FTS fixed-bed reactor based on Nano-structured Iron catalyst ...

Petroleum & CoalISSN 1337-7027Available online at www.vurup.sk/petroleum-coalPetroleum & Coal 55 (2) 82-92, 2013MODELING OF FISCHER–TROPSCH SYNTHESIS PACKED BED REACTOR FORPRODUCING LIQUID FUELS FROM NATURAL GASMohammad IraniGas Division, Research Institute of Petroleum Industry (RIPI), Tehran, Iran.Received January 2, 2013, Accepted March 30, 2013AbstractA tubular pilot scale <strong>fixed</strong>-<strong>bed</strong> <strong>reactor</strong> for the Fischer–Tropsch Synthesis (<strong>FTS</strong>) was simulated to numericallydemonstrate the conversion of synthesis gas (CO+H 2 ) to higher hydrocarbons over an iron <strong>based</strong> catalyst.The <strong>reactor</strong> was a 3.1 cm diameter and 2.75 m length steel tube. The feed temperature were between563- 583 K. Saturated water was employed to control the peak temperature within the catalyst <strong>bed</strong>,which is critical for the stability of iron <strong>based</strong> catalyst. In this research, computational fluid dynamics(CFD) was used to model the interacting phenomena such as non-ideality of mixture, reaction andhydrodynamics in a <strong>fixed</strong>-<strong>bed</strong> <strong>reactor</strong> for the <strong>FTS</strong>. Synthesis gas conversion, product selectivity, andtemperature were measured as a function of <strong>reactor</strong> length. <strong>FTS</strong> can be conducted with very lowtemperature range between 563 and 583K within a wide range of CO conversion using saturated wateras coolant. By using saturated water, <strong>reactor</strong> exhibited good isothermal condition under most simulatedconditions. Very good agreement between pilot experimental data and the model was achieved. Resultsshow that increase in feed temperature have a significant effect on the yield of products.Keywords: Numerical modeling; Fischer–Tropsch synthesis; packed <strong>reactor</strong>; CFD methods; saturated water.1.IntroductionThe Fischer–Tropsch synthesis (<strong>FTS</strong>) is a key step in the conversion of natural gas and coalor biomass into liquid fuels (synfuels) through the so-called gas-to-liquids (GTL) and coal/biomass-to-liquids (CTL/BTL) processes. Among them, GTL is particularly attractive from thepoint of view of operating costs, carbon and thermal efficiencies as well as environmentalimpact [1- 3] . The <strong>FTS</strong> is the catalytic conversion of synthesis gas (CO+H 2 ) into a multi-componentmixture of hydrocarbons and water. The commercial <strong>FTS</strong> plants have utilized either Fe or Cocatalysts using <strong>FTS</strong> to produce liquid fuels (gasoline and diesel) [4, 5] .The <strong>FTS</strong> can be viewedas a polymerization reaction where chain growth is the basic feature. Various types of <strong>reactor</strong>s(including fluidized <strong>bed</strong>, multi-tubular <strong>fixed</strong>-<strong>bed</strong> and slurry) have been considered during the<strong>FTS</strong> process development. The <strong>fixed</strong>-<strong>bed</strong> FT process, being one of the most competing <strong>reactor</strong>technologies, occupies a special position in <strong>FTS</strong> industrial processes [6-9] . Due to the high demandon gasoline in the world and its higher price relative to that of diesel, production of gasolinefrom the FT process, becomes more favorable. The octane number of FT gasoline is lower thanthat of the gasoline obtained from crude oil processing, since the FT gasoline mainly consistsof n-paraffin. To promote the yield and quality of the gasoline from <strong>FTS</strong>, bi-functional catalystshave received extensive attention in the recent years [10] .In this research, the modified bi-functional Fe-HZSM5 catalyst has been used. Such a processremoves the need for cumbersome upgrading units for GTL plants [11] . To achieve