Ind. Eng. Chem. Fundam., Vol. 18, No. 2, 1979 149 t t , t, = constants defined in eq C7 u = liquid reactant concentration, dimensionless u1 = liquid reactant concentration in region 1,dimensionless uz = liquid reactant concentration in region 2, dimensionless
V = total volume of the pellet, cm3 V , = wetted region of the cylindrical pellet, cm3 V , = dry region of the pellet, cm3 Vs = wetted region of the spherical pellet, cm3 Vw = wetted region of the pellet, cm3 Greek Letters ai,= matrix element defined in eq 13 t = concentration of reactant in the vapor phase, dimensionless ~ C = E external contacting efficiency, dimensionless qr = fractional pore-fill-up, dimensionless 7TB = effectiveness factor in a trickle-bed reactor, dimensionless 0 = azimuthal or polar angle for cylindrical and spherical shapes, radians Bo = angle to which external catalyst surface is wetted for cylindrical and spherical shapes, radians OT = effectiveness factor in a completely wetted pellet, dimensionless 7mm= effectiveness factor in a trickle-bed in absence of mass transfer limitations, dimensionless A = modified modulus of Aris defined in eq 63 pnl, pn2 = dual-series modifiers appearing in eq 60 and 61 v = coordinate in the normal direction i1 = dimensionless I coordinate t 2= dimensionless y coordinate Eo = dimensionless artificial interface location $ = Thiele modulus [ = L ( k / D , ) 1 / 2 dimensionless ] = Thiele modulus [ = L(k'/D,)l/z]for corresponding vapor phase reaction in dry region of the pellet appearing in eq la, dimensionless * , , ( F )= function defined in eq 60 and 61 Literature Cited Aris, R., Chem. Eng. Sci., 6, 262 (1957). Bablojan, A. A., Akad. Nauk Armjan, SSR Dokl., 149 (1964). Blanch, G., SIAM Rev., 6(4), 383 (1964). Chu, C., Chon, K., J . Catal., 17, 71 (1970).
Colombo, A. J., Baldi, G., Sicardi, S.,Chem. Eng. Sci., 31, 1101 (1976). Collins, W. D., Arch. Rat. Mech. Anal., 11, 122 (1962). Collins, W. D., Proc. Cambridge Philos. SOC., 57, 367 (1964). Cooke, J. C., Glasgow Math. J . , 9, 30 (1968). Cooke, J. C., Glasgow Math. J . , 11, 9 (1970). Cooke, R. G., "Infinite Matrices and Sequence Spaces", Macmillan, London, 1950. Davidson, J. F., Cullen, E. J., Hansen, D.. Roberts, D., Trans. Inst. Chern. Eng., 37, 122 (1959). DudukoviB, M. P., AIChE J . . 23, 940 (1977). Dudukovie, M. P.. Mills, P. L., ACS Symp. Ser., No. 65, 387 (1976). Frye, C. G., Mosby, J. F., Chem. Eng. Prog., 63, 66 (1967). Germain. A. H., Lefebvre, A. G., L'Homme, G. A,, Adv. Chern. Ser., No. 133, 164 (1974). Henry, H. C.. Gilbert, J. B., Id.Eng. Chem. Process Des. Dev., 12, 328 (1973). Hobson, E. W., "The Theory of Spherical and Ellipsoidal Harmonics", Chelsea Publishing Co., New York, N.Y., 1955. Kantorovich, L. V., Krylov, V. I., "Approximate Methods of Higher Analysis", Eng. Transl., C. D. Benster, Noordhoff, Groningen, 1958. Kesten, A. S.,Sangiovanni, J. J., Chem. Eng. Sci., 26, 533 (1971). Lapidus, L., Ind. Eng. Chern., 49, 1000 (1957). Mears, D. E., Adv. Chem. Ser., No, 133, 218 (1974). Meyer, W. W., Hegedus, L. L., Aris, R., J . Catal., 42, 135 (1976). Mills, P. L., DudukoviB, M. P., submitted to Chem. Eng. Sci. (1979). Onda, K., Takeuchi, H., Kayama, Y., Kagaku Kogaku, 31, 126 (1967). Pismen, L. M., Chem. f n g . Sci., 31, 693 (1976). Ramachandran, P. A., Smi!h, J. M., Submitted to AIChE J . (1978). Riesz, F., "Les Systemes d Equations Linearires 6 une InfinitB dInconnues", Gauthier-Villars, Paris, 1913. Rony, P. R., Chem. Eng. Sci., 23, 1021 (1968). Satterfield, C. N., Pellossof, A. A., Sherwood, T. K., AIChEJ., 15, 226 (1969). Satterfield, C. N., Ozel, F., AIChE J . , 19, 1259 (1973). Satterfield, C. N., AIChE J . , 21, 209 (1975). Schiesser, W. E., Lapidus, L., AIChE