Ind. Eng. Chem. Res. 1997, 36, 3223
3223
FCC Riser Unit Operated in the Heat-Transfer Mode: Kinetic Modeling A. Blasetti Departamento de Ingenieria Quı´mica, Facultad de Ingenierı´a, Universidad Nacional de la Patagonia, 9000 Comodoro Rivadavia, Chubut, Argentina
H. de Lasa* Chemical Reactor Engineering Centre, Faculty of Engineering Science, University of Western Ontario, London, Ontario, Canada N6A 5B9
A pilot-plant unit, namely, Multicrackex, for the catalytic cracking of hydrocarbons with the riser and regenerator units under direct heat exchange conditions was developed in the course of the present study. A two-levels pseudofactorial experimental program was designed using the synthetic gas oil SF-135 (CANMET) and a commercial equilibrium catalyst (Akzo Octaboost). Using the experimental temperature profile inside the riser, the reaction rate constants and activation energies were evaluated for the four lump model. These parameters were precisely estimated ((7% average), and the adequacy of the model was tested by statistical analysis, showing model predictions inside the (15-20% error range. The experimental results and model predictions indicate that endothermic effects of the cracking reactions and gas oil vaporization are neutralized by the heat transfer from the regenerator to the riser. 1. Introduction Remarkable changes have influenced FCC technology in recent years. The latest innovations include improvements in the regenerator (Yan and Green, 1989; Avidan and Chou, 1989), short-contact time reactors (Gartside, 1989; Bartholic, 1989), multiple risers (Herbst et al., 1988; Farnsworth, 1988), and catalyst coolers (Barnes, 1989; Harandi and Owen, 1989). Nevertheless, the units previously described do not seem to take advantage of the heat released in the regenerator and to promote a direct exchange process with the riser. This option may be considered to achieve better control of the riser-regenerator temperature and to process heavier hydrocarbon feedstocks. 2. Experimental Section 2.1. Description of the Unit. The concept of the unit developed in this study, the so-called Multicrackex design, is based on an up-flow reactor (riser) operating in the heat exchange mode with a fluidized bed of hot catalyst (regenerator). Instead of the typical adiabatic riser operating in a conventional FCC unit, this unit promotes the heat transfer between regenerator and reactor. In the present study, the heat transfer process was accomplished by placing several riser reactor tubes inside a regenerator vessel, which were arranged as a bundle of vertical tubes. Both the regenerator and the riser tubes were made of Inconel 601. The regenerator of the unit had an outside diameter of 0.266 m and a height of 3.25 m. The riser had an outside diameter of 0.0334 m and a total height of 3.46 m. The unit was designed to be operated up to 179 kPa and 973 K. Air was used to fluidize the catalyst inside the regenerator. Fluidization air was evenly distributed using a perforated grid. The typical catalyst flows in the riser ranged between from 6 to 20 kg/h delivering catalyst-oil ratios between 1 and 12. S0888-5885(95)00704-4 CCC: $14.00
Figure 1 presents a general overview of the pilot plant showing the unit main components: (a) the regenerator windbox for air distribution; (b) the lower and the upper regenerator sections, holding the dense bed and the freeboard, respectively; (c) the riser tubes located inside the regenerator (not shown in this figure) and connected to the riser elbow at the top of the unit; (d) the riser injectors placed at the bottom of the riser unit; (e) the catalyst feeding line, left-hand side of the lower regenerator section, bringing hot catalyst from the regenerator to the riser injectors; (f) the regenerator and riser cyclones separating catalyst from fluidization air and hydrocarbon vapors, respectively; (g) the first and second hoppers allowing spent catalyst to be collected. The unit was operated in the batch mode, and this provided additional information on the masses of the solids conveyed, the masses of hydrocarbons adsorbed on the catalyst, and mass of coke. Auxiliary equipment, not shown in Figure 1, also included a fluidized bed vaporizer, a product condenser, a gas-liquid separator, a water pump, and air assistance to the injectors. Once gaseous products and unconverted reactants were separated from the catalyst, they were directed to a condenser and a gas-liquid separator. Afterwards, the gas phase was either vented to the atmosphere or sent to a gas bag, whereas the liquid phase was continuously accumulated in the separator. Additional details concerning the pilot plant are reported by Blasetti (1994). 2.2. Experimental Program. The experimental program was designed to study the performance of the above-described pilot plant unit. One objective of this program was to test the unit in a wide range of operating conditions. The second objective was to obtain kinetic parameters required by the mathematical riser model. Experiments were performed using a synthetic crude (CANMET SF-135) and a equilibrium catalyst (Akzo Octaboost 6XX series, MAT ) 66 wt %). Data for the feedstock are reported in supporting information. © 1997 American Chemical Society
3224 Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997
Figure 2. Representation of a theoretical 23 factorial design and true experimental conditions covered in the Multicrackex unit. Figure 1. General view of the Multicrackex unit.
