Kinetic Modeling of Hydrodesulfurization of Oil Fractions: Light Cycle

This implies relating the rate equations of substituted S-containing components to those of the heads of the family. By way of example, hydrodesulfuri...
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Ind. Eng. Chem. Res. 1998, 37, 4231-4240

4231

Kinetic Modeling of Hydrodesulfurization of Oil Fractions: Light Cycle Oil Vale´ rie Vanrysselberghe† and Gilbert F. Froment*,‡ Laboratorium voor Petrochemische Techniek, Universiteit Gent, Krijgslaan 281, B-9000 Gent, Belgium

The paper presents a methodology for the kinetic modeling of hydrodesulfurization of oil fractions. Instead of lumping the S components, these are considered individually. To avoid an untractable number of parameters, a structural contribution approach is applied. This implies relating the rate equations of substituted S-containing components to those of the heads of the family. By way of example, hydrodesulfurization of a light cycle oil on a commercial CoMo/Al2O3 catalyst was studied in a completely mixed multiphase flow reactor. The surface reaction between adsorbed reactants and two competitively adsorbed hydrogen atoms was the rate-determining step for both hydrogenolysis on σ sites and hydrogenation on τ sites. Structural contributions were derived for hydrogenolysis and hydrogenation of methyl-substituted benzothiophenes and dibenzothiophenes. Introduction Sulfur has to be removed from oil fractions for technical and environmental reasons. In the European Community the diesel sulfur content has been limited to 0.05 wt % since Oct 1996. For the year 2000 this content will have to be lowered to 0.035 wt %. Light cycle oil (LCO) contains various methyl-substituted benzothiophenes, dihydrobenzothiophenes, dibenzothiophenes, and naphthothiophenes (Depauw and Froment (1997)) which are relatively refractory to hydrodesulfurization (HDS). So far HDS of oil fractions has been studied in terms of lumps of S components which were converted according to first-order or second-order kinetics. Deep HDS requires a more accurate kinetic modeling considering individual components and rate equations of the Hougen-Watson type accounting for the adsorption of the various species. If the kinetic modeling is based upon individual components, the number of rate parameters becomes overwhelming. That is why Froment et al. (1994) proposed an approach based upon structural contributions. In this concept the rate equations of substituted S components are related to the rate equation of the head of family or parent molecule. The methodology to be followed in the case of complex oil fractions is illustrated in the present paper. For a better understanding the numbering of the carbon atoms in benzothiophene and dibenzothiophene is shown

Experimental Program The experiments were performed in a RobinsonMahoney reactor with complete mixing of both the gas † Present address: Fina Research S.A., Zone Industrielle C, B-7181 Seneffe (Feluy), Belgium. ‡ Present address: Department of Chemical Engineering, Texas A&M University, College Station, TX 77843-3122.

and the liquid phases. The feedstock was a LCO containing 1.28 wt % sulfur. The temperature was varied between 513 and 593 K, the pressure between 60 and 80 bar, the molar hydrogen-to-hydrocarbon ratio between 2.3 and 3.5, and the liquid pumping rate between 15 and 27 mL/h. Details on the experimental equipment and the method of analysis and on the catalyst properties and pretreatment procedure were given in previous papers (Vanrysselberghe and Froment (1996), Froment et al. (1997)). To avoid diffusional limitations, the catalyst was crushed to a size between 710 and 800 µm. In each experiment the intrinsic rates of disappearance of benzothiophene, 30 identified methyl-substituted benzothiophenes, and 10 identified methyl-substituted dibenzothiophenes were determined. Results and Discussion First-Order Kinetics. For the sake of comparison with published data, the intrinsic rate of hydrodesulfurization through simultaneous hydrogenolysis and hydrogenation of benzothiophene, dibenzothiophene, the methyl-substituted benzothiophenes, and the methylsubstituted dibenzothiophenes was first expressed in terms of simple first-order kinetics. First-order kinetics for the decomposition of a large number of substituted benzothiophenes and dibenzothiophenes in complex mixtures have been published before. Kabe et al. (1992, 1993) found in their study of hydrodesulfurization of a light oil (245-374 °C) on a CoMo/Al2O3 catalyst that benzothiophenes with substituents in positions 2, 3, and/or 7 were less reactive than benzothiophene. The most refractive methylsubstituted benzothiophene was 2,3,7-trimethylbenzothiophene (2,3,7-TriMeBT). Dibenzothiophenes with substituents in positions 4 and/or 6 were less reactive than other substituted dibenzothiophenes. Similar results were obtained by Ma et al. (1994, 1995a, 1996) in their study on hydrodesulfurization of various substituted benzothiophenes and dibenzothiophenes in a diesel fuel, a gas oil, and a vacuum gas oil, on CoMo/ Al2O3 and NiMo/Al2O3 catalysts. Kilanowski et al. (1978) also showed that methyl substituents in positions 2, 3, and/or 7 reduce the hydrodesulfurization rate.

10.1021/ie970895x CCC: $15.00 © 1998 American Chemical Society Published on Web 09/24/1998

4232 Ind. Eng. Chem. Res., Vol. 37, No. 11, 1998

Figure 1. Effect of methyl substituents on the first-order rate coefficient for the hydrodesulfurization of substituted benzothiophenes and dibenzothiophenes at 513 K.

