Kinetic Modeling of Naphtha Catalytic ReformingReactionsJorge Ancheyta-Jua´rez*and Eduardo Villafuerte-Macı´asInstituto Mexicano del Petro´leo,Eje Central La´zaro Ca´rdenas152,Me´xico07730D.F.,Mexico, and Instituto Polite´cnico Nacional,ESIQIE,Me´xico07738D.F.,MexicoReceived February21,2000In this work a kinetic model for the naphtha catalytic reforming process is presented.The model utilizes lumped mathematical representation of the reactions that take place,which are written in terms of isomers of the same nature.These groups range from1to11atoms of carbon for paraffins,and from6to11carbon atoms for naphthenes and aromatics.The cyclohexane formation via methylcyclopentane isomerization and paraffins isomerization reactions were considered in the model.Additionally,an Arrhenius-type variation was added to the model in order to include the effect of pressure and temperature on the rate constants.The kinetic parameters values were estimated using experimental information obtained in a fixed-bed pilot plant.The pilot reactor was loaded with different amounts of catalyst in order to simulate a series of three reforming reactors.The reformate composition calculated with the proposed model agrees very well with experimental information.1.IntroductionCatalytic reforming of straight run naphthas is a very important process for octane improvement and produc-tion of aromatic feedstocks for petrochemical industries. Hydrogen and lighter hydrocarbons are also obtained as side products.Generally,the reforming is carried out in three or four fixed bed reactors which operate adiabatically at temperatures between450and520°C, total pressures between10and35atm,and molar hydrogen-to-hydrocarbon ratios between3and8.The feed to the first reactor is a hydrodesulfurized naphtha cut,composed of normal and branched paraffins,five-and six-membered ring naphthenes,and single-ring aromatics.A large number of reactions occur in catalytic reform-ing,such as dehydrogenation and dehydroisomerization of naphthenes to aromatics,dehydrogenation of paraf-fins to olefins,dehydrocyclization of paraffins and olefins to aromatics,isomerization or hydroisomerization to isoparaffins,isomerization of alkylcyclopentanes,and substituted aromatics and hydrocracking of paraffins and naphthenes to lower hydrocarbons.The major reactions in the first reactor are endothermic and very fast,such as dehydrogenation of naphthenes.As the feedstock passes through the reactors,the reactions become less endothermic and the temperature dif-ferential across them decreases.Recently there has been a renewed interest in the reforming process,first,because reformate is a major source of aromatics in gasoline,and second,because of the new legislation of benzene and aromatics content in commercial gasolines.In this sense,refiners have reduced the severity of the industrial reforming plants in order to decrease the amount of aromatics in gasoline, however it adversely affects the reformate octane.1 Because of these reasons,it is very important to develop an appropriate kinetic model capable of predict-ing the detailed reformate composition in order to use it,in combination with a catalytic reforming reactor model,for simulation and optimization purposes. Various kinetic models to represent catalytic reform-ing have been reported in the literature,which have different levels of sophistication.2-6All of these models consider some or all of the reactions mentioned earlier and they idealize the complex naphtha mixture so that each of the three hydrocarbon classes,paraffins,naph-thenes,and aromatics,is represented by a single compound having the average properties of that