Ind. Eng. Chem. Res. 1994,33, 2975-2988
2975
Kinetic Modeling and Reactor Simulation in Hydrodesulfurization of Oil Fractions? Gilbert F. Froment; Guy k Depauw, and Valerie Vanrysselberghe Laboratorium voor Petrochemische Techniek, Universiteit Gent, Krijgslaan 281, B-9000 Gent, Belgium
An adiabatic multiphase reactor for diesel hydrodesulfurization (HDS) was simulated with a one-dimensional heterogeneous model. A diesel-type mixture containing benzothiophene, dibenzothiophene, and 4,6-dimethyldibenzothiophenea s sulfur components and quinoline as nitrogen component was chosen as feed. A kinetic modeling for the HDS of dibenzothiophene and alkyl-substituted dibenzothiophenes based upon structural contributions was developed. According to a molecular approach the total number of rate and adsorption parameters for the HDS of a set of (substituted)-dibenzothiophenesis 1133. In the structural contribution approach introduced here the total number of parameters has been reduced to 93.
Introduction Sulfur is present in many forms in petroleum fractions: mercaptans R-SH, sulfides R-S-R', disulfides R-S-S-R, polysulfides R-S,-R', thiophene, benzothiophene (BT), dibenzothiophene (DBT), and their alkyl derivatives. In addition, various nitrogen-containing components like pyridine and alkylpyridines, quinoline and alkylquinolines, benzoquinolines, acridines, indoles, and carbazoles are also present. Sulfur has to be removed from oil fractions for both technical and environmental reasons. The specifications on diesel for example are getting more stringent. From October 1993 onward the sulfur content of diesel for highway traffic is limited to 0.05 w t % in the United States. At present the maximum sulfur content in Western Europe is 0.2-0.3 wt %, depending upon the country, but the specification imposed by the European Union from Oct 1, 1996, onward for class 3 standard diesel for long-haul traffic and off-highway applications is 0.05 wt % S. For class 1and 2 diesels, which will be used for transportation buses and cars in urban areas, the limits will be respectively 0.001 and 0.03 wt % S. This is a serious challenge. Are the present-day catalysts adequate for reducing the sulfur content to such levels? Can modeling and simulation contribute to the new developments? What is the level of sophistication that has to be introduced in the reactor model? The hydrodynamics in HDS reactors is not well understood. Calculating accurate thermodynamic properties for such complex mixtures is another problem. Kinetics is a major element of reactor modeling and simulation. The literature on the conversion of key componentsis rather abundant, but the information is seldom coordinated. Most of the rate equations published to date are simple first order disappearance kinetics. The rate of HDS of the oil fraction is then generally lumped into a single second order reaction, to account for the large variation of the reaction rates of the various feed components. The developmentof deep HDS processes imposed by the new specifications will definitely require more accurate kinetics. The present paper deals with various aspects of the simulation of an adiabatic multiphase reactor for diesel desulfurization and with the derivation of a set of adequate kinetic equations for the conversion of a at the Symposium on Catalytic Reaction Engineering for Environmentally Benign Processes at the San Diego ACS Meeting, March 13-18, 1994. t Presented
complex mixture of sulfur- and nitrogen-containing components.
Scrutiny of Reactor Modeling Aspects Reactor Model Equations. The hydrodesulfurization of diesel fractions is performed in a multiphase fxed bed reactor. Three phases are present in the reactor: the fmed bed of porous catalyst particles, a vapor phase, and a liquid phase flowing cocurrently downward. The liquid feed is usually a blend of straight-run gas oil and light cycle oil from a FCC or coker unit. The sulfur content of the liquid feed is typically 0.5-2.0 wt %. It is reduced by the hydrotreatment to 0.2-0.05 wt %. The gas phase consists mainly of hydrogen, hydrogen sulfide, ammonia, and vaporized diesel components. The liquid phase consists of the gasoil components, including the sulfur- and nitrogencontaining components and dissolved gases like hydrogen, hydrogen sulfide, ammonia, and light hydrocarbons. In commercial applications trickle and pulse flow are the most likely flow regimes. Trickle flow features are a continuous gas phase and a dispersed liquid phase flowing as a laminar film or as rivulets over the particles. The pulse flow regime is obtained a t higher liquid and gas throughputs. According to Wammes et al. (1990) the pulse flow regime is not attained at high pressures and realistic liquid flow rates, if the molecular weight of the gas phase is of the order of that of nitrogen. In a hydroprocessing unit operating, for example, at 310 "C and 50 bar, the molecular weight of the gas phase is approximately 20 g/mol. Therefore, strong indications exist that trickle flow is the dominating flow regime. Besides, it is commonly accepted that in commercial hydroprocessing reactors all the particles are completely wetted when the gas and liquid are adequately distributed (Shah, 1979). The model developed in the following pages is a one-dimensional heterogeneous model with both the gas and liquid phase in plug flow (Froment and Bisschof, 1990). The steady state continuity equation for a component i of the gas phase can be written as
1
dF,G
2
szdz
atz=O
= 1,..., N
(1)
F. =F". rG LG
The liquid phase and the gas phase are not necessarily
0888-5885I94l2633-2975$04.50/0 0 1994 American Chemical Society
2976 Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994
in equilibrium. The molar flow rate of a component i in the gas phase ( F ~ Gcan ) only change by transfer to or from the liquid phase, since the gas phase only contacts the liquid phase. The interphase mass transfer rate is described in terms of the two-film model:
rG
N i = K -Hi
C.
with
’,)
1 1 -=-+kGHi
KL
1 kL
(2)
The interphase mass transfer flux is calculated for each component of the mixture. Shah et al. (1978) considered deviations from plug flow in the liquid phase not to be important in most commercial trickle bed reactors, in contrast with laboratory trickle flow reactors. The criterion of Mears (1971) for isothermal trickle flow reactors was used to estimate the importance of axial dispersion in the liquid phase. Mears’ criterion sets a bed length below which axial dispersion effects may be significant. This minimum bed length is given by 2 .
