Energy & Fuels 2000, 14, 373-379
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A Simple Method for Estimating Gasoline, Gas, and Coke Yields in FCC Processes Jorge Ancheyta-Jua´rez*,†,‡ and Jose´ A. Murillo-Herna´ndez‡ Instituto Mexicano del Petro´ leo, Eje Central La´ zaro Ca´ rdenas 152, Col. San Bartolo Atepehuacan, Me´ xico 07730 D.F., Me´ xico, and Instituto Polite´ cnico Nacional, ESIQIE, UPALM, Me´ xico 07738 D.F., Me´ xico Received June 30, 1999
In this work we propose a simple method to estimate gasoline, gas, and coke yields in the catalytic cracking process. The method requires only experimental information about the variation with time of product yields, which are correlated using a third-order polynomial. Combined cracking and decay constants in the 3- and 4-lump kinetic models reported in the literature are estimated by linear regression analysis using experimental data and the proposed methodology. The kinetic model differential equations were solved using a fourth order Runge-Kutta method in order to evaluate FCC product yield-conversion relationships. The proposed methodology gives accurate predictions of product yields in the FCC process with average deviations less than 3% with respect to experimental data.
1. Introduction Fluid catalytic cracking (FCC) is one of the most important conversion processes in a petroleum refinery. The objective of the FCC unit is to convert low-value, high-boiling point feedstocks into more valuable products such as gasoline and lighter products. Cracking reactions in the riser also produce deposition of coke on the catalyst, and catalyst activity is restored by burning off the coke with air in the regenerator. The catalyst-burning step supplies the heat for the reactions through circulation of catalyst between reactor and regenerator.1 Gasoline formation is of major importance for the development of a FCC catalyst because it determines the selectivity of the desired and unwanted products. The MAT (Microactivity Test) technique, a normalized ASTM procedure for a standard feedstock which allows us to change easily the reactions conditions, is the one of the most common ways for catalyst evaluation and kinetic measurements. Wallestein and Alkemade2 proposed a procedure to evaluate selectivity data obtained from the cracking of vacuum gas oil on an FCC catalyst in a microactivity test unit. They obtained empirical relationships containing only two parameters for the interrelation of conversion and yields. The parameters were estimated by fitting these functions to the experimental data by nonlinear least-squares methods. It was shown that the reliability of the estimated parameters and predicted * Author to whom correspondence should be addressed at Instituto Mexicano del Petro´leo, Eje Central La´zaro Ca´rdenas 152, Me´xico 07730 D. F., Mexico. Fax: +52-5-368-9371. E-mail:
[email protected]. † Instituto Mexicano del Petro ´ leo. ‡ Instituto Polite ´ cnico Nacional, ESIQIE, UPALM. (1) Sadeghbeigi, R. Fluid Catalytic Cracking Handbook: Design, Operation and Troubleshooting of FCC Facilities’ Gulf Publishing Co.: Houston, TX, 1995. (2) Wallenstein, D.; Alkemade, U. Appl. Catal. A 1996, 137, 37-54.
values were considerably improved as compared to those obtained by other methods (curve fitting and data interpolation by flexible ruler or use of second-order polynomials). However, the application of the empirical functions obtained by using this procedure is only to represent the relationship between conversion and product yields and kinetic parameters cannot be determined. Since FCC feedstocks consist of thousands of components, the estimation of intrinsic kinetic constants is very difficult, thus, the lumping of components according to the boiling range is generally accepted. Most of the kinetic models available in the literature predict the product yields using only a few lumps. This is because models with many pseudocomponents require more experimental information in order to estimate their kinetic parameters and they cannot be assumed to be more precise than simpler models. The only difference is that higher parameter models predict the products distribution with more detail. However, the differential equations derived from reaction kinetics and reactor mass balance are not applicable for the evaluation of routine catalyst screening because of the small number of observation available compared with the number of estimated parameters. Hari et al.3 used a simplified description of the product yield distribution in terms of three lumped components, i.e., the charge material (gas oil: over 370 °C), gasoline and middle distillates (C5-370 °C cut), and the remaining coke and gas. The gas oil to gasoline and middle distillates and gas oil to coke and gas reactions were assumed to be of order one and two, respectively. The gasoline and middle distillates to coke and gas reaction was assumed to be first order. The kinetic (3) Hari, C.; Balaraman, K. S.; Balakrishnan, A. R. Chem. Eng. Technol. 1995, 18, 364-369.