gas oil lump
Table 1. Factor Levels Selected for the Experimental Program (Blasetti, 1994)
(-) low range (+) high range (0) center
regenerator temp, °C
riser contact time based on entry conditions, s
catalyst-to-oil ratio
580-610 700-730 640-670
1.5-2.5 4.5-5.5 3.0-4.0
1.0-3.5 7.0-12.0 5.0-7.0
A pseudofactorial design, investigating the effects of different variables, was implemented (Blasetti, 1994). This approach was of significance for this study given the complex operation of the unit. A 2k factorial design (k < 4) requires three independent variables (factors) at three different factor levels. Difficulties in matching a fixed set of experimental conditions suggested the definition of factor ranges, as shown in Table 1. Figure 2 shows the experimental conditions covered, while Table 2 gives the experimental results. Mass balances included independent measurements of the reactants and products. Only runs with mass balances close to 91.0-109.0% were further considered. This acceptable error range was determined by the statistical analysis of errors propagation (Blasetti, 1994). 3. Modeling 3.1. Four-Lump Model Equations. A four-lump model was adopted to represent the cracking of gas oil into gasoline, light gases, and coke. According to this, gasoline may react to produce light gases and coke at different rates. While catalytic cracking of gas oil was represented by a pseudo-second-order reaction rate, the gasoline lump was represented by a pseudo-first-order reaction rate:
(y1Ff)2 -r1 ) (k1,2 + k1,3 + k1,4) φ MW1
(1)
gasoline lump 1 φ (2) r2 ) [k1,2(y1Ff)2 - k2,4(y2Ff) - k2,3(y2Ff)] MW2 light gases 1 φ r3 ) [k1,3(y1Ff)2 + k2,3(y2Ff)] MW3
(3)
1 φ r4 ) [k1,4(y1Ff)2 + k2,4(y2Ff)] MW4
(4)
coke
with the activity decay function (Froment and Bischoff, 1961, 1962) defined as
φ ) e-kdCc
(5)
3.2. Mass and Energy Conservation Equations. Continuity equations for the risers of the Multicrackex unit (small diameter/length ratio) were represented as
dyi Fp(1 - )AMWi ) ri dz Ff
(6)
dCc Fp(1 - )AFf ) rC dz Fs
(7)
Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 3225 Table 2. Summary of Operating Conditions and Experimental Results
run
104 × total feed rate, kg/sa
C/O, kgcat/ kggasoil
at 0.076 m
31 32 53 17 21 20 23 15 47 16 36 29 24 19 51 44 43 42 33 37 52 49 50 40 48 38 46
4.2 4.1 4.0 5.7 7.1 7.1 5.5 5.7 5.1 7.3 4.2 4.2 5.5 6.4 7.1 4.7 4.6 4.5 4.0 7.3 7.1 5.4 5.2 7.1 5.0 7.1 5.0
9.50 6.60 5.60 6.70 8.40 13.50 4.40 7.60 4.20 3.40 4.80 5.50 5.20 11.30 1.20 10.10 5.40 6.70 1.60 5.90 6.74 11.00 11.80 4.90 2.00 7.20 6.40
778.8 804.0 828.4 771.2 700.8 708.3 655.8 708.1 720.5 755.2 780.8 752.7 750.9 676.4 631.3 683.5 673.5 684.3 821.9 651.5 694.4 723.3 722.1 609.7 622.3 677.8 655.0
a
riser temp profile, K at at at 0.483 m 0.889 m 1.295 m 896.1 907.2 878.2 880.2 782.6 784.7 797.5 830.3 838.7 894.8 865.1 912.6 840.0 768.0 781.1 782.6 815.1 782.6 854.3 835.9 810.5 811.1 799.5 780.9 859.1 839.4 840.0
850.8 865.9 858.1 852.9 769.6 763.4 847.3 810.1 803.7 865.5 840.9 870.9 815.5 746.0 742.6 743.5 782.1 743.7 845.0 779.1 771.4 779.8 768.4 731.5 820.3 786.6 786.2
