Energy & Fuels 1991,5,453-458
l-n-alkyldibenzothiophenes.In addition, the l-n-alkyldibenzothiophenes were found to occur in Athabasca maltene and in the maltene of several of the heavy oils and bitumens of northern Alberta. The predominance of the l-n-alkyl substitution pattern of the dibenzothiophene nucleus suggests that they were derived from a precursor substance possessing a linear carbon framework. Various selective oxidation methods permitted the separation of several classes of compounds which occur in small amounts in the pyrolysis oil. The alkylbenzenes were isolated and n-alkylbenzenes and monomethyl n-alkylbenzenes were found to be the most abundant homologous series. The most abundant of the monomethyl n-alkylbenzenes at most carbon numbers was found to be the o-methyl isomer followed by the m- and p-methyl isomers. The predominance of the o-methyl isomer suggests that the various n-alkylbenzenes were derived by the cyclization of a percursor substance possessing a linear carbon framework. Finally, several series of 9-n-alkylfluorenes were observed by conversion to their corresponding fluoren-9-01s which have previously been observed in Athabasca maltene.99*'6The n-alkyl substituent at position 9 of the fluorene nucleus suggests that it too is derived by the cyclization of a precursor substance possessing a linear carbon framework. Previously, we reported the abundant occurrence of several homologous series of thiophenes, 2,Cdi-n-alkylbenzo[ b]thiophenes, thiolanes, and thianes in Athabasca asphaltene pyrolysis oil, all of which had n-alkyl substituents, suggesting that they were derived from a precursor possessing a linear carbon f r a m e ~ 0 r k . lThe ~ quantity of terpenoid-derived polycyclic systems in Athabasca asphaltene pyrolysis oil is small in comparison with the quantity of material possessing a linear carbon framework.
453
This contrasts with the distillable portions of Athabasca maltene, which are dominated by homologous series of polycyclic systems possessing a terpenoid carbon framework. Field ionization mass spectrometry has shown that the bulk of the distillable portion of the maltene consists of a complex mixture of compounds whose distribution by carbon number suggests that they are derived from terpenoid precursors." Finally, ruthenium-catalyzed oxidation of the nondistillable portion of Athabasca maltene has suggested that it, like the asphaltene, is composed mainly of material possessing a linear carbon framew0rk.u Apparently, the high molecular weight componenta of Athabasca bitumen are composed mainly of material possessing a linear carbon framework while the lower molecular weight portion of the bitumen is dominated by substances derived from an underlying terpenoid carbon framework. This distinction is accentuated in Athabasca bitumen compared to conventional petroleums, since biodegradation has removed most of the n-alkyl-substituted materials from the low molecular weight portion of Athabasca bitumen which resulted from the thermal maturation of asphaltene, leaving the biodegradation-resistant polycyclics and high molecular weight materials behind. Acknowledgment. The financial support of the Alberta Oil Sands Technology and Research Authority is gratefully acknowledged. We thank Dr. Theodore J. Cyr for many helpful discussions and suggestions on asphaltene chemistry and the Oil Sands Sample Bank of the Alberta Research Council for the various heavy oil and bitumen samples. (47) Payzant, J. D.; Hogg, A. M.; Montgomery, D. S.; S t r a w , 0. P. AOSTRA J. Res. 1985,1, 175-182,183-202,203-210.
Influence of Supercritical Fluid Solvent Density on Benzyl Phenyl Ether Pyrolysis: Indications of Diffusional Limitations Benjamin C. Wu,Michael T. Klein,* and Stanley I. Sandler Center for Catalytic Science and Technology, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716 Received November 28,1990. Revised Manuscript Received February 19, 1991 The influence of supercritical solvent density on the pyrolysis of benzyl phenyl ether (BPE) in tetralin and supercritical toluene is interpreted in terms of transport limitations. Reaction at varying toluene densities highlighted the transport dependence of the BPE fission rate constant. The conversion of BPE decreased from 0.55 to 0.15 as the toluene density increased from 0.0 to 0.75. The yield and selectivity of BPE rearrangement products were also density dependent. These results were explained and modeled quantitatively in terms of the cage effect theory. Introduction The potential for the use of SCF solvents in reaction processes is motivated in part by their extreme compressibility. The density, dielectric constant, solubility parameter, and transport properties of a SCF solvent vary between gas- and liquidlike extremes with modest changes
* Author to whom correspondence should be addressed.
