Understanding Riser and Downer Based Fluid Catalytic Cracking

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Ind. Eng. Chem. Res. 2009, 48, 12–26

Understanding Riser and Downer Based Fluid Catalytic Cracking Processes by a Comprehensive Two-Dimensional Reactor Model Changning Wu, Yi Cheng,* and Yong Jin Department of Chemical Engineering, Beijing Key Laboratory of Green Chemical Reaction Engineering and Technology, Tsinghua UniVersity, Beijing 100084, P.R. China

A two-dimensional reactor model incorporating hydrodynamics, mass balance, energy balance, and a 4-lump/ 14-lump kinetic model was established to simulate the riser and downer based fluid catalytic cracking (FCC) processes. The kinetic parameters of the 4-lump kinetic model were re-evaluated from the originally published experimental data for a more reliable description of the FCC process. The 14-lump kinetic model based on a molecular description of cracking and hydrogen transfer reactions was to include more details about the feedstock composition, reaction mechanisms, and the products distribution for a better understanding on the reactor performance for FCC process. This comprehensive model captured the key characteristics of the gas-solid reacting flows in the riser and downer, i.e., the uniformity of flow structures, the distinct backmixing behavior in the riser and downer, and the momentum and energy balances during the complex FCC reactions. The model predictions were first validated against industrial data from several literature sources and found to agree with each other reasonably well. Then, the simulations were carried out to fully understand the different reactor performances of riser and downer in the application of FCC refining processes. It can be concluded that the downer benefits from its advantages of the plug-flow nature and uniform flow structures, tending to have more products in the middle distillates, e.g., gasoline and light olefins, especially under high-severity operations. Better control of the reaction extent for increased selectivity to desired intermediate products would allow the use of downer reactors for the larger-scale practical applications in the FCC process, together with the valuable byproduction of light olefins. 1. Introduction A fluid catalytic cracking (FCC) unit converts low value heavy hydrocarbons into a series of more valuable products such as gasoline and light olefinic compounds. In a riser reactor of a commercial FCC unit, hot regenerated catalyst particles come in with liquid vacuum gas oil (VGO), which is vaporized and then converted into the products. The reactor performance in terms of overall conversion of VGO and the yields of different products is of primary concern, where a higher conversion and higher yields of gasoline and light olefins is desirable.1 The risers have served as the major commercial reactor for the FCC process over the past decades. However, both theoretical and experimental studies on the hydrodynamics and mixing behavior in risers reveal that there exists a strongly nonuniform flow structure with severe backmixing of solid particles.2,3 This limits further improvement of the products distribution in risers which can be made by changing the operating conditions. As an alternative, a downer reactor was proposed in the 1980s to achieve better reaction control owing to the much more uniform flow and narrower residence time distribution (RTD) for either gas or solids than the riser.4–6 Extensive studies have been conducted and shown great potential of a downer being applied in high-severity operated processes and ultrashort contact time systems where the intermediates are the desired products (see review articles refs 3, 6, and 7). It has been reported that in comparison with risers, the downer reactors can improve the selectivity to the desired products significantly, e.g., the increased yields of propylene and gasoline, and the reduced dry gas and coke formation.8–10 Abul-Hamayel9 summarized his research work on the comparison of riser and downer based FCC processes operated under * To whom correspondence should be addressed. Fax: 86-1062772051. E-mail: [email protected].

high-severity conditions in the pilot-plant experiments. Product yields in the riser and downer FCC reactors at a certain conversion of 80% are listed in Table 1. Hydrotreated vacuum gas oil (VGO) based on Arabian light crude was used as the feed, with the feeding rate of 0.4-1.2 kg/h. The reactor outlet temperature was about 600 °C. It was observed that at the same conversion the downer has a higher yield of gasoline and lower yields of coke and dry gas under a smaller catalyst-to-oil ratio compared with the riser. An industrial demonstration of an FCC downer reactor with a capacity of 150 000 t/y was built in Ji’nan refinery (SINOPEC) in 2003. A patented technique,11 i.e., a coupled riser to downer (RtoD) reactor, was adopted in this demonstration unit for combined advantages of both the riser and downer. The test results in the industry indicated that the selectivity to desired products could be improved in the coupling reactor as a result of the introduction of the downer part.12 When the downer was operated as the FCC reactor separately, the yields of gasoline, liquefied petroleum gas (LPG), and propylene were increased by 3.90, 8.14, and 4.30 wt %, respectively, in contrast to a conventional riser. Meanwhile, the diesel oil and dry gas were decreased by 10.48 and 1.83 wt %, respectively. Coke had little change in yield.13 For a better understanding of the reactor design for FCC processes, this work aims to build a mathematical model which can predict the conversion and yields pattern achievable in an FCC riser/downer reactor as a function of feed atomization characteristics, reactor geometry, operating conditions, and characteristics of the feed and catalyst. The reactor geometry can be simply characterized by the reactor height and the column diameter. The operating conditions play important roles in FCC reactor performance, with the key parameters as the feeding rate of gas oil, catalyst-to-oil ratio, mass flow rate of steam, preheat temperature of gas oil, regenerated catalyst temperature,

10.1021/ie800168x CCC: $40.75  2009 American Chemical Society Published on Web 06/25/2008

Ind. Eng. Chem. Res., Vol. 48, No. 1, 2009 13 Table 1. Yields of Products at a Certain Conversion of 80% parameters conversion (wt %) cat/oil ratio

9

downer

riser

80.0 20.0

80.0 29.4

5.8 23.7 23.3 21.0 48.5 11.3 8.7 2.0

6.8 30.9 29.2 26.6 39.9 10.6 8.8 3.0

yields (wt %) H2-C2 (dry gas) C3-C4 (LPG) C2-C4 olefins C3-C4 olefins gasoline light cycle oil (LCO) heavy cycle oil (HCO) coke

etc. The catalysts that are often-used commercially mainly contain one of the following acidic zeolites, e.g., USY, REUSY, REY, REHY, etc. Since the reaction kinetics are strongly dependent on the catalysts, the yields of FCC products are remarkably influenced by the selections of catalysts and feedstocks as well. The kinetic model is highly responsible for an adequate determination of the mass concentrations of each mixture component along the riser/downer reactor, where the lumped kinetic models have been successfully developed to describe the catalytic cracking reactions in microactivity and industrial reactors. More details will be discussed in section 2.3. The feed atomization has great impact on the initial contact efficiency between gas oil droplets and catalysts. Little of the existing research investigated the atomization effect on FCC process.1,14–16 Different models proposed by many researchers1,15–29 considered the complicated processes involving mass transfer, momentum transfer, heat transfer, and catalytic cracking kinetics in the FCC reactor, varying from simple one-phase to threephase models and one-dimensional (1D) to three-dimensional (3D) models, such as the 1D two-phase model by Han and Chung,23 1D three-phase model by Gupta and Rao,1 and 2D single-phase model by Souza et al.28 in recent publications. Souza et al.28 classified the fluid flow models for riser reactors

Figure 2. Reaction schemes of the FCC process: (a) 4-lump reaction kinetics; (b) 14-lump reaction kinetics.