class. The kinetic model of Krane et al.3is one of the more elaborate models which considers all possible reactions for each individual hydrocarbon.However,the temper-ature and pressure dependency on the rate constants was not reported.In addition,this model does not consider the formation of the main benzene precursor (N6:cyclohexane)via isomerization of methylcyclopen-tane(MCP),and it does not take into account the reaction rates of hydrocarbons with11atoms of carbon because only hydrocarbon up to10atoms of carbon are considered.In the present paper the Krane et al.model is extended in order to consider these deficiencies.*To whom correspondence should be addressed.Instituto Mexicano del Petro´leo.FAX:(+52-5)587-3967.E-mail:jancheyt@imp.mx.(1)Unzelman,G.H.Oil Gas J.1990,88(15),43.(2)Smith,R.B.Chem.Eng.Prog.1959,55(6),76-80.(3)Krane,H.G.;Groh, A. B.;Shulman, B. D.;Sinfeit,J.H. Proceedings of the5th World Petroleum Congress1959,39-51.(4)Henningsen,J.;Bundgaard,N.M.Chem.Eng.1970,15,1073-1087.(5)Ramage,M.P.;Grazianai,K.R.;Krambeck,F.J.Chem.Eng. Sci.1980,35,41-48.(6)Padmavathi,G.;Chaudhuri,K.K.Can.J.Chem.Eng.1997,75, 930-937.1032Energy&Fuels2000,14,1032-103710.1021/ef0000274CCC:$19.00©2000American Chemical SocietyPublished on Web08/02/20002.Kinetic ModelThe proposed kinetic model is an extension of the model reported by Krane et al.,3which utilizes lumped mathematical representation of the reactions that take place.These representations are written in terms of isomers of the same nature(paraffins,naphthenes,or aromatics).These groups range from1to10carbon atoms for paraffins,and from6to10carbon atoms for naphthenes and aromatics.The Krane model includes the chemical reactions summarized in the first column of Table1.2.1.Kinetic Constants for C11Hydrocarbons.A catalytic reforming feedstock includes compounds hav-ing carbon number up to C11as can be seen in Table2. The Krane model groups in three lumps the hydrocar-bons with10and11atoms of carbon(P10+)P10+P11, N10+)N10+N11,and A10+)A10+A11,called in general as C10+)C10+C11).This implies that the reaction ratefor each hydrocarbon has the following equation:Equation1can also be written as a function of C10and C11and their individual kinetic constants(k10and k11) as follows:From eqs1and2the following expression can be obtained:whereEquations3and5can be used for evaluating the individual kinetic constants for hydrocarbons with10 and11atoms of carbon,k10and k11,respectively.In this calculation,the two ratios defined by eqs4and5are needed.To evaluate the constant R for each hydrocarbon type (eq4),various PIONA analysis of the feedstock of an industrial catalytic reforming plant in a period of three months were used.The individual and average values of these analysis are presented in Table2.The different values of R are:P10/P11)9.099,N10/N11)5.087,and A10/A11)24.294.The values of K(eq5)were obtained by extrapolation using various kinetic constant ratios reported by Krane et al.3(k7/k6,k8/k7,k9/k8,and k10/k9)as a function of the number of atoms of carbon.Figure1shows this proce-dure for two reactions of hydrocracking of paraffins to paraffins with less number of carbon atoms.The com-plete results of these extrapolations and the final values of the individual kinetic constants for hydrocarbon with 10and11atoms of carbon are presented in Table3.2.2.Benzene Formation.The Krane model does not consider neither the cyclohexane formation via MCP isomerization(MCP T N6)nor the MCP production from P6(P6T MCP).The Krane model only takes into account the following path reaction:P6T N6T A6.As it was mentioned before,it is very important to accurately predict benzene content in reformate.Be-cause it is impossible to tell exactly how much benzene is produced by each of the various identified reaction mechanisms,7the assumption that all benzene is pro-duced via cyclohexane dehydrogenation was considered in the present work,and the reaction network shown in Figure2,which includes the already mentioned path reaction with MCP,was added to the Krane model. 