min
2 0 d p CiL0 =In pea,
ce
(3)
The Peclet number has been correlated to the liquid phase Reynolds number, under trickle flow conditions, by Hochman and Effron (1969). For typical conditions in a HDS reactor, M e a d criterion is well satisfied, so that dispersion effects in the liquid phase do not have to be accounted for as far as predicted exit values are concerned. The influence of liquid wall flow can also be neglected, since the ratio of reactor diameter to particle diameter is greater than 1000. The liquid phase contacts the gas phase and the solid phase, which is reflected in the continuity equations for the reacting species by two terms, accounting respectively for the liquid-solid and the gas-liquid interphase mass transfer:
1 @iL ’ k,uv”(C;s- CiL) K a Hi Qdz
+
The effective diffusivity accounts for the porosity of the catalyst particle and for the tortuosity of the pore network. No heat exchange with the surroundings of the reactor has to be accounted for, since hydroprocessing reactors are operated adiabatically. Three energy equations are considered, one for each phase. The catalyst particles are assumed to be isothermal. The energy transfer between the gas phase and the liquid phase is made up of a conductive heat flux and a convective contribution due to the transport of enthalpy by the interphase mass transfer. The energy equation for the gas phase is
N
TG = TGo
atz=O
The partial molar enthalpy of component i at the gasliquid interface is considered to be the gas phase partial molar enthalpy at the interface temperature TI,since the heat of vaporization and condensation is accounted for in the liquid phase equation. For the liquid-solid heat transfer a convective transfer term is considered. The energy equation for the liquid phase is written
dTL
u,LeLC,L
-= hpv”(Ts-
dz
The model accounts for concentration gradients inside the catalyst particles, where the reactions take place. The pores are considered to be completely filled with liquid. The continuity equation for component i inside a spherical catalyst is written
dP
=-
2
TL = TLo
atz=O
and for the solid phase is
e&
rljrj(C~,,...,TS)(-Mj) = hp,”(T,
N,
- TL)
(9)
j=l
The two-phase pressure drop is expressed in terms of the single-phase flow pressure drops (BG and BL), calculated from the Ergun equation (Larkins et al., 1961). (10)
atz=O
K,u,’’(C~~ - CiL)=
+ cPiL(TI- TL)) (8)
i=l
b= 0.666
at
TL) +
N
CN,a;(Mi,
where
at[=O
-
N,
i = 1, ...,N (4)
with boundary conditions:
TL) + hLa;(TI
+
0.416 (logl,,(m))2
Pt =PtO
Rate Equations. In the example to follow, benzothiophene, dihydrobenzothiophene,dibenzothiophene, and 4,6-dimethyldibenzothiophenewere chosen as sulfur components. A set of rate equations, describing the hydrodesulfurization of benzothiophene in the liquid phase by a CoMo catalyst supported on alumina, was developed by Pille and Froment (1994). Benzothiophene (BT)is desulfurized in ethylbenzene in two ways, direct hydrogenolysis and hydrogenation t o dihydrobenzothiophene (DHBT), followed by hydrogenolysis to ethyl-
Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 2977 benzene (EB). The rate equations are
A1203 catalyst is described by the kinetic equation of Miller and Hineman (1984). The rate equations mentioned above do not account for the competitive adsorption of other sulfur components or hydrocarbons.
Estimation of the Physical Properties
At 533 K, for example, the parameters take on the following values:
-3
The rate equations for dibenzothiophene hydrodesulfurization of Broderick and Gates (1981) were modified into the following rate equation for the direct hydrogenolysis:
with
k , = 7.84 x kDgT,o
lo8 exp(-158000/RT) = 5.31 m3/kmoi
kmol/(kg,,, s)
KH,,, = 4.02 m 3 h O i KH,s,o= 1.72
and for the hydrogenation of dibenzothiophene,
with
k , = 4.17 x
lo3 exp(-99100/RT)
m3/(kgcats) K D g T , r = 3.97 x 10 exp(-14100/RT) m3/kmol The hydrodesulfurization rate of 4,6-dimethyldibenzothiophene was derived from the desulfurization rate of dibenzothiophene by weighing the latter with the ratio of the pseudo first order desulfurization rate coefficients of 4,6-dimethyldibenzothiopheneand dibenzothiophene. This ratio is 1/15 a t 573 K (Houalla et al., 1980). Quinoline was chosen as nitrogen component. The hydrodenitrogenation reaction of quinoline (Q) t o npropylcyclohexane (PCH) in the liquid phase on a CoMo/
The critical temperature, critical pressure, heat of formation, Gibbs free energy of formation, and ideal gas heat capacity, which are required for the calculation of various physical data, were taken from the literature. Group contribution methods were used when specific values were not available. The acentric factor was calculated by means of the Lee-Kesler method (Lee and Kesler, 1975). Various data like the heats of reaction in the liquid phase, the heats of vaporization, the heat capacity of the gas phase and the liquid phase, the equilibrium constants of the reactions in the liquid phase, the densities of gas phase and liquid phase, and the Henry coeffkients were obtained from calculations based on the Peng-Robinson equation of state. For hydrogen and hydrogen sulfide in the liquid phase binary interaction parameters were used in the PengRobinson equation of state. These were obtained respectively from Moysan et al. (1983) and Graboski and Daubert (1978b). The viscosity of the gas phase and the liquid phase was determined with the method of Brulez and Starling (1984). The thermal conductivity of both phases was calculated using the method of Chung et al. (1988). The diffusion coefficients were obtained from the Wilke-Chang method (Wilke and Chang, 1955). The mass transfer coefficient k ~ a ;a t the liquid side of the gas-liquid interface was derived from a correlation presented by Sat0 (19721, and the gas side mass transfer coefficient kw,' at that interface was derived from Reiss' correlation (1967). The liquid-solid mass transfer coefficient was obtained from the correlation of Van Krevelen and Krekels (1948). The heat transfer coefficients were derived from the mass transfer coefficients using the Chilton-Colburn analogy (1934).
Integration Method The integration in the axial direction was performed using a fourth order Runge-Kutta routine with variable step size. The intraparticle integration was carried out with an orthogonal spline collocation method. The temperature of the solid phase and the surface concentrations are unknowns, since resistance to mass and heat transfer is accounted for at the catalyst surface. An initial guess has to be made to perform the intraparticle integration. The initial guesses are then updated, using a Newton-Raphson method, until the required accuracy is obtained.
Results of the Simulation and Discussion In the example to follow a synthetic feed mixture with diesel characteristics was chosen, consisting of paraffins, naphthenes, aromatics, sulfur, and nitrogen components. The sulfur content of the feed, 1.82 wt %, had to be reduced to 0.05 wt %. Benzothiophene, dihydrobenzothiophene, dibenzothiophene, and 4,6-dimethyldibenzothiophene were taken as sulfur-containing components and quinoline as the nitrogen-containing component.
