Energy & Fuels 2009, 23, 979–983
979
Development of a Kinetic Model for Catalytic Reforming of Naphtha and Parameter Estimation Using Industrial Plant Data Mirko Z. Stijepovic,*,† Aleksandra Vojvodic-Ostojic,‡ Ivan Milenkovic,‡ and Patrick Linke† Department of Chemical Engineering, Texas A&M UniVersity at Qatar, Post Office Box 23874, Doha, Qatar, and Petroleum Industry of Serbia, Oil Refinery, PanceVo 26000, SpoljnostarceVacka 199, Serbia ReceiVed September 17, 2008. ReVised Manuscript ReceiVed NoVember 30, 2008
In the present paper, a semi-empirical kinetic model for catalytic reforming has been developed. In the developed model, the component “lumping” strategy is based on a paraffins, olefins, naphthalenes, and aromatics (PONA) analysis. “Activation energy lumps” are introduced to take into account different values of activation energies within specific reaction classes. The parameters of the model have been estimated by bench marking with industrial data. Simulation results have been found to be in very close agreement with plant data. One of the advantages of the present kinetic model is that it predicts the concentration of hydrogen and light gases very well. Because it is formulated from basic principles, this kinetic model with some modification can be applied to any catalytic reformer.
Introduction The use of catalytic naphtha reforming is as important now as it has been for over 50 years of its commercial use. Catalytic reforming is essentially a treatment to improve the octane number of a gasoline. It involves the reconstruction of lowoctane hydrocarbons in the naphtha into more valuable highoctane gasoline components without significantly changing the boiling point range. There has been renewed interest in the reforming process because of environmental regulations that restrict the allowable concentrations of benzene and other aromatics in gasoline and also the increasing demand for hydrogen: the latter is used as a reactant in the hydrotreating processes for sulfur reduction in gasoline and diesel fuels. Also, one of the developments that will affect catalytic reforming in the very near future is the increasing amount of hydrocarbons produced using Fischer-Tropsch synthesis (FTS). Because these hydrocarbons contain a large fraction of low-octane hydrocarbons, catalytic reforming seems to be the major candidate process for upgrading FTS products. Engineering and applied science problems often require the ability to predict the response of dependent variables to changes of independent variables. Use of a mathematical model as a tool for monitoring day to day performance in terms of yield, temperature drops across reactors, heater duties, catalytic deactivation, etc. becomes an integral part of the catalytic reforming process. When modeling reactor systems, appropriate descriptions of the reaction kinetics are of major importance and it has always been a challenge. For catalytic reforming, many kinetic models and kinetics studies have been published.1-22 * To whom correspondence should be addressed: Department of Chemical Engineering, Texas A&M University at Qatar, P.O. Box 23874, Doha, Qatar. Telephone: +974-671-88-42. E-mail: mirko.stijepovic@ qatar.tamu.edu. † Texas A&M University at Qatar. ‡ Petroleum Industry of Serbia. (1) Mills, G. A.; Heinemann, H.; Milliken, T. H.; Oblad, A. G. Ind. Eng. Chem. 1953, 45 (1), 134–137. (2) Smith, R. B. Chem. Eng. Prog. 1959, 55 (6), 76–82. (3) Krane, H. G.; Groh, A. B.; Shulman, B. L.; Sinfelt, J. H. Proc. World Pet. Congr. 1959, 3, 39–53.
