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    I n d . E n g . Chem. Res. 1994,33, 2975-2988 2975

    Kinetic Modeling and Reactor Simulation in Hydrodesulfurizationof Oil Fractions?Gilbert F. Froment; Guyk Depauw, and Valerie VanrysselbergheLaboratorium voor Petrochemische Techniek, Universiteit Gent, Krijgslaan 281, B-9000 Gent, Belgium

    An adiabatic multiphase reac tor for diesel hydrodesulfurization (HDS) was simulated wi th aone-dimensional heterogeneous model. A diesel-type mixture containing benzothiophene,dibenzothiophene, and 4,6-dimethyldibenzothiophene s sulfur components and quinoline asnitrogen component was chosen as feed. A kinetic modeling for the HDS of dibenzothiopheneand alkyl-substituted dibenzothiophenes based upon structural contributions was developed.According to a molecular approach the total number of rate and adsorption parameters for th eHDS of a se t of (substituted)-dibenzothiophenes s 1133. In the structura l contribution approachintroduced here th e total number of parameters has been reduced to 93.Introduction

    Sulfur is present in many forms in petroleum frac-tions: mercaptans R-SH, ulfides R-S-R', disulfidesR-S-S-R, polysulfides R-S,-R', thiophene, ben-zothiophene (BT), dibenzothiophene (DBT), and theiralkyl derivatives. In addition, various nitrogen-contain-ing components ike pyridine and alkylpyridines, quino-line and alkylquinolines, benzoquinolines, acridines,indoles, and carbazoles are also present.Sulfur has to be removed from oil fractions for bothtechnical and environmental reasons. The specifica-tions on diesel for example are getting more stringent.From October 1993 onward the sulfur content of dieselfor highway traffic is limited to 0.05 w t in the UnitedStates. At present the maximum sulfur content inWestern Europe is 0.2-0.3 wt , depending upon thecountry, but the specification imposed by the EuropeanUnion from Oct 1 1996, onward for class 3 standarddiesel for long-haul traffic and off-highway applications

    is 0.05 w t S. For class 1and 2 diesels, which will beused for transportation buses and cars in urban areas,the limits will be respectively 0.001 and 0.03 w t S.This is a serious challenge. Are the present-day cata-lysts adequate for reducing the sulfur content to suchlevels? Can modeling and simulation contribute to thenew developments? What is the level of sophisticationthat has to be introduced in the reactor model? Thehydrodynamics in HDS eactors is not well understood.Calculating accurate thermodynamic properties for suchcomplex mixtures is another problem. Kinetics is amajor element of reactor modeling and simulation. Theliterature on the conversion of key components s ratherabundant, but the information is seldom coordinated.Most of the rate equations published to date are simplefirs t order disappearance kinetics. The rate of HDS fthe oil fraction is then generally lumped into a singlesecond order reaction, to account for the large variationof the reaction rates of the various feed components. Thedevelopmentof deepHDS processes imposed by the newspecifications will definitely require more accuratekinetics. The present paper deals with various aspectsof the simulat ion of an adiabatic multiphase reactor fordiesel desulfurization and with the derivation of a setof adequate kinetic equations for the conversion of at Pre se n te d at the Symposium on C ata ly t ic Reac t ion Engi-ne e r ing for Environmenta l ly Benign Processes at t h e S a nDiego ACS Meet ing , March 13-18, 1994.

    0888-5885I94l2633-2975$04.50/0

    complex mixture of sulfur- and nitrogen-containingcomponents.Scrutiny of Reactor Modeling Aspects

    Reactor Model Equations. The hydrodesulfuriza-tion of diesel fractions is performed in a multiphasefx ed bed reactor. Three phases are present in thereactor: the fmed bed of porous catalyst particles, avapor phase, and a liquid phase flowing cocurrentlydownward. The liquid feed is usually a blend ofstr aight- run gas oil and light cycle oil from a FCC orcoker unit. The sulfur content of the liquid feed istypically 0.5-2.0 wt . It is reduced by the hydrotreat-ment to 0.2-0.05 wt . The gas phase consists mainlyof hydrogen, hydrogen sulfide, ammonia, and vaporizeddiesel components. The liquid phase consists of the gas-oil components, including the sulfur- and nitrogen-containing components and dissolved gases like hydro-gen, hydrogen sulfide, ammonia, and light hydrocarbons.In commercial applications trickle and pulse flow arethe most likely flow regimes. Trickle flow features area continuous gas phase and a dispersed liquid phaseflowing as a laminar film or as rivulets over theparticles. The pulse flow regime is obtained at higherliquid and gas throughputs. According to Wammes etal. (1990) the pulse flow regime is not attained at highpressures and realistic liquid flow rates, if the molecularweight of the gas phase is of the order of that ofnitrogen. In a hydroprocessing unit operating, forexample, at 310 C and 50bar, the molecular weight ofthe gas phase is approximately 20 g/mol. Therefore,strong indications exist that trickle flow is the dominat-ing flow regime. Besides, it is commonly accepted thatin commercial hydroprocessing reactors all the particles

    are completely wetted when the gas and liquid areadequately distributed (Shah, 1979). The model devel-oped in the following pages is a one-dimensional het-erogeneous model with both the gas and liquid phasein plug flow (Froment and Bisschof, 1990). The steadysta te continuity equation for a component i of the gasphase can be written as

    = 1 ...,N 1)dF Gs z d zF. =F .a t z = O rG LG

    The liquid phase and the gas phase are not necessarily0 1994 American Chemical Society

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    Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 2977A1203 catalyst is described by the kinetic equation ofMiller and Hineman (1984).