J . , 7, 163 (1961). Schwartz, J G., Weger, E., DudukoviC, M. P., AIChf J . , 22, 953 (1976). Schwartz, J. G., DudukoviE, M. P., Weger, E., Fourth Int. Symp. Chem. Reaction Eng. Preprints, Heidelberg, W. Germany, Apr 6-8, 1976. Sedriks, W., Kenny, C. N., Chem. Eng. Sci., 28, 559 (1973). Sneddon, I.N., "Mixed Boundary Value Problems in Potential Theory", Wiley, New York, N.Y., 1966. Tranter, C. J., Proc. Glasgow Math. Assoc., 4, 49 (1959). Tranter, C. J.. Proc. Glasgow Math. Assoc., 4, 198 (1960). Tranter, C. J., Roc. Glasgow Math. Assoc., 6, 136 (1964). Weekman, V. W., Ind. Eng. Chem., 61(2), 53 (1969). Whiteman. J. R., Quart. J . Mech. Appl. Math., 21, 41 (1968). Whittaker. E. T., Watson, G. N., "A Course of Modetn Analysis", 4th ed,Cambridge University Press, 1946. Yitzhaki, D., Aharoni, C., AIChE J . , 23, 342 (1977).
Received for review June 12, 1978 Accepted January 25, 1979
Solid Solubilities of Heavy Hydrocarbons in Supercritical Solvents Michael E. Mackay and Michael E. Paulaitis" Department of Chemical Engineering, University of Delaware, Newark, Delaware
1971 1
A calculational method is presented for determining the solubility of condensed, nonvolatile components in supercritical solvents by treating the supercritical fluid-phase mixture as an expanded liquid. The procedure is directly applicable to phase equilibrium calculations associated with extraction processes utilizing supercritical solvents. Two mixture parameters are required in the formulation for a binary system-an activity coefficient at infinite dilution for the heavy solute and a binary interaction parameter (Le., k , , in the Redlich-Kwong equation of state). The advantage of this approach is that both mixture parameters exhibit consistent, predictable behavior for highly asymmetric mixtures in the vicinity of the critical region. The utility of this method is illustrated using experimental data for the solubility of solid naphthalene in supercritical carbon dioxide and in supercritical ethylene.
Introduction
Renewed interest in utilizing supercritical fluids as solvents for new high-pressure gas extraction processes is increasing and is based on the appreciable increase in solvent power of the supercritical fluid at temperatures and pressures not far removed from the critical point. The primary advantage of this extraction method over more conventional separation methods is that the separation can 0019-7874/79/1018-0149$01.00/0
be accomplished at relatively moderate temperatures and hence is particularly well suited for recovering nonvolatile species that are not stable at high temperatures. Another advantage of solvent extraction with supercritical fluids is that the enhanced solubility effect is completely reversible and very sensitive to changes in temperature and pressure. Consequently, the separation process can be controlled closely and is capable of being highly selective. 0 1979 American Chemical Society
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Ind. Eng. Chem. Fundam., Vol. 18, No. 2 , 1979
At present, thermodynamic correlations for predicting the solubility of heavy solutes in supercritical solvents are limited by a lack of understanding of both the dense-fluid state and highly asymmetric mixtures containing complex molecules. In this work, a thermodynamic model for the supercritical fluid-phase mixture is formulated by treating this state as an expanded liquid and utilizing activity coefficients a t infinite dilution in the phase equilibrium calculations. The formulation offers the possibility of predicting solubilities of heavy solutes in supercritical solvents and provides a reliable method for correlating and extending experimental solubility data.