The first significant attempt to model a reforming system was made by Smith,2 who considered naphtha to consist of only three basic components: these were paraffins, naphthenes, and aromatics. In more extensive attempts to model reforming reactions of whole naphtha, Krane et al.3 recognized the presence of various carbon numbers. Kmak5 presented a model that incorporated the catalytic nature of the reactions with HougenWatson-type kinetics. Ramage et al.7,8 developed a detailed kinetic model based on extensive studies of an industrial pilot plant reactor. Kmak’s model was later refined by Marin et al.11 Similarly, Krane’s model was refined by Ancheyta el al.15,16,20,21 Joshi et al.19 proposed a rigorous pathway approach for catalyst reforming. In all of the above models, the level of sophistication (4) Henningsen, J.; Bundgaard-Nielson, M. Br. Chem. Eng. 1970, 15 (11), 1433–1436. (5) Kmak, W. S.; Stuckey, T. W. AICHE National Meeting 1973; paper 56a. (6) Kugelman, A. M. Hydrocarbon Process. 1976, 95–102. (7) Ramage, M. P.; Graziani, K. P.; Krambeck, F. J. Chem. Eng. Sci. 1980, 35, 41–48. (8) Ramage, M. P.; Graziani, K. R.; Shipper, P. H.; Krambeck, F. J.; Choi, B. C. AdV. Chem. Eng. 1987, 13, 193–266. (9) Jenkins, J. H.; Stephens, T. W. Hydrocarbon Process. 1980, 163– 167. (10) Marin, G. B.; Froment, G. F. Chem. Eng. Sci. 1982, 37 (5), 759– 773. (11) Marin, G. B.; Froment, G. F.; Lerou, J. J.; De Backer, W. Eur. Fed. Chem. Eng. 1983, 2 (27), 1–7. (12) Van Trimpont, P. A.; Marin, G. B.; Froment, G. F. Ind. Eng. Chem. Res. 1988, 27, 51–57. (13) Turpin, L. E. Hydrocarbon Process. 1992, 81–92. (14) Ako, C. T.; Susu, A. A. Chem. Eng. Technol. 1993, 16, 10–16. (15) Ancheyta, J. J.; Aguilar, R. E. Oil Gas J. 1994, 93–95. (16) Aguilar, R. E.; Ancheyta, J. J. Oil Gas J. 1994, 80–83. (17) Padmavathi, G.; Chaudhuri, K. K. Can. J. Chem. Eng. 1997, 75, 930–937. (18) Taskar, U.; Riggs, J. H. AIChE J. 1997, 43 (3), 740–753. (19) Joshi, P. V.; Klein, M. T. ReV. Proc. Eng. Chem. 1999, 2 (3), 125– 132. (20) Ancheyta, J. J.; Villafuerte, M. E. Energy Fuels 2000, 14, 1032– 1037. (21) Ancheyta, J. J.; Villafuerte, M. E.; Diaz, G. L.; Gonzalez, A. E. Energy Fuels 2001, 15, 887–893. (22) Liu, K.; Fung, S. C.; Ho, T. C.; Rumschitzki, D. S. J. Catal. 2002, 206, 188–201.
10.1021/ef800771x CCC: $40.75 2009 American Chemical Society Published on Web 01/02/2009
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StijepoVic et al.
Table 1. Kinetic Scheme and Estimated Parameters A (kmol kgcat-1 Pa-1 s-1) Dehydrogenation 2.735 × 101 3.340 × 100 6.620 × 101 7.005 × 101
N6 T A6 + 3H2 N7 T A7 + 3H2 N8 T A8 + 3H2 N9+ T A9+ + 3H2 n-P6 T i-P6 n-P7 T i-P7 n-P8 T i-P8 n-P9+ T i-P9+ n-P6 T N6 + H2 n-P7 T N7 + H2 n-P8 T N8 + H2 n-P9+ T N9+ + H2 i-P8 T N8 + H2 i-P9+ T N9+ + H2
126.12 124.74 121.62 121.62
Isomerization 9.822 × 10-5 3.610 × 10-2 7.400 × 10-2 4.022 × 10-1
179.43 167.47 168.48 168.48
Cyclization 6.722 × 100 1.377 × 102 1.513 × 102 1.877 × 102 8.593 × 10-1 1.163 × 100
188.31 188.70 188.38 188.38 194.99 194.99
A (kmol kgcat-1 Pa n-P9 + H2 T n-P8 + P1 n-P9 + H2 T n-P7 + P2 n-P9 + H2 T n-P6 + P3 n-P9 + H2 T P5 + P4 n-P8 + H2 T n-P7 + P1 n-P8 + H2 T n-P6 + P2 n-P8 + H2 T P5 + P3 n-P8 + H2 T 2P4 n-P7 + H2 T n-P6 + P1 n-P7 + H2 T P5 + P2 n-P7 + H2 T P4 + P3 n-P6 + H2 T P5 + P1 n-P6 + H2 T P4 + P2 n-P6 + H2 T 2P3 i-P9 + H2 T i-P8 + P1 i-P9 + H2 T i-P7 + P2 i-P9 + H2 T i-P6 + P3 i-P9 + H2 T P5 + P4 i-P8 + H2 T i-P7 + P1 i-P8 + H2 T i-P6 + P2 i-P8 + H2 T P5 + P3 i-P8 + H2 T 2P4 i-P7 + H2 T i-P6 + P1 i-P7 + H2 T P5 + P2 i-P7 + H2 T P4 + P3 i-P6 + H2 T P5 + P1 i-P6 + H2 T P4 + P2 i-P6 + H2 T 2P3
Ea (kJ/mol)
