Energy & Fuels 2002, 16, 593-600
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A New Approach to Determining Product Selectivity in Gas Oil Cracking Using a Four-Lump Kinetic Model Siauw Ng,*,† Jinsheng Wang,‡ Yuxia Zhu,† Ligang Zheng,‡ Fuchen Ding,§ Liying Yang,| and Sok Yui⊥ National Centre for Upgrading Technology, 1 Oil Patch Drive, Suite A202, Devon, Alberta, Canada T9G 1A8, CANMET Energy Technology Centre, 1 Haanel Drive, Nepean, Ontario, Canada K1A 1M1, Beijing Institute of Petrochemical Technology, Daxing, Beijing, China 102600, Centre for Chemical Engineering, Beijing Institute of Clothing Technology, Beijing, China 100029, and Syncrude Research Centre, 9421-17Avenue, Edmonton, Alberta, Canada T6N 1H4 Received July 17, 2001. Revised Manuscript Received December 15, 2001
A simplified four-lump model for fluid catalytic cracking (FCC) as reported in the literature has been examined. The model, which relates the coke yield to other yields, is important to FCC operation but requires intensive data analyses. In this article, a new methodology that can validate the model and substantially simplify the data treatments is proposed. The method is applicable to both steady-state FCC riser cracking and unsteady-state microactivity tests (MAT). An explicit expression, derived for the coke yield as a function of conversion, is shown to describe the reported data well. The method is independent of the catalyst decay function and the reaction order of gas oil cracking. This enables the model to be applicable to many systems, even noncatalytic pyrolysis. A case study of the model, which uses the proposed method, suggests that for a given feed-catalyst system the relative rates of coke formation from either gasoline or gas oil may be the same for different reactors.
1. Introduction Fluid catalytic cracking (FCC) converts heavy oil into valuable gasoline, with light gas and coke produced concurrently as byproducts. In a commercial FCC unit (FCCU), coke deposited on the catalyst is burnt off in the regenerator to provide heat for vaporizing and cracking the heavy feed in the riser reactor. The exothermic coke burning, the endothermic feed preheat, vaporization, and reactions keep FCC operation in heat balance. Excessive coke yield can upset the heat balance causing adverse effects on FCCU functionality, lowering the catalyst activity, and favoring the production of lowvalue products such as dry gas. Therefore, the prediction of coke yield is essential in optimizing the FCC unit’s design and operation. An empirical correlation was proposed by Voorhies1 for coke formation in fixed-bed cracking:
Cf ) Atcn
(1)
This equation is of limited use as it does not relate the coke yield to other product yields (i.e., it does not bring forth useful information about the catalytic cracking selectivity). As well, the relationship obtained from a * To whom correspondence should be addressed. E-mail: sng@ nrcan.gc.ca. Fax: 1-780-987-5349. † National Centre for Upgrading Technology. ‡ CANMET Energy Technology Centre. § Beijing Institute of Petrochemical Technology. | Centre for Chemical Engineering. ⊥ Syncrude Research Centre. (1) Voorhies, A. Ind. Eng. Chem. 1945, 37, 318-322.