in pressure.'J Thii allows regulation of pressure to control and manipulate SCF solvent properties, which can in turn influence reaction rates and sele~tivities.~In this work (1) Paulaitia, M. E.; Krukonis, K. J.; Kurnik, R. T.; Reid, R. C. Supercritical Fluid Extraction. Reu. Chem. Eng. 1983, 1(2). ( 2 ) Paulaitis, M. E.; Penninger, J. M. L.; Gray, R. D., Jr.; Davidson, P. Chemical Engineering at Supercritical Fluid Conditions; AnnArbor Science: Ann Arbor, MI, 1983.
0SS7-0624/91/2505-0453$02.50/00 1991 American Chemical Society
Wu et al.
454 Energy & Fuekr, Vol. 5, No. 3,1991
Table I. Rate Constants for Elementary Steps (k), in Terms of the Cage Effect Formalism and Rate Constants (A) for Subelementary Stepsa reaction k [A
AB
+ B]*
-.
A+B
A2
XlX2
L1+ X2
bond fission
-+
A + BH*
[A + BH]*
4
AH
+B
X2hl A-1
hydrogen abstraction [A + B]* A @-scission A2
C& Ll
A+B
B
4
4
+ hz
[A + B]* -AB
Xzh1 A-1
+ he
radical recombination O k
= kht/(l
+ Da); Da = ~ p - , e - ~ - 1 / ~ ~ / 3 The D d ~effectiveness -~. factor (7 = (1 + Da)-') Damkdhler number usage follows standard
c~nvention.~'
encountered pair and A2/(hl + A,) represents the probability of its disen~ounter.~Thus A1A2/(A-1 + A,) is the familiar rate constant k for the elementary step of bond fission. Equation 2 also expresses the rate in terms of an effectiveness factor (7)and the "intrinsic" rate constant khp Note that this defines 7 and kinp The latter is the value of the fission rate constant in the absence of a dif-
fusion limitation. The effectiveness factor 7 = 1/(1+ Da), where Da = ~ p - , e ; ~ - 1 / ~ ~ / 3isDunity d ~ -in~ the , absence of a diffusion limitation and drops as (1 + Da)-' as diffusional limitations intrude (high Da, low D ) . Table I summarizes the terms composing kht for bond fission and the other elementary steps of pyrolysis, namely, hydrogen abstraction, &scission, and radical recombination. This shows clearly the relationship between the A's for the subelementary steps and the k's for the elementary steps. In each of these rate constants, the collision frequency, Y = GRTP'/Lh is estimated as the pseudovibrational energy for a caged [A + B]*. P'(~1112)is a packing parameter providing an estimate of the collisions within the cage that are actually between the reaction partners. The steric factor, p, is the fraction of collisions between the encountered pair where the reaction partners [A + B]* are properly aligned for reaction to occur, as in traditional collision theory. E* is the activation energy, dABis the collision diameter of the reactants, and D is the diffusivity. Thus the influence of diffusion is quantitatively summarized in the Damkohler number, Da. Because of the changes in typical small-molecule diffusivities from lo-' cmz/s in the gas phase to cmz/s in the liquid phase, it is reasonable to expect Da, and therefore the influence of diffusion, to vary through the supercritical region from gas- to liquidlike. For Da >> 1,the reaction proceeds with the intrinsic reaction rate, khv In this case,collision theory, or transition-state theory: would be appropriate. For Da L 1,the effect of diffusion is significant and the cage effect, or "reactions in solution", formalism is appropriate. Experimental systems involving highly reactive free-radical intermediates, where Da L 1 could be anticipated, were therefore chosen to study the influence of diffusion on elementary reaction rates in SCF solvents. The reaction of benzyl phenyl ether proceeds via a mechanism involving bond fission (F), hydrogen abstraction (H), &scission (B), and radical termination steps (T)! Thermochemical estimates for related representative reactions6suggest that DaH lo-', DaB lo*, and DaF DaT 1 can be expected at liquid conditions ( D 10" cm2/s). Therefore, the bond fission and radical recombination elementary steps of BPE pyrolysis offered an opportunity to assess the influence of diffusion on reaction rates. In addition, BPE pyrolysis in the liquid phase yields
(3) Moore, J. W.; Pearson, R. G. Kinetics and Mechanism, 3rd ed.; Wiley: New York, 1981. (4) Rabinowitch,E. Collision,Co-ordination, Diffusion and Reaction Velocity in Condensed Systems. Trans. Faraday SOC.1937, 33, 1225-1233.