Cracking 3.496 × 10-2 7.860 × 10-6 9.314 × 10-4 1.794 × 10-1 1.000 × 10-6 1.000 × 10-6 1.450 × 10-5 1.230 × 10-5 1.000 × 10-6 3.350 × 10-5 2.430 × 10-6 5.420 × 10-4 1.000 × 10-6 6.375 × 10-3 2.810 × 10-4 1.165 × 10-1 3.611 × 10-2 6.299 × 10-2 1.390 × 10-4 5.636 × 10-3 2.283 × 10-2 1.858 × 10-2 3.425 × 10-2 5.300 × 10-4 1.000 × 10-6 1.160 × 10-6 3.450 × 10-6 1.210 × 10-6
-2
s-1)
Ea (kJ/mol) 230.274 230.274 230.274 230.274 230.274 230.274 230.274 230.274 230.274 230.274 230.274 230.274 230.274 230.274 230.274 230.274 230.274 230.274 230.274 230.274 230.274 230.274 230.274 230.274 230.274 230.274 230.274 230.274
varies from just a few “lumps” to a very detailed kinetic model. It is well-known from previous publications that rate coefficients in kinetic models depend upon the feedstock, catalyst properties, process conditions, and design of reactors. From this, one can conclude that there is no one general kinetic model for the catalytic reforming process. In this paper, the focus is on developing a general frame for modeling of the catalytic reforming process rather than on developing a general model for predicting the performance of the catalytic reformer. Model Development The chemical description of the naphtha feedstock is solely composed of normal and branch paraffins, five- and six-membered ring naphthenes, and six-membered ring aromatics. In a typical feed, gas chromatography (GC) analysis has revealed the presence of more than 300 components with the carbon number in the range from 5 to 12. Therefore, a detailed, mechanistic kinetic model that considers all of the components and reactions is too complex to implement. Thus, “lumped” models are commonly used to break the feed down into characteristic reactive groups and to describe the reaction kinetics of the complex processes in a tractable manner.
Table 2. Molar Fraction of Components in the Feedstock components
run 1 (%)
run 2 (%)
run 3 (%)
run 4 (%)
P5 n-P6 n-P7 n-P8 n-P9+ i-P6 i-P7 i-P8 i-P9+ N6 N7 N8 N9+ A6 A7 A8 A9+ total
0.75 4.81 5.42 4.73 14.28 4.45 5.26 5.77 11.05 4.14 7.84 7.38 15.84 0.44 1.48 2.42 3.94 100
1.18 5.18 5.46 4.57 13.73 5.39 5.86 5.81 10.49 4.39 7.75 7.23 15.26 0.39 1.33 2.22 3.76 100
0.95 5.52 5.31 4.55 13.90 5.80 5.42 5.67 10.54 4.34 7.61 7.21 15.45 0.41 1.28 2.21 3.83 100
1.24 5.51 5.39 4.53 13.38 6.09 5.84 5.79 10.39 4.43 7.63 7.24 15.12 0.37 1.23 2.14 3.68 100
These are very capable of describing the relationships between the process variables and the reaction rates. It is always a major issue to decide how complex a model should be. If the model is too detailed, it is very hard to estimate parameters, and also, large experimental data sets are necessary to estimate parameters in a robust manner. This is a major issue particularly when data from industrial plant experiments are used to determine the model parameters. By their very nature, industrial data will be subject to more noise and uncertainty than similar data generated in a high-quality research and development laboratory environment. By way of contrast, if the model is too simple, it will not be capable of giving a good match with experimentally observed values. Thus, the questions remain: how much detail should be incorporated into the model, and how many adjustable parameters are required to both accurately match plant data and also give good predictions of plant behavior under differing conditions. Model complexity will always to some extent depend upon the number of components involved, as well as the number of reactions. In next section of this paper, a strategy for defining kinetic “lumps” and reaction schemes is outlined.