Figure 3. Validation of the hydrodynamics model by the experimental data of Viitanen:42 (a) axial variations of particle velocity (gas velocity given by the experimental data), (b) axial variation of the fluidized bulk density.

Figure 1. Schematic of riser and downer reactors in the simulations.

into three categories: (a) 1D models, normally with simplified formulation and solution; (b) semiempirical models; and (c) models based on phenomenological concepts, more detailed than

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Ind. Eng. Chem. Res., Vol. 48, No. 1, 2009

Table 2. Operating Conditions of Industrial FCC Riser Reactors

a

parameter

value

catalyst flow rate (kg/s) catalyst-to-oil ratio, CTO gas oil feed rate (kg/s) reactor pressure (kPa) feed temperature (K) catalyst inlet temperature (K) riser height (m) riser inside diameter (m) particle diameter (µm) particle density (kg/m3) steam (wt %) vaporization temperature (K) heat of vaporization (kJ/kg) gas oil specific heat (J/kg K) catalyst specific heat (J/kg K) steam specific heat (J/kg K) Axial Peclet number radial Peclet number

144 7.2 20 284a 494 960 33 0.8 70b 1500b 7c 698.2b 156b 2600 1150 2000 4 200

Data from ref 43. b Data from ref 37. meter to enable the simulation.

c

Table 3. General Operating Conditions of the Industrial Riser in Qianguo Petroleum Refinery parameters

value

riser height (m) riser inside diameter (m) catalyst-to-oil ratio, CTO gas oil feed rate (kg/s)

36.2 0.8 6.30 25.52

components of feedstock paraffins (wt %) naphthalene (wt %) aromatics (wt %) steam (wt %) operating pressure (kPa) temperature of feed oil (K) temperature of steam (K) temperature of cycled oil (K) particle diameter (µm) particle density (kg/m3) catalyst inlet temperature (K) vaporization temperature (K) heat of vaporization (kJ/kg) gas oil specific heat (J/kg K) cycled oil specific heat (J/kg K) catalyst specific heat (J/kg K) steam specific heat (J/kg K) axial Peclet number radial Peclet number

Assumed operating para-

a

65.06 20.11 14.83 7 342 463.2 623.2 573.2 63 1383 963.2 698.2a 156a 2600 3000 1150 2000 4 200

Data from ref 37.

Table 4. Comparison of Model Predictions with the Plant Data Reported by Wei46 products gas residence time (s) slip factor (-) pressure drop (kPa) catalyst density (kg/m3) outlet temperature (K)

plant data

model results

error

3.4 1.35 25.9 41.2 776.2

2.9 1.42 19.0 31.1 771.6

-0.5 0.07 -6.9 -10.1 -4.6

5.79 21.74 48.90 15.29 8.28 72.47 23.57

5.30 19.50 51.39 18.92 4.89 75.21 23.81

-0.49 -2.24 2.49 3.63 -3.39 2.73 0.26

product yields (wt %) Figure 4. Comparison of model predictions with the plant data reported by Ali et al.37

the other models. According to Theologos and Markatos,17 the overall performance of the riser can be predicted by onedimensional mass, energy, and chemical species balances, which suggested that simplified models, as in the works of Han et al.30 and Souza,31 may be good enough to be used for an optimization purpose. The third type of model uses a simultaneous solution of the conservation equations of mass, momentum, energy, and species for each phase of the fluid flow (two-phase, gas and catalyst; three-phase, gas, catalyst, and liquid droplets). These models are more suitable for theoretical studies of the physics of the multiphase flow phenomena inside the reactors,28,32,33 but subject to the limitation of the current understanding and modeling capability on the complex physics especially when coupled with the chemical reactions. The semiempirical models are somewhat the compromise between the model accuracy and the convenience in real applications. Bolkan-Kenny et al.18 compared riser and downer reactors for FCC process by a one-dimensional hydrodynamic model incorporated with a three-lump kinetic model. A typical commercial reactor with 35 m in height and 1 m in diameter was adopted for both the riser and downer. The results of the simulations showed that the downer reactor would provide improved conversions, yields, and selectivites compared with those of the riser, in the case of using a highly active and quickly deactivate zeolite catalysts instead of a commercial silicaalumina catalyst.

heavy fuel oil light cycle oil gasoline cracking gas coke conversion (wt %) gas and coke (wt %)

To consider the large difference in mixing behavior of gas and solids in risers and downers, Wei et al.20 developed a onedimensional pseudohomogeneous dispersion model. The model combined a 4-lump cracking kinetic model, hydrodynamic models for both the riser and downer separately, and the dispersion model, to predict the FCC reactor performance. The results showed that axial gas backmixing in the riser and the downer is a very important factor that influences the yield of gasoline. When the axial Peclet number was changed from 0.1 to 1000, the yield of gasoline was increased approximately 11% under the same conversion. Keep in mind that the axial Peclet numbers are less than 10 in risers and larger than 100 in downers. These reactor simulations suggested that because of the great reduction of axial backmixing in the downer the yield of gasoline is much higher than that in the riser. In the two research works18,20 mentioned above, some insights in understanding the differences between FCC riser and downer reactors were obtained. However, the fluid flow models employed are oversimplified so that the influences on the conversion and products yields due to the radial nonuniformity and the effect of heat transfer cannot be evaluated. It is reported that the radial nonuniformity can lead to variations in the conversion and the yields of products up to 20% between the

Ind. Eng. Chem. Res., Vol. 48, No. 1, 2009 15

Figure 5. Comparison of model predictions with the pilot-plant data: (a, c, e) adapted from the work of Abul-Hamayel;9 (b, d, f) model predictions. Table 6. Yields of Products at a Certain Conversion of ∼78.6%

Table 5. Parameters in the Simulation parameter

value

products

gas oil feed rate (kg/s) CTO (kg/kg) reactor pressure (kPa) feed temperature (K) catalyst inlet temperature (K) riser height (m) riser inside diameter (m) steam (wt %)

0.05 (∼30 b/d) 8-28 250 453 973 3.0 0.1 10

conversion (wt %) catalyst-to-oil ratio reactor outlet temperature (°C)

central region and the near-wall region in the riser.15,19 On the other hand, Theologos et al.34 indicated that energy balance is a fundamental element in the catalytic cracking process in a riser. The heat lost by the hot regenerated catalyst in the reaction zone of a riser is distributed among heating and vaporization of the liquid feed (60-85%), endothermic heat of cracking reactions (10-35%), and heat losses (5%).34 A reactor model incorporated with the energy balance should supply a prediction closer to the physical nature of FCC process than the case of neglecting the energy balance.

downer

riser

error

78.5 21.0 613.2

78.7 25.0 608.0

-4

37.8 24.5 21.5 16.2

+4.7 -0.4 -0.2 -4.1

yields (wt %) gasoline light gases gas oil coke

42.5 24.1 21.3 12.1

Fligner et al.,19 Derouin et al.,21 Deng et al.,25 Martin et al.,35 and Wu et al.36 have all reported 2D models for FCC risers considering the radial nonuniformity of fluid flow, and all of them assumed the risers to be isothermal. Berry et al.15 proposed a 2D model to predict the conversion and yields pattern in the riser section of FCC unit incorporated with the energy balance, where a parametric study on the influence of the droplet diameter of liquid feeds and the feed penetration into the riser was also undertaken. Berry et al.15 also found dominant differences in their predictions with the plant data reported by Ali et al.37 and

