Ind. Eng. Chem. Res. 1997, 36, 5049-5053
5049
A Dispersion Model for Fluid Catalytic Cracking Riser and Downer Reactors† Wei Fei,* Ran Xing, Zhou Rujin, Luo Guohua, and Jin Yong Department of Chemical Engineering, Tsinghua University, Beijing 100084, People’s Republic of China
A dispersion reactor model of both riser and downer reactors for the fluid catalytic cracking is proposed. The model combines the four-lump cracking kinetics, the hydrodynamic model for both the riser and downer, and the dispersion mixing model to predict the fluid catalytic cracking reaction performance. The results show that the axial gas backmixing has a large influence on the gasoline yields of the reactor. When the axial Peclet number changes from 0.1 to 1000, the yield of gasoline will increase approximately 11% under the same conversion. Considering the large reduction of axial gas backmixing in the downer compared with that in the riser, the gasoline yield can be increased 5.5% for the downer reactor, which is consistent with the experimental result. It is found that the overcracking rate will greatly influence the reaction performance in the riser. The plug-flow assumption for the riser reactor is oversimplified in the catalytic cracking process. 1. Introduction
2. Dispersion Model
The gas-solid concurrent downflow circulating fluidized-bed (downer) reactor is a new type of “short contact” reaction system for its significant advantages of short gas-solid contact time and uniform gas and solids residence time (Berg et al., 1989; Gartside, 1989). Hydrodynamic study in downflow systems was pioneered by Shimizu et al. (1978). More recently, investigators at Tsinghua University (Wang et al., 1992; Cao et al., 1994; Wei et al., 1994, 1995) have carried out a series of hydrodynamic and mixing studies in downers. They have found that the radial solids fraction profile in the downer is much flatter than that in the riser, which results in a large reduction of gas and solids backmixing. This advantage makes the downer reactor the most attractive reactor for the catalytic cracking of hydrocarbons. Fluid catalytic cracking (FCC) is the largest and most economic catalytic process in the world; a little increase in selectivity or yield of gasoline is very important to the process. The downer reactor shows a large potential for improving the yield of the FCC process. The gas and solids mixing in the reactor largely influences the yield and selectivity of the cracking process, which is why the downer reactor is the most promising reactor for the cracking process. The reactor models proposed by Kraemer and de Lasa (1988), Gianetto et al. (1994), and Bolkan-Kenny et al. (1994) assumed that the gas and solids in the reactor are plug flow. The gas and solids mixing studies in the riser and downer show that axial mixing in the riser is far from plug flow. The assumption of plug flow in the riser may oversimplify the modeling process. In this paper, the cross-sectional average hydrodynamics are measured in a cold model of a pilot-scale downer to verify the proposed one-dimensional hydrodynamic model. A four-lump kinetic network is combined with a one-dimensional dispersion mixing model to form a dispersion reactor model. The influence of operating conditions as well as mixing on the yields was simulated in order to reveal the advantages of the downer reactor for the cracking process.