941.8 943.4 878.9 910.1 810.2 806.2 814.7 862.6 850.3 918.1 891.5 934.7 868.1 792.3 815.8 824.9 846.6 824.7 858.6 898.5 853.5 848.7 842.1 841.0 868.1 896.0 908.1
at 3.022 m
gasoline yield, wt %
light gases yield, wt %
coke yield, wt %
convrsn, wt %
783.8 781.5 756.7 785.2 742.1 763.2 702.6 757.7 710.5 872.5 737.6 724.0 783.6 757.0 669.4 702.4 719.0 702.2 725.8 770.9 771.9 727.6 728.7 740.2 683.7 768.1 731.1
22.65 30.97 29.78 22.71 24.36 30.92 23.83 22.16 26.86 12.69 24.69 31.13 25.68 24.43 4.30 33.85 21.34 25.84 22.88 16.21 18.83 40.18 35.64 17.64 11.31 17.67 22.37
30.59 28.26 23.54 28.23 6.23 7.70 13.10 6.75 9.12 16.41 25.30 21.83 20.81 10.31 1.49 8.49 7.59 10.27 14.74 13.09 5.64 14.19 12.20 3.80 7.35 10.98 14.46
10.34 10.26 6.48 7.80 5.85 8.92 4.80 6.08 5.51 3.32 6.77 7.31 4.38 8.90 1.55 8.87 5.91 8.02 3.02 5.36 5.20 8.67 9.22 5.12 3.77 6.85 6.99
63.58 69.49 59.81 58.74 36.43 47.53 41.73 34.98 41.49 32.42 56.75 60.26 50.88 43.64 7.35 51.21 34.83 44.14 40.64 34.67 29.67 63.04 57.07 26.56 22.43 35.51 43.82
Gas oil plus steam and nitrogen.
Furthermore, the energy balance equation for the riser operated in heat transfer conditions with the regenerator is as follows:
∆HrFf dy1 + πDU(TReg - TRis) dTRis MW0 dz ) dz FfCpf + FsCps
(8)
For the Multicrackex, eq 8 cannot be solved unless the overall heat-transfer coefficient between the riser and regenerator is known. Therefore, the continuity equations were decoupled from the enthalpy balance by using the experimental temperature profile (Table 2). 3.3. Reparameterization of Arrhenius Expressions. Assuming an Arrhenius-type dependence of the kinetic parameters with the temperature, the parameters were expressed as
ki, j ) Ai, je-Ei,j/RT
(9)
The kinetic parameters obtained from eq 9 may show a mutual adverse effect of one parameter estimate (parameter correlation). Centering of some variables may often be helpful to reduce parameter interaction (Draper and Smith, 1981). Agarwal and Brisk (1985) showed that this reparameterization reduces the correlation between preexponetial factors and activation energies. Therefore, ki, j constants were reparameterized by centering the data at T* ) 793 K:
[ (
ki, j ) Ai, j exp -
)]
Ei, j 1 1 R T T* (i ) 1, 2, ..., np; j ) 1, 2, ..., nr) (10)
Equation 10 requires the knowledge of the temperature profile inside the riser. To ease the solution, the
Table 3. Reaction Rate Constants and Activation Energiesa i, j
Ai, j, 1/s
Ei, j, kcal/mol
ki, jb
1,2 1,3 1,4 2,3 2,4 D
0.319 × 106 0.501 × 108 0.110 × 104 0.1299 × 1016 0.1422 × 107
19208.33(( 4.5%) 28857.85(( 3.8) 13176.78(( 7.5) 59414.46(( 9.8%) 25261.9(( 7.2%)
1.626((3.4%) 0.559(( 4.9%) 0.257(( 3.7%) 0.054(( 24.9%) 0.155(( 9.1%) 406.4(( 2.0%)
a i, j represents paths between different lumps of the four-lump model. 1 ) gas oil, 2 ) gasoline, 3 ) light gases, 4 ) coke, D ) for the deactivation constant. b k1,2, k1,3, and k1,4 are expressed in m6/(kgcatkmol s). k2,3 and k2,4 are expressed in m3/(kgcat s). kd is expressed in kgcat/kgcoke at 793 K.