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riser and downer, i.e., the uniformity of flow structures, the distinct backmixing behavior in the riser and downer, and the momentum and energy balances during the complex FCC reactions, in order to implement reliable model predictions using much less computation time than a computational fluid dynamics (CFD) model. The lumped kinetics scheme is carefully chosen by considering the type of catalysts used in the experiments or in the industry. The different reactor performance of the riser and downer are paid much attention to evaluate the future development of downer reactors in the FCC process. 2. Mathematical Model Figure 1 shows the sketch of a riser and downer in the modeling system. Regenerated catalysts, gas oil, and steam enter the system from the bottom of the riser or top of the downer; whereas the products, the deactivated catalysts, and steam leave the reactor from the other end. 2.1. Mass and Energy Governing Equations. The steadystate conservation equations of mass and energy for the twophase reacting flow model in the riser and the downer are given as eqs 1–3, which take into account the change of gas densities due to cracking reactions and thereafter the gas velocities along the reactor length. εFguz

Figure 6. Comparison of model predictions in the riser with the downer reactor both at industrial scale: (a) conversion vs CTO ratio, (b) selectivity to products vs CTO ratio.

εFguzc¯p

had to adjust the values of the activation energy to match the plant data. However, an approximately 40 °C deviation of riser outlet temperature still occurred between the prediction and the plant data after the adjustment of activation energy. This fact may be caused by the different characteristics of the catalyst used in the plant while another catalyst was used in the experiments when evaluating the kinetic parameters. Also, the accuracy of the proposed model may be another factor influencing the simulation results. In the present work, a 2D reactor model incorporating hydrodynamics, mass balance, energy balance, and a 4-lump/ 14-lump kinetic model is established to simulate the reactor performance of a riser and downer in the FCC process. The aim is to provide a solid base of modeling framework from an engineering viewpoint. Therefore, efforts are made to capture the key characteristics of the gas-solid reacting flows in the

)

(

∂T ∂ ∂T 1 ∂ ∂T ) λ + rλ ∂z ∂z ∂z r ∂r ∂r

)

( )

(

)

(1)

∑ (∆H )εF w +N Q i

g i

s

s

i

(2)

( )

(

)

∂Ts ∂ ∂Ts ∂Ts 1 ∂ ) λs + rλs - NsQs (3) ∂z ∂z ∂z r ∂r ∂r In eqs 1–3, the terms on the left-hand side are due to the convection, and the first two terms on the right-hand side are due to the diffusion/conduction. The third terms in both eqs 1 and 2 come from the contribution of the chemical reactions. The last terms in both eqs 2 and 3 represent the interphase heat transfer between the gas and solid phase. The term Ez is the axial effective diffusivity in squared meters per second; Er is the radial effective diffusivity in squared meters per second. In the simulation, the effective diffusivities are calculated by evaluating the axial and radial Peclet numbers (Pez and Per) in the riser or the downer. The details of the above model equations including the boundary conditions are listed in Appendix A. (Note: Equation A.9 is taken from ref 51.) In the present model, the vaporization of the gas oil is assumed to be 100% and occurs right at the moment of contacting with the hot, regenerated catalyst. Therefore, it is necessary to make a correction on the temperature of the catalyst that comes from the regenerator.28 To close the energy balance, the temperature drop of the catalysts at the reactor inlet is determined by the energy balance equation, in which the gas oil and the steam are heated to the vaporization temperature of gas oil (e.g., 698 K). 2.2. Hydrodynamics Model. A semiempirical model approach is employed to characterize the riser/downer hydrodynamics. First, a one-dimensional model based on the conservation of materials and momentum is solved to obtain the axial distributions of pressure, averaged solids fraction, gas velocity, and solids velocity. Subsequently, the radial profiles of the local solids fraction, gas velocity, and slip velocity at each crosssection are calculated using empirical correlations in the literature, which is of importance in the model especially for the riser because of its severe nonuniformity in the radial flow εsFsuz,sc¯p,s

Figure 7. Variations of temperatures with the distance to reactor inlet in riser and downer reactors. Operating conditions are given in Table 2, except that CTO ) 10.2 for the riser and the reacting flow moves cocurrently along the force of gravity in the downer.

(

∂yi ∂ ∂yi ∂yi 1 ∂ ) EzFg + rErFg + εFgwi ∂z ∂z ∂z r ∂r ∂r


Figure 8. Two-dimensional distribution of conversion and selectivity to gasoline in riser and downer based FCC processes: (a) conversion in the riser, (b) conversion in the downer, (c) selectivity to gasoline in the riser, and (d) selectivity to gasoline in the downer.

Figure 9. Radial distribution of gas temperature, conversion, and selectivity to gasoline in riser and downer based FCC processes.

structure. The local solids velocity is calculated by the gas velocity and slip velocity in the same radial location. Since the

gas density varies along either the riser or the downer height due to the cracking reactions, the hydrodynamics model is

18


2.3. Reaction Kinetics. A 4-lump reaction kinetic model and a 14-lump model are used in the present work to describe the complex chemical reactions in gas-solid two-phase flows in the FCC process. The reaction schemes for these kinetic models are shown in Figure 2. 4-Lump Kinetic Model. The four lumps are gas oil (A), gasoline (B), light gases (C), and coke (D). The gas oil is cracked to gasoline, light gases, and coke. The rate laws with respect to the gas oil reactions are second-order on the concentration of gas oil, while the rates of gasoline consumption are first-order on its concentration. The deactivation of the catalyst due to coke deposition was described by Gianetto et al.38 as the following expression,

(

φ(CC) ) exp -R

yDwT mc

)

(4)

Multiplied by the above deactivation function of catalyst, the rate laws of the reactions can be written as, rA ) -φ(k1 + k2 + k3)CA2

[

rB ) φ

Figure 10. Comparison of selectivity and product yields as a function of Pez or Per in riser and downer based FCC processes with a variable range of (50%.