10.1021/ef990140y CCC: $19.00 © 2000 American Chemical Society Published on Web 02/19/2000
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parameters were obtained from MAT experimental data. A deviation of 15 to 20% was observed between experimental and predicted values using this method, which is quite high. In the present work we propose a simple method for calculating gasoline, gas, and coke yields-conversion relationships in FCC process using experimental information obtained in a Microactivity unit with catalyst and feedstock recovered from an industrial unit and experimental information reported in the literature. The proposed method only requires MAT data about the variation of product yields with time and a simple linear regression analysis in order to determine the kinetics parameters of a 4-lump model reported in the literature. The novelty of this methodology is that it does not requires nonlinear regression analysis for parameter estimation, which may present problems to find the global minimum of the objective function, commonly the sum of squares errors between experimental and calculated yields, depending on the initial values of the kinetic parameters.
Ancheyta-Jua´ rez and Murillo-Herna´ ndez
Figure 1. 3-lump kinetic model.
2. Methodology Figure 2. 4-lump kinetic model.
2.1. Choosing the Kinetic Models. Many complex reactions occurs in the catalytic cracking process, but the ones of primary interest are those that crack molecules into smaller ones and thus reduce their boiling point to the more useful range of gasoline and light products.4 The first method to obtain a kinetic representation of complex reactions was to lump molecules in distillation cuts and to consider pseudo-chemical reactions between these lumps. In the case of gas oil and heavier fractions that are fed into FCC reactors, they can contain thousands of different compounds, producing many different products. The earliest kinetic study of this process focused on the conversion of heavy oil to gasoline and was based on just two lumps: those materials boiling above the gasoline range and everything else.5 In the other extreme is the single-events method, the most advanced method6 that permits a mechanistic description of catalytic cracking based on the detailed knowledge of the mechanism of the various reactions involving carbenium ions. However, the application of this method to catalytic cracking of real feedstocks is difficult because of analytical complexity and computational limitations.7 Moreover, for reactor design and simulation purposes kinetic models with a few lumps have been found to describe the FCC process with acceptable accuracy, which take into account the major industrial products in the catalytic cracking process. (4) Krambeck, F. J. An industrial viewpoint on lumping. Kinetics and Thermodynamic Lumping of Multicomponent Mixtures. Elsevier Science Publishers B. V.: New York, 1991; pp 111-129. (5) Blanding, F. H. Ind. Eng. Chem. 1953, 45, 1186-1197. (6) Feng, W.; Vynckier, E.; Froment, G. F. Ind. Eng. Chem. Res. 1993, 32, 2997-3005. (7) Van Landeghem, F.; Nevicato, D.; Pitault, I.; Forissier, M.; Turlier, P.; Derouin, C.; Bernard, J. R. Appl. Catal. A 1996, 138, 381405.