(5) Schlosberg,R. H.; Davis, W. H.; Aahe, T. R. Pyrolysis Studies of Organic Oxygenates. 2. Benzyl Phenyl Ether Pyrolysis under Batch Autoclave Conditions. Fuel 1981, 60(3), 201. (6) Stein, S. R. A Fundamental Chemical Kinetics Approach to Coal Conversion. ACS Symp. Ser. 1981, No. 169,97-129.
we examined the dependence of benzyl phenyl ether (BPE) pyrolysis on the density of supercritical toluene as a means to study nonelectrostatic solvent effects. In particular, we sought to probe the effect on the reaction kinetics of the dramatic changes in reactant-product diffusivities brought about by the changes in density from gaslike to liquidlike extremes. It is, therefore, informative to compare liquid- and gas-phase theories of reaction kinetics as the limiting cases to which a SCF solvent model must reduce in the limit of high and low density, respectively. The classic model for reactions in liquid solution involves the cage effect theo~ 7 . ~ In 3 ~its simplest form, it is a recognition of the serial events of diffusion and chemical transformation in an overall chemical reaction. This is illustrated in eq 1 for unimolecular bond fission. Note that, in eq 1, the ele-
AB
* A
hl
[A + B]* - A A2
+B
(1)
mentary step of AB bond fission to products A and B has been written in terms of the "subelementary" steps of fission (A,) to an encountered pair [A + B]*, association of the encountered pair (h,), and disencounter (A,). Together, these steps represent a sequence where the initially formed radicals are trapped in the solvent cage as the encountered pair [A + B]*, and the overall elementary reaction of AB fission to A and B is realized only when the members of the encountered pair diffuse apart with rate constant A, to break off an encounter. The competition between the recombination (L,) and disencounter (A,) rates controls the overall rate of the elementary AB fission reaction. The final result is shown as eq 2, where A, AB represents the rate of forming the
-
-
-
--
Energy & Fuels, Vol. 5, No. 3,1991 466
Benzyl Phenyl Ether Pyrolysis T a b l e 11. Experimental Conditions for BPE/Tetralin Pyrolysis in SC Toluene temperature/ O C 320 time/min 30 reactor volume/cmg 0.59 BPE loading/g 0.00048 BP loading/g 0.00042 tetralin loading/g 0.00909 toluene loading/g 0.38
c
0.9 I 0.8
U
I
I 0.00 / 0.2
0
0
0
O ' r 0.4
I
I
I
I
0.0
02
0.4
0.6
0.3
-
model fit
0.8
0.0
0.0
toluene density (s/cm3)
Figure 1. Effect of supercritical toluene density on BPE yield (2' = 320 "C).
two rearrangement isomers, o-hydroxydiphenylmethane (OHD) and p-hydroxydiphenylmethane (PHD)? These are postulated to form via recombination of the resonance forms of the benzyl and phenoxy radicals trapped in a solvent cage. Thus, both the overall kinetics of BPE disappearance and the density dependence of the selectivities to the rearrangement products, OHD and PHD, would provide evidence of transport limitation in SCF solvents.
