Lumping and Modeling FCC Reactions

1.0Introduction

The kinetics modeling of catalytic cracking has been traditionally based on using a lumping strategy: chemical species with similar behaviors are grouped together forming a smaller number of pseudo species (Coxson and Bischoff, 1987). Commercial FCC feedstocks usually contain thousands of chemical species with a wide distribution of boiling temperatures. Even the cracking of gasoline range hydrocarbons can include a quite wide distribution of molecular weights, from C1 to C20. Thus, lumping of species is important to make the kinetic modeling a tractable exercise.

In general, there are two basic techniques in lumping the catalytic cracking of VGO. The first method is to lump molecules in different distillation cuts pseudo-species and to consider chemical reactions between these lumps. These lumps are usually the feedstock and the final cracking products, like gasoline, LCO, light gases, and coke. The second approach is to lump different products based on main chemical families such as paraffins, olefins, naphthenes, and aromatics. With this approach important reaction data such as the reaction type (cracking, hydrogen transfer, or condensation) and stoichiometry can be included. It is worth mentioning that the second approach can be used to describe the different reaction pathways (Pitault et al, 1994).

In this respect, the first lumping model proposed was the three lump model advanced by Weekman and Nace (1970). The three lumps was later modified, by Yen et al., (1987), proposing a more sound approach with four lumps where coke and gases were separated. A more complicated and detailed lump model (10-lumps) describing in more detail the feedstock was proposed by Jacob et al., (1976). The 10-lump model is of special importance to FCC model development since its rate constants should not depend, in particular, on the feedstock composition.

Regarding product distribution, gas composition was reported in detail by a model developed by John and Wojciechowski in 1975. Propylene, n-butane, and butene were considered both primary and secondary products. However, coke, methane, ethane, ethylene, and iso-butane were postulated as secondary products only. This model was modified later on by Corma et al (1984) by considering propane and isobutene as both primary and secondary products.

Takatuska et al (1987) used a six lumps model including the heavy feedstock (vacuum reside), the vacuum gas oil (VGO) and the heavy cyclic oil (HCO), the light cyclic oil (LCO), the gasoline, the light gases, and the coke.

In 1990 (Kraemer et al.,), proposed an eight lump model. The feedstock was separated into heavy and light fractions: a) heavy paraffins, heavy naphthenes and heavy aromatics with boiling point in the 343(C+ range and b) light paraffins, light naphthenes, and light aromatics with boiling points in the 220(C to 343(C range. It was assumed that the heavy oil lumps can crack into light oil lumps, gasoline, and light gases and coke. It was also considered that the light gas oil lump can form gasoline, light gases and coke. It was hypothesized that gasoline can crack, in turn, into light gases and coke. The more restricted number of kinetic parameters make this model more tractable.

There was during the 90s an attempt to develop a second generation of lumping models based on reaction mechanisms and elementary steps (Liguras and Allan, 1990). Froment and co-workers also proposed single event models involving a detailed description of VGO catalytic cracking (Vynckier and Froment, 1991; Feng et al., 1993). This model considered, between other factors a mechanism including carbenium ions. However, the second generation of FCC models had many drawbacks given the extensive computational calculations. Furthermore, several important reactions like hydrogen transfer and coke formation were not included and this caused major predication problems.

In 1994, Pitault at al., proposed a model where lumps were classified by chemical family (e.g. paraffins, olefins, naphthenes, and aromatics) and molecular weight or boiling range. This approach was applied to the light gases, gasoline, LCO and feedstock cuts. It has to be emphasized that this model has the flexibility of being able to include important reactions like coking and hydrogen transfer. Reaction order and stoichiometry for the different lumps reaction were defined and examined with experimental data.

2.0- The Three Lump Model

The three lump model consists of one a feedstock lump ( gas oil, VGO or any other heavy feed) and two product lumps: a) gasoline b) coke + light gases. The gasoline lump contains the fraction between C5 up to the hydrocarbons with a 220(C boiling temperature. The coke + light gases lump contains in addition to coke, C4 and lighter than C4 hydrocarbons. This model can be represented as follows:

The three lump model.