Kinetics Scheme Construction The compositional information is often categorized into the classes of normal and branched-chain paraffins, naphthenes, and aromatics: this is referred to as paraffins, olefins, naphthalenes, and aromatics (PONA) analysis (ASTM D5134).23 Kinetic lumps in the present model are based on PONA compositional determinations. Although Kuo et al.24 (and after them Weekman25) developed a lumping method for complex systems, these methods require extensive compositional analysis. The main reason why lumping strategies are based on a PONA analysis is that this type of composition analysis is a widespread method for assessing feedstock processability and describing reformate quality. Following this method, several hundred components can be lumped into just 18 pseudo-components. As previously mentioned, these are classified into four molecular classes: n-paraffins, i-paraffins, naphthenes, and aromatics. All components within these lumps are considered to have similar properties, as well as kinetic behavior. Thermo-physical properties of pseudo-components with a carbon number up to eight are determined by assuming equilibrium among the corresponding individual species. Components with a carbon number of nine or more are lumped in four pseudo-components: aromatics (A9+), n-paraffins (n-P9+), i-paraffins (i-P9+), and naphthenes (N9+). For the C9+ fraction, average thermo-physical properties are used. (23) American Society for Testing and Materials (ASTM). Annual Book of ASTM Standards; ASTM: West Conshohocken, PA, 1999; ASTM D513498. (24) Kuo, J. W.; Wei, J. Ind. Eng. Fundam. 1969, 8, 124–133. (25) Weekman, V. W. Chem. Eng. Prog. Monogr. Ser. 1979, 75 (11), 3–11.
Catalytic Re-forming of Naphtha
Energy & Fuels, Vol. 23, 2009 981 Table 3. Actual and Simulated Reformate Composition in Mole %
run 1
run 2
run 3
run 4
components
experiment (%)
simulated (%)
experiment (%)
simulated (%)
experiment (%)
simulated (%)
experiment (%)
simulated (%)
n-P6 n-P7 n-P8 n-P9+ i-P6 i-P7 i-P8 i-P9+ N6 N7 N8 N9+ A6 A7 A8 A9+
6.03 2.52 0.63 0.32 14.10 9.01 3.21 0.49 0.69 0.59 0.28 0.09 4.26 14.54 19.00 24.23
5.95 2.56 0.64 0.39 14.19 9.14 3.14 0.45 0.67 0.59 0.26 0.01 4.16 14.73 19.22 23.90
6.54 2.48 0.58 0.31 15.57 8.90 2.92 0.51 0.70 0.57 0.26 0.08 4.37 14.42 18.49 23.34
6.36 2.58 0.61 0.38 15.36 9.30 3.17 0.43 0.70 0.59 0.25 0.01 4.33 14.46 18.51 22.95
6.37 2.60 0.67 0.32 15.50 9.39 3.38 0.69 0.68 0.61 0.28 0.10 4.13 13.81 18.00 23.46
6.71 2.53 0.63 0.40 15.57 9.07 3.11 0.45 0.72 0.58 0.25 0.01 4.29 14.07 18.40 23.21
6.63 2.54 0.61 0.31 15.97 9.14 3.05 0.65 0.71 0.58 0.26 0.12 4.31 14.02 18.17 22.95
6.66 2.50 0.58 0.35 16.18 9.09 3.11 0.40 0.69 0.57 0.24 0.01 4.40 14.18 18.36 22.67
Table 4. Actual and Simulated Recycle Gas Composition in Mole % run 1
run 2
run 3
run 4
components
experiment (%)
simulated (%)
experiment (%)
simulated (%)
experiment (%)
simulated (%)
experiment (%)
simulated (%)
H2 P1 P2 P3 P4 P5
71.47 12.44 7.09 4.66 2.95 1.40
71.70 11.56 6.92 4.40 3.50 1.92
71.14 12.53 7.16 4.70 3.02 1.44
71.51 11.70 6.98 4.44 3.49 1.89
71.40 12.34 7.04 4.69 3.07 1.45
71.76 11.42 6.84 4.45 3.58 1.96
70.64 12.85 7.33 4.69 3.01 1.49
71.11 11.87 7.07 4.44 3.53 1.98
Table 5. Actual and Simulated Values of the Temperature Difference across Each Catalyst Bed run 1 ∆T1 ∆T2 ∆T3 total
run 2
run 3
run 4
experiment
simulated
experiment
simulated
experiment
simulated
experiment
simulated
53.0 23.6 4.6 81.2
53.6 23.4 5.0 81.9
53.6 22.2 3.6 79.4
52.9 22.1 4.8 79.8
54.3 24.2 4.3 82.8
53.1 22.2 4.5 79.9
54.6 24.0 5.1 83.7
53.5 22.5 4.7 80.6