MA k C 2 - (k4 + k5)CB MB 1 A

( (

) )

rC ) φ

MB MA k C 2+ kC MC 2 A MC 4 B

rD ) φ

MB MA k C 2+ kC MD 3 A MD 5 B

]

(5) (6) (7) (8)

The temperature dependence of the kinetic parameters appearing in above equations is described by Arrhenius expressions,

( )

-Ej (9) RT The values of the frequency factors and activation energies corresponding to USSY (ultrastable submicron Y) catalyst reported by Gianetto et al.38 were coupled into the twodimensional reactor model for riser unit by Berry et al.,15 but poor predictions of the conversion and the yields compared with the plant data were obtained in their work. The model predictions were then improved by adjusting the activation energies for the reactions of gas oil consumption.15 This work makes two reasonable modifications on the 4-lump kinetic model based on the re-evaluation of the kinetic parameters from available data in the literature. It can be found that among the published experimental data of Gianetto et al.38 some runs of data are not acceptable due to the large evident errors. The four runs of data for USSY catalyst (large zeolites), i.e., (550 °C, 10 s), (525 °C, 10 s), (500 °C, 5 s), and (550 °C, 3 s), are discarded in the process of re-evaluating the kinetic parameters. In addition, it is also found that the value of the deactivation function corresponding to the given exponential decay constant (R ) 391) in eq 4 is much smaller than the other reported results, e.g., kj ) Aj exp

φ(CC) ) Figure 11. Influence of CTO ratio on the riser/downer based FCC processes: (a) conversion, selectivity to gasoline, and selectivity to coke; (b) olefin content in gasoline, yield of light olefins, and selectivity to light olefins.

actually coupled into the above 2D mass and energy governing equations and solved iteratively. The model equations are given in Appendix B. (Note: Equation B.28 is taken from ref 61.)

BC + 1 , BC + exp(ACCC)

CC )

yDwT × 100 mc

(10)

where the constants AC and BC were taken as 4.29 and 10.4, respectively.16,39 When the yield of coke arrives at 3% (5%), for the case of a catalyst-to-oil (CTO) ratio of 5, the two deactivation functions have the values 0.096 vs 0.485 (0.020 vs 0.137). The overestimation of deactivation of the catalyst will make the model

Ind. Eng. Chem. Res., Vol. 48, No. 1, 2009 19 Table 7. Kinetic Constants for the 4-Lump Kinetic Model reactionsa gas oil to gasoline gas oil to light gases gas oil to coke gasoline to light gases gasoline to coke deactivation a

Aj 6.651((1.329) × 104 m6/mol/kgcat/s 2.411((0.516) × 106 m6/mol/kgcat/s 1.766((52.47) × 105 m6/mol/kgcat/s 8.650((92.90) × 102 m3/kgcat/s 2.233((7.968) × 101 m3/kgcat/s φ(tc) ) 1/(1 + βtcγ), β ) 162.15, γ ) 0.76; tc (h)

Ej (J/mol)

∆Hr (J/mol)b

9.820((0.128) × 104 1.261((0.014) × 105 1.324((2.228) × 105 1.137((4.284) × 105 5.912((2.546) × 104

195000 670000 745000 512500 550000

Variance of residuals ) 0.034. b Data from ref 16.

predictions on the conversion and the product yields less than the plant data, which had been observed by Berry et al.15 It may be caused by the small yields of coke measured in the riser simulator proposed by Gianetto et al.38 For the riser simulator, a deactivation function in terms of the catalyst residence time would be more favorable to describe the catalytic cracking behavior well. The hyperbolic function, i.e., φ(tc) ) 1/(1 + βtγc ) proposed by Gross et al.40 is introduced in the current work, instead of eq 4. The re-evaluated kinetic parameters are listed in Appendix C. The new kinetic model has been tested to simulate different FCC riser reactors well in this work. 14-Lump Kinetic Model. In the 4-lump kinetic model, the feed oil was assumed to consist of only one volatile component (gas oil). However, it is necessary to tell more detailed components of heavy fuel oil, light cycle oil, gasoline, and light gases. Pitault et al.39 proposed a kinetic model based on the molecular description for the cracking reactions and the hydrogen transfer reactions, together with the use of lumps for families of alkanes, alkenes, cycloalkanes, alkenic cycloalkanes, and aromatics, in an attempt to describe an industrial feedstock, however using only a limited number of reactions. On the basis of Pitault’s work, a 14-lump kinetic model was proposed by Guo et al.41 with further simplification on the chemical compositions of some lumps. Lumps are defined by the chemical family (e.g., paraffin, olefin, naphthene, and aromatic) and by the molecular weight, which includes five levels of lumps, i.e., heavy fuel oil (HFO, >350 °C), light cycle oil (LCO, 215-350 °C), gasoline, liquefied petroleum gas (LPG), and coke. Dry gas, mainly produced by thermal cracking reactions, is not included in the lumping model, but its yield can be correlated with both feed stock property and products. The HFO lump consists of three components: paraffins (PH), naphthenes (NH), and aromatics (AH). In the LCO/gasoline level, the four components of paraffins (PL/PG), olefins (OL/OG), naphthenes (NL/NG), and aromatics (AL/AG) are considered. In the LPG level, only paraffins (PS) and olefins (OS) are considered. Lumps react according to the known chemistry of catalytic cracking reactions, including the mechanisms of beta scission, cyclization, aromatization, hydrogen transfer, condensation, and condensation plus hydrogen transfer reactions. Two factors are taken into consideration for the deactivation of the catalyst. One is due to the adsorption of heavy aromatics on the catalyst. Another is the deposition of coke on the activity sites. The detailed reaction network is given in Appendix C. 3. Results and Discussion 3.1. Comparison with Published Data on Industrial FCC Risers. 3.1.1. Case Study 1: Data of Viitanen.42 Figure 3 shows the comparison of the predicted axial variations of particle velocity and fluidized bulk density with the measured results reported by Viitanen.42 The predictions are seen to be in reasonable agreement with the experimental results. Though the dominant difference of the fluidized bulk density between

the prediction and the plant data could be observed at the bottom region of the riser, the proposed hydrodynamics model is acceptable to provide the flow fields for the simulation of FCC process. 3.1.2. Case Study 2: Data of Ali et al.37 Essentially, the proposed computational model requires detailed information about the feed oil/steam as well as the design and the operating conditions of the industrial reactors. However, adequate and complete information is seldom available from the published data on the industrial reactors.16 It is necessary to make some suitable assumptions and simplifications to enable the simulations. The plant data reported by Ali et al.37 was obtained from the FCCU riser of Regina Refinery, Consumers’ Co-operative Refineries Ltd. As shown in Table 2, the riser was operated at the solids flux of 288 kg/m2 s and CTO ratio of 7.2. It can be deduced from another detailed report about the same FCC unit by Dahlstrom et al.43 that the employed catalyst was probably USY-based, according to the properties of the equilibrium catalysts, the yields pattern of several runs (especially for the ratio of C5 + gasoline to conversion, vol %/vol %),44 and the high RON (research octane number) of the gasoline (>91.7).45 Thus, it is more reasonable to predict the product yields using the kinetic parameters corresponding to a USY-based catalyst (e.g., the USSY-style catalyst used by Gianetto et al.38). The 4-lump kinetic model is employed in the simulation. The comparisons of the predicted results with the plant data are plotted in Figure 4. The differences between the predicted yields of all lumps and the plant data are at the level of 1-4 wt %, showing reasonably good agreement. The model prediction of the riser outlet temperature is in closer agreement with the plant data than the reported predictions by Ali et al.37 and Berry et al.15 3.1.3. Case Study 3: Data of Wei.46 Wei46 reported the conversion of gas oil and detailed product yields of an industry riser at Qianguo Petroleum Refinery, China. As shown in Table 3, the riser was operated with the solids flux of 320 kg/m2s and CTO ratio of 6.3. A hybrid catalyst (DOCR-1) with majority of REUSY zeolite and Chinese Jilin atmospheric residue47 were used in the FCC operation. The 14-lump kinetic model is accordingly employed in the simulation. The comparisons of the predicted results with the plant data are shown in Table 4. It can be seen that the predicted results agree well with the plant data in terms of the conversion, the product yields, the hydrodynamics, and the temperature at the reactor outlet. The simulations can be carried out with very stable convergence, which indicates that the framework of the reactor model is well proposed. About -25% and -40% deviations of the catalyst density and the yield of coke, respectively, may be attributed to the limitations of the proposed hydrodynamics model and the 14-lump kinetic model. 3.2. Reactor Performances in the Riser with Downer Based on the 4-Lump Kinetic Model. Figure 5a, c, and e summarizes the comparative results of riser and downer based FCC processes at high-severity operations in the pilot-plant