Experimental Results BPE was pyrolyzed in tetralin and toluene by experimental procedures described elsewheree8 The reaction conditions are summarized in Table 11. The pressure was increased via addition of toluene. Phase behavior calculations from a modified flash calculationsJO using the Peng-Robinson equation state verified that a single phase existed at all experimental conditions. The irreversibility of the reaction to toluene and phenol was confirmed by pyrolyzing BPE at T = 320 O C and phiuem = 0.75 g/cmS for 6 h, which yielded 99.9% conversion of BPE. The results of these experiments are summarized in Figures 1and 2. Figure 1shows that the recovery of BPE Cyi = N~/NBPED, where Ni is the mole number of i) increased significantly from 0.45 under neat pyrolysis conditions to 0.85 at phlurne = 0.75 g/cmS. Figure 2 shows that the selectivity (yj/x, where x is the conversion) to the rearrangement isomer o-hydroxydiphenylmethane(OHD) increased from 0.02 under neat conditions to 0.14 at phlueas = 0.75 g/cm3. The yield (yj = Nj/N~pm)of OHD also increased from -0.01 to 0.02 under the same conditions. (7) Hart, L. S.; Waddington, C. R. Aromatic Rearrangements in the Benzene Series. Part 4. Intramolecularity of both the ortho- and paraRearrangements of Benzyl Phenyl Ether as rhown by Labelling Experiments. J. Chem. Soc., Perkin Tram. 2 1986,1676-1612. (8) Wu, B. C. Ph.D. Thesis, Solvent Effbcte of Reactions in Supercritical Fluids. University of Delaware, Newark, 1990. (9) Wu, B. C.; Klein, M. T.; Sandler, S. I. Reactions in and with Supercritical Fluids Effect of P h Behavior on Dibenzyl Ether Pyrolysis Kinetics. Ind. Eng. Chem. Res. 1989,28,266-269. (10)Wu, B. C.; Klein, M. T.; Sandler, S. I. The Effect of Fluid Phase on BPE Pyrolysis. Presented at the AIChE 1988 Annual Meeting, Washington, DC,1988.
0.2
0.4
0.6
0.8
toluene density (g/cm3)
Figure 2. Effect of supercritical toluene density on OHD yield and selectivity (5" = 320 "C).
P
+
-
+ PH (P)
k4
P + P w Figure 3. Representative elementary steps for BPE pyrolysis
in tetralin.
which indicates that the increase in selectivity can be attributed to both a decrease in BPE conversion ( x ) and an increase in OHD yield. The selectivity to the other rearrangement isomer, p-hydroxydiphenylmethane (PHD), remained essentially constant up to phluells = 0.21 g/cmS, above which the selectivity dropped to below detectable limits ( Y B ~ E< 0.001). The object of this analysis is to explain the observations of Figures 1and 2. The pyrolysis mechanism of BPE is summarized first. This allows application of the cage effect formalism to the relevant individual reaction steps. After a brief discussion on diffusion coefficient estimation techniques, the derived model is optimized to the experimental data.
BPE Pyrolysis Mechanism The pyrolysis mechanism of BPE proceeds through a free-radical mechanism where bond fission and radical recombination proceed at steady-state rates comparable The neat pyrolysis to that of hydrogen mechanism is extremely complex and does not readily lend (11) Korobkov, V. Y.;Grigorieva, E. N.; Bykov, V. I.; Senko, 0. V.; Kalechitz, I. V. Effect of the Structure of the Coal-related Model E t b m on the Rate and Mechanism of Their Thermolysis 1. Effect of the Number of Methylene Group in the R-(CH,),-O-(CH,),-R Structure. Fuel 1988a, 67,657-662.
Wu et al.