Thermodynamic Model The solubility of a condensed, nonvolatile solute (component 2 ) in a supercritical solvent (component 1)is determined from standard thermodynamic relationships by equating the condensed-phase and fluid-phase fugacities for the heavy component
fzC = fzF The fugacities are calculated from conveniently chosen constitutive equations, related to the phases in equilibrium and to the nature of the mixture components. For the supercritical fluid phase, the binary mixture is not far removed from its critical point and contains components that are very dissimilar in molecular nature. These conditions impose extremely high demands on the constitutive relations required to evaluate the fugacity for this phase. The conventional approach is to treat the supercritical fluid as a highly compressed gas and determine the fluid-phase fugacity from volumetric properties f2F
0000 1
'
0
I
50
I
100
I
150
I
200 PRESSURE ( a t m )
I
250
300
Figure 1. Experimental and calculated solubilities for solid naphthalene in supercritical ethylene at 1 2 and 35 "C.
component in the light solvent. A convenient choice for the reference pressure is the critical pressure of the solvent P,. At this pressure, the solubility of the heavy component is negligible and the activity coefficient is essentially the activity coefficient a t infinite dilution, rz"(P,),which is a constant a t a fixed temperature. For the limited solubility range under consideration, it is a good approximation to use both this infinite-dilution activity coefficient and the partial molar volume at infinite dilution in eq 3. The resulting expression for the fluid-phase fugacity becomes
= Y2hP
where y2 is mole fraction of the heavy solute and P is the system pressure. The fugacity coefficient &, which characterizes the nonideal behavior of the supercritical fluid with respect to the ideal-gas state, is obtained from an equation of state using exact thermodynamic relationships (Sandler, 1977). Accurate determination of the solubility requires accurate evaluation of the fugacity coefficient and provides a stringent test for any equation of state. At moderate pressures-below the critical pressure of the light component-it is convenient to use the virial equation of state to calculate the fugacity coefficient, since reliable methods are available for obtaining second virial coefficients for these mixtures (Kaul and Prausnitz, 1977). A t higher pressures, the utility of the virial equation is limited by a lack of knowledge about higher-order virial coefficients, and the fugacity coefficient must be determined from an empirical equation of state, such as a Redlich-Kwong type equation. The resulting solubility calculations will be very sensitive to the empirical mixing rules that are required for these equations of state. An alternative approach is to treat the supercritical fluid as an expanded liquid. At a fixed temperature T , the fluid-phase fugacity is a function of pressure P and mole fraction y z
The standard-state fugacity f2OL is the fugacity of the pure liquid, determined a t the temperature T and an arbitrary, fixed reference pressure Po. The activity coefficient y2 is also evaluated a t the fixed reference pressure and, at constant temperature, is a function of composition only. The effect of pressure is accounted for by the Poynting correction and the partial molar volume of the heavy
Since the supercritical fluid mixture is highly compressible in the critical region, an equation of state will be required to evaluate the partial molar volume a t infinite dilution
(5) However, the equation of state is introduced in a more limited sense here than in eq 2, as a Poynting correction for pressures above the critical pressure of the solvent, while the mixture nonidealities (at the critical pressure) are accounted for by the activity coefficient a t infinite dilution. The infinite-dilution activity coefficient will be a characteristic parameter for the binary mixture and therefore is obtained from mixture data. Data Reduction Experimental data for the solubility of solid naphthalene in supercritical ethylene (Diepen and Scheffer, 1953; Tsekhanskaya et al., 1964) and in supercritical carbon dioxide (Tsekhanskaya et al., 1964) are used to demonstrate the utility of this approach and compare it with the method of treating the supercritical fluid as a highly compressed gas. The experimental solubility data are depicted in Figures 1, 2, and 3 over a range of pressures above the critical pressure of the light component and for various isotherms above the critical temperature of the light component. For these calculations, the solubility of the supercritical solvent in the solid phase is considered negligible and the condensed-phase fugacity is the fugacity for pure solid naphthalene. A t the fixed temperature T , this fugacity is
Ind. Eng. Chem. Fundam., Vol. 18, No. 2, 1979
151
Table I. Binary Interaction Parameters Obtained from Eq 7 temp, system CO,-C, C,H,-C,
1
' k , , = 1(ala2)"21.
