Development of the Kinetic Model
The kinetic model used for the simulation of catalytic reforming reactors is an extension of that reported by Krane et al. (1959), 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 original model reported by Krane et al. (1959) includes 53 chemical reactions, which are summarized in Table 4.4 .
TABLE 4.4. Chemical Reactions Considered in the Original Kinetic Model Reported by Krane et al. (1959), Activation Energies, and Factors for Pressure Effect for Each Reforming Reaction
|
Reactiona |
Number of Reactions |
EAj (kcal/mol) |
|
Paraffins |
||
 |
4 |
45 |
 |
21 |
55 |
|
Subtotal |
25 |
|
|
Naphthenes |
||
 |
5 |
30 |
 |
6 |
55 |
 |
5 |
45 |
|
Subtotal |
16 |
|
|
Aromatics |
||
 |
5 |
40 |
 |
4 |
45 |
 |
1 |
30 |
|
Subtotal |
10 |
|
Reaction |
ak |
|
Isomerization |
0.370 |
|
Dehydrocyclization |
-0.700 |
|
Hydrocracking |
0.433 |
|
Hydrodealkylation |
0.500 |
|
Dehydrogenation |
0.000 |
"n, number of atoms of carbon
To account for more reactions and have better naphtha composition predictability, the original model was modified in several ways, described below.
Kinetic Parameters for Hydrocarbons with 11 Atoms of Carbon Typical naphthas used as feed in catalytic reforming include hydrocarbons with up to 11 atoms of carbon, as can be seen in Table 4.5. The original Krane et al. (1959) model considers reactions only for hydrocarbons with 10 atoms of carbon. To maintain the original values of kinetic parameters, it was assumed that the hydrocarbons reported as having 10 atoms of carbon are, in fact, a lump of hydrocarbons with 10 and 11 atoms of carbon: C+0 = C10 + Cn. In such a way, the different hydrocarbon species can be delumped as follows:
TABLE 4.5. Typical Compositions of Various Feeds to Catalytic Reforming Process
|
|
|
Naphthas |
|
|
Average Value |
||
|
1 |
2 |
3 |
4 |
5 |
6 |
||
|
n-Paraffins |
|
|
|
|
|
|
|
|
C4 |
0 |
1.568 |
0 |
0 |
0 |
0 |
0.261 |
|
C5 |
1.818 |
11.368 |
9.818 |
10.362 |
1.983 |
1.392 |
6.124 |
|
C6 |
9.633 |
8.034 |
8.356 |
8.412 |
9.467 |
9.477 |
8.897 |
|
C7 |
8.116 |
6.778 |
7.114 |
7.148 |
8.386 |
8.402 |
7.657 |
|
C8 |
6.464 |
5.326 |
5.602 |
5.616 |
6.640 |
6.683 |
6.055 |
|
C9 |
4.454 |
3.514 |
3.858 |
3.809 |
4.625 |
4.68 |
4.157 |
|
C10 |
1.640 |
1.403 |
1.707 |
1.635 |
1.948 |
2.066 |
1.733 |
|
CU |
0.297 |
0.266 |
0.321 |
0.292 |
0.318 |
0.370 |
0.311 |
|
Subtotal |
32.422 |
38.257 |
36.776 |
37.274 |
33.367 |
33.07 |
35.194 |
|
i- Paraffins |
|||||||
|
C4 |
0 |
0.076 |
0 |
0 |
0 |
0 |
0.013 |
|
C5 |
0.565 |
6.459 |
3.191 |
3.771 |
0.794 |
0.453 |
2.539 |
|
C6 |
8.868 |
7.289 |
7.548 |
7.495 |
5.373 |
5.413 |
6.998 |
|
C7 |
6.779 |
5.676 |
5.973 |
5.965 |
6.943 |
6.963 |
6.383 |
|
C8 |
7.070 |
5.897 |
6.310 |
6.187 |
7.289 |
7.344 |
6.683 |
|
C9 |
6.241 |
5.066 |
5.499 |
5.311 |
6.448 |
6.509 |
5.846 |
|
C10 |
3.526 |
2.84 |
3.384 |
3.221 |
3.899 |
4.402 |
3.545 |
|
CU |
0.212 |
0.203 |
0.281 |
0.254 |
0.289 |
0.374 |
0.269 |
|
Subtotal |
33.261 |
33.506 |
32.186 |
32.204 |
31.035 |
31.458 |
32.275 |
|
Naphthenes |
|||||||
|
C5 |
0.897 |
0.977 |
0.973 |
0.978 |
0.333 |
0.286 |
0.741 |
|
C6 |
5.069 |
4.345 |
4.435 |
4.434 |
5.226 |
5.166 |
4.779 |
