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A Strategy for Kinetic Parameter Estimation in the Fluid Catalytic

Cracking Process

J orge Ancheyta-J uarez,*,, Felipe Lopez-Isunza, Enrique Aguilar-Rodrguez, andJ uan C. Moreno-Mayorga

In st ituto M exicano del Petro leo, Eje Central La zaro Ca rdenas 152, Me xico D. F . 07730, M exico,I n s t i t u t o Pol i t e cn ic o N a cio n a l , ESI Q I E, M e xico D. F. , Mexico, and Universidad Auto nomaM et r o p ol i t a n a I z t a p a la p a, M e xico D. F . , Mexico

A strategy is proposed to estimate lumped kinetic constants in fluid catalytic cracking (FCC)reactions. This method decreases the number of simultaneously estima ted para meters. The3-, 4-, and a new 5-lump kinetic models and experimental data obtained at 480, 500, and 520 Cin a m icro activi ty r e actor are u sed to i l lustra te t h e p roced u re. Activat ion e n erg ies for e achinvolved reaction a re a lso reported.

Introduction

The fluid catalytic cracking (FCC) process is the heartof a modern refinery oriented towa rd ma ximum gasolineproduction. Within the entire refinery process, thisp roce ss of f ers t h e g rea t e s t p ot e n t ia l f or in cre a s in g

profitability; even a small improvement giving highergasoline yields can result in a substantial economic gain.Thus, the economic incentive for a better understandingof the FC C unit is immense (Krishna an d P ar kin, 1985).

Many complex react ions occur during the FCC pro-ce ss , bu t t h e o n es of p rima ry in t ere s t a re t h o s e t h a tcrack large molecules into smaller ones and thus reducetheir boiling point t o the more useful ran ge of ga soline,light cycle oil, and ga seous products. The descriptionof comp le x mix t u res by lu mpin g la rg e n u mbers ofchemical compounds into smaller numbers of pseudocom-p on e n t s h a s bee n w idely u s e d in in du s t ry t o p rov idet ra c t a ble a p p rox ima t ion s t o t h e s t oich iome t ry a n dkinetics of such mixtures (Kra mbeck, 1991).

The number of lumps of the proposed m odels for

cata lytic cra cking reactions ha s been increased t o obta ina m ore deta iled prediction of product distr ibution. Thefirst kinetic m odel (3-lump), developed by Weekman(1968), lumps reactant and all products into three majorgroups: unconverted gas oil, gasoline, and light ga s pluscoke. Yen et a l. (1987) a nd L ee et a l. (1989) present eda 4-lump kinetic model which is similar to the 3-lumpmodel of Weekman, t he ma in difference being tha t cokeis independently considered as one lump, the otherlumps being feed, gasoline, and C 1-C 4 g a s . Co rel la e ta l. (1991) developed a 5-lump kinet ic model wh ich ta kesin t o a c cou n t t h e h e a v y f ra c t ion . M a y a a n d L op e z-Isunza (1993) modified t his model to incorpora te thecracking of ga soline a nd ga s to coke. Another 5-lump

model w as used by L ar occa et al . (1990) where ga s oilwa s s p l i t in t o p a ra f f in s , n a p h t h e n e s , a n d a ro ma t ic s .T h is mo de l is s imila r t o t h a t s t u die d by Co x s o n a n dBischoff (1987) which is essentially the 10-lump modelgrouped int o six pseudocomponents.

A 6-lump kinetic model (resid, VGO/HC O, LCO,gasoline, gas, and coke) was used by Takatsuka et al .(1987, previously publish ed in Sekiyu Gakkaishi, 1984,22, 533-540) to predict th e ca ta lytic cra cking of residual

oil. This model wa s suggested by C orella et a l. (1988,1989) to be of bett er use in t he cat a lytic cracking of gasoil ; although they presented a st rat egy to calculate thekinetic param eters, the values of these para meters andthe a pplicat ion of the model ha ve not been determ ined.

Oliveira and Biscaia (1989) proposed a 4-lump model

to describe the catalytic cracking of gasoline (gasoline,ga s1, g a s2, and coke), and they incorporated this modelin t o a g a s oi l-ra n g e p a ra f f in ic comp ou n ds cra c k in gmodel (6-lump kinetic model).