fixed-bed unit may not be applicable to reactors of other types. Weekman2 and Weekman and Nace3 proposed a simple three-lump model, followed by a more complicated version by Wojciechowski.4 In principle, they lumped the reactant and all products into three: the feed (gas oil), the gasoline, and the light gas (C1-C4 hydrocarbons) plus coke. These models led to a relationship between the gasoline yield and the gas oil conversion. However, because light gas and coke are taken as one lump, the coke yield cannot be determined separately. Since these studies, more complex kinetic models for the FCC process have been developed. These include: the four-lump models by Yen et al.5 and Lee et al.;6 the fivelump model by Larocca et al.,7 Corella and Frances,8 and Maya and Lo´pez;9 the six-lump model by Takatsuka et al.;10 and the ten-lump model by Jacob et al.11 In the present study, we concentrated on the four-lump model proposed by Lee et al.6 due to its simplicity and inclusion (2) Weekman, V. W. Ind. Eng. Chem. Proc. Des. Dev. 1968, 7, 9095. (3) Weekman, V. W.; Nace, D. M. AIChE J. 1970, 16, 397. (4) Wojciechowski, B. W. Can. J. Chem. Eng. 1968, 46, 48. (5) Yen, L. C.; Wrench, R. E.; Ong, A. S. Oil Gas J. 1988, 86(2), 67-70. (6) Lee, L. S.; Chen, Y. W.; Huang, T. N.; Pan, W. Y. Can. J. Chem. Eng. 1989, 67, 615-618. (7) Larocca, M.; Ng, S.; de Lasa, H. Ind. Eng. Chem. Res. 1990, 29, 171-180. (8) Corella, J.; Frances, E. ACS Symp. Ser. 1991, 452, 165-182. (9) Maya, Y. R.; Lo´pez, I. F. Av. Ing. Quim. 1993, 14, 39-43. (10) Takatsuka, T.; Sato, S.; Morimoto, Y.; Hashimoto, H. Int. Chem. Eng. 1987, 27, 107-116. (11) Jacob, S. M.; Gross, B.; Voltz, S. E.; Weekman, V. W. AIChE J. 1976, 22, 701-713.
10.1021/ef0101762 CCC: $22.00 © 2002 American Chemical Society Published on Web 03/19/2002
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dy4 k14 k24 y2 )dy1 k1 k1 y 2
(9)
1
Figure 1. A simplified four-lump kinetic model for cracking of gas oils.
of coke as a separate product. This model was recently studied by Ancheyta-Jua´rez and Murillo-Herna´ndez,12 who proposed a method to estimate kinetic parameters in nonlinear differential equations associated with the model without numerical computation. They expressed product yields as polynomial functions of on-stream time. In this work, we take a different approach that not only simplifies data analyses, but also allows validation and application of the model to both steadyand unsteady-state experiments, including microactivity tests (MAT). 2. Summary of the Simplified Four-Lump Kinetic Model Figure 1 illustrates the four-lump model for reactions in a riser, as proposed by Lee et al.6 This model, referred to “the simplified model” (as opposed to the comprehensive one proposed by Yen et al.5), can be mathematically expressed as
dy1 ) - (k12 + k13 + k14)Φy12 ) -k1Φy12 dtv
y1 )
Rtc
Solution of eq 7 gives the gasoline yield y2 in terms of y1:
y2 ) r12r2 exp(-r2/y1)
[
y1 1 exp(r2) - exp(r2/y1) r2 r2
]
Ein(r2) + Ein(r2/y1) (11) where r12 ) k12/k1, r2 ) k2/k1, and Ein(x) ) x (1/x)exp(x) dx ∫-∞ In a case study, Lee et al.6 utilized the experimental catalytic cracking data at three temperatures (482, 549, and 616 °C) and two catalyst-to-oil ratios (3 and 4) from Wang.13 They calculated the catalyst decay parameters and the rate constants at each temperature, and the frequency factors and the activation energies in the Arrhenius equation for each reaction in the four-lump model. 3. New Methodology
dy3 ) k13Φy12 + k23Φy2 dtv
(4)
dy4 ) k14Φy12 + k24Φy2 dtv
(5)
Φ ) exp(-Rtc)
(6)
where k1 ) k12 + k13 + k14 and k2 ) k23 + k24. The parameters tv and Φ in eqs 3-5 can be eliminated through arrangements with eq 2:
(7)
1
In this study, a comprehensive examination was performed on the simplified model with a new approach to making the model suitable for more general applications. It should be noted that the study emphasized the product selectivity at a given conversion rather than at given test conditions that determine the conversion and the product selectivity. One can still pursue estimation of conversion by making use of eq 10, or the equivalent, if the catalyst does not follow the exponential decay function as described by eq 6. A new methodology was proposed for the following purposes. 3.1. For Validating the Model. The four-lump model was developed based on a number of assumptions which may not be applicable to all systems. The validity of the model should be checked against experimental data prior to the laborious computations. The following simple graphical method is thus proposed for this purpose. From eq 7 we obtain
y2 2
k13 k23 y2 dy3 )dy1 k1 k1 y 2
(10)
Rtc + k1tv[1 - exp(-Rtc)]
(2)
dy2 ) k12Φy12 - (k23 + k24)Φy2 ) k12Φy12 - k2Φy2 dtv (3)
k12 k2 y2 dy2 )+ dy1 k1 k1 y 2
These equations have the following boundary conditions: when y1 ) 1 (conversion ) 1 - y1 ) 0), y2 ) y3 ) y4 ) 0. The gas oil conversion (1 - y1) can be obtained by combining eqs 2 and 6, followed by integration:
y1 (8)
1
(12) Ancheyta-Jua´rez, J.; Murillo-Herna´ndez, J. A. Energy Fuels 2000, 14, 373-379.