|
C7 |
6.934 |
6.038 |
6.071 |
6.065 |
7.179 |
7.157 |
6.574 |
|
C8 |
5.112 |
4.307 |
4.593 |
4.565 |
5.320 |
5.461 |
4.893 |
|
C9 |
1.842 |
1.535 |
1.655 |
1.578 |
1.938 |
1.970 |
1.753 |
|
C10 |
0.495 |
0.398 |
0.558 |
0.492 |
0.561 |
0.641 |
0.524 |
|
CU |
0.096 |
0.085 |
0.106 |
0.099 |
0.105 |
0.125 |
0.103 |
|
Subtotal |
20.445 |
17.685 |
18.391 |
18.211 |
20.662 |
20.806 |
19.367 |
|
Aromatics |
|||||||
|
C6 |
1.393 |
1.074 |
1.200 |
1.199 |
1.380 |
1.351 |
1.266 |
|
C7 |
3.506 |
2.676 |
3.024 |
3.038 |
3.634 |
3.576 |
3.242 |
|
C8 |
5.326 |
4.015 |
4.529 |
4.542 |
5.507 |
5.428 |
4.891 |
|
C9 |
2.908 |
2.186 |
2.956 |
2.671 |
3.488 |
3.218 |
2.905 |
|
C10 |
0.707 |
0.569 |
0.903 |
0.830 |
0.891 |
1.056 |
0.826 |
|
CU |
0.032 |
0.032 |
0.035 |
0.031 |
0.036 |
0.037 |
0.034 |
|
Subtotal |
13.872 |
10.552 |
12.647 |
12.311 |
14.936 |
14.666 |
13.164 |
The reaction rate equation originally reported for each hydrocarbon can then be expressed as
This equation can also be written as a function of C10 and C11 and their individual kinetic parameters (k10 and k11):
By combining Eqs. (4.22) and (4.23), the following relationship can be derived:
where
Equations (4.24) to (4.26) can be used to calculate the values of the individual kinetic parameters for hydrocarbons with 10 and 11 atoms of carbon, k10 and k11, respectively. For this calculation, the relationships defined by Eqs. (4.25) and (4.26) are needed.
To determine the value of the constant R for each hydrocarbon type [(Eq. (4.25)], typical feed used in a commercial catalytic reforming unit was analyzed during different periods of time. Feed compositions are reported in Table 4.5. From this table, the corresponding values of R for this specific feed are
For calculation of RP, the total amount of paraffin was used: that is, the sum of n- and /-paraffins. The values of K [Eq. (4.26)] were obtained for each reaction by extrapolation of the relationships calculated with the original kinetic parameters reported by Krane et al. (1959) as a function of the number of atoms of carbon (e.g., k7/k6, k8/k7, k9/k8- and k10/k9). Figure 4.5 illustrates this procedure for two reactions of hydrocracking of paraffins to paraffins with fewer carbon atoms. Details on the final set of individual kinetic parameters for the reactions of hydrocarbons with 10 and 11 atoms of carbon are provided in Table 4.6 .
Figure 4.5. Example of the extrapolation procedure to calculate the constant K.
Reactions for the Formation of Benzene The original model proposed by Krane et al. (1959) does not take into account either the formation of cyclo-hexane (N-) via methylcyclopentane (MCP) isomerization ( MCP o N6) or the production of MCP from P6 (P6 o MCP). The Krane et al. (1959) model considers only the path reaction P6 o N6 o A6. Due to the importance of benzene content in reformate for accurate prediction, it is necessary to add those reactions in which benzene is taking part. Thus, the reaction network shown in Figure 4.6 and the corresponding contribution to the reaction rate equations were added to the kinetic model. Also, it was assumed that all the benzene is produced via cyclohexane dehydrogenation.