20


experiments.9 It is observed that at the same conversion downer requires a smaller catalyst-to-oil ratio to obtain a higher yield of gasoline and a lower yield of coke. A series of simulations are carried out to disclose the different reactor performances for the riser and the downer based FCC processes on a scale of 30 b/d as in the demonstration plant proposed by Fujiyama et al.48 The operating conditions in the simulations are listed in Table 5 with some necessary assumptions. Since the objective of the comparison is to tell the inherent different performances of the riser and downer, the trends of the variations due to the reactor type are focused on. Figure 5b, d, and f plots the results of model predictions. The same trends with the experimental results can be observed from the simulations. Table 6 compares the yields of products in riser and downer FCC reactors at a certain conversion of about 78.6%. To reach this conversion, the downer requires a smaller CTO ratio than the riser. However, the yield of the desired intermediates (such as gasoline) is increased by 4.7 wt % and the yield of the undesired products (such as coke) is decreased by 4.1 wt %. Both the results from the experiments and from the simulations have demonstrated the advantage of the downer applied in the FCC process. These results are very convincing to investigate larger-scale applications of downers as a novel FCC process. On the basis of the reasonably good comparative predictions on the FCC riser and downer reactors at the pilot-plant scale, the proposed model is further used to simulate the large-scale riser and downer reactors at industrial size. As shown in Figure 6a, under the condition of the same conversion, the downer requires a smaller CTO ratio, which is consistent with the trend observed in Figure 5. The variations of the selectivities to products with CTO ratio are plotted in Figure 6b. The influences of the CTO ratio on the selectivities to products in the riser reactor are more significant than those in the downer reactor, especially for the selectivities to gasoline and coke. Both the selectivity to gasoline and the selectivity to coke are equivalent in the two different reactors at the CTO ratio of about 8.5. At a higher CTO ratio than 8.5, the downer shows better selectivities to products than the riser. Higher CTO ratios bring better performance to the downer reactor. It can be concluded that the downer reactor has better control on some desired intermediate products (e.g., gasoline) than the riser reactor due to the near-plug flow nature, especially under the conditions of high-severity operations (e.g., high CTO ratio). The above phenomena could be explained further by observing the spatial distributions of chemical species concentration and gas temperature in the riser/downer reactor. Figure 7 plots the axial temperature profiles of gas and solid phase in riser/downer reactor, which has the same conversion as in the case of Figure 6 (CTO ratio of 10.2 for the riser reactor and 7.2 for the downer reactor; Pez ) 100, Per ) 200 used in the downer simulation). In the simulations, the other operating conditions are given in Table 2. On the basis of the assumption that the vaporization of the gas oil is complete and occurs right at the moment of contact with the hot regenerated catalyst, the gas phase will be heated by the hot catalyst from the gas oil vaporization temperature to a “two-phase mixture temperature” sharply in the inlet region of the reactor. A further gentle decrease of the mixture temperature is caused by the endothermic catalytic reactions in the reactor. There is a temperature difference of about 150 K between the vaporization temperature of gas oil and the “two-phase mixture temperature”. Hence, the energy balance is necessary to be considered in the reactor model for FCC process.

Two-dimensional distributions of conversion and selectivity to gasoline in the riser and downer reactors are illustrated in Figure 8. As shown in Figure 8a and b, the conversion in the near-wall region is larger than that in the central region in both of the two kinds of reactors. Obviously, the conversion is very nonuniform along the radial direction at each cross-section in the riser due to the strongly nonuniform flow structure, but rather uniform in downer. In fact, there exists evident backmixing of solid particles in the accelerating region in the riser, especially when the gas velocity is not high enough and the diameter of the riser column is large. However, due to the limitation of the framework of Eulerian-Eulerian (two-fluid) approach in which the particle phase is assumed as a continuous medium, the proposed model cannot consider the backmixing of solid particles at the particle scale. In the present model, the derivation caused by the simplification on the backmixing of solid particles is partially expressed by evaluating the different magnitude of effective diffusivities in the riser and downer reactors and estimating the catalyst activity with the cross-sectional averaged particle residence time in the reactor. The nonuniform flow structure in the radial direction could be revealed by the spatial distribution results of the selectivity to gasoline as plotted in Figure 8c and d. Similar to the comparative results of conversion, the selectivity to gasoline at each cross-section in the downer is significantly larger than the one at the corresponding cross-section in the riser, which can be attributed to the uniformity of the flow structure and little backmixing of solid particles in downer reactors. The radial distributions of gas temperature, conversion, and selectivity to gasoline at the axial locations of 1, 10, 20, and 30 m are clearly demonstrated in Figure 9. The gas temperature in the riser reactor varies evidently between the central region and the near-wall region at the riser base (see Figure 9a), which is mainly due to the significant nonuniformity of the solids concentration and velocity along the radial direction. The variation of conversion between the central region and the nearwall region exceeds 30 wt % at the riser base and 10 wt % higher in the riser (see Figure 9c), similar to the results of 20 wt % at the riser base observed by Fligner et al.19 and Berry et al.15 The large variation of conversion at the riser base is caused by the higher CTO ratio in the present riser case than a commercial riser unit (i.e., 10.2 vs 7.2). The variation of selectivity to gasoline between the central region and the nearwall region is about 7% at the riser base and 2% higher in the riser (see Figure 9e). In comparison with the riser, the downer shows rather ideal distributions of gas temperature, conversion, and selectivity to gasoline along the radial direction as shown in Figure 9b, d, and f. The near-plug flow structure in the downer results in the uniform radial distributions of gas temperature, reaction extent, and chemical species concentration, with the good control on the intermediate products (e.g., gasoline). 3.3. Sensitivity Analysis of Key Model Parameters (Pez and Per). The axial and radial effective diffusivities are two key parameters representing the degree of mixing characteristics of the gas species in axial and radial directions. For simplification, the axial and radial Peclet numbers of gas phase in riser or downer reactor are given as constants according to the experimental studies both from laboratory-scale or industrial reactors, and then, the effective diffusivities can be determined. Figure 10 shows the selectivity to gasoline and product yields as a function of Pez or Per in riser and downer based FCC processes. The simulations are carried out under the conditions listed in Table 5, while the CTO ratio is set as 25 for the riser and 21 for the downer. It can be found that selectivity to

