Jerzy Szczygie?*,Marek Stolarski

Department of Chemistry,Wroclaw University of Technology,ul.Gdańska 7/9,Poland

Keywords:Coal extract Benzene insolubles Catalyst Depolymerization Kinetics

ABSTRACT Efficiency and selectivity of hydrogenating depolymerization of the coal extract benzene-insoluble part over the heterogeneous Co–Mo/Al2O3 catalystwere assessed using a mathematicalmodel.The analyticalequations of the mathematicalmodelwere generated based on materialbalance incorporating the physico-chemicalphenomena(reaction and diffusion)both in the autoclave and the catalyst grain.The equations offer the possibility for predicting changes of the reactants in the autoclave during the process and for determining the distribution of reactant concentrations in the grain as a function of its radius.The analytical equations of the model serve as the basis of the algorithm for assessing the in fluence of restrictive diffusion on the effectiveness and selectivity of the catalyst,and also for defining the optimal radii of the catalyst's pores to enable free transport of reactants in the grain interior.

1.Introduction

Liquefaction shows promise as a process for clean and effective upgrading of coal[1].Despite a large amount of effort involved and work done,coal liquefaction has not yet become competitive in economic terms.To develop a cost-effective process,itis essentialto understand the mechanism underlying coal liquefaction,as well as the role of catalysts in such processes.

One of the methods for converting coals into liquid fuels involves extraction of the coal with a hydrogen donor solvent followed by catalytic hydrogenating depolymerization of the coal extract.An essential stage in the hydrogenation of coal extracts to syncrude oil is catalytic depolymerization of heavy group components,i.e.benzene insolubles and asphaltenes.

Typical coal extracts obtained by extractive decomposition of bituminous coalmay contain more than 50%(by mass)ofheavy group components,including a substantial amount of the benzene insoluble fraction.That is why investigations into the kinetics and mechanism governing the catalytic hydrogenation of benzene insolubles and asphaltenes,and specifically studies on the role of the catalyst in the process[2–7],greatly facilitate the optimization of the parameters for the conversion of coal extracts into syncrude oils.

The kinetics of hydrogenation of coal[8–16]and heavy group components isolated from direct coal hydrogenation products and coal extracts has been the subject of many studies[8,9,13,14,17].So far,numerous kinetic models,simple and sophisticated,incorporating many lumps of conversion for heavy group components in the process of their catalytic depolymerization,have been developed based on the available data.This is attributable to the continuing effort to find the best fitting of experimental data with the results obtained from mathematical modeling of the process.Such fitting substantiates the theoretical assumptions for the physicochemical phenomena involved in the process and reflected in the equations of the mathematical model.All the studies have remarkably increased knowledge not only aboutthe chemical structure of coal,but also about the kinetics and mechanism of its hydrogenation.Nevertheless,analysis of the results obtained so far has revealed divergent views about the hydrogenation kinetics for coal and coal extracts.The underlying reason is the great number of factors affecting the progress of the process,such as the parameters of hydrogenation(temperature,hydrogen pressure or reaction time)or the parameters and grain size of the catalyst's porous structure.Another contributory factor in the assessment of the process kinetics is the type of the apparatus used(periodic and flow reactors).

The aim of this work was to develop a mathematical model describing the progress of hydrogenating depolymerization of benzene insolubles over a Co–Mo/Al2O3catalyst and assess the contribution of the catalyst to the effectiveness and selectivity of the process.Upon analysis ofthe physicochemicalphenomena occurring in the catalystpores(reaction,diffusion)and after establishing the material balance,the model offers the possibility of building such concentration profiles where the concentration ofdepolymerization reactants in the grain interioris related to the pore radius,and their concentration in the autoclave is related to the varying time of the reaction.Based on the analytical relations obtained,an algorithm was proposed for assessing the in fluence of restrictive diffusion on the effectiveness and selectivity of the catalyst,as well as for establishing the optimal pore radii in order to provide free transport of the reactants in the grain interior.