456 Energy & Fuels, Vol. 5, No. 3,1991
itself to the present study of transport effects because of the large number of elementary steps that are involved. The introduction of tetralin (T),however, simplifies the to the steps shown in Figure 3. reaction ~cheme'~J~J' The thermal cleavage of the C-O bond gives a phenoxy and a benzyl radical (8). These radicals then abstract hydrogen from either the original substrate, BPE, or tetralin to give the two major products, phenol and toluene (OH) and the derivative BPE and tetralyl radicals ( p ) , respectively. The termination step is the recombination of two p radicals. In the presence of tetralin the overall rate of BPE consumption through the steps shown in Figure 3 is r = -d[BPE]/dt = kl[BPE] + k2[8][BPE] (3) where the apparent rate constants, ki, are defined as vikintj as in eq 2. Recall that, in the cage effect formalism, the rate constants kland k2 for the elementary steps of bond fwion and hydrogen abstraction, respectively, are modeled in terms of rate constants (A's) for diffusion, disencounter, etc. The reduction of eq 3 to observable species (BPE,T) concentrations requires information on the relative rates of rl and r2 of Figure 3. The terms on the right-hand side of eq 3 can be related through the experimental selectivitys (0.6) to either phenol or toluene (OH) as
(4)
Moreover, the relative rates of hydrogen abstraction steps 2 and 3 were determined through an experiment wherein deuterated tetralin (ClJll2) was substituted for fully protonated tetralin (Cld-Il2). The fraction of toluene that was singly deuterated at the low conversion of 8% provided the relative rates of steps 2 and 3 as k2[BPE]/ k,[T] = 0.67. Substitution into eq 4 then gives the hydrogen abstraction rates as a function of the bond fission step
Figure 4. Application of cage effect formalism to BPE pyrolysis.
distinguish it from unencountered pairs. The low experimental selectivites (> ha;the isomerization reactions to OHD and PHD are via energetically less favorable resonance forms. Thus the and X2 in kinetically significant route involves X1, hl, Figure 4. This indicates that the overall formation of disencountered fl radicals will be governed by kl for unimolecular fission in Table I, i.e., kl = qlkht,l, where ql = (1 + ~ p , e - ~ ' - 1 / ~ ~ / 3 D d and ~ - ~ kht,l ) - l = up, e-pIfRT. Substitution into eq 6 gives -d[BPE]/dt = 1.32v1kint,l[BPE] (7) Integration of eq 7 provides the relationship between YBPE and 91 88 YBPE = [BPEI/[BPEIo = 1 - ex~[-1*32~1kint,1tI (8)
k2[O][BPE] = 0.32kl[BPE] (5) This combines with eq 3 to give the pseudo-first-order rate expression r = -d[BPE]/dt = 1.32kl[BPE] (6)
which provides an explicit account of the influence of diffusion on reactions in supercritical fluid solvents. Comparison with experimental data now requires a model for the influence of the experimental variables on the diffusion coefficient.
where the effective fmt-order decomposition rate constant is given by kd = 1.32kl. Since both r2/r3and Sm remained essentially constant over the entire range of experimental densities, the coefficient 1.32 in eq 6 is not dependent on the diffusivity. With the rate expression for BPE consumption explicit in the effective rate constant kl,the cage effect formalism can now be applied. Figure 4 illustrates the cage effect formalism for the diffusion-limited pyrolysis of BPE as a set of steps analogous to those in Figure 3. The unimolecular fission of the C-0 bond in BPE gives benzyl (8) and phenoxy radicals (@)that can be trapped within a solvent cage. This geminate pair [B + @]*is considered a unique species to
Diffusion in SCF Solvents The challenge to modeling diffusion coefficients in supercritical fluids is to account for the wide range of densities that can be encountered. For instance, the present experiments span the range of densities 0 < pr < 2.0. At pr = 0, the neat pyrolysis of BPE proceeds in a gaslike environment, and kinetic theory based diffusion models may be appropriate. At the other extreme, pr = 2.0,the SCF solvent is liquidlike and hydrodynamic theories are likely to give better estimates. A dearth of experimental diffusivity data adds to the difficulty. The available estimation methods include kinetic theory based models,l5J6hydrodynamic models,17J8combinations
(12)Korobkov, V. Y.;Gri orieva, E. N.; Bykov, V. I.; Senko, 0. V.; Kalechitz, I. V. Effect of the !tructure of the Coal-relatedModel Ethenr on the Rate and Mechanism of Their Thermolysis 2. Effect of Subatituenta in the CEH5-CH-0-CEHI-X Structure. Fuel 1988b,67,663. (13)Collins, C. J.; haaen, V. F.; Benjamin, B. M.; Kabalka, G. W. Carbon-carbon Cleavage during Asphaltene Formation. Fuel 1977,56, 107. (14)&to, Y.; Yamakawa, T. Thermnl Decompwition of Benzyl Phenyl Ether and Benzyl Phenyl Ketone in the Preaence of Tetralin. Ind. Eng. Chem. Fundam. 1986,24(1),12-15.
