1032
Energy & Fuels 2000, 14, 1032-1037
Kinetic Modeling of Naphtha Catalytic Reforming Reactions Jorge Ancheyta-Jua´rez* and Eduardo Villafuerte-Macı´as Instituto Mexicano del Petro´ leo, Eje Central La´ zaro Ca´ rdenas 152, Me´ xico 07730 D.F., Mexico, and Instituto Polite´ cnico Nacional, ESIQIE, Me´ xico 07738 D.F., Mexico Received February 21, 2000
In 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 from 1 to 11 atoms of carbon for paraffins, and from 6 to 11 carbon 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. Introduction Catalytic reforming of straight run naphthas is a very important process for octane improvement and production 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 between 450 and 520 °C, total pressures between 10 and 35 atm, and molar hydrogen-to-hydrocarbon ratios between 3 and 8. The feed to the first reactor is a hydrodesulfurized naphtha cut, composed of normal and branched paraffins, fiveand six-membered ring naphthenes, and single-ring aromatics. A large number of reactions occur in catalytic reforming, such as dehydrogenation and dehydroisomerization of naphthenes to aromatics, dehydrogenation of paraffins 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 differential 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 * To whom correspondence should be addressed. Instituto Mexicano del Petro´leo. FAX: (+52-5) 587-3967. E-mail:
[email protected].
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 predicting 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 reforming have been reported in the literature, which have different levels of sophistication.2-6 All 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, naphthenes, and aromatics, is represented by a single compound having the average properties of that class. The kinetic model of Krane et al.3 is one of the more elaborate models which considers all possible reactions for each individual hydrocarbon. However, the temperature 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 methylcyclopentane (MCP), and it does not take into account the reaction rates of hydrocarbons with 11 atoms of carbon because only hydrocarbon up to 10 atoms of carbon are considered. In the present paper the Krane et al. model is extended in order to consider these deficiencies. (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 the 5th World Petroleum Congress 1959, 39-51. (4) Henningsen, J.; Bundgaard, N. M. Chem. Eng. 1970, 15, 10731087. (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.
10.1021/ef0000274 CCC: $19.00 © 2000 American Chemical Society Published on Web 08/02/2000
Naphtha Catalytic Reforming Reactions
Energy & Fuels, Vol. 14, No. 5, 2000 1033 Table 1. Reactions of the Krane et al.1 and the Proposed Kinetic Models
2. Kinetic Model The proposed kinetic model is an extension of the model reported by Krane et al.,3 which 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 from 1 to 10 carbon atoms for paraffins, and from 6 to 10 carbon atoms for naphthenes and aromatics. The Krane model includes the chemical reactions summarized in the first column of Table 1. 2.1. Kinetic Constants for C11 Hydrocarbons. A catalytic reforming feedstock includes compounds having carbon number up to C11 as can be seen in Table 2. The Krane model groups in three lumps the hydrocarbons with 10 and 11 atoms of carbon (P10+ ) P10 + P11, N10+ ) N10 + N11, and A10+ ) A10 + A11, called in general as C10+ ) C10 + C11). This implies that the reaction rate for each hydrocarbon has the following equation:
dC+ 10 1 d SV
( )
+ + ) k+ 10C10 ) k10(C10 + C11)
(1)
Equation 1 can also be written as a function of C10 and C11 and their individual kinetic constants (k10 and k11) as follows:
dC+ 10 ) k10C10 + k11C11 1 d SV
( )
(2)
From eqs 1 and 2 the following expression can be obtained:
k10 )
k+ 10(R + 1) (R + K)
(3)
where
R)
C10 C11
(4)
K)
k11 k10
(5)
Equations 3 and 5 can be used for evaluating the individual kinetic constants for hydrocarbons with 10 and 11 atoms of carbon, k10 and k11, respectively. In this calculation, the two ratios defined by eqs 4 and 5 are needed. To evaluate the constant R for each hydrocarbon type (eq 4), 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 Table 2. The different values of R are: P10/P11 ) 9.099, N10/N11 ) 5.087, and A10/A11 ) 24.294. The values of K (eq 5) 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. Figure 1 shows this procedure for two reactions of hydrocracking of paraffins to
number of reactions reactiona paraffins Pn f Nn Pn f Pn-i + Pi subtotal naphthenes Nn f An Nn f Nn-i + Pi Nn f Pn subtotal aromatics An f An-i + Pi An f Pn An f Nn subtotal total a
Krane model
this work
4 21 25
6 26 32
5 6 5 16
6 11 7 24
5 4 1 10 53
7 5 1 13 71
n: number of atoms of carbon (1 e i e 5)
paraffins with less number of carbon atoms. The complete results of these extrapolations and the final values of the individual kinetic constants for hydrocarbon with 10 and 11 atoms of carbon are presented in Table 3. 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 (P6 T MCP). The Krane model only takes into account the following path reaction: P6 T N6 T A6. As it was mentioned before, it is very important to accurately predict benzene content in reformate. Because it is impossible to tell exactly how much benzene is produced by each of the various identified reaction mechanisms,7 the assumption that all benzene is produced via cyclohexane dehydrogenation was considered in the present work, and the reaction network shown in Figure 2, 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.8 Therefore, 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 reforming conditions.9 Hence, 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 serious 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 temperature range in which Krane fit the parameters (800960 °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; p 184.