2.3.Isomerization of Paraffins.Isomerization of normal paraffins to isoparaffins is highly desirable reaction that contributes to the increase of reformate octane numbers during naphtha reforming.These are moderately fast reactions catalyzed by acid sites,and the reaction rate increases with increasing temperature and pressure.8Therefore,the splitting of paraffins lumps in n-paraffins and i-paraffins is a very important aspect to be considered.It is common to assume that the isomerization reactions are rapid enough to closely approach thermodynamic equilibrium at normal reform-ing conditions.9Hence,in this work the paraffins distribution was calculated by known equilibrium. 2.4.Effects of Pressure and Temperature on Kinetic Constants.The Krane model satisfactorily describes the reforming process,although its only seri-ous limitation is that it does not include the influence of temperature on the kinetic constants.In other words, this model is limited to the representation of isothermal operation at some point within the experimental tem-perature range in which Krane fit the parameters(800-960°F).To overcome this limitation,an Arrhenius-type variation of the rate constants was previously re-(7)Turpin,L.E.Hyd.Proc.1992(June),81-91.(8)Padmavathi,G.;Chaudhuri,K.K.Can.J.Chem Eng.1997,75, 930-937.(9)Gates,B.C.;Katzer,J.R.;Schuilt,G.C.A.Chemistry of Catalytic Processes;McGraw-Hill book Co.:New York,1979;p184.d C10+ d(1SV))k10+C10+)k10+(C10+C11)(1)d C10+ d(1SV))k10C10+k11C11(2)k 10)k10+(R+1)(R+K)(3)R)C10C11(4)K)k11k10(5)Table1.Reactions of the Krane et al.1and the ProposedKinetic Modelsnumber of reactionsreaction a Krane model this workparaffinsP n f N n46P n f P n-i+P i2126subtotal2532naphthenesN n f A n56N n f N n-i+P i611N n f P n57subtotal1624aromaticsA n f A n-i+P i57A n f P n45A n f N n11subtotal1013total5371a n:number of atoms of carbon(1e i e5)Naphtha Catalytic Reforming Reactions Energy&Fuels,Vol.14,No.5,20001033ported.10The activation energy values for all reactions were taken from the literature.4Another limitation of the Krane model is that experi-mental data do not include variations in operating pressure.The model,therefore,is valid only at the base pressure (300psig).It is well-known that pressure affects the equilibrium conversion of reforming reactions in which a change of volume occurs as a result of the chemical reaction.Thus,in this work a factor that accounts for the pressure effect on the rate constant was also included.10,11The equation for the combined effect of temperature and pressure on the kinetic constants can be expressedas follows.10The values of activation energies and pressure effect factors are given in Tables 4and 5,respectively.2.5.The Proposed Kinetic Model.On the basis of the above discussion,the chemical reactions included in the proposed kinetic model are presented in the second column of Table 1.This model has 18more reactions compared to the Krane model.Four more lumps can be directly predicted with this new model,P 11,N 11,A 11,and MCP,and by equilibrium calculations,six iso-paraffin lumps (i-P 5,i-P 6,i-P 7,i-P 8,i -P 9,i -P 10)can also be estimated.In addition,benzene formation can be more accurately calculated,since the reactions between N 6and MCP were incorporated to the model.3.Pilot Plant