Energy & Fuels 1994,8, 1024-1032
1024
A Rationale for Heating Rate and Coal Type Effects on Liquids Yields and Substrate Morphology Changes during Rapid Pyrolysis George S. Darivakis, Jack B. Howard, and William A. Peters* Department of Chemical Engineering and Energy Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307 Received December 15, 1993. Revised Manuscript Received June 21, 1994@
A recent analysis by Darivakis et al. holds that during pyrolysis, liquids production is enhanced when bonds connecting liquids precursors to coal break at virtually identical rates. By analyzing coal thermal depolymerization statistics, this approach relates molecular weight (MW) distributions of primary pyrolysis liquids to coal molecular structure with known mathematical functions. Here it is shown that this analysis provides a plausible, internally consistent, and fimdamentallybased rationale for several macroscopic and non-obviously related chemical and physical effects of heating rate and coal type on pyrolysis: (a) higher liquids yields from bituminous coals than from lignites; (b) increasing liquids yields and bubble concentrations in softened coal with increasing heating rate; and (c) that lignites, in contrast to bituminous coals, do not soften over wide ranges of heating rates, but can be made to soften at very high heating rates. Also presented are experimentally determined yields and number average MWs of tars from pyrolysis of a North Dakota lignite at heating rates of 1000 and 4000 " U s , and temperatures of 600-1000 "C.
Introduction Coal type and heating rate can significantly affect substrate morphology and liquids yields during coal pyrolysis. Coal pyrolysis liquids are complex organic mixtures, typically of wide ranging volatility, molecular weight (MW), and chemical functionality. This paper categorizes these liquids as tars and extractables, Le., organic compounds, condensed outside the coal at or near room temperature, or recovered from cooled char by solvent extraction. Using pyridine1-' and other strong solvent^,^^^ maximum tar and extractables yields are typically 15-30 wt %2,3 and 30-50 wt % of coal, respectively, for bituiminous but more like 5-10 wt and 0-10 wt %1-9 for lignites. Lignites and bituminous coals also differ in their physical @Abstractpublished in Advance ACS Abstracts, August 1, 1994. (1)Fong, W. S. Plasticity and Agglomeration in Coal Pyrolysis Sc.D. Thesis, Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 1986. (2) Fong, W. S.;Khalil, Y. F.; Peters, W. A,; Howard, J. B. Plastic Behavior of Coal Under Rapid Heating High-Temperature Conditions. Fuel 1986, 65, 195-201. (3)Fong, W. S.;Peters, W. A.; Howard, J . B. Kinetics of Generation and Destruction of Pyridine Extractables in a Rapidly Pyrolysing Bituminous Coal. Fuel 1986, 65,251-254. (4) Oh, M. S.Softening Coal Pyrolysis. Sc.D. Thesis, Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 1985. (5) Oh, M. S.; Peters, W. A,; Howard, J . B. An Experimental and Modeling Study of Softening Coal Pyrolysis. MChE J . 1989,35,775797. .
(6) Griffin, T. P. Intraparticle Secondary Reactions of Tar During Bituminous Coal Pyrolysis. Ph.D. Thesis, Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 1989. (7) Griffin, T. P.; Howard, J. B.; Peters, W. A. An Experimental and Modeling Study of Heating Rate and Particle Size Effects in Bituminous Coal Pyrolysis. Energy Fuels 1993, 7,297-305. ( 8 ) Unger, P. E.; Suuberg, E. M. Molecular Weight Distributions of Tars Produced by Flash Pyrolysis of Coals. Fuel 1984, 63, 606. (9) Darivakis, G. S.Primary Liquid Products from Rapid F'yrolysis of Coals and Lignites. Sc.D. Thesis, Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 1989.