Ind. Eng. Chem. Res., Vol. 48, No. 1, 2009 21 Table 8. Reaction Networks of the 14-Lump Kinetic Model and the Kinetic Parameters for an REUSY-type Catalyst reaction r

Ar (m3/kgcat s)

Er (J/mol)

∆Hra (J/mol)

1.926E+04 4.348E+04 5.460E+03 5.067E+04 2.287E+04 3.554E+04 3.223E+04 6.720E+03 9.510E+03 6.860E+03 3.580E+03 1.630E+03 1.188E+04

2.31E+04 2.31E+04 2.31E+04 2.31E+04 2.31E+04 2.70E+04 2.70E+04 2.70E+04 2.70E+04 2.31E+04 2.31E+04 2.31E+04 2.31E+04

2.671E+04 4.810E+03

-2.88E+04 -2.88E+04

3.515E+04 1.257E+05

5.64E+04 5.64E+04

9.440E+03 1.649E+04 3.525E+04

-1.71E+04 -1.71E+04 -1.71E+04

k21 8.951E-03 3.152E+04 k22 2.652E-02 1.383E+04 k23 8.923E-04 4.000E+01 k24 7.111E-03 7.300E+02 ) 1.2 in this study; variance of residuals ) 0.026

-1.71E+04 -1.71E+04 -1.71E+04 -1.71E+04

kr

β scission P H f PL + O L PL f PG + OG PG f PS + OS OL f 2OG OG f 2OS AH f AL + OL AL f AG + OG AH f AL + PL AL f AG + PG NH f NL + OL NL f NG + OG NH f 2OL NL f 2OG

k1 k2 k3 k4 k5 k6 k7 k8 k9 k10 k11 k12 k13

OL f NL OG f NG

k14 k15

2.684E+00 9.328E+01 1.317E-02 1.624E+01 1.226E+00 9.184E-01 2.984E+01 1.770E-01 1.146E-02 1.843E-01 9.419E-02 1.201E-02 1.982E-02 cyclization 4.750E+00 1.145E-02 aromatization

NL f AL NG f AG

k16 k17

NL + i(OG/OS) f AL + i(PG/PS) NG + i(OG/OS) f AG + i(PG/PS) AH + m(OG/OS) f coke + m(PG/PS)

k18 k19 k20

4.534E+01 5.834E+06 hydrogen transfer 3.756E-03 1.644E-03 6.050E-03

condensation and hydrogen thansfer AL + 2OG + k(OG/OS) f coke + k(PG/PS) AL + 4OS + k(OG/OS) f coke + k(PG/PS) AG + 2OG + k(OG/OS) f AL + k(PG/PS) AG + 4OS + k(OG/OS) f AL + k(PG/PS) i ) 3, m ) k ) 2; β a

Data from ref 45.

gasoline, yield of gasoline, and yield of coke vary with Pez and Per in the riser more sensibly than in the downer, which is due to the strong interaction between diffusion and convection of the gas-solids flow in the riser. When Pez and Per vary to a degree of (50% referring to the base conditions (Pez ) 4 for riser, 100 for downer; Per ) 200 for both), the ranges of the concerned results are marked by the blocks filled with the three colors in Figure 10. It can be observed that the conclusions given in section 3.2 are still appropriate. Most of the results in the simulations are not found to be sensitive to the two key model parameters. 3.4. Further Comparison of the Riser and Downer Based on the 14-Lump Kinetic Model. For better description on the feedstock composition, reaction mechanisms, and products distribution, the 14-lumped kinetic model is chosen and coupled into the present two-dimensional reactor model for FCC process. Selectivity to gasoline and selectivity to light olefinic compounds and gasoline composition (e.g., olefin content in gasoline) are important concerns of FCC technologies, which face the growing demand on the production of ethylene and propylene as well as environmental concerns about cleaner fuels for automobiles.8,49 Figure 11 shows the influence of the CTO ratio on the riser/downer based FCC processes, where the two reactors have the same geometry, operating pressure, inlet temperature of catalyst, and flow rates of feed oil and steam listed in Table 3 (Pez ) 100, Per ) 200 used in the downer simulation). As shown in Figure 11a, higher conversion, higher selectivity to gasoline, and lower selectivity to coke can be obtained in the downer reactor at the same CTO ratio. A similar conclusion was drawn by Abul-Hamayel et al.,9 that is, that at the same conversion the downer requires a smaller CTO ratio, while it obtains higher yield of gasoline and lower yields of

coke. In Figure 11b, it is seen that at any CTO ratio, both the yield of light olefins and selectivity to light olefins (i.e., the mass fraction of OS in the total cracking gas) in the downer are higher than the ones in the riser. The olefin content in gasoline decreases with the increased CTO in the two kinds of reactors, about a 1% drop per increase of 1 in CTO. The drops are a bit gentler than the experimental results.50 A larger drop of olefin content with the increase of CTO can be observed in the downer than in the riser. Overall, the 14-lump kinetic model together with the two-dimensional reactor model behaves well in predicting the riser or downer reactor performance for FCC process. It forms a solid base to understand the FCC process and its optimization on the process conditions with the novel reactor design such as the coupled riser-downer reactors proposed for the integration of refining and petrochemical applications.7,11 4. Conclusions A two-dimensional reactor model incorporating hydrodynamics, mass balance, energy balance, and 4-lump/14-lump kinetic model has been established to simulate the riser and downer based FCC processes. The model was first validated against industrial riser data from several literature sources and found to agree with the plant data reasonably well. The simulations were then carried out to understand the inherently different performances of riser and downer based FCC processes. Both of the results from the reported experiments and simulations presented here indicated that the downer only requires a smaller catalyst-to-oil ratio to reach the same conversion as the riser. Also, a higher yield of gasoline and a lower yield of coke can be obtained in the downer. In comparison with risers, downer

22


reactors can take advantage of their plug-flow nature and uniform flow structure, which ensures better control on reaction extent for increased selectivity to desired intermediate products. In other words, the downer tends to have more products in the middle distillates, e.g., gasoline and light olefins. The model and the current results would provide strong support for investigating larger-scale applications of downers in the FCC process. Acknowledgment

A.2. Boundary Conditions.

{

z ) 0, inlet (considering backmixing) ∂yi (0, r) ) uz(0, r)[yi,0 - yi(0, r)] -Ez ∂z ∂Tj -λj (0, r) ) Fjuz,j(0, r)c¯p,j[Tj,0 - Tj(0, r)] ∂z P ) Pin, uz ) ug,in, uz,s ) us,in T ) Tg,in, Ts ) Ts,in, yi ) yi,0

{ { {

z ) L, outlet (fully developed) ∂yi (L, r) ) 0 ∂z ∂Tj (L, r) ) 0 ∂z r ) 0, axisymmetric axis ∂yi (z, 0) ) 0 ∂z ∂Tj (z, 0) ) 0 ∂z

The authors would like to thank SINOPEC for the financial support. Dr. Y. Cheng would like to thank the Chinese Ministry of Education for A Foundation for the Author of National Excellent Doctoral Dissertation of P.R. China (No. 200245) and Specialized Research Fund for the Doctoral Program of Higher Education (No. 20050003028). Appendix A: Mass and Energy Balance Equations A.1. Governing Equations A.1.1. Continuity Equations for Two Phases. ∂(εFguz) 1 ∂(rεFgur) + )0 ∂z r ∂r

(A.1)

∂(εsFsuz,s) 1 ∂(rεsFsur,s) + )0 ∂z r ∂r A.1.2. Individual Species Balances.