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Energy & Fuels, Vol. 14, No. 5, 2000
Ancheyta-Jua´ rez and Villafuerte-Macı´as
Table 2. PIONA Analysis of a Catalytic Reforming Feedstock n-paraffins C4 C5 C6 C7 C8 C9 C10 C11 i-paraffins C4 C5 C6 C7 C8 C9 C10 C11 naphthenes C5 C6 C7 C8 C9 C10 C11 aromatics C6 C7 C8 C9 C10 C11
sample 1
sample 2
sample 3
sample 4
sample 5
sample 6
average
0.000 1.818 9.633 8.116 6.464 4.454 1.640 0.297
1.568 11.368 8.034 6.778 5.326 3.514 1.403 0.266
0.000 9.818 8.356 7.114 5.602 3.858 1.707 0.321
0.000 10.362 8.412 7.148 5.616 3.809 1.635 0.292
0.000 1.983 9.467 8.386 6.640 4.625 1.948 0.318
0.000 1.392 9.477 8.402 6.683 4.680 2.066 0.370
0.261 6.124 8.897 7.657 6.055 4.157 1.733 0.311
0.000 0.565 8.838 6.759 7.070 6.241 3.526 0.212
0.076 6.459 7.269 5.656 5.897 5.066 2.840 0.203
0.000 3.191 7.448 5.932 6.310 5.499 3.384 0.281
0.000 3.771 7.469 5.965 6.187 5.311 3.221 0.254
0.000 0.794 4.845 6.943 7.289 6.448 3.899 0.289
0.000 0.453 5.299 6.963 7.344 6.509 4.402 0.374
0.013 2.539 6.861 6.370 6.680 5.846 3.545 0.269
0.897 5.069 6.934 5.112 1.842 0.495 0.096
0.977 4.345 6.038 4.307 1.535 0.398 0.085
0.973 4.435 6.071 4.593 1.655 0.558 0.106
0.978 4.434 6.065 4.565 1.578 0.492 0.099
0.333 5.226 7.179 5.320 1.938 0.561 0.105
0.286 5.166 7.157 5.461 1.970 0.641 0.125
0.741 4.783 6.574 4.893 1.753 0.524 0.103
1.393 3.506 5.326 2.908 0.707 0.032
1.074 2.676 4.015 2.186 0.569 0.032
1.200 3.024 4.529 2.956 0.903 0.035
1.199 3.038 4.542 2.671 0.830 0.031
1.380 3.634 5.507 3.488 0.891 0.036
1.351 3.576 5.428 3.218 1.056 0.037
1.266 3.242 4.891 2.905 0.826 0.034
as follows.10 The values of activation energies and pressure effect factors are given in Tables 4 and 5, respectively.
ki ) k0i
Figure 1. Evaluation of the constant K for P11 dehydrogenation reactions.
ported.10 The activation energy values for all reactions were taken from the literature.4 Another limitation of the Krane model is that experimental data do not include variations in operating pressure. The model, therefore, is valid only at the base pressure (300 psig). 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.10,11 The equation for the combined effect of temperature and pressure on the kinetic constants can be expressed (10) Ancheyta, J. J.; Aguilar, R. E. Oil Gas J. 1994, Jan. 31, 9395. (11) Jenkins, J. H.; Stephens, T. W. Hyd. Proc. 1980 (Nov), 163167.