measured temperature profile was superimposed to the mass balance equations. 4. Determination of Kinetic Parameters 4.1. Objective Function. Model-dependent variables should have a constant error variance, and the errors should be uncorrelated and normally distributed. Thus, various parameters in eq 10 were adjusted using a weighted least-squares algorithm for nonlinear parameters (Marquardt, 1963). Evaluation of the kinetic constants required integration of eqs 6 and 7. With this end, a fourth order Runge-Kutta method of fixed interval size was employed, minimizing the following objective function: NYobs
min S2(ki,Ei) ) min [
wiY(Yexp - Ycal)2 + ∑ i)1
NCobs
∑ i)1
NGobs
wiG(Gexp - Gcal)2 +
wiC(Cexp - Ccal)2] ∑ i)1
(11)
with “exp” and “cal” representing the experimental and calculated values and wi representing the weighting factors.
3226 Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 Table 4. Lack of Fit Test for the Four-Lump Model (Gas Oil SF-135 (CANMET), Catalyst Octaboost 6XX Series (Akzo) (Blasetti, 1994)) source
deg of freedom
sum of squares (SS)
mean square (MS)
F ratio at 0.95
residuals (RE) pure error (PE) lack of fit (LOF)
n - p (70) ne ) nre - m (9) n - p - ne (61)
3.9529 0.6095 RE - PE ) 3.3433
0.056 47 0.067 7 0.05481
F(61,9) ) 2.79 LOF/PE ) 0.81 not significant
4.2. Statistical Analysis of Parameter Estimates and Model. A total of 11 parameters (10 kinetic constants and 1 deactivation constant) were simultaneously adjusted, and the precision of these parameters was evaluated. The values of the kinetic constants and energies of activation obtained, 95% confidence limits (nonlinear hypothesis), are presented in Table 3. Given the low parameter correlation coefficients (refer to supporting information), it can be argued that the kinetic constants were precisely estimated. These results are particularly relevant for the large number of parameters adjusted. 4.3. Lack of Fit (LOF) Test and Residuals. Experimental errors for a nonlinear model cannot be exactly determined but can be approximated. Complications, such as independent variable deviations from fixed settings, made it difficult to obtain “true” experimental repeats. Thus, to overcome this limitation, ranges of operating conditions (Table 1) helped to identify a series of repeat runs (“quasi-repeats”). Quasirepeats are also useful to approximate the pure error sum of squares (Draper and Smith, 1981). The sum of squares of residuals can be evaluated from the variance of residuals. This sum of squares contains the error in the experimental data or pure error (PE) and the lack of fit (LOF) of the model used. The lack of fit test presented in Table 4 shows that the MS(LOF)/ MS(PE) ratio was greater than the F-test distribution for 69 and 9 degrees of freedom F(69,9). This means that the MS(LOF)/MS(PE) ratio for the model is not significant. Therefore, it can be concluded that the model is adequate. Regarding model residuals, autocorrelation and partial autocorrelation functions were used to detect the residual trends. It was shown (refer to supporting information) that autocorrelation and partial autocorrelation functions cut off to zero with spikes inside the 95% confidence limit bands. Thus, by analogy, residuals were found to behave as white noise, and it can be concluded that the model represents the experimental data. 5. Discussion of Results Model predictions were compared to the experimental data under the conditions described in Table 2. There was good agreement between the experimental and calculated yield values (refer to supporting information). Typically, gas oil conversion, gasoline, light gases, and coke predictions were inside a (15% to (20% error band with some scattering for light gases attributed to gasoline overcracking. Therefore, the four-lump model and the piston flow model can be safely used to represent and extrapolate the performance of the Multicrackex unit. Furthermore, by means of computer simulation, the performance of the riser with heat exchange (Multicrackex) was compared to the one of an adiabatic riser (no heat exchange allowed). For the adiabatic riser simulation, the four-lump kinetic model (eqs 6-8) and the set of kinetic constants and the thermodynamic
Table 5. Ranges and Equations for Thermodynamic Parameters Evaluation: Adiabatic Riser Simulation Using Equation 8 heat of cracking, ∆Hr [kcal/kmol] Cps [kcal/(kg K)] specific heat of the steam [kcal/(kg K)] specific heat of gas oil [kcal/(kg K)] specific heat of gasoline [kcal/(kg K)] specific heat of light gases [kcal/(kg K)] Cpf [kcal/(kg K)] vapor density [kg/m3]
47927 0.26 0.50-0.53 0.75-0.83 0.73-0.81 0.68-0.70 ∑yiCpi [P/(RT)][1/(∑yi/Mi)]
Figure 3. Prediction of the following parameters in the riser with heat exchange (Multicrackex) for run 50: (a) gas oil conversion, (b) gasoline, (c) light gases, (d) coke. Regenerator temperature ) 918 K, mixing temperature ) 722 K, C/O ) 11.80.