The reaction order assigned to the three lumps based on the crackabilities of different lump pseudospecies. Since the feedstock (VGO or gas oil) contains a mixture of several thousands compounds of widely different properties, it was suggested that a second order should be assigned to the cracking of VGO (Weekman and Nace; 1970). However, since gasoline contains a restricted range of molecular weight hydrocarbons (C5 to C12), it was argued that a first order should be given to the gasoline cracking (Weekman and Nace; 1970). This assignment of reaction orders is still recommended by many researchers (Corma and Martinez-Triguero, 1994; Sedran , 1994).

Based on these assumptions the following equations can be considered:

a-) gas oil cracking can be represented as;

b-) gasoline formation can be modeled as;

c-) light gases and coke can be represented as;

It can be stated that numerous experimental and analytical studies have been developed using the three lump model (Shah et al., 1977; Paraskos et al.,1976; Corella et al., 1986). In 1971, Nace et al., reviewed the three lump model for a large number of feeds and examined the influence of feed composition on the kinetic rate constants and on the deactivation of the FCC catalysts. These authors concluded (Table 2.1) that the overall VGO cracking rate constant is much larger than the gasoline cracking rate constant for different VGO composition. Nace et al., (1971) reported for instance, that increasing the ratio of paraffins to naphthenes led to a decrease in the rate of gasoline formation and to gasoline overcracking, and to increased catalyst deactivation. These authors also reported that, whereas the rate of reaction can vary by a factor of 4, in the range of composition studied, gasoline selectivity did not seem to vary substantially.

In 1978, Wojciechowski et al., carried out an experimental study on the cracking activity and the gasoline selectivity of two different catalysts in which one contained LaX and the other contained LaY zeolites. These authors carried out their work at different temperatures. They concluded that LaY catalyst had higher activity and better gasoline selectivity than LaX. By referring to their results, it can be inferred that the gasoline overcracking rate constant was negligible while compared to the VGO cracking rate constant.

Table 2.1.The three lump model rate constants for different VGO compositions. kT1, kT2, kT0, kT3 represent the gasoline formation rate constant, the coke and gases formation rate constant, the overall VGO cracking rate constant, and the gasoline overcracking rate constant respectively (Nace et al., 1971).

Kinetic rate constants at 900 _F (hr-1)

Charge StockkT0 kT1kT3 kT2/kT1kT3/kT1

P1231.826.31.830.830.06

P2232.726.21.090.800.03

P3334.028.01.860.820.05

N1139.233.51.540.850.04

N2234.229.42.350.860.07

N3236.231.02.020.850.06

PN33236.430.91.940.850.05

PA31324.721.02.870.850.12

PA32322.918.61.950.810.09

PA33322.117.61.480.800.07

PA331315.512.62.660.810.17

PA34322.117.81.780.810.08

PA37310.37.712.180.750.21

PA38321.116.61.660.790.08

AA45412.39.32.280.760.19

PC32319.315.01.150.780.06

In 1984, Corma et al., conducted an experimental work to investigate the kinetic of VGO cracking on RE-HY zeolite using a fixed bed microreactor. According to these results (Table 2.2), at 524(C, the ratio of the gasoline overcracking rate constant to the VGO cracking rate constant is very small (0.006).

In 1986 Corella et al., applied the three lump models to study the kinetics of VGO cracking in a FCC pilot plant unit. These authors were able to develop a kinetic model claiming that this model was able to simulate the commercial FCC units.

In 1988, Kramer and de Lasa studied the kinetics of the paraffinic VGO cracking under operating conditions similar to those found in commercial risers. On the basis of the three lump model and the assumption that the riser simulator operated as a batch reactor, they were able to develop a reliable model to predict the paraffinic VGO conversion. Reported kinetic constants at two different temperatures are shown in Table 2.3. In this study, the gasoline cracking rate constant was assumed to be zero and this was consistent with previous studies.

2.1-The Four Lump Model

In 1987, Yen et al. introduced the four lump model splitting the light gases + coke lump in two separate lumps: a) coke and b) light gases. These authors used a second order reaction for VGO cracking. The kinetic parameters were determined from riser pilot plant data and were correlated with feedstock characteristics, and operating conditions. This model is claimed to predict very effectively the coke yield for VGO cracking in FCC pilot plants and commercial units. Table 2.2:Calculated values for the kinetic constants of the triangular reaction scheme. kT0, kT1, kT2, kT3 represent the overall VGO cracking rate constant, the gasoline formation rate constant, the gas and coke formation rate constant and the gasoline overcracking rate constant respectively (Corma et al., 1984).