behavior during pyrolysis. Prescribed heating under inert or reducing atmospheres transforms most bituminous coals into a viscous, liquid mass (molten coal) that flows under a shear stress, and typically contains minerals, unsoftened macerals, volatiles-filled bubbles, and resolidifed melt.16-18 Lignites generally do not soften or greatly modify their open porous structure, during pyrolysis. The low tar yields and lack of softening of lignites have been attributed to immobilization,or consumption, (10)KO,G. H. Pyrolysis of Different Coal Types. Ph.D. Thesis, Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 1988. (11)Ko, G. H.; Sanchez, D. M.; Peters, W. A.; Howard, J. B. Correlations for Effects of Coal Type and Pressure on Tar Yields From Rapid Devolatilization. Proceedings, Twenty-Second Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, 1989; pp 115-124. (12) Suuberg, E. M. Rapid Pyrolysis and Hydropyrolysis of Coal. Sc.D. Thesis, Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 1977. (13) Suubere. E. M.: Peters. W. A.: Howard. J. B. Product ComDosition and Kine& of Lignite Pyrolysis. Ind. kng. Chem. ProcessDes. Dev. 1978. 17. 37-46. (14)Suuberg, E. M.;Peters, W. A,; Howard, J . B. A Comparison of the Rapid Pyrolysis of a Lignite and a Bituminous Coal. In Thermal Hydrocarbon Chemistry; Oblad, A. G., Davis, H. G., Eddinger, R. T., Eds.; Adu. Chem. Series No. 183;American Chemical Society: Washington, DC, 1979; pp 239-257. (15) Howard, J. B.Funadmentals of Coal, Pyrolysis and Hydropyrolysis. In Chemistry of Coal Utilization, Second Supplementary Volume; Elliott, M. A,, Ed.; Wiley: New York, 1981; Chapter 12. (16) Van Krevelen, D. W. The Transformation of Coal Into Coke. Coal Typology-Chemistry-Physics-Constitution; Elsevier, New York, 1961; Chapter XIV, pp 473-478. (17) Loison, R.;Peytavy, A.; Boyer, A. F.; Grillot, R. The Plastic Properties of Coal. In Chemistry of Coal Utilization, Supplementary Volume; Lowry, H. H., Ed.; John Wiley and Sons: New York, 1963, Chapter 4. (18)Habermehl, D.; Orywal, F.; Beyer, H.-D. Plastic Properties of Coal. In Chemistry of Coal Utilization, Second Supplementary Volume; Elliott, M. A., Ed.; John Wiley and Sons: New York, 1981; Chapter 6. (19) Suuberg, E. M.; Lee, D.; Larsen, J. W. Temperature Dependence of Crosslinking Processes in Pyrolysing Coals. Fuel 1985, 64, 1668. -
?
~1
-
0887-0624/94/2508-102~~~4.~0lQ 0 1994 American Chemical Society
Effects of Coal Type and Heating Rate on Pyrolysis
of liquidlike tar precursors by rapid polymerization or cross-linking of oxygen functional groups.zo~zlIn support of this explanation; (a) lignites cross-link at temperatures as low as 400 "CL9and have more oxygen functional groups than do bituminous coals; (b) in pyrolysis of model compounds, oxygen functional groups inhibit liquids formationz0 and participate in crosslinking.z1 However, consideration of heating rate effects together with the behavior of various coals and coalrelated substrates during pyrolysis suggests that additional insights into solid fuel devolatilization are possible by refining this explanation. Lignin and wood are paleobotanic precursors of coal, and richer in oxygen and oxygen functional groups than lignites. Yet tar yields from ~ o o d or ~ lignin22,z4 ~ 8 ~ ~ pyrolysis are higher than those from lignites and bituminous coals, i.e., > 50 w t %. Kola found that, for similar pyrolysis conditions, lignite tars evolve at lower temperatures and over wider temperature ranges than do tars from bituminous coals, implying a more narrow distribution of tar generation rates for bituminous coals. The heating rate literature has some discrepancies, possibly from experimental or analytical difficulties in eliminating cofactors. Despite this, it begets important teaching for the present analysis. Gibbins-Matham and KandiyotiZ5 report that increasing