2978 Ind. Eng. Chem. Res., Vol. 33,No. 12,1994 Table 1. Composition of the Synthetic Diesel Type Feed feed components composition (mol %) total: 10.4 sulfur components 7.22 Benzothiophene 2.33 Dibenzothiophene 4,6-Dimethyldibenzothiophene 0.831 0.0281 Dihydrobenzothiophene nitrogen component total: 1.53 Quinoline 1.53 paraffins total: 30.0 1.13 n-Clz 1.23 n-Cls 1.79 n-Clc 5.71 n-Cx 5.56 n-Cx 5.07 n-Cu 4.08 n-Cls 3.02 n-C19 2.41 n-Czo naphthenes total: 31.0 0.153 n-propylcyclohexane 17.3 n-nonylcyclohexane 13.5 cis-decalin aromatics total 27.0 ethylbenzene 0.0282 n-nonylbenzene 6.14 indene 2.63 indane 5.92 naphthalene 7.27 anthracene 2.72 biphenyl 2.32 cyclohexylbenzene 3.42 10-3
gas. Thermodynamic equilibrium was assumed between the gas and the liquid phase at the reactor inlet. The reactor geometry, catalyst properties and inlet conditions are given below as follows. Reactor geometry: diameter, 2.82m; length, 7.625m. Catalyst properties: equivalent diameter of a catalyst particle, 1.3 x m; porosity of the catalyst, 0.6 mP/ mp3;bulk density of the bed, 710 kgcaJmr3;density of catalyst, 1420 kg,,Jmp3. Inlet conditions: inlet temperature, gas and liquid phase 590 K inlet pressure, 5000 kPa; WIFs, 0.92kgcat m ~liquid t ~ flow rate, h/(mol of S); LHSV,3.16 m ~ ~ / ( h); 1550 tons/day (1805 m3/day); gas flow rate, 116 tons/ day (314000 m3 (NTP)/day); total sulfur content, 1.82 wt %; nitrogen content, 0.117wt %. The components of the diesel-type mixture are distributed over both the liquid phase and the gas phase. The components in the gas phase are also considered for the calculation of the sulfur content of the dieseltype mixture, while hydrogen sulfide present in the gas or liquid phase is not. The evolution of the sulfur content of the diesel-type mixture through the reactor is shown in Figure 1. Benzothiophene reacts faster than dibenzothiophene. The slowest reaction is the removal of the 4,6-dimethyldibenzothiophene. The major fraction of the sulfur removal takes place in the initial part of the reactor, which is reflected in a significant temperature increase. The maximum difference between gas and liquid phase temperature amounts to 5 "C close to the inlet and drops below 0.1 "C at the reactor outlet. The temperature increase between inlet and exit amounts to 27 "C. It should be noted that the hydrogenation reactions of aromatic components like naphthalene and anthracene were not considered. The temperature and concentration differences between the liquid bulk phase and the catalyst surface were found to be negligible. The evolution of the molar flux of hydrogen in the liquid and in the gas phase are shown in Figure 2. The molar flux of hydrogen in the liquid phase that would be in equilibrium with the molar flux of hydrogen in the gas phase is also represented. The liquid phase in the
+
Table 2. Composition of the Treat Gas (Recycle Make-up Gas) composition component (mole fraction) hydrogen 0.618 0.0133 hydrogen sulfide nitrogen 0.0681 ammonia 0.00219 methane 0.255 ethane 0.0431
The composition of the diesel-type feed is given in Table 1, and the composition of the treat gas in Table 2. This treat gas consists of make-up gas and recycle
mole fraction r S 0.08
P P W
-
- 0.07
6
I
1
- Total sulfur content
-
0.06
-
0.05
4-..-. - 4,6Dimethyldibenzothbphena - 0.04 5- Dihydrobenzothlophene 6Mole fraction YS in the gas phase
-
o . ~
,
- 0.02
0
2
0.01
- 0
4
6
Axial position [m] Figure 1. Axial profile of the sulfur content of the diesel-type mixture and of the mole fraction of H2S in the gas phase.
Ind. Eng. Chem. Res., Vol. 33, No. 12,1994 2979
1 2 14
...... '. .......... ........
1
'
................. ..... .....................2
3
3
-(FH)
Molar flux of hydrogen in the liquid phase
. (Q
Molar flux of hydrogen in the liquid phase if saturated with hydrogen
' '
-
---- (qGMolar flux of hydrogen in the gas phase
0.75
..........................................................
12
0.5
10
0.25
------_____ ------ --__.___
4 -
8
0
1
I
I
2
4
6
Axial position [rn]
Figure 2. Axial molar flux profile of hydrogen in both phases. mole fraction %S
PPMS
0.08 18,000
16,000 - 0.06
14,000
12,000
2 Without resistanceto gas-liquid mass transfer ( liquid saturated with hydrogen )
10,000 8,000
- 0.03
6,000 4,000
2,000 0
I
0
I
2
0
6
4
Axial position [rn]
Figure 3. Axial profile of the sulfur content of the diesel-type mixture and the mole fraction of HzS in the gas phase.
initial part of the reactor is far from being saturated with hydrogen. The axial profiles of the sulfur content of the diesel-type mixture in both cases (liquid saturated with hydrogen and no saturation) are presented in Figure 3. The conversion of the sulfur components is lower when the resistance to gas-liquid mass transfer is considered, Since the hydrodesulfiuization rates are favored by higher hydrogen concentrations. In Figure 4 the sulfur content at the reactor exit is shown as a function of the inlet temperature and pressure. Additional catalyst volume, more severe reaction conditions, or more active catalysts are required if the future specifications have to be satisfied. The removal of nitrogen components is slower than the sulfur removal, as shown in Figure 5.
The intraparticle diffusion limitations are reflected in the values of the effectiveness factors given in Table 3. These are arrived from the calculated intraparticle gradients.
Kinetic Modeling of the Hybgenolysis and Hydrogenation ofDibenzothiophene and Alkyl-SubstitutedDibenzothiophene Detailed kinetic equations for the conversion of benzothiophene (BT) and dibenzothiophene (DBT) were mentioned in the section ,on multiphase reactor simulation. They distinguished between a-sites, on which the hydrogenolysis reactions take place and z-sites, on which the hydrogenations take place. They account for
2980 Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 ppmwS at the reactor exit 1,800
I
I
I
4,500
6,000
5.500
400 4,000
Ida-
6,000
[kpel
Figure 4. Sulfur content of the diesel-type mixture at the reactor exit as a function of temperature and pressure. Initial sulfur content: 1.82 wt %. Mole fraction NH:,
PpmwN 1,180
0.003
1,160
O.OM8
1,140
0.0026
1,120
0.0024
1,100
0.-
...1,080
\
2
0.002
e .
1 - Nitrogen content of the diesel type mixture 2 Mole fraction of NHI in the gas phase
,/ ,a’
1,m . e .
1,040
4
2
6
0.0018
0.0016
Axial position [m]
Figure 5. Axial profile of the nitrogen content of the diesel-type mixture and of the mole fraction of NH3 in the gas phase.
competitive adsorption of H2, H2S, and the other reacting species on both the 0- and t-sites. Two rate equations were used by Broderick and Gates (1981) for the conversion of DBT, containing a total of six kinetic and adsorption coefficients. What if the oil fraction contains not only DBT, but all mono-, di-, and trisubstituted DBT? Is it possible to maintain a Hougen-Watson approach accounting for the adsorption of the species in that case? It is possible to account for the complete reaction network of each sulfur-containing feed component? The problem will be illustrated for the hydrogenolysis and hydrogenation of DBT and the methyl-substituted DBT. Reaction Networks and Kinetic Modeling at the Molecular Level. The complete reaction network for
dibenzothiophene, for 4-methyldibenzothiophene,for 4,6-dimethyldibenzothiophene, for 1,6-dimethyldibenzothiophene, and for 1,2,6-trimethyldibenzothiophene are shown in Figures 6, 7, 8, 9, and 10, respectively. There are 215 rate equations for hydrogenolysis and 282 rate equations for the hydrogenations in the reaction networks of DBT and mono-, di-, and trisubstituted DBT. As shown in Table 4, these rate equations contain 497 kinetic coefficients and 636 adsorption equilibrium constants. For each substituted DBT (s-DBT), one adsorption equilibrium constant on the a-sites, K D B Tand , ~ , one rate coefficient for the hydrogenolysis into biphenyl, ~ D B T , ~ , have to be considered. This leads to 44 different adsorption equilibrium constants for substituted DBT and 44 rate coefficients for substituted DBT hydro-
Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 2981 Table 3. Values of Effectiveness Factors for the Various Reactionsa axial position (m)
reaction DBT-BPH DBT-CHB DMDBT-DMBPH DMDBT-DMCHB BT-DHBT BT-EB DHBT-EB Q-PB
0 0.23 0.55 0.36 0.56 0.31 0.37 9.9 1
1
0.91 0.93 0.92 0.94 0.44 0.44 0.63 1
2 0.94 0.94 0.97 0.98
1
DBT, dibenzothiophene; BPH, biphenyl; CHB, cyclohexylbenDMBPH, 4,4'-dizene; DMDBT, 4,6-dimethyldibenzothiophene; methylbiphenyl; DMCHB, 4,6-dimethylcyclohexylbenzene;BT, benzothiophene; DHBT, dihydrobenzothiophene; EB, ethylbenzene; Q, quinoline; PB, propylbenzene.