A T:45'C TSEKHANSKAYA, el al 11964) V T=45'C DIEPEN ond SCHEFFER 11953) O T = L J ' C TSEKHANSKAYA. el 0 1 1 1 9 6 4 ) O T = Z 5 ' C DIEPEN ond SCHEFFER ( 1 9 5 3 ) CALCULATED FROM EQUATION 8
0H 8
nH,
0
150
100
50
200
250
CO,-C, n H, C,H,
I
I
I
--
I
I
--
-
-
--.-m-
W
35 45 55 12 25 35
-0.005 -0.010 -0.020 -0.070 -0.080 -0.105
0.085 0.070 0.040 0.015 0.0 - 0.05
temp, system
300
PRESSURE l a t m )
I
PengRobinsod
[a,,/
Table 11. Mixture Parameters Obtained from Eq 8
Figure 2. Experimental and calculated solubilities for solid naphthalene in supercritical ethylene at 25 and 45 "C. 0 1000
RedlichKwong'
[Tc,,/(Tc,Tc,)"21. b S 1 2 = 1-
-
0000l
'C
'k , ,
=
-c, n H,
'C
RedlichKwong'
In y 2 m
35 45 55 12 25 35 45
0.08 0.08 0.08 0.03 0.03 0.03 0.03
6.768 6.745 6.413 7.359 7.313 6.888 6.321
1 - [Tc,2/(TclTc2)1'Zl.
W
---
0 0 I 00 : X
-
a .0 u
z 0
--
The pure-component fugacity ratio for solid and subcooled liquid naphthalene is obtained from
-
0
aoo010~
5 W
s:
-
--
00001 0
3 -x Tz35'C TSEKHANSKAYA. e l 0 1 1 1 9 6 4 1 T = 4 5 ' C TSEKHANSKAYA, el 01 ( 1 9 6 4 ) A T = 5 5 * C TSEKHANSKAYA, et 01 ( 1 9 6 4 1 CALCULATED FROM EQUATION a
I
I
I
I
I
1
50
100
150
200
250
300
-
-
where fioS is the fugacity of pure solid naphthalene a t the temperature T and reference pressure P.The integration in eq 6 is accomplished by assuming the molar volume of solid naphthalene is constant over the indicated pressure range. If eq 2 is used for the supercritical fluid-phase fugacity, then the reference pressure in eq 6 is chosen to be the saturated vapor pressure of naphthalene PzAT at the fixed temperature T. The solubility of naphthalene in the supercritical fluid phase is obtained by substituting eq 2 and 6 into eq 1
where $ I is ~the ~fugacity ~ ~coefficient for the saturated vapor. If, instead, eq 4 is used for the supercritical fluid-phase fugacity, the reference pressure in eq 6 is taken to be the critical pressure of the solvent, and the resulting solubility expression, a t a fixed temperature, becomes
where the normal melting temperature Tm2of naphthalene is substituted for the triple point temperature. The last three terms in eq 9 are much less significant than the first, and to a good approximation, the fugacity ratio a t any temperature is determined from the normal melting temperature and the heat of fusion, AhZfu*, a t this temperature. To determine the fugacity coefficient in eq 7 and the partial molar volume a t infinite dilution in eq 8, the Redlich-Kwong equation of state (Redlich and Kwong, 1949) was chosen, using the mixing rules given by Chueh and Prausnitz (1967). Solubility calculations with eq 7 are also accomplished using the Peng-Robinson equation of state (Peng and Robinson, 1976). The mixing rules for both equations of state contain an adjustable binary parameter that characterizes deviations from the geometric mean average for molecular interactions between unlike mixture species. Values for this binary interaction parameter are obtained by fitting the experimental solubility data using eq 7 and 8. The best-fit values are given in Tables I and 11, respectively. Solubility calculations with eq 8 also require a second mixture parameter, the infinite-dilution activity coefficients, which are likewise obtained from the experimental data and given in Table 11. The solubilities calculated from eq 8 with the parameters in Table I1 are depicted in Figures 1, 2, and 3 with the experimental data. Discussion of Results The solubility calculations performed with eq 7 require pure-component properties for the mixture constituents and one binary interaction parameter for each pair of components in the system. In principle, this parameter is considered to be a true molecular constant, independent of temperature, pressure, and composition, and is well
152
Ind. Eng. Chem. Fundam., Vol. 18, No. 2, 1979
Table 111. Density-Corrected Activity Coefficients a t Infinite Dilution for Naphthalene in Supercritical CO, temp, system
co,-c,
0%
"C
press, atm
corr 7 , -
35 45 55
120 150 2 30
40.9 34.0 27.5
comparison is made a t constant density-corresponding to saturated liquid COz at 20 "C-by adjusting the pressure of supercritical COz at a fixed temperature, and calculating a "density-corrected" activity coefficient at infinite dilution 300
310
320
330
340
350
1031~
Figure 4. Temperature dependence of yzmfor COz-C,oHB and C2H,-C,JIs compared with eq 10.
