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Ind. Eng. Chem. Res. 1997, 36, 5170-5174
A Strategy for Kinetic Parameter Estimation in the Fluid Catalytic Cracking Process Jorge Ancheyta-Jua´ rez,*,†,‡ Felipe Lo´ pez-Isunza,§ Enrique Aguilar-Rodrı´guez,† and Juan C. Moreno-Mayorga† Instituto Mexicano del Petro´ leo, Eje Central La´ zaro Ca´ rdenas 152, Me´ xico D. F. 07730, Mexico, Instituto Polite´ cnico Nacional, ESIQIE, Me´ xico D. F., Mexico, and Universidad Auto´ noma Metropolitana Iztapalapa, Me´ xico D. F., Mexico
A strategy is proposed to estimate lumped kinetic constants in fluid catalytic cracking (FCC) reactions. This method decreases the number of simultaneously estimated parameters. The 3-, 4-, and a new 5-lump kinetic models and experimental data obtained at 480, 500, and 520 °C in a microactivity reactor are used to illustrate the procedure. Activation energies for each involved reaction are also reported. Introduction The fluid catalytic cracking (FCC) process is the heart of a modern refinery oriented toward maximum gasoline production. Within the entire refinery process, this process offers the greatest potential for increasing profitability; even a small improvement giving higher gasoline yields can result in a substantial economic gain. Thus, the economic incentive for a better understanding of the FCC unit is immense (Krishna and Parkin, 1985). Many complex reactions occur during the FCC process, but the ones of primary interest are those that crack large molecules into smaller ones and thus reduce their boiling point to the more useful range of gasoline, light cycle oil, and gaseous products. The description of complex mixtures by lumping large numbers of chemical compounds into smaller numbers of pseudocomponents has been widely used in industry to provide tractable approximations to the stoichiometry and kinetics of such mixtures (Krambeck, 1991). The number of lumps of the proposed models for catalytic cracking reactions has been increased to obtain a more detailed prediction of product distribution. The first kinetic model (3-lump), developed by Weekman (1968), lumps reactant and all products into three major groups: unconverted gas oil, gasoline, and light gas plus coke. Yen et al. (1987) and Lee et al. (1989) presented a 4-lump kinetic model which is similar to the 3-lump model of Weekman, the main difference being that coke is independently considered as one lump, the other lumps being feed, gasoline, and C1-C4 gas. Corella et al. (1991) developed a 5-lump kinetic model which takes into account the heavy fraction. Maya and Lo´pezIsunza (1993) modified this model to incorporate the cracking of gasoline and gas to coke. Another 5-lump model was used by Larocca et al. (1990) where gas oil was split into paraffins, naphthenes, and aromatics. This model is similar to that studied by Coxson and Bischoff (1987) which is essentially the 10-lump model grouped into six pseudocomponents. A 6-lump kinetic model (resid, VGO/HCO, LCO, gasoline, gas, and coke) was used by Takatsuka et al. (1987, previously published in Sekiyu Gakkaishi, 1984, 22, 533-540) to predict the catalytic cracking of residual * Author to whom correspondence should be addressed. Fax: (+52-5) 368-9371. † Instituto Mexicano del Petro ´ leo. ‡ Instituto Polite ´ cnico Nacional. § Universidad Auto ´ noma Metropolitana Iztapalapa. S0888-5885(97)00271-6 CCC: $14.00
oil. This model was suggested by Corella et al. (1988, 1989) to be of better use in the catalytic cracking of gas oil; although they presented a strategy to calculate the kinetic parameters, the values of these parameters and the application of the model have not been determined. Oliveira and Biscaia (1989) proposed a 4-lump model to describe the catalytic cracking of gasoline (gasoline, gas1, gas2, and coke), and they incorporated this model into a gas oil-range paraffinic compounds cracking model (6-lump kinetic model). The 10-lump model developed by Jacob et al. (1976) achieved kinetic constant independency from composition by lumping gas oil component types into light and heavy fractions (paraffins, naphthenes, aromatic rings, and aromatic substituent groups). However, it was shown by Coxson and Bischoff (1987) that there were virtually no differences between the 6-lump and 10lump kinetic models. John and Wociechowsky (1975) and Corma et al. (1984) proposed reaction schemes for the catalytic cracking of gas oil in which the gas composition was considered in detail. All the aforementioned models have been studied extensively. However, the functions derived from reaction kinetics of those models with a large number of lumps are not applicable for the evaluation of routine catalyst screening because of the small number of observations available compared with the number of estimated parameters (Wallensein and Alkemade, 1996). In the present work we propose a strategy for estimating kinetic constants in FCC reactions which decreases the number of simultaneously estimated parameters. The method is illustrated using the 3-, 4-, and a new 5-lump kinetic models consecutively. Kinetic Models The earliest kinetic model developed by Weekman (1968) involves parallel cracking of gas oil to gasoline and gas plus coke, with consecutive cracking of the gasoline to gas plus coke (Figure 1). For gas oil (y1) cracking, the rate is assumed to be second order
dy1 ) -k0y12φ dt
(1)
k0 ) k1 + k3
(2)
where
© 1997 American Chemical Society
Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 5171 Table 1. Simultaneous Parameters To Be Estimated lumps
original estimation
sequential strategy
3 4 5
4 6 9
4 2 3
stocks with high metal levels are used) becomes very important to design and simulate gas compressors. Also it can be applied as a useful tool for studies of catalyst deactivation due to the presence of high metal contents in the feedstock. The 5-lump kinetic model is shown in Figure 3. The gas oil (y1) cracking rate is similar to eq 1 with
Figure 1. 3-Lump kinetic model.