The 10-lump model developed by J acob et al. (1976)a chieved kinetic consta nt independency from composi-tion by lumping gas oil component types into light andheavy fra ct ions (para ffins, naphthenes, aromatic rings,a n d a ro ma t ic s u bs t i t u en t g rou p s). H o we ve r , i t wa sshown by Coxson a nd Bischoff (1987) that there w erevirtually no differences between the 6-lump and 10-lump kinetic models.

J ohn and Wociechowsky (1975) a nd Corma et al .(1984) proposed react ion schemes for the cata lyt iccracking of gas oil in which the gas composit ion was

considered in detail.All t he a forementioned models ha ve been st udied

extensively. However, the functions derived from rea c-t ion kinetics of those models with a large number oflumps ar e not a pplicable for the evaluation of routineca t a ly st s cre en in g beca u s e of t h e s ma ll n u mber ofobservations available compared with the number ofestima ted pa ra meters (Wallensein a nd Alkemade, 1996).

In the present work we propose a strategy for est i-ma t in g k in e t ic c on s t a n t s in F CC re a ct ion s wh ich de -cre a s es t h e n u mber of s imult a n e ou s ly e s t ima t e d p a -ra meters. The method is il lustrat ed using the 3-, 4-,and a new 5-lump kinetic models consecutively.

Kinetic ModelsThe earliest kinetic model developed by Weekman

(1968) involves parallel cracking of gas oil to gasolinea n d g a s p lu s c o k e , wi t h c o n s e c u t iv e c ra c k in g o f t h egasoline to gas plus coke (Figure 1).

F o r g a s o i l (y1) cra c k in g , t h e r a t e is a s s u med t o besecond order

wh e re

* Author to whom correspondence should be addressed.F a x : (+52-5) 368-9371.

Ins titu to Mexican o del P etroleo. Ins titu to P olitecnico Na ciona l. Un iversidad Autonoma Metropolitan a Izta palapa .

dy1

d t ) -k0y1

2 (1)

k0 ) k1 + k3 (2)

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S0888-5885(97)00271-6 CCC : $14.00 1997 American C hemical Society

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estimat ed with the previous model, and only three (k2,1,1or k2,1,2, k3,1,1or k3,1,2a n d k4) are unknown.

Advantages and Limitations. Th e s e q u en t ia lmethod proposed in this paper decreases the numberof parameters est imated simultaneously (Table 1) inorder t o est imate kinetic par am eters of gas oil cat alyt iccracking models. The resulting decrease in t he numberof simultaneously est imat ed para meters ma kes it m orel ik el y t h a t on ly on e s et of p a r a m et e rs e xi st s t h a t

sa tisfies th e objective function (sum of squa re errors ofpredicted and experimental yields).

D u e t o t h e h ig h n u mbe r o f k in e t ic p a ra me t e rs in -volved in the FC C reactions, the sequential method isvery convenient because the probability of uniquenessof solution is enhanced. I t is importa nt to note that n oconvergence problems w ere fa ced d uring the regressiona n a ly s is .

The study of ca ta lytic cracking reactions ha s followedthe lumping methodology. Some of the products a relu mpe d a n d t re a t e d k ine t ica l ly a s on e s p e cies wit hvar ious cracking reaction orders. The weakn ess of thesemodels is that the kinetic constants are a function offeedstock properties; however, th ese models ha ve beenwidely used in the most a dvanced riser models. Theimmen s e comp le xit y of g a s oi l ma k e s i t e xt re melydiff icu l t t o ch a ra ct e rize a n d de scribe k in et ics on amolecular level. Therefore, the lumping of many simi-larly behaving compounds into groups is necessary.

The strategy proposed in this paper could be used toest imate para meters in kinetic models with more thanfive lumps. However, in order to improve estima tions,mo re e x p e rime n t s wo u ld be re q u ire d; t h e la rg e r t h es a mp le s ize c o mp a re d wit h t h e n u mbe r o f u n k n o wnpara meters, the better a re the est imations in the sensethat the errors will be smaller.

Results and Discussion

I n orde r t o a p ply t h e s t ra t e g y f or t h e e s t ima t ion ofkinetic consta nts, experiments were performed in afixed-bed reactor described by ASTM D 3907-92 (mi-croa c t ivi t y t e s t ). Th e f ee dst o ck a n d ca t a ly s t we revacuum ga s oil an d a n equilibrium cat alyst, both comingfrom a n industrial cata lyt ic cracking unit . The aim ofthe experiments w as to find out the product distr ibutiona s a function of the w eight-hourly spa ce velocity (WHS V).