[ (
EAj 1 1 R T0 T
)]( ) P P0
Rk
(6)
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 18 more reactions compared to the Krane model. Four more lumps can be directly predicted with this new model, P11, N11, A11, and MCP, and by equilibrium calculations, six iso-paraffin lumps (i-P5, i-P6, i-P7, i-P8, i-P9, i-P10) can also be estimated. In addition, benzene formation can be more accurately calculated, since the reactions between N6 and MCP were incorporated to the model. 3. Pilot Plant Experiments 3.1. Materials. The feedstock used in this study was an hydrodesulfurized straight-run naphtha (distillation range: 82.3-168.1 °C and density of 0.74 g/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 0.5 wppm sulfur, and its water content was less than 1 wppm. The feedstock was derived from a crude oil with the following properties: 26.9°API, 2.3 wt % sulfur, 4.5 wt % asphaltenes, 5.9 wt % Conradson carbon, and 54 and 266 wppm of Ni and V, respectively. The catalyst used in this investigation was a commercial available Pt-Re reforming sample (Pt, 0.29 wt %; Re, 0.29 wt
Naphtha Catalytic Reforming Reactions
Energy & Fuels, Vol. 14, No. 5, 2000 1035
Table 3. Individual Kinetic Constants for Hydrocarbons with 10 and 11 Atoms of Carbon reaction PfN Pn f Pn-1 + P1 Pn f Pn-2 + P2 Pn f Pn-3 + P3 Pn f Pn-4 + P4 Pn f Pn-5 + P5 NfP NfA Nn f Nn-1 + P1 Nn f Nn-2 + P2 Nn f Nn-3 + P3 An f An-1 + P1 An f An-2 + P2 AfP a
C6/C5
C7/C6
C8/C7
C9/C8
C10/C9
C11/C10
k+10a
k10
k11
1.1667 1.2000
1.0000 1.0000 1.1852
2.2931 1.3571 1.3888 1.3438
1.3609 1.5789 1.5600 1.5814 1.5714
1.4033 1.6333 1.6154 1.6029 1.6182
1.4645 1.6678b 1.6499b 1.6170 1.6212
0.1351 2.2587
2.3500 2.3678
1.1489 1.1395 14.111
1.0000 1.0000 1.0551 1.0551
5.0000
1.2000 1.2000 1.0000
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.0254 0.0049 0.0063 0.0109 0.0089 0.0124 0.0054 0.2450 0.0134 0.0134 0.0080 0.0006 0.0006 0.0016
0.0243 0.0046 0.0059 0.0103 0.0084 0.0117 0.0054 0.2450 0.0134 0.0134 0.0080 0.0006 0.0006 0.0016
0.0356 0.0077 0.0097 0.0166 0.0135 0.0191 0.0054 0.2450 0.0134 0.0134 0.0080 0.0006 0.0008 0.0016
1.0000
1.0000
Original kinetic constant. b Values evaluated with Figure 1. Table 4. Activation Energies for Each Reforming Reaction4 reaction j paraffins Pn f Nn Pn f Pn-i + Pi naphthenes Nn f An Nn f Nn-i + Pi Nn f Pn aromatics An f An-i + Pi An f Pn An f Nn
Figure 2. Reaction network for benzene formation. 2
%) having a surface area of 221 m /g, pore volume of 0.36 mL/ gm, and particle diameter of 1.6 mm. 3.2. Pilot Plant Tests. The tests were performed in a fixedbed pilot plant with hydrogen recycle. The unit consists of a stainless steel reactor (internal diameter of 2.5 cm and length of 25 cm), which was operated in isothermal mode by independent temperature control of a three-zone electric furnace. The tests were carried out at pressure of 10.5 kg/cm2; molar H2/hydrocarbon ratio of 6.5; and temperatures of 490, 500 and 510 °C. To simulate a series of three reforming reactors, the pilot reactor was loaded with different amounts of catalyst, 6, 15, and 30 mL keeping the same naphtha flow at a constant value of 102 mL/h in order to have different space-velocities (WHSV), 17.72, 7.09, and 3.54 h-1, respectively. These amounts of catalyst and WHSV were selected in order to have 20% of the total mass of catalyst in the first reactor, 30% in the second reactor, and 50% 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 with 20% of the total mass of catalyst. The temperature drop, measured with an axial thermocouple, was less than 5 °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 analyzed on paraffins, i-paraffins, naphthenes, and aromatics by GC.
4. Results and Discussion 4.1. Reforming Experiments. Table 7 shows the detailed composition of the reformate as a function of reaction temperatures at WHSV of 3.54 h-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 13.28 mol % to 52.8, 56.66, and 61.19 mol % at 490, 500, and 510 °C, respectively. It should be noted that the most important increase is observed in lighter aromatics, especially A6, A7, and A8.