THDBT
Figure 7. &action network for HDS of 4-methyldibenzothiophene.
CHB
it BCH
Figure 6. Reaction network for HDS of dibenzothiophene.
genolysis. Hydrogenolysis of the 44 substituted DBT leads to only 29 different substituted biphenyl molecules, due to rotation of the phenyl rings in biphenyl with respect to each other (Streitwieser and Heathcock, 1985). Consequently, 29 adsorption equilibrium constants for substituted biphenyl (s-BPH) on the 0-sites, KBPH,,,,have to be retained. For each substituted DBT, one adsorption equilibrium is required, which leads constant on the t-sites, KDBT,~, to 44 different adsorption equilibrium constants for substituted DBT on the t-sites. Hydrogenation of each of the 4 monosubstituted DBT, of each of the 12 nonsymmetrical disubstituted DBT, and of each of the 24 trisubstituted DBT leads to two different substituted tetrahydrodibenzothiophene(s-THDBT)molecules. Hydrogenation of each of the four symmetrical disubstituted DBT results in one type of tetrahydrodibenzothiophene molecules. Consequently, 84 (4 x 2 12 x 2 24 x 2 4) rate coefficients for the hydrogenation of substituted DBT, ~ D B T , ~and , 84 adsorption equilib-
+
+
+
it Figure 8. Reaction network for HDS of 4,6-dimethyldibenzothiophene.
rium constants for the resulting product substituted tetrahydrodibenzothiophene,KTHDBT,~, have to be evaluated. Also, 84 rate coefficients for the further hydrogenation of substituted tetrahydrodibenzothiophene into substituted hexahydrodibenzothiophene (s-HHDBT),k T m B T , r , as well as 84 adsorption equilibrium constants for the
2982 Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 Table 4. Total Number of Parameters for the Hydrosulfurization of Dibenzothiophene and Methyl-Substituted Dibenzothiophene: Molecular Approach a-Sites 44 1 adsorption (s)-DBT KDBT,dm;n;P) hydrogenolysis (s)-DBT kDBT,dm;nP) 44 + 1 adsorption (s)-BPH KBPH,dm;nP) 29 1 adsorption (s)-THDBT KmBT,dm;np) 84 + 1 hydrogenolysis (S)-THDBT kTHDBT,dm;n;p) 84 4- 1 adsorption (s)-HHDBT K"DBT,dm;n;P) 84 f 1 hydrogenolysis (s)-"DBT kmDBT,dm;n;p) 84 + 1 adsorption (s)-CHB Kcm,dm;n;p) 55 + 1 adsorption HZ KHZP 1 adsorption H2S KH~s,~ 1 5-Sites 44 1 adsorption (s)-DBT KDBT,,(m;nP) hydrogenation (s)-DBT kDBT,r(m 84 1 adsorption (SI-THDBT KTHDBT,r(m;n;P) 84 + 1 hydrogenation (s)-THDBT kTHDBT,r(m;n;p) 84 + 1 adsorption (s)-HHDBT KHHDBT,r(m;n;p) 84 + 1 adsorption (s)-BPH KBpH,r(m;n;PI 29 + 1 hydrogenatin (s)-BPH kBw,r(m;nP) 55 + 1 adsorption (s)-CHB KCHB,r(m;n;P) 55 1 hydrogenation (s)-CHB kcm,,(m;n;p) 55 + 1 adsorption (s)-BCH KBcH,,(m;n;p) 29 + 1 adsorption Hz KH2.r 1 adsorption H2S KH~s,~ 1
+ +
+ +
+
total
Figure 9. Reaction network for HDS of 1,6-dimethyldibenzothiophene .
1133
For each of the 84 substituted tetrahydrodibenzothiophenes, one adsorption equilibrium constant on and one rate coefficient for the the a-sites, KTHDBT,~, hydrogenolysis into substituted cyclohexylbenzene, KTHDBT,~, have t o be introduced. Hydrogenolysis of the 84 substituted tetrahydrodibenzothiophenes leads to only 55 different substituted cyclohexylbenzene molecules, due to rotation of the phenyl and cyclohexyl rings in cyclohexylbenzene with respect to each other. Consequently, 55 adsorption equilibrium constants for substituted cyclohexylbenzene (s-CHB) on the a-sites, K C H B ,have ~ , to be retained. Also, for each of the 84 substituted hexahydrodibenzothiophenes, one adsorpand tion equilibrium constant on the a-sites, KHHDBT,~, one rate coefficient for the hydrogenolysis into substituted cyclohexylbenzene, ~ H H D B T , ~have , to be considered. For each of the 29 substituted biphenyls, one adsorption equilibrium constant on the r-sites, KBPH,~, has t o be determined. Hydrogenation of each of the 3 monosubstituted biphenyls, of each of the 8 nonsymmetrical disubstituted biphenyls, and of each of the 15 trisubstituted biphenyls gives two different substituted cyclohexylbenzene molecules. Hydrogenation of each of the three symmetrical disubstituted biphenyls gives one type of substituted cyclohexylbenzene molecules. Consequently, 55 (3 x 2 8 x 2 15 x 2 3) rate coefficients for the hydrogenation of substituted biphenyl into substituted cyclohexylbenzene, KBPH,~, and 55 adsorption equilibrium constants for the product subare stituted cyclohexylbenzene on the r-sites, KcHB,~, introduced. For each of the 55 substituted cyclohexylbenzenes, one rate coefficient for the hydrogenation into substituted bicyclohexyl (s-BCH), K C H B , ~ , has to be considered. Hydrogenation of the 55 different substituted cyclohexylbenzenes results in only 29 different substituted bicyclohexyls, so that 29 adsorption equilibrium constants for substituted bicyclohexyl, KBCH,~, have to be retained. In addition, for nonsubstituted DBT, one of each of the above parameters has to be evaluated. Also adsorp-
+
Figure 10. Reaction network for HDS of 1,2,64rimethyldibenzothiophene.
product substituted hexahydrodibenzothiophene, KHHDBT,~, have to be considered.