parameters reported, in Tables 3 and 5, respectively, were employed. A number of simulations of the Multicrackex unit and an adiabatic riser, Figures 3-6, illustrate typical trends. For the adiabatic riser, runs 50 and 31 in Figures 4 and 6, a progressive and consistent increase with residence time of the four lumps (gas oil converted, gasoline, light gases, and coke) was observed. It was also noticed in Figures 3 and 5 that Multicrackex simulation shows the presence of a maximum gasoline yield, with the magnitude of this maximum being related to the severity of the operating conditions. There were also in the Multicrackex unit simulation oscillations in the gas oil conversion, gasoline, light gases, and coke curves. These trends were the result of temperature fluctuations inside the riser with heat exchange (Table 2). These temperature changes were qualitatively consistent throughout the entire experimental program and can be summarized as follows: (a) There is first, close to the riser entry between the 0.075- and 0.483-m lengths, temperature increases resulting from the dominant influence of heat transfer from the dense fluidized bed to the catalyst suspension flowing in the riser tubes.
Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 3227
Figure 4. Predictions of the following parameters in the adiabatic riser: (a) gas oil conversion, (b) gasoline, (c) light gases, (d) coke, (e) riser temperature. Mixing temperature ) 722.0 K, C/O ) 11.80.
Figure 5. Prediction of the following parameters in the riser with heat exchange (Multicrackex) for run 31: (a) gas oil conversion, (b) gasoline, (c) light gases, (d) coke. Regenerator temperature ) 970 K, mixing temperature ) 778.8 K, C/O ) 9.50.
(b) Following this initial temperature increase, an important temperature drop was observed. This drop was attributed to cracking endothermicity and cracking reactions, significantly progressing in the 0.4830.889-m riser length. (c) Moreover, between the 0.889- and 1.295-m riser lengths, the temperatures rose again. At these conditions, catalytic cracking endothermal contribution and moderate and heat fluxes from the dense-phase regenerator become more dominant. (d) Finally, at the riser exit (3.022 m), lower temperatures were systematically recorded. This temperature drop was assigned to the following factors: (a) an increased heat dissipation in the upper section of the unit; (b) heat fluxes from the regenerator freeboard region being significantly reduced. Regarding the adiabatic riser and Multicrackex unit simulations, both gas oil conversions and lump selectivities are considerably different. For instance, for the set
Figure 6. Predictions of the following parameters in the adiabatic riser: (a) gas oil conversion, (b) gasoline, (c) light gases, (d) coke, (e) riser temperature. Mixing temperature ) 752.7 K, C/O ) 5.60.
