazilian research funding institutionCNPq-CTPetro-Conselho Nacional de DesenvolvimentoIron catalysts used for FTS reactions also presentCientfico. .a side WGS reaction, which consumes CO and lowersNomenclaturethe conversion of CO into hydrocarbons. Water per-area, m2meable membranes can be used to remove water fromCi,jconcentration of component i in phase j, mol/m3the reaction media, thus preventing the WGS reaction- diffusivity, m2/sfrom occurring or decreasing its reaction rate.H一reactor height, mMembrane reactors are an interesting reactor de-一overall kinetic rate constant of the F ischer-sign for Fischer Tropsch synthesis when iron catalystsTropsch Synthesisare employed, since it is capable of increasing hydro-ket - kinetic rate constant of ethene formationcarbon production and diminishing unwanted side re--kinetic rate constant of the initiation of the alkylactions. As such, the slurry membrane reactors are amechanismgood alternative to produce liquid fuels and olefins.ki2 - kinetic rate constant of the initiation of thealkenyl mechanismThe operating conditions can be set to control thekmet一kinetic rate constant of methane formationcarbon product distribution, removing water throughko2kinetic rate constant of ethene formationthe membrane. Further research still has to be done: termination into olefintowards the development of more selective water per-中国煤化工meable membranes.kolef2:.MHC N M H Germination into olefinof tne alkenyl mecnanismAcknowledgementskp - kinetic rate constant of the propagation of theThe authors gratefully acknowledge the financialallkyl mechanism114Fabiano A. N. Fernandes / Journal of Natural Gas Chermistry Vol. 16 No.2 2007kp2 - kinetic rate constant of the propagation of theSubscriptsalkenyl mechanism一large bubbles phasekp - kinetic rate constant of the termination intogas phaseparaffin of the alkyl mechanism. liquid phasekwGs- kinetic rate constant of the water-gas- shift reac-. membrane or membrane permeation zonetionKi 一equilibrium constant of reaction i or adsorptionReferencescoefficient of component ikL.a一volumetric mass transfer cofficient, s-1[1] de Swart J W A, Krishna R. Chem Eng Proc, 2002,m$ - solubility coefficient41: 35P:一 partial pressure, MPa[2] Dry M E. Catal Today, 1990, 6(3): 183- total pressure in the reaction zone, MPa[3] Akgerman A, Smith J M. Topical Report, DOERi - rate of reaction i, mol/s:geatProject DE-AC22 -89PC89867, 1989temperature, K[4] Steynberg A P, Nel H G, Silverman R W. CanadianUbr一small bubbles rising velocity, m/sPatent 2293659, 1997Uc - gas superficial velocity, m/s[5] van der Laan G P, Beenackers A A C M, Krishna R.Us一 suspension velocity, m/sChem Eng Sci, 1999, 54: 5013Xco - - carbon monoxide conversion[6] Maretto C, Krishna R. Catal Today, 1999, 52: 279[7] Krishna R, SieS T. Puel Proc Tech, 2000, 64: 73ac. - - expansion cofficient{8] Brady R C, Pettit R. J Am Chem Soc, 1980, 102:- permeability6181-- holdup[9] Raje A P, Davis B H. Catal Today, 1997, 36: 335- - stoichiometric coefficient[10] Donelly T J, Satterfield C N. Appl Catal, 1989, 52:- - catalyst density, g/m393Superscripts[11] FernandesF A N. Chem Eng Tech, 2005, 28: 930[12] FernandesF A N. Ind Eng Chem Res, 2006, 45: 10471 - large bubble[13] Espinoza R L, Santamaria J M, Menendez M A, Coro-- - small bubblenas J, Irusta S. Canadian Patent 02334731, 1999中国煤化工MYHCNMHG