2.Experimental

2.1.Preparation of benzene insoluble fractions of coal extract

The benzene insoluble fractions(referred to as BIF or benzene insolubles)used in this study were separated from a coal extract obtained by treating bituminous coal(Type 32,coal mine Jankowice,Poland)with a hydrogen-saturated anthracene oil(distillation fraction 320–360 °C)at 10 MPa for 1 h.The coal extract was separated from the unreacted coal by filtration and thereafter dissolved in a 5fold amount of benzene.The benzene insoluble fraction was filtered and the residue was completely extracted with benzene in the Soxhlet apparatus.The group components obtained via this route served as feedstock for further kinetic studies.From the mixture of filtrate and benzene extract,benzene was distilled off first,followed by asphaltenes,which were precipitated with a 20fold amount of the isooctane:benzene(10:1)mixture.The precipitated asphaltenes were filtered and thereafter completely extracted with isooctane in the Soxhlet apparatus.Oil components were distilled off from the filtrate and isooctane extract mixture.

The initial composition of the coal extract included 34.0%(by mass)of benzene insolubles(BIF)；16.0%(by mass)of benzene-soluble isooctane-insoluble compounds,i.e.asphaltenes(A)；and 50%(by mass)of isooctane-soluble compounds,i.e.oils(O).

2.2.Catalytic hydrogenation of benzene insolubles

Experiments were carried out with 20 g of benzene insolubles in the presence of5.0 g ofCoMo/Al2O2catalystand 3.0 g ofCS2in a shaking autoclave at 400,430 and 460°C under hydrogen pressure of 29.4 MPa.The catalyst(symbol G1,manufactured by Zak?ady Chemiczne w O?wi?cimiu,Poland)was composed of 1.6%(by mass)CoO,16.8%(by mass)MoO3,and 81.6%(by mass)Al2O3.The autoclave was heated at the rate of 20°/min and maintained at a predetermined temperature for 20 to 25 min.Measurements were performed to establish the amount,density and composition(determined by gas chromatography)of gaseous product.Solid and liquid reaction products were removed from the autoclave by careful washing with benzene.The content of oils,asphaltenes and benzene insoluble product was then determined by solvent analysis as described above.The following group components were selected for further analysis:

(1)benzene insolubles(denoted by BIF),

(2)asphaltenes=benzene-soluble isooctane-insoluble product(denoted by A),

(3)oils=isooctane-soluble product(denoted by O or O*),

(4)gases(denoted by G).

The results of analysis are compiled in Table 1.According to the methodology adopted for kinetic studies,products are treated as chemical individuals,and conversions between group components as chemical reactions.

3.Chemistry of Conversion of Coal Extract Group Components and the Role of the Catalyst

Hypotheses about trends in the conversions and kinetics of hydrogenating depolymerization of heavy coal extract group components should be based on the knowledge of their chemicalstructure,which despite extensive research is still insufficiently understood.

Table 1 Experimental results of catalytical depolymerization of the benzene-insoluble part of coal extract

Although the literature contains many references to this issue,most of the investigations reported there pertain to the chemical structure of asphaltenes regarded as an intermediate product of coal-to-oil conversion[18–23].The chemical structure of coal-derived asphaltenes is in fluenced by the parent coal properties and production conditions[18,20].Asphaltenes isolated from hydrogen-donor extracts,with a molecular weight of 664–996× 10-27kg,have lower H/C and O/C atomic ratios,higher aromaticity factor(fa=70–85),and higher contents of basic nitrogen as compared with asphaltenes separated from bituminous and brown coal tar,or from products of toluene supercritical gas extraction of bituminous coal[18,20].There is a wide diversity of views about the origin of asphaltenes.According to some researchers,they are chemical combinations that form during thermal treatment of coal or its derivatives；according to others,asphaltenes occur naturally in the parent coal.Sternberg postulates that asphaltenes are composed of complexes bound with hydrogen bridges[24].In addition to non-covalent hydrogen bridges,asphaltenes contain covalent bonds characterized by low dissociation energies,e.g.methylene or oxygen bridges.These bridges connect statistical structural units that are probably built of 2 or 3 concentrated aromatic rings with one or two alicyclic rings which contain heteroatoms(mainly nitrogen)and are substituted with hydroxyl groups or short alkyl ligands[20].