+
+
Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 2983 Table 5. Hydrogenolysis Rate Coefficients of Thiophene,' Benzothiophene,' and Selected Methyl-SubstitutedDibenzothiophened Reactant
Structure
Pseudo-firstorder rate constant 3 m 1 (kgcat s)
thiophene
1.38 x 10-
benzothiophene
8.11 X I O - ~
dibenzothiophene
7.38 x 10-
Assumption 2: Methyl groups at a distance from the sulfur atom beyond the a-position only exert electronic effects on the adsorption. Assumption 3: Only methyl groups on the aromatic ring exert an electronic influence. Assumption 4: Methyl groups in the 4- and 6-positions also sterically hinder the adsorption. Assumption 6: Once a molecule is adsorbed, only the electronic effects of the methyl groups are of importance. The adsorption equilibrium constants for (substituted) DBT ((s)-DBT)can then be expressed as follows: DBT 1-MeDBT 2-MeDBT
2,Sdlmethyldlbenzothlophene
6.72 x 10-
3,7-dimethyl-
3.53 x 10-
4-MeDBT
6.64~10-~
1,7-DiMeDBT
3-MeDBT
dibenzothlophene emethyldibenzothlophene
1,8-DiMeDBT 1,g-DiMeDBT
4,Mimethyl-
4.92~10.~
dibenzothiophene
2,7-DiMeDBT 2,8-DiMeDBT
a Reaction conditions: 0.25 mol % reactant concentration, 300 "C, 71 atm, CoMo/AlzOs catalyst (Nag et al., 1979). Reaction conditions: 0.15 mol % reactant concentration, 300 "C, 102 atm, CoMo/AlzOs catalyst (Houalla et al., 1980).
tion equilibrium constants for H2 and H2S on the a-sites and the mites have to be determined. This leads t o a total of 1133 parameters. A kinetic model containing 1133 parameters is clearly unrealistic. A different approach is required to reduce this number. Kinetic Modeling Based upon Structural Contributions. What is proposed in this section is to go beyond the molecular level in the modeling of the reaction rates. For reactions involving substituted components, the rates are related whenever possible t o those of a nonsubstituted reference component in terms of the influence of the substituents on the adsorption equilibrium constants and the rate coefficients. To get some feeling of the influence of the substituents, Table 5 presents first order rate coefficients for the hydrogenolysis of various sulfur-containingcomponents in multiphase operation, free of diffusional limitations (Nag et al., 1979; Houalla et al., 1980). It may be concluded that the position of the methyl substitutents is more important than their number. This was confirmed by the data of Kilanowski et al. (1978). Effects of Methyl Substituents on the Hydrogenolysis Reactions. The hydrogenolysis reactions involve vertical adsorption of the molecules through the S-atom on the a-sites (Houalla et al., 1978; Kabe et al., 1993). The assumptions which permit the reduction of the number of parameters for the hydrogenolysis steps along the structural contributions approach are as follows. Assumption 1: In the adsorption electronic and steric effects are to be considered separately.
3,7-DiMeDBT 1,6-DiMeDBT 2,6-DiMeDBT 3,6-DiMeDBT 4,6-DiMeDBT 1,2-DiMeDBT 1,3-DiMeDBT 1,4-DiMeDBT 2,3-DiMeDBT 2,4-DiMeDBT 3,4-DiMeDBT
2984 Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994
1,2,8-TriMeDBT
with
KELDBT(m;n;p) f ~KE DBT(m;O;O) L 1,2,g-TriMeDBT
K E L ~ ;n ~ ;o) ~ = ( K~ E L ~ ~;PI~ ( ~
;O
1,3,6-TriMeDBT 1,3,7-TriMeDBT 1,3,8-TriMeDBT
and KsTDBT(4;0;0) = KsTDBT(m;4;0) = KsTDBT(m;4;p) = KsTDBT(m ;0;6) = K s ~ ~;72~;6)~ ( m
+
KsTDBT(4;0;6) = KsTDBT(m;4;6) f KS,DBT(4;0;0) KsTDBT(m;O;6) with
1,3,9-TriMeDBT 1,4,6-TriMeDBT 1,4,7-TriMeDBT 1,4,8-TriMeDBT 1,4,9-TriMeDBT 2,3,6-TriMeDBT 2,3,7-TriMeDBT 2,3,8-TriMeDBT 2,3,9-TriMeDBT 2,4,6-TriMeDBT 2,4,7-TriMeDBT 2,4,8-TriMeDBT 2,4,9-TriMeDBT 3,4,6-TriMeDBT 3,4,7-TriMeDBT
4, m =e 4 , p f 6 The adsorption equilibrium constants for the various substituted DBT are related to that of DBT through five multiplying factors. Instead of 45 different parameters in the molecular approach, only 6 parameters appear in the approach based upon structural contributions: KDBT u, K E L ~ ~ ~ ( ~ ; K OE ; OL) ~ , ~~(~ K; ~~ ~ ~; ~O~)(,m ; n ; p ) , KsTDBT(4; 0;0), and KsFBT(4; 0;6). The rate coefficient for the hydrogenolysis of (substituted) DBT into (substituted) biphenyl ((s)-BPH) depends only on the number of methyl groups. There are four rate coefficients: KDBT,AO;O;O) for DBT, ~DBT,&;O;O) = ~DBT,~(O;O;O) K E L ~ ~ ~ ( ~ ; O ; for O ) mono-Me-DBT, k~~~,a(m;= n ; ~DBT,~(O;O;O) O) k~~~~~(m for; di-men;O) DBT, and k ~ ~ ~ , , , ( m ;=n~DBT,~(O;O;O) ;p) k ~ ~ ~ ~ ~ (for m;n;p) tri-Me-DBT with k ~ ~ ~ ~ ~ ( fm ~; ~n E; Lp ~) ~ ~ ( and ~ ; O ; O ) ~ D B T , A ~ ; ~=; O~)D B T , A ~ ; O ; ~ ) . The adsorption equilibrium constant for the product (substituted) biphenyl on the a-sites is assumed to depend only on the total number of methyl groups: KB~H,,,(O;O;O) for biphenyl, K ~ p ~ , , , ( m ; 0=; 0K~p~,J0;0;0) ) KEL+&~H(~;O;O) for monomethylbiphenyl, K~p~,o(m;n;O) = KBPH,AO;O;O) K E L + S T ~ ' ~ ( ~for ; ~dimethylbiphenyl, ;O) K E L + S T ~ ~ ~for( ~ ; ~ ; P ) and K ~ p ~ , o ( m ; n= ; pKBPH,,,(O;O;O) ) = K~p~,dm;O;p). trimethylbiphenyl with K~p~,o(m;n;O) Tetrahydrodibenzothiophenecontains a benzene ring and a thiophenic ring. For the hydrogenolysis of substituted tetrahydrodibenzothiophene(s-THDBT), it can be assumed that methyl groups in the 7-, 8-, and 9-positions have no influence on the adsorption equilibrium constant. Methyl groups in the 1-, 2-, and 3-positions only have an electronic influence on the adsorption. Methyl groups in the 6-position only sterically hinder the adsorption through the sulfur atom. Methyl groups in the 4-position have an influence on the adsorption resulting from both electronic effects and steric hindrance. The steric hindrance of a methyl group in the 4-position, i.e., on the phenyl moiety, is not the same as that of a methyl group in the 6-position, which is on a partially hydrogenated phenyl moiety. Also,