Geneste et al. (1980) and Levache´ et al. (1981) concluded that 2-methyl-, 3-methyl-, and 2,3-dimethylbenzothiophene showed a lower hydrogenation rate than benzothiophene. The latter authors did not consider the hydrogenolysis reactions. Similar results were obtained in the present study. Benzothiophenes with substituents in positions 2, 3, and/or 7 were less reactive than benzothiophene. This decline in the hydrodesulfurization rate was less pronounced for a methyl substituent in position 3 than for a methyl group in position 7. The most important reduction in the hydrodesulfurization rate was caused by a methyl group in position 2. Substituents in positions 4, 5, and/or 6 increase the hydrodesulfurization rate with respect to benzothiophene. Among the benzothiophenes studied here, 2,3,7-TriMeBT was the most refractive. Dibenzothiophenes with substituents in positions 4 and/or 6 were less reactive than dibenzothiophene. This is in agreement with literature results (Houalla et al. (1977, 1980), Kilanowski et al. (1978), Kabe et al. (1992, 1993), and Ma et al. (1994, 1995a, 1996)). Methyl groups in other positions lead to hydrodesulfurization rates higher than that of dibenzothiophene. This is in contrast with the literature observations. Kabe et al. (1992, 1993) and Ma et al. (1994, 1995a, 1996) found that methyl groups in positions 1, 2, and/or 3 had no influence on the hydrodesulfurization rate. Houalla et al. (1980) found that the first-order rate coefficient for the HDS of DBT is almost identical with that of 2,8DiMeDBT (dimethyldibenzothiophene) and is about 2 times larger than that of 3,7-DiMeDBT. The effect of methyl substituents on the first-order rate coefficient for hydrodesulfurization of substituted benzothiophenes and dibenzothiophenes is shown in Figure 1 at a temperature of 513 K. The sequence is identical at the other temperatures. (Substituted) benzothiophenes were found to be 1-3 orders of magnitude more reactive than (substituted) dibenzothiophenes. Similar results were obtained by Nag et al. (1979), Kabe et al. (1992, 1993), and Ma et al. (1994, 1995a, 1996). Structural Contribution Approach for HDS of Complex Mixtures. The first-order rate coefficient reported in the preceding section is an ill-defined conglomerate containing the hydrogen concentration and the adsorption group on both types of active sites, σ and τ. This means that it will vary with the feedstock composition, so that an extensive experimental effort is required for each new feedstock. To come to invariant parameters, it is necessary in the first place to distinguish between hydrogenolysis and hydrogenation reactions. Further, the Hougen-Watson concept accounts for the adsorption of the reacting species. Also, it is logical to assume that the structure of the rate equations for substituted benzothiophenes or dibenzothiophenes is identical with that of the head of the family or parent

molecule. On this basis, Froment et al. (1994) proposed an approach in which the rates of reactions involving substituted components are related to those for a nonsubstituted reference component through structural contributions. The latter account for the electronic effects and the steric hindrance of the substituents on the rate coefficients and the adsorption equilibrium constants. Example of Application: Data on Model Components Available. The Hougen-Watson rate equation for hydrodesulfurization of a methyl-substituted dibenzothiophene is related to that for nonsubstituted dibenzothiophene through structural contributions in the following way

rsDBT ) CsDBTCH2

[

fsDBT,σkDBT,σKDBT,σKH,σ + DENσ fsDBT,τkDBT,τKDBT,τKH,τ (1) DENτ

]

with

DENσ ) (1 +

∑i Ki,σCi + xKH,σCH )3

DENτ ) (1 +

∑i Ki,τCi + xKH,τCH )3

2

2

The functional forms of DENσ and DENτ are identical with those determined in the study on hydrodesulfurization of dibenzothiophene (Vanrysselberghe and Froment (1996)). In the HDS of LCO the denominators DENσ and DENτ contain the concentrations of all adsorbing species of the LCO multiplied by their respective adsorption equilibrium constant. Therefore, DENσ and DENτ vary with composition and temperature. Froment et al. (1997) expressed the variation with concentration in terms of the molar-averaged conversion of the LCO. In complex mixtures such as LCO, DENσ and DENτ are not directly accessible since not all adsorbing species are identified. The development of Hougen-Watson kinetics for hydrodesulfurization of aromatic sulfur components in complex mixtures involves two steps. The first step is the determination of the values of the denominators DENσ and DENτ and their evolution with the temperature and the composition of the reacting mixture. DENσ and DENτ can be calculated when kinetic equations are available for model components, so that the products ki,σKi,σKH,σ and ki,τKi,τKH,τ, appearing in the numerators, are known. These products do not vary with the mixture composition. The products ki,σKi,σKH,σ and ki,τKi,τKH,τ were determined for hydrogenolysis of dibenzothiophene and for hydrogenation of dibenzothiophene, biphenyl, and naphthalene (Vanrysselberghe and Froment (1996), Froment et al. (1997)), respectively. On the basis of the rate equations involved in the reaction network of dibenzothiophene and naphthalene, DENσ and DENτ were then estimated for each LCO experiment, i.e., for each composition and temperature in the completely mixed reactor. Once DENσ and DENτ are known, the second step, i.e., the calculation of the numerical values of the structural contributions, can be undertaken. It is thereby assumed that the electronic effects on the rate coefficient and the adsorption equilibrium constant are independent of the position of the sub-

Ind. Eng. Chem. Res., Vol. 37, No. 11, 1998 4233

xj )

1 7

7

xiyi ∑ i)1

(2)

yi ∑ i)1

Figure 2. DENσ and DENτ at 593 K as a function of the molaraveraged conversion of LCO.

stituent. In eq 1, fsDBT,σ represents the products of the contributions of electronic and steric hindrance effects of the substituents on the rates of hydrogenolysis taking place on the σ sites

MeDBT no Me in 4 or 6

sDBT sDBT fsDBT,σ ) kEL,σ (m;0;0)KEL,σ (m;0;0)

fsDBT,σ ) sDBT sDBT sDBT sDBT (m;0;0)kST,σ (4;0;0)KST,σ (4;0;0) kEL,σ (m;0;0)KEL,σ

4-MeDBT

DiMeDBT no Me in 4 or 6 sDBT sDBT (m;n;0)KEL,σ (m;n;0) fsDBT,σ ) kEL,σ

fsDBT,σ ) sDBT sDBT sDBT sDBT (m;n;0)kST,σ (4;0;0)KST,σ (4;0;0) kEL,σ (m;n;0)KEL,σ

1 Me in 4 or 6

fsDBT,σ ) sDBT sDBT sDBT sDBT (m;n;0)kST,σ (4;6;0)KST,σ (4;6;0) kEL,σ (m;n;0)KEL,σ

4,6-DiMeDBT TriMeDBT

no Me in 4 or 6 sDBT sDBT fsDBT,σ ) kEL,σ (m;n;p)KEL,σ (m;n;p)

fsDBT,σ ) sDBT sDBT sDBT sDBT (m;n;p)kST,σ (4;0;0)KST,σ (4;0;0) kEL,σ (m;n;p)KEL,σ