optimumcondition for the best performance of process, the <strong>reactor</strong> should be simulated exactly byconsidering non-idealities. Clearly, due to the complexity of <strong>FTS</strong> reaction system, variety ofproducts (C 1 -C 20 ) and operating condition of this process, a suitable <strong>reactor</strong> model with consideringthermodynamic non-idealities ,from which the selectivity and heat transfer informationcan be determined in a qualitative fashion, has not been presented yet [12,13] .Bub et al. [14] and Jess et al. [15] developed a two-dimensional, pseudo-homogeneous modelthat was used to predict product distribution and performed the conceptual design of a <strong>fixed</strong>-<strong>bed</strong>

eactor for converting nitrogen rich syngas. Atwood and Bennet [16] have proposed a onedimensional,homogeneous plug flow model. Wang et al. [17] devised a comprehensive onedimensionalheterogeneous <strong>reactor</strong> model to simulate the performance of <strong>fixed</strong>-<strong>bed</strong> FT<strong>reactor</strong>s for hydrocarbon production. Liu et al. [18] have studied the steady state and dynamicbehavior of the FT <strong>fixed</strong>-<strong>bed</strong> <strong>reactor</strong> using a two-dimensional heterogeneous model. Also,Marvast et al. [19] have simulated the behavior of the FT <strong>fixed</strong>-<strong>bed</strong> <strong>reactor</strong> using a twodimensionalheterogeneous model at steady state condition.In the present work, we report a computational fluid dynamic (CFD) study to investigateperformance of a bi-functional Fe-HZSM-5 catalyst in a pilot scale tubular <strong>fixed</strong>-<strong>bed</strong> <strong>reactor</strong>for <strong>FTS</strong>, coupling the exothermic <strong>FTS</strong> with saturated water for heat removal. The CFD is apowerful tool for simulating complex reacting flows [20-24] . The aim of our study was to analyzethe conditions under which the synthesis reaction could be conducted at a reasonably highCO conversion close to the isothermal condition at temperatures between 563 and 583 K.The simulation results have been validated with pilot experimental data.2. Process descriptionThe <strong>FTS</strong> has been investigated in a pilot scale of a <strong>fixed</strong> <strong>bed</strong> <strong>reactor</strong> which was packed withbi-functional Fe-HZSM5 catalyst (metal part: 100 Fe/5.4 Cu/7K2O/21SiO2, acidic part:SiO2/Al 2 O 3 =14). There was a jacket around the <strong>reactor</strong> which boiling water flowing throughit to remove the heat of reaction. The temperature of boiling water could be controlled measuringpressure of the system. The pilot has been designed and constructed by the Research Instituteof Petroleum Industry, National Iranian Oil Company (RIPI-NIOC) in 2008 [12] . The characteristicsof the pilot plant are shown in Table 1. The object is to find the profiles of temperature andconcentration of various species along the <strong>fixed</strong>-<strong>bed</strong> <strong>reactor</strong> length at different conditionsand recognize the optimum condition.Table1 <strong>FTS</strong> pilot plant characteristicsTube Dimension(mm) 31×3×2.75Number of tubes 1Molar Ratio of H2/Co 1Feed Temperature(K) 563,573 and 583Catalyst sizes (mm) 1.5×4Catalyst density(kg/m 3 ) 1290Bulk density(kg/m 3 ) 730Reactor pressure(bar) 17Cooling temperature (K) Saturated water (563,573 and 583)GHSV(Nl/hr) 3Bed Voidage 0.383. Mathematical Model3.1. Governing equationsIn order to model the problem, five sets of equations should be solved; continuity equation,momentum balance, energy and species transport equations. The mass conservation,momentum, and total enthalpy equations, may be expressed as follows, respectively:.( v ) 0(1) .(v v) P.i Tvv g Sn (3).(v( H.( vCi– Di P)) .( C) Riii1h j ) .(q) SiM. Irani/Petroleum & Coal 55(2) 82-92, 2013 83R(2)(4)