n
K,,THDBT(~.O.O) 9 , = K STTHDBT(m;4;0) = KSTTHDBT(4;O;p) = KsTTHDBT(m;4p) = THDBT
KST
3,4,8-TriMeDBT 3,4,9-TriMeDBT
(4;np)
withp
f
6 and n # 6
KsTTmBT(O;O;6)= KsTTHDBT(O*6.p) ,, = KS,THDBT(m;O;6) = KsTTHDBT(m;n;6) = ~ ~ ~ ~ ~ ~ ~with ~ m( f m4 and ; 6n t p 4) = K STTHDBT(m;4;6) = KSTTHDBT(4;6;p) KSTTHDBT(4.0-6) 9 ,
Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 2986 HHDBT KEL (m;n;O)= KELHHDBT(m;np)
and KELTHDBT(m;O;O) = KEL THDBT(m;O;p) with m = 1 , 2 , 3, 4 a n d p = 6, 7 , 8 , 9 K E , T ~ ~ ~ ~ ( T T=z ;KEL o ; oTHDBT ) (m;n;p) with m = 1 , 2 , 3 , 4 ; n = 6 , 7 , 8 a n d p > n THDBT THDBT KEL (m;n;O) = K E L (m;n;p)
with m = 1 , 2 , 3;p = 6, 7, 8 , 9 and n > m The approach reduces the number of parameters from 85 t o 6: KwBT,,,, K E L ~ ~ ~ ~ ~ (KELTHDBT(m;n;O), ~;O;O), K s ~ ~ ~ ~ ~ ( 4K; 0~ ;T0~) ~ , ~ ~ ~and ( OK; sO~ ~; "~~)~,( 4 ; 0 ; 6 ) . For the rate coefficient for the hydrogenolysis of (substituted) tetrahydrodibenzothiophene into (substituted) cyclohexylbenzene ((s)-CHB),only the number of methyl groups on the aromatic ring has to be considO ) ~THDBT,u(O;O;O) ered: kTHDBT,u(O;O;O),~ T H D B T , ~ ~ ; O ; = ~ E L ~ ~ ~ ~ ( ~ and ; O ;~ TO H) D, B T , A ~ ; ~ ; = O ) KTHDBT,AO;O;O) k~~l"D"(m;n;O). The same has t o be done for the hydrogenolysis of (substituted) hexahydrodibenzothiophene ((s)-HHDBT), which has only one benzene ring. Only methyl substituents on this ring are considered to have an electronic influence. Consequently, for the hydrogenolysis of substituted hexahydrodibenzothiophene, it may be assumed that methyl groups in the 7-, 8-, and 9-positions have no influence on the adsorption equilibrium constant for hexahydrodibenzothiophene. Methyl groups in the 1-, 2-, and 3-positions only have an electronic influence on the adsorption. Methyl groups in the 6-position only sterically hinder the adsorption through the sulfur atom. Methyl groups in the 4-position have an influence on the adsorption, due to electronic effects as well as steric hindrance. Again, the steric hindrance of a methyl group in the 4-position, i.e., on a phenyl moiety, is not the same as that of a methyl group in the 6-position which is on a cyclohexyl moiety. Also, KSTHHDBT(4;0;0) = KSTHHDBT(m.4.0) 7 , = HHDBT "DBT(m.4.P) = KST (4;');~)= KST 9 , HHDBT
KST
(4;np)
withpg6andnt6
KSTHHDBT(0;O;6) = K s T " ~ ~ ~ (9 O, * ~=* P )
K s T ~m ;0;6) ~ ~= ~K s( T " ~ ~m;n;6) ~( = KSTHHDBT(m;6;p)with m t 4 and n t 4 KST
"DBT(4*0-6) 9 , = K ST"DBT(m;4;6) = Ks~"~~~(4;6;p)
+
KSTHHDBT(4;0;6) * KSTHHDBT(4;0;0) KSTHHDBT(0.0*6) ,, and KELHHDBT(m;O;O) = KEL HHDBT(m;O;p) with m = 1 , 2 , 3 , 4 a n d p = 6, 7, 8 , 9 KELHHDBT(m;0;o) = KEL THDBT(m;n;p) with m = 1 , 2 , 3 , 4 ; n = 6, 7 , 8 a n d p > n
with m = 1 , 2 , 3 ; p = 6, 7 , 8 , 9 and n m Instead of 85 parameters, only 6 parameters have to KHHDBT,~,K E L " ~ ~ ~ ( ~ ; O ; O ) , be determined: KELHHDBT(m;n; 01, 4;0;01, 0;0;61, and KsFBT(4;0;6). The rate coefficient for the hydrogenolysis of (substituted) hexahydrodibenzothiophene into (substituted) cyclohexylbenzene depends only on the number of methyl groups on the aromatic ring: ~HHDBT,~O;O;O), ~ H H D B T , ~ ~ ; O ; O=) KHHDBT,~(O;O;O)~ E L ~ ~ ~ ~ ( ~ and ; O ; O ) , ~ H H D B T , ~ ;= ~ ;~HHDBT,JO;O;O) ~ ) k~~~~~~(m;n;O). The adsorption constant for (substituted) cyclohexylbenzene on the m i t e s , KcHB,,,, depends on the number of methyl groups on the phenyl moiety and the cyclohexyl moiety. Consequently, eight different parameters have to be retained. In total there are 215 hydrogenolysis rate equations with 42 parameters which need to be determined from experimental data. Effects of Methyl Substituents on the Hydrogenations. Hydrogenation reactions involve flat adsorption of the molecules on the z-sites of the catalyst (Houalla et al., 1978; Kilanowski et al., 1978; Kabe et al., 1993). This suggests the following assumption: Assumption 6: Only the number of substituents and not their position relative to the sulfur atom has to be taken into account for the adsorption on the r-sites and for the reaction between adsorbed species. Assumption 6 leads t o four adsorption equilibrium constants for the (substituted) DBT ((SI-DBT): KDBT,,(O;O;O) for DBT itself, KDBT,,(~;O;O) = KDBT,,(O;O;O) K E L + s T ~ ~ ~ ( ~for ; O mono-Me-DBT, ;O) KDBT,r(m;n;O) = KDBTJO;O;O)K E L + s T ~ ~ ~ (for ~ ; ~di-me-DBT, ;O) and K D B T , , ~ ;=~KDBT,,(O;O;O) ;~) K E L + s T ~ ~for ~ (tri~;~;~) Me-DBT. Assumption 6 also leads to four rate coefficients for the hydrogenation of (substituted)DBT into (substituted) tetrahydrodibenzothiophene ((SI-THDBT: ~DBT,~(O;O;O)for DBT itself, k ~ ~ ~ , , ( m ;=o kDBT,r(O;O;O) ;o) kELDBT(m;O;O)for mono-Me-DBT, ~ D B T , , ( ~ ; ~ ; O = ) kDBT,r(O;O;O) k ~ ~ ~ ~ ~ ( m for ; n ; di-Me-DBT, O) and k ~ ~ ~ , , ( m ;= n ;~DBT,~(O;O;O) p) k~~~~~(m for; n tri-Me;p) DBT with k ~ ~ ~ ~ ~ ( m#; n ~; ~p E) L ~ ~ ~ ( ~ and ; O ; O ) k ~ ~ ~ , , ( r n ; n=; kO~) ~ ~ , ~ ( m ;Eight 0 ; p adsorption ). equilibrium constants for (substituted) tetrahydrodibenzothiophene, KTmBT,?,are considered, depending on the methyl groups on the phenyl moiety and the partially hydrogenated phenyl moiety. The rate coefficient for the further hydrogenation of (substituted) tetrahydrodibenzothiophene into (substituted) hexahydrodibenzothiophene ((s)-HHDBT) depends on the number of methyl groups on the aromatic ring: kTHDBT,r(O;O;O), kTHDBT,r(m;O;O) = kTHDBT,r(O;O;O) kELTHDBT(m;O;O),and kTHDBT,r(m;n;O) = kTHDBT,r(O;O;O) kELTHDBT(rn;n;O)* The adsorption equilibrium constant for (substituted) hexahydrodibenzothiophene depends on the number of methyl groups on the phenyl moiety and the cyclohexyl moiety. Eight different adsorption equilibrium constants have to be considered. Biphenyl (BPH) consists of two phenyl moieties. It is first hydrogenated into cyclohexylbenzene (CHB). The adsorption equilibrium constant for (substituted) biphenyl ((s)-BPH),KBPH,,,depends on the total number of methyl substituents. Therefore, four adsorption equilibrium constants are considered: KBPH,~(O;O;O) for biphenyl, KBpH,r(m;O;O)z KBHP,r(O;O;O)KEL+STBPH(m;O;O) for monomethylbiphenyl, KBpH,r(m;n;O)= KBPH,r(o;o;o)