In contrast, the more lumps a model includes, intrinsically more kinetic parameters that need to be estimated and, consequently, more experimental information is required. Based on the aforementioned considerations and taking into account that coke formation, which supplies the heat required for the heating and vaporization of the feedstock and to perform the endothermic reactions, and gas production become very important to design and simulate the air blower and gas compressor, respectively, in the present work a 4-lump kinetic model was used to evaluate gasoline, gas, and coke yields. 2.2. Reaction Kinetics. To evaluate the kinetic parameters included in the 4-lump model, it is easier to calculate first some parameters with a 3-lump model, which will be the same in both models8 (e.g., gas oil to gasoline cracking kinetic constant). The 3-lump model (Figure 1) involves parallel cracking of gas oil (y1) to gasoline (y2) and gas plus coke (y3), with consecutive cracking of the gasoline to gas plus coke.9 The 4-lump model (Figure 2) involves also parallel cracking of gas oil (y1) to gasoline (y2), gas (y31) and coke (y32), with consecutive cracking of the gasoline to gas and coke.10 For gas oil cracking the rate is assumed to be second order and for gasoline first order.5 The kinetic rate equations for these models are as follows, φ, the catalyst decay function, was considered equal for all reactions, this means that a nonselective deactivation function was (8) Ancheyta-Jua´rez, J.; Lo´pez, F.; Aguilar, E.; Moreno, J. C. Ind. Eng. Chem. Res. 1997, 36, 5170-5174. (9) Weekman, V. M. Ind. Eng. Chem. Prod. Res. Dev. 1968, 7, 9095. (10) Lee, L. S.; Chen, Y. W.; Huang, T. N.; Pan, W. Y. Can. J. Chem. Eng. 1989, 67, 615-619.
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used. 3-lump kinetic model:9
dy1 ) -k1y21φ - k3y21φ ) -(k1 + k3)y21φ ) -koy21φ dt dy2 ) k1y21φ - k2y2φ ) (k1y21 - k2y2)φ dt dy3 ) (k3y21 - k2y2)φ dt
tained by dividing eqs 5-7 by eq 1. The resulting equations are the following (x ) 1 - y1):
() () ()
(1) (2) (3)
4-lump kinetic model:10
dy1 ) -k1y21φ - k31y21φ - k32y21φ ) dt -(k1 + k3)y21φ ) -koy21φ (4) dy2 ) k1y21φ - k21y2φ - k22y2φ ) (k1y21 - k2y2)φ dt
(6)
dy32 ) (k32y21 + k22y2)φ dt
(7)
2.3. Estimation of Kinetic Parameters. The kinetic parameters can be estimated using eqs 1-7. First, the variation with time of experimental yields data (gas oil, gasoline, gas, and coke) can be fitted using the following polynomial functions:
yi ) ai,0 + ai,1t + ai,2t2 + ... + ai,ntn y′i )
dyi ) ai,1 + 2ai,2t + ... + nai,ntn-1 dt
(8) (9)
Combining eqs 1-7 the following expressions can be obtained, which are straight lines:
( ) ( ) ( ) -
() ()
y′1 + y′2 y21 ) k2φ + k3φ y2 y2
y′1 + y′3 y21 ) -k2φ - k1φ y2 y2
-
(10)
(11)
()
y′1 + y′31 y21 ) -k21φ + (k1φ + k32φ) y2 y2
(16)
dy31 k31φ k21φ y2 y2 ) + ) r31 + r21 2 2 dx k0φ k0 φ y y1 1
(17)
y2 dy32 k32φ k22φ y2 ) r32 + r22 2 ) + dx k0φ k 0 φ y2 y1 1
(18)
where
r1 )
k1φ k1 ) k0φ k0
(19)
r2 )
k2φ k2 ) k0φ k0
(20)
r21 )
k21φ k21 ) k0φ k0
(21)
r22 )
k22φ k22 ) k0φ k0
(22)
r31 )
k31φ k31 ) k0φ k0
(23)
r32 )
k32φ k32 ) k0φ k0
(24)
(5)
dy31 ) (k31y21 + k21y2)φ dt
(12)
The left-hand side (LHS) of eqs 10-12 can be evaluated from eqs 8 and 9, which are determined with experimental data. With intercept and slope of eqs 1012, k1φ, k2φ, k3φ, k21φ, and k32φ, can be evaluated. The other parameters (k22φ and k31φ) can be obtained using the following equations:8,11
k0φ ) k1φ + k3φ
(13)
k2φ ) k21φ + k22φ
(14)
k3φ ) k31φ + k32φ
(15)
2.4. Evaluation of Products Yields. Gasoline, gas, and coke yields-conversion relationships can be ob-
() () ()
dy2 k1φ k2φ y2 y2 ) ) r1 - r2 2 dx k 0 φ k 0 φ y2 y1 1