(

)

(A.2)

(

)

∂(εFguzyi) 1 ∂(rεFguryi) ∂ ∂yi ∂yi 1 ∂ + ) EF + rE F + ∂z r ∂r ∂z z g ∂z r ∂r r g ∂r εFgwi(A.3) A.1.3. Energy Balances for Two Phases. ∂(εFguzc¯pT) 1 ∂(rεFgurc¯pT) ∂ ∂T 1 ∂ ∂T + ) λ + rλ ∂z r ∂r ∂z ∂z r ∂r ∂r

( )

(

)

∑ (∆H )εF w +N Q (A.4) i

i

g i

s

s

( ) ( )

∂(εsFsuz,sc¯p,sTs) 1 ∂(rεsFsur,sc¯p,sTs) ∂ ∂Ts 1 ∂ + ) λs + ∂z r ∂r ∂z ∂z r ∂r ∂Ts rλs - NsQs(A.5) ∂r Eqs 1–3 are simplified from eqs A.1–A.5, based on the assumptions of ur ) 0 and ur,s ) 0. Ez )

UgLch , Pez

Er )

Ug(2R) Per

(A.6) (A.7)

Qs ) πdpλNu(Ts - T)

(A.8)

Nu ) 0.66Res Pr /2.55 Res )

1/3

Fguslipdp µg

(A.9) (A.10)

Pr ) c¯pµg/λ

(A.11)

Fg ) PMavg/RT

(A.12)

Mavg )

∑ y / ∑ (y /M ) i

i∈gas

i

i∈gas

i

(A.15)

(A.16)

r ) R, wall (adiabatic) ∂yi (z, R) ) 0 ∂z (A.17) ∂Tj (z, R) ) 0 ∂z In the simulation, physical properties of the gas phase are assumed to vary only with gas temperature as follows, λ ) 5.526 × 10-5T - 0.0115 W/m K, µg ) 1.672 × 10-6√T - 1.058 × 10-5 Pa · s, jcp ) 2.52T + 981.0 J/kg K.52 Thermal conductivity of solid phase is assumed to be λs ) 0.0454 W/m K.16 Appendix B. Hydrodynamics Model A semiempirical approach is employed to describe the riser/ downer hydrodynamics. The two-dimensional flow field is determined by axial distributions of hydrodynamic characteristics and radial correlations of corresponding characteristics. The axial distributions are solved by a one-dimensional model based on the conservation of materials and momentum. The empirical correlations describing the radial profiles of local hydrodynamic characteristics are from the published literature. B.1. Riser Equations B.1.1. Continuity Equations for Two Phases. d(εgFgVg) ) 0, Gg ) εgFgVg ) const (B.1) dz d(εsFsVs) ) 0, Gs ) εsFsVs ) const (B.2) solids phase: dz B.1.2. Conservation Equations of Momentum. gas phase:

Ns ) 6εs/πdp3

1/2

(A.14)

(A.13)

gas phase:

d(εgFgVg2) dP )- FD - Ffg - εgFgg (B.3) dz dz

d(εsFsVs2) ) FD - Ffs - εs(Fs - Fg)g (B.4) dz (B.5) closure relationship: εg + εs ) 1

solids phase:

B.1.3. Drag Force and Friction. FD )

3 CD ε F (V - Vs)2 4 dp s g g

(B.6)


A modified drag coefficient expression was proposed by Qian,53

( ) ()

CD Rer ) 1.405(εg)2.322 CDs Ret

-0.932

dp D

0.105

η(D)

(B.7)

Equation B.7 was modified from the drag coefficient expression proposed by Bai et al.54 Though the two expressions have the same format for correlation as CD/CDs ∝ a(εjg)b(Rer/Ret)c(dp/ D)d, there exists an essential difference in the model, i.e. the setting of boundary conditions. Qian53 used an inlet boundary condition instead of a fully developed boundary condition based on the length of accelerating zone, making the one-dimensional hydrodynamics model closer to the physical nature. The parameters in eq B.7 were estimated from the experimental data in a riser small- or medium-sized in diameter (D < 0.5 m) and could hardly be directly used for predicting the gas-solid flow in industrial risers with much a larger diameter in the range 0.8-1.8 m. Consequently, a correction factor due to the column diameter, η(D), is introduced here.55 0.5e8(D-0.8) 1 + e8(D-0.8)

η(D) ) 1 -

{

(B.8)

24 (1 + 0.15Rer0.687), Rer e 1000 CDs ) Rer Rer > 1000 0.44, Rer )

Fgutdp µg

(B.11)

{

Reg )

uslip )

{

0.67 u¯slip

(B.14)

(B.16)

B.1.4. Superficial Gas Velocity and Solids Velocity.

Vs ) Ug )

εg

Gg

Gs

(B.18)

Fs(1 - εg) ntRT

(B.19)

P(πD2/4) B.1.5. Boundary Conditions. z)0:

P ) P0,

εg ) εg,0,

Ug ) Ug,0

(B.20)

B.1.6. Radial Profiles of Voidage and Velocities. The following shows the radial voidage profile by Wei et al.:56 1-ε ) 2.2 1 - εg

2 r 1 + exp 10 - 7.665 R

(

)

, r e R - δD

(B.23)

r > R - δD

)

(B.24)

d(εgFgVg2) dP )- FD - Ffg + εgFgg dz dz (B.25)

gas phase:

d(εsFsVs2) ) FD - Ffs + εs(Fs - Fg)g dz (B.26)

B.2.2. Drag Force and Friction. 3 CD ε F |V - Vs|(Vg - Vs) 4 dp s g g

(B.21)

where the validation range is 2.0 < Ug < 10.5 m/s, 30 < Gs
2300

[

uz 3n + 1 r ) 1Ug n+1 R

(

(B.9)

Fgdp|Vg - Vs| µg

Ret )

180 kg/m s and 0.68 < jεg < 0.96, with an average standard deviation of 8.3%. The following shows the radial gas velocity profile by Derouin et al.:21 2

Fr )

Ug

(B.29)

√gdp

B.2.3. Radial Profiles of Voidage and Velocities. Below is the radial voidage profile by Wang et al.:62 1-ε r r ) 0.8 + 30 1 - exp -130 1 R R 1 - εg

) [

(

(

2

)]

(B.30)

where the validation range is 2.0 < Ug < 8.0 m/s and 3 < Gs < 160 kg/m2 s. The following shows the radial gas velocity profile by Deng et al.:25 uz r )2 1Ug R

(

1/7

)

