Energy & Fuels 1994,8, 659-670
659
FLASHCHAIN Theory for Rapid Coal Devolatilization Kinetics. 4. Predicting Ultimate Yields from Ultimate Analyses Alone Stephen Niksa Molecular Physics Laboratory, SRI International, 333 Ravenswood Avenue, Menlo Park, California 94025 Received September 16, 1993. Revised Manuscript Received February 8, 1994'
FLASHCHAIN is being developed to predict yields and product characteristics from any coal for any operating conditions. This extension demonstrates the theory's utility for the usual situation where the ultimate analysis is the only sample-specificinformation available. The original formulation is intact, although the submodel for coal constitution has been extended to assign the elemental compositions of bridges, nuclei, char links, and peripheral groups. This analysis reveals that the elemental compositions of whole coals are very poor indicators of the compositions of labile bridges, the key reaction centers. Most striking of all, the H/C ratios of bridges actually increase with increasing carbon content, whereas the whole-coal ratios diminish. All three atomic ratios for bridges, (H/C)B, (O/C)B,and (O/H)B,exhibit a far stronger rank dependence than their analogs for the whole coal, with very much more sample-to-sample variability. In light of these findings, it is inconceivable that the rates of bridge conversions are rank-independent. Parameters in the rate law for bridge conversion in FLASHCHAIN are now explicitly related to the elemental compositions of bridges. The (O/C)B ratio is the best regression variable for the rate constant for bridge conversion because oxygen is the most effective promoter of pyrolytic decompositions. The (O/H)Bratio is best for the selectivity between scission and condensation into char links because oxygenpromotes cross-linkingbut hydrogen addition to broken bridge fragments stabilizes them. These extensions are evaluated in comparisons against a database of 21 coals that span all ranks from lignite to anthracite. In four out of five cases, predicted total and tar yields are within experimental uncertainties. Accurate predictions for an additional eight high-volatile (hv) bituminous coals stringently demonstrate the theory's ability to chart the substantial variation in yields often seen for a group of coals with similar nominal properties. In light of this performance and the compelling chemical implications of the atomic ratios for bridges, FLASHCHAIN'S bridge properties should also be useful for interpreting yields from other coal conversion schemes, regardless of any connections to devolatilization modeling.
Introduction
yields, in part 4, and devolatilization rates, in part 5, for the usual situation where the ultimate analysis is the only Three phenomenological models have been developed sample-specific information available. The point of to predict the devolatilization behavior of any coal a t any departure for this paper is a sensitivity analysis in part 33 operating c~nditions.l-~ All represent devolatilization as that suggests that predicted ultimate yields based only on a depolymerization that disintegrates coal's macromothe coal's ultimate analysis and linear regressions of all lecular structure into smaller volatile fragments with other input data are as reliable as those based on the subsequent reintegration of larger intermediates into char. complete set of coal-specific input data. Among their most notable performance milestones, these Two basic questions must be addressed to bring this models represent all continuous trends in the yields of tar suggestion to fruition. First, among the various morphoand noncondensible gases with coal rank and, in many logical, structural, and chemical attributes that are defined cases, accurately depict sample-to-sample variations as by the theory, which ones can convey the distinctive well. The superior performance of these models can be behavior of each coal sample? As seen below in the attributed to their elaborate submodels for coal's macrooverview of FLASHCHAIN's submodel for coal's chemical molecular configuration and chemical constitution. Howconstitution, the characteristics of some specific structural ever, along with more illuminating structural features, components show far more variability than analogous these approaches incorporate far more input data than is properties of whole coals. These are clearly the best rank normally at hand for routine engineering applications. parameters for devolatilization modeling and may also Parts 4 and 5 of the FLASHCHAIN series aim to prove useful as regression variables to relate coal type to demonstrate the theory's utility in predicting ultimate the yields from other coal-based processes. The second basic question addresses how the reactivity parameters * Abstract published in Advance ACS Abstracts, March 15, 1994. (1)Niksa, S.; Kerstein, A. R. Energy Fuels 1991, 5 , 647. depend on the structural parameters. "Rank-independent (2) Niksa, S. Energy Fuels 1991,5, 665. rate constants" is one long-standing tenet of the pyrolysis (3) Niksa, S. Energy Fuels 1991,5,673. modeling community that does not survive the analysis (4) Fletcher, T. H.; Kerstein, A. R.; Pugmire,R. J.; Solum, M. S.;Grant, D. M. Energy Fuels 1992,6,414. behind the current extensions to this theory. (6) Solomon,P.R.;Hamblen,D.G.;Serio,M.A.;Yu,Z.-Z.;Charpenay, S . FueZ 1993, 72, 469. Extensions to the theory are evaluated in comparisons 0887-0624/94/2508-0659$04.50/0