22S DijvjC j1jij1 21 v v jSR jhMjjR j0 (5)Where, represents mixture density, v is velocity vector, and H, h i are total enthalpyand enthalpy of species, respectively and C i stands for concentration of chemical species. Pis the static pressure, S is the model-dependent source term from porous-media and S R isthe heat of reaction . The catalyst zone considered as a porous media that modeled by theaddition of a momentum source term to the standard momentum equation. The source termis composed of two parts: a viscous loss term (Darcy, the first term on the right-hand sideof Equation 5) and an inertial loss term (the second term on the right-hand side of Equation5). v is the magnitude of the velocity and D and C are prescri<strong>bed</strong> matrices. The momentumsink contributes to the pressure gradient in the porous cells, causing a pressure drop that isproportional to the fluid velocity in the cells [25] .Due to complexity of the <strong>FTS</strong> reaction system, variety of products (C 1 - C 20 ) and operatingcondition of the process, non-ideal thermodynamic behavior of system should be consideredusing Eqs 6 to 8 [12,13] . Hereupon, a suitable EOS (equation of state) should be used forcalculation of mixture density and species fugacity (f i ). For this study Peng-Rabinson equationwas chosen as a suitable EOS which its parameters has been listed in table 2.Table 2 Parameters of Peng-Rabinson EOSσ ε Ω Ψ1 21 2(Tr;) 1 Z bPbeta RTf P y 20.37464 1.542260.26992 1 TZ Z1 Z q 0.07779 0.45724Pr, Tr12r2(Tr) , q Tbiln i ( Z 1) ln( Z beta ) I qibmaq bRT aqiq xibi[i] 2. - a (6)b1 Z 1 betaI ln() Z beta1i2ii2M. Irani/Petroleum & Coal 55(2) 82-92, 2013 84r3.2 Computational domain and boundary conditionsThe schematic of the setup is given in figure1, A two- dimensional system (2.75 m x 31mm)which was fed with synthesis gas (a mixture of carbon monoxide and hydrogen). Furthermore,the <strong>reactor</strong> was divided in two sections:1) top zone fluid, 2) reaction (catalyst) zone. Packed

M. Irani/Petroleum & Coal 55(2) 82-92, 2013 85<strong>bed</strong> was considered as a porous media due to the large value of N (tube-to-catalyst diameterratio) [26] .Figure.1 Schematic of <strong>fixed</strong>-<strong>bed</strong> <strong>reactor</strong> and its boundary conditionsThe mass-flow-inlet boundary condition was used for gas flow to the modeled <strong>reactor</strong>.The pressure-outlet boundary condition was specified at the bottom of the <strong>reactor</strong>. The <strong>FTS</strong>reaction is exothermic and if the heat of reaction isn’t removed, temperature run away willbe taken place. In this study saturated water was used for heat removal, so heat absor<strong>bed</strong>by water generates steam and <strong>reactor</strong> was assumed to be isothermal. The source term (S)for boundary cells (walls in reaction zone) should be included as follows:S H ( T) H ( T)(7)Which H (T )of reaction) and (T ) is enthalpy at temperature T (the increased temperature due to releasing heatH is enthalpy at temperature T (the desired temperature for reaction).3.3. Products and rate equationsWhen rate equations include in the CFD simulation, chemical kinetic calculations are verycomputer time consuming, especially for a complex reaction scheme like <strong>FTS</strong> [17] . In somesimulation studies the complexity of the <strong>FTS</strong> chemistry has been reduced by using a set ofglobal one-step reaction for selected mechanism [19] . The Fischer–Tropsch reactants andproducts which considered in this study consist of: CO, H 2 , CO, CO 2 , H 2 O, CH4, C 2 H 4 , C 2 H 6 ,C 3 H 8 , n-C 4 H 10, i- C 4 H 10 and C 5 +. The following reactions listed in Table 3 are leading Fischer–Tropsch reactions [27] :Table 3 List of <strong>FTS</strong> reactionsNum.Reaction stoichiometry1 CO 3H2CH4 H2O2 2CO 4H2 C2H4 2H2O3 2 5HCH H OCO2 2 6224 3CO 7H2 C3H8 3H2O5 4CO 9H2 n C4H10 4H2O6 4CO 9H2 iC4H10 4H2O7 8.9618.05HCH ( C ) 8.H O8CO HCO2 8.96 12.36 59622OCO2 H2The general form of reaction rate equation is like Eq. (8) and for <strong>FTS</strong> its kinetic parameters [27]are given in table 4:Rmoli hr.grcat E fi kiexp RT f2h2co(8)