characterized for an extensive amount of mixture data in the literature (Oellrich e t al., 1977). Two conclusions are evident concerning the behavior of this parameter in eq 7 , for both the Redlich-Kwong and Peng-Robinson equations of state. First, the binary interaction parameters for both mixtures are highly temperature dependent, decreasing as the temperature increases away from the critical temperature. This behavior holds for both equations of state. Second, although the orders of magnitude of the binary interaction parameters are reasonable, the negative values for these highly asymmetric mixtures are not expected, based on simple molecular arguments. Negative values are obtained for both equations of state, but predominantly for the Redlich-Kwong equation. The results show that these empirical equations of state and their associated mixing rules are not adequate for mixtures containing large and small molecules and for situations in the critical region. The practical consequence of this conclusion is that estimating a single, characteristic binary interaction parameter is not feasible. Since the solubility calculations are sensitive to the value of this parameter, predicting solubilities with this approach does not appear promising. The alternative method of calculating solubilities with eq 8 gives results in good agreement with the experimental data as shown in Figures 1, 2, and 3. The binary interaction parameters for the Redlich-Kwong equation of state are constant with temperature for each system, and the values of 0.08 for COZ-CloH8and 0.03 for CzH4-CloH8 appear reasonable and consistent with one another when compared with other data involving COz and CzH4 (Oellrich et al., 1977). The temperature dependence, noted previously for the binary interaction parameters in Table I, is now absorbed into the activity coefficients at infinite dilution. This dependence is defined rigorously by the Gibbs-Helmholtz relation
[
&*E
=
R
where the excess partial molar enthalpy hzEis a constant over the limited temperature interval of the experimental data. Figure 4 illustrates the comparison between this relation and the infinite-dilution activity coefficients in Table 11. The agreement indicates that the observed temperature dependence of y Z mis consistent with eq 10 and suggests that reliable temperature extrapolations can be made. The activity coefficients a t infinite dilution obtained for the naphthalene-supercritical COz mixtures can be compared with yZmvalues obtained from experimental data for the solubility of solid naphthalene in liquid COz. This
yzmexp
LcPDn; -
The infinite-dilution activity coefficients for naphthalene in supercritical COz, corrected to this density, are listed in Table I11 for the three isotherms in Figure 3. Extrapolating these three points to 20 OC gives a value of 57.1 for y2m. A t 20 "C, the mole fraction of naphthalene in liquid COz is 0.00662 (Quinn, 1928) which corresponds to a value of 40.0 for yzm.The agreement between these two values is quite good and implies that the yzmparameters in Table I1 are not just fitted results but are consistent with the independent experimental data. This comparison also suggests that, for a given system, y2mvalues required in eq 8 may be obtained from solubility data in the liquid solvent. The method of calculating solubilities from eq 8, using two mixture parameters, compares favorably with the procedure using eq 7 and one mixture parameter and with previous methods for predicting solubilities from pure component data only (Prausnitz, 1965). This result is to be expected, but it is not sufficient justification alone for incorporating additional mixture parameters to calculate solubilities, since provisions must ultimately be made to extend the use of such parameters to multicomponent mixtures. The important argument for using two parameters is that both exhibit behavior consistent with the molecular thermodynamic basis on which they were formulated. Therefore the method offers the possibility of predicting solubilities by developing reliable thermodynamic correlations for estimating these mixture parameters-such as group contribution theories for predicting activity coefficients (Fredenslund et al., 1975)-and also provides a dependable means of correlating and extending experimental solubility data. Conclusions The method presented here is a useful procedure for determining the solubility of a heavy solute in a supercritical solvent, not far removed from its critical point. The procedure requires two parameters which must be obtained from mixture data: the activity coefficient a t infinite dilution for the heavy component and the binary interaction parameter (k12 in the Redlich-Kwong equation of state) for calculating the partial molar volume at infinite dilution. The advantage of this method is that both mixture parameters exhibit behavior consistent with the molecular thermodynamic basis on which they were formulated. This offers the possibility of reliably estimating these parameters to predict solubilities, as well as providing a dependable means of correlating and extending experimental data. The extension of this method to multicomponent mixtures should be straightforward. A t present, however, more experimental solubility data are needed for binary mixtures to extend this method over a more comprehensive range of heavy components and solvent systems.