    The rate equations mentioned above do not accountfor the competitive adsorption of other sulfur compo-nents or hydrocarbons.

    benzene (EB). The rate equations are

    At 533 K, for example, the parameters take on thefollowing values:

    - 3

    The ra te equations for dibenzothiophene hydrodesulfu-rization of Broderick and Gates (1981) were modifiedinto the following rate equation for the direct hydro-genolysis:

    withk , = 7.84 x l o 8 exp(-158000/RT) kmol/(kg,,, s)

    k D g T , o = 5.31 m3/kmoi KH,,, = 4.02 m 3 h O iKH,s,o= 1.72

    and for the hydrogenation of dibenzothiophene,

    withk , = 4.17 x l o 3 exp(-99100/RT) m3/(kgcat )K D g T , r = 3.97 x 10 exp(-14100/RT) m3/kmol

    The hydrodesulfurization rate of 4,6-dimethyldiben-zothiophene was derived from th e desulfurization rateof dibenzothiophene by weighing the latter with theratio of the pseudo first order desulfurization ratecoefficients of 4,6-dimethyldibenzothiophene nd diben-zothiophene. This ratio is 1/15 a t 573 K (Houalla et al.,1980).Quinoline was chosen as nitrogen component. Thehydrodenitrogenation reaction of quinoline (Q) t o n-propylcyclohexane (PCH) n the liquid phase on a CoMo/

    Estimation of the Physical PropertiesThe critical temperature, critical pressure, heat offormation, Gibbs free energy of formation, and ideal gas

    hea t capacity, which are required for the calculation ofvarious physical da ta, were taken from the literature.Group contribution methods were used when specificvalues were not available. The acentric factor wascalculated by means of the Lee-Kesler method (Lee andKesler, 1975). Various data like the hea ts of reactionin the liquid phase, the heats of vaporization, the heatcapacity of the gas phase and the liquid phase, theequilibrium constants of the reactions in the liquidphase, the densities of gas phase and liquid phase, andthe Henry coeffkients were obtained from calculationsbased on the Peng-Robinson equation of state. Forhydrogen and hydrogen sulfide in the liquid phasebinary interaction parameters were used in the Peng-Robinson equation of state . These were obtained re-spectively from Moysan et a l. (1983) and Graboski andDaubert (1978b). The viscosity of the gas phase andthe liquid phase was determined with the method ofBrulez and Starl ing (1984). The thermal conductivityof both phases was calculated using the method ofChung e t al . (1988). The diffusion coefficients wereobtained from the Wilke-Chang method (Wilke andChang, 1955).

    The mass transfer coefficient k ~ a ; t the liquid sideof the gas-liquid interface was derived from a correla-tion presented by Sat0 (19721, and the gas side masstransfer coefficientkw, at t ha t interface was derivedfrom Reiss' correlation (1967). The liquid-solid masstransfer coefficient was obtained from the correlationof Van Krevelen and Krekels (1948). The heat transfercoefficients were derived from the mass transfer coef-ficients using the Chilton-Colburn analogy (1934).Integration Method

    The integration in the axial direction was performedusing a fourth order Runge-Kutta routine with variablestep size. The intraparticle integration was carried outwith an orthogonal spline collocation method. Thetemperature of the solid phase and the surface concen-trations are unknowns, since resistance to mass andheat transfer is accounted for at the catalyst surface.An initial guess has to be made t o perform the intra-particle integration. The initial guesses are then up-dated, using a Newton-Raphson method, until therequired accuracy is obtained.Results of the Simulation and Discussion

    In the example o follow a synthetic feed mixture withdiesel characteristics was chosen, consisting of paraffins,naphthenes, aromatics, sulfur, and nitrogen compo-nents. The sulfur content of the feed, 1.82 wt , hadto be reduced t o 0.05 wt . Benzothiophene, dihy-drobenzothiophene, dibenzothiophene, and 4,6-dimeth-yldibenzothiophene were taken as sulfur-containingcomponents and quinoline as the nitrogen-containingcomponent.

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    2978 Ind. Eng. Chem. Res., Vol. 33,No. 12,1994Table 1. Composition of the Synthetic Diesel Type Feed

    feed components composition (mol )sulfur componentsBenzothiopheneDibenzothiophene4,6-DimethyldibenzothiopheneDihydrobenzothiophenenitrogen componentQuinolineparaffinsn-Clz

    n-Clsn-Clcn - C xn - C xn - C un-Clsn-C19n-Czonaphthenesn-propylcyclohexanen-nonylcyclohexanecis-decalinethylbenzenen-nonylbenzeneindeneindanenaphtha leneanthracenebiphenylcyclohexylbenzene

    aromatics

    total: 10.47.222.330.8310.0281total: 1.531.53total: 30.01.131.231.795.715.565.074.083.022.41total: 31.00.15317.313.5total 27.00.02826.142.635.927.272.722.323.42 10-3

    Table 2. Composition of the Treat Gas RecycleMake-up Gas)component composition(mole fraction)

    hydrogenhydrogen sulfidenitrogenammoniamethanee thane

    0.6180.01330.06810.002190.2550.0431The composition of the diesel-type feed is given inTable 1, and the composition of the tr eat gas in Table2. This trea t gas consists of make-up gas and recycle