2986 Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 Table 6. Total Number of Parameters for the and of Dibenzothiophene and KBPH,,(~= ; ~KBPH,~(O;O;O) ;~) K E L + s T ~ ’ ~ (for ~ ;tri~ ; ~ ) Hydrodesulfurization Methyl-Substituted Dibenzothiophene: Structural methylbiphenyl with K~p~,~(m;lz;O) = K ~ p ~ , , ( m ; 0 ;In p). Contribution Approach contrast to the hydrogenation of dibenzothiophene, the a-Sites rate coefficient for the hydrogenation of (substituted) 5+1 adsorption (s)-DBT KDBT,u(m;n;p) biphenyl, ~ B P H , , , only depends on the number of methyl 3+1 hydrogenolysis (s)-DBT kDBT,dm;n;P) groups on the phenyl moiety which undergoes hydro3+1 adsorption(s)-BPH KsPH,dm;nP) genation. This results in only three rate coefficients for 5+1 adsorption (s)-THDBT KmBT,dm;n;p) the hydrogenation of all biphenyls: k ~ p ~ , ~ ( 0 ; 0 ; 0 ) , hydrogenolysis (s)-THDBT 2+1 kmBT,dm;np) 5+1 adsorption M-HHDBT KmBT,dm;n;p) kBPH,r(m;O;O) = k ~ p ~ , , ( o ; o ; O )~ E L ~ ’ ~ ( ~ ; O ; O ) and , 2+1 hydrogenolysis (s)-HHDBT kmBT,dm;np) kBpH,r(m;n;O) = k ~ p ~ , ~ ( o ; OkELBPH(m;rt;O). ;o) 7+1 adsorption(s)-CHB Kcm,dm;n;p) Cyclohexylbenzene consists of one phenyl moiety and 1 adsorptionH2 KHDP one cyclohexyl moiety. It is hydrogenated into bicyclo1 adsorptionH2S KH~s,~ hexyl, which consists of two cyclohexyl moieties. The z-Sites adsorption equilibrium constant for (substituted)cyclo3+1 adsorption(s)-DBT KDBT,r(m;n;PI hexylbenzene ((s)-CHB),KCm,?,depends on the number 3+1 hydrogenation (s)-DBT kDBT,dm;n;P) of methyl groups on the phenyl moiety as well as on 7+1 adsorption(s)-THDBT KTHDBT,r(m;n;PI 2+1 the number of substituents on the cyclohexyl moiety. hydrogenation (s)-THDBT kmBT,Am;n;p) 7+1 adsorption (SI-HHDBT KHHDBT,dm;nP) Eight different adsorption equilibrium constants are 3+1 adsorption (s)-BPB KBw,r(m;nP) considered. 2+1 hydrogenation (s)-BPH kBPH,z(m;nP) For the rate coefficient for the hydrogenation of 7+1 adsorption (s)-CHB Kcm,Am;n;p) (substituted)cyclohexylbenzene into (substituted)bicy2+1 hydrogenation (s)-CHB kcm,Am;n;p) clohexyl ((s)-BCH), ~ c H B , ~only , the number of methyl 3+1 adsorption (s)-BCH KBCH,r(m;n;p) 1 adsorptionHz KHZJ groups on the phenyl moiety is important. Three rate 1 KH~s,~ coefficients are considered: kCHB,r(o;o;o), k c ~ ~ , , ( m ; O ; o ) , adsorptionH2S and ~ c H B , , ( ~ ; ~ ; O ) . total 93 The adsorption equilibrium constant for (substituted) bicyclohexyl, KBCH,,depends on the total number of provide significant parameter values. Also, of the 93 methyl groups on both moieties. Four adsorption equiparameters 70 are adsorption equilibrium constants and librium constants are considered: KBCH,,(O;O;O)for this number could be considerably reduced through KBCH,,(~;O;O) = KBCH,,(O;O;O) analogies and reasonable simpljfying assumptions. When bicyclohexyl, KEL+sT~~~(~;O;O) for mono-Me-BCH, KBCH,,(~;~;O) = only the disappearance of the sulfur-containing compoKBCH,,(O;O;O)K E L + s T ~ ~ ~for ( ~di-Me-BCH, ; ~ ; O ) and nents, the production of H2S, and the hydrogenation of K B C H , ~ ~=;KBCH,AO;O;O) ~;~) K ~ ~ + s ? ~ ~ ( m for ; n ;trip) substituted DBT are considered, 215 rate equations for Me-BCH with &c~,,(m;n;O)= K ~ c ~ , , ( r n ; O ; p ) . hydrogenolysis and 170 rate equations for hydrogenaIn total there are 282 hydrogenation rate equations tion have to be retained. The number of parameters is containing 51 parameters which need t o be determined then reduced to 71, of which 54 are adsorption equilibfrom experimental data. rium constants. The approach can also be applied t o nitrogen-containing compounds. Conclusions Acknowledgment The modeling of HDS reactors still presents a number of serious challenges, associated with the hydrodynamThis work was partly funded by the European Comics, but also with the complex nature of the feed. mission under the Joule program Contract No. JOU2Accounting for the thermodynamic properties of such a 0121. V.V. and G.A.D. are also grateful for a contribumixture is not a simple task, even if the basic data are tion from the Center of Excellence Grant awarded to available or can be estimated. The kinetic aspects of the Laboratorium voor Petrochemische Techniek by the the transformation of the large number of S- and Belgian Ministry of Science. N-components is a formidable problem, however, requiring extensive experimentation for each catalyst Nomenclature retained for the process. The kinetic modeling applied a,’ = gas-liquid interfacial area per unit reactor volume, up to now is not satisfactory as a basis for the more mi2/mr3 stringent requirements HDS will be facing in the future. a / = liquid-solid interfacial area per unit reactor volume, A new approach is proposed in this paper. Instead of mi2/mr3 lumping components and reactions, it retains the details C, = molar concentration of component i, m0Ym3 of the reaction network of every feed component. Two C,G= molar concentration of i in gas