)
(
)
k1 dy2 k12 + k2 dy1 k1
(12)
Substituting y2/y12 into eq 9 yields (13) Wang, I. High-Temperature Catalytic Cracking. Ph.D. Dissertation, Fuels Engineering Department, University of Utah, Salt Lake City, UT, 1974.
Product Selectivity in Gas Oil Cracking
dy4 )
(
)
k24 k14 k12k24 + d dy k1 k1 k2 k2 2
Energy & Fuels, Vol. 16, No. 3, 2002 595
(13)
where d ) -dy1 is derived from ) 1 - y1, which represents the gas oil conversion. Rearrangment after integration of eq 13 with initial conditions (y4 ) y2 ) 0 when ) 0) yields
(
)
k24 y2 k14 k12k24 y4 + ) k1 k1k2 k2
(14)
The terms y4/ and y2/ represent the coke selectivity and the gasoline selectivity, respectively. Obviously, if the model holds, a plot of y4/ versus y2/ will yield a straight line, of which the intercept and the slope are k14/k1 + (k12k24/k1k2) and -k24/k2, respectively. This is the most important finding in this article. With the same mathematical manipulation, one may also derive an equation similar to eq 14 for y3/:
(
)
k23 y2 k13 k12k23 y3 ) + k1 k1k2 k2
(15)
Thus, a plot of light gas selectivity versus gasoline selectivity will also show a linear correlation with intercept and slope as k13/k1 + (k12k23/k1k2)and -k23/k2, respectively. However, eqs 14 and 15 are not both independent as one can be derived from the other. 3.2. For Yield Prediction. Substituting y2 in eq 11 into eq 14, followed by rearrangement, yields
y4 ) r14 +
r12r24 r12r24 exp(r2 - r2/y1) - r14y1 + r2 r2 r12r24 exp(-r2/y1)[Ein(r2) - Ein(r2/y1)] (16)
In this equation, parameters r12 ) k12/k1 and r2 ) k2/k1 can be obtained from regression analysis of a set of experimental data with eq 11, as described previously. Parameters r14 ) k14/k1 and r24 ) k24/k1 can also be determined, likewise, through eq 16 after substitution of r12 and r2 with known values. In this study, r14 and r24 were readily obtained from the intercept and the slope in the linear plot of coke selectivity versus gasoline selectivity (such as in Figure 2):
Intercept ) k14/k1 + (k12k24/k1k2) ) r14 + (r12r24/r2) (17) Slope ) -k24/k2 ) -r24/r2
(18)
The light gas yield can be calculated from the relation
y3 ) 1 - y1 - y2 - y4
(19)
3.3. For MAT Application. Equations 2-5 should also be applicable to instantaneous yields of other plug flow reactors, in addition to risers. Among such reactors, a fixed-bed microactivity test (MAT) unit is of particular interest due to its popular use as a primary tool for assessing the performance of FCC catalysts. Because the process is unsteady and the product is collected over a period of time, MAT results are, by nature, timeaveraged yields for the unsteady-state system. Therefore, MAT yields and product distribution tend to be different from those obtained from comparable riser