0 1994 American Chemical Society
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660 Energy &Fuels, Vol. 8, No. 3, 1994
against a database of 21 coals that span all ranks from lignite to anthracite. A subset of an additional eight high volatile (hv) bituminous coals is used to stringently demonstrate the theory’s ability to chart the substantial variation in yields often seen for a group of coals with similar nominal properties. These evaluations emphasize ultimate yields of tar and noncondensible gas for atmospheric pyrolysis under conditions of rapid heating. Transient yields and evolution rates based on only the ultimate analysis will be considered in part 5, and the theory’s performance for very broad ranges of temperature, time, heating rate, and pressure is described in part 2.2
Overview of the Theory The submodels for coal’s morphology and chemical constitution and the rate mechanisms for the process chemistry and volatiles escape retain all the features in their original formulation.1 Coal is modeled as a mixture of chain fragments ranging in size from a monomer to the nominally infinite chain, The chains are constructed from only four structural components: aromatic nuclei (A), labile bridges (B), char links (C), and peripheral groups (S). Aromatic nuclei are immutable units having the characteristics of the hypothetical aromatic cluster based on l3C NMR analysis. They also contain all the nitrogen in the coal. Nuclei are interconnected by two types of linkages, labile bridges or char links. The fraction of all links that are labile is denoted by P(0).Labile bridges are the key reaction centers. They represent groups of aliphatic, alicyclic, and heteroatomic functionalities, not distinct chemical bonds. All the oxygen, sulfur, and the aliphatic hydrogen and carbon in the whole coal’s organic portion are relegated to bridges. Peripheral groups are the remnants of broken labile bridges and therefore have the same composition. Char links are completely aromatic with no heteroatoms. Any chemical property of the unreacted coal is expressed as a sum of the properties of the nucleus, weighted by and unity, of the bridges, weighted by 1-p(O)(l -P(O)), of the char, weighted by p(O)(l - P(0)).In these expressions p(0) denotes the probability for intact links throughout the whole coal initially. The molecular weights of the four structural components are used to define mass fractions of all the reaction species: that of the aromatic nucleus, MWA,is used to normalize those of labile bridges (MWB/MWA),char links (MWC/MWA),and noncondensible gases (MWG/MWA),which is directly related to the weight of peripheral groups. Connectedness among nuclei is an important aspect of coal rank independent of chemical constitution. In FLASHCHAIN, the initial coal configuration is specified by the proportions of broken bridges and intact linkages, usingp(0). Since the number of linkednuclei in a fragment denotes its size, the fraction of broken bridges specifies the initial fragment size distribution. This distribution is empirically related to extract yields in pyridine, Y p y ~ , to specify the value of p ( 0 ) . Qualitatively, fragment distributions skewed toward smaller sizes correspond to coals with substantial amounts of readily extractable material. Initially and throughout devolatilization, fragments in the condensed phase are subdivided into reactant, intermediate, and metaplast lumps. Metaplast fragments are the smallest, comprising all potential tar species. Reactant species are nonvolatile, comprising the upper portion of the size distribution that extends to nominally
infinite chain lengths. Intermediate species are also nonvolatile, having sizes between those of the metaplast and reactant. In the theory’s four-step reaction mechanism, bridge conversiongovernsboth tar and gas formation. Conversion of a bridge initiates two distinct reaction pathways, either to generate smaller fragments with new peripheral groups on their newly-created ends or to form a new refractory char link accompanied by the immediate release of noncondensible gases. These pathways are designated as bridge scission and spontaneous condensation, respectively. Spontaneous condensation depletes the bridge population without inducing fragmentation, thereby suppressing the production of tar precursors. For both processes, the dissociation energies of labile bridges are represented by a single Gaussian distribution with mean E g and variance cr2. The same pseudofrequency factor, AB,is applied to both processes. A coefficient, VB, specifies the selectivity between scission and spontaneous char condensation, which also varies with rank. As an analog to cross-linking, additional char links and gases may also form by bimolecular recombination between the ends of metaplast