Table 4 <strong>FTS</strong> parameters of reaction ratesK 1 (mol s -1 kg -1 cat /kPa) E 1 (J mol -1 )1 2.044 e-2 156932 6.255 e-5 20.3843 3.423 e-4 1.56074 5.972 e-6 164.065 6.482 e-6 86.9346 6.482 e-6 81.7537 3.168 e-5 738.788 3.168 e-5 5532.93.4. Material propertiesThe specific heat of each species was defined as piecewise-polynomial function of temperature.Besides to consider variation of density with temperature and composition, compressibilityfactor (Z) was calculated using Peng-Rabinson EOS and also the density of gas mixture wasdefined as follow:P M Z RTWhere R is the universal gas constant, M G is the molecular weight of gas mixture and P isthe operating pressure (taken to be 17 bar). For other thermal properties of the mixture suchas molecular viscosity, thermal conductivity and diffusivity coefficient, the relations in appendixwere used [28].The steps implemented in the solution procedure are as follows:1. Calculation of the gas-phase transport properties.2. Calculation of the density of gas mixture using Peng-Rabinson EOS.3. Calculation of the thermodynamic properties such as fugacity coefficients andcompressibility factors using special subroutines.4. Determination of the rate of consumption of reactants and production of products per unitvolume.5. Determination of the source terms for all the conservation equations.6. Solving the conservation equations.The finite volume method has been used to discrete the partial differential equations ofthe model, using the SIMPLE method for pressure–velocity coupling.4. RESULTS AND DISCUSSIONM. Irani/Petroleum & Coal 55(2) 82-92, 2013 86The geometry and grid was created in Gambit (Figure 2), the pre-processor of Fluent. Thegeometry consists of a rectangle, 2.75m in length and 31mm in width, with uniform structuredgrids to simulate fluid flow. A parametric study was done by varying the gas inlet temperature.In all cases, <strong>reactor</strong> pressure and H 2 /CO ratio are kept constant at 17 bar and 1, respectively.Based on the variation of gas inlet temperatures, three set of simulations were performed.(9)Figure 2 Mesh configuration of computational domainFigure 3 presents the contour of velocity in the <strong>reactor</strong>. As can be seen, in the first zoneof the <strong>reactor</strong> the velocity has the maximum value and in catalyst region, it is decreased dueto the pressure drop in the reaction zone.Figure 4 shows the mass fraction profiles of product species along the <strong>reactor</strong> length forthe case with the inlet gas temperature of 573 K. As shown in figure 4 the mass fraction ofproduct species is continuously increasing from the inlet to the outlet and there is a jump in

Mass FractionM. Irani/Petroleum & Coal 55(2) 82-92, 2013 87the end zone of the <strong>reactor</strong> due to the decrease in mass fraction of CO. (considering reactionrates, denominator is fugacity of CO).Figure.3 Contour of velocity (operating condition: T=573, P=17 bar)0.140.120.10.08methaneetilenpropaanEthaneButhaneC5+CO0.060.040.0200 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75Reactor length(m)Figure. 4. Mass fraction of species along the <strong>reactor</strong> length at T=573As depicted in figure 5 in the case with temperature of 563 the C 5+ selectivity was lessthan the case with temperature of 573. When the temperature was increased to 583K, C 5+selectivity was declined because of activation of water-gas-shift reaction at this temperatureand increasing of CO 2 production.Based on the production of heavier products in reaction zone, density increases along the<strong>reactor</strong> length (Figure 7).