480 _C503 _C524 _C

kT0 (h-1) x 10-52.915.1411.07

kT1 (h-1) x 10-52.444.218.96

kT2 (h-1) x 10-50.470.932.11

kT3 (h-1) x 10-216.2130.7165.82

Table 2.3:Calculated values for the kinetic constants of the triangular reaction scheme. kT0, kT1, kT2, kT3 represent the overall VGO cracking rate constant, the gasoline formation rate constant, the gas and coke formation rate constant and the gasoline overcracking rate constant respectively (Kramer and de Lasa, 1988).

T, _CkT0kT1kT3kT2

5004.113.040.001.07

5505.033.120.001.91

*Units of kT0, kT1, and kT2 are 1/(g of oil-g of catalyst-s).

Unit of kT3 are 1/(g of catalyst-s).

In 1994 Gianetto et al. studied the effect of the crystal size of the Y-zeolite on gasoline composition. They used the Riser Simulator to carry out their experimental work. A four lump model was applied as follows:

where the rates of gasoline formation and gasoline consumption were described as,

a-) gas oil consumption rate

b-) gasoline formation rate

c-) light gases formation rate

d-) coke formation rate

EMBED Equation.3

These authors found that the zeolite catalysts with small crystals were moderately more active than those with large crystals. Moreover, they pointed out that the gasoline overcracking was negligible for both small crystal zeolites and large crystal zeolites, since the calculated constants were very small.

In 1994, Farag et al. studied the effect of the addition of metal traps in the FCC catalysts. Experimental runs were performed in a microcatalytic fixed bed reactor. It was concluded that the addition of the metal traps was beneficial for the gasoline yield and research octane number. The four lump model was used to evaluate the kinetics constants. The equations developed from the four lump model were also reliable to evaluate the adsorption constants for VGO, gasoline, and light gases. It was also reported that the values for the kinetic constants for the cracking of gasoline to coke and light gases were very close to zero.

More recently Ali and Rohani (1997) developed a simple dynamic model to describe the dynamic behavior of the FCC unit (riser-regenerators and their interactions). The four lump model was employed to simulate the cracking reactions. Their model was able to simulate the data of an industrial scale unit reasonably well.

Juarez et al., (1997) extended the four lump model to five lumps. These authors further divided the gases lump into two different lumps: a) dry gas, b) liquefied petroleum gas (LPG). Note that LPG can be formed either directly from gas oil or as a secondary product from gasoline overcracking. On the other hand, dry gas (H2, C1, C2) can be formed either directly from gas oil cracking or as a secondary product from gasoline and LPG cracking. The five lump model can be schamatically represented as:

The five lump model

2.2Catalyst Deactivation

Catalyst deactivation in FCC process can take place due to several factors. Catalyst pellets can lose its shape or mass due to attrition and high temperatures (sintering). Catalyst poisoning can also take place given the effect of impurities contained in the feedstock. Typical contaminants are hydrocarbons containing S, N, O, Ni and V (Larocca, 1988; Larocca et al., 1990; Farag, 1993).

However, under normal FCC conditions coke is the most important factor affecting catalyst activity. As catalytic reactions proceed coke deposits on the catalyst surface. Coke covers the catalyst active sites leading to catalyst activity decay.

In this respect, important modelling efforts have been addressed to model catalyst deactivation due to coke. These models are reviewed in the following section.

2.2.1-Catalyst activity decay functions

Two main approaches have been used, so far, to represent the effect of coking phenomena on catalyst decay. The first approach uses the catalyst coke content (Froment and Bischoff, 1961; 1962). The second approach relates catalyst deactivation to time-on-stream (TOS) (Wojciechowski, 1968;1974).

2.2.1.1-Decay model based on time-on-stream

The time-on-stream decay model (TOS) represents a first approach to catalyst deactivation. This approach assumes that the coking rate is independent of reactant composition, extent of conversion, and hydrocarbon space velocity (Yates.,1983).

In this respect, Weekman (1968) employed to describe catalyst deactivation, the following two simple relations;

a)- exponential decay law (= exp (-(t) (2.7.4.a)

b)- power decay law (= t-n (2.7.4.b)where t represents catalyst time-on-stream, ( and n are rate constants of the catalyst decay function.