fragments, which introduces rate parameters AR and ER. The direct conversion of peripheral groups into noncondensible gases is modeled as a first-order reaction with parameters AG and EG. Tar formation proceeds by the flash distillation analogy? in which a phase equilibrium relates the instantaneous mole fractions of like fragments in the tar vapor and condensed phase. I t is also the basis for predicted tar molecular weight distributions (MWDs). Raoult’s law for the phase equilibrium in continuous mixtures characterizes the impact of fragment size on the phase change, and the saturated vapor pressure of metaplast incorporates three parameters, Pc,Avm, andz. No finite-rate mass transport phenomena are involved because all volatiles are presumed to escape in a convective flow that is initiated by the chemical production of noncondensible gases. Consequently, the model is currently formulated for coal particle sizes that are small enough that intraparticle gradients are negligible, as for coals in the pulverized fuel grade. This phenomenology has already explained all continuous trends in the devolatilization behavior of different coal types. The theory’s central premise is that the partitioning of the elements among aliphatic, heteroatomic, and aromatic constituents largely determines the devolatilization behavior of any coal type. The abundance of labile bridges in lignites promotes their extensive conversion to noncondensible gases, but their oxygen promotes the charring of bridges into refractory links, which inhibits fragmentation of the macromolecules into tar. Conversely, the paucity of labile bridges in lowvolatility coals suppresses gas yields. These coals also have too few labile bridges for extensive fragmentation, so their tar yields are also relatively low. High-volatile bituminous coals generate an abundance of tar precursors, so a competition between flash distillation and repolymerization into larger, refractory fragments determines their tar yields.
Extensions to the Submodel for Coal’s Chemical Constitution The coalification diagram in Figure 1is developed from the database that enters into the data evaluations. Its (6)Niksa, S. AIChE J . 1988, 34, 790.
Energy &Fuels, Vol. 8, No. 3, 1994 661
Flashchain Theory
STRUCTURAL PARAMETERS
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REACTIVITY PARAMETERS AC/Cl.ls',Hla'.B
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(7)van Krevelen, D. W. Coal; Coal Science and Technology 3; Elsevier: Amsterdam,1981.
1 I
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subsets will be described later. For the moment, this diagram provides a context for the basic questions behind the extensions in this paper. The loose band of points arching downward from the upper right quadrant toward the origin charts the extent of coalification. The band has implications for reactivity variations among different coal types in so far as younger samples in the upper right contain far more oxygen and somewhat more hydrogen than the older low volatility samples at O/C = 0.03.7But sampleto-sample variability is the most striking feature of a coalification diagram, and the most relevant one here. Samples with H/C ratios between 0.75 and 0.9 can have O/C ratios from 0.05 to 0.3, which is nearly the range for the entire rank spectrum. Although the range of H/C values associated with particular values of O/C is not nearly as broad, it is still substantial enaugh to indicate different reactivities. Even though the sample-to-sample variability is clearly expressed on the diagram, the connections to reactivity, particularly devolatilization behavior, require extensive elaboration. We need to identify how the variations in a coal's composition affect ita devolatilization behavior and then express the impact in terms of the reactivity parameters in FLASHCHAIN. The reactivity parameters must be related to the theory's structural parameters which, in turn, must be evaluated from the ultimate analysis alone. For the sake of discussion, it is more expedient to invert this sequence by first developing the relations between the ultimate analysis and the structural parameters that can clearly express the sample-to-sample variability. Relationships among structural and reactivity parameters will be considered afterwards. A schematic of the extended scheme to assign the structural parameters from the input data appears in Figure 2. Input measurements that must be assigned for every sample appear within circles, and the structural parameters assigned by the model appear within inverted triangles. The rectangular boxes indicate algebraic relations, which are elemental balances and basic definitions developed in parts 1 and 3. Values for the structural parameters are assigned as solutions to this system of algebraic equations.
I
7 q y v ? 2 5 * v d /
OIC
Figure 1. Coalification diagram for all of the coal samples in this study. The three primary subsets are based on laboratory studiesreported by Freihaut and Proscia12 (O),Xu and TomitaIs (@), and Chen and Niksa14Jb (0). Sources for the subset of hv bituminous coals (v)are given in Table 5.