2.5. Advantages and Limitations of the Proposed Methodology. The methodology proposed in this paper can be used to evaluate the combined kinetic parameters and decay function (kiφ) involved in the 4-lump kinetic model using experimental data obtained in a microactivity plant and a simple linear regression analysis. With this method, the initializing problems of kinetic parameters values, that could converge to local minimum of the objective function, which are frequently found in nonlinear parameter estimation, could be avoided. In addition, the deactivation function (φ) can be removed from the equations to be integrated (eqs 1618) by dividing the combined parameters (kiφ) by k0φ, as was shown in eqs 19-24. The kinetic models based on lumping methodology for catalytic cracking reactions, in which some of the products are lumped and treated kinetically as one species with various cracking reaction orders, have been widely used in the most advanced riser models.12-14 However, the weakness of these models is that the kinetic constants are a function of feedstock and catalyst properties.15,16 (11) Oliveira, L.; Biscaia, E. Ind. Eng. Chem. Res. 1989, 28, 264271. (12) Arbel, A.; Huang, Z.; Rinard, I. H.; Shinnar, R. Ind. Eng. Chem. Res. 1995, 34, 1228-1243. (13) Kumar, S.; Chadha, A.; Gupta, R.; Sharma, R. Ind. Eng. Chem. Res. 1995, 34, 3737-3748. (14) Lo´pez, F.; Ancheyta-Jua´rez, J. 5th World Congr. of Chem. Eng., San Diego, CA, July 1996, pp 287-292. (15) Ancheyta-Jua´rez, J.; Lo´pez, F.; Aguilar, E. Ind. Eng. Chem. Res. 1998, 37, 4637-4640.
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Table 1. Experimental Data Reported in the Literature at 548.9 °C and C/O of 420 space velocity (h-1)
conversion (wt %)
gas oil yield (wt %)
gasoline yield (wt %)
gas yield (wt %)
coke yield (wt %)
10 20 30 60
82.38 71.18 62.04 49.26
17.62 28.82 37.96 50.74
54.16 48.65 43.85 37.67
21.08 16.81 13.60 8.85
7.14 5.72 4.59 2.74
The values of the kinetic parameters obtained with this method can be used as initial values to estimate kinetic constants in models with more than four lumps (i.e., 5-lump,17 6-lump,18,19 etc.), and the convergence problems to local minimum of the objective function may be reduced. 3. Results and Discussion 3.1. Experimental Data Reported in the Literature. Experimental information reported by Wang20 at reaction temperature of 548.9 °C and catalyst-to-oil ratio (C/O) of 4 was used first for validating the proposed method. The variation of total conversion, gasoline, gas, and coke yields with space-velocity are shown in Table 1. These literature data were used to obtain the following polynomial functions between time and product yields. The best fit was found with a third-order polynomial (TOP) obtaining correlation coefficients very close to unity (r2 > 0.999). These equations are valid only for the range of times and space-velocities (WHSV from 10 to 60 h-1) from which they were derived (Table 1). In this case, a higher order polynomial should not be used because of the small number of experimental data. -1
y1 ) 0.67722-1.92703 × 10 t + 2.382 × 10-2t2 - 9.36667 × 10-4t3 (25) y2 ) 0.30171 + 8.13817 × 10-2t 6.29 × 10-3t2 - 1.01667 × 10-4t3 (26) y3 ) 0.02107 + 1.11322 × 10-1t 1.753 × 10-2t2 + 1.03833 × 10-3t3 (27) y31 ) 0.02172 + 7.77133 × 10-2t 1.158 × 10-2t2 + 6.46667 × 10-4t3 (28) Figure 3 shows a comparison of the difference between experimental (Table 1) and calculated conversions using eq 25 and those determined with second-order polynomial (SOP) as were used by Wollanston and Alkemade2 to compare their OPE functions (Optimum Performance Envelope). It is clear that TOP are more accurate than SOP. The reduction in absolute error is better than that reported in ref 2, where SOP were (16) Jacob, S. M.; Gross, B.; Voltz, S. E.; Weekman, V. W. AIChE J. 1976, 22, 701-713. (17) Ancheyta-Jua´rez, J.; Lo´pez, F.; Aguilar, E. Appl. Catal. A 1999, 177, 227-235. (18) Corella, J.; Frances, E. Fluid Catalytic Cracking II, ACS Symposium Series; 1991, 452, 165-182. (19) Takatsuka, T.; Sato, S.; Morimoto, Y.; Hashimoto, H. Int. Chem. Eng. 1987, 27, 107-116. (20) Wang, Y. Ph.D. Dissertation. Fuels Engineering Department, University of Utah, UT 1970.