Olefins are not considered because of the fact that their concentration in the reaction system is very low and they have little end effect on the final product distribution. Each of the general feed constituents can partake in several competing reactions. Thus, paraffins can undergo the following type of reactions: isomerization, dehydrocyclization, hydrocracking, and hydrogenolysis. Branched-chain paraffins have higher octane values than linear paraffins; therefore, the isomerization reaction is of importance in reforming to produce gasoline. The reactivity of paraffins in isomerization reactions increases as the paraffin carbon number increases. Also, isomerization reaction rates increase with an increase in the temperature. The predicted distributions of concentrations of individual isomers seldom match the precise actual values, but good approaches to reality are possible.9 Dehydrocyclization is the most critical reactions in reforming. The conversion of paraffins to naphthenes increases with an increase in the paraffin carbon number. Van Trimpont et al.12 pointed out that the ring closure is the slowest reaction for normal paraffins, with six and seven carbon atoms. Ring closure of n-heptane is much faster than that of n-hexane. Van Trimpont et al.12 attributed this observed discrepancy to differences between the stability of the corresponding carbonium ion intermediates, as well as to the number of available reaction pathways. Ancheyeta et al.20,21 reported that heavier paraffins for cyclic compounds cyclizate more easily, and this behavior is attributed to the differences in probability of ring formation, which increase with the molecular weight. According to Marin et al.,10 i-hexanes do not cyclize to form corresponding homologues. Liu et al.22 reported that the rate of cyclization of i-heptanes was negligible related to that of n-heptane. Ako et al.14 reported that the cyclization rate of i-octanes were much larger than that of n-octane. It should be pointed out that results reported by Ako et al.14 were obtained by a pulsed experimental technique at 1.8 atm pressure and temperatures in the range of 573-673 K, which are far below typical industrial conditions. These results have
to be used with caution because the conclusion is inconsistent with the theory of available reaction pathways.12 In the present model, it has been assumed that normal and branched-chain paraffins with eight or more carbon atoms undergo dehydrocyclization reactions, as well as normal paraffins with six and seven carbon atoms. The dehydrocyclization reactions of branch paraffins with six- and sevenmembered carbon atoms are excluded from the kinetic scheme. Hydrocracking and hydrogenolysis reactions produce less valuable products then other reactions. Acid cracking (hydrocracking) is characterized by formation of C3 and C4 paraffins because of the carbon ion mechanism.10 Metal cracking (hydrogenolysis) as shown by Sinfelt26 is random and forms more C1 and C2 paraffins than acid cracking. In the present model, hydrocracking and hydrogenolysis are lumped into one reaction class. Naphthenes undergo the following types of reactions: dehydrogenation, isomerization, hydrocracking, and hydrogenolysis. The conversion of naphthenes to aromatics is the primary naphthene reaction and the most rapid of all general reactions. At typical reforming conditions, these reactions essentially attain complete equilibrium conversion to aromatics. The reactivity of dehydrogenation reactions increases with an increase in the naphthene carbon number. Isomerization of alkylcyclopentanes to alkylcyclohexanes is similar to the isomerization of paraffins. In the present model, alkylcyclopentanes and alkylcylohexanes are lumped into one molecular class; therefore, these reactions are not incorporated into the kinetic scheme. The extent of naphthene cracking is considerably less than that of paraffins because the concentration of naphthenes is very low as a result of their rapid conversion to aromatics. These reactions are not incorporated into the kinetic scheme because they are very slow, and in our opinion, they play no significant effect on end-product distribution. (26) Sinfelt, J. H. AdV. Catal. 1974, 23, 451–457.