SelectivityM. Irani/Petroleum & Coal 55(2) 82-92, 2013 882015T=563 K10T=573 KT=583 K500 0.5 1 1.5 2 2.5Reactor length (m)Figure. 5. Selectivity of species at different temperatures along the <strong>reactor</strong> length4.1. Control of the <strong>FTS</strong> temperatureAs mentioned before, the aim of this study was to analyze the conditions that the <strong>FTS</strong>could be conducted in a <strong>fixed</strong>-<strong>bed</strong> <strong>reactor</strong> at a reasonably high CO conversion near isothermalcondition at any desired reaction temperature between 563 and 583 K. To this end, a seriesof CFD simulations have been carried out in which the significant result of this simulationstudy has been confirmation of the isothermicity exhibition of the <strong>fixed</strong>-<strong>bed</strong> <strong>reactor</strong>. As anexample, figure 6 shows the distribution of temperatures along the <strong>reactor</strong> length at steadystate condition for a simulation conducted under conditions of T=573 K, P=17 bar.Figure.6 Contour of temperature (operating condition: T=573, P=17 bar)As shown in this figure, temperature profiles of two cases were presented. In case 1 heatremoval was done with saturated water and in case 2 without heat removal. As can be seen,the maximum difference of temperature inside the <strong>fixed</strong>-<strong>bed</strong> <strong>reactor</strong> is lower than 14K, andthe mean temperature of the solid is about 575 K, close to the coolant. Interestingly, the tempe-

M. Irani/Petroleum & Coal 55(2) 82-92, 2013 89rature of the fluid inside the catalyst zone, where the reaction takes place, is almost constant atabout 577 K, that is well-suited. If there isn’t any heat removal in <strong>reactor</strong>, the temperatureat the front of catalytic <strong>bed</strong> is increased to 685 K and the average temperature of the fluid incatalytic <strong>bed</strong> will remain on 650 K. This temperature is not suitable for catalyst performanceand catalyst degradation will occurred. These results presage a very efficient heat exchangeperformance of the saturated water. It should be noted that the saturated water temperaturecan be controlled with pressure. The maximum change in temperature of the <strong>FTS</strong> stream insidethe <strong>reactor</strong> from the entry to the exit is about 10–15 K (Figure 7). Therefore, almost isothermal<strong>FTS</strong> can be achieved by setting the operating pressure at a value which the saturation temperatureof liquid water is slightly below the temperature of the FT synthesis. The pressure ofboiling water system has to be reduced when the CO conversion increases, to have efficientheat-removal capacity.Figure.7 Profile of density (operating condition: T=573, P=17 bar)4.2. Quantitative validationDespite the fact that the results shown in figures 3 to 8 were used for qualitative validationof the model and the solution procedure, in order to ensure the accuracy of the model, quantitativecomparison of experimental data obtained from pilot and their corresponding simulated resultsis shown in table 5. Since it was limited to use the finite number of thermocouples, (point 1:beginning of catalytic <strong>bed</strong>; point 2: middle of catalytic <strong>bed</strong>; point 3: end of catalytic <strong>bed</strong>) onlythree experimental data of temperatures have been obtained and compared against theircorresponding simulated results. As this table shows, the errors at all times are less than fivepercent, since simulation is <strong>based</strong> on the CFD approach and no empirical correlation has beenused in the simulation.Table 5 Comparison between measured and predicted values for the pilot-scale <strong>FTS</strong>processesexperimental simulation Error (%)X CO (%) 60.7 58.59 3.476112C5+ selectivity (g/g feed) 18 17.29 3.944444Temperature at point 1(K) 588 590 0.340140Temperature at point 2(K) 575 573 0.347826Temperature at point 3(K) 573 573 05. ConclusionsThe detailed kinetics is em<strong>bed</strong>ded into the <strong>reactor</strong> model .The non-ideal thermodynamicbehavior of mixture is correlated by using Peng-Rabinson EOS. The <strong>reactor</strong> model is tested