k0 ) k1 + k3 Figure 2. 4-Lump kinetic model.
k3 ) k3,1 + k3,2 k3,1 ) k3,1,1 + k3,1,2
(9)
Gasoline (y2) cracking rate is the same as in eq 3 with
k2 ) k2,1 + k2,2 k2,1 ) k2,1,1 + k2,2,2
For LPG (y3′′) and dry gas (y5) rates, the following expressions are used
Figure 3. 5-Lump kinetic model.
For gasoline (y2) cracking, the rate is assumed to be first order
dy2 ) (k1y12 - k2y2)φ dt
(3)
The gas plus coke yield (y3) is determined with
dy3 ) (k3y12 + k2y2)φ dt
(10)
dy3′ ) (k3,1,1y12 + k2,1,1y2 - k4y3′′)φ dt
(11)
dy5 ) (k3,1,2y12 + k2,1,2y2 - k4y3′′)φ dt
(12)
Coke production (y4) rate is similar to eq 8.
(4) Strategy for Parameter Estimation
The weakness of this model is that the coke generated in the cracking reaction cannot be unambiguously determined. The 4-lump kinetic model proposed by Yen et al. (1987) and Lee et al. (1989) considers the coke as a lump which is separate from that of gases (Figure 2). For gas oil (y1) and gasoline (y2), the rates are similar to eqs 1 and 3, respectively, with
k0 ) k1 + k3 k3 ) k3,1 + k3,2
(5)
k2 ) k2,1 + k2,2
(6)
For gas (y3′) and coke (y4) production, the rates are
dy3 ) (k3,1y12 + k2,1y2)φ dt
(7)
dy4 ) (k3,2y12 + k2,2y2)φ dt
(8)
We consider that it is necessary to predict the dry gas yield (hydrogen, methane, ethane, and ethylene) separately from that of LPG (propane, propylene, n-butane, isobutane, and butenes) in a gas lump. As in the case of the 4-lump model in which the accurate prediction of coke formation aids heat integration and reactor temperature control, the prediction of dry gas (when feed-
Method Description. In order to illustrate the proposed method for kinetic parameter estimation, we used the exponential law to represent the catalyst activity decay
φ ) e-kdtc
(13)
Equation 13 has only one parameter (kd) to be estimated. The method begins with the 3-lump kinetic model, which has four parameters to be computed, k1, k2, k3, and kd (eqs 1-4 and 13). The estimation can be performed by using nonlinear regression techniques, such as the Marquardt method (1963). The next step is to use the 4-lump kinetic model which usually has six unknown parameters, k1, k2,1, k2,2, k3,1, k3,2, and kd, given in eqs 1, 2, 5-8, and 13. With the previous model (3-lump), some parameters are already known (k1, k2, k3, and kd), where k2 and k3 include the constants k2,1, k2,2, k3,1, and k3,2, respectively (eqs 5 and 6). If one of the parameters k2,1 or k2,2 and k3,1 or k3,2 is fixed, the others could be evaluated by using eqs 5 and 6. Therefore, the problem has been reduced to calculating only two parameters instead of computing the original six constants. This procedure is repeated with the 5-lump kinetic model represented by eqs 1, 2, 6, and 9-13. In this case, six parameters are known, k1, k2,2, k3,2, kd, k2,1,1, or k2,1,2, and k3,1,1 or k3,1,2. Two parameters (k2,1 and k2,2) are
5172 Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 Table 2. Kinetic Parameters at 500 °C
a
parameter
reaction
3 lumps
k1 k2 k2,1 k2,1,1 k2,1,2 k2,2 k3 k3,1 k3,1,1 k3,1,2 k3,2 k4 kd
GO f Gne Gne f gas + coke Gne f gas Gne f LPG Gne f dry gas Gne f coke GO f gas + coke GO f gas GO f LPG GO f dry gas GO f coke LPG f dry gas
0.1942 0.0093
4 lumps SSa 0.1942
5 lumps 0.1942
4 lumps OEa 0.1947
0.0093
0.0089 0.0061 0.0032 2 × 10-8
2 × 10-8
1 × 10-8
0.0488 0.0348
0.0365 0.0357 0.0001 0.0140 0.0020 0.0875
0.0140 0.0875
0.0875
0.0139 0.0874
SS, sequential strategy; OE, original estimation.