In order to model the dispersion reactor, some realistic simplifying assumptions are necessary. The system is assumed to operate at steady state. Due to rapid mixing of gas and solids, high heat- and mass-transfer rates are assumed. The axial gas backmixing largely influences the yield of the cracking process; it is found that the axial gas mixing Peclet number is around 4 (Luo and Yang, 1990; Wei et al., 1993; Li and Wu, 1990). The axial gas dispersion of a pilot-scale downer reactor was studied by Wei et al. (1995) using a steady-state tracer method. They found that the axial Peclet number is 1-2 orders of magnitude larger than that in the upflowing riser. These mixing studies in both the riser and downer indicate that the dispersion model can describe the mixing process and that a certain extent of gas and solids mixing occurs in both the riser and downer. Because of the large difference in axial dispersion for the riser and downer reactors, our reactor model will take the axial dispersion into account to find the difference of gasoline yield in the fluid catalytic cracking process. The following model assumptions are made: 1. The axial mixing of gas and solids can be described by a one-dimensional pseudo-dispersion model with two dispersion coefficients. 2. The cracking reaction rate is controlled by chemical reaction kinetics. Solids and gas are well mixed over the cross section of the reactor. 3. Solids in the riser are in thermal equilibrium with the gas in the same cross section. 4. The reaction occurs at constant temperature. 2.1. Material and Heat Balance. The dispersion model is combined with the four-lump kinetic model of gas-oil catalytic cracking and the axial voidage distribution model for both the riser and downer, as well as the close-close boundary conditions of Danckwerts (1953) in order to develop a dispersion reactor model. The material balance for a generic component is formulated as follows:
* Author to whom correspondence is addressed. † This paper was submitted for the Engineering Foundation Conference in Banff, Canada. S0888-5885(97)00218-2 CCC: $14.00
d2yi 2
dl
)
(
)
Pe dyi + r(i) L dl
© 1997 American Chemical Society
(i ) 1, 2, 3, 4)
(1)
5050 Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997
Figure 1. Axial particle velocity profiles in the riser and downer.
With Danckwerts’ (1953) boundary conditions:
l)0
dyi Pe ) (yi|l)0+ - yi|l)0-) dl L
l)L
dyi )0 dl Figure 2. Four-lump kinetic model.
where the rate of reaction r(i) is obtained from the kinetic model and the voidage results from the hydrodynamic study at a given location l. The volumetric expansion due to generation of moles is taken into account by calculating the superficial gas velocity at the exit of each control volume. The above model equations are coupled two-stage, nonlinear, ordinary differential equations with boundary value problems. It is impossible to obtain an analytical solution for the model. The shooting method is used in finding the numerical solutions of the model. To obtain the numerical solutions, first, the material and heat balances of the overall reactor are calculated. Initial values for the first step of the equations are given by computing results of the plug-flow model and CSTR model. With these initial values and the boundary conditions in the outlet of the reactor, the simulator computes conditions for each incremental step in space using an integration module of one-stage, stiff differential equations, until the entire reactor is computed. Next, the boundary conditions in the inlet of the reactor are used to check whether or not the numerical solution meets the boundary conditions with acceptable tolerance. If not, the Broyden method for solving nonlinear equations is used to obtain the initial values for the next round of iteration. The iteration continues until the solution meets the boundary conditions with acceptable tolerance. This computing process is called the shooting method. In a given control volume, first, the hydrodynamic parameters and the reaction rates are solved by using separate modules. Then, the information gathered from these modules is coupled in the material balance function and flow rates of all components are computed. Finally, the gas velocity is corrected for volumetric expansion. The values at the exit of a given control volume are used as input values to the adjacent control volume. In order to be consistent and to be realistic, in this study all performances are based on weight fraction.