Isomerization of Paraffins The reactions of isomerization of n-paraffins to i-paraffins are highly desired during catalytic reforming of naphtha, since the i-paraffins produced contribute to the increase in octane number of the refor-mate. Isomerization is a fast reaction catalyzed by acid sites, and it reaches equilibrium at catalytic reforming conditions. Hence, paraffin distribution can be estimated by thermodynamic equilibrium calculation.
For the following general isomerization reaction:
the equilibrium constant (Ke) is
TABLE 4.6. Individual Kinetic Constants for Hydrocarbons with 10 and 11 Atoms of Carbon
|
Reaction |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
— |
— |
2.2931 |
1.3609 |
1.4033 |
1.4645 |
0.0254 |
0.0243 |
0.0356 |
 |
1.1667 |
1.0000 |
1.3571 |
1.5789 |
1.6333 |
1.6678 |
0.0049 |
0.0046 |
0.0077 |
 |
1.2000 |
1.0000 |
1.3888 |
1.5600 |
1.6154 |
1.6499 |
0.0063 |
0.0059 |
0.0097 |
 |
— |
1.1852 |
1.3438 |
1.5814 |
1.6029 |
1.6170 |
0.0109 |
0.0103 |
0.0166 |
 |
— |
— |
— |
1.5714 |
1.6182 |
1.6212 |
0.0089 |
0.0084 |
0.0135 |
 |
— |
— |
— |
— |
— |
— |
0.0124 |
0.0117 |
0.0191 |
 |
— |
0.1351 |
2.3500 |
1.1489 |
1.0000 |
1.0000 |
0.0054 |
0.0054 |
0.0054 |
 |
— |
2.2587 |
2.3678 |
1.1395 |
1.0000 |
1.0000 |
0.2450 |
0.2450 |
0.2450 |
 |
— |
— |
— |
14.111 |
1.0551 |
1.0000 |
0.0134 |
0.0134 |
0.0134 |
 |
— |
— |
— |
— |
1.0551 |
1.0000 |
0.0134 |
0.0134 |
0.0134 |
 |
— |
— |
— |
— |
— |
1.0000 |
0.0080 |
0.0080 |
0.0080 |
 |
— |
— |
— |
5.0000 |
1.2000 |
1.0000 |
0.0006 |
0.0006 |
0.0006 |
 |
— |
— |
— |
— |
1.2000 |
1.0000 |
0.0006 |
0.0006 |
0.0008 |
 |
— |
— |
1.0000 |
1.0000 |
1.0000 |
1.0000 |
0.0016 |
0.0016 |
0.0016 |
aExtrapolated values.
‘Original kinetic parameters reported by Krane et al. (1959). ‘Calculated values of kinetic parameters.
Figure 4.6. Reaction network for benzene formation.
The effect of temperature on equilibrium constant is given by (Smith et al. 1996) where AG° is the reaction standard Gibbs energy. AG° can be determined as 
where
To calculate AG° with Eq. (4.33) – the following dependence of heat capacity on temperature can be used:
By sustituting Eq. (4.34) in Eq. (4.33), the integrals can be evaluated using the following final forms:
To employ the foregoing procedure for equilibrium calculation of the paraffin isomerization reactions that occur in catalytic reforming, some thermody-namic data are required, which are depicted in Table 4.7. For example, for the isomerization of n-hexane, four isomers are obtained: 2-methylpentane, 3- methylpentane, 2,2 – dimethylbutane, and 2,3 – dimethylbutane. Each isomeri-zation reaction needs to be considered separately. The values calculated for all parameters required to evaluate AG° are reported in Table 4.8. With AG°, Ke is then computed using Eq. (4.32)- Once the values of all Ke have been determined, the formula needed to calculate the composition (y ) of all isomers is deduced from Eq. (4.31):
TABLE 4.7. Thermodynamic Data of Various Paraffins
|
Name |
A |
B |
|
n -Butane |
2.266 |
7.91E-02 |
|
;-Butane |
-0.332 |
9.19E-02 |
|
«-Pentane |
-0.866 |
1.16E-01 |
|
2-Methylbutane |
-2.275 |
1.21E-01 |
|
2,2-Dime thylpropane |
-3.963 |
1.33E-01 |
|
7!-Hexane |
-1.054 |
1.39E-01 |
|
2-Methylpentane |
-2.524 |
1.48E-01 |
|
3-Methylpentane |
-0.570 |
1.36E-01 |
|
2,2-Dime thylbutane |
-3.973 |
1.50E-01 |
|
2,3-Dimethylbutane |
-3.489 |
1.47E-01 |
|
n -Heptane |
-1.229 |
1.62E-01 |
|
2-Methylhexane |
-9.408 |
2.06E-01 |
|
3-Methylhexane |
-1.683 |
1.63E-01 |
|
2,2-Dime thylpentane |
-11.966 |
2.14E-01 |
|
2,3-Dimethylpentane |
-1.683 |
1.63E-01 |
|
2,4-Dime thylpentane |
-1.683 |
1.63E-01 |
|
3,3-Dime thylpentane |
-1.683 |
1.63E-01 |
|
3-Ethylpentane |
-1.683 |
1.63E-01 |
|
n-Octane |
-1.456 |
1.84E-01 |
|
2-Methylheptane |
-21.435 |
2.97E-01 |
|
3-Methylheptane |
-2.201 |
1.88E-01 |
|
4-Methylheptane |
-2.201 |
1.88E-01 |
|
2,2-Dime thylhexane |
-2.201 |
1.88E-01 |
|
c |
D |
H° |
G° |
|
-2.65E-05 |
-6.74E-10 |
-30.15 |
-4.10 |
|
^.41E-05 |
6.92E-09 |
-32.15 |
-4.99 |
|
-6.16E-05 |
1.27E-08 |
-35.00 |
-2.00 |
|
-6.52E-05 |
1.37E-08 |
-36.92 |
-3.54 |
|
-7.90E-05 |
1.82E-08 |
-39.67 |
-3.64 |
|
-7.45E-05 |
1.55E-08 |
-39.96 |
-0.06 |
|
-8.53E-05 |
1.93E-08 |
^1.66 |
-1.20 |
|
-6.85E-05 |
1.20E-08 |
-41.02 |
-0.51 |
|
-8.31E-05 |
1.64E-08 |
^4.35 |
-2.30 |
|
-8.06E-05 |
1.63E-08 |
^2.49 |
-0.98 |
|
-8.72E-05 |
1.83E-08 |
^4.88 |
1.91 |
|
-1.50E-04 |
4.39E-08 |
^6.59 |
0.77 |
|
-8.92E-05 |
1.87E-08 |
^5.96 |
1.10 |
|
-1.52E-04 |
4.15E-08 |
^9.27 |
0.02 |
|
-8.92E-05 |
1.87E-08 |
-A1.62 |
0.16 |
|
-8.92E-05 |
1.87E-08 |
^8.28 |
0.74 |
|
-8.92E-05 |
1.87E-08 |
-48.17 |
0.63 |
|
-8.92E-05 |
1.87E-08 |
^5.33 |
2.63 |
|
-1.00E-04 |
2.12E-08 |
^9.82 |
3.92 |
|
-2.81E-04 |
1.10E-07 |
-51.50 |
3.05 |
|
-1.05E-04 |
2.32E-08 |
-50.82 |
3.28 |
|
-1.05E-04 |
2.32E-08 |
-50.69 |
4.00 |
|
-1.05E-04 |
2.32E-08 |
-53.71 |
2.56 |
|
2,3-Dimethylhexane |
-2.201 |
1.88E-01 |