Figure 3. Comparison between SOP (b) and TOP (O) for conversion prediction.
compared with OPE. This means that eqs 25-28 are adequate to represent the variation with time of FCC product yields. The corresponding time derivatives of eqs 25-28 are
y′1 ) -0.19270 + 0.4764t - 0.00281t2
(29)
y′2 ) 0.08138 - 0.01258t - 0.00031t2
(30)
y′3 ) 0.11132 - 0.03506t + 0.00311t2
(31)
y′31 ) 0.07771 - 0.02316t + 0.00194t2
(32)
The LHS of the straight lines given by eqs 10-12 can be obtained by using the polynomial functions (eqs 2528) and time derivatives expressions (eqs 29-32). With these expressions more points can be calculated than those determined experimentally. The kinetic constants obtained with intercept and slope lines are the following: k1φ ) 0.7116, k2φ ) 0.0438, k3φ ) 0.2458, k21φ ) 0.0354, and k32φ ) 0.0544. The other kinetic constants calculated with eqs 13 and 14 are: k22φ ) 0.0084 and k31φ ) 0.1914. These calculated parameters are combined cracking and decay constants because they include the catalyst deactivation function (φ). By using the combined cracking and decay constants (kiφ) and eqs 19-24, the values of r1, r2, r21, r22, r31, and r32 can be calculated, which are 0.7433, 0.0458, 0.0369, 0.0088, 0.1999, and 0.0568, respectively. With these values, eqs 16-18 could be solved numerically using a fourth-order Runge-Kutta method with the boundary condition: y1 ) 1, y2 ) y31 ) y32 ) 0 at x ) 0. Figure 4 shows the experimental and predicted yields for gasoline, gas, and coke. It can be seen that the kinetic parameters obtained with the proposed methodology predicted very well products yields with average deviations less than 3%. Hari et al.3 followed a similar procedure to evaluated the combined cracking and decay constants (kiφ) with experimental data obtained in a MAT unit at a reaction
Gasoline, Gas, and Coke Yields in FCC Processes
Figure 4. Experimental (symbols) and predicted (lines) gasoline, gas, and coke yields using data reported in the literature.