Regarding TOS models, Szepe and Levenspiel (1971) showed that many deactivation functions could be derived by assuming the rate of catalyst decay as a function of the number of active sites. Thus, the rate of catalyst activity decay can be expressed as a function of the fraction of remaining active sites as follows;

-d( /dt =kd ( n (2.7.4.c)

-d( /dt =kd1 C2go ( (2.7.4.d)

where ( is the fraction of remaining active sites, t is the catalyst time-on-stream, kd and kd1 catalyst decay constants, n the order of catalyst activity decay and Cgo is the gas oil feedstock concentration.

Wojciechowski (1974) suggested a more detailed form of the power law by integrating eq (2.7.4.c) with ( =1 at t=0. This yields the following:

( = [1+ kdt(n-1)]-N (2.7.4.e)

It should be mentioned that this form of deactivation function has been widely used in the literature being able to represent both gas oil cracking (Campbell and Wojciechowski, 1971; John and Wojciechowski,1975) and cracking of model compounds (Corma and Wojciechowski.,1984, Abbot and Wojciechowski, 1987; Kennedy et al,1991).

Regarding the exponential form of the deactivation function ((=exp(-(t)) it has also been used frequently in the technical literature. Kraemer et al (1987,1990) employed this form to represent gas oil cracking in a CREC Riser Simulator. Liguras and Allen (1989) used this equation to describe the cracking of model compounds using an amorphous silica-alumina-zirconia catalyst. Ali and Rohani (1997) also used the exponential decay function in the case of a dynamic model for FCC units.

More recently, a modified exponential function, (=exp(-(tn) was considered. This empirical relation was used to represent activity decay for the cracking of 2-methylpentane on USY zeolite (Babitz et al., 1997). It was found that the 0.4 value was adequate for the n parameter. Hopkins et al (1996), used the same equation with n=0.5 and this for the modeling of catalytic activity decay while cracking hexane.

2.2.1.2- Decay model based on coke content

To provide, however, a more sound approach to catalyst decay, the catalyst deactivation function (() was related to the coke content Cc. With this end, several forms are proposed in the technical literature as follows (Froment and Bischoff , 1962 and 1979);

a) (= exp (-(Cc)

(2.7.4.f1)

b) (=1/(1+(Cc)

(2.7.4.f2)

c) (=1/(1+(Cc)2

(2.7.4.f3)

d) (=1-(Cc

(2.7.4.f4)

e) (=(1-(Cc)2

(2.7.4.f5)

where ( is a constant which can be found by fitting the experimental data.

Another alternative deactivation function based on coke content was proposed by Gross et al (1974). In this function the effect of coke content was expressed with a two parameter function, ( and n as follows;

(=1/(1+(Ccn) (2.7.4.g)

Acharya et al., (1989) investigated silica alumina catalyst deactivation for cumene cracking. It was hypothesized that the coking reaction takes place as a consecutive step to the main reaction. The modified deactivation function is based on the observation that after a very sharp initial activity decline there is a slow activity decay and finally a stablization on a steady activity level. The proposed expression is given as;

(m=(R+(1-(R)exp(-(Cc) (2.7.4.h)

where ( and (R represent a deactivation coefficient, and a residual activity level respectively. Note that various model parameters of eq(2.7.4.h) are obtained by nonlinear regression fitting of the experimental data.

Regarding further efforts on catalyst deactivation, as a function of coke content (Cc), Forissier and Bernard (1991) suggested an empirical relation taken into account site coverage, pore plugging, and diffusion limitations caused by pore plugging. They suggested a deactivation function with the following form;

(=(B+1)/(B+exp(ACc)) (2.7.4.i)

where Cc is the catalyst coke content expressed in wt%, A and B are two constants which are functions of feedstock composition, determined by the appropriate fitting of the experimental data.

In this respect, Forissier et al (1991) established a distinction between catalyst deactivation ((1) and coke formation ((2) relating these two functions as follows;

(2 = (1 (Cmc-Cc)/Cmc (2.7.4.j)

with Cmc representing the maximum coke fraction observed on the catalyst.

The use of (2 suggests that the coke concentration, Cc, can reach a limiting level Cmc at the early stages of the reaction. Then coke formation is halted and a residual activity is available for other cracking reactions (Pitault et al.,1994).