(15)Chapman, S.;Cowling, T. G. Mathematical Theory of NonUniformGases, 2nd ed.; Cambridge University Press: Cambridge, U.K., 14.51.
(16)Monchick, L.;Mason, E. A. Transport Properties of Polar Gases. sen: J . Chem. Phys. 1961,35,1676-1697. (17)Debenedetti, P. G.;Reid, R. C. Binary Diffusion in Supercritical Fluids. In Supercritical Fluid Technology; Penninger, J. M. L., Rodsz, M.,McHugh, M., Krukonia, V. J., Ma.;Elsevier: Amsterdam, 1986,Vol. 45, pp 225-244.
Energy & Fuels, Vol. 5, No. 3, 1991 457
Benzyl Phenyl Ether Pyrolysis
of kinetiehydrodynamic models,*= empirical models,%% and molecular dynamicsm calculations. The most common method for estimating diffusivities in dilute gasesz7was developed independently by Chapmanl6 and Enskog. This is the approach adopted herein; the considerations given to other models is summarized elsewheres. The Chapman-Enskog model is derived from solving the Boltzmann equation, explicitly detailing the collisions between two molecules, to give D12= 2.264
X
1 I
/
10" 0.0
This is accurate to an average of 8% in dilute gasesz7 and is recommended by various researcher^.^^^^^^^^ For higher densities, the Enskog-Thorne modification of eq 9, summarized by eq 10, for the decrease in available free volume and the subsequent increase in the probability for collision,'s is recommended. In eq 10, Xlzis the correction Dlzp (at T and P) (DlZp)O(at T and a t low pressure)
= 1/x12 (10)
factor that accounts for the probability of collisions, Le., a free-volume correction, as given by
This formulation is reasonably accurate up to moderate densities.The model appears to breakdown, however, a t densities above pc.9r113sThe range of applicability for (18) Debenedetti, P. G.;Reid, R. C. Diffusion and Mass Transfer in Supercritical Fluids. AIChE J. 1986,32, 2034-2046. (19) Baleiko, M. 0.; Davis, H. T. Diffusion in Binary Dense Gas Mixtures of Loaded Sphere and Rough Spheres. J. Phys. Chem. 1974, 78, 1664-1572. (20) Hynes, J. T.; Kapral, R.; Weinberg, M. Molecular Theory of
Translational Diffusion: Microscopic Generalization of the Normal Velocity Boundary Condition. J. Chem. Phys. 1979, 70,1456-1466. (21) Sung, W.; Stell, G. Theory of Transport in Dilute Solutions, Suspensions, and Pure Fluids: 1. Translational Diffusion. J. Chem. Phys. 1984,80,3350-3366. (22) Hippler, H.; Schubert, V.; Troe, J. A Low-pressure Extension of the Stokes-Einstein Relationship. Ber. Bunsen-Gee. Phys. Chem. 1986, 89,760-763. (23) Mathur,
/
1
G.P.; Thodos, G. The Thermal Conductivity and Dif-
fusivity of Gases for Temperature to 10,OOOo K. AZChE J. 1965, 11,
164-167. (24) Slattery, J. C.; Bird, R B. Calculation of the Diffusion Coefficient
of Dilute Gases and of the Self-diffusion Coefficient of Dense Gases. AIChE J. 1958,4(2), 137-142. (26) Takahashi, S. Preparation of a Generalized Chart for the Diffusion Coefficients of Gases at High Pressures. J. Chem. Eng. Jpn. 1974, 7,417-420. (26) Alder, B. J.; Gase, D. M.; Wainwright, T. E. Studies in Molecular