The range of values of the WHSV was 5-50 h-1, whilethe cata lyst-to-oil rat io (C/O) wa s kept consta nt at 5.Experiments w ere car ried out a t r eactor temperat uresof 480, 500, and 520 C. The products mea sured in ea chexperiments w ere dry gas (C 2 an d lighter), LP G (com-bined C 3C 4) , gasoline, coke, and unconverted gas oil(light cycle plus decanted oils).

Table 2 shows a n exam ple of th e estima tion of kineticparameters using the experimental data obtained in theMATr eactor at 500 C. The same stra tegy wa s followedfor para meter estimation at 480 and 520 C. The resultsobtained for the 4-lump model considering the origina lestimation (six par am eters instead of two) ar e presentedin t h e s a me t a ble. I t c a n be obs erv ed t h a t t h e k in e t icconstants are almost identically predicted using bothme t h ods (O E : or ig in a l e s t ima t ion a n d SS : s e q ue n t ia lstrategy); however, the sequential strategy decreasesthe number of simultaneously estimated parameters, ascan be seen in Table 1.

Var ious a uthors ha ve found t hat the kinetic consta ntfor the cra cking of ga soline to gas plus coke is very sma ll

compared with other constants (see data compiled byForissier and B ernar d, 1989). In this w ork, it wa s foundtha t the kinetic constan t w hich really has a sma ll valuecompared with the others is only the gasoline-to-cokecracking consta nt (k2,2 in 4- a nd 5-lump m odels). Thisresult was also found by Oilveira and Biscaia (1989)wh en they used a 4-lump model to describe the ga solinecracking; moreover, the 5-lump model proposed byCorella et a l. (1991) does not consider t he coke forma tionby gasoline cracking.

Some results of product selectivities given by the ki/k0ra tio are presented in Ta ble 3. The selectivity va luesca lc ula t e d in t h is p a p e r s h o w g ood a g re e men t wit hl it e ra t u r e i n f or m a t i on . L P G a n d d r y g a s p r es en t edselectivit ies a round 0.656 and 0.344 (k2,1,1/ k2a nd k2,1,2/k2ra tios), respectively, w ith respect t o overa ll ga solinecracking.

Activation energies for each involved reaction calcu-lated in the range of 480-520 C are shown in Table 4.It can be observed tha t not a ll activation energies evalu-at ed in this w ork are in the r ange of those reported inthe literature. These differences are due ma inly to thetype of cata lyst, feedstock, reactor, a nd operating condi-tions used in the experiments. Informa tion is not ava il-able in the literat ure for act ivat ion energies of the fol-lowing rea ctions: gas oil to LP G , gas oil to dry gas, ga so-l in e t o L P G , g a s o l in e t o dry g a s , a n d L P G t o dry g a s .

Figures 4 and 5 show a comparison of predicted a ndexperimental results for gas oil, gasoline, LPG, dry gas,

Table 2. Kinetic Parameters at 500 C

pa r a m et er r ea ct ion 3 lum ps 4 lum ps S S a 5 lum ps 4 lum ps OE a

k1 G O f G n e 0.1942 0.1942 0.1942 0.1947k2 G n e f ga s + coke 0.0093k2,1 G n e f ga s 0.0093 0.0089k2,1,1 G n e f L P G 0.0061k2,1,2 G n e f dr y ga s 0.0032k2,2 G n e f coke 2 10-8 2 10-8 1 10-8

k3 G O f ga s + coke 0.0488k3,1 G O f ga s 0.0348 0.0365k3,1,1 G O f L P G 0.0357k

3,1,2 G O f dr y ga s 0.0001

k3,2 G O f coke 0.0140 0.0140 0.0139k4 L P G fdr y ga s 0.0020kd 0.0875 0.0875 0.0875 0.0874

a SS, sequential s trategy; OE, original est imation.

Table 3. Product Selectivities

l i t er a t u r e d a t a

select ivit y t h is w or k va lue sour ce

k1/k0 0.799 0.78a Corella et a l. (1986)0.75a Kra emer and de Lasa (1988)

k3,1/k0 0.143 0.164b Lee et al. (1989)k3,2/k0 0.058 0.064b Lee et al. (1989)

a 500 C. b 482.2 C.