Experiments3.1.Materials.The feedstock used in this study was an hydrodesulfurized straight-run naphtha (distillation range:82.3-168.1°C and density of 0.74g/mL)recovered from an industrial naphtha HDS unit.The composition as determined by GC analysis is presented in Table 6.The hydrodesulfurized naphtha contained less than 0.5wppm sulfur,and its water content was less than 1wppm.The feedstock was derived from a crude oil with the following properties:26.9°API,2.3wt %sulfur,4.5wt %asphaltenes,5.9wt %Conradson carbon,and 54and 266wppm of Ni and V,respectively.The catalyst used in this investigation was a commercial available Pt -Re reforming sample (Pt,0.29wt %;Re,0.29wt(10)Ancheyta,J.J.;Aguilar,R.E.Oil Gas J.1994,Jan.31,93-95.(11)Jenkins,J.H.;Stephens,T.W.Hyd.Proc.1980(Nov),163-167.Table 2.PIONA Analysis of a Catalytic Reforming Feedstocksample 1sample 2sample 3sample 4sample 5sample 6average n -paraffinsC 40.000 1.5680.0000.0000.0000.0000.261C 5 1.81811.3689.81810.362 1.983 1.392 6.124C 69.6338.0348.3568.4129.4679.4778.897C 78.116 6.7787.1147.1488.3868.4027.657C 8 6.464 5.326 5.602 5.616 6.640 6.683 6.055C 9 4.454 3.514 3.858 3.809 4.625 4.680 4.157C 10 1.640 1.403 1.707 1.635 1.948 2.066 1.733C 110.2970.2660.3210.2920.3180.3700.311i -paraffins C 40.0000.0760.0000.0000.0000.0000.013C 50.565 6.459 3.191 3.7710.7940.453 2.539C 68.8387.2697.4487.469 4.845 5.299 6.861C 7 6.759 5.656 5.932 5.965 6.943 6.963 6.370C 87.070 5.897 6.310 6.1877.2897.344 6.680C 9 6.241 5.066 5.499 5.311 6.448 6.509 5.846C 10 3.526 2.840 3.384 3.221 3.899 4.402 3.545C 110.2120.2030.2810.2540.2890.3740.269naphthenes C 50.8970.9770.9730.9780.3330.2860.741C 6 5.069 4.345 4.435 4.434 5.226 5.166 4.783C 7 6.934 6.038 6.071 6.0657.1797.157 6.574C 8 5.112 4.307 4.593 4.565 5.320 5.461 4.893C 9 1.842 1.535 1.655 1.578 1.938 1.970 1.753C 100.4950.3980.5580.4920.5610.6410.524C 110.0960.0850.1060.0990.1050.1250.103aromatics C 6 1.393 1.074 1.200 1.199 1.380 1.351 1.266C 7 3.506 2.676 3.024 3.038 3.634 3.576 3.242C 8 5.326 4.015 4.529 4.542 5.507 5.428 4.891C 9 2.908 2.186 2.956 2.671 3.488 3.218 2.905C 100.7070.5690.9030.8300.891 1.0560.826C 110.0320.0320.0350.0310.0360.0370.034Figure 1.Evaluation of the constant K for P 11dehydrogena-tion reactions.k i )k i0[E Aj R (1T 0-1T)](P P 0)R k(6)1034Energy &Fuels,Vol.14,No.5,2000Ancheyta-Jua ´rez and Villafuerte-Macı´as%)having a surface area of221m2/g,pore volume of0.36mL/ gm,and particle diameter of1.6mm.3.2.Pilot Plant Tests.The tests were performed in a fixed-bed pilot plant with hydrogen recycle.The unit consists of a stainless steel reactor(internal diameter of2.5cm and length of25cm),which was operated in isothermal mode by inde-pendent temperature control of a three-zone electric furnace.The tests were carried out at pressure of10.5kg/cm2;molar H2/hydrocarbon ratio of6.5;and temperatures of490,500and 510°C.To simulate a series of three reforming reactors,the pilot reactor was loaded with different amounts of catalyst,6,15, and30mL keeping the same naphtha flow at a constant value of102mL/h in order to have different space-velocities(WHSV), 17.72,7.09,and 3.54h-1,respectively.These amounts of catalyst and WHSV were selected in order to have20%of the total mass of catalyst in the first reactor,30%in the second reactor,and50%in the third reactor.The catalyst beds were diluted with an inert with the same particle size as the catalyst itself in order to have a better distribution of heat losses over the reactor,so that equalization of the temperature can take place more readly.The degree of dilution was varied depending on the amount of catalyst loaded in the reactor.The highest dilution was used