The least recognized group component comprises benzene insolubles；among them are pre-asphaltenes,of which some part is insoluble in benzene but soluble in pyridine or THF[20].Compared with asphaltenes,benzene insolubles–and among them preasphaltenes with a higher thermal stability–are characterized by a noticeably lower hydrogen content and a higher content of heteroatoms,mainly nitrogen and oxygen.Pre-asphaltenes also display a higher molecular weight(1411–1660× 10-27kg),which is probably attributable to the formation of internal salts between the base nitrogen in the pyridine group and the acid phenol group.It is inherent in this structure that oxygen in the acid part occurs in form of phenolic hydroxyl group,and nitrogen is of an acid nature as in pyrrole.Base nitrogen occurs in the pyridine ring,and oxygen either in the ether ring or in the ether group.The complex is formed via the hydrogen bond between the acid phenol group and the base nitrogen group[25].

Fig.1.Network of reactions(conversions)in the depolimerization of benzene-insoluble process:BIF=benzene insoluble；A=asphaltenes；O and O*oils from consecutive and parallel reaction respectively.

As can be seen,the bonds and interactions between structural units in the molecules of asphaltenes and benzene insolubles are highly diverse and have a decisive in fluence on the interactions between molecules.Because of the wide spectrum of bonding power,the molecules ofthe group components are very unstable in relation to energy stimuli.With the rise in temperature,bonds of higher energy(ranging from non-covalent(hydrogen)bonds to covalent ones,such as methylene,oxygen or nitrogen bridges)undergo cleavage and thus enhance conversions of asphaltenes,pre-asphaltenes and benzene insolubles.

The primary reaction in the hydrogenating depolymerization ofbenzene insolubles and asphaltenes is the decomposition reaction.Molecules formed as a result of decomposition preserve their polar centers and are prone to re-polymerization.The high reaction temperature induces not only cracking of the covalent bonds that connect the aromatic structural units,but also thermal cracking of alkyl side ligands.This leads to the formation of molecules which become components of hydrocarbon gases.Further conversions of primary products are related with hydrogenation stabilizing the radical fragments of depolymerization.This stage can be carried out over a catalyst with accessible hydrogenating active sites dispersed on the developed intrinsic surface.The rate of this stage,however,is limited by geometry.Because of the large size of the radical fragments,their mobility in the catalyst's pores declines and thus reduces the rate of the process.To improve the conditions forthe transportofradicals inside the pores,itis essential to choose an optimal porous structure able to minimize the restrictive diffusion of reactants in the catalyst's pores[26–29].

3.1.Preliminary verification of the kinetic scheme(Model 1)

Fig.1 shows the conversion network,which by intuition,as well as based on the general knowledge of the process,can be realized in the course of hydrogenating depolymerization of the BIF.

Good approximation of experimental results(Table 1)by the integrated equations ofthe setbelow(which represents the conversion network proposed):

substantiates the adequacy of the adopted description and the choice of the network of the reactions describing the process[Fig.2(a)–(c)].The effective rate constants of conversions(calculated for Model 1 with the optimizing procedures of the Matlab program as the more effective ones)(Table 2)can be used at a further stage for the construction of the kinetic–diffusion model(Model 2)of the process,with the inclusion of the reactions and reagent transport resistances in the catalystgrain.The effective rate constants were used forthe assessment of theoretical rate constants(ki),which are related to the catalyst's unit surface and reflect its activity.