operations under steady-state conditions. Nevertheless, MAT testing is quite useful to provide relative activity, selectivity, and product quality information which, when properly interpreted, can accurately predict riser behavior.14-16 Here, we show that our method is also applicable to MAT results. In MAT testing, the coke yield is often determined by in situ regeneration of the spent catalyst in the reactor. Thus, the coke yield includes the noncatalytic “feed coke”,17 which may form on the catalyst surface and reactor inner wall. The amount of “feed coke” depends principally on the Conradson carbon content (CCR) yc in the gas oil. To take the “feed coke” into consideration, eq 14 is expressed by
(
)
y4 - yc k24 y2 k14 k12k24 ) + - yc k1 k1 k2 k 2 - yc
(20)
The terms (y4 - yc)/( - yc) and y2/( - yc) represent the corrected coke selectivity and gasoline selectivity, respectively. The equivalent expression, including the time-averaged yields, is thus
(
)
k24 yj2 k14 k12k24 yj4 - yc ) + j - yc k1 k1 k2 k2 j - yc
(21)
Thus, a plot of (yj4 - yc)/(j - yc) versus yj2/(j - yc) will yield a linear relationship, if the model holds. The intercept and slope will be k14/k1 + (k12k24/k1k2) and -k24/k2, respectively. The equivalent expressions with the time-averaged effect for eqs 11, 16, and 19 become
yj2 )
∫0t
c
[
r12r2 exp(-r2/y1)
y1 1 exp(r2) - exp(r2/y1) r2 r2
]
Ein(r2) + Ein(r2/y1) dt/tc (22) yj4 )
∫0t
{
c
r14 +
r12r24 r12r24 exp(r2 - r2/y1) r2 r2
}
r14y1 + r12r24 exp(-r2/y1)[Ein(r2) - Ein(r2/y1)] dt/tc
yj3 ) 1 - yj1 - yj2 - yj4
(23) (24)
yj2 and yj4 are not given as a function of yj1. The equations should be applicable to both fluid-bed and fixed-bed MAT units.18 4. Results and Discussion 4.1. Validation of the Four-Lump Model. Experimental data at 549 °C from Wang13 were used to verify (14) Moorehead, E. L.; McLean, J. B.; Cronkright, W. A. Microactivity Evaluation of FCC Catalysts in the Laboratory: Principles, Approaches and Applications. In Fluid Catalytic Cracking: Science and Technology, Studies in Surface Science and Catalysis; Magee, J. S., Mitchell, M. M., Jr., Eds.; Elsevier Science Publishers B. V.: New York, 1993; Vol. 76, pp 223-255. (15) Ng, S. H.; Briker, Y.; Zhu, Y.; Gentzis, T.; Ring, Z.; Fairbridge, C.; Ding, F.; Yui, S. Energy Fuels 2000, 14, 945-946. (16) Ng, S.; Yang, H.; Wang, J.; Zhu, Y.; Fairbridge, C.; Yui, S. Energy Fuels 2001, 15, 783-785. (17) Rawlence, D. J.; Gosling, K. Appl. Catal. 1988, 43, 213-237. (18) Nace, D. M.; Voltz, S. E.; Weekman, V. W. Ind. Eng. Chem. Proc. Des. Dev. 1971, 10, 530-538.