against the measured data from pilot-scale and satisfactory agreements are found betweenpredictions of model and experimental results. The numerical investigation reveals that theproposed model can allow us to gain a quantitative insight into the complicated <strong>fixed</strong>-<strong>bed</strong><strong>FTS</strong> system. From the simulation data presented in this paper, a <strong>reactor</strong> optimization strategycan be deduced; operating at the highest possible conversion to achieve the maximum C 5+yield while minimizing temperature run away. The simulated <strong>reactor</strong> exhibited good isothermicityunder most simulated conditions by using saturated water as heat removing system.Increasing of feed temperature can increase syngas conversion; however it suppressesremarkably the overall yield of C 5+ products. Therefore the selection of feed temperature isimportant on the premier of keeping a satisfied syngas conversion for enhancement of theoverall yield of C 5+ products.NomenclatureM. Irani/Petroleum & Coal 55(2) 82-92, 2013 90P Pressure, bar T Temperature, Kg gravity acceleration, m.s -2 f fugacity, barv velocity, m.s -1 k i Kinetic Constant, mol.hr -1 .gr -1 .bar -1H Total enthalpy, kJ.kg -1 .s -1 E i Activation Energy, kJ.kmol -1h Enthalpy of species, kJ.kg -1 .s -1 R Global Gas Factor, kJ.kmol -1 .K -1j Mass flux, kg.m -2 .s -1 M i Molecular Weight, kg.kmol -1q Heat flux, kJ.m -2 .s -1 V Volume, m 3S Momentum source term, x i mass fractionD ij Diffusivity coefficient, D Total Diffusivity Coefficient, m 2 .s -1C i Concentration, kmol.m 3 k m Thermal Conductivity, kJ.m -1 .K -1Z Compressibility FactorGreek LettersSubscriptρ Density, kg.m -3 i species numberμ Viscosity, kg.m -1 .s -1 j second species numberφ i Fugasity coefficient m mixtureReferences[1] Bartholomew, C.H., Farrauto, R. J.: Fundamentals of Industrial Catalytic Processes,New Jersey: John Wiley & Sons Inc. – AIChE, Hoboken, 2006, 398.[2] Dry, M.E., Steynberg, P.: Studies in Surface Science and Catalysis, 2004, 152:406.[3] Davis, B.H.: Fischer−Tropsch Synthesis: Comparison of Performances of Iron andCobalt Catalysts, Ind. Eng. Chem. Res., 2007, 46 (26), pp 8938–8945.[4] Reidel, T., Schulz, H., Schaub, G., Jun, K., Hwang, J., Lee, K.: Topics in Catalysis,2003, 26:41.[5] De Deugd, R.M., Kapteijn, F., Moulijn, J. A.: Topics in Catalysis, 2003, 26:29.[6] Steynberg, A.P., Dry, M. E., Havis, B.H., Berman, B. B.: Studies in Surface Scienceand Catalysis, 2004, 152:64.[7] Dry, M.E.: Practical and Theoretical Aspects of the Catalytic Fischer-Tropsch Process,Applied Catalysis A: General, 1996, 138:319.[8] Sie, S.T. : Process development and scale up: IV Case history of the development ofa Fischer-Tropsch synthesis process, Rev. Chem. Eng. 1998, 14, 109–157.[9] Davis, B.H.: Topics in Catalysis, 2005, 32:143.[10] Nakhaei Pour, Zamani, Y., Tavasoli, A., Shahri, S.M. K., Taheri , S.A.: Study onproducts distribution of iron and iron–zeolite catalysts in Fischer–Tropsch synthesis ,Fuel, 2008, 87:2004.[11] Fischer–Tropsch pilot plant of Research Institute of Petroleum Industry and NationalIranian Oil Company (RIPI-NIOC), Tehran 18745-4163, Iran, 2004.[12] Irani, M., Bozorgmehry, R.B., Pishvaie, M. R., Tavasoli, A.: Investigating the effectsof mass transfer and mixture non-ideality on multiphase flow hydrodynamics usingCFD methods, Iran. J. Chem. and Chem. Eng., 2009.