4.Construction of the Kinetic–Diffusion Model(Model 2)

Defined in the adopted kinetic scheme(Fig.1)and treated as reactions,the changes in the hydrogenating depolymerization process over a catalyst occur at different rates.In such instance,under the same process conditions,slower reactions may occur in the kinetic regions,while the faster ones are limited by restrictive diffusion and thus reduce the rate of the entire process,where the extent of mass transfer is in fluenced by the porous structure of the catalyst grain.The character of the effect of diffusion limitation on the overall rate and selectivity of composite reactions depends on the structure of the complex conversions.A complete mathematical model describing the process of hydrogenating depolymerization is to be built based on the analysis of material and heat balance at the level of both catalyst grain and autoclave.Assumption of adiabatic conditions for the process reduces the model equations to those resulting from mass balance only.

4.1.Model at the grain level

The boundary conditions have been formulated as follows:

This set of differential equations results from the material balance in the catalyst's grain,where the reactants transported in the pores undergo first-order reactions(according to the adopted kinetic scheme)on the intrinsic surface of these pores.In fluenced by the value of parameter q,the equations of set(2)generate analytical expressions that relate the normalized values of reactant concentrations to the normalized values of the grain radius for different grain shapes:slab(q=0),cylinder(q=1)and sphere(q=2)(Table 3).The parameters of these expressions(D and k)can be estimated(similarly as in Model 1)at the stage of their assessment,after the equations describing the change in reactant concentrations over time(in the autoclave)had been fitted to the experimental results.

4.2.Model at the autoclave level

Upon substitution of the reaction time parameter for the coordinate of reactor length,the model of a reactor with ideal plug flow can be used to describe the process in an autoclave with ideal mixing.Hence,the distribution of reagent concentrations(predicted in Fig.1)over time can be described by the following set of equations:

The initial conditions being:

where:

t coordinate of time,

ri(i=BIF,A,O,O*,G)velocity of formation or disappearance of the reactant at moment t defined by the flux value calculated in terms of Eq.(4):

Fig.2.Change in substrate content at time t.Line for Model 1 and experimental points:(a)400 °C；(b)430 °C；(c)460 °C.

?

Table 3 Equations describing the concentrations of depolimerization substrates inside a slab-shaped spherical and cylindrical grain according to Fig.1

where:

?0=modified Thiele modulus incorporating the components of conversions of paraffins to asphaltenesand gases

Eqs.(6a)–(6f)that describe the process at the autoclave level,together with the equations that define the change in the reactant concentrations at the level of the slab-shaped grain(Table 3),provide a full range of analytical relations that depict the process of hydrogenating depolymerization at the adopted assumptions.When use is made of appropriate relations included in Table 3(for the spherical or cylindrical grain),an analogous model of the process may incorporate the shape of the grain,as well as the physicochemical phenomena occurring in the grain(reaction and mass transport).

5.Efficiency and Selectivity

5.1.Efficiency

The coefficient of catalyst grain efficiency,η,is defined by the general equation:

where rBIFis the rate of conversion(disappearance)of the starting compound(BIF)in the grain's unit volume.

In the absence ofrestrictive diffusion in the grain and atthe assumption that first-orderreactions are involved in the process(Fig.1)(intrinsic reaction rate),the rate of feedstock conversion is defined as follows:

The actual rate of feedstock disappearance can be calculated by virtue of equation:

Ifwe incorporate the reduced values of z/R0=ρa(bǔ)nd CBIF/CBIF,s=cBIF,and take into account the value for the slab-shaped grain(Vz/Sz=R0),we have:

where:

υ= 1,2,3 for slab,cylinder and sphere,respectively,

υ= shape factor of the catalyst

υ = 1a an in finite slab,υ =2a an in finite cylinder,υ=3a an in finite sphere

?=

0modified Thiele modulus incorporating c onversions of benzene insolubles to asphaltenesand gasesand if we furthermore take into account the relation(derived earlier)that defines the stream of the feedstock(BIF)on the grain surface(Table 3),Eq.(10)becomes:

5.2.Selectivity

The relations of Eq.(6)offer the possibility of controlling the profiles of reactant concentrations during hydrogenating depolymerization of benzene insolubles in the autoclave according to the adopted scheme.The model includes the effect of the conditions of reactant transport in the(slab-shaped)grain of the catalyst over which the process is conducted.Having such a model,it is possible to discuss the overall selectivity of the reactions(conversions)included in the scheme.Selectivity defined as the ratio of the quantity of product expected to the quantity of feedstock(BIF)converted takes the form of the following expression:

which,after substituting appropriate relations of Eq.(6),generates equations that describe the change in selectivity of the adopted reactants in the course of the process.Hence,for asphaltenes we obtain:

for oils from consecutive reactions we have:

and for oils from the parallel reaction we can write:

It is essential to note that the selectivity of the oils produced by the parallel reaction does not depend on the duration of the process；it depends only on the values of the kinetic constants(rate constants).And that is why the selectivity of these oils takes a constant value in fluenced by the quotient of appropriate rate constants.

Dividing each of the equations incorporated in set(3)by the first equation we obtain the following general relations:

which after integration(under boundary conditions of the system)give equations that relate the concentrations of particular conversion products(under conditions of restrictive diffusion)to the co-existing unreacted feedstock:

where:

Fig.3.Change in reactant content at time t.Line for Model 2 and experimental points:(a)400 °C；(b)430 °C；(c)460 °C.

Upon substitution of

the equations may be useful when determining the effect of feedstock conversion,(100-cBIF),on the maximal yield of the product desired(asphaltenes,oils),and when assessing the effectofdiffusion on this yield.

After incorporation of Eqs.(17)and(18)into Eq.(12),we can assess the selectivity of the process as a function of the reacted part of the feedstock.

6.Model Parameter Estimation and Concentration Profiles

The parameters of Model 2[set of Eq.(6)]are the following effective coefficients of diffusion:benzene insolubles and asphaltenes(considered as chemical individuals)in the catalyst grain,(DBIF,ef；DA,ef)；Thiele moduli of relevant conversions in the kinetic scheme,(?1,?2,?3,?4)；time of induction,τ0,and feedstock(BIF)concentration after time ∞,(CBIF,∞).Thus the rate constants of the reactions(conversions)related to the unitsurface ofthe catalystare explicitly described by the estimated values of the model parameters.The parameters of the model were estimated for each temperature by minimizing the objective function

Xi,jexperimental value of i th component concentration at the j th moment of time,

Xi,j(ti) value of i th component concentration at the j th moment of time calculated from the model.

To carry out the task of nonlinear programming defined in this way,use was made of the optimizing procedures implemented in Mathematica(Minimize),Global Optimalization 7.0(GlobalSearch)and Matlab(ktrlink).In order to achieve the best solution of the problem for the systems chosen,optimization was performed using the relations between theoretical and effective values of the rate constants of conversion(conditional optimization):

The kefvalues were calculated from an additionally performed numerical estimation of these parameters via fitting of the kinetic equations represented by Fig.1 to the experimental results；Matlab —ktrlink,tab(2).

Fig.4.Profiles of reactant concentrations in catalyst grain:400 °C(dashed line)；460 °C(solid line).

Although all of the procedures[for the conditions of Eq.(22)]indicated a global minimum of function(21),the GlobalSearch and ktrlink procedures were found to be most effective(Table 2).The numerical values ofthe rate constants ofconversions,calculated using the estimated parameters,increase with the rise in temperature,according to general laws.Even though they represent conversions of group components and not individual reactions,they ful fill,approximately,the Arhenius law(Fig.5)and thus confirm the correctness of reduction in the number ofreactants for the depolymerization ofbenzene insolubles,as well as the correctness of the assumptions about the directions of conversions in the investigated process.The fitting of the theoretical curves representing Model 2 was found to be satisfactory(Fig.3a–c).

7.Optimal Radius of the Catalyst

Fig.5.Arrhenius lines for reaction rate constants(Fig.1)in Model 2.

Fig.6.Yield of depolymerization reactants related to conversion of benzene insolubles:400 °C(dashed line)；460 °C(solid line).