heating rate increased tar yields from bituminous coals. In screen heater experiments, Griffin6 et al.7 found that the magnitude and direction of heating rate effects depend on temperature and particle size. At a final (peak) temperature of 800 "C, tar yield from 63-75-pm particles of Pittsburgh No. 8 bituminous coal on average increased as heating rate was increased from 10 to 20 000 "Us, but for 106-125-pm particles remained constant or declined slightly above 1000 "C/s. At a higher temperature (1000 "C),for the same heating rate range, a maximum in tar yield from the 106-125-pm particles is indicated at about 1000 "C/s. Mackowsky and WolP6 found that increasing heating rate increased coal plasticity. From electron micrographs of pyrolysis chars, Griffin6et al.7inferred that at high heating rates (-10 000 "C/s) many small bubbles are formed during pyrolysis of softening coal, while slower heating (-10 "C/s) produces a few large bubbles. Coals which show no softening under slow heating, may soften and swell when heated more r a p i d l ~ ;e.g., ~ ~a, lignite ~~ pyrolyzed at 20 000 "C/s softened like a bituminous coal.27 Tar from pyrolysis of a North Dakota lignite attained its (20)Wolfs, P. M. J.;Van Krevelen, D. W.; Waterman, H. I. Chemical Structure and Properties of Coal X X V The Carbonization of Coal Model. Fuel 1960,39,25. (21)Solomon, P. R.; Squire, K. R.; Carangelo, R. M. Mechanism of Coal Tar Formation. Presented at the International Conference on Coal Science, Sydney, Australia, 1985. (22)Nunn, T. R. Rapid Pyrolysis of Sweet Gum Wood and Milled Wood Lignin. S. M. Thesis, Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 1981. (23)Nunn, T. R.; Howard, J. B.; Longwell, J. P.; Peters, W. A. Product Compositions and Kinetics in the Rapid Pyrolysis of Sweet Gum Hardwood. Ind. Eng. Chem. Process Des. Deu. 1985,24, 836844. (24)Nunn, T. R.; Howard, J. B.; Longwell, J. P.; Peters, W. A. Product Compositions and Kinetics in the Rapid Pyrolysis of Milled Wood Lignin. Ind. Eng. Chem. Process Des. Deu. 1985,24,844-852. (25)Gibbins-Matham, J.;Kandiyoti, R. Coal Pyrolysis Yields from Fast and Slow Heating in a Wire Mesh Apparatus with a Gas Sweep. Energy Fuels 1988,2,505. (26)Mackowsky, M. T.; Wolff, E. M. Microscopic Investigation of Pore Formation During Coking. In Coal Science; Advances in Chemistry Series; American Chemical Society: Washington, DC, 1966;Vol. 55, pp 527-548.
Energy & Fuels, Vol. 8, No. 5, 1994 1025
apparent ultimate yield at a 150-200 "C lower temperature when heating at 4000 "C/s than at 1000 "C/S.~ This indicates that tar evolution occurs over a more narrow range of temperatures at the higher heating rate. For a North Dakota ligniteg and a Pittsburgh No. 8 bituminous ~ o a l , the ~ J average molecular weight of pyrolysis tar decreased as heating rate increased. Mathematical models at various levels of physicochemical and mathematical sophistication, e.g., refs 1-7,lO-15, and 27-39, have been developed to account for the above and many other features of coal devolatilization. The objectives here are neither to introduce a new coal pyrolysis model nor to dogmatize specific submodels. Instead, the aim is to demonstrate that a particular, pseudomechanistic perspective on how primary liquids form during thermal depolymerization of coal (Darivakis et a1.9~~0) provides plausible and internally consistent explanations for several intriguing aspects of coal pyrolysis: higher liquids yields from bituminous coals than lignites; increasing liquids yields and bubble concentrations in softened coal with increasing heating rate; and the lack of thermal softening in lignites without very rapid heating. Also presented are new experimental data on yields and number average molecular weights of tars from rapid pyrolysis of North Dakota Zap lignite, as affected by heating rate and temperature.