for experiments with20%of the total mass of catalyst.The temperature drop,measured with an axial thermocouple,wasless than5°C.Reformate samples were collected in a high-pressure product receiver.The remaining C4-cracking products were removed by distillation afterward.The stabilized reformate was ana-lyzed on paraffins,i-paraffins,naphthenes,and aromatics by GC.4.Results and Discussion4.1.Reforming Experiments.Table7shows the detailed composition of the reformate as a function of reaction temperatures at WHSV of3.54h-1.It can be observed that aromatics hydrocarbons in the feedstocks pass thought the unit essentially unchanged,and their yields are higher as the reactor temperature increases. Therefore,the total amount of aromatics increases from 13.28mol%to52.8,56.66,and61.19mol%at490,500, and510°C,respectively.It should be noted that the most important increase is observed in lighter aromat-ics,especially A6,A7,and A8.Naphthenes react relatively easily and are highly selective to aromatics compounds via dehydrogenation. This reaction proceeds essentially to completion.In this work,N6,N9,N10,and N11disappear completely and the conversion of N7and N8is higher than82%.It was also confirmed that naphthenes dehydrogenation is favored by high reaction temperature as they were almost completely converted at temperatures higher than490°C(>86%conversion of total amount of naphthenes).This is the main reason because naph-thenes are the most desirable components in reforming feedstocks.The paraffins isomerization reaction is very important because naphthas contain a high percentage of normal paraffins,which,after isomerization,yield products with a higher octane number.This reaction occurs rapidly at commercial operating temperatures and it is limited by the thermodynamic equilibrium.The temperature has little influence on it because the heat of reaction isTable3.Individual Kinetic Constants for Hydrocarbons with10and11Atoms of Carbon reaction C6/C5C7/C6C8/C7C9/C8C10/C9C11/C10k+10a k10k11 P f N 2.2931 1.3609 1.4033 1.46450.02540.02430.0356 P n f P n-1+P1 1.1667 1.0000 1.3571 1.5789 1.6333 1.6678b0.00490.00460.0077P n f P n-2+P2 1.2000 1.0000 1.3888 1.5600 1.6154 1.6499b0.00630.00590.0097 P n f P n-3+P3 1.1852 1.3438 1.5814 1.6029 1.61700.01090.01030.0166 P n f P n-4+P4 1.5714 1.6182 1.62120.00890.00840.0135 P n f P n-5+P50.01240.01170.0191 N f P0.1351 2.3500 1.1489 1.0000 1.00000.00540.00540.0054 N f A 2.2587 2.3678 1.1395 1.0000 1.00000.24500.24500.2450 N n f N n-1+P114.111 1.0551 1.00000.01340.01340.0134 N n f N n-2+P2 1.0551 1.00000.01340.01340.0134 N n f N n-3+P3 1.00000.00800.00800.0080 A n f A n-1+P1 5.0000 1.2000 1.00000.00060.00060.0006 A n f A n-2+P2 1.2000 1.00000.00060.00060.0008 A f P 1.0000 1.0000 1.0000 1.00000.00160.00160.0016 a Original kinetic constant.b Values evaluated with Figure1.Figure2.Reaction network for benzene formation.Table4.Activation Energies for Each ReformingReaction4reaction j E Aj(kcal/mol) paraffinsP n f N n45P n f P n-i+P i55naphthenesN n f A n30N n f N n-i+P i55N n f P n45aromaticsA n f A n-i+P i40A n f P n45A n f N n30Table5.Factors for Pressure Effect10reaction k R kisomerization0.370dehydrocyclization-0.700hydrocracking0.433hydrodealquilation0.500Table6.PIONA Analysis of the Pilot Plant Feedstock n-paraffins i-paraffins naphthenes aromatics C4C5 3.80 3.400.42C6 4.40 6.70 3.210.80C7 3.20 6.20 5.80 3.22C8 6.36 6.52 4.71 4.71C9 5.098.32 3.56 4.21C10 2.97 6.220.60 2.70C11 2.200.400.30Naphtha Catalytic Reforming Reactions Energy&Fuels,Vol.14,No.5,20001035low.In this work,the naphtha used in the experiments has a high paraffin content(34.56mol%n-paraffins and 34.69mol%i-paraffins).The