I
I
4
wc.o/c.s/c
eq 4.5;IV
I
I I
PARAMETER VALUES FIXED FOR ALL COAL TYPES Eb, Ar. El. Ag. Ep
Figure 2. Schematic illustration of the extended submodel for the structuraland reactivity parametersin FLASHCHAIN.Input data needed for every sample appearwithin circles, and structural parameters assigned in the submodel appear within inverted triangles.
The ultimate analysis is now the only sample-specific input requirement. Carbon and proton aromaticities (fa' and Hf,'), the number of carbons per aromatic cluster (AC/ Cl), pyridine extract yields, YPYR, [which determine p(0)I and the average molecular weight of noncondensibles, MWG,are assigned from regressions with carbon content of separate databases given in part 3,3 because they only weakly affect the predictions. The weight ratio MWc/ MWB is arbitrarily assigned as 0.45 for all coal types, because we have no experimental information on how much of a labile bridge is expelled as gas during spontaneous condensation. The labile bridge fraction, P(O),is evaluated from the new nonlinear relation with carbon content in Figure 3. This parameter cannot be assigned by any analytical method, which is especially unfortunate because predicted yields from this and any other depolymerization model are very sensitive to its value. Its relationship to carbon content in Figure 3 is consistent with the view that spontaneous condensation of labile bridges into char links is an aspect of coalification as well as dev~latilization,~ in that the labile bridge fraction diminishes with coal rank. It also undergoes an abrupt transition in the hv bituminous range. This specific functional form for P ( 0 ) is qualitatively similar to the linear regression reported previously3 but quantitatively different because the database behind Figure 3 contains an ample number of lignites and lowvolatility samples, whereas the original one did not. The sequence of calculations to evaluate the structural model parameters from the input data has not been changed, nor have any new parameters been added. Nevertheless, by incorporating the regressions in carbon
Niksa
662 Energy & Fuels, Vol. 8,No. 3, 1994
c
0
%
.
% 0
V
c e2
Carbon Content, w t % daf
Figure 3. Postulated relation between the labile bridge fraction,
F(O),and carbon content.The symbol legend is defined in Figure 1.
content into the structural model, all the structural parameters are now assigned from the ultimate analysis alone. With regard to predicting trends in the decomposition chemistry of different coals, no aspect of the chemical constitution is more essential than the elemental compositions of the reactants. In FLASHCHAIN, labile bridges and peripheral groups are the only structural components that are reactants in the process chemistry, and both components have the same chemical constitution. Their compositions are assigned from the entire ultimate analysis,fa', Hf,',p(0),a n d P ( 0 ) plus the molecular weights of the structural elements as apparent in Figure 2. We denote the atomic ratios for the labile bridges as (H/C)B and (O/C)B; unsubscripted symbols denote whole-coal properties. These ratios are assigned directly from the numbers of the respective atoms, which are specified from two basic relations. The carbon balance for monomers is 1 = C A + (1 - PIC,
+ PCC
(1)
where Ci = ci/cT,CT = AC/Cl/f,', the total number of carbons per monomer, and P = p(O)(l - Fb(O)), the weighting factor for the contribution from char links in any whole coal property. The definition of the carbon aromaticity is expressed as f,' = C A
+ CC
(2)
Subtracting eq 2 from eq 1 and rearranging yields the normalized numer of carbon atoms per labile bridge: (3)
The hydrogen content of labile bridges equals the entire amount of nonaromatic hydrogen in the whole coal, so that (H/C)Bis given by (4) Since labile bridges contain all the coal's oxygen, (O/C)B is given by (5)
Elemental compositions for all of the remaining structural
elements were defined in a similar manner. As seen in the collection of their definitions in Table 1,these FLASHCHAIN parameters can be evaluated for any coal sample, independent of any interest in devolatilization modeling. It stands to reason that, since labile bridges are the key reaction centers in FLASHCHAIN, their chemical compositions dictate the rank dependence, if any, of the rate parameters for bridge conversion. The three atomic ratios for bridges in Figure 4 are positively striking in this regard. The H/C ratios of bridges in Figure 4a become larger for coals of higher rank, even though the ratios for the whole coals diminish. Across the rank spectrum, bridge-based values double from 1.5 to 3 while whole coal values are halved from 0.8 to 0.4. The reason is that the number of labile bridges available to incorporate the aliphatic hydrogen diminishes much faster with coal rank than the pool of aliphatic hydrogen does. The steep nonlinearity in F(0)in Figure 3 is therefore directly responsible. It is also important to note that the sample-to-sample variations in this bridge property are far larger than for the whole coal values. The rank dependence of the (O/C)Bvalues in Figure 4b does not go counter to that for the whole coal property, but the bridge values are at least twice