of conditions of run 50 with TReg ) 923 K and C/O ) 11.8 (Figure 4), simulation results give 44% and 55% outlet gas oil conversion for the adiabatic riser and the Multicrackex unit, respectively. As well, run 50, involving a mixing temperature of 722 K, yields along the adiabatic riser a significant temperature drop (∆TRis ) 16.5 K). Although the final gasoline yields for run 50 (Figures 3 and 4), for the adiabatic riser and for the Multicrackex unit, are much alike, axial gasoline profiles showed quite different trends. Furthermore, model predictions also demonstrate that higher fractions of light gases should be expected in a riser unit with heat exchange. Furthermore, when the mixing temperature was increased up to 778 K for run 31 (TReg ) 990 K, C/O ) 9.5), the overall gas oil conversion at the outlet of the adiabatic riser and at the outlet of the Multicrackex unit became relatively similar, 62% and 57%, respectively. Moreover, a comparison of the gasoline and light gases selectivities in the riser with heat exchange (Figure 5) demonstrates that these fractions are very sensitive to changes in residence time. Thus, to obtain similar gasoline yields in the riser with heat exchange and in the adiabatic riser, residence times in the Multicrackex unit should be kept below 1 s. Otherwise, the formation of light gases and coke in the riser with heat exchange become too dominant, reducing correspondingly the amount of gasoline fractions. Reviewing various simulation results for the Multicrackex unit (additional examples in the supporting information), it can be observed that the residence times required for maximum gasoline yields shift toward smaller residence times, while the average riser temperature is increased. This demonstrates that the maximum gasoline yields are affected by the reactor temperature and that between 70 and 95% of this maximum can, at the higher temperatures, be achieved at residence times close to 500 ms. These results are consistent with recent developments with novel downflow reactors, such as the QC (Quick Contact) reaction system (Gartside, 1989). It is claimed that the contact times in the QC unit, from the injection point to the gas-solid separation and quenching point, are on the order of 200 ms. Bartholic (1989) also
3228 Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997
proposed a horizontal contactor-reactor, claiming operation with very active catalyst and contact times as short as 100 ms. Although the units just mentioned are basically operated in the downflow mode, the performance of the Multicrackex at similar levels of contact times demonstrates that selectivity of the cracking reactions can be directed to the production of higher gasoline or light gases as desired by the refining operation. 6. Conclusions The results of this study show that a riser with heat exchange, Multicrackex, introduces advantages over conventional adiabatic risers in terms of yielding increased selectivity toward specific lumps. This is achieved when operating conditions and unit geometry are properly selected. As well, unit testing with a planned experimental program is important and provides precise kinetic parameters with acceptable confidence limits and low interaction. Therefore, it is expected that predictions in the Multicrackex from the application of these parameters are accurate. Supporting Information Available: Tables and figures providing additional information regarding gas oil characteristics, parameter estimation, and modeling results (10 pages). Ordering information is given in any current masthead page. Nomenclature A ) Riser cross-section area [m2] Ai, j ) i, jth preexponential factor [1/s] C ) concentration of any component [kmol/m3] Cc ) coke concentration [kgcoke/kgcat] Cexp ) experimental coke yield Ccal ) calculated coke yield Cps ) catalyst specific heat [kcal/(kg K)] Cpf ) specific heat of gases inside the riser [kcal/(kg K)] D ) Riser diameter [m] Ei, j ) i, jth energy of activation [kcal/kmol] Ff ) mass flow rate of gases in the riser [kg/s] Fs ) mass flow rate of catalyst in the riser [kg/s] Gexp ) experimental light gases yield Gcal ) calculated light gases yield kd ) deactivation constant [kgcat/kgcoke] ki, j ) i, jth reaction rate constant k1,2 ) gasoline formation rate constant in the four-lump model [m6/(kgcat kg s)] k1,3 ) light gases formation rate constant in the four-lump model [m6/(kgcat kg s)] k1,4 ) coke formation rate constant in the four-lump model [m6/(kgcat kg s)] k2,3 ) gasoline cracking to light gases rate constant in the four-lump model [m3/kgcat s] k2,4 ) gasoline cracking to coke rate constant in the fourlump model [m3/(kgcat s)] m ) number of repeated groups MS ) mean square MWi ) molecular weight of component i in gas phase for the four-lump model: i ) 1, gas oil; i ) 2, gasoline; i ) 3, light gases; i ) 4, coke [kg/kmol] n ) number of data points ner ) number of data points in repeat groups np ) number of parameters nr ) number of reactions NYobs ) total number of gasoline yield observations NCobs ) total number of coke yield observations NGobs ) total number of light gases yield observations