1 Me in 4 or 6

1 Me in 4 and 1 Me in 6

and fsDBT,τ the contributions of electronic and steric hindrance effects of the substituents on the rates of hydrogenation taking place on the τ sites

fsDBT,τ )

sDBT sDBT sDBT (m;0;0) ) KEL,σ (m;n;0) ) kEL,σ (m;0;0) ) KEL,σ sDBT (m;n;0) ) 1 kEL,σ

fsDBT,σ )

sDBT sDBT sDBT sDBT (m;n;p)KEL,σ (m;n;p)kST,σ (4;6;0)KST,σ (4;6;0) kEL,σ

MeDBT

with xi the conversions of a set of selected components (BT, DBT, naphtho[2,1-b]thiophene, 4-MeDBT, 4,6DiMeDBT, naphthalene, and phenanthrene) and yi the corresponding mole fractions in the LCO feed. The experimental results with the LCO revealed that the introduction of a methyl group in positions 1, 2, and/ or 3 does not influence the rate of hydrogenolysis. These substituents are remote from the sulfur atom and do not cause steric hindrance on the vertical adsorption through the sulfur atom or on the surface reaction on the σ sites. In that case fsDBT,σ ) 1. Methyl groups in positions 4 and/or 6 cause a decrease in the rate of hydrogenolysis compared to that of dibenzothiophene, so that fsDBT,σ < 1. This is due to the steric hindrance of these methyl substituents. The experiments with the model components 4-MeDBT and 4,6-DiMeDBT (Vanrysselberghe et al. (1998)) showed that those substituted components had a lower adsorption equilibrium constant on the σ sites than DBT. Furthermore, the rate coefficient for the hydrogenolysis reaction decreased in the order DBT > 4-MeDBT > 4,6-DiMeDBT. Methyl-substituted dibenzothiophenes have a higher rate of hydrogenation than dibenzothiophene itself, so that fsDBT,τ > 1. The experiments with the model components 4-MeDBT and 4,6-DiMeDBT demonstrated that methyl groups increase both the adsorption equilibrium constant on the τ sites and the rate coefficient for the hydrogenation surface reaction (Vanrysselberghe et al. (1998)). The structural contributions for hydrogenolysis and hydrogenation of the mono- and dimethyldibenzothiophenes as defined by Froment et al. (1994) can be calculated from the results with the LCO in combination with the data obtained from the model components 4-MeDBT and 4,6-DiMeDBT (Vanrysselberghe et al. (1998)). The structural contributions for the hydrogenolysis reaction on the σ sites of the various monoand dimethyldibenzothiophenes are given by

sDBT sDBT kEL+ST,τ (m;0;0)KEL+ST,τ (m;0;0)

DiMeDBT

sDBT sDBT (m;n;0)KEL+ST,τ (m;n;0) fsDBT,τ ) kEL+ST,τ

TriMeDBT

sDBT sDBT (m;n;p)KEL+ST,τ (m;n;p) fsDBT,τ ) kEL+ST,τ

The variation of DENσ and DENτ with the mixture composition at 593 K in the completely mixed reactor is shown in Figure 2. The mixture composition is expressed in terms of a molar-averaged conversion, defined as follows:

sDBT (4;0;0) ) KST,σ

sDBT (4;6;0) ) KST,σ

sDBT kST,σ (4;0;0) )

sDBT kST,σ (4;6;0) )

for all m and n

K4-MeDBT,σ ) 0.31006 KDBT,σ

K4,6-DiMeDBT,σ ) 0.23835 KDBT,σ

[

]

k4-MeDBT,σ 10550 ) 5.38218 exp kDBT,σ RgasT

k4,6-DiMeDBT,σ ) kDBT,σ

[

2.63801 × 10-3 exp

]

16547 RgasT

sDBT sDBT (4;0;0) ) 0.588 and kST,σ (4;6;0) ) At 573 K, e.g., kST,σ sDBT 0.0850. The structural contributions KST,σ (4;0;0) and sDBT (4;6;0) are temperature-independent since the KST,σ adsorption equilibrium constants KDBT,σ, K4-MeDBT,σ, and

4234 Ind. Eng. Chem. Res., Vol. 37, No. 11, 1998 Table 1. Kinetic Analysis of the Data at All Temperaturesa parameter kBT,σKBT,σ kBT,τKBT,τ Fregr value ) 15 997

A# Ea A# Ea

sDBT sDBT KEL,σ (m;n;p) ) kEL,σ (m;n;p) ) 1

parameter value

lower limit

upper limit

t value

1.001 × 103 1.503 × 105 3.631 × 101 2.073 × 105

9.621 × 102 1.468 × 105 3.486 × 101 2.023 × 105

1.040 × 103 1.538 × 105 3.776 × 101 2.124 × 105

5.117 × 101 8.548 × 101 5.009 × 101 8.236 × 101

a Parameter estimates for the hydrodesulfurization of benzothiophene, their corresponding 95% confidence intervals, and t values and the Fregr value.

K4,6-DiMeDBT,σ do not significantly vary with temperature (Vanrysselberghe and Froment (1996), Vanrysselberghe et al. (1998)). The electronic effects of the substituents on the rate coefficient and the adsorption equilibrium constant are weak or negligible, confirming quantumchemical ab initio calculations on the free molecules using the MOPAC package and calculations of Ma et al. (1995b). Because of the flat adsorption on the τ sites, only the number of methyl groups and not their position relative to the sulfur atom has to be taken into account for the adsorption and the reaction between the adsorbed species on the τ sites. Therefore, in the hydrogenation reactions electronic and steric effects of the methyl substituents are lumped. On the τ sites the following structural contributions for hydrogenation of the monoand dimethyldibenzothiophenes were obtained sDBT KEL+ST,τ (m;0;0) )

K4-MeDBT,τ ) KDBT,τ

[ ]

K4,6-DiMeDBT,τ sDBT KEL+ST,τ (m;n;0) ) ) KDBT,τ

6962 RgasT

[

6.33930 × 10-2 exp 1 2 k4-MeDBT,τ + k4-MeDBT,τ ) ) kDBT,τ

]