Dynamics. VIII. The Transport Coefficienta for a Hard-Sphere Fluid. J. Chem. Phya. 1970,53,3813-3826. (27) Cussler, E. L. Diffusion-Moas Transfer in Fluid Systems; Cambridge University Prese: Cambridge, U. K., 1984. (28) Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomenono; Wiley New York, 1960. (29) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. Properties of Gases and Liquids, 4th ed.; McGraw Hill: New York, 1987. (30) Dawaon, R., Khoury, F.,Kobayashi, R. Self-Diffusion Measurementa in Methane by Puled Nuclear Magnetic Resonance. AZChE J. 1970,16,726-729. (31) pylqond, J. H., Alder, B. J. Corrections to the Kinetic Theory of Flud D h i o n . 11. Binary Mixtures. J. Chem.Phys. 1970,52,923-926. (32) Jom, J.; Lamb,D. M. Tramport and Intermolecular Interactions in Compressed Supercritical Fluids. ACS Symp. Ser. 1987, No. 329, 16-28. _. __ (33) Kennedy, J. T.; Thodos, G.The Transport Properties of Carbon Dioxide. AZChE J. 1961, 7, 625-631. (34) Balenkovic, 2.;Myers, M. N.; Giddinge, J. C. Binary Diffusion in Dense Gases to 1360 atm by the Chromatographic Peak-Broadening Method. J. Chem. Phys. 1970,52,915-922.
0.2
0.4
0.6
0.8
toluene density (g/cm3)
Figure 5. Effed of toluene density on Da for bond fission in BPE
pyrolysis.
the model seems to vary and errors are usually more pronounced above the critical point. To date, however, the Enskog-Thorne formulation remains the most reliable and recommended estimation t e c h n i q ~ e . ~ i ~ * ~ * ~ * ~ ~
Model Predictions Equations 9,10, and 11amount to a model for assessing the influence of the experimental reaction conditions on diffusion coefficients in SCF solvents. This couples with eq 8 and the network of Figure 4 to assess the influence of transport properties on BPE pyrolysis in tetralin and toluene. Qualitatively, as the diffusion coefficient decreased, the effectiveness factor also decreased. Therefore, the observed increase in BPE yield &e., recovered BPE) of Figure 1 can be attributed directly to the decrease in diffusivity. More quantitative analysis required optimization of the parameters of eq 8. The intrinsic rate constant was regressed from the neat pyrolysis data (where Dal is 0) as khbl = 1.7 X 104/min-'. The effectiveness factor vl = 1/(1+ Dal), where Dal = ~ p - ~ e - ~ - 1 / ~ ~ comprises /3Dd~-~, the parameters v, P - ~ and , E*-l. The collision frequency, u, is estimated as the pseudovibrational energy multiplied by the probability, P', that the collision involves the geminate pair, i.e., v = 6RTPYLh. P'= 1/12 for the case where the number of nearest neighbors is 12. For this case v = 1.24 X 1013s-l. The activation energy for radical recombination is essentially negligible (E-l 01, and dm is approximately 11.5 A. The diffusion coefficient was estimated by using the Enskog-Thorne eqs 9-11. The steric factor, p-l was the sole parameter obtained from the data as the optimized value of 0.086. The correlation of BPE yield based on eq 8 is shown as the solid line in Figure 1, a very reasonable fit.
-
-
Discussion The conversion of BPE decreased as the toluene density increased. The effect of density, and therefore diffusivity, on the conversion was derived from cage effect formalism as eq 8. The estimated diffusion coefficient of the benzyl and phenoxy radicals decreased from a gaslike value of 0.02 cm2/s at neat conditions to a liquidlike value of 0.0002 cmz/s a t ptoluene = 0.75 g/cm3. The corresponding effect of density on Da is shown in Figure 5. As the toluene density increased, Da also increased, and therefore the efficiency, vl, of the reaction rate decreased. Finally, the (35) Swaid, I.; Schneider, G. M. Determination of Binary Diffusion Coefficients of Benzene and Some Alkylbenzener in Supercritical COn between 308 and 328 K in the Pressure Range 80 to 160 bar with Supercritical Fluid Chromatography. Ber. Bunsen-Ges. Phys. Chem. 1979, 83,969-974.