A PseudomechanisticView of the Formation of Coal Pyrolysis Liquids This analysis, described in detail by Darivakis et al.,9)40draws on the picture of Larsen and K o v a ~ , ~ l (27)Solomon, P. R.; Squire, K. R. Experiments and Modeling of Coal Depolymerization. Prepr. Pap.-Am. Chem. SOC.,Diu. Fuel Chem. 1985,30,(4),346. (28)Lewellen. P. C. Product DecomDosition Effects in Coal Pvrolvsis. S. M. Thesis, Department of Chemilal Engineering, Massaihusetts Institute of Technology, Cambridge, MA, 1975. (29)James, R.K.; Mills, A. F. Analysis of Coal Particle Pyrolysis. Lett. Heat Mass Transfer 1976,3,1. (30)Hsu,J. Swelling, Mass Transport, and Chemical Kinetics in Bituminous Coal Pyrolysis. Ph.D. Thesis, Department of Chemical Engineering, Massachusetts institute of Technology, Cambridge, MA, 1989. (31)Gavalas, G. R. Coal Pyrolysis; Elsevier: New York, 1982. (32)Gavalas, G. R.;Cheong, P. H.; Jain, R. Model of Coal Pyrolysis. 1. Qualitative Development. Znd. Eng. Chem. Fundam. 1981,20, 113-122. (33)Gavalas, G. R.; Jain, R.; Cheong, P. H. Model of Coal Pyrolysis. 2. Quantitative Formulation and Results. Znd. Eng. Chem. Fundam. 1981,20,122-132. (34)Niksa, S.;Kerstein, A. R. The Distributed-Energy Chain Model for Rapid Coal Devolatilization Kinetics. Part 1. Formulation. Combust. Flame 1986,66, 95-109 (35)Niksa, S.The Distributed-Energy Chain Model for Rapid Coal Devolatilization Kinetics. Part 2. Transient Weight Loss Correlations. Combust. Flame 1986,66,111-119. (36)Solomon, P. R.;Hamblen, D. G.; Carangelo, R. M.; Serio, M. A.; Deshpande, G. V. A General Model of Coal Devolatilization. Energy Fuels 1988,2,405-422. (37)Niksa. S. RaDid Coal Devolatilization as an Eouilibrium Flash Distillation. k C h E J. ~ 1988,34,790-802. (38)Grant, D.M.;Pugmire, R. J.; Fletcher, T. H.; Kerstein, A. R. Chemical Model of Coal Devolatilization Using Percolation Lattice Statistics. Energy Fuels 1989,3,175-186. (39)Niksa, S.;Lau, C.-W. Global Rates of Devolatilization for Various Coal Types. Combust. Flame 1993,94,293-307. (40) Darivakis, G. S.; Peters, W. A,; Howard, J. B. Rationalization for the Molecular Weight Distributions of Coal Pyrolysis Liquids. AIChE J. 1990,36,1189-1199. (41)Larsen, J.W.; Kovac, J. Polymer Structure of Bituminous Coals. In Organic Chemistry of Coal; Larsen, J . W., Ed.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978;Vol. 71, pp 36-49. ~~~~~~~
~~
~
~~
1
~~~~~
~
~
~
Darivakis et al.
1026 Energy & Fuels, Vol. 8, No. 5, 1994
Lucht and pep pa^,^^ and Green et al.43that the organic part of coal has a cross-linked macromolecular structure, in which monomers, possibly of different molecular structure, are chemically bonded to form oligomers of various degrees of polymerization (DP). The model The function fckf),the Pearson Type I11 pdf,44has been equates liquids precursors, P, with oligomers of various used in its mathematically equivalent form, the gamma sizes (i.e. DP), liberated by thermal depolymerization distribution function F ( 0 , to empirically correlate exof the coal, as proposed, inter alia,by Gavalas et a1.,32~33 perimentally determined MWD’s for coal liquids (e.g. Niksa and K e r ~ t e i nN, ~i~k ~ a ,Solomon ~ ~ , ~ et ~ al.,36and Nik~a~~) Grant et al.38 The present analysis assumes that on average, two linkages, i and j, must rupture to fully disconnect an oligomer P, from the parent coal, A P (a detached oligomer = a liquids precursor) A
k,
E
ki
(1)
I L
C (a cross-linked product)
where I, an intermediate formed by scission of one linkage, is still attached to the reacting substrate, i.e., the coal, and ki, k,, k,, and k-, are respectively the rate constants for breaking linkages i and j, for cross-linking of I to form an immobile product C, and for free-radical reattachment of I to A. Rupture of one linkage would suffice to liberate monomers on the ends of polymeric chains, while three or more linkages would need to break to release cross-linked monomers or oligomers. Since A, I, and C are immobile, mass-transfer limitations, if any, affect only P. Three attributes of the kinetic behavior of eq 19v40 help connect liquids formation to coal molecular structure: (a) even relatively small differences in the dissociation rates of i and j, where by convention, linkage i