13645 RgasT

[

81078 RgasT

1.28404 × 1011 exp -

112852 RgasT

k4,6-DiMeDBT,τ ) kDBT,τ

[

]

kBT,σKBT,σKH,σ kBT,τKBT,τKH,τ + DENσ DENτ

[

] ]

1 2 and k4-MeDBT,τ are the rate coefficients for the k4-MeDBT,τ two parallel hydrogenations of 4-MeDBT. At 573 K, e.g., sDBT sDBT (m;0;0) ) 1.04, KEL+ST,τ (m;n;0) ) 1.11, KEL+ST,τ sDBT sDBT kEL+ST,τ(m;0;0) ) 6.05, and kEL+ST,τ(m;n;0) ) 6.67. A comparison between the conversions for the methyl- and dimethyldibenzothiophenes calculated through the structural contributions and the experimental conversions obtained with the LCO is given in Figure 3. The agreement between the experimental values and the model predictions is good. From the experiments with the LCO, it is further derived that for the hydrogenolysis reaction of the trimethyldibenzothiophenes:

(3)

The values for KH,σ and KH,τ were derived in a previous study on hydrodesulfurization of dibenzothiophene (Vanrysselberghe and Froment (1996)). The parameters kBT,σKBT,σ and kBT,τKBT,τ at a given temperature were obtained by minimization of the objective function S(θ) from the experimental data on the disappearance of benzothiophene in the LCO:

S(θ) )

∑ (xBTj - xˆ BTj)2 98 min θ

(4)

j)1

DENσ and DENτ are known from the treatment of the data on substituted dibenzothiophenes, as explained in the previous section. For the estimation of the parameters in the kinetic analysis of the data at all temperatures, a reparametrization was carried out:

[ (

kBT,sKBT,s ) A# exp -

1.48162 × 108 exp sDBT kEL+ST,τ (m;n;0) )

rBT ) CBTCH2

j)nexp

2.41099 × 10-1 exp

sDBT kEL+ST,τ (m;0;0)

sDBT (m;n;p) To obtain the structural contributions KEL+ST,τ sDBT and kEL+ST,τ(m;n;p) for the hydrogenation of the trimethyldibenzothiophenes, additional experiments with a trimethyldibenzothiophene are necessary. Example of Application: No Data on Model Components. Rate equations for hydrodesulfurization of benzothiophene were available (Van Parys et al. (1986)) but on a different CoMo/Al2O3 catalyst. To calculate the structural contributions for the methylsubstituted benzothiophenes, the kinetic parameters for hydrodesulfurization of the nonsubstituted head of the family, benzothiophene, have to be determined first on the present catalyst using the LCO experiments. The Hougen-Watson rate equation for the sulfur removal of benzothiophene itself in the LCO is written as

)]

Ea 1 1 Rgas T Tm

The parameters A# and Ea, their corresponding 95% confidence intervals, the calculated t values, and the Fregr value are shown in Table 1. The regression was found to be significant, and all parameters were statistically significant. The parameters kBT,σKBT,σ and kBT,τKBT,τ (containing A, not A#) can be written as

kBT,σKBT,σ )

[

150297 m3/(kgcat h) RgasT

[

207325 m3/(kgcat h) RgasT

1.54237 × 1017 exp kBT,τKBT,τ )

1.35198 × 1021 exp -

] ]

As for the methyl-substituted dibenzothiophenes, the Hougen-Watson rate equation for hydrodesulfurization of the methyl-substituted benzothiophenes is related to that for benzothiophene (eq 1) through structural contributions. fsBT,σ can be written as follows:

Ind. Eng. Chem. Res., Vol. 37, No. 11, 1998 4235

MeBT no Me in 2 or 7 sBT sBT fsBT,σ ) kEL,σ (m;0;0;0)KEL,σ (m;0;0;0)

2-MeBT

sBT sBT (m;0;0;0)KEL,σ (m;0;0;0) × fsBT,σ ) kEL,σ sBT sBT (2;0;0;0)KST,σ (2;0;0;0) kST,σ

7-MeBT

sBT sBT (m;0;0;0)KEL,σ (m;0;0;0) × fsBT,σ ) kEL,σ sBT sBT (7;0;0;0)KST,σ (7;0;0;0) kST,σ

DiMeBT no Me in 2 or 7 sBT sBT fsBT,σ ) kEL,σ (m;n;0;0)KEL,σ (m;n;0;0)

1 Me in 2

sBT sBT (m;n;0;0)KEL,σ (m;n;0;0) × fsBT,σ ) kEL,σ sBT sBT (2;0;0;0)KST,σ (2;0;0;0) kST,σ

1 Me in 7

sBT sBT (m;n;0;0)KEL,σ (m;n;0;0) × fsBT,σ ) kEL,σ sBT sBT (7;0;0;0)KST,σ (7;0;0;0) kST,σ

2,7-DiMeBT sBT sBT (m;n;0;0)KEL,σ (m;n;0;0) × fsBT,σ ) kEL,σ sBT sBT (2;7;0;0)KST,σ (2;7;0;0) kST,σ

TriMeBT no Me in 2 or 7 sBT sBT fsBT,σ ) kEL,σ (m;n;p;0)KEL,σ (m;n;p;0)

1 Me in 2

1 Me in 7

fsBT,σ )

sBT sBT kEL,σ (m;n;p;0)KEL,σ (m;n;p;0) × sBT sBT (2;0;0;0) kST,σ(2;0;0;0)KST,σ

sBT sBT (m;n;p;0)KEL,σ (m;n;p;0) × fsBT,σ ) kEL,σ sBT sBT (7;0;0;0)KST,σ (7;0;0;0) kST,σ

1 Me in 2 and 1 Me in 7 sBT sBT (m;n;p;0)KEL,σ (m;n;p;0) × fsBT,σ ) kEL,σ sBT sBT (2;7;0;0)KST,σ (2;7;0;0) kST,σ

no Me in 2 or 7 sBT sBT fsBT,σ ) kEL,σ (m;n;p;q)KEL,σ (m;n;p;q) sBT sBT (m;n;p;q)KEL,σ (m;n;p;q) × fsBT,σ ) kEL,σ sBT sBT (2;0;0;0)KST,σ (2;0;0;0) kST,σ