EAj (kcal/mol) 45 55 30 55 45 40 45 30
Table 5. Factors for Pressure Effect10 reaction k
Rk
isomerization dehydrocyclization hydrocracking hydrodealquilation
0.370 -0.700 0.433 0.500
Table 6. PIONA Analysis of the Pilot Plant Feedstock C4 C5 C6 C7 C8 C9 C10 C11
n-paraffins
i-paraffins
naphthenes
aromatics
3.80 4.40 3.20 6.36 5.09 2.97 2.20
3.40 6.70 6.20 6.52 8.32 6.22
0.42 3.21 5.80 4.71 3.56 0.60 0.40
0.80 3.22 4.71 4.21 2.70 0.30
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 N11 disappear completely and the conversion of N7 and N8 is higher than 82%. It was also confirmed that naphthenes dehydrogenation is favored by high reaction temperature as they were almost completely converted at temperatures higher than 490 °C (> 86% conversion of total amount of naphthenes). This is the main reason because naphthenes 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 is
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Energy & Fuels, Vol. 14, No. 5, 2000
Ancheyta-Jua´ rez and Villafuerte-Macı´as
Table 7. Composition of Different Reformates at WHSV of 3.54 h-1 reaction temperature
n-paraffins P11 P10 P9 P8 P7 P6 P5 total i-paraffins iP10 iP9 iP8 iP7 iP6 iP5 total naphthenes N11 N10 N9 N8 N7 N6 MCP total aromatics A11 A10 A9 A8 A7 A6 total
490 °C
500 °C
510 °C
0.01 0.09 0.40 1.22 2.91 5.50 5.25 15.38
0.01 0.00 0.28 0.91 2.44 5.21 4.96 13.97
0.00 0.00 0.18 0.63 1.97 4.40 4.85 12.03
0.28 1.50 3.75 7.99 9.39 6.39 29.30
0.17 1.24 2.74 7.27 9.48 6.18 27.08
0.85 0.67 2.01 6.07 9.83 5.53 24.96
0.00 0.00 0.01 0.63 0.33 0.01 1.35 2.33
0.00 0.00 0.02 0.66 0.31 0.01 1.23 2.23
0.00 0.00 0.01 0.38 0.27 0.01 1.15 1.82
0.97 5.60 12.51 15.63 12.80 5.29 52.80
1.10 5.75 13.17 16.86 13.88 5.90 56.66
1.25 5.99 14.17 18.20 15.02 6.56 61.19
low. In this work, the naphtha used in the experiments has a high paraffin content (34.56 mol % n-paraffins and 34.69 mol % i-paraffins). The most difficult reaction to promote is the dehydrocyclization 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. The 71 kinetic parameters of the proposed kinetic model were estimated using the experimental information obtained at reaction temperature of 490 °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 into 24 simultaneous differential equations, which comprise the kinetic model. The kinetic model was incorporated into an isothermal 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
Table 8. Kinetic Constants of the Proposed Model reaction step
k
reaction step
k
reaction step
k
P11 f N11 P10 f N10 P9 f N9 P8 f N8 P7 f N7 P6 f N6 P6 f MCP P11 f P10+P1 P11 f P9 + P2 P11 f P8 + P3 P11 f P7 + P4 P11 f P6 + P5 P10 f P9 + P1 P10 f P8 + P2 P10 f P7 + P3 P10 f P6 + P4 P10 f 2P5 P9 f P8 + P1 P9 f P7 + P2 P9 f P6 + P3 P9 f P5 + P4 P8 f P7 + P1 P8 f P6 + P2 P8 f P5 + P3
0.0356 0.0243 0.0500 0.0266 0.0076 0.0000 0.0042 0.0075 0.0100 0.0135 0.0135 0.0191 0.0015 0.0054 0.0160 0.0095 0.0095 0.0030 0.0039 0.0068 0.0058 0.0019 0.0056 0.0034
P 8 f P4 P 7 f P6 + P1 P 7 f P5 + P2 P 7 f P4 + P3 P 6 f P5 + P1 P 6 f P4 + P2 P6 f 2P3 P 5 f P4 + P1 P 5 f P3 + P2 N11 f P11 N10 f P10 N 9 f P9 N 8 f P8 N 7 f P7 N 6 f P6 MCP f P6 N11 f N10+P1 N11 f N9 + P2 N11 f N8 + P3 N10 f N9 + P1 N10 f N8 + P2 N10 f N7 + P3 N 9 f N8 + P 1 N 9 f N7 + P 2
0.0070 0.0027 0.0018 0.0043 0.0018 0.0016 0.0025 0.0018 0.0022 0.0050 0.0054 0.0054 0.0025 0.0019 0.0204 0.0008 0.0134 0.0134 0.0080 0.0134 0.0134 0.0080 0.0127 0.0127
N 8 f N7 + P1 N11 f A11 N10 f A10 N 9 f A9 N 8 f A8 N 7 f A7 N 6 f A6 A11 f P11 A10 f P10 A 9 f P9 A 8 f P8 A 7 f P7 A11 f A10 +P1 A11 f A9 + P2 A10 f A9 + P1 A 1 f A 8 + P2 A10 f A7 + P3 A 9 f A 8 + P1 A 9 f A 7 + P2 A 8 f A 7 + P1 A 6 f N6 MCP f N6 N6 f MCP