as large. Here too the sample-to-sample variability is larger in the bridgebased values. Only the bridge-based (O/H)Bratio appears in Figure 4c for sake of clarity. Coal-based values exhibit the same trend with values that are one-third lower and, again, show much less sample-to-sample variability than the bridge-based values. There are two important conclusions to draw from the disparate elemental compositions of bridges in this model and whole coals. First, the pronounced sample-to-sample variability of the bridge-based values makes them superior regression variables for devolatilization modeling and, in all likelihood, most other coal processing schemes as well. Second, it is inconceivable that the conversion rates of the labile bridges in different coal types are the same, and that the same rate constants can be applied to all coals. Across the rank spectrum, (O/C)Bfalls by a factor of three and (O/H)B falls by a factor of eight. According to the free radical chain reaction mechanisms that, in actuality, govern the chemistry of coal devolatilization, there is no doubt that nominal reaction rates for oxidative pyrolysis are far faster than for pyrolysis alone. Consequently, the bridge conversion rates for diverse coal types must diminish with increasing rank. Beyond this qualitative tendency, however, it is hard to assemble evidence that reveals the rank dependence of bridge decomposition rates because the overall rates of evolutionof the products are not the same as these chemical reaction rates. Since coal devolatilization is a depolymerization, no products necessarilyform whenever bridges break. In fact, according to FLASHCHAIN, most bridge scissionsamong the longest fragments (in the intermediate and reactant lumps) cannot possibly generate tar molecules. Only scissions that make fragments whose sizes fall into the range of tar precursors (metaplast) have the potential to influence the tar evolution rate. Moreover, according to the flash distillation analogy, the instantaneous rate of tar evolution is also influenced by temperature and pressure as well as all factors that govern the rate of consumption of tar precursors via bimolecular recombinations. The interactions among these mechanisms are so complex that it is futile to try to infer anything
Flashchain Theory
Energy & Fuels, Vol. 8, No. 3, 1994 663
Table 1. Definitions of Carbon Numbers and Atomic Ratios for Bridges, Char Links, and Aromatic Units C numbep
component bridge
char link
o/c
H/C
N/C
SIC ~
(E)L c 1-f.' 0
0.45MW,
(HIc
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(c)f.'
aromatic unit
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Hf,' (1-f.') (1 -8) f.'
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(d77
about the rates of the chemical processes that underlie devolatilization from rates of tar evolution or total weight loss. However, according to FLASHCHAIN, the evolution rates of all noncondensible gases are the key to understanding how the chemical reaction rates for bridge conversion depend on coal rank because most noncondensibles form by spontaneous condensation of labile bridges into char. Gas evolution is not inhibited in any way by transport resistances or vapor pressure considerations and, most important, the energy distribution for the primary mechanism of gas formation, spontaneous charring, is also applied to the bridge scission process. Accordingly, the clearest view on the rank dependence of bridge conversion rate parameters is apparent in observed yields of gas for diverse coal types. Total gas yields reported by Xu and Tomita for eight different coals are normalized by the respective ultimate values in Figure 5. These data are for 4-s isothermal reaction periods following heatup at 3000 K/s to the indicated temperatures. Two features identify a continuous trend in the rate parameters for bridge conversion with rank. First, the temperature to achieve any particular conversion level shifts to higher values for coals of higher rank; e.g., the temperature for a 30 % fractional conversion increases from 720 K for a lignite to 920 K an anthracite. Second, the temperature interval required to complete gas evolution shrinks with coals of higher rank, from more than 600 K for the lignite to less than 400 K for the anthracite. Hence, we see that the chemical mechanisms responsible for these yields shifts from a complex, multicomponent process for lignites, consistent with the abundance of heteroatoms in their bridges, to a simpler conversion scheme for low-volatility coals, consistent with the largely hydrocarbon character of their bridges (cf. Figure 4). Both of these tendencies are implemented in FLASHCHAIN by diminishing bridge conversion rates for coals of higher rank in proportion to the reductions in (O/C)B. To impose the shift to higher onset temperatures for coals of higher rank, either AB or EB could be correlated with (O/C)Bbecause perturbations in either parameter cause identical changes in the bridge conversion rate. Although variations in EB are more satisfying from a theoretical perspective, ABis used in this regression because it is easier to implement, and because the parameters in distributed energy rate laws have no fundamental significanceanyway.