temperature of 528 °C, WHSV of 10 h-1, and catalystto-oil ratio of 3.65 using a modified 3-lump kinetic model (gas oil: over 370 °C; gasoline and middle distillates: C5-370 °C; and coke plus gas). Gasoline plus middle distillates formation and cracking reactions were assumed to be of first-order reaction while gas oil to gas plus coke cracking was considered as a second-order reaction. They used an exponential law (φ ) e-kdtc) taken from the literature21 to evaluate the deactivation constant (kd) in order to calculate the individual kinetic parameters (k1, k2, and k3). However, as was shown before, it is not necessary to evaluate the decay function (φ), because it can be eliminated by using the kinetic constants relationships given by eqs 19-24. The use of a deactivation function obtained from a correlation published in the literature21 is probably one of the reasons these authors obtained high deviations between experimental and predicted yield values (1520%), since the experimental information was determined using different feedstocks, catalysts, and operating conditions. Another important reason that could explain the high deviations obtained by Hari et al.3 is that they assumed first order for gas oil to gasoline and middle distillates reaction. 3.2. Experimental Data Obtained in This Work. A vacuum gas oil (API gravity: 25.5, molecular weight: 352, sulfur: 1.98 wt %, aniline point: 79 °C, Ni + V, 0.9 wppm) and an equilibrium catalyst (surface area: 155 m2/g, average bulk density: 890 kg/m3) were recovered from the circulating inventory of a catalytic cracking plant, and both were used in this study for MAT experiments. Experimental runs were performed at reaction temperature of 500 °C and constant catalyst-to-oil (C/O) ratio of 5. WHSV was varied in the range 6-50 h-1. Product yields are shown in Figure 5 as a function of WHSV. (21) Weekman, V. W. Ind. Eng. Chem. Proc. Des. Dev. 1969, 8, 385391.
Energy & Fuels, Vol. 14, No. 2, 2000 377
Figure 5. MAT experimental yields versus WHSV at 520 °C and C/O of 5.
The fraction of gasoline was defined by the cut point at C5-220 °C. The product yields were calculated as weight percent of the reactant. Mass balances were performed for each run in the range 100 ( 5%, and the conversion in weight percent was evaluated as the sum of C5 + gasoline, gases, and coke, representing 100% minus unconverted gas oil yield. To ensure that the data were collected in the true kinetic regime and transport effects were insignificant, the following criteria were examined and satisfied:
L 20m 1 ln (332 vs 0.2) > dp Pe 1-x
(33)
where
Pe ) 0.087 Re0.23 p
() L dp
(34)
The Thiele modulus (φs) presented values lower than 0.065, therefore the isothermal effectiveness factor (η) is essentially equal to unity. By using the methodology proposed in this work, the following relationships values between kinetic parameters were found: r1 ) 0.7992, r2 ) 0.0383, r21 ) 0.0383, r22 ) 4 × 10-8, r31 ) 0.1432, and r32 ) 0.0576. Figure 6 shows a comparison between experimental data obtained in this work and predicted product yields-conversion relationships. It can be seen again that the proposed methodology predicts sufficiently well the FCC product yields. The FCC process can be applied to many different type of feedstocks and its chemical composition has a strong effect on the rates of cracking reactions and catalyst decay. The most significant effect in product yields is given by properties such as ASTM distillation, density, refractive index, sulfur, conradson carbon, nitrogen, and metal contents and carbon distribution. Feedstocks with high naphthenics and low aromatics carbon contents show the best cracking capability. The opposite behavior is found in feedstocks with low naphthenics and high aromatics contents. In addition,
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based only on MAT data and each laboratory uses a particular set of test experimental conditions. However, it has to be pointed out that the relative comparison of selectivity trends from various catalysts’ MAT data is considered valid and indeed the technique has proved to be useful.24 Using the microactivity unit it is possible to generate detailed information about FCC product distribution for a given catalyst and operating conditions. The experimental results obtained in a MAT plant can be used to show the dependence of product yields on the level of conversion. The MAT unit can also be used for developing kinetic models of the cracking reactions which can be incorporated in a FCC reactor-regenerator mathematical model to be applied for design, simulation, or optimization purposes. Of course, in these mathematical models the differences in the behavior of industrial FCC units compared to the MAT reactor, such as hydrodynamics, heat balance, etc., have to be taken into account. Figure 6. Experimental (symbols) and predicted (lines) gasoline, gas, and coke yields using data obtained in this work.