estimated with the previous model, and only three (k2,1,1 or k2,1,2, k3,1,1 or k3,1,2 and k4) are unknown. Advantages and Limitations. The sequential method proposed in this paper decreases the number of parameters estimated simultaneously (Table 1) in order to estimate kinetic parameters of gas oil catalytic cracking models. The resulting decrease in the number of simultaneously estimated parameters makes it more likely that only one set of parameters exists that satisfies the objective function (sum of square errors of predicted and experimental yields). Due to the high number of kinetic parameters involved in the FCC reactions, the sequential method is very convenient because the probability of uniqueness of solution is enhanced. It is important to note that no convergence problems were faced during the regression analysis. The study of catalytic cracking reactions has followed the lumping methodology. Some of the products are lumped and treated kinetically as one species with various cracking reaction orders. The weakness of these models is that the kinetic constants are a function of feedstock properties; however, these models have been widely used in the most advanced riser models. The immense complexity of gas oil makes it extremely difficult to characterize and describe kinetics on a molecular level. Therefore, the lumping of many similarly behaving compounds into groups is necessary. The strategy proposed in this paper could be used to estimate parameters in kinetic models with more than five lumps. However, in order to improve estimations, more experiments would be required; the larger the sample size compared with the number of unknown parameters, the better are the estimations in the sense that the errors will be smaller. Results and Discussion In order to apply the strategy for the estimation of kinetic constants, experiments were performed in a fixed-bed reactor described by ASTM D 3907-92 (microactivity test). The feedstock and catalyst were vacuum gas oil and an equilibrium catalyst, both coming from an industrial catalytic cracking unit. The aim of the experiments was to find out the product distribution as a function of the weight-hourly space velocity (WHSV). The range of values of the WHSV was 5-50 h-1, while the catalyst-to-oil ratio (C/O) was kept constant at 5. Experiments were carried out at reactor temperatures of 480, 500, and 520 °C. The products measured in each experiments were dry gas (C2 and lighter), LPG (combined C3C4), gasoline, coke, and unconverted gas oil (light cycle plus decanted oils).
Table 3. Product Selectivities literature data selectivity
this work
value
source
k1/k0
0.799
k3,1/k0 k3,2/k0
0.143 0.058
0.78a 0.75a 0.164b 0.064b
Corella et al. (1986) Kraemer and de Lasa (1988) Lee et al. (1989) Lee et al. (1989)
a
500 °C. b 482.2 °C.
Table 2 shows an example of the estimation of kinetic parameters using the experimental data obtained in the MAT reactor at 500 °C. The same strategy was followed for parameter estimation at 480 and 520 °C. The results obtained for the 4-lump model considering the original estimation (six parameters instead of two) are presented in the same table. It can be observed that the kinetic constants are almost identically predicted using both methods (OE: original estimation and SS: sequential strategy); however, the sequential strategy decreases the number of simultaneously estimated parameters, as can be seen in Table 1. Various authors have found that the kinetic constant for the cracking of gasoline to gas plus coke is very small compared with other constants (see data compiled by Forissier and Bernard, 1989). In this work, it was found that the kinetic constant which really has a small value compared with the others is only the gasoline-to-coke cracking constant (k2,2 in 4- and 5-lump models). This result was also found by Oilveira and Biscaia (1989) when they used a 4-lump model to describe the gasoline cracking; moreover, the 5-lump model proposed by Corella et al. (1991) does not consider the coke formation by gasoline cracking. Some results of product selectivities given by the ki/ k0 ratio are presented in Table 3. The selectivity values calculated in this paper show good agreement with literature information. LPG and dry gas presented selectivities around 0.656 and 0.344 (k2,1,1/k2 and k2,1,2/ k2 ratios), respectively, with respect to overall gasoline cracking. Activation energies for each involved reaction calculated in the range of 480-520 °C are shown in Table 4. It can be observed that not all activation energies evaluated in this work are in the range of those reported in the literature. These differences are due mainly to the type of catalyst, feedstock, reactor, and operating conditions used in the experiments. Information is not available in the literature for activation energies of the following reactions: gas oil to LPG, gas oil to dry gas, gasoline to LPG, gasoline to dry gas, and LPG to dry gas. Figures 4 and 5 show a comparison of predicted and experimental results for gas oil, gasoline, LPG, dry gas,
Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 5173
can predict suitably the experimental results for the range of WHSV considered in this paper (5-50 h-1).