    P P W

    gas. Thermodynamic equilibrium was assumed be-tween the gas and the liquid phase a t the reactor inlet.The reactor geometry, catalyst properties and inletconditions are given below as follows.Reactor geometry: diameter, 2.82m; length, 7.625m.Catalyst properties: equivalent diameter of a catalystparticle, 1.3 x m; porosity of the catalyst, 0.6mP/mp3;bulk density of the bed, 710 kgcaJmr3;density ofcatalyst, 1420 kg,,Jmp3.Inlet conditions: inlet temperature , gas and liquidphase 590K nlet pressure, 5000 kPa; WIFs,0.92kgcath/(mol of S);LHSV, .16m ~ ~ / ( m ~ t ~); liquid flow ra te,1550 ons/day (1805 m3/day); gas flow rate, 116 tons/day 314 00 m3 (NTP)/day); total sulfur content , 1.82wt ; nitrogen content, 0.117wt .The components of the diesel-type mixture are dis-tributed over both the liquid phase and the gas phase.The components in the gas phase are also consideredfor the calculation of the sulfur content of the diesel-type mixture, while hydrogen sulfide present in the gasor liquid phase is not. The evolution of the sulfurcontent of the diesel-type mixture through the reactoris shown in Figure 1. Benzothiophene reacts faster thandibenzothiophene. The slowest reaction is the removalof the 4,6-dimethyldibenzothiophene. The major frac-tion of the sulfur removal takes place in the initial partof the reactor, which is reflected in a significant tem-pera ture increase. The maximum difference betweengas and liquid phase temperature amounts to 5 C closet o the inlet and drops below 0.1 C at the reactor outlet.The temperature increase between inlet and exit amountst o 27 C. It should be noted tha t the hydrogenationreactions of aromatic components like naphthalene andanthracene were not considered. The temperature andconcentration differences between the liquid bulk phaseand the catalyst surface were found to be negligible. Theevolution of the molar flux of hydrogen in the liquid andin the gas phase a re shown in Figure 2. The molar flux

    of hydrogen in the liquid phase that would be inequilibrium with the molar flux of hydrogen in the gasphase is also represented. The liquid phase in themole fraction r S

    0.08

    - 0.07-I - 0.06

    - 0.05otal sulfur content4-..-. - 4 6Dimethyldibenzothbphena - 0.045- - Dihydrobenzothlophene6- Mole fraction YS in the gas phase o . ~

    - 0.02- 0.01

    - 00 2 4 6Axial position [m]Figure 1. Axial profile of th e sulf ur content of the diesel-type mi xture a nd of the mole fraction of H2S in the gas phase.

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    Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 2979

    14

    12

    10

    1 FH)2 . ' Q Molar flux of hyd rogen in the liquid phaseMolar flux of hydrogen in he liquid phase

    if saturated with hydrogen' 3 - - - - qG olar flux of hydrogen in the gas p hase.......................... -..................... ........................................................... . ' 3 - - - - qG olar flux of hydrogen in the gas p hase...... . . . . . . .......... -........ .................... ..........................................................

    _ _ _ _ _4 - -__ .___

    0.75

    0.5

    0.25

    I I68 0 2 4Axial position [rn]

    Figure 2. Axial molar flux profile of hydrogen in both phases.P P M S mole fraction S

    0.0818 000

    16,00014,00012,00010,0008,000

    6,0004,0002,000

    0

    - 0.06

    2 Without resistance o gas-liquid mass transfer( iquid saturated with hydrogen )

    - 0.03

    I I 00 2 4 6Axial 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 saturatedwith hydrogen. The axial profiles of the sulfur contentof the diesel-type mixture in both cases (liquid saturatedwith hydrogen and no saturation) are presented inFigure 3. The conversion of the sulfur components islower when the resistance to gas-liquid mass transferis considered, Since the hydrodesulfiuization rates arefavored by higher hydrogen concentrations.In Figure 4 the sulfur content at the reactor exit isshown as a function of the inlet temperature andpressure. Additional catalyst volume, more severereaction conditions, or more active catalysts are requiredif the future specifications have to be satisfied. Theremoval of nitrogen components is slower than thesulfur removal, as shown in Figure 5.

    The intraparticle diffusion limitations are reflectedin the values of the effectiveness factors given in Table3. These are arrived from the calculated intraparticlegradients.Kinetic Modeling of he Hybge nolys is andHydrogenation ofDibenzothiophene andAlkyl-SubstitutedDibenzothiophene

    Detailed kinetic equations for the conversion of ben-zothiophene (BT) and dibenzothiophene (DBT) werementioned in the section ,on multiphase reactor s imula-tion. They distinguished between a-sites, on which thehydrogenolysis reactions take place and z-sites, onwhich the hydrogenations take place. They account for

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    2980 Ind. Eng. Chem. Res., Vol. 33, No. 12,1994

    .

    ,/ a.

    ppmwS at the reactor exit1,800

    1 Nitrogen content of the diesel type mixture2 Mole fractionofNHI in the gas phase

    400 I I I4 000 4 500 6 000 5.500 6,000Ida [kpel

    Figure 4. Sulfur content of the diesel-type mixture at t he reactor exit as a function of temperature and pressure. Initial sulfur content:1.82wt .PpmwN Mole fractio n NH:,