The only way to restrict bridge conversions to narrower temperature intervals for coals of higher rank is to regulate the standard deviation about the mean energy for bridge conversion, u. This parameter is also expressed as an increasing function of (O/C)B. The scission selectivity coefficient is evaluated as the decreasing function of (O/H)Bin Figure 6a. The monotonically decreasing dependence is appropriate because oxygen promotes cross-linkingand hydrogen atoms inhibit it by stabilizing large polynuclear free radicals; it is also consistent with the connection between cross-linking and COn evolution that is o b s e r ~ e d . ~By r ~ virtue of its relationship with (O/H)B, YB now exhibts very substantial sample-to-sample variability, as seen in its relation to carbon content in Figure 6b. ABand UB exhibit comparable sample-to-sample variability because of their associations with (O/C)B. The remaining reactivity parameters have the same values for all coal types. The three parameters in the saturated vapor pressure of metaplast are constant to emphasize their dependence on fragment size, consistent with measured vapor pressures of synthetic liquids that show a strong dependence on molecular size, but insensitivity to structural factors.lOJ1 The rate parameters for bimolecular recombination show no rank dependence for two reasons. First, the chemical constitution of broken bridges in different coals is probably more uniform than whole bridges because of preferential elimination of heteroatoms and a tendency for the formation of unsaturated hydrocarbon functionalities in the bridge conversion chemistry. Second, the role of bimolecular recombination is particularly pronounced in high volatile bituminous coals only? so the true impact of rank on these rate constants is difficult to discern in evaluations against measured yields and tar characteristics. Similarly, AGand EG are constants because gas production via peripheral group elimination is almost negligle for all coal types. Model Parameters
The extended submodel for the structural and reactivity parameters will be evaluated with yields from the 29 coals in the coalification diagram in Figure 1. Three subsets of (8)Suuberg, E. M.; Lee, D.; Lareen, J. W. Fuel 1985,64, 1668. (9)Solomon, P. R.; Serio, M. A.; Deshpande, G. V.; Kroo, E. Energy Fuels 1990,4,42. (10)Hartounian, H.; Allen, D. T. Fuel 1989,68,480. ( 1 1 ) Vajdi, L. E.; Allen, D. T. Fuel 1989, 68,1388.
Niksa
664 Energy &Fuels, Vol. 8,No. 3, 1994 I
3
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100
800
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1100
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1200
Temperature, K
Carbon Content, Wt.% daf
Figure 5. Fractional gas yields for diverse coals for a nominal heating rate of 3000 K/s and 4 s a t the indicated temperatures reported by Xu and Tomita.ls All values are normalized by the yields at 1200 K. This data set includes two lignites (0,0 ) ;four
.,v, hv bituminous coals (0, coals (e, 0).
v);and two low volatility bituminous
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the coal database each represent the devolatilization behavior of nearly the entire rank spectrum. The samples in Freihaut and Proscia's laboratory studies12are uniformly distributed in rank, whereas Xu and Tomita's subsetl3 emphasizes hv bituminous coals and Chen and Niksa's samples emphasize low-volatility ~ o a l s . ' ~ The J ~ fourth subset contains only hv bituminous coals because an abundance of these samples is needed to illustrate the (12) Freihaut, J. D.; Proscia, W. M. FinalReporton U. S.DOEContract No. DE-AC22-89PC89759, Pittsburgh Energy Technology Center, 1991. (13) Xu,W.-C.; Tomita,A. Fuel 1987,66 (5), 632. (14) Chen, J. C.; Niksa, S. Energy Fuels 1992, 6, 154. (15) Chen, J. C.; Niksa, S. Symp. (Znt.)Combust., [Proc.] 19 1992, 1269.
c
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8
0
0.2
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70
80
90
100
Carbon Content, Wt.% daf
Figure 6. Scission selectivity coefficient, m, versus (a, top) (o/ H)Band (b, bottom) carbon content. The symbol legend is d e f i e d in Figure 1.