|
2,4-Dimethylhexane |
-2.201 |
1.88E-01 |
|
2,5-Dimethylhexane |
-2.201 |
1.88E-01 |
|
3,3-Dimethylhexane |
-2.201 |
1.88E-01 |
|
3,4-Dimethylhexane |
-2.201 |
1.88E-01 |
|
3-Ethylhexane |
-2.201 |
1.88E-01 |
|
2,2,3 -Trime thylpentane |
-2.201 |
1.88E-01 |
|
2,2,4 -Trime thylpentane |
-1.782 |
1.86E-01 |
|
2,3,3 -Trime thylpentane |
-2.201 |
1.88E-01 |
|
2,3,4 -Trime thylpentane |
-2.201 |
1.88E-01 |
|
2 Methyl-3-ethylpentane |
-2.201 |
1.88E-01 |
|
3 Methyl-3-ethylpentane |
-2.201 |
1.88E-01 |
|
«-Nonane |
0.751 |
1.62E-01 |
|
2,2,3 Trimethylhexane |
-10.899 |
2.52E-01 |
|
2,2,4 Trimethylhexane |
-14.405 |
2.64E-01 |
|
2,2,5 Trimethylhexane |
-12.923 |
2.62E-01 |
|
3,3 Diethylpentane |
-16.067 |
2.69E-01 |
|
2,2,3,3 Tetramethylpentane |
-13.037 |
2.60E-01 |
|
2,2,3,4 Tetramethylpentane |
-13.037 |
2.60E-01 |
|
2,2,4,4 Tetramethylpentane |
-16.099 |
2.79E-01 |
|
2,3,3,4 Tetramethylpentane |
-13.117 |
2.61E-01 |
|
«-Decane |
-1.890 |
2.30E-01 |
|
3,3,5 Trimethylheptane |
-16.808 |
2.94E-01 |
|
2,2,3,3 Tetramethylhexane |
-14.052 |
2.94E-01 |
|
2,2,5,5 Tetramethylhexane |
-14.890 |
2.97E-01 |
|
-1.05E-04 |
2.32E-08 |
-51.13 |
4.23 |
|
-1.05E-04 |
2.32E-08 |
-52.44 |
2.80 |
|
-1.05E-04 |
2.32E-08 |
-53.21 |
2.50 |
|
-1.05E-04 |
2.32E-08 |
-52.61 |
3.17 |
|
-1.05E-04 |
2.32E-08 |
-50.91 |
4.14 |
|
-1.05E-04 |
2.32E-08 |
-50.40 |
3.95 |
|
-1.05E-04 |
2.32E-08 |
-52.61 |
4.09 |
|
-1.02E-04 |
2.19E-08 |
-53.57 |
3.27 |
|
-1.05E-04 |
2.32E-08 |
-51.73 |
4.52 |
|
-1.05E-04 |
2.32E-08 |
-51.97 |
4.52 |
|
-1.05E-04 |
2.32E-08 |
-50.48 |
5.08 |
|
-1.05E-04 |
2.32E-08 |
-51.38 |
4.76 |
|
-4.61E-05 |
-7.12E-09 |
-54.74 |
5.93 |
|
-1.71E-04 |
4.75E-08 |
-57.65 |
5.86 |
|
-1.84E-04 |
5.23E-08 |
-58.13 |
5.38 |
|
-1.85E-04 |
5.39E-08 |
-60.71 |
3.21 |
|
-1.91E-04 |
5.51E-08 |
-55.44 |
8.38 |
|
-1.81E-04 |
5.12E-08 |
-56.70 |
8.20 |
|
-1.81E-04 |
5.12E-08 |
-56.64 |
7.80 |
|
-2.06E-04 |
6.15E-08 |
-57.83 |
8.13 |
|
-1.82E-04 |
5.15E-08 |
-56.46 |
8.15 |
|
-1.26E-04 |
2.70E-08 |
-59.67 |
7.94 |
|
-2.07E-04 |
5.86E-08 |
-61.80 |
8.02 |
|
-2.11E-04 |
6.17E-08 |
-61.66 |
11.28 |
|
-2.14E-04 |
6.25E-08 |
-68.32 |
4.66 |
TABLE 4.8. Example of Calculation of Ke for the Isomerization of n-Hexane (T = 400 K)
 |
 |
 |
 |
 |
 |
 |
|||||
|
-1.47 |
0.0087 |
 |
- 1.14 |
- 1.200 |
3.32 |
|
0.484 |
- 0.0031 |
 |
- 0.45 |
-0.303 |
1.35 |
|
-2.919 |
0.0113 |
 |
- 2.24 |
- 1.890 |
6.62 |
|
-2.435 |
0.0079 |
-6.1E- 06 7.8E- 10 – 2.53 |
- 0.92 |
-0.455 |
1.58 |