2.2. Hydrodynamic Model. For one-dimensional axial flow in the downer, gas and solids suspension undergoes a three-section axial flow structure: the first acceleration section, the second acceleration section, and the constant velocity section. The hydrodynamics can be described by a one-dimensional model proposed by Wang et al. (1992). Figure 1a shows the axial average particle velocity profiles at different gas velocities. The points are the experimental data which show that the hydrodynamic model can describe the experimental data well. For the hydrodynamic model in the riser, a modified Li-Kwauk model was used. Figure 1b shows the axial average particle velocity in the riser, predicted by the model and the experimental data; this model predicted the data well. Details of the model are reported elsewhere (Wei et al., 1996). Upon comparison the profiles of particle velocity in the riser and downer, it can be found that the axial particle velocity develops slower in the riser than in the downer. 2.3. Four-Lump Kinetic Model. Gianetto et al. (1994) published information on the four-lump kinetic model of the gas oil catalytic cracking reaction. Figure 2 shows the four-lump kinetic model for catalytic cracking of gas oil where the overall reaction rate k0 ) k1 + k3, the overcracking reaction rate k2 ) k21 + k22, and the byproducts reaction rate k3 ) k31 + k32. According to Gianetto et al. (1994), the catalytic cracking rate is second order to gas oil and can be expressed as follows:
rA ) -φ(k1 + k3)CA2
(2)
where φ is catalyst deactivation factor, which is a function of coke generation. Assuming that all reactions have the same deactivation reaction factor φ and this factor is a function of the coke content of catalyst, the
Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 5051 Table 1. Commercial FCC Reaction Data Daqing gas oil density (20 °C), g/cm3 coke, mol % catalyst type distribution product, wt % gasoline gas coke conversion, wt %
0.8593 0.55 Y15 37.56 30.92 2.92 71.40
Table 2. Kinetic Parameters for the Daqing Gas Oil k1, m6/(kmol‚kgcat‚s) k2, m3/(kgcat‚s) k31, m6/(kmol‚kgcat‚s) k32, m6/(kmol‚kgcat‚s) R
7.216 × 106 5.369 2.063 × 106 4.199 × 105 400
deactivation reaction rate can be expressed as follows:
φ ) exp(-RYDWT/mc)
(3)
Figure 3. Axial profiles of conversion and yield in the riser and downer.
For the gasoline lump, gas oil will convert to gasoline and gasoline can also overcrack to form coke and gas. The gasoline generation rate can then be expressed as follows:
rB ) φk1V1CA2 - φk2CB
(4)
The kinetic parameters of the four-lump model change with the properties of the gas oil. In order to examine the cracking behaviors of a typical Chinese feedstock, the Daqing gas oil is used. Its kinetic parameters are determined by fitting the commercial riser data taken from a 1 million ton/y FCC riser, as shown in Table 1. According to the cracking behaviors of the gas oil, the coke formation rate k22 in the overcracking of the gasoline is very slow in comparison with gas formation rate k21; it can be considered as zero in this modeling. In order to guarantee the accuracy of the kinetic model for simulation purposes, the model parameters are evaluated by fitting the data obtained from commercial FCC riser reactors. The obtained kinetic parameters for the Daqing gas oil are listed in Table 2. 3. Simulation Results and Discussion 3.1. Axial Profiles of Gasoline Yield in the Riser and Downer. In order to demonstrate the features of the reactor model, the dimensions of a typical commercial reactor with 45 m height are chosen. Typical axial profiles of gas-oil conversion, gasoline yield, light oil yield, and coke formation for both the riser and downer reactors are plotted in Figure 3. The operation parameters such as reaction temperature, catalyst circulation rate, diameter of the reactor, and properties of the feedstock are kept constant. As shown in Figure 3, because the axial Peclet numbers in the riser and downer are 4 and 100, respectively, the profiles of gasoil conversion, gasoline yield, and light oil yield in the downer are steeper than those in the riser. The concentration of gas oil in the inlet region of the downer is much higher than that in the riser. The kinetic studies show that the cracking reaction is second order to gas oil and first order to gasoline, which results in the cracking rate in the inlet region of the downer being much higher than that in the riser. The above two reasons make a higher yield of gasoline and conversion of the gas oil in the downer than in the riser, as shown in Figure 3.
Figure 4. Effect of axial dispersion on the gasoline yield.