is assumed to be weaker than linkage j, can significantly delay formation of P from I. This leaves more time for depletion of I by recombination with the substrate (k-i) and by cross-linking (kc); (b) when linkages i and j are “kinetically identical”, i.e., dissociate at the same rate, P formation is strongly favored, and so also is production of liquids when P is unaffected by mass transfer or secondary reactions; and (c) two linkages of very different chemical structure will still be “kineticallyidentical” if, at the heating conditions of interest, they exhibit the same fission rates. As a pragmatic simplification the analysis assumes that P becomes liquids without modification by mass transfer or secondary reactions. The model then determines the molecular weight distributions MWD’s AM‘), of pyrolysis liquids as the probability density function (pdf) for finding oligomers of different sizes, bonded in the parent coal structure by kinetically identical linkages of a given type.9,40The resulting pdf contains three parameters, each of which is a different index of the global or average molecular structure of the coal: r the average number of bonds that must break to liberate a liquids precursor, M the molecular wight of a monomer, and yi the fraction of kinetically identical linkages of a particular type, i, in the coal structure (42) Lucht, L. M.; Peppas, N. A. Cross-Linked Structures in Coals: Models and Preliminary Experimental Data. In New Approaches in Coal Chemisty; Blaustein, B. D., Bockrath, B. C., Friedman, S., Eds.; ACS Symposium Series; American Chemical Society, Washington, DC, 1981; Vol. 169, pp 43-59. (43)Green, T.; Kovac, J.; Brenner, D.; Larsen, J. W. The Macromolecular Structure of Coals. In Coal Structure; Meyers, R. A,, Ed.; Academic Press: New York, 1982.
where I is the molecular weight. The present methodology interprets the empirical parameters a, p, and y , of F(I) in terms of more fundamental quantities related to coal molecular s t r u ~ t u r e g , ~ ~
a=r
(4)
p = M/yi
(5)
y=M
(6)
Molecular Weight Distributions for Liquids from Lignite Pyrolysis MWD’s measured for liquids from rapid pyrolysis of Pittsburgh No. 8 bituminous coal are well correlated by eqs 2 and 3.40 To further test the present methodology, eq 3 was best fitted to MWD’s for tars from pyrolysis of a lower rank fuel, a North Dakota lignite (PSOC No. 1507) at 600 “C under 1atm of helium, at 1000 “Us, in an electrical screen heater r e a ~ t o r .The ~ MWD’s were measuredg by calibrated gel permeation chromatography (GPC), using procedures described in more detail by D a r i v a k i ~ .In ~ brief, the GPC system was calibrated using actual pyrolysis liquids, Le., tars and extractables from cooled chars, from this lignite. Portions of these two liquids were fractionated on a preparative scale GPC. The average elution volumes of different fractions were determined on a smaller scale GPC system. The number-average MW of each fraction was measured independently by vapor pressure osmometry (VPO), allowing M W to be related to elution volume. The resulting calibration curvegshowed reasonable linearity, and little difference for the tars vs the extractables. The VPO measurements were performed at 25 “C using dichloromethane as the solvent on a KNAUER vapor pressure osmometer, which was calibrated with benzil. This calibration was checked by measuring MW’s of known materials, resulting in an accuracy of 87% or better, i.e., maximum relative error of 13%, for compounds with molecular weights ranging from about 160 to 9000 amu. With y , i.e., i@, fured a t 100 amu, the resulting best fit values of a and p, i.e., of r and M/yi, respectively, eqs 4 and 5,were 3 and 163, and the observed and predicted MWD’s agreed well (Figure 1). Considering the uncertainties in this analysis, these and M/yi values are reasonable, given perceptions about lignite macromolecular structure. A modestly substituted, six-carbon (44) Zalen, M.; Severo, N. C. Probability Functions. In Handbook of Mathematical Functions With Formulas, Graphs and Mathematical
Tables; Abramowitz, M., Stegun, I. A., Eds.; US.National Bureau of Standards-Applied Mathematics Series 55; U S . Government Printing Office: Washington, DC, 1972; Chapter 26.