    1,180

    1,160

    1,140

    1,120

    1,100

    1 080

    1,m1,040

    ...-2 \

    0.003

    O.OM8

    0.0026

    0.0024

    0.-

    0.002

    0.0018

    0.00162 4 6Axial position [m]Figure5. 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 react-ing species on both the 0 and t-sites. Two rateequations were used by Broderick and Gates (1981) forthe conversion of DBT, containing a total of six kineticand adsorption coefficients.What if the oil fraction contains not only DBT, butall mono-, di-, and trisubstituted DBT? Is it possibleto maintain a Hougen-Watson approach accounting forthe adsorption of the species in that case? It is possiblet o account for the complete reaction network of eachsulfur-containing feed component?The problem will be illustrated for the hydrogenolysisand hydrogenation of DBT and the methyl-substitutedDBT.Reaction Networksand KineticModeling at theMolecular Level. The complete reaction network for

    dibenzothiophene, for 4-methyldibenzothiophene, or4,6-dimethyldibenzothiophene,or 1,6-dimethyldiben-zothiophene, and for 1,2,6-trimethyldibenzothiopheneare shown in Figures 6, 7, 8, 9, and 10, respectively.There are 215 rate equations for hydrogenolysis and282 rate equations for the hydrogenations in the reac-tion networks of DBT and mono-, di-, and trisubst itutedDBT. As shown in Table 4 these ra te equations contain497 kinetic coefficients and 636 adsorption equilibriumconstants.For each subst ituted DBT (s-DBT), one adsorptionequilibrium constant on the a-sites,K D B T , ~ ,nd one ratecoefficient for the hydrogenolysis into biphenyl, ~ D B T , ~ ,have to be considered. This leads to 44 differentadsorption equilibrium constants for substituted DBTand 44 rate coefficients for substituted DBT hydro-

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    Table 3. Values of Effectiveness Factors for the VariousReactionsaaxial position m)

    reaction 0 1 2DBT-BPH 0.23 0.91 0.94DBT-CHB 0.55 0.93 0.94DMDBT-DMBPH 0.36 0.92 0.97DMDBT-DMCHB 0.56 0.94 0.98BT-DHBT 0.31 0.44BT-EB 0.37 0.44DHBT-EB 9.9 0.63Q-PB 1 1 1DBT, dibenzothiophene; BPH, biphenyl; CHB, cyclohexylben-zene; DMDBT, 4,6-dimethyldibenzothiophene;MBPH, 4,4'-di-methylbiphenyl; DMCHB, 4,6-dimethylcyclohexylbenzene; T,benzothiophene; DHBT, dihydrobenzothiophene; EB, ethylben-zene; Q, quinoline; PB , propylbenzene.

    THDBT

    CHB

    i tBCH

    Figure 6. Reaction network for HDS of dibenzothiophene.genolysis. Hydrogenolysis of the 44 substitu ted DBTleads t o only 29 different substituted biphenyl mol-ecules, due to rotation of the phenyl rings in biphenylwith respect to each other (Streitwieser and Heathcock,1985). Consequently, 29 adsorption equilibrium con-stants for substitu ted biphenyl (s-BPH) on the 0-sites,KBPH,,,, ave to be retained.For each substituted DBT, one adsorption equilibriumconstant on the t-sites,KDBT,~ ,s required, which leadsto 44 different adsorption equilibrium constants forsubstitu ted DBT on the t-sites. Hydrogenationof eachof the 4 monosubstituted DBT, of each of the 12nonsymmetrical disubstituted DBT, and of each of the24 trisubstituted DBT leads t o two different substitutedtetrahydrodibenzothiophene s-THDBT) molecules. Hy-drogenation of each of the four symmetrical disubsti-tuted DBT results in one type of tetrahydrodiben-zothiophene molecules. Consequently, 84 (4 x 2 12x 2 + 24 x 2 +4) rate coefficients for the hydrogenationof substitu ted DBT, ~ D B T , ~ ,nd 84 adsorption equilib-

    Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 2981

    Figure 7. &action network for HDS of 4-methyldibenzothiophene.

    i t

    Figure 8. Reaction network for HDS of 4,6-dimethyldiben-zothiophene.rium constants for the resulting product substitutedtetrahydrodibenzothiophene,K T H D B T , ~ ,ave to be evalu-ated.Also, 84 rate coefficients for the further hydrogenationof substituted tetrahydrodibenzothiophene nto substi-tuted hexahydrodibenzothiophene(s-HHDBT),k T m B T , r ,as well as 84 adsorption equilibrium constants for the

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    2982 Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994

    Figure 9. Reaction network for HDS of 1,6-dimethyldiben-zothiophene.

    Figure 10. Reaction network for HDS of 1,2,64rimethyldiben-zothiophene.

    product substituted hexahydrodibenzothiophene,KHHDBT,~,ave to be considered.

    Table 4. Total Number of Parameters for theHydrosulfurization of Dibenzothiophene andMethyl-Substituted Dibenzothiophene: MolecularApproacha-Sitesadsorp tion (s)-DBT KDBT,dm n P) 44 1hydrogenolysis (s)-DBT kDBT,dm;nP) 44 1adsorption (s)-BPH KBPH,dm;nP) 29 1adsorption (s)-THDBT Km BT ,dm ;np ) 84 + 1hydr ogen olysis (S)-TH DBT kTHDBT,dm;n;p) 84 4 1adsorption (s)-HHDB T K DBT,dm;n;P) 84 f 1hydrogenolysis (s)- DBT kmDB T,dm;n;p) 84 + 1adsorption (s)-CHB Kcm ,dm;n;p ) 55 1adsorption HZ KHZP 1a dsorpt ion H 2S K H ~ s , ~ 15-Sitesadsorp tion (s)-DBT KDBT,,(m;nP) 44 1hyd rog enat ion (s)-D BT kDBT,r(m 84 1

    hyd rog enat ion (s)-T HD BT kTHDBT,r(m;n;p) 84 + 1ads orp tion (s)- BP H KBpH,r(m;n PI 29 1hydrogenatin (s)-BPH kBw,r(m ;nP) 55 + 1adsorp tion (s)-C HB KCHB,r(m;n;P) 55 1hydrogenation (s)-CHB kcm,,(m;n;p) 55 1ad so rp tio n Hz KH2.r 1adsorption H2S K H ~ s , ~ 1