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an d coke yields using the 5-lump kinetic model. Otherresults with the 3-and 4-lump models are presented inF ig ure 6. Th e s t a n da rd e rrors o f t h e e s t ima t io n s f orall t he products w ere less tha n 2.5. The 5-lump model

can predict suitably the experimental results for therange of WHSV considered in this paper (5-50 h-1).

Conclusions

The proposed strategy for kinetic parameter estima-t io n in f lu id c a t a ly t ic c ra c k in g ( F CC) re a c t io n s wa sapplied successfully using experimental data obtainedin a microactivity r eactor. This method decreases thenumber of simultaneously est imated parameters, andconsequently the probability of uniqueness of solution

is enha nced.The experimental data were well represented by a

new 5-lump kinetic model using the previous kineticpara meters est ima ted with 3- and 4-lump models. Inaddit ion, it was found that the gasoline cracking reac-t ion can be neglected since the kinetic constant wasmany orders of magnitude less than the others.

The predict ion of LPG , dry gas, and coke separa telycan be used to design an d simulat e gas compressors inFCC units a nd to perform cata lyst deactivat ion studieswhen feedstock w ith h igh level of metals ar e used.

Nomenclature

kd ) deactivation constant (s-1)k1 ) k in e t ic c on s t a n t f or t h e r e a ct i on G O f G n e ( w t

fraction-1 s-1)k2 ) kinet ic cons t a nt for t he r ea ct ion Gn e f ga s + coke

(s-1)k2,1 )kinet ic cons t a nt for t he rea ct ion G ne fga s (s-1)k2,1,1 )kinet ic const a nt for t he rea ct ion G ne f L P G (s-1)k2,1,2 ) kinetic consta nt for th e reaction G ne fdry ga s (s-1)k2,2 )kinet ic cons t a nt for t he rea ct ion G ne fcoke (s-1)k3 ) kinet ic cons t a nt for t he rea ct ion GO f ga s + coke

(wt fraction-1 s-1)k3,1 ) k i ne t ic con s t a n t f or t h e r e a ct i on G O f g a s ( w t

fraction-1 s-1)k3,1,1 ) kinet ic cons t a nt for t he rea ct ion GO f L P G (w t

fraction-1 s-1)k3,1,2 ) kinetic constant for the reaction GO fdry ga s (w t

fraction-1 s-1)k3,2 ) kinet ic cons t a nt for t he rea ct ion GO f coke (wt

fraction-1 s-1)k4 ) kinetic constant for the reaction LPG f dry gas (s-1)k0 ) global gas oil cracking kinetic constan t (wt fra ction-1

s-1)t )t ime (s)tc ) catalyst residence time (s)y1 ) gas oil yield (wt fraction)y2 ) gasoline yield (wt fraction)y3 ) g a s +coke yield (wt fraction)y3 )ga s yield (w t fra ct ion)y3 ) L P G yield (w t fra ct ion)y4 ) coke yield (wt fraction)y5 ) dry ga s (w t fra ct ion)

Greek Symbols

) deactivation function

Acknowledgment

The aut hors t ha nk Inst ituto Mexican o del P etroleo(FIES-95-95-IV Project), CONACyT, and the BritishCouncil for their financial support.

Literature Cited

(1) Corella, J . ; Frances, E. Analysis of the riser reactor of a fluidcracking unit . Fluid Cat alyt ic Cra cking I I . ACS Sym p. Ser. 1991,452, 165-182.

Table 4. Activation Energies (kcal/mol)

kinetic model

pa r am et er r ea ct ion3

lumps4

lumps5

lumpsliterature

d a t a a

k1 G O f G n e 13.7 1 3.7 1 3.7 10-36k2 G n e f ga s + coke 15.7 15-29k2,1 G n e f ga s 15.7 13-15k2,1,1 G n e f L P G 17.5k2,1,2 G n e f dr y ga s 10.8k2,2 G n e f coke 15.9 15.9 18-27k3 G O f ga s + coke 11.1 9-18

k3,1 G O f ga s 12.6 17-21k3,1,1 G O f L P G 12.5k3,1,2 G O f dr y ga s 11.8k3,2 G O f coke 7.6 7.6 11-15k4 L P G fdr y ga s 9.5

a Taken from refs 3-5, 8, 9, 14, 15, 17, 21.

