Energy & Fuels 1994,8, 1223-1227
1223
Enhancement of Coal Liquefaction Kinetics: Effect of a Multicomponent Mixture on the Attributes of an Optimal Chain-TransferSolvent Dean M. Fake, Concetta LaMarca,? and Michael T. Klein* Center for Catalytic Science and Technology, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716 Received February 22, 1994. Revised Manuscript Received July 14, 199@
The kinetics analysis aimed at specifing the attributes of an optimal chain-transfer solvent for coal liquefaction was extended to include the reality of the distributions of functional groups and bonds in coal. In particular, the possibility that the desirable enhancement predicted for the liquefaction rate was an artifact of the two-lump coal-solvent model, with the coal being characterized as a single pseudo species, was tested. Thus, Gaussian-distributed coal and solvent bond strengths were considered to assess the importance of the off-optimal interactions that could be anticipated in a multicomponent mixture. The results show that significant enhancement can be maintained in the mixture. Indeed, in several instances, the distribution of coal bond strengths improved the obtained enhancement.
Introduction Coal liquefaction is a complex process that includes a significant thermal reaction of a multicomponent hydrocarbon mixture comprising the nominal reactant coal and a solvent. Viewed at its most coarse level, the thermal reaction involves at least coal (1)and solvent (2) reaction lumps. Since thermal chemistry is largely by mechanisms of elementary steps involving free radicals derived from both coal and solvent, the “cross” or “interaction” freeradical steps appear t o be a reasonable source of rate and selectivity enhancement or suppression due to the solvent. Along these lines, LaMarca et a1.l formulated a hybrid-mechanistic model of this reaction in terms of a two component Rice-Herzfeld chain reaction. They showed that the “liquefaction”rate, i.e., the rate of the coal @lH) lump, could be significantly affected and, indeed, improved by the choice of an optimal solvent (p2H). In short, a narrow range of solvent-H bond strength (dopzH) provided a solvent-derived radical @2) of intermediate, optimal stability so that its generation and subsequent reaction with coal @lH) were both kinetically significant. However, the narrowness of the optimal bond strength (do@)window raises the issue of the distribution of both coal and solvent bond strengths present during actual liquefaction. In particular, it seemed cogent to determine the role of “offoptimal” coal-solvent interactions in coal liquefaction and discern whether a liquefaction rate enhancement could still be anticipated.
Background The basic analysis of LaMarca et al.’ models the coalsolvent mixture as a two-lump mixture (A1 = p1H = coal; A2 = p2H = solvent) reacting through the classical Rice+
Current address: DuPont Engineering, Newark, DE 19714.
* Corresponding author.
@
Abstract published in Advance ACS Abstracts, September 1,1994.
Herzfeld kinetics of Figure 1. This mechanism can be solved using the usual assumptions of pseudo steady state on the radical concentrations and the long kinetic chain length approximation2 to yield the enhancement, defined in eq 1. Under the conditions of statistical
E=
rAl(Al+%)
rA
(1) 1
termination3 and small klllk1 A1 (Le., fast ,&scission), the enhancement can be expressed succinctly as in eq 2,where b’l = kldk’21, 8’1= k’211k11, and S 2 = AdA1. The
hydrogen abstraction rate constant ratios k‘1 and 8‘1 can be related to the enthalpy of reaction of the elementary steps through the Polanyi structure-reactivity relationship. The enthalpies, in turn, can be expressed in terms of the bond strengths dopl-H, dogl.+, and dopz-H. The resulting dependence of the enhancement on the bond strengths is given by eq 3.
E=
1 + S 2 eXP[a(dopl-H- dop2-HYRTI 1 + S 2 exp[a(dopl-,
+ dogl-H - 2doPz-~)/RTI (3)
Figure 2, a and b, illustrates the implication of eq 3 for bond strengths surrounding the range of a typical coal and liquefaction solvent. Figure 2a is for a coal with doglH = 87 kcallmol and Figure 2b is for a coal with dopclH= 82 kcallmol. Figure 2a,b shows the similar trends of regions where E 1 and E = 1 separated by (1)LaMarca, C.; Libanati, C.; Klein, M. T.; Cronauer, D. C. Enhancing Chain Transfer during Coal Liquefaction: A Model System Analysis. Energy Fuels 1993,7,473-478. (2) Gavalas, G. R. The Long Chain Approximation in Free Radical Reaction Systems. Chem. Eng. Sci. 1966,21,133-141. (3)Pryor, W.A. Free Radicals McGraw-Hill: New York, 1966.