    ads orp tion (SI-T HD BT KTHDBT,r(m;n;P) 84 + 1ads orp tion (s)- HH DB T KHHDBT,r(m;n;p) 84 1

    adsorp tion (s)-B CH KBcH,,(m;n;p) 29 + 1total 1133For each of the 84 substituted tetrahydrodiben-zothiophenes, one adsorption equilibrium constant onthe a-sites, KTHDBT,~,nd one rate coefficient for thehydrogenolysis into substituted cyclohexylbenzene,K T H D B T ~ have t o be introduced. Hydrogenolysis of the84 substituted tetrahydrodibenzothiophenes leads t oonly 55 different substituted cyclohexylbenzene mol-ecules, due to rotation of the phenyl and cyclohexyl ringsin cyclohexylbenzene with respect to each other. Con-sequently, 55 adsorption equilibrium constants forsubstituted cyclohexylbenzene (s-CHB) on the a -sites,K C H B , ~ ,ave to be retained. Also, for each of the 84substituted hexahydrodibenzothiophenes,one adsorp-tion equilibrium constant on the a-sites, KHHDBT,~,ndone rate coefficient for the hydrogenolysis into substi-tuted cyclohexylbenzene, ~ H H D B T , ~ ,ave to be consid-ered.For each of the 29 substi tuted biphenyls, one adsorp-tion equilibrium constant on the r-sites, K B P H , ~ ,as t obe determined. Hydrogenation of each of the 3 mono-substituted biphenyls, of each of the 8 nonsymmetricaldisubstituted biphenyls, and of each of the 15 trisub-stituted biphenyls gives two different substituted cy-clohexylbenzene molecules. Hydrogenation of each ofthe three symmetrical disubstituted biphenyls gives onetype of substitu ted cyclohexylbenzene molecules. Con-sequently, 55 (3 x 2 8 x 2 15 x 2 3) rate

    coefficients for the hydrogenation of substituted biphe-nyl into substituted cyclohexylbenzene, K B P H ~ and 55adsorption equilibrium constants for the product sub-stituted cyclohexylbenzene on the r-sites, KcHB ~reintroduced.For each of the 55 substituted cyclohexylbenzenes, onerate coefficient for the hydrogenation into substitutedbicyclohexyl (s-BCH), K C H B ~ has t o be considered.Hydrogenation of the 55 different substituted cyclo-hexylbenzenes results in only 29 different substitutedbicyclohexyls, so that 29 adsorption equilibrium con-stants for substituted bicyclohexyl, KBCH ~ave to beretained.In addition, for nonsubstituted DBT, one of each ofthe above parameters has to be evaluated. Also adsorp-

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    Table 5. Hydrogenolysis Rate CoefficientsofThiophene, Benzothiophene, and SelectedMethyl-SubstitutedDibenzothiophenedReactant Structure Pseudo-first-order rate constant

    3m 1 (kgcat s)thiophene

    benzothiophene

    dibenzothiophene

    2,Sdlmethyl-dlbenzothlophene3,7-dimethyl-dibenzothlophene

    emethyl-dibenzothlophene

    4,Mimethyl-dibenzothiophene

    1.38 x 10-

    8.11 X I O - ~

    7.38 x 10-

    6.72 x 10-

    3.53 x 10-

    6 . 6 4 ~ 1 0 - ~

    4 . 9 2 ~ 1 0 . ~

    a Reaction conditions: 0.25 mol reacta nt concentration, 300C, 71 atm, CoMo/AlzOs catalyst (Nag et al., 1979). Reactionconditions: 0.15 mol reacta nt concentration, 300 C, 102 a tm,CoMo/AlzOs catalyst (Houa lla et al., 1980).tion equilibrium constants for H and H2S on the a-sitesand the mi te s have to be determined. This leads t o atotal of 1133 parameters. A kinetic model containing1133 parameters is clearly unrealistic. A differentapproach is required to reduce this number.Kinetic Modeling Based upon Structural Con-tributions. What is proposed in this section is to gobeyond the molecular level in the modeling of thereaction rates. For reactions involving substitutedcomponents, the rates are related whenever possible t othose of a nonsubstituted reference component in termsof the influence of the substituents on the adsorptionequilibrium constants and the rate coefficients.To get some feeling of the influence of the substitu-ents, Table 5 presents first order rate coefficients forthe hydrogenolysis of various sulfur-containingcompo-nents in multiphase operation, free of diffusional limita-tions (Nag et al., 1979; Houalla et al., 1980). It may beconcluded that t he position of the methyl substitutentsis more important than their number. This was con-firmed by the data of Kilanowski et al. (1978).Effects of Methyl Substituents on the Hydro-genolysis Reactions. The hydrogenolysis reactionsinvolve vertical adsorption of the molecules through theS-atom on the a-sites (Houalla et al., 1978; Kabe et al.,1993). The assumptions which permit the reduction ofthe number of parameters for the hydrogenolysis stepsalong the struc tural contributions approach are asfollows.Assumption 1: In the adsorption electronic andsteric effects are t o be considered separately.

    Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 2983Assumption 2: Methyl groups at a distance from thesulfur atom beyond the a-position only exert electroniceffects on the adsorption.Assumption 3: Only methyl groups on the aromaticring exert an electronic influence.Assumption 4: Methyl groups in the 4- and 6-posi-tions also sterically hinder the adsorption.Assumption 6: Once a molecule is adsorbed, onlythe electronic effects of the methyl groups are of

    importance.The adsorption equilibrium constants for (substituted)DBT ((s)-DBT)can then be expressed a s follows:DBT1-MeDBT2-MeDBT3-MeDBT4-MeDBT

    1,7-DiMeDBT1,8-DiMeDBT1,g-DiMeDBT2,7-DiMeDBT2,8-DiMeDBT3,7-DiMeDBT1,6-DiMeDBT

    2,6-DiMeDBT

    3,6-DiMeDBT

    4,6-DiMeDBT

    1,2-DiMeDBT1,3-DiMeDBT1,4-DiMeDBT

    2,3-DiMeDBT2,4-DiMeDBT

    3,4-DiMeDBT

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    2986 Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994KEL+sT~~ ~;~;O)or dimethylbiphenyl, andK B P H , , ( ~ ; ~ ; ~ )KBPH,~(O;O;O)E L + s T ~ ~ ( ~ ; ~ ; ~ )or tri-methylbiphenyl with K~p~,~(m;lz;O)K~p~, , m;0;p ) .ncontrast to the hydrogenation of dibenzothiophene, therate coefficient for the hydrogenation of (substituted)biphenyl, ~ B PH , , ,only depends on the number of methylgroups on the phenyl moiety which undergoes hydro-genation. This results in only three ra te coefficients forthe hydrogenation of all biphenyls: k ~ p ~ , ~ ( 0 ; 0 ; 0 ) ,kBPH,r m;O;O) = k ~ p ~ , , o ; o ; O ) E L ~ ~ ( ~ ; O ; O ) , ndkBpH,r(m;n;O)= k ~ p ~ , ~ o ; O ; o )ELBPH(m;rt;O).Cyclohexylbenzene consists of one phenyl moiety andone cyclohexyl moiety. It is hydrogenated into bicyclo-hexyl, which consists of two cyclohexyl moieties. Theadsorption equilibrium constant for (substituted)cyclo-hexylbenzene ((s)-CHB),KCm,?,depends on the numberof methyl groups on the phenyl moiety as well as onthe number of substituents on the cyclohexyl moiety.Eight different adsorption equilibrium constants areconsidered.For the rate coefficient for the hydrogenation of(substituted)cyclohexylbenzene into (substituted)bicy-clohexyl ((s)-BCH),~ c H B , ~ ,nly the number of methylgroups on the phenyl moiety is important. Three ratecoefficients are considered: kCHB,r(o;o;o), k c ~ ~ , , ( m ; O ; o ) ,and ~ c H B , , ( ~ ; ~ ; O ) .The adsorption equilibrium constant for (substituted)bicyclohexyl, KBCH,,epends on the total number ofmethyl groups on both moieties. Four adsorption equi-librium constants are considered: KBCH,, O;O;O)orbicyclohexyl, KBCH,,(~;O;O) = KBCH,, O;O;O)KEL+sT~~~ ~;O;O)or mono-Me-BCH, KBCH,,(~;~;O)KBCH,,(O;O;O)KEL+sT~~~ ~;~;O)or di-Me-BCH, andK B C H , ~ ~ ; ~ ; ~ )KBCH,AO;O;O)~ ~ + s ? ~ ~ ( m ; n ; p )or tri-Me-BCH with c~,,(m;n;O) K ~ c ~ , , ( r n ; O ; p ) .In total there are 282 hydrogenation rate equationscontaining 51 parameters which need t o be determinedfrom experimental data.Conclusions

    The modeling of HDS reactors still presents a numberof serious challenges, associated with the hydrodynam-ics, but also with the complex nature of the feed.Accounting for the thermodynamic properties of such amixture is not a simple task, even if the basic data areavailable or can be estimated. The kinetic aspects ofthe transformation of the large number of S- andN-components is a formidable problem, however, re-quiring extensive experimentation for each catalystretained for the process. The kinetic modeling appliedup t o now is not satisfactory as a basis for the morestringent requirements HDS will be facing in the future.A new approach is proposed in this paper. Instead oflumping components and reactions, it retains the detailsof the reaction network of every feed component. Twolevels of modeling are discussed.According to a molecular approach the total numberof parameters of the 215 hydrogenolysis rate equationsand the 282 hydrogenation rate equations for the HDSof the DBT and all substituted DBT networks consid-ered here is 1133 (Table 4). In the st ructural contribu-tion approach the total number of parameters for allthe complete networks has been reduced t o 93. All theparameters for the hydrogenolysis and the hydrogena-tion reactions a re listed in Table 6. This is still arelatively large number, but the number of responsesper S-component in the feed is of the order of 9. Athoughtfully designed experimental program should

    Table 6. Total Number of Parameters for theHydrodesulfurization of Dibenzothiophene andMethyl-Substituted Dibenzothiophene: StructuralContribution Approacha-Sitesadsorption (s)-DBT KDBT,u m;n;p)hydrogenolysis (s)-DBT kDBT,dm;n;P)adsorption (s)-BPH KsPH,dm;nP)adsorption (s)-THDBT K m B T , d m ; n ; p )

    adsorptionM-HHDBT K m B T , d m ; n ; p )hydrogenolysis (s)-HHDBT k m B T , d m ; n p )adsorption (s)-CHB K c m , d m ; n ; p )adsorptionH2S K H ~ s , ~

    hydrogenolysis (s)-THDBT k m B T , d m ; n p )

    adsorptionH2 KHDPz-Sitesadsorption (s)-DBT KDBT,r m n PIhydrogenation(s)-DBT kDBT,dm;n;P)adsorption (s)-THDBT KTHDBT,r m n PI

    adsorption (SI-HHDBT KHHDBT,dm;nP)hydrogenation(s)-BPH kBPH,z m;nP)hydrogenation(s)-THDBT k m B T , A m ; n ; p )adsorption (s)-BPB K Bw ,r m;nP)adsorption (s)-CHB K c m,Am;n;p )hydrogenation(s)-CHB k c m , A m ; n ; p )adsorption (s)-BCH KBCH,r m;n;p)adsorptionHz KHZJadsorptionH2S K H ~ s , ~total