3.2. Effect of Gas Backmixing on the Yield of Gasoline. The gap of gas backmixing between the riser and downer is more than 1 order of magnitude. This large difference in gas mixing is the major reason why a high yield of an intermediate species, gasoline, without overcracking to gas and coke can be achieved in the downer. How much the gas backmixing affects the yield of gasoline is very important for the reactor. Due to the very complex reaction network and many factors which can influence the yield of gasoline, the comparison is at the same reaction conversions of 62% and 70%. The other operation parameters such as reaction temperature, catalyst circulation rate, diameter of the reactor, and properties of the feedstock are kept constant in the comparison. The effect of Pe on the yield of gasoline was plotted in Figure 4. The influence of axial Peclet number on the gasoline yields shapes like “S” shape; the gasoline yield hardly changes with Pe when Pe is less than 0.1. There exists a Pe-sensitive region in which the yield of gasoline increases largely with an increase of Pe. The gasoline yield in this Peclet number sensitive range increases about 11%. When Pe is larger than 1000, the yield of gasoline will be the same as that in the plug-flow reactor. Both the riser and downer reactors are in the Pe-sensitive region; they cannot be
5052 Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 Table 3. Yields of the Derby Demonstration Unit operating mode product yield
riser
MSCC
C2, fuel oil equivalent, vol % C3 + C4, vol % gasoline (C5, 430 °F), vol % light cycle oil (430-680 °F), vol % buttoms (680+ °F), vol % coke, wt %
7.4 21.5 50.4 21.6 9.1 5.8
3.6 20.4 57.0 20.6 9.0 5.5
considered as CSTR or plug flow. A little increase of Pe will increase the yield of gasoline. Although there exists a large difference in axial particle velocity profiles in the riser and downer, the influence of axial Peclet number on the gasoline yield in both the riser and downer is almost the same, which implies that the axial particle velocity does not influence the gasoline yield significantly under the same gas-oil conversion, while gas mixing plays a very important role in improving gasoline yield. In catalytic cracking of gas oil, however, the economic consequences of even very small incremental changes in gasoline yield are large. The precise magnitude of gasoline yield, of course, depends upon the mixing parameter and kinetic scheme used in the calculations. Therefore, it does appear that gas backmixing effects can have a non-negligible effect upon the economic performance of a fluidized-bed reactor. Upon comparison of the riser with the downer, Pe increases about 1 order of magnitude. This increase of Pe increases the yield of gasoline about 5.1% under a gas-oil conversion of 62%. That makes the downer reactor very attractive as a new type of reactor for catalytic cracking of gas oil. As the gas-oil conversion increases, the difference of gasoline yield between the riser and downer will further increase. As shown in Figure 4, when the conversion varies from 62.0 to 70.0%, the difference of the yield increases from 5.1 to 5.5%. Kauff et al. (1996) reported a comparison study of the riser and downer reactors in a commercial miniscale plant. Table 3 shows the yield summary from the test data set of a coastal FCC unit which could operate in a riser cracking or downer (MSCC) mode, demonstrating the yield benefits on MSCC. The most distinguishing characteristics of MSCC yield performance are the extraordinarily low yield of dry gas and the high yield of the gasoline product. The gasoline yield is 6.6% (vol %) higher in the downer reactor than in the riser reactor, which is consistent with the modeling results shown in Figure 4. The above numerical simulation shows that gas backmixing has a large influence on the reaction performance over a wide range of Peclet number. Plug flow or CSTR assumption will make the reactor model oversimplified in the riser and downer modeling. 3.3. Effect of Overcracking on the Yield of Gasoline. The overcracking reaction rate of gasoline can also influence the yield of gasoline in the reactor. As shown in Figure 5, the higher the overcracking rate, the lower the gasoline yield. At the same time, an increase of the overcracking rate will result in expanding the Peclet number sensitive range of the reactor under the same gas-oil conversion. As the overcracking rate increases, the gasoline yield difference between the riser and downer also increases. Figure 6 simulates the gasoline yield change with gas-oil conversion under different overcracking rates. No matter whether the reactor is plug flow or with some extent of dispersion,
Figure 5. Effect of the overcracking rate on the gasoline yield.