0 1994 American Chemical Society
1224 Energy & Fuels, Vol. 8, No. 6, 1994
Fake et al.
Ai 3 Pi + P i
81 + A i -%PiH + p i
P1 + A2 .%P1H + 1 2 P I + A2 ~2
P1+
2Pl P1
I
I
A1
5Q i + P I
--
IO
80
90 100 d i Z H(kcallmol)
110
Figure 3. Predicted enhancement in liquefaction rate for a coal with bond strengths dopl-H = 82 kcal/mol and dog,-H = 81 kcal/mol. Sz = 10.
PI
products
+ P2
2P2
I
5 + p2
+ A2 5 A2 + PI PI
E
Figure 1. Lumped reaction mechanism of coal liquefaction.
The early LaMarca et al.' analysis modeled coal as a single pair of doplH - dop,H bond strengths. This allows the solvent-induced enhancement t o be mapped out for a range of solvent d o P Zbond ~ strengths. Figure 3 presents results for d o p l ~= 87 kcaVmol and d o p l=~82 kcaVmol as a two-dimensional slice of Figure 2, a or b, along the line d o p l=~ 82 kcaVmol or doplH = 87 kcaV mol, respectively. For this hypothetical coal, the opti~ 90 kcal/ mal solvent bond strength occurs at d o p z= mol. Figure 3 emphasizes the narrowness of the optimal solvent window and suggests that closer scrutiny should be placed on the approximation that coal has two discrete bond strengths.
Extension to Distributed Coal and Solvent Lumps The purpose of the present analysis is to bring a more realistic representation of coal and the liquefaction solvent structural distributions to the foregoing analysis. The first step toward this goal was to consider limiting-case models where the coal and solvent were represented with dOpl+, d O p l - ~ ,and dOpZ+ bond strength distributions. Thus, the enhancement of eq 1was more generally approximated as that of eq 4,where p l ( d o p l ~ ) ,
Figure 2. (a, top) The rate enhancement, E(d",,-H, doB1-H, dorz+) versus dopl.+ and dorz-H for dopl-H = 87 kcal/mol. (b, , versus bottom) The rate enhancement, ,!?(do,,+, d o p l - ~ doPz-H) d 0 b 1 - and ~ dopz+ for doP1+= 82 kcal/mol and Sz = 10.
a ridge with E > 1. For a coal with a range of bond strengths, the choice of solvent will be influenced by the way in which these off-optimal regions (E 5 1) are combined with the optimal region (E > 1).
P 2 ( d 0 p 1 H ) , and p3(dopz~) are the distribution functions of bond strengths. Evaluation of the integral of eq 4 would provide an estimate of the enhancement due to a distribution of coal moiety-solvent moiety interactions. Equation 4 estimates the overall enhancement through a direct comparison of the average rate in the presence of solvent with the average neat rate. In general, this estimate may be affected by two competing factors. First, the overall enhancement is dominated by the solvent's effect on the coal moiety with largest neat p ) rA1(Al)).That is, a small reaction rate ( r ~ ~ ( A l , Aversus effect on a reactive coal moiety outweighs a large effect on a refractory coal moiety. Second, the overall enhancement is more sensitive to the solvent's effect on coal moieties with hydrogen bond strengths closest to the mean. These coal species are more likely and therefore contribute more significantly.
Energy & Fuels, Vol. 8, No. 6, 1994 1225
Enhancement of Coal Liquefaction Kinetics 1.5
1
Y
C 0
E
1
8
3 0.5 W 70
80
90
100
110
p2H bond strength (kcdmol) Figure 6. Predicted enhancement in liquefaction rate for a coal with a normally distributed dapl-H. dopl-H= 82 kcaymol, do,gl-H = 87 kcaymol, and SZ= 10. (0) ud',,-H = 0.1 kcaymol, (A) ud~,,+,
Figure 4. Neat coal thermolysis rate for a range of hydrogen bond strengths.