982 Energy & Fuels, Vol. 23, 2009
StijepoVic et al. constituent components. Components that have carbon numbers of eight or more are treated as one AEL in a specific reaction class. Also, components with six and seven carbon atoms are treated separately within a specific reaction class. Cracking reactions are treated as irreversible reactions, and activation energies for all reactions are assumed to be equal.
Reactor Model Under typical reactor operating conditions, radial and axial dispersion effects are assumed to be negligible because the reactor diameter is much larger than the diameter of the catalyst particle. Also, the uncertainty associated with diffusion effects within individual catalyst pellets is lumped into the kinetic-rate parameters. Thus, a perfect plug flow behavior is assumed. The pressure drop is implemented in the model as a linear function of the catalyst load in each bed. The following equations defined the mathematical model: Figure 1. Reformate composition profiles.
dFi ) ri dW dT ) dW
(1)
∑rH ∑FC i
f,i
(2)
i p,i
where Fi denotes the molar flow rate of component i (kmol/s), ri denotes the overall reaction rate of component i (kmol kgcat-1 s-1), Hf,i denotes the heat of formation of component i (kJ/kmol), Cp,i denotes the ideal gas heat capacity for component i (kJ kmol-1 K-1), and W denotes the catalyst load (kgcat).
Results and Discussion
Figure 2. Temperature profile through the reactor system.
Aromatics are assumed to undergo only hydrodealkylation reactions. Other aromatics reactions are neglected because aromatics that are produced do not crack, re-open, or rehydrogenate to any appreciable extent.9 Hydrodealkylation of aromatics to respective homologues of lower carbon number occurs in the reforming process but to a considerably less extent than other primary reactions; thus, these reactions are also excluded from the kinetic scheme. The chosen kinetic scheme is constructed according to above considerations and is described in Table 1. In the present model, reactions between components are assumed to be elementary and reaction rates are functions of the partial pressures of reacting components. Dehydrogenation of naphthene, isomerization of paraffin, and dehydrocyclization of paraffin reactions are treated as reversible. Microscopic reversibility is satisfied with equilibrium constants, calculated using the van’t Hoff equation. Heats of reaction and free energy data are determined a priori from thermodynamics. With the carbon number, the selectivity changes considerably between six-, seven-, and eight-carbonmembered species in a given molecular class. For hydrocarbons containing eight or more carbon atoms, the selectivity within a molecular class does not vary significantly because of the similarity of their aromatization.6 Note that Ramage et al.8 in their extended publication pointed out that their kinetic model relied on the same assumption. Most of the published models assume equal activation energies for all reactions within the specific reaction class. From our perspective, this assumption is incorrect. Marin et al.10 and, after them, van Trimpont et al.12 reported different activation energies for C6 and C7 reforming reactions using the same model. In this model, the activation energies are treated separately for different “activation energy lumps” (AELs). AELs are defined for all reversible reactions according to the carbon number of the
A modified Moore27 approach for practical model development is used for adapting the model parameters to match to refinery observations. The present model has 53 parameters that are estimated by bench-marking with experimental data. This was obtained from industrial experiments that have been conducted on a semi-regenerative unit at the Oil Company of Serbia. The platforming unit that was observed consists of three adiabatic fix bed reactors, with heat exchangers between the beds. The inlet temperature to each reactor was changed one at a time. After every change, measurements of compositions and flow rates were performed over 24 h. In our opinion, this is sufficient time for the system to reach a new steady state. Compositions of liquid streams were determined by PONA analysis (ASTM D5134) and were checked by the ASTM D683928 method. The composition of the feedstock is given in Table 2. The composition of recycled gas was determined by the UOP 53929 method. Flow rates, temperatures, and pressures were obtained from installed measurement equipment in the process unit. The model equations were integrated numerically by Gear’s method using inlet data from individual experiments as the initial conditions. A standard nonlinear least-squares method was adopted to regress the model parameters by minimizing the weighted sum of squares between the observed and predicted values of molar flow rates of components at the outlet of the last reactor and the temperature at the outlet of each bed. (27) Moore, C. E. Hydrocarbon Process. 1991, 92–94. (28) American Society for Testing and Materials (ASTM). Annual Book of ASTM Standards; ASTM: West Conshohocken, PA, 2008; ASTM D683902. (29) American Society for Testing and Materials (ASTM). UOP Laboratory Test Methods; ASTM: West Conshohocken, PA, 1997; UOP 539-97.