    5 + 13 + 13 + 15 + 12 + 15 + 12 + 17 + 1113 + 13 + 17 + 12 + 17 + 13 + 12 + 17 + 12 + 13 + 111

    93provide significant parameter values. Also, of the 93parameters 70 are adsorption equilibrium constants andthis number could be considerably reduced throughanalogies and reasonable simpljfying assumptions. Whenonly the disappearance of the sulfur-containing compo-nents, t he production of H2S, and the hydrogenation ofsubstituted DBT are considered, 215 rate equations forhydrogenolysis and 170 rate equations for hydrogena-tion have to be retained. The number of parameters isthen reduced to 71, of which 54 are adsorption equilib-rium constants . The approach can also be applied t onitrogen-containing compounds.Acknowledgment

    This work was partly funded by the European Com-mission under the Joule program Contract No. JOU2-0121. V.V. and G.A.D. are also grateful for a contribu-tion from the Center of Excellence Grant awarded t othe Laboratorium voor Petrochemische Techniek by theBelgian Ministry of Science.Nomenclaturea = gas-liquid interfacial area per unit reactor volume,a / = liquid-solid interfacial area per unit reactor volume,C, = molar concentration of component i m0Ym3C,G= molar concentration of i in gas bulk, mol/mc3C,L= molar concentration of in liquid bulk, mo l /m ~~C,, = molar concentration of i inside the solid, mollm?C = molar concentration of fluid reactant i at surface ofC ~ G specific heat of gas phase, J/(kg K)c p ~ specific heat of liquid phase, J/(kg K)D,, = effective diffusivity of component i for transport in ad = equivalent particle diameter, mpd, = reactor diameter,mfc = friction factorF, = molar flow rate of component i moYsh = heat transfer coefficient, J/(m? s K)

    mi2/mr3mi2/mr3

    solid, mol/m?

    pseudocontinuum, mp/(q,t s)

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    Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 2987H = atomic hydrogenHZ= molecular hydrogenHzS= hydrogen sulfideHHDBT = hexahydrodibenzothiophenei = component iI = interfaceL = liquid phasep = pellets = inside solid; also superficial velocityTHDBT= tetrahydrodibenzothiophenez = with respect to the hydrogenation function,u = with respect to the hydrogenolysis functionSuperscriptsBCH = bicyclohexylBPH = biphenylCHB = cyclohexylbenzeneDBT = dibenzothiopheneIGM = ideal gas mixturef = at the reactor exitHHDBT = hexahydrodibenzothiophene= at the reactor inlet; also pure components = condition at external surfaceTHDBT = tetrahydrodibenzothiophene

    hf = heat transfer coefficient for the film surrounding aHi = Henry's law coefficient, partial molar enthalpy of- AH ) = heat of reaction, J/molAHi, = heat of vaporization of species i , J/molk = reaction rate coefficient, moY(kgCat )k G = mass transfer coefficient from gas to gas-liquidinterface, based on concentration driving force, m ~ ~ / ( m i ~

    S)k~ = mass transfer coefficient from gas-liquid interfacet o liquid bulk, based on concentration driving force, m ~ ~ /(mi2S)

    particle, J/(mi2s K)species i , m~~bar/mol, or J/mol

    kl = liquid-solid mass transfer coefficient, m ~ ~ / ( m i ~)KA = K-factor of species A or adsorption equilibriumK,,o= adsorption equilibrium constant of component onKi,r= adsorption equilibrium constant of component i onKL = overall mass transfer coefficient in terms of liquidMi = molecular mass of species i, kg/molN = number of speciesN , = number of reactionsN , = rate of transfer of i from the gas bulk to the liquid

    bulk, mol/(mi2 )n = reaction orderpt = total pressure, Paq = heat flux, J/mi2sr, = reaction rate of reactionj per unit catalyst mass forR = gas law constant, J/(mol K)ReG = Reynolds number for the gas phase, d,G/pGReL = Reynolds number for the liquid phase, d /pLS = stoichiometric coefficient matrix; sb,i] is the stoichio-T = absolute temperature, KU , G = superficial gas velocity, r n ~ ~ / ( m , ~)u L l ~superficial liquid velocity, m~ ~ / ( m ?)XA = mole fraction of componentA in the liquid phaseYA = mole fraction of componentA in the gas phasez = axial coordinate in reactor, m,Greek Symbolsd~ = frictional pressure drop per unit length for gas flowonly, Palm,d~ = frictional pressure drop per unit length for liquid flowonly, Palm,,G = two-phase frictional pressure drop, Palm,