high aromatic feedstocks and fractions that boil above 482 °C presented the highest coke yield. Long straightchain paraffins are important to the economics of an FCC unit, because these molecules are cracked catalytically and the unit conversion is increased. 3.3. Prediction of Product Yields-Conversion Relationship beyond the Gasoline Overcracking. Figure 5 shows that gasoline yield is always increasing, it means that the reaction was studied below the overcracking. However, the last points (at low WHSV) indicate the beginning of the overcracking, as can be seen by the tendency of the gasoline yield curves, which seem to have a maximum near the small values of space - velocity (WHSV < 6 h-1). In a MAT evaluation of routine catalyst screening, only five experiments at five different catalyst-to-oil ratios are usually performed, and it is not common to study the cracking process beyond the gasoline overcracking region, as can be found in various studies reported in the literature.2,22,23 This is because the main objective of the MAT unit is to simulate the catalyst behavior at commercial FCC operating conditions and the trend in catalytic cracking units is to decrease the over-cracking reactions in order to maximize gasoline production. Although the experimental data in this work were obtained below the gasoline overcracking reaction, it was possible to predict sufficiently well the maximum gasoline yields for a given conversion level, with the solution of the 4-lump model differential equations using the kinetic parameters estimated with the proposed methodology (Figures 4 and 6). 3.4. Some Applications of the MAT Test. The MAT test gives information which is not directly applicable to the prediction of catalyst performance in commercial units (for instance, the long contact time in the MAT test is not representative of commercial operations). As a consequence, usually screening and selection are not (22) Lappas, A. A.; Patiaka, D. T.; Dimitriadis, B. D.; Vasalos, I. A. Appl. Catal. A 1997, 152 7-26. (23) Mota, C.; Rawet, R. Ind. Eng. Chem. Res. 1995, 34, 4326-4332.
Conclusions An easy procedure, which uses the 3- and 4-lump kinetic models, has been developed to evaluate gasoline, gas, and coke yields in the catalytic cracking process. The combined cracking and decay constants included in the kinetic models were estimated using a simple linear regression analysis and experimental data obtained in a microactivity plant. The proposed methodology showed accurate predictions of products yields-conversion relationships with average deviations less than 3% with respect to experimental data. Acknowledgment. The authors thank Instituto Mexicano del Petro´leo for its financial support. Nomenclature ai,0-ai,n: dp: ki: kd: k0: k1: k2: k21: k22: k3: k31: k32: L: m: n: Pe: Rep: ri: t: tc: WHSV: x: yi:
polynomial coefficients particle diameter, cm kinetic constant for the cracking or formation of component “i” deactivation constant global gas oil cracking kinetic constant, wt frac-1 h-1 gasoline formation kinetic constant, wt frac-1 h-1 gasoline cracking kinetic constant, h-1 gasoline to gases kinetic constant, h-1 gasoline to coke kinetic constant, h-1 gas oil to gases plus coke kinetic constant, wt frac-1 h-1 gas oil to gases kinetic constant, wt frac-1 h-1 gas oil to coke kinetic constant, wt frac-1 h-1 Catalyst bed length, cm reaction order polynomial order Peclet number Reynolds number based on particle diameter kinetic constants ratio defined by eqs 19-24 Time, min catalyst contact time, min weight hourly space velocity, h-1 conversion, wt frac yield of component “i”, wt frac
(24) Sedran, U. A. Catal. Rev.-Sci. Eng. 1994, 36, 405-431.
Gasoline, Gas, and Coke Yields in FCC Processes y′i: y1: y2: y3: y31: y32:
time derivatives of component “i” gas oil yield, wt frac gasoline oil yield, wt frac gases plus coke yield, wt frac gases yield, wt frac coke yield, wt frac
Energy & Fuels, Vol. 14, No. 2, 2000 379 Greek symbols η: isothermal effectiveness factor φ: catalyst decay function Thiele modulus φ s: EF990140Y