Corma et al., (1994) studied paraffins catalytic cracking. These authors suggested that the use of a TOS decay model is not consistent with a kinetic model in which the product olefins are strongly adsorbed on the catalyst. To account for this, the following model was suggested;

d(/dt = -kmd (m X (2.7.4.k)

where kmd and m are the decay model parameters and X is the conversion.

In this respect, this model assumed that there is a direct relationship between coke formation and catalyst deactivation. In fact, eq (2.7.4.k) can be derived from Froment and co-workers model as follows;

dCc/dt = r0c ( (2.7.4.l)

where (= exp (-(Cc), and r0c is the rate of coke formation. If coke formation reaction is assumed to be first order and m=2, equation (2.7.4.l) is obtained.

More recently, a mathematical expression of ( versus catalyst coke content (Cc) was suggested (Van Landeghem et al., 1996). This model can be expressed as;

d(/dCc = F( + E( (1-() (2.7.4.m)

where F is proportional to the remaining activity and E is proportional to the lost activity. Based on these assumptions the following deactivation function was postulated;

( = (E+F)/(E+F exp[(E+F)Cc]) (2.7.4.n)

where E and F values are adjustable parameters calculated for each feedstock.

2.3- Conclusions

In conclusion, while the mechanism of coke formation is not yet well understood, two types of models have been proposed in the technical literature for catalyst deactivation. One of these model is based on the time-on-stream and this represent a rather rudimentary approach to catalyst decay modeling. A second approach is to relate catalyst decay to coke content, being this a more sound mechanistic description of catalyst decay. ReferencesAcharya, D.R., Huges, R., and Li, K., Deactivation of Silica-Alumina Catalyst During the Cumene Cracking Reaction, Applied Catalysis A, 52, pp 115-129, (1989).

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Gross, B., Nace, D.M., and Voltz, S.E., Application of a Kinetic Model for Comparision of Catalytic Cracking in a Fixed Bed Microreactor and a Fluidized Dense Bed. Ind. Eng. Chem. Proc. Des. Dev., 13, pp199-203 (1974).

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Kraemer, D.W., Larocca, M., and de Lasa, H.I, Deactivation of Cracking Catalysts in Short Contact Time Reactors: Alternative Models. Can. J. Chem. Eng., (1990).

Larocca, M., Fast Catalytic Cracking with Nickel and Vanadium Contaminants. Ph.D. Thesis, The University of Western Ontario, London, Ontario, Canada (1988).

Larocca, M., Ng, S., and de Lasa, H., Cracking Catalyst Deactivation by Nickel and Vanadium Contaminants, Ind. Eng. Chem. Res. Vol, 29, pp2181, (1990).

Liguras, D.K, and Allen, D.T, Sensitivity of Octane Number to Catalytic Cracking Rates and Feedstock Structure AIChE, 36(10), pp1617-1621, (1990).

Nace, D. M., Voltz, S. E. and Weekman, V. M. Application of a Kinetic Model for Catalytic Cracking. Effects of Charge Stocks. Ind. Eng. Chem. Proc. Des. Dev., 10, 530-537 (1971).Paraskos, J.A., Shah, Y.T., Mckinney, J.D., and Carr, N.L., A Kinetic Model for Catalytic Cracking in a Transfer Line Reactor, Ind. Eng. Chem. Prod. Des. Dev., 15, pp165-169 (1976).

Pitualt, I., Nevicato, D. Foressier, M. and Bernard, J-R. Kinetic Model Based on a Molecular Description for Catalytic Cracking of Vacuum Gas Oil. Chem. Eng. Sci, vol. 49, no. 24A, pp. 4249-4262 (1994).

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Shah, Y.T., Huling, G.P., Paraskos, J.A. and Mckinney, J.D., A Kinetic Model for an Adiabatic Transfer Line Catalytic Reactor, Ind. Eng. Chem. Prod. Des. Dev., 16, pp89-94 (1977).

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Vynckier, E. and Froment, G.F, Modeling of the Kinetics of Complex Processes Based Upon Elementary Steps. In Kinetic and Thermodynamic Lumping of Multicomponent Mixtures. Editted by Astarita, G, and Sandlers, S.I., pp131-161 (1991).

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VGO

Light gases

Coke

k

k

31

32

k

11

Gasoline

k

22

21

k

(A)

(B)

_1035105131.doc

Gas oil

Gasoline

Light gases&coke

k

T11

k

T3

k

T2

Gas oil

Gasoline

Light gases&coke