Energy & Fuels, Vol. 8, No. 5, 1994 1027
Effects of Coal Type and Heating Rate on Pyrolysis 0.003
rr
2
1
E l ; ( 2 )chemical homogeneity with a strong temperature dependence of the rate constant: ki = kj = k2, and E2 = 67.5 kcaymol; and (3) chemical homogeneity with the rate constant less strongly dependent on temperature than in case 2: ki = kj = k l , and E1 = 55.6 kcavmol. The preexponential factors k1, and kzo are given above, and the final temperature, 1166 K, was chosen to provide vertually identical dissociation rates for linkages i and j, i.e., to make k1 k2. Figure 3 shows that for variations in heating rate from 1 to 100 000 Ws, the selectivity t o P is consistently highest for more rapidly reacting, chemically identical linkages, i.e. case 3. Two kinetically identical, but more slowly reacting linkages, case 2 , give the next highest selectivity; because these two linkages dissociate simultaneously but more slowly than in case 3, there is greater opportunity for crosslinking of I, particularly a t lower heating rates. The lowest selectivity arises for two linkages of different stability, Figure 3, curve 1; significant amounts of I accumulate by rupture of the more labile linkage before much P is generated by breaking the more stable bond. This gives more time for cross-linkingto consume newly formed I. This analysis identifies two factors that enhance the selectivity toward a product P of two sequential reactions: the absolute stability of the two bonds anchoring P to a substrate, and the ability of these bonds to react simultaneously at identical rates. The analysis further implies that the presence of a very labile linkage in a coal macropolymer may not facilitate high liquids yields in coal pyrolysis, if repolymerization can rapidly con-
200
I
I
I
100
1000
I
TEMPERATURE ('C)
Figure 4. Effect of heating rate and peak pyrolysis temperature on the number-average molecular weight of tar from pyrolysis of a North Dakota, Zap, lignite in an electrical screen heater r e a ~ t o r .Holding ~ time 50 ms, nominal quench rate 10 000 " U s , P = 1 atm of helium, particle size = 75-90 pm. Points: experimental results. sume intermediates antecedent to liquids precursors, e.g., moiety I in eq 1. This would arise if (a) the weak linkage, i, is present in concentrations too low (i.e., in the present terminology its yi value is too small) to allow molecules in the liquids boiling range to be liberated by severing only this linkage; and (b) there are insufficient concentrations of other linkages, j, k, etc., able to dissociate as rapidly as linkage i. Figure 3 also shows that the selectivity to P from chemically heterogeneous reactions, case 1,approaches the selectivities from both chemically homogeneous cases at very high heating rates (-100 000 Ws). This reinforces the conclusion that increasing heating rate can reduce, and ultimately eliminate, differences in the kinetics of two sequential reactions. In the terminology of the analysis, a coal containing two chemically different linkages in fractionsy, andyb can be made to behave as though it contained one thermally labile linkage in a fraction (Ya Yb) if that coal is heated sufficiently rapidly to a final temperature at which the dissociation rates of the two linkages become essentially identical.
+
Temperature and Heating Rate Effects on Yields and MW of Pyrolysis Liquids Molecular weight distributions of tars from pyrolysis of a North Dakota Zap lignite (PSOC No. 1507) at
different temperatures and heating rates were measured by gel permeation chromatography (GPC).g Number-average molecular weights (M,) were calculated for each case (Figure 4). By definition, M , is the mean of the pdf for molecular weight. If the present analysis is correct, M,, would be the mean of AM) or F ( I )(eqs 2 and 31, i.e.44
M , = ?.(myi)+
a = a$ + y
(7)
and effects of pyrolysis conditions on M , should be and explainable in terms of effects of pyrolysis on r ,
a,
Yi.
Effects of Coal Type and Heating Rate on Pyrolysis
Energy & Fuels, Vol. 8, No. 5, 1994 1029
Focus first on the observed monotonic decline in Mn heating rate, so that M 4 = MI, and eq 9 becomes with increasing temperature (Figure 4). To test the r 4 f ~ i 4< rlfyil (10) present analysis, consider how temperature should affect r, i@,and yl. The average number of bonds that Mathematically, this inequality is satisfied by any of must break in order to liberate a liquids precursor, r, the following possibilities: would be expected to scale directly with the degree of cross-linking in the substrate. Suuberg et al.'sl9 experiA* ~ i , > 4 Yi,l and r4 Irl for all y i and r values ments on solvent swelling of chars from pyrolysis of (11) different coal types show that the degree of cross-linking in the chars increases as pyrolysis temperature inB. yi,4 > yi,l and 7 4 > rl creases. Thus to the extent that cross-linking in these for some y i and r values (12) chars mimics pyrolysis-induced cross-linking in that portion of the parent coal able to disengage liquids C. ~ i ,