[ 54 (1 - Rr ) ]

exp -

2/5

(B.31)

The following two equations show the radial slip velocity profile by Cao et al.:63

24


uslip ) 5.478(1 - ε)0.539 Re )

( ) Re Ret

0.042

FgUgdp µg

(B.32) (B.33)

where the validation range is 2.0 < Ug < 8.0 m/s and 0 < Gs/ Gg < 5 both for eqs B.31 and B.32. Appendix C. Reaction Kinetics C.1. 4-Lump Kinetic Model The equations below show the reaction rate expressions for eqs 1 and 2: wA ) -φ(k1 + k2 + k3)FgyA2Fsεs/MA

(C.1)

wB ) φ[k1FgyA2/MA - (k4 + k5)yB]Fsεs

(C.2)

wC ) φ[k2FgyA2/MA + k4yB]Fsεs

(C.3)

wD ) φ[k3FgyA2/MA + k5yB]Fsεs

(C.4)

φ ) 1/(1 + βtcγ)

(C.5)

The kinetic constants refer to Table 7, including the data of heats of reactions. C.2. 14-Lump Kinetic Model All the considered reactions in the 14-lump kinetic model are listed in Table 8 in detail. The total reaction rate of lump j is given as rj )

∑υ R -∑R ij ij

i

jk

(C.6)

k

where νij is the stoichiometric coefficient and Rij (mol/m3 s) represents the rate of formation of the product j from reactant i though reaction r. For reactions 1-17 in Table 8, the rate of formation is Ri,j )

( )

φ(tc) Fsεs Fg (krCi) 1 + kAhyAh εg

(C.7)

where kr is the kinetic constant (m3/kg s), Ci is the concentration of reactant i in moles per kilogram, φ(tc) is the catalyst decay function, the factor of 1/(1 + kAhyAh) represents the effect of catalyst deactivation caused by heavy aromatics’ adsorption on catalyst, and kAh ) 12.8 is used in this work.64 For reaction 18-24 in Table 8, condensation and condensation plus hydrogen transfer reactions, the order one versus each reactant is supposed (global order is two) by Pitault et al.39 For instance, the rate of formation of reaction 24 is given as

( )(

φ(tc) Fsεs F -k24CAGCOS 1 + kAhyAh g εg βOCOG COS - k24CAGCOS (C.8) k24CAGCOG βOCOG + COS βOCOG + COS

RAG,AL )

)

where the fractions βOCOG/(βOCOG + COS) and COS/(βOCOG + COS) are the probabilities of reaction with OG and OS. The reported experimental data and kinetic parameters65–67 corresponding to the 14-lump kinetic models were incorporated with the deactivation function as φ(tc) ) exp(-36tc) (tc, h),68 which underestimated the deactivation of the catalyst (for example, φ(tc) ) 0.942 at tc ) 6.0 s). Here, the kinetic parameters (only for frequent factors) were re-evaluated by

introducing the widely used deactivation function as φ(tc) ) 1/(1 + 162.15tc0.76). Due to the limited published experimental data, some of the re-evaluated parameters were achieved with large uncertainty of about 100% as for reactions 6, 9, 12, 13, 18, 19, 20, 21, and 23. List of Symbols AC ) constant in eq 10, Ai ) aromatics in lump i Aj ) frequency factor, m6/mol kgcat s, second order; m3/kgcat s, first order BC ) constant in eq 10, CC ) coke weight percentage on catalyst, % CD ) drag coefficient, CDs ) standard drag coefficient, Ci )concentration, mol/m3 or mol/kg cp ) heat capacity, J/kg K D ) diameter of reactor, m dp ) mean particle diameter, m Ej ) activation energy, J/mol Er ) radial dispersion coefficient, m2/s Ez ) axial dispersion coefficient, m2/s FD ) drag force between gas and particles, N/m3 Ffg ) friction force between gas and wall, N/m3 Ffs ) friction force between solids and wall, N/m3 fg ) gas-wall fraction factor, (-) Fr ) Froude number, () Ug/(gdp)1/2) fs ) solids-wall fraction factor, g ) acceleration due to gravity, m/s2 Gg ) gas circulation rate, kg/m2 s Gs ) solids circulation rate, kg/m2 s H ) height of reactor, m kAh ) absorption of heavy aromatics rate constant, kj ) kinetic rate constant, m6/mol kgcat s, second order; m3/kgcat s, first order Lch ) axial distance between injection and sampling points of tracer, m () 2) Mavg ) mean molecular weight of gas phase, kg/mol mc ) mass of catalyst in the cell in the reactor, kg Mj ) molecular weight, kg/mol Ni ) naphthenes in lump i Ns ) number density of particle phase, 1/m3 Nu ) Nusselt number, Oi ) olefins in lump i P ) pressure, Pa Per ) radial Peclet number, Pez ) axial Peclet number, Pi ) paraffins in lump i Pr ) Prandtl number based on gas properties, (Pr ) jcpµg/λ) Qs ) heat flux between gas and solids phase, J/s R ) gas constant () 8.314 J/mol K); or radius of reactor, m r ) radial position, m Re ) Reynolds number, Rij ) rate of formation of the product j from reactant i, mol/m3 s rj ) rate of reaction of component j, mol/kgcat s T ) temperature, K t ) time, s tc ) catalyst residence time, s Ug ) superficial gas velocity, m/s ur ) gas velocity in the r-direction, m/s uslip ) slip velocity () uz - uz,s in this study), m/s uz ) gas velocity in z-direction, m/s Vg ) cross-sectionally averaged gas velocity, m/s Vs ) cross-sectionally averaged particle velocity, m/s

Ind. Eng. Chem. Res., Vol. 48, No. 1, 2009 25 wj ) variation rate of the yield of component j with time due to the reactions, 1/s wT ) total weight of hydrocarbons in the cell in the reactor, kg yi ) weight fraction of component j, z ) axial position, m Greek Letters ∆Hj ) heat of reaction j, J/kg R ) constant of deactivation of catalyst, β ) constant in the deactivation function proposed by Gross et al.,40 βO ) constant represents the difference of reactivity between OG and OS, γ ) constant in the deactivation function proposed by Gross et al.,40 δD ) wall layer thickness, m ε ) local voidage in the reactor, ε ) overall average voidage in the riser, jεg ) cross-sectionally averaged voidage in reactor, jεs ) cross-sectionally averaged solids holdup in reactor, εs ) local solids holdup in the reactor, η ) correction factor for drag coefficient, φ ) deactivation function, λ ) thermal conductivity, W/m K µ ) gas viscosity, Pa · s νij ) stoichiometric coefficient, Fg ) gas density, kg/m3 Fs ) particle density, kg/m3 Subscripts C ) coke g ) gas phase G ) gasoline H ) heavy fuel oil L ) light fuel oil r ) radial direction S ) liquefied petroleum gas s ) solids phase (particle phase) z ) axial direction

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ReceiVed for reView January 30, 2008 ReVised manuscript receiVed April 13, 2008 Accepted April 16, 2008 IE800168X

Understanding Riser and Downer Based Fluid Catalytic Cracking

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