Figure 6. Influence of the overcracking rate on the downer gasoline yield.
the gasoline yield has a maximum value. An increase of the overcracking rate will decrease the maximum yield of gasoline. As the overcracking rate increases, the gas-oil conversion at which the yield of gasoline reaches a maximum will also decrease. An increase of gas backmixing also decreases the gasoline yield, as shown by the comparison of the dashed line with the solid line in Figure 6. While the change in gas backmixing does not change, the gas-oil conversion at the yield of gasoline achieves the maximum value, as shown in Figure 6. An increase of the overcracking rate will enlarge the difference of maximum gasoline yield between the plug-flow and downer reactor. The reduction of gas backmixing and the decrease of the overcracking rate both reduce the gasoline overcracking to coke and dry gas; it is important to distinguish the differences between these two factors in order to properly model the reactor. As shown in Figure 3, an increase of Peclet number will reduce the gasoline
Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 5053
backmixing to the inlet of the reactor and as such steepen the axial concentration profiles; while the influence of the overcracking rate is caused by the catalyst as well as the properties of the feedstock, it does not steepen the axial concentration profiles. Usually the reactor model is checked by the outlet concentration of the reactor; the conversion and yield along the axial direction in the reactor are difficult to obtain. This makes it difficult to find the different influences of the gas backmixing and the overcracking rate in the model. If the riser reactor is assumed as plug flow, the effect of gas backmixing on the overcracking of gasoline is also assumed as the influence of the overcracking rate. In this oversimplified model it is difficult to show the advantage of the downer reactor in the catalytic cracking process, which have been reported by many investigators. This calls for more detailed determination of the cracking reaction rate under the condition of plug flow or CSTR. Because of the above-indicated reasons, determination of the overcracking rate and measurement of the gas backmixing are very important to estimate the extent of dispersion on the cracking reactor. 4. Conclusions A preliminary dispersion reactor model for the catalytic cracking of the Daqing gas oil is conducted. Work to date shows that axial gas backmixing in the riser and the downer is a very important factor that influences the yield of gasoline. Reactor simulations suggest that because of the great reduction of axial gas backmixing in the downer, its yield of gasoline is much higher than that in the riser which is widely used commercially. The modeling results show that both the gas backmixing and the overcracking rate of gasoline largely influence the gasoline yield in the reactor. It is very important to determine the overcracking rate as well as gas backmixing in the dispersion model of the reactor. Nomenclature CA ) molar concentration of gas oil (gmol/cm3) CB ) molar concentration of gasoline (gmol/cm3) k1 ) individual kinetic constant for gas oil cracking to gasoline in the four-lump model (m6/(kmol‚kg of catalyst‚s)) k21 ) individual kinetic constant for gasoline cracking to light gases in the four-lump model (m3/(kg of catalyst‚s)) k22 ) individual kinetic constant for gasoline cracking to coke in the four-lump model (m3/(kg of catalyst‚s)) k31 ) individual kinetic constant for gas oil cracking to light gases in the four-lump model (m6/(kmol‚kg of catalyst‚s)) k32 ) individual kinetic constant for gas oil cracking to coke in the four-lump model (m6/(kmol‚kg of catalyst‚s)) k2 ) summation of k21 and k22 (m3/(kg of catalyst‚s)) k3 ) summation of k31 and k32 (m6/(kmol‚kg of catalyst‚s)) l ) axial location in the reactor (m) L ) length of the reactor (m)
mc ) mass of catalyst (g) Pe ) Peclet number rA ) reaction rate of gas oil cracking (gmol/(g of catalyst‚s)) rB ) reaction rate of gasoline formation (gmol/(g of catalyst‚s)) S ) space velocity (F0/FLvr) V1 ) stoichiometric coefficient for gasoline formation from gas oil (MA/MB) WT ) total weight of hydrocarbons in the reactor (g) yi ) weight fraction YD ) weight fraction of coke Greek Symbols R ) exponential decay function φ ) fraction of active sites
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Received for review March 18, 1997 Revised manuscript received July 15, 1997 Accepted July 24, 1997X IE9702183
X Abstract published in Advance ACS Abstracts, November 1, 1997.