1 Me in7

2-MeBT sBT sBT fsBT,τ ) kEL+ST,τ (m;0;0;0)KEL+ST,τ (m;0;0;0) × sBT sBT (2;0;0;0)KEL,τ (2;0;0;0) kEL,τ

3-MeBT sBT sBT fsBT,τ ) kEL+ST,τ (m;0;0;0)KEL+ST,τ (m;0;0;0) × sBT sBT (3;0;0;0)KEL,τ (3;0;0;0) kEL,τ

DiMeBT no Me in 2 or 3 sBT sBT fsBT,τ ) kEL+ST,τ (m;n;0;0)KEL+ST,τ (m;n;0;0) 1 Me in 2 sBT sBT fsBT,τ ) kEL+ST,τ (m;n;0;0)KEL+ST,τ (m;n;0;0) × sBT sBT (2;0;0;0)KEL,τ (2;0;0;0) kEL,τ

1 Me in 3 sBT sBT fsBT,τ ) kEL+ST,τ (m;n;0;0)KEL+ST,τ (m;n;0;0) × sBT sBT (3;0;0;0)KEL,τ (3;0;0;0) kEL,τ

2,3-DiMeBT sBT sBT fsBT,τ ) kEL+ST,τ (m;n;0;0)KEL+ST,τ (m;n;0;0) × sBT sBT (2;3;0;0)KEL,τ (2;3;0;0) kEL,τ

TriMeBT no Me in 2 or 3 sBT sBT (m;n;p;0)KEL+ST,τ (m;n;p;0) fsBT,τ ) kEL+ST,τ 1 Me in 2 sBT sBT fsBT,τ ) kEL+ST,τ (m;n;p;0)KEL+ST,τ (m;n;p;0) × sBT sBT (2;0;0;0)KEL,τ (2;0;0;0) kEL,τ

1 Me in 3 sBT sBT fsBT,τ ) kEL+ST,τ (m;n;p;0)KEL+ST,τ (m;n;p;0) × sBT sBT (3;0;0;0)KEL,τ (3;0;0;0) kEL,τ

1 Me in 2 and 1 Me in 3 sBT sBT fsBT,τ ) kEL+ST,τ (m;n;p;0)KEL+ST,τ (m;n;p;0) × sBT sBT (2;3;0;0)KEL,τ (2;3;0;0) kEL,τ

TetraMeBT no Me in 2 or 3 sBT sBT (m;n;p;q)KEL+ST,τ (m;n;p;q) fsBT,τ ) kEL+ST,τ

TetraMeBT

1 Me in 2

MeBT no Me in 2 or 3 sBT sBT fsBT,τ ) kEL+ST,τ (m;0;0;0)KEL+ST,τ (m;0;0;0)

fsBT,σ )

sBT sBT kEL,σ (m;n;p;q)KEL,σ (m;n;p;q) × sBT sBT (7;0;0;0) kST,σ(7;0;0;0)KST,σ

1 Me in 2 and 1 Me in 7 sBT sBT (m;n;p;q)KEL,σ (m;n;p;q) × fsBT,σ ) kEL,σ sBT sBT (2;7;0;0)KST,σ (2;7;0;0) kST,σ

fsBT,τ can be written as follows:

1 Me in 2 sBT sBT fsBT,τ ) kEL+ST,τ (m;n;p;q)KEL+ST,τ (m;n;p;q) × sBT sBT (2;0;0;0)KEL,τ (2;0;0;0) kEL,τ

1 Me in 3 sBT sBT fsBT,τ ) kEL+ST,τ (m;n;p;q)KEL+ST,τ (m;n;p;q) × sBT sBT (3;0;0;0)KEL,τ (3;0;0;0) kEL,τ

1 Me in 2 and 1 Me in 3 sBT sBT fsBT,τ ) kEL+ST,τ (m;n;p;q)KEL+ST,τ (m;n;p;q) × sBT sBT (2;3;0;0)KEL,τ (2;3;0;0) kEL,τ

If only data on the HDS of LCO is used and no information is available on the HDS of model compo-

4236 Ind. Eng. Chem. Res., Vol. 37, No. 11, 1998

nents, only the f groups containing several structural contributions can be determined. The total number of f groups to be determined amounts to 14. To reduce the number of parameters, it was attempted to derive structural contributions in di-, tri-, and tetrasubstituted benzothiophenes from the values obtained from monosubstituted components. Several possibilities, such as additivity and multiplication of the effect of a methyl group in the various positions, were considered. The best fit of the experimental data was obtained by multiplying the structural contributions for the monosubstituted benzothiophenes. Since the electronic effect is identical regardless of the position of the substituent, the following relations are obtained: sBT sBT kEL,σ (m;n;0;0)KEL,σ (m;n;0;0) ) sBT sBT (m;0;0;0)KEL,σ (m;0;0;0)]2 [kEL,σ sBT sBT kEL,σ (m;n;p;0)KEL,σ (m;n;p;0) ) sBT sBT (m;0;0;0)KEL,σ (m;0;0;0)]3 [kEL,σ sBT sBT kEL,σ (m;n;p;q)KEL,σ (m;n;p;q) ) sBT sBT (m;0;0;0)KEL,σ (m;0;0;0)]4 [kEL,σ sBT sBT kST,σ (2;7;0;0)KST,σ (2;7;0;0) ) sBT sBT sBT sBT (2;0;0;0)KST,σ (2;0;0;0)kST,σ (7;0;0;0)KST,σ (7;0;0;0) kST,σ sBT sBT (m;n;0;0)KEL+ST,τ (m;n;0;0) ) kEL+ST,τ sBT sBT (m;0;0;0)KEL+ST,τ (m;0;0;0)]2 [kEL+ST,τ sBT sBT kEL+ST,τ (m;n;p;0)KEL+ST,τ (m;n;p;0) ) sBT sBT (m;0;0;0)]3 [kEL+ST,τ(m;0;0;0)KEL+ST,τ sBT sBT kEL+ST,τ (m;n;p;q)KEL+ST,τ (m;n;p;q) ) sBT sBT (m;0;0;0)]4 [kEL+ST,τ(m;0;0;0)KEL+ST,τ sBT sBT kEL,τ (2;3;0;0)KEL,τ (2;3;0;0) ) sBT sBT sBT sBT (2;0;0;0)KEL,τ (2;0;0;0)kEL,τ (3;0;0;0)KEL,τ (3;0;0;0) kEL,τ