p ) number of parameters to estimate P ) pressure [atm] R ) universal gas constant [atm m3/(kmol K)] r1 ) rate of reaction of gas oil in the four-lump model [kmol/ (kgcat s)] r2 ) rate of reaction of gasoline in the four-lump model [kmol/(kgcat s)] r3 ) rate of reaction of light gases in the four-lump model [kmol/(kgcat s)] r4 ) rate of reaction of coke in the four-lump model [kmol/ (kgcat s)] S2 ) sum of squares T ) temperature [K] T* ) reference temperature (793 K) TRis ) riser temperature [K] TReg ) regenerator temperature [K] U ) global heat-transfer coefficient [W/(m2 K)] wiY ) gasoline yield weighting factors wiG ) light gases yield weighting factors wiC ) coke yield weighting factors yi ) mass fraction for the ith component: i ) 1, gas oil; i ) 2, gasoline; i ) 3, light gases; i ) 4, coke Yexp ) experimental gasoline yield. Ycal ) calculated gasoline yield z ) axial position in the reactor [m] Greek Symbols RD ) catalyst deactivation constant ∆Hr ) heat of cracking [kcal/kmol] ∆T ) temperature drop along the adiabatic riser [K] ) void fraction along the reactor φ ) activity decay function based on coke-on-catalyst µf ) viscosity of the gas mixture inside the riser [cP] Ff ) density of the fluid ) P/(RT) [1/(∑yi/MWi)] [kg/m3] Fp ) density of particle [kg/m3] Subscripts cat ) catalyst D ) deactivation i ) ith component obs ) experimental observations
Literature Cited Agarwal, A. K.; Brisk, M. L. Sequential Experimental Design for Precise Parameter Estimation: 1. Use of Reparameterization. Ind. Eng. Chem. Process Des. Dev. 1985, 24, 203. Avidan, A.; Chou, T. S. Fluid Catalytic Cracking Regeneration with Spent Catalyst Separator. European Patent Application No. 309244, 1989. Barnes, P. H. Apparatus and Process for Carrying out a Chemical Reaction in a Fluidized Bed. U.K. Patent No. 2212737, 1989. Bartholic, D. Ultra-Short Contact Time Fluidized Catalytic Cracking Process, European Patent Application No. 315179, 1989. Blasetti, A. P. Multitubular Reactor Exchanger for FCC: Design and Kinetic Modelling. Ph.D. Thesis, The University of Western Ontario, London, Ontario, Canada, 1994. Blasetti, A. P.; Ng, S.; de Lasa, H. I. In Catalytic Cracking of Gas Oil in a Novel FCC Pilot Plant Unit with Heat Exchange: Reactor Performance. Proc. Fourth Int. Conf. Circulating Fluidized Beds, Pennsylvania; Avidan, A., Ed.; AIChE: New York, 1993; p 458. Draper, N.; Smith, H. Applied Regression Analysis, 2nd ed.; John Wiley and Sons: New York, 1981. Farnsworth, C. Methods and Apparatus for Catalytically Converting Fractions of Crude Oil Boiling Above Gasoline. U.S. Patent 4786400, 1988. Froment, G. F.; Bischoff, K. B. Non-steady State Behaviour of Fixed Bed Catalytic Reactors due to Catalyst Fouling. Chem. Eng. Sci. 1961, 16, 189. Froment, G. F.; Bischoff, K. B. Kinetic Data and Product Distribution from Fixed Bed Catalytic Reactors Subject to Catalyst Fouling. Chem. Eng. Sci. 1962, 17, 105.
Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 3229 Gartside, R. J. QCsa new Reaction System, in Fluidization VI, Proc. Int. Conf. on Fluidization; Grace, J. R., Shemilt, L., Bergougnou, M. A., Eds.; Engineering Foundation: New York, 1989; p 25. Harandi, M.; Owen, H. Conversion of Alkanes to Alkylenes in an External Catalyst Cooler for the Regenerator of an FCC Unit. U,S. Patent 4840928, 1989. Herbst, J.; Owen H.; Shipper, P. Multiple Riser Fluidized Catalytic Cracking Process Utilizing Hydrogen and Carbon-Hydrogen Contributing Fragments. U.S. Patent 4717466, 1988. Marquardt, D. W. An algorithm for least squares estimation of nonlinear parameters. J. Soc. Ind. Appl. Math. 1963, 11, 431.
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Received for review November 27, 1995 Revised manuscript received February 10, 1997 Accepted March 26, 1997X IE950704V
X Abstract published in Advance ACS Abstracts, June 15, 1997.