most difficult reaction to promote is the dehy-drocyclization of paraffins,which consists of molecular arrangements of a paraffin to a naphthene.Heavy paraffins(P9,P10,and P11)have conversions higher than 92%and lighter paraffins showed lower values(Table 7).This is because the increase in the probability of ring formation is high as the molecular weight of the paraffin increases.Similarly to the naphthenes dehydrogenation reaction,paraffins dehydrocyclization is favored at high reaction temperatures.4.2.Kinetic Parameters of the Proposed Model. The71kinetic parameters of the proposed kinetic model were estimated using the experimental information obtained at reaction temperature of490°C and different WHSV.For each reaction step,a kinetic expression was formulated as a function of product yields and kinetic constants.All reactions are presumed to be pseudo-first order with respect to the hydrocarbon.The equations for all the reaction steps are combined into24simultaneous differential equations,which comprise the kinetic model. The kinetic model was incorporated into an isother-mal plug flow reactor model.To ensure that the data were collected in the true kinetic regime and transport effects were insignificant,the following criteria were examined and satisfied:12whereTo evaluate the product yields as a function of reactor length from a set of kinetic constants a pseudo-homogeneous model13was used,which was solved with a Runge-Kutta method.The minimization of the objective function,based on the sum of square errors between experimental and calculated yields,was applied to find the best set of kinetic parameters.This objective function was solved using the least squares criterion with a nonlinear regression procedure based on Marquardt’s algorithm.14 Most of the initial values of the kinetic parameters were those reported by Krane et al.3The best values of all the kinetic constants are presented in Table8.4.3.Validation of the Kinetic Model.The conver-sion of some selected hydrocarbon types(n-P5,i-P5,P6, P7,MCP,N6,N7,and A6)as a function of position in the catalyst bed is shown in Figure3.The solid lines represent the values calculated with the proposed kinetic model and the symbols the experimental data. It can be observed that the calculated compositions agree very well with experimental information with average deviation less than3%.It can also be seen from Figure3that,as the naphtha passes through the catalyst bed,A6concentration increases.The same behavior was found with all aromatics compounds.The concentration of N6and N7 and heavy paraffins(P7-P11,only P7is shown in Figure 3)decrease as they undergo conversion.A high rate of(12)Mears,D.Ind.Eng.Chem.Proc.Des.Dev.1971,10,541.(13)Foment,G.F.;Bischoff,K.B.Chemical Reactor Analysis and Design;John Wiley&Sons:1990.(14)Marquardt,D.W.J.Soc.Ind.Appl.Math.1963,2,431-441.position of Different Reformates at WHSVof3.54h-1reaction temperature490°C500°C510°C n-paraffinsP110.010.010.00P100.090.000.00P90.400.280.18P8 1.220.910.63P7 2.91 2.44 1.97P6 5.50 5.21 4.40P5 5.25 4.96 4.85total15.3813.9712.03 i-paraffinsi P100.280.170.85i P9 1.50 1.240.67i P8 3.75 2.74 2.01i P77.997.27 6.07i P69.399.489.83i P5 6.39 6.18 5.53total29.3027.0824.96 naphthenesN110.000.000.00N100.000.000.00N90.010.020.01N80.630.660.38N70.330.310.27N60.010.010.01MCP 1.35 1.23 1.15total 2.33 2.23 1.82 aromaticsA110.97 1.10 1.25A10 5.60 5.75 5.99A912.5113.1714.17A815.6316.8618.20A712.8013.8815.02A6 5.29 5.90 6.56total52.8056.6661.19Table8.Kinetic Constants of the Proposed Model reaction step k reaction step k reaction step kP11f N110.0356P8f P40.0070N8f N7+P10.0007 P10f N100.0243P7f P6+P10.0027N11f