Catalytic Re-forming of Naphtha
Estimated parameters are listed in Table 1. It should be pointed out that solution of the nonlinear least-squares method strongly depends upon the initial guess. In the present studies, these initial guesses for parameters were taken from the literature.2-4,17,20 The parameters that give the best regression are those listed in Table 1. Table 3 shows the reformate composition obtained by simulation and that reported for the commercial reforming unit. It can be observed that the maximum absolute difference between these two values is 0.41% and, also, that the simulated values for all runs are very close to the experimental ones. Table 4 shows the recycle gas composition obtained by both simulation and experiment. It can be observed that the maximum absolute difference between these two values is 0.97%. One of the advantages of the present kinetic model is that it predicts the concentration of hydrogen and light gases very well. The comparisons of experimentally observed temperature drops to those predicted by the model are presented in Table 5. Excellent agreement is present between the predictions and the values reported for the commercial plant. Figure 1 shows the composition profiles of reformate through each reactor bed. The fractional catalyst weight is chosen as a convenient manner for indicating the position in each catalyst bed. From Figure 1, it is clear that, as is expected, naphthenes rapidly dehydrogenated to aromatics. These reactions are fastest in the first segment of every bed, and in this part, the temperature drops very rapidly because of the endothermic nature of these reactions (Figure 2). The mole fraction of branched-chain paraffins decreases slowly through each reactor bed, while n-paraffins show more activity, with the mole fractions decreasing faster. This is also the expected behavior of normal and branched-chain paraffins because of the fact that n-paraffins isomerize very fast to i-paraffins, as well as being more active in cyclization reactions. It should be pointed out that temperature and composition profiles presented in Figures 1 and 2 show very good agreement with profiles reported in previous papers.4,8,21
Energy & Fuels, Vol. 23, 2009 983
One of the model limitations is caused by the component lumping. Because the relative concentrations of species making up individual kinetic lumps can change as the reactions proceed, predictions from this model cannot be extrapolated to conditions of other feedstocks. They are specific for the feedstock, catalyst, and operating conditions used to evaluate the kinetic parameters. Thus, this paper should be regarded as a method for finding the kinetic parameters for a particular system and not as a general model applicable to a wide variety of situations. However, because it is formulated from basic principles and because data necessary for parameter estimation is available in any refinery, this model with some modifications can be applied to any catalytic reformer system for semi-regenerative, cyclic, or continuous plaforming. A limitation of the proposed model is that it does not take into account catalyst deactivation. Conclusion A method for parameter estimation for a model of catalytic reforming of naphtha has been postulated. The model developed includes a kinetic model that takes into account the most important reactions of the catalytic reforming process. Reformate composition and temperature profiles have been obtained to provide information about the extent of conversion in each of the beds. The simulation results have been found to be in very close agreement with plant data. Acknowledgment. The authors thank Petroleum Industry of Serbia for providing industrial data used in this study and Nebojsa Jancic for providing guidance for this work. Also, the authors thank Professor Simon Waldram of Texas A&M University at Qatar for technical assistance, useful comments, and suggestions. Supporting Information Available: Thermo-physical properties of pseudo-components and reaction rate equilibrium constants. This material is available free of charge via the Internet at http://pubs.acs.org. EF800771X