Based on the above assumptions, the following six groups of structural contributions were estimated: sBT sBT f3,σ ) f4,σ ) f5,σ ) f6,σ ) kEL,σ (m;0;0;0)KEL,σ (m;0;0;0) sBT sBT (m;0;0;0)KEL,σ (m;0;0;0) × f2,σ ) kEL,σ sBT sBT (2;0;0;0)KST,σ (2;0;0;0) kST,σ sBT sBT (m;0;0;0)KEL,σ (m;0;0;0) × f7,σ ) kEL,σ sBT sBT (7;0;0;0)KST,σ (7;0;0;0) kST,σ

f4,τ ) f5,τ ) f6,τ ) f7,τ ) sBT sBT (m;0;0;0)KEL+ST,τ (m;0;0;0) kEL+ST,τ sBT sBT (m;0;0;0)KEL+ST,τ (m;0;0;0) × f2,τ ) kEL+ST,τ sBT sBT (2;0;0;0)KEL,τ (2;0;0;0) kEL,τ sBT sBT (m;0;0;0)KEL+ST,τ (m;0;0;0) × f3,τ ) kEL+ST,τ sBT sBT (3;0;0;0)KEL,τ (3;0;0;0) kEL,τ

The parameters fi,σ and fi,τ at a given temperature were obtained by minimization of the objective function S(θ):

i)ncomp j)nexp

S(θ) )

∑ ∑ (xij - xˆ ij)2 98 min i)1

θ

(5)

j)1

The parameter estimates showed an Arrhenius temperature dependence. For the estimation of the parameters in the kinetic analysis of the data at all temperatures, a reparametrization was performed:

[ (

fi,s ) A# exp -

)]

Ea 1 1 Rgas T Tm

The parameters A# and Ea, their corresponding 95% confidence intervals, the calculated t values, and Fregr value are shown in Table 2. The regression was found to be significant, and all parameters were statistically significant. The parameters fi,σ and fi,τ (containing A, not A#) can be written as follows:

[ ] [ ] [ [ ] [ ] [

f2,σ ) 3.84047 × 10-2 exp

2745 RgasT

f7,σ ) 3.20070 × 10-3 exp

17073 RgasT

f3,σ ) f4,σ ) f5,σ ) f6,σ ) 4.81232 × 101 exp f2,τ ) 8.37053 × 101 exp f3,τ ) 2.33432 exp -

]

17896 RgasT

26327 RgasT

9932 RgasT

f4,τ ) f5,τ ) f6,τ ) f7,τ ) 1.24161 × 101 exp -

]

9903 RgasT

At 573 K, e.g., f2,σ ) 0.0683, f7,σ ) 0.115, f3,σ ) f4,σ ) f5,σ ) f6,σ ) 1.13, f2,τ ) 0.334, f3,τ ) 0.290, f4,τ ) f5,τ ) f6,τ ) f7,τ ) 1.55. A methyl substituent in positions 2 and/or 7 decreases the hydrogenolysis rate with respect to that of benzothiophene. This is due to the steric hindrance of the methyl groups on the vertical adsorption through the sulfur atom and the surface reaction between the adsorbed species on the σ sites. A methyl group in position 2 is closer to the sulfur atom than a methyl group in position 7; therefore, its effect on the hydrogenolysis rate is more pronounced than that of a methyl group in position 7. Methyl substituents in positions 3, 4, 5, and/or 6 have almost no influence on the hydrogenolysis rate compared to that of benzothiophene. Those substituents are remote from the sulfur atom and do not hinder the vertical adsorption through the sulfur atom. From the experiments with substituted dibenzothiophenes, it follows that for substituted benzothiophenes the presence of methyl groups leads to a higher adsorption equilibrium constant on the τ sites, regardless of their position. Furthermore, in benzothiophenes with a methyl group in position 2, the C2-C3 bond, which is hydrogenated before hydrogenolysis occurs, has a lower bond order than that in benzothiophene. This is also true for benzothiophenes with a methyl group in position 3. Quantum-chemical calculations using MOPAC showed that methyl groups in positions 4, 5, 6, and/or 7 do not influence the C2-C3 bond order. For the substituted benzothiophenes, Ma et al. (1995b) related

Ind. Eng. Chem. Res., Vol. 37, No. 11, 1998 4237 Table 2. Kinetic Analysis of the Data at All Temperaturesa structural contributions f2,σ f7,σ f3,σ ) f4,σ ) f5,σ ) f6,σ f2,τ f3,τ f4,τ ) f5,τ ) f6,τ ) f7,τ Fregr value ) 19 882

parameter value A# Ea A# Ea A# Ea A# Ea A# Ea A# Ea

10-2

6.974 × -2.745 × 103 1.309 × 10-1 -1.707 × 104 9.840 × 10-1 1.790 × 104 2.739 × 10-1 2.633 × 104 2.695 × 10-1 9.932 × 103 1.443 9.903 × 103

lower limit 10-2

6.646 × -5.277 × 103 1.212 × 10-1 -2.369 × 104 9.578 × 10-1 1.544 × 104 2.469 × 10-1 1.540 × 104 2.450 × 10-1 2.033 × 103 1.374 4.632 × 103

upper limit 10-2

7.302 × -2.121 × 102 1.406 × 10-1 -1.046 × 104 1.010 2.035 × 104 3.009 × 10-1 3.725 × 104 2.941 × 10-1 1.783 × 104 1.511 1.517 × 104

t value 4.248 × 101 -2.168 2.694 × 101 -5.162 7.509 × 101 1.460 × 101 2.029 × 101 4.820 2.195 × 101 2.515 4.198 × 101 3.758

a

Parameter estimates for fi,σ and fi,τ, their corresponding 95% confidence intervals, t values, and the Fregr value for the methyl-substituted benzothiophenes.