The rate at which the catalytic conversion of benzene insolubles occurs is limited by the restrictive diffusion of large BIF molecules in the catalyst's pores.If the diffusion rate is significantly lower than the intrinsic surface-reaction rate,only the extrinsic portion of the grain is utilized,which reduces the effectiveness of the catalyst.Transport conditions in the grain can be improved by the choice of an appropriate porous structure,which facilitates access to the intrinsic surface and active sites for the reactants.As for the depolymerization of benzene insolubles,the requisite for defining the efficiency of a porous catalyst is good knowledge of how the relationship between the size of the diffusing molecule and the radii of the pores in fluences the effective coefficient of diffusion.Investigations into restrictive diffusion of molecules with similar sizes(2.5–10 nm)in the catalyst's pores and in membranes have been reported since the 1950s[30–39].The problem of optimizing the pore radius in the case of large molecule conversion on the intrinsic surface of the grain was examined by Rajagopalan and Luss(1979),and also by Ruckenstein and Tsai(1981),DO(1984)[32–34].The existence of an optimal pore radius can be inferred from the fact that the increase in its value has two conflicting effects:the intrinsic surface of the grain decreases,and the rate of reactant diffusion to the active sites on that surface increases.It has been found that the optimal pore diameter cannot be larger than five times the diameter of the diffusing molecule[31].

7.1.Definition of the problem

Fig.7.Selectivity of depolymerization products related to conversion of benzene insolubles:400 °C(dashed line)；460 °C(solid line).

Fig.8.Effectofrestrictive diffusion on the selectivity ofdepolymerization products related to reaction time:400 °C(dashed line)；460 °C(solid line).

To optimize the pore radius of the catalyst for the process of liquid fuel production from coal by hydrogenating depolymerization of benzene insolubles,itis necessary to scrutinize the equation ofmass balance in the catalyst's grain,taking into account two basic physicochemicalphenomena:diffusion and reaction.Considering conversion as a firstorder reaction,we can write the balance equation in the form of:

The effective coefficient of diffusion(Deff)is a function of the ratio of the molecule diameter to the average diameter of the catalyst's pore:

as well as a function of the equilibrium partition coefficient(KP=Cp/Cb).In the case of benzene insoluble conversion it should be expected that Cp＜Cb,and that the partition coefficient can be estimated from the formula:

Fig.9.Plot of reaction rate vs.reactant radius/average pore radius ratio.

where:

ds,dpBIF molecule diameter and catalyst pore diameter,respectively

Cp,Cbconcentration at pore inlet and bulk concentration,respectively.

For such conditions(Kp＜1)Renkin's theoretical relation becomes[36]:

where:

with:

and Eq.(23)can be written as:

Since the intrinsic surface of the grain is related to pore radius and pore volume by virtue of

and assuming that pore volume does not change with the change in pore radius,the intrinsic surface of the grain is inversely proportional to the pore radius.

Substituting the relations of Eqs.(26)and(30)into Eq.(29)we obtain:

The solutions to this form of the equation for different shapes of the grain(Table 1)now describe the analytical relations of feedstock(BIF)concentration distribution in the differently shaped catalyst grains,with consideration of the size of their pores.

The optimal value of λ is such that under conditions of equilibrium enables the largest possible feedstock stream to be directed to the interior of the grain where the concentration of the feedstock on the extrinsic surface equals C.The in-grain conversion of the feedstock conveyed by this stream per unit time is a measure of the effective rate constant value.Making use of the analytical relations derived earlier for the assessment of the feedstock stream(Table 3),as well as the relations of Eqs.(10)and(31)for the slab-shaped catalyst grain,we obtain:

The value of kefdescribed by the relations of Eq.(32)increases with the value of λ and decreases with the value of(1- λ)when λ increases.Hence,we have an optimal value of λ for which the dimensionless reaction rate is maximal,as can be seen in Fig.9.The existence ofthe optimal pore size is substantiated by the factthatthe increase in pore size,which reduces the limitations of feedstock transport in the grain,simultaneously diminishes the grain's intrinsic surface where the reaction occurs.