    E = bed void fraction, mP/m,3vr = effectiveness factor of reaction r for solid particle6 = radial coordinate, mpp~ = gas viscosity, Pa sp~ = liquid viscosity, Pa sQB = catalyst bulk density, kgcaJmr3ef= fluid density, kg/m?@G= gas density, k g / m ~ ~Q L = liquid density, k g / m ~ ~e, = density of the catalyst, kgcaJm,3u = hydrogenolysis site5 = hydrogenation siteS = cross section of reactor, m1.2SubscriptsBCH = bicyclohexylBPH = biphenylCHB = cyclohexylbenzeneDBT = dibenzothiophenef = fluidG = gas phase

    constant of componentA, m ~ ~ / m o la-sites, mL3/kmolmites, mL3flunolconcentration gradient, m ~ ~ / ( m i ~)

    heterogeneous reaction, mol/(kgcat )

    metric coefficient of component i in reactionj

    Literature CitedBroderick, D. H.; Gates , B. C. Hydrogenolysis an d Hydrogenationof Dibenzothiophene C atalyze d by Sulfided COO- Mo ody-Al203: The Reaction Kinetics. AZChE J . 1981,27, 63.BrulB, M. R.; Starling , K. E. Thermoph ysical Properties of ComplexSystems: Applications of Multiproperty Analysis. Znd. Eng .Che m. Process Des. Deu. 1984, 3, 33.Chilton, T. H.; Colburn, A. P. Mass transfer (absorption) coef-ficients. Prediction from data on heat tra nsfer and fluid friction.Ind . Eng . C he m. 1934,26, 183.Chung, T.; Ajlan, M.; Lee, L. L.; Starling, K. E. GeneralizedMultiparameter Correlation for Nonpolar and Polar FluidTransport Properties. Znd. En g. C hem. Res. 1988,27, 71.Froment, G. F.; Bischoff, K. B. Chemical Reactor Analysis andDesign, 2nd ed.; J. Wiley: New York, 1990.Graboski, M. S.;Dau bert, T. E. A modified Soave Equation of Statefor Phase Equilibrium C alculations 2. Systems containing COz,HzS, Nz and CO. Znd. Eng . Chem . Process Des. Dev. 1978,17,448.Hochman, J. M.; E fio n, E. Two-Phase Concurrent Downflow inPacked Beds. Znd. Eng. C hem. Fundam. 1969,48, 3.Houalla, M.; ag, N. K.; Sapre, A. V.; Broderick, D. H.; G ates, B.C. Hydrodesulfurization of Dibenzothiophene Catalyzed bySulfided CO0-MOOdy-&03: The Reaction Netw ork. M C h E J.1978,24, 015.Houalla, M.; Broderick, D. H.; Sapre,A. V.; Nag, N. K.; De Beer,V. H. J.;Gates, B. C.; Kwart, H. Hydrodesulfurization of Methyl-Subs tituted Dibenzothiophenes Catalyzed by Sulfided Co-Mol

    Ish ihar a, A,; Kabe, T. Deep Desulfurization of Light Oil. 3. Effectsof Solven ts on Hydrodesu lfurization of Dibenzothiophene. Znd.Eng. C hem. Res . 1993,32, 53.Kabe, T., Ishih ara A., Zhan, Q. Deep Desulfurization of Ligh t Oil.Part 2: Hydrodesulfurization of Dibenzothiophene, 4-Meth-yldibenzothiophene and 4,6-Dimethyldibenzothiophene. p p l .Catal. 1993, 7, 1.Kilanowski, D. R.; Teeuwen, H.; De Beer, V. H. J.; Gates, B. C.;Schu it, G. C. A.; Kwart, H . Hydrodesulfurization of Thiophene,Benzothiophene, Dibenzothiophene, and Related CompoundsCatalyzed by Sulfided CoO-Mo03/y-A1203: Low-Pressure Re-activity Studies. J. Catal. 1978,55 29.Lark ins, R. P.; White, R. R.; Jeffrey, D. W. Two-Phase Co ncurr entFlow in Packed Beds. AZChE J . 1961,47, 31.Lee, B. I.; Kesler, M. G. A Generalized Therm odynamic CorrelationBased on Three-Parameter Corresponding States. AZChE J.1975, 1, 10.Mears, D. E. The Role of Axial Dispersion in Trickle-FlowLaboratory Reactors. Chem. Eng. Sci . 1971,26, 361.Miller, J. T.; Hineman, M. F. Non-First-Order Hydrodenitroge-nation Kinetics of Quinoline. J . Catal . 1984,85, 17.

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    2988 Ind. Eng. Chem. Res., Vol. 33,No. 2, 1994Moysan, J. M.; Huron, M. J.;Paradowski, H .; Vidal, J. Predictionof the Solubility of Hydrogen in Hydrocarbon Solvents throughCubic Equations of State. Chem. Eng. Sei. 1983,38, 085.Nag, N. .; apre, A. V.; Broderick, D. H.; Gates, B. C. Hydrode-sulfurization of Polycyclic Aromatics Catalyzed by SulfidedCo0-M003/y-&03: The Relative Reactivities. J . Catal .1979,57, 09.Pille, R.; Froment, G. F. To be published.Peng, D. Y.; Robinson, D. B. A New Two-Constant Equation ofState. Znd. Eng . Chem. Fundam . 1976,15, 9.Reid, C. . ; Prausnitz, J.M.; Poling, B. E. The Properties of Gases& Liquids; McGraw-Hill: New York, 1987.Reiss, L. P. Cocur rent gas-liquid contacting in packed bed columns.Ind. Eng . Chem . Process Des. Dev. 1967, , 486.Sato, Y.; Hirose, H.; Takahash i, F.; Toda, M. Performance. of Fixed-Bed Catalytic Reactor with Cocurrent Gas-Liquid Downflow.First Pacific Chemical Engineering Congress; 1972; 187.Sha h, Y. T. Gas-Liquid-SolidReactor Design; McGraw-Hill: NewYork, 1979.

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    Received for review Ma rc h 15, 994Revised manuscript received A ugus t 4, 994Accepted Se p te mbe r 6, 994@@ Abstra c t publ ished in Advance AC S Abs trac ts, November1,1994.