Table 4. Activation Energies (kcal/mol) kinetic model parameter
reaction
k1 k2 k2,1 k2,1,1 k2,1,2 k2,2 k3 k3,1 k3,1,1 k3,1,2 k3,2 k4
GO f Gne Gne f gas + coke Gne f gas Gne f LPG Gne f dry gas Gne f coke GO f gas + coke GO f gas GO f LPG GO f dry gas GO f coke LPG f dry gas
a
3 4 5 literature lumps lumps lumps dataa 13.7 15.7
13.7
13.7
15.7 15.9
17.5 10.8 15.9
11.1 12.6 7.6
12.5 11.8 7.6 9.5
10-36 15-29 13-15 18-27 9-18 17-21 11-15
Taken from refs 3-5, 8, 9, 14, 15, 17, 21.
Conclusions The proposed strategy for kinetic parameter estimation in fluid catalytic cracking (FCC) reactions was applied successfully using experimental data obtained in a microactivity reactor. This method decreases the number of simultaneously estimated parameters, and consequently the probability of uniqueness of solution is enhanced. The experimental data were well represented by a new 5-lump kinetic model using the previous kinetic parameters estimated with 3- and 4-lump models. In addition, it was found that the gasoline cracking reaction can be neglected since the kinetic constant was many orders of magnitude less than the others. The prediction of LPG, dry gas, and coke separately can be used to design and simulate gas compressors in FCC units and to perform catalyst deactivation studies when feedstock with high level of metals are used. Nomenclature
Figure 4. Experimental and predicted gas oil, gasoline, and LPG yields. Reactor temperature: (]) 480 °C, (O) 500 °C, (+) 520 °C.
Figure 5. Experimental and predicted dry gas and coke yields. Reactor temperature: (]) 480 °C, (O) 500 °C, (+) 520 °C.
kd ) deactivation constant (s-1) k1 ) kinetic constant for the reaction GO f Gne (wt fraction-1 s-1) k2 ) kinetic constant for the reaction Gne f gas + coke (s-1) k2,1 ) kinetic constant for the reaction Gne f gas (s-1) k2,1,1 ) kinetic constant for the reaction Gne f LPG (s-1) k2,1,2 ) kinetic constant for the reaction Gne f dry gas (s-1) k2,2 ) kinetic constant for the reaction Gne f coke (s-1) k3 ) kinetic constant for the reaction GO f gas + coke (wt fraction-1 s-1) k3,1 ) kinetic constant for the reaction GO f gas (wt fraction-1 s-1) k3,1,1 ) kinetic constant for the reaction GO f LPG (wt fraction-1 s-1) k3,1,2 ) kinetic constant for the reaction GO f dry gas (wt fraction-1 s-1) k3,2 ) kinetic constant for the reaction GO f coke (wt fraction-1 s-1) k4 ) kinetic constant for the reaction LPG f dry gas (s-1) k0 ) global gas oil cracking kinetic constant (wt fraction-1 s-1) t ) time (s) tc ) catalyst residence time (s) y1 ) gas oil yield (wt fraction) y2 ) gasoline yield (wt fraction) y3 ) gas + coke yield (wt fraction) y3′ ) gas yield (wt fraction) y3′′ ) LPG yield (wt fraction) y4 ) coke yield (wt fraction) y5 ) dry gas (wt fraction) Greek Symbols φ ) deactivation function
Acknowledgment
Figure 6. Experimental and predicted gases and gases plus coke yields. Reactor temperature: (]) 480 °C, (O) 500 °C, (+) 520 °C.
and coke yields using the 5-lump kinetic model. Other results with the 3- and 4-lump models are presented in Figure 6. The standard errors of the estimations for all the products were less than 2.5. The 5-lump model
The authors thank Instituto Mexicano del Petro´leo (FIES-95-95-IV Project), CONACyT, and the British Council for their financial support. Literature Cited (1) Corella, J.; Frances, E. Analysis of the riser reactor of a fluid cracking unit. Fluid Catalytic Cracking II. ACS Symp. Ser. 1991, 452, 165-182.