8.Conclusions

Verification of the mathematical model with experimental results has confirmed the correctness ofthe kinetic scheme for the hydrogenating depolymerization of benzene insolubles.The beneficial role of the catalyst consists most probably in the stabilization and hydrogenation ofthe radicaldepolymerization fragments on the active sites.These radical fragments are large enough to hinder their mobility in the catalyst's pores.To reduce the effectof geometry on the rate of the process atthat stage,it is essential to find an optimal porous structure for the grain,with the ability of minimizing the restrictive diffusion of the feedstock in the catalyst's pores.It has been demonstrated that the optimal radius of the catalyst depends on the value of the Thiele modulus,and that it ranges from 0.2(for ? =2)to 0.4(for ? =0.5),when defined by the ratio of the reagent's molecule radius to the grain's pore radius(λ).The analytical equations of the mathematical model were generated based on material balance,which includes the physicochemical phenomena(reaction and diffusion)occurring both in the autoclave and in the catalyst's grain.With such equations it is possible to predict changes in the concentrations of the reagents during the process(Fig.3)and the distribution of concentrations in the grain as a function of its radius(Fig.4).Analysis of Eqs.(17)to(20)has revealed that irrespective of temperature the quantity of oil components formed during the parallel reaction directly from benzene insolubles is in linear relation to the quantity of feedstock converted.Oil components obtained indirectly via asphaltenes are formed after complete BIF conversion(Fig.6).Under conditions of restrictive diffusion,the selectivity[Eq.(12)]of the oils generated in the parallel reaction depends solely on the kinetic parameters.This is why selectivity stabilizes at a high level as a function of both feedstock conversion(Fig.7)and time(Fig.8).The selectivity of the reaction where oils are formed from asphaltenes is low and rises slightly as feedstock conversion increases.Fig.8,which relates the selectivity ofsome reactions to time and temperature,corroborates the above mentioned findings.Thus,the selectivity of the benzene insolubles→asphaltenes reaction decreases with time and temperature[plots(1,1′,1″)],which indicates that with the rise in temperature the quantity of the oils obtained directly from benzene insolubles(parallel reaction)increases,although at higher temperatures(430 and 460°C)the selectivity of the oils generated via this route is much the same,approaching 0.45.The selectivity of the asphaltenes→oils reaction decreases with temperature and increases with time,reaching an asymptotic value of about 0.25(also at 430 and 460°C).Only at lower temperatures(400°C)and after a certain time was the selectivity of the asphaltenes→oils reaction higher than that of the benzene insolubles→oils reaction.And this implies that under such conditions most of the oil components are formed in the consecutive reaction.Hence,taking account of the fact that oil components are the final product,the process should be conducted at higher temperatures,because then the selectivity of the benzene insolubles→oils reaction is higher.Nomenclature

a activity of grain

Cii=BIF,A,O,O*,concentrations of reactants in autoclave

CBIF,fconcentrations of benzene insolubles after time t=∞

Ci,gconcentrations of reactants in catalyst grain

Cbbulk concentration

Cpconcentration at pore mouth

Dbbulk diffusivity

Di,efeffective coefficients of diffusion

dsmolecule diameter

dpaverage pore diameter

Kpequilibrium partition coefficient

k1,k2,k3,k4experimentalreaction rate constant related to unitmass of catalyst

kii=1.4 rate constant per surface of catalyst substance

Ρppellet density

R0grain radius

Sginternal surface area per gram of catalyst pellet

Vgpore volume per gram of catalyst pellet

γ grain density

εppellet voidage

λ ratio of reactant molecular size to pore size

ρ reduced grain radius

τ tortuosity factor

Acknowledgments

The results published were generated using the supercomputer‘nova’at Wroclaw Centre for Networking and Supercomputing.

Financial support by MNiSzW(S405 62)is gratefully acknowledged.