Figure 3. Parity plot for the conversion of methyl- and dimethyldibenzothiophenes in LCO.

a lower C2-C3 bond order to a lower hydrogenation rate. In the modeling of the rates in the HDS of LCO, the denominator DENτ in the rate equations is identical for all components; therefore, a large adsorption equilibrium constant results in a large hydrogenation rate. Consequently, methyl groups in positions 4, 5, 6, and/ or 7 increase the hydrogenation rate compared to that of benzothiophene. Therefore, with benzothiophenes with a methyl group in positions 2 and/or 3, the negative effect of the methyl substituent on the C2-C3 bond order must be more pronounced than the positive effect on the adsorption equilibrium constant; thus, a methyl substituent in positions 2 and/or 3 decreases the hydrogenation rate with respect to that of benzothiophene. The comparison between the experimental and the calculated conversions for a number of methyl-substituted benzothiophenes is shown in Figures 4-7. The agreement between the experimental values and the model predictions is good. Application to Other Complex Feedstocks. The structural contributions approach derived in this study can be applied to predict Hougen-Watson kinetics for hydrodesulfurization of methyl-substituted benzothiophene and methyl-substituted dibenzothiophene in any real feedstock. For this purpose the conversions of benzothiophene, dibenzothiophene, or methyl-substi-

Figure 4. Parity plot for the conversion of methylbenzothiophenes in LCO.

tuted benzothiophenes and dibenzothiophenes, components for which the structural contributions are now available, have to be measured at the desired molaraveraged conversion of the mixture and a given temperature. From the Hougen-Watson rate equations for hydrodesulfurization of these components, the numerical values for both denominators DENσ and DENτ are calculated (Froment et al. (1997)). The procedure is then repeated for various temperatures and molar-averaged conversions of the real feedstock. The kinetic modeling of the hydrodesulfurization reactions based on structural contributions can be applied to other families of sulfur molecules such as dihydrobenzothiophenes, naphthothiophenes, and benzonaphthothiophenes. Data obtained from model components in combination, if necessary, with experiments with a real feedstock containing those molecules are required to calculate the structural contributions. Depending on the molecular structure of the nonsubstituted head of family, different structural contributions will have to be considered. In this paper, the approach was illustrated for the benzothiophene and dibenzothiophene family. Conclusions A model for predicting Hougen-Watson kinetics of hydrodesulfurization of benzothiophene, dibenzothio-

4238 Ind. Eng. Chem. Res., Vol. 37, No. 11, 1998

Figure 5. Parity plot for the conversion of a number of dimethylbenzothiophenes in LCO.

Figure 7. Parity plot for the conversion of tetramethylbenzothiophenes in LCO.

stituents in positions 2 and/or 3 decrease the hydrogenation rate while substituents in positions 4, 5, 6, and/ or 7 increase the hydrogenation rate compared to that of benzothiophene. On the basis of experiments with the LCO, the groups of structural contributions were calculated. Acknowledgment This work was partly funded by the European Commission under the Joule program (Contract JOU2-0121). V.V. is also grateful for a contribution from the Center of Excellence Grant awarded to the Laboratorium voor Petrochemische Techniek by the Belgian Ministry of Science and for financial support from Fina Research, who also provided the light cycle oil. The model components 4-MeDBT and 4,6-DiMeDBT were provided by Total. Nomenclature Figure 6. Parity plot for the conversion of a number of trimethylbenzothiophenes in LCO.

phene, and methyl-substituted benzothiophenes and dibenzothiophenes in any real feedstock was developed. For the dibenzothiophene family, methyl groups in positions 4 and/or 6 reduce the rate of hydrogenolysis with respect to that of dibenzothiophene while methyl groups in the other positions do not influence the hydrogenolysis rate. Methyl substituents increase the hydrogenation rate with respect to that of dibenzothiophene. The structural contributions for hydrogenolysis and hydrogenation of the mono- and dimethyldibenzothiophenes were calculated from experimental results with the LCO and model components. Benzothiophenes are 1-3 orders of magnitude more reactive than dibenzothiophenes. For the benzothiophene family, methyl groups in positions 2 and/or 7 reduce the hydrogenolysis rate with respect to that of benzothiophene. Methyl groups in positions 3, 4, 5, and/or 6 have no influence on the hydrogenolysis rate. Methyl sub-

Ci ) liquid concentration of component i, kmol/mL3 Ea ) activation energy, kJ/kmol ki,s ) rate coefficient for the reaction of component i on s sites, kmol/(kgcat h) sBT kEL,σ (m;0;0;0) ) electronic effect of one methyl group on the rate coefficient for the hydrogenolysis reaction of a MeBT on the σ sites sBT kEL,σ (m;n;0;0) ) electronic effect of two methyl groups on the rate coefficient for the hydrogenolysis reaction of a DiMeBT on the σ sites sBT kEL,σ (m;n;p;0) ) electronic effect of three methyl groups on the rate coefficient for the hydrogenolysis reaction of a TriMeBT on the σ sites sBT kEL,σ (m;n;p;q) ) electronic effect of four methyl groups on the rate coefficient for the hydrogenolysis reaction of a TetraMeBT on the σ sites sDBT kEL,σ (m;0;0) ) electronic effect of one methyl group on the rate coefficient for the hydrogenolysis reaction of a MeDBT on the σ sites sDBT kEL,σ (m;n;0) ) electronic effect of two methyl groups on the rate coefficient for the hydrogenolysis reaction of a DiMeDBT on the σ sites