Figure 4. Experimental and predicted gas oil , gasoline, and LP Gyields. Reactor temperature: (]) 480 C , (O) 500 C, (+) 520 C.

Figure 5. Experimental and predicted dry gas and coke yields.Reactor temperature: (]) 480 C, (O) 500 C, (+) 520 C.

Figure 6. Experimental a nd predicted gases a nd ga ses plus cokeyields. Reactor temperature: (]) 480 C , (O) 500 C, (+) 520 C.

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(2) Corella, J . ; Fran ces, E. Modelling some revamps of the riserreactors of the FCCU s: La teral downstr eam quench flow injectionsand cross sectional area variation.AI ChE Symp. Ser. 1992,8(291),110-119.

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(5 ) Cor e lla , J . ; M or a le s , F . G . ; P r ov os t , M . ; Es p in os a , A. ;Serra no, J . The selective deactivat ion kinetic model applied to thekinetics of the catalyt ic cracking (FCC process). Proc. of the Int.Co n f . in Ad v . Ch e m. En g . Kanpur, India , 1989, J an 4-6, 192-210.

(6) Corma, A.; J uan, J . ; Ma rtos, J .; S oriano, J . M. 8 t h I n t e r .Cong. on Cat. Berlin, 1984, II, 293-304.

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(1 2) K r a m b e ck , F . J . An in d u st r ia l v iew p oin t on lu m pin g .Kin e t ic s a n d Th e r mo d y n a mic L u mp in g o f Mu lt ic o mp o n e n t Mix - tures; E lsevier Science P ublishers B .V.: Amsterdam , 1991; pp111-129.

(13) Krishna, A. S . ; Parkin, E. S . Modelling the Regeneratorin Commercial Fluid Catalyt ic Cracking Units . Chem. En g. Prog.1985, 31 (4), 57-62.

(1 4) L a r occ a , M . ; N g , S . ; d e L a s a , H . F a s t Ca t a ly t ic Cr a c kin gof Heavy G as Oils : Modelling Coke Deact ivat ion.Ind . Eng. Chem.Res. 1990, 29, 171-180.

(15) Lee, L. S . ; Chen, Y. W.; Huang, T. N.; Pan, W. Y. FourLump K inetic Model for F CC Pr ocess.Ca n . J . Ch em. E n g .1989,67, 615-619.

(16) Marq uardt , D. W. Solution of non-linear squa res est ima-t ion of non-linear parameters. J . So c . I n d . Ap p l. Ma t h . 1963, 2,431-441.

(17) Ma ya, Y. R. ; Lopez, I . F. Un esquema cinet ico par a elcraqueo cata l tico de gasoleos en un rea ctor de lecho tr a nsport a do.A v . I n g . Q u i m . 1993, 14, 39-43.

(18) Oliveira , L. L. ; Biscaia , E. C. Catalyt ic Cracking KineticModels . Parameter Est imation and Model Evaluat ion. I n d . E n g .Chem. Res. 1989, 2 8, 264-271.

(19) Takatsuka, T.; Sato, S . ; Morimoto, Y. ; Hashimoto, H. Areaction model for fluidized-bed catalytic cracking of residual oil.I n t . Ch em. E n g .1987, 27 (1), 107-116.

(20) Wallenstein, D.; Alkemade, U. Modelling of selectivity dataobtained from microact ivity test ing of FCC cat alyst . Ap p l . Ca t a l . ,A 1996, 137, 37-54.

(21) Weekman, V. M. A Model of Ca ta lytic Cra cking Conversionin Fixed, Moving and Fluid-Bed Reactors. I n d . En g . Ch em. Pr o d .Res. Dev. 1968, 7, 90-95.

(22) Yen, L. C. ; Wrench, R. E. ; Ong, A. S . React ion kineticcorrelat ions for predict ing coke yield in f luid cata lyt ic cracking.K a t a l i st i cs 8 t h A n n u a l F l u i d C a t C r a ck i n g S y m p . B u d a p e s t ,H u n g r a. J une 1987, 7:1-7:7.

Received for review April 10, 1997Revised man uscript received August 14, 1997

Accepted August 24, 1997X

IE970271R

X Abstra ct published inA dvanceACS Abstracts,October 15,1997.

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