Ind. Eng. Chem. Fundam., Vol. 18, No. 2, 1979
Nomenclature a = attraction parameter in the Peng-Robinson equation AC,, = constant-pressure molar heat capacity change on fusion f = fugacity h = molar enthalpy Ahfu8= molar heat of fusion hE = excess partial molar enthalpy k = binary interaction parameter for the Redlich-Kwong equation n = number of moles P = total pressure R = gas constant T = absolute temperature V = total volume u = molar volume Au = molar volume change of fusion = partial molar volume Greek Letters 4 = fugacity coefficient y = activity coefficient w = acentric factor 6 = binary interaction parameter for the Peng-Robinson equation Subscripts 1,2 = components c = critical property m = melting point
153
Superscripts c = condensed phase F = supercritical fluid phase = infinite dilution 0 = reference state OL = pure liquid OS = pure solid SAT = saturation Literature Cited Chueh, P. L., Prausnitz, J. M., Ind. Eng. Chem. Fundam., 6 , 492 (1967). Diepen, G. A. M., Scheffer, F. E. C., J . Phys. Chem., 57, 575 (1953). Fredenslund, Aa., Jones, R . L., Prausnitz, J. M., AIChE J . , 21, 1086 (1975). Kaul, 5. K., Prausnitz, J. M.. Ind. Eng. Chem. Fundam., 18, 335 (1977). Kaul, B. K., Prausnitz, J. M., AIChE J., 24, 223 (1977). Oellrich, L., Plocker, U., Prausnitz, J. M., Knapp, H., Chem. Ing. Tech., 40, 955 (1977). Peng, D.-Y., Robinson, D. B., Znd. Eng. Chem. Fundam., 15, 59 (1976). Prausnitz, J. M., NBS Technical Note 3 76, (July 1965). Quinn, E. L., J . Am. Chem. SOC., 50, 672 (1928). Redlich, O.,Kwong, J. N. S.,Chem. Rev., 44, 233 (1949). Sandler, S.I., "Chemical and Engineering Thermodynamics", Wiley, New York, N.Y., 1977. Tsekhanskaya, Y. V., Iomtev, M. B., Mushkina, E. V., Russ. J . Phys. Chem., 38, 1173 ( ,964).
Received f o r review July 5 , 1978 Accepted January 4, 1979
The authors gratefully acknowledge the financial support provided for this work by the National Science Foundation under Grant NO. ENG78-05584.
Mechanism and Kinetics of Selected Hydrogen Transfer Reactions Typical of Coal Liquefaction Donald C. Cronauer," Douglas M. Jewell, Yatish T. Shah,* and Rajiv J. Modi Gulf Research & Development Company, Pittsburgh, Pennsylvania 15230
A series of hydrogen transfer reactions has been done using model compounds (donors and acceptors) at reaction conditions consistent with coal liquefaction. Emphasis was placed upon acceptors having C-C linkages and oxygen compounds with functionality likely to be present in coal. The cracking of dibenzyl was shown to be faster than that of diphenylbutane, diphenylmethane, and I-phenylhexane at 400-450 O C . With oxygen-containing compounds, the relative order of reactivity was: furans < phenols < ketones < aldehydes < chain ethers. A study of hydrogen transfer using either a deuterium atmosphere or deuterium-tagged donors was undertaken with the oxygen-containing compounds. It was shown that much of the hydrogen necessary to stabilize free radicals comes from the donor solvent or intramolecular rearrangement and not from dissolved gas.
Introduction In a recent paper, Cronauer et al. (1978) reported the mechanism and kinetics of reactions between dibenzyl and a variety of hydrogen donor solvents. The major conclusion of this study was that the breakage of the carbon-carbon bond in dibenzyl occurs purely thermally and its rate is independent of the nature of the hydrogen donor solvent present during reaction. Coal liquefaction is accomplished by a combination of the dissolution of low molecular weight species and the cracking of larger species. The resulting free radicals are stabilized by the abstraction of hydrogen from a donor solvent or from the coal liquids themselves. The reaction of model hydrogen acceptors and donors similar to those 0019-7874/79/1018-0153$01 .OO/O
during coal liquefaction is the subject of this study. In this paper, we first briefly extend our previous work on the reactions between hydrogen donor solvents and a compound having C-C bonds. The role of catalyst in cracking of dibenzyl and the reactions of a good donor solvent with other types of C-C bond compounds (e.g., stilbene and noncondensed analogues of dibenzyl) are examined. Subsequently, we report the mechanism and kinetics of reactions between hydrogen donor solvents (e.g., tetralin) and a variety of oxygen compounds with functionality likely to be present in coal. Experimental and Analytical Procedures The kinetic experiments were performed in a manner similar to that of the previous study (Cronauer et al., 1978). 0 1979 American Chemical Society