To develop these ideas further, consider a Gaussian distribution, where pj(doj)is proportional to the exponential of the square of bond strength deviations. In comparison, eq 3 shows that the enhancement of an isolated coal moiety is, at most, proportional to the exponential of the bond strengths. Therefore, at bond strengths similar to the mean bond strength, the overall enhancement is more sensitive to the magnitude of the rate rather than the moiety's distance from the mean. That is, close to the mean bond strength, r~~varies much more than pj(doj) and contributions to E reflect the variations in T - A ~ .Further out, the roles are reversed. Since, clearly, the variation in ?'A1 for a coal moiety depends on its bond strengths, the relative sensitivity of these two competing factors varies over the range of coal and solvent bond strengths. Figure 4 presents the neat rate of coal pyrolysis over a wide range of coal hydrogen bond strengths normalized by (aAlW),where a and w are the initiation and termination rate constants, respectively. This normalization removes an initiation offset in Figure 4 and focuses attention on the variation of rate through H-abstraction propagation steps. Notice how the rate increases as doptH increases and dohlH decreases. The solvent's effect on large doplH and small dohlH coal moieties will dominate the estimate of overall enhancement. The denominator of eq 4 can be calculated by averaging over this surface about the mean coal bond strengths. A similar surface to Figure 4 can be generated for the reaction rate in the presence of a solvent. The shape of these surfaces depends on the solvent hydrogen bond strength. The calculation of the numerator of eq 4 is equivalent to averaging over all of these surfaces. To fix ideas, the model of a single-valued solvent and a coal with a distribution of bond strengths was considered first. Four of the eight possible subcases were modeled: 1. Both dohlHand doplH were single valued. 2. doplH was distributed normally and doplH was single valued. This case represents a coal with a pyrolysis chain propagated by one predominant /3 radical, such as the benzyl radical. Anthony and Howard4 (4) Anthony, D. B.; Howard, J. B. Coal Devolatilization and Hydrogasification. AIChE 1976,22(4), 625-656.
= 2.0 kcal/mol, and (B)
= 5.0 kcaymol.
1
1.5
0
70
80
90
100
110
p2H bond strength (kcaYmo1) Figure 6. Predicted enhancement in liquefaction rate for a goal with a normally distributed doB1-H. dopl-H = 82 kcaumol, d O p l -= ~ 87 kcal/mol, and SZ= 10. (0) Ud*b1-H = 0.1 kcaymol, (A) udd'g1-H = 2.0 kcal/mol, and (B) udofil-H= 5.0 kcal/mol.
modeled the overall activation energy with a Gaussian distribution with success. 3. dohlHwas single valued and doplH was normally distributed. This case models a coal with one predominant p radical which fragments into many different /3 radicals. 4. Both dohlH and doplH were distributed normally. Case 1 has been considered by LaMarca et a1.l and has been presented here as background. The resulting enhancement curve for case 2 (dohlHdistributed normally) is shown in Figure 5 as a plot of E ( a o h l doplH, ~, doh& as a function of dopzHfor parametric values of 0dopla. Note that the maximum potential E decreases as UddqrlH increases, but also that the performance of solvents with bond strengths lower than the optimum solvent increases. Figure 6 illustrates the evaluation of eq 4 for case 3, as a plot of the enhancement versus the liquefaction solvent dohzHbond strength for varying aJoBlH. Notice here that a broader spectrum of do,glH decreases the maximum potential enhancement in liquefaction rate and shifts the optimal solvent to a higher solvent H bond strength. These two examples indicate that the qualitative effect of increasing the spread of a coal-hydrogen bond strength distribution can depend on the type of coal radical and the average of its bond strength distribution. Since the /3 radicals are fragments of the ,u radicals, it seems reasonable to consider the case where both the /3H and ,uH bond strengths are distributed with a similar standard deviation. Figure 7 presents the predicted
Fake et al.
1226 Energy & Fuels, Vol. 8, No. 6, 1994 Neat Coal Elementary Reactions
Coal-Solvent Liquefaction Elementary
Reactions A,%
P,
+ 8: AH+^
A+A,+
,, + A,LA, + p , L
Q#+ 8,
8%+ 0, 2 . . 8t+p,-
P.
0 70
90 100 dL2H (kcaUmo1)
80
+ Pj
1
-
p>
l