Ind. Eng. Chem. Res., Vol. 37, No. 11, 1998 4239 sDBT kEL,σ (m;n;p) ) electronic effect of three methyl groups on the rate coefficient for the hydrogenolysis reaction of a TriMeDBT on the σ sites sBT kEL,τ (2;0;0;0) ) extra electronic effect of a methyl group in position 2 on the rate coefficient for the hydrogenation reaction of benzothiophenes on the τ sites sBT kEL,τ (3;0;0;0) ) extra electronic effect of a methyl group in position 3 on the rate coefficient for the hydrogenation reaction of benzothiophenes on the τ sites sBT kEL,τ (2;3;0;0) ) extra electronic effect of two methyl groups in position 2 and 3 on the rate coefficient for the hydrogenation reaction of benzothiophenes on the τ sites sBT kEL+ST,τ (m;0;0;0) ) electronic and steric effect of one methyl group on the rate coefficient for the hydrogenation reaction of a MeBT on the τ sites sBT kEL+ST,τ (m;n;0;0) ) electronic and steric effect of two methyl groups on the rate coefficient for the hydrogenation reaction of a DiMeBT on the τ sites sBT kEL+ST,τ (m;n;p;0) ) electronic and steric effect of three methyl groups on the rate coefficient for the hydrogenation reaction of a TriMeBT on the τ sites sBT kEL+ST,τ (m;n;p;q) ) electronic and steric effect of four methyl groups on the rate coefficient for the hydrogenation reaction of a TetraMeBT on the τ sites sDBT kEL+ST,τ (m;0;0) ) electronic and steric effect of one methyl group on the rate coefficient for the hydrogenation reaction of a MeDBT on the τ sites sDBT kEL+ST,τ (m;n;0) ) electronic and steric effect of two methyl groups on the rate coefficient for the hydrogenation reaction of a DiMeDBT on the τ sites sDBT kEL+ST,τ (m;n;p) ) electronic and steric effect of three methyl groups on the rate coefficient for the hydrogenation reaction of a TriMeDBT on the τ sites sBT kST,σ (2;0;0;0) ) steric effect of a methyl group in position 2 on the rate coefficient for the hydrogenolysis reaction of benzothiophenes on the σ sites sBT kST,σ (7;0;0;0) ) steric effect of a methyl group in position 7 on the rate coefficient for the hydrogenolysis reaction of benzothiophenes on the σ sites sBT kST,σ (2;7;0;0) ) steric effect of two methyl groups in positions 2 and 7 on the rate coefficient for the hydrogenolysis reaction of benzothiophenes on the σ sites sDBT kST,σ (4;0;0) ) steric effect of a methyl group in positions 4 or 6 on the rate coefficient for the hydrogenolysis reaction of dibenzothiophenes on the σ sites sDBT kST,σ (4;6;0) ) steric effect of two methyl groups in positions 4 and 6 on the rate coefficient for the hydrogenolysis reaction of dibenzothiophenes on the σ sites Ki,s ) adsorption coefficient of component i on s sites, mL3/ kmol sBT KEL,σ (m;0;0;0) ) electronic effect of one methyl group on the adsorption of a MeBT on the σ sites sBT KEL,σ (m;n;0;0) ) electronic effect of two methyl groups on the adsorption of a DiMeBT on the σ sites sBT KEL,σ (m;n;p;0) ) electronic effect of three methyl groups on the adsorption of a TriMeBT on the σ sites sBT KEL,σ (m;n;p;q) ) electronic effect of four methyl groups on the adsorption of a TetraMeBT on the σ sites sDBT KEL,σ (m;0;0) ) electronic effect of one methyl group on the adsorption of a MeDBT on the σ sites sDBT KEL,σ (m;n;0) ) electronic effect of two methyl groups on the adsorption of a DiMeDBT on the σ sites sDBT KEL,σ (m;n;p) ) electronic effect of three methyl groups on the adsorption of a TriMeDBT on the σ sites sBT KEL,τ (2;0;0;0) ) extra electronic effect of a methyl group in position 2 on the adsorption of benzothiophenes on the τ sites

sBT (3;0;0;0) ) extra electronic effect of a methyl group in KEL,τ position 3 on the adsorption of benzothiophenes on the τ sites sBT KEL,τ (2;3;0;0) ) extra electronic effect of two methyl groups in positions 2 and 3 on the adsorption of benzothiophenes on the τ sites sBT KEL+ST,τ (m;0;0;0) ) electronic and steric effect of one methyl group on the adsorption of a MeBT on the τ sites sBT KEL+ST,τ (m;n;0;0) ) electronic and steric effect of two methyl groups on the adsorption of a DiMeBT on the τ sites sBT KEL+ST,τ (m;n;p;0) ) electronic and steric effect of three methyl groups on the adsorption of a TriMeBT on the τ sites sBT KEL+ST,τ(m;n;p;q) ) electronic and steric effect of four methyl groups on the adsorption of a TetraMeBT on the τ sites sDBT KEL+ST,τ (m;0;0) ) electronic and steric effect of one methyl group on the adsorption of a MeDBT on the τ sites sDBT (m;n;0) ) electronic and steric effect of two methyl KEL+ST,τ groups on the adsorption of a DiMeDBT on the τ sites sDBT KEL+ST,τ (m;n;p) ) electronic and steric effect of three methyl groups on the adsorption of a TriMeDBT on the τ sites sBT KST,σ (2;0;0;0) ) steric effect of a methyl group in position 2 on the adsorption of benzothiophenes on the σ sites sBT KST,σ (7;0;0;0) ) steric effect of a methyl group in position 7 on the adsorption of benzothiophenes on the σ sites sBT KST,σ (2;7;0;0) ) steric effect of two methyl groups in positions 2 and 7 on the adsorption of benzothiophenes on the σ sites sDBT KST,σ (4;0;0) ) steric effect of a methyl group in position 4 or 6 on the adsorption of dibenzothiophenes on the σ sites sDBT KST,σ (4;6;0) ) steric effect of two methyl groups in positions 4 and 6 on the adsorption of dibenzothiophenes on the σ sites ncomp ) number of components nexp ) number of experiments ri ) total rate of disappearance of component i, kmol/(kgcat h) Rgas ) gas law constant, kJ/(kmol K) S(θ) ) objective function T ) temperature, K Tm ) average temperature, K xi ) conversion of component i xˆ i ) calculated conversion of component i yi ) mole fraction of component i in LCO feed

Greek Symbols σ ) hydrogenolysis site τ ) hydrogenation site Subscripts 4,6-DiMeDBT ) 4,6-dimethyldibenzothiophene 4-MeDBT ) 4-methyldibenzothiophene BT ) benzothiophene DBT ) dibenzothiophene H ) atomic hydrogen H2 ) molecular hydrogen sBT ) methyl-substituted benzothiophene sDBT ) methyl-substituted dibenzothiophene σ ) with respect to the hydrogenolysis function

4240 Ind. Eng. Chem. Res., Vol. 37, No. 11, 1998 τ ) with respect to the hydrogenation function

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Received for review December 9, 1997 Revised manuscript received June 22, 1998 Accepted July 23, 1998 IE970895X