0.0007 0.6738 0.3198 0.2205 0.2150 0.0788 0.1368 0.0016 0.0016 0.0016 0.0011 0.0016 0.0006 0.0006 0.0006 0.0006 0.0000 0.0005 0.0005 0.0001 0.0015 0.0238 0.0040
examined and satisfied:12
L 1 20n ln > dp Pe 1 - x
(7)
where
Pe ) 0.087Re0.23 p
() L dp
(8)
To evaluate the product yields as a function of reactor length from a set of kinetic constants a pseudohomogeneous model13 was 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.3 The best values of all the kinetic constants are presented in Table 8. 4.3. Validation of the Kinetic Model. The conversion 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 Figure 3. 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 than 3%. It can also be seen from Figure 3 that, as the naphtha passes through the catalyst bed, A6 concentration increases. The same behavior was found with all aromatics compounds. The concentration of N6 and N7 and heavy paraffins (P7-P11, only P7 is 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.
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Energy & Fuels, Vol. 14, No. 5, 2000 1037
account the most important reactions of this process in terms of isomers of the same nature (paraffins, naphthenes, and aromatics). The groups range from 1 to 11 carbon atoms for paraffins and from 6 to 11 atoms of carbon for naphthenes and aromatics. Paraffins and MCP isomerization reactions are also included, and the effects of temperature and pressure on the kinetic constants were added as an Arrhenius-type variation. The proposed kinetic model has 24 differential equation with 71 kinetic 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 than 3%. Nomenclature
Figure 3. Experimental (points) and calculated (lines) reformate composition at 510 °C.
conversion of naphthenes was found in the first 30% of the catalyst bed. After 60% of the catalyst bed, naphthenes concentration approaches a very low steady-state value. The relative rates of naphthenes and paraffins conversion are very different in the first 20-30% of the catalyst bed. While N6 and N7 are almost totally converted in this section, MCP and paraffins have a low conversion. This means that MCP is much less reactive than N6 or N7. The A6 composition calculated with the proposed kinetic model matches very well with experimental data with a maximum deviation of 2%. Conclusions A new kinetic model for naphtha catalytic reforming reactions has been developed. The model takes into
A10 ) aromatics with 10 atoms of carbon A10+ ) aromatics with 10+11 atoms of carbon A11 ) aromatics with 11 atoms of carbon C10 ) hydrocarbons with 10 atoms of carbon C10+ ) hydrocarbons with 10+11 atoms of carbon C11 ) hydrocarbons with 11 atoms of carbon dp ) particle diameter EA ) activation energy ki ) kinetic constant at T kio ) kinetic constant at To k10 ) kinetic constant for hydrocarbons with 10 atoms of carbon k10+ ) kinetic constant for hydrocarbons with 10+11 atoms of carbon k11 ) kinetic constant for hydrocarbons with 11 atoms of carbon L ) reactor length n ) reaction order N10 ) naphthenes with 10 atoms of carbon N10+ ) naphthenes with 10+11 atoms of carbon N11 ) naphthenes with 11 atoms of carbon P ) reaction pressure Po ) base reaction pressure P10 ) paraffins with 10 atoms of carbon P10+ ) paraffins with 10+11 atoms of carbon P11 ) paraffins with 11 atoms of carbon Pe ) Peclet number Rep ) Reynolds number based on particle diameter SV ) space velocity T ) reaction temperature To ) base reaction temperature x ) conversion
Acknowledgment. The authors wish to thank Instituto Mexicano del Petro´leo for its financial support EF0000274