bulk, mol/mc3 of modeling are discussed. levels C,L= molar concentration of i in liquid bulk, m o l / m ~ ~ According to a molecular approach the total number C,, = molar concentration of i inside the solid, mollm? of parameters of the 215 hydrogenolysis rate equations C:, = molar concentration of fluid reactant i at surface of and the 282 hydrogenation rate equations for the HDS solid, mol/m? of the DBT and all substituted DBT networks considC ~ G = specific heat of gas phase, J/(kg K) ered here is 1133 (Table 4). In the structural contribuc p =~ specific heat of liquid phase, J/(kg K) tion approach the total number of parameters for all D,, = effective diffusivity of component i for transport in a the complete networks has been reduced t o 93. All the pseudocontinuum, mp/(q,t s) parameters for the hydrogenolysis and the hydrogenad, = equivalent particle diameter, mp tion reactions are listed in Table 6. This is still a d, = reactor diameter, m, relatively large number, but the number of responses fc = friction factor per S-component in the feed is of the order of 9. A F, = molar flow rate of component i, moYs thoughtfully designed experimental program should h = heat transfer coefficient, J/(m? s K)
KEL+sT~’~(~;~;O) for dimethylbiphenyl,
Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 2987 hf = heat transfer coefficient for the film surrounding a H = atomic hydrogen particle, J/(mi2 s K) HZ= molecular hydrogen Hi = Henry's law coefficient, partial molar enthalpy of HzS = hydrogen sulfide species i, m~~bar/mol, or J/mol HHDBT = hexahydrodibenzothiophene (-AH) = heat of reaction, J/mol i = component i AHi, = heat of vaporization of species i , J/mol I = interface k = reaction rate coefficient, moY(kgCats) L = liquid phase k G = mass transfer coefficient from gas to gas-liquid p = pellet interface, based on concentration driving force, m ~ ~ / ( m i ~s = inside solid; also superficial velocity S) THDBT = tetrahydrodibenzothiophene k~ = mass transfer coefficient from gas-liquid interface z = with respect to the hydrogenation function, to liquid bulk, based on concentration driving force, m ~ ~ /u = with respect to the hydrogenolysis function (mi2S) Superscripts kl = liquid-solid mass transfer coefficient, m ~ ~ / ( s) mi~ KA = K-factor of species A or adsorption equilibrium BCH = bicyclohexyl constant of component A, m ~ ~ / m o l BPH = biphenyl K,,o = adsorption equilibrium constant of component i on = cyclohexylbenzene CHB a-sites, mL3/kmol = dibenzothiophene DBT Ki,r = adsorption equilibrium constant of component i on IGM = ideal gas mixture mites, mL3flunol f = at the reactor exit KL = overall mass transfer coefficient in terms of liquid HHDBT = hexahydrodibenzothiophene concentration gradient, m ~ ~ / ( s) mi~ ' = at the reactor inlet; also pure component Mi = molecular mass of species i, kg/mol s = condition at external surface N = number of species THDBT = tetrahydrodibenzothiophene N , = number of reactions N, = rate of transfer of i from the gas bulk to the liquid Literature Cited bulk, mol/(mi2s) n = reaction order Broderick, D. H.; Gates, B. C. Hydrogenolysis and Hydrogenation pt = total pressure, Pa of Dibenzothiophene Catalyzed by Sulfided COO-Moodyq = heat flux, J/mi2 s Al203: The Reaction Kinetics. AZChE J . 1981,27,663. r, = reaction rate of reactionj per unit catalyst mass for BrulB, M. R.; Starling, K. E. Thermophysical Properties of Complex heterogeneous reaction, mol/(kgcats) Systems: Applications of Multiproperty Analysis. Znd. Eng. Chem. Process Des. Deu. 1984,23,833. R = gas law constant, J/(mol K) Chilton, T. H.; Colburn, A. P. Mass transfer (absorption) coefReG = Reynolds number for the gas phase, d,G/pG ficients. Prediction from data on heat transfer and fluid friction. ReL = Reynolds number for the liquid phase, d&/pL Ind. Eng. Chem. 1934,26,1183. S = stoichiometric coefficient matrix; sb,i] is the stoichioChung, T.; Ajlan, M.; Lee, L. L.; Starling, K. E. Generalized metric coefficient of component i in reactionj Multiparameter Correlation for Nonpolar and Polar Fluid T = absolute temperature, K Transport Properties. Znd. Eng. Chem. Res. 1988,27,671. U,G = superficial gas velocity, r n ~ ~ / ( s) m,~ Froment, G. F.; Bischoff, K. B. Chemical Reactor Analysis and u L= l ~superficial liquid velocity, m ~ ~ / ( m s) ? Design, 2nd ed.; J. Wiley: New York, 1990. XA = mole fraction of component A in the liquid phase Graboski, M. S.;Daubert, T. E. A modified Soave Equation of State for Phase Equilibrium Calculations 2. Systems containing COz, YA = mole fraction of component A in the gas phase HzS, Nz and CO. Znd. Eng. Chem. Process Des. Dev. 1978,17, z = axial coordinate in reactor, m,
Greek Symbols d~ = frictional pressure drop per unit length for gas flow only, Palm, d~ = frictional pressure drop per unit length for liquid flow only, Palm, &,G = two-phase frictional pressure drop, Palm, E = bed void fraction, mP/m,3 vr = effectiveness factor of reaction r for solid particle 6 = radial coordinate, mp p~ = gas viscosity, Pa s p~ = liquid viscosity, Pa s QB = catalyst bulk density, kgcaJmr3 ef = fluid density, kg/m? @G = gas density, k g / m ~ ~ QL = liquid density, k g / m ~ ~ e, = density of the catalyst, kgcaJm,3 u = hydrogenolysis site 5 = hydrogenation site S2 = cross section of reactor, m1.2
Subscripts BCH = bicyclohexyl BPH = biphenyl CHB = cyclohexylbenzene DBT = dibenzothiophene f = fluid G = gas phase
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Received for review March 15,1994 Revised manuscript received August 4,1994 Accepted September 6,1994@ @
Abstract published in Advance ACS Abstracts, November
1, 1994.