[13] Irani, M., Bozorgmehry, R.B., Pishvaie, M. R.,: Impact of Thermodynamic Nonidealitiesand Mass Transfer on Multi-phase Hydrodynamics,Sci. Iranica, 2010.[14] Bub, G., Bearns, M., Bussemier, B., Frohning, C.: Chemical Engineering Science,2003, 58:867.[15] Jess, A., Popp, R., Hedden, K.: Fischer-Trospch synthesis with nitrogen- rich syngas:Fundamentals and <strong>reactor</strong> design aspects, Applied Catalysis A, 1999, 186:321.[16] Atwood, H.E., Bennet, C.O.: Ind. Eng. Chem. Proc. Des. Dev.1979, 18:163.[17] Wang, Y.N., Xu, Y.Y., Li, Y.W., Zhao, Y.L., Zhang, B.J.: Chem. Eng. Sci., 2003,58:867.[18] Liu, Q. S., Zhang, Z.X., Zhou, J. L.: J.Nat.Gas Chem. 1999, 8:137.[19] Marvast, M.A., Sohrabi, M., Zarrinpashneh, S., Baghmisheh ,Gh.: Chem. Eng. andTech., 2005, 1:28.[20] Amirshaghaghi, H., Zamaniyan, A., Ebrahimi, H., Zarkesh, M.: Numerical simulationof methane partial oxidation in the burner and combustion chamber of autothermalreformer, Applied Mathematical Modelling,34(2010) 2312-2322.[21] Jazbec, M., Fletcher, D. F., Haynes, B. S.: Simulation of the ignition of lean methanemixtures using CFD modelling and a reduced chemistry mechanism, AppliedMathematical Modeling, 24, 8-9(2000) 689-696.[22] Pougatch, K., Salcudean, Gartshore,M. I.: A numerical model of the reactingmultiphase flow in a pulp digester, Applied Mathematical Modeling, 30 (2006) 209–230.[23] Shang, Z.: CFD of turbulent transport of particles behind a backward-facing stepusing a new model—k-e-Sp, Applied Mathematical Modeling, 29 (2005) 885–901.[24] Gerber, A.G., Dubay, R., Healy, A.: CFD-<strong>based</strong> predictive control of melt temperaturein plastic injection molding, Applied Mathematical Modeling 30 (2006) 884–903.[25] Fluent, Incorporated: FLUENT 6 USER Manual, Lebanon (NH): Fluent Inc., 2001.[26] Foumeni, E.A., Moallemi, H.A., Mcgreavy, C., Castro, A.A.: Canad. J. Chem. Eng.,1991, 69:1010.[27] Marvast, M.A.: Ph.D. Thesis, Amirkabir University of Technology: Tehran- Iran, 2005.[28] Poling, B.E., Prausnitz, J. M., O’Connell, J.P.: The Properties of Gases & Liquids, 5 thed., New York: McGraw-Hill, 2000.[29] Mason, E.A., Saxena, S.C.: Phys. Fluids, (1958) 1:361.Corresponding author, PhD of Chemical Engineering. postal address: Gas Division, ResearchInstitute of Petroleum Industry (RIPI), West Blvd., Near Azadi Sports Complex, Tehran, Iran.Phone: +98 (21) 48252403, Fax: +98 (21) 44739716, E-mail address: Iranim@ripi.ir orMohammadirani@yahoo.comAppendixThermophysical properties in the gas phase were calculated using the following relations [28].Binary DiffusivityFuller’s method was used to determine diffusivity:AndDDM M/ M M1.75 1 2 1 2 0.04357 T(A.1)1 13 3 2P(V1V2)(1 xixjDi, m ) nj1ij(A.2)Where V i is found for each component by summing atomic diffusion volumes given in [28] .Gas-Phase Mixture ViscosityM. Irani/Petroleum & Coal 55(2) 82-92, 2013 91Wilke’s method has been used to determine the gas-phase viscosity. It is expressed as

nmx (A.3)x WhereAndiji ni1j 10.5 M1i j M81i MjijjjMi 0.50.25 2 (A.4)ji (A.5)j Mi ijiMjGas-Phase Mixture Thermal ConductivityThermal conductivity of the gas mixture was determined as follows. However, anadditional factor proposed by Mason and Saxena [29] was used:kmWhereAndn ni1j 1x kixjiAij k Mj 1i k jM i Aij0.5 M 81i M j 1.065AM0.5 0.252(A.6)(A.7)j iji Aij(A.8)iMjSpecific heatCmPni1x CiiPM. Irani/Petroleum & Coal 55(2) 82-92, 2013 92(A.9)

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