Wu et al.
458 Energy & Fuels, Vol. 5, No. 3,1991
optimized value p = 0.086 is not numerically significant because of the order-of-magnitude accuracies in the estimates of the other parameters. However, it is satisfying that p < 1. The formation of OHD and PHD suggests the presence of a cage effect even at neat pyrolysis conditions. Following Figure 4, the rate of OHD formation is
-=(
d[OHD] dt
A-1
+ A2h1h3 + A3 + X'3 )[BPE]
and the selectivity is given as d[OHD] X 3 X l / ( h 1 + A3 + X'3 SoHD = -d [BPE] 1.32dht~
+ X2)
(12)
(13)
Equations 12 and 13 suggest that, as the diffusion rate and q1 and X2 diminish, the OHD yield and selectivity would increase. This was observed experimentally and is shown in Figure 2. Since OHD is stable at these conditions? the increase in ita yield and selectivity is due to the diffusion limitation on the disencounter required to make phenol and toluene from BPE. OHD formation does not require disencounter of the caged pair. Therefore, its yield and selectivity increase with increasing diffusion limitations. As the density approaches a liquidlike value of Pbluene 0.75 g/cm3, the selectivity approaches that observed in the liquid phase SoHD = Y O H D / X = 0.14.1° The corresponding rate equation for PHD is given as
-=(
d[PHD] dt
hl
+ A2X1X'3 + A3 + X'3 ) W E 1
(14)
-
The yield of PHD drops to below detectable levels (yi
< 0.OOOl)a t ptoluene 0.3 g/cm3. This suggests that
and, therefore, X3 might also be affected by diffusion. In order to form PHD, the geminate pair [B + B]* must rotate 180°. The increase in SC density, and therefore viscosity, might act as a barrier to this rotation process. This barrier to rotation is similar to that observed in the isomerization of tram-stilbene in high-pressure compressed gases.% The (36)h e , M.; Holton, G . R., Hochstraeser, R. M. Observation of the Kramers Turnover Region in the Isomerism of Trans-Stilbene in Fluid Ethane. Chem. phy8. Lett. 1985, I18(4), 35s363. (37) Carberry, J. J. Chemical and Catalytic Reaction Engineering; McGraw Hill: Princeton, NJ, 1976.
formation of OHD, requiring only 60° rotation, must be similarly but less dramatically affected.
Summary and Conclusion The reaction of BPE in tetralin and SC toluene allowed study of diffusion limitations on pyrolysis kinetics. The conversion of BPE decreased significantly with increases in toluene density. This was interpreted as a decrease in the initiation reaction rate through diffusion limitations as described through cage effect theory. In addition, the formation of the two isomers, OHD and PHD, is evidence for the presence of a cage even a t low SC densities. (A +
B)* A, B AB BPE D Da
Nomenclature caged or encountered radical pair
disencountered free radicals generic reactant benzyl phenyl ether (PhCh20Ph) diffusivity, cm2/s Damkohler number?' up-le-E*/RT collision diameter, cm dAB E* activation energy, kcal/mol k rate constant for elementary step (e.g., fission, H abstraction, @-scission,radical recombination), s-l or M-' s-l value of rate constant for elementary step in the kint absence of a diffusion limition, s-l or M-' s-l L Avogadro's number MW molecular weight N molecule number P' packing parameter collision theory steric factor P-' T temperature t time, s X reactant conversion, 1 - NBpE/NBpm free volume correction factor Xl2 recovery (reactant) or yield (product) Ni/NBpm Yi Greek Symbols effectivenessfactor, (1 + Da1-l 11 rate constant for "subelementary" step (e.g., dixi sencounter, association of encounter, formation of encounter), s-l or M-' s-l U pseudovibrational energy of caged species, s-l P density, g cm-3 U Chapman-Enskog parameter n Chapman-Enskog parameter Registry No. BPE,946-80-5.