5174 Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 (2) Corella, J.; Frances, E. Modelling some revamps of the riser reactors of the FCCUs: Lateral downstream quench flow injections and cross sectional area variation. AIChE Symp. Ser. 1992, 8 (291), 110-119. (3) Corella, J.; Fernandez, A.; Vidal, J. M. Ind. Eng. Chem. Process Des. Dev. 1986, 25, 554-562. (4) Corella, J.; Provost, M.; Espinosa, A.; Gutierrez-Morales, F. Problemas en el modelado cine´tico de sistemas reaccionantes catalı´ticos extremadamente completos, ra´pidos y con desactivacio´n. Aplicacio´n al Proceso FCC. Proceedings of the XI Iberoamerican Symposium on Catalysis, Guanajuato, Me´xico, 1988, 415-421. (5) Corella, J.; Morales, F. G.; Provost, M.; Espinosa, A.; Serrano, J. The selective deactivation kinetic model applied to the kinetics of the catalytic cracking (FCC process). Proc. of the Int. Conf. in Adv. Chem. Eng. Kanpur, India, 1989, Jan 4-6, 192210. (6) Corma, A.; Juan, J.; Martos, J.; Soriano, J. M. 8th Inter. Cong. on Cat. Berlin, 1984, II, 293-304. (7) Coxson, P. G.; Bischoff, K. B. Lumping Strategy. 1. Introduction Techniques and Applications of Cluster Analysis. Ind. Eng. Chem. Res. 1987, 26, 1239-1248. (8) Forissier, M.; Bernard, J. R. Modelling the Microactivity test of FCC Catalysts to Compute Kinetic Parameters. AIChE Meeting, Houston, TX, 1989. (9) Jacob, S. M.; Gross, B.; Voltz, S. E.; Weekman, V. W. A Lumping and Reaction Scheme for Catalytic Cracking. AIChE J. 1976, 22 (4), 701-713. (10) John, T. M.; Wojciechowsky, B. W. J. Catal. 1975, 37, 240250. (11) Kraemer, D. W.; de Lasa, J. M. Ind. Eng. Chem. Res. 1988, 27, 2002-2008. (12) Krambeck, F. J. An industrial viewpoint on lumping. Kinetics and Thermodynamic Lumping of Multicomponent Mixtures; Elsevier Science Publishers B.V.: Amsterdam, 1991; pp 111-129. (13) Krishna, A. S.; Parkin, E. S. Modelling the Regenerator in Commercial Fluid Catalytic Cracking Units. Chem. Eng. Prog. 1985, 31 (4), 57-62.
(14) Larocca, M.; Ng, S.; de Lasa, H. Fast Catalytic Cracking of Heavy Gas Oils: Modelling Coke Deactivation. Ind. Eng. Chem. Res. 1990, 29, 171-180. (15) Lee, L. S.; Chen, Y. W.; Huang, T. N.; Pan, W. Y. Four Lump Kinetic Model for FCC Process. Can. J. Chem. Eng. 1989, 67, 615-619. (16) Marquardt, D. W. Solution of non-linear squares estimation of non-linear parameters. J. Soc. Ind. Appl. Math. 1963, 2, 431-441. (17) Maya, Y. R.; Lo´pez, I. F. Un esquema cine´tico para el craqueo catalı´tico de gaso´leos en un reactor de lecho transportado. Av. Ing. Quim. 1993, 14, 39-43. (18) Oliveira, L. L.; Biscaia, E. C. Catalytic Cracking Kinetic Models. Parameter Estimation and Model Evaluation. Ind. Eng. Chem. Res. 1989, 28, 264-271. (19) Takatsuka, T.; Sato, S.; Morimoto, Y.; Hashimoto, H. A reaction model for fluidized-bed catalytic cracking of residual oil. Int. Chem. Eng. 1987, 27 (1), 107-116. (20) Wallenstein, D.; Alkemade, U. Modelling of selectivity data obtained from microactivity testing of FCC catalyst. Appl. Catal., A 1996, 137, 37-54. (21) Weekman, V. M. A Model of Catalytic Cracking Conversion in Fixed, Moving and Fluid-Bed Reactors. Ind. Eng. Chem. Prod. Res. Dev. 1968, 7, 90-95. (22) Yen, L. C.; Wrench, R. E.; Ong, A. S. Reaction kinetic correlations for predicting coke yield in fluid catalytic cracking. Katalistics’ 8th Annual Fluid Cat Cracking Symp. Budapest, Hungrı´a. June 1987, 7:1-7:7.
Received for review April 10, 1997 Revised manuscript received August 14, 1997 Accepted August 24, 1997X IE970271R
X Abstract published in Advance ACS Abstracts, October 15, 1997.