A110.6738 P9f N90.0500P7f P5+P20.0018N10f A100.3198 P8f N80.0266P7f P4+P30.0043N9f A90.2205 P7f N70.0076P6f P5+P10.0018N8f A80.2150 P6f N60.0000P6f P4+P20.0016N7f A70.0788 P6f MCP0.0042P6f2P30.0025N6f A60.1368 P11f P10+P10.0075P5f P4+P10.0018A11f P110.0016 P11f P9+P20.0100P5f P3+P20.0022A10f P100.0016 P11f P8+P30.0135N11f P110.0050A9f P90.0016 P11f P7+P40.0135N10f P100.0054A8f P80.0011 P11f P6+P50.0191N9f P90.0054A7f P70.0016 P10f P9+P10.0015N8f P80.0025A11f A10+P10.0006 P10f P8+P20.0054N7f P70.0019A11f A9+P20.0006 P10f P7+P30.0160N6f P60.0204A10f A9+P10.0006 P10f P6+P40.0095MCP f P60.0008A1f A8+P20.0006 P10f2P50.0095N11f N10+P10.0134A10f A7+P30.0000 P9f P8+P10.0030N11f N9+P20.0134A9f A8+P10.0005 P9f P7+P20.0039N11f N8+P30.0080A9f A7+P20.0005 P9f P6+P30.0068N10f N9+P10.0134A8f A7+P10.0001 P9f P5+P40.0058N10f N8+P20.0134A6f N60.0015 P8f P7+P10.0019N10f N7+P30.0080MCP f N60.0238 P8f P6+P20.0056N9f N8+P10.0127N6f MCP0.0040 P8f P5+P30.0034N9f N7+P20.0127Ldp>20nPeln11-x(7)Pe)0.087Rep0.23(L d p)(8)1036Energy&Fuels,Vol.14,No.5,2000Ancheyta-Jua´rez and Villafuerte-Macı´asconversion of naphthenes was found in the first30%of the catalyst bed.After60%of the catalyst bed,naph-thenes concentration approaches a very low steady-state value.The relative rates of naphthenes and paraffins con-version are very different in the first20-30%of the catalyst bed.While N6and N7are almost totally converted in this section,MCP and paraffins have a low conversion.This means that MCP is much less reactive than N6or N7.The A6composition calculated with the proposed kinetic model matches very well with experimental data with a maximum deviation of2%.ConclusionsA new kinetic model for naphtha catalytic reforming reactions has been developed.The model takes into account the most important reactions of this process in terms of isomers of the same nature(paraffins,naph-thenes,and aromatics).The groups range from1to11carbon atoms for paraffins and from6to11atoms of carbon for naph-thenes and aromatics.Paraffins and MCP isomerization reactions are also included,and the effects of temper-ature and pressure on the kinetic constants were added as an Arrhenius-type variation.The proposed kinetic model has24differential equa-tion with71kinetic parameters,which were estimated using experimental information obtained in a fixed-bed pilot plant.The calculated reformate composition agrees very well with experimental data with average deviation less than3%.NomenclatureA10)aromatics with10atoms of carbonA10+)aromatics with10+11atoms of carbonA11)aromatics with11atoms of carbonC10)hydrocarbons with10atoms of carbonC10+)hydrocarbons with10+11atoms of carbonC11)hydrocarbons with11atoms of carbond p)particle diameterE A)activation energyk i)kinetic constant at Tk i o)kinetic constant at Tok10)kinetic constant for hydrocarbons with10atoms of carbonk10+)kinetic constant for hydrocarbons with10+11atoms of carbonk11)kinetic constant for hydrocarbons with11atoms of carbonL)reactor lengthn)reaction orderN10)naphthenes with10atoms of carbonN10+)naphthenes with10+11atoms of carbonN11)naphthenes with11atoms of carbonP)reaction pressurePo)base reaction pressureP10)paraffins with10atoms of carbonP10+)paraffins with10+11atoms of carbonP11)paraffins with11atoms of carbonPe)Peclet numberRe p)Reynolds number based on particle diameterSV)space velocityT)reaction temperatureTo)base reaction temperaturex)conversionAcknowledgment.The authors wish to thank In-stituto Mexicano del Petro´leo for its financial support EF0000274Figure3.Experimental(points)and calculated(lines)refor-mate composition at510°C.Naphtha Catalytic Reforming Reactions Energy&Fuels,Vol.14,No.5,20001037。