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Figure 2. Linear relationship between coke or light gas selectivity and gasoline selectivity at 549 °C based on experimental data from Wang.13 Table 1. Equation Parameters at 549 °C
parameter r12 r14 r2 r24
this study, using data from Wang13 0.060 0.012
calculated from rate constants reported by Lee et al.6 0.751 0.063 0.041 0.008
the validity of the model. Figure 2 shows a linear relationship between y4/ and y2/ with an intercept 0.2822 and a slope -0.2961. These data were used for subsequent analyses. Figure 2 also includes a linear plot of light gas selectivity against gasoline selectivity. 4.2. Estimation of Product Yields. When substituting into eqs 17 and 18 the known intercept and slope from Figure 2, along with r12 ) k12/k1 ) 0.751 and r2 ) k2/k1 ) 0.041 (as calculated from the rate constants reported by Lee et al.6), we obtain 0.060 and 0.012 for r14 and r24, respectively. Table 1 gives a comparison between our results and those from Lee et al.6 They are reasonably close. Accordingly, the coke yield at a given conversion ( ) 1 - y1) can be directly estimated from eq 16 without numerically solving the differential eq 9 and curve fitting for the coke yield. The light gas yield was calculated from eq 19 with known values of y1, y2, and y4. Figure 3 shows the calculated coke and light gas yields, which are in good agreement with the actual yields. 4.3. Comparison of Data Fittings between the Two Four-Lump Models. The more comprehensive four-lump model proposed by Yen et al.5 differs from the simplified one in that the coke formation from the light gas is considered with a rate constant k34. The resultant expression for coke yield contains six rate constants and is quite complex. If k34, presumably small, is neglected, the computation can be greatly simpified. Fitting eq 16 to the coke yield data used by Yen et al.5 in their model enables a comparison of data fittings between the two models. Figure 4 shows that the two models give close results. Compared with known experimental values, the comprehensive and the simplified models give residual squares ∑ δ2 of 1.55 and 0.57,
respectively. Unfortunately, other yields, which should be utilized for a more complete study to confirm the validity of the present model, were not reported. 4.4. Application to MAT and Riser Studies. Both fluid-bed and fixed-bed results from catalytic cracking of five gas oils in a MAT unit are demonstrated. These are the oil sands-derived vacuum gas oils (VGOs), including a deasphalted oil VGO (DA) and its hydrotreated product (HTDA), a hydrotreated coker VGO (HTC), a virgin VGO (VIR), and a hydrocracker bottoms VGO (HCB). They were cracked at 510 °C and 30 s oil injection time with an equilibrium catalyst Engelhard Dimension 60, in a MAT unit consisting of both fluidbed and fixed-bed reactors. Feed properties are summarized in Table 2. Detailed feed analyses and MAT procedures can be found elsewhere.15,16,19,20 Table 3 gives the MAT data and the results from a pilot plant study19 using the same feeds and catalyst at temperatures of 490-525 °C. Figure 5 shows the linear correlation between coke selectivity and gasoline selectivity for both MAT results (CCR-corrected) and the riser result (no CCR correction). The slopes, intercepts, and the coefficients of determination R2 for various feed-reactor systems are given in Table 4. 1. Implication of the Slopes. A visual inspection in Figure 5 supported by the slope values in Table 4 indicates that for a given feed-catalyst system the straight lines are mostly parallel to each other, keeping in mind that in the riser study (1) there are only three data points for each feed and (2) the gasoline fraction was obtained from two distillation units: true boiling point (ASTM D2892) and vacuum (ASTM D1160) units (MAT gasoline yield was calculated based on simulated distillation ASTM D2887 and the total liquid product yield). This is an interesting observation. Note that, physically, the slope (-k24/k2 ) -k24/(k23 + k24)) of each line represents the rate of coke formation from gasoline, relative to the gasoline overall cracking rate (to form (19) Yui, S.; Matsumoto, N.; Sasaki, Y. Oil Gas J. 1998, 96(3), 43-51. (20) Ng, S. H. Energy Fuels 1995, 9, 216-224.
Product Selectivity in Gas Oil Cracking
Energy & Fuels, Vol. 16, No. 3, 2002 597
Figure 3. Comparison of the actual coke or light gas yields with those calculated from the proposed methodology.
Figure 4. Comparison of actual coke yields (∆) with predicted yields from the two four-lump models. Table 2. Summary of Feedstock Properties feed name
DAa
HTDAa
HTCa
VIRa
HCBa
SF-135
density at 15 °C, g/mL hydrogen, wt % H/C atomic ratio total nitrogen, wppm total sulfur, wt % MCR, wt % Ni+V, wppm aromatic carbon, % aniline point, °C 343 °C-, wt % 524 °C+, wt %
0.9776 11.1 1.556 3050 3.54 5.37 36.6 24.4 62.8 10.8 38.1
0.9430 11.8 1.619 2450 0.70 2.00 10.9 20.9 81.0 1.5 36.9
0.9511 11.5 1.562 2150 0.43 0.50 0 24.7 63.6 4.5 8.3
0.9712 11.1 1.549 1930 3.25 0.33 0.1 25.4 50.8 6.0 2.0
0.8643 13.7 1.892