dramatic variations in both their constitution and devolatilization behavior. All the sample-specific input data for the FLASHCHAIN simulations in this paper (and in part 5) are collected in Table 2. In this and subsequent tabulations, the database is organized by carbon content. Ultimate analyses reported in the literature were simply recast into the atomic ratios for the entire organic portion of the whole coal. In the sample labels for the three subsets that cover
Flashchain Theory
Energy & Fuels, Vol. 8, No. 3, 1994 665
Table 2. b u t Data ~~
sample F1443 XTMW C1488 XTSB C1493 F1493 XTWD F1499 XTHV (21451 XTLD F1451 XTNV F1516 CCBM C1516 XTKS C1521 (21508 XTHG F1468 MFNG MOHS MSBG LNBY PSOC-102 ARPIT PSOC-1099 BRTN
7% C
H/C O/C N/C 0.017 0.931 0.306 66.5 0.006 0.890 0.298 67.4 0.012 0.863 0.260 69.5 0.015 0.790 0.200 71.8 0.858 0.136 0.018 74.1 0.017 0.798 0.179 75.5 0.010 0.890 0.140 78.5 0.825 0.122 79.9 0.017 0.021 0.747 0.114 80.3 0.018 0.815 0.077 82.5 0.076 0.022 0.780 83.5 0.017 0.803 0.079 84.0 0.014 0.713 0.080 84.2 0.017 0.079 0.803 87.4 0.021 0.754 0.036 87.5 0.015 0.676 0.018 88.7 0.021 0.590 0.026 89.4 0.019 0.643 0.024 89.6 0.012 0.614 0.030 89.9 0.011 0.423 0.010 93.7 0.237 0.024 94.3 0.007 HvA Bituminous Subset 0.017 0.849 0.090 77.7 0.014 0.862 0.096 79.4 0.016 0.835 0.094 80.5 0.018 0.785 0.097 81.0 0.017 0.769 0.092 81.2 0.017 0.760 0.080 83.2 0.069 0.018 0.821 83.3 0.017 0.797 0.063 85.8
S/CXlO3 6 2 2 15 26 28 2
N/A 2
7 3 7 2 10
3 11
3 3 3 3 N/A 29 25 10 7 9 4 7 5
many ranks, the first letter is the first initial of the first author in the supporting publications; Le., F denotes Freihaut and Proscia; C denotes Chen and Niksa; and XT denotes Xu and Tomita. Succeeding digits denote the number of the sample in the Penn State Coal Bank or, alternatively, a two-letter suffix denotes the sample names assigned by Xu and Tomita to their subset. Sample labels in the hv bituminous subset are more cryptic, except for the two samples from Penn State and for the Pittsburgh No. 8 hvA bituminous from the Argonne Premium Coal Bank (ARPIT). Among samples with increasing carbon contents in Table 2, the nominal tendencies are for diminishing H/C and O/C ratios, and rank-independent N/C and S/C ratios, except for the exceptionally high sulfur contents in both Illinois No. 6 samples (No. 1493). Of course there are very substantial and erratic variations in all four ratios. It is also interesting to note in the three cases in which the same coals appear in the F- and C-subsets, the atomic ratios are the same for the Pittsburgh No. 8 hvA samples (1451),significantly different for the Illinois No. 6 samples (1493), and completely different for the low- volatility samples (1516). Although these samples were acquired and distributed by the same agency, different size fractions were used in these two lab studies. Structural parameters assigned for this database appear in Table 3. The average weights of the monomer units monotonically decrease with increasing carbon content, in accord with the trend in the values based on 13CNMR analy~is.~ The sample-to-sample variability seen in the NMR-based values has been sacrificed for the expedience of evaluating the aromaticities and carbon numbers from regressions. The weights and carbon numbers of the aromatic nuclei grow with carbon content, reaching a maximum for lv bituminous coals. They also exhibit sample-to-sample variability. However, the maximum is probably an artifact of the assumed straight-chain configuration in this model, which allows only two linkages
per nucleus. It is not evident in 13C NMR values, which grow monotonically throughout all ranks even though the number of attachments per nucleus (from 13CNMR) shows no rank dependence at all.4 The weights of labile bridges diminish for ranks through hv bituminous and then grow as the labile bridge fraction plummets for low volatility coals (cf. Figure 3). Even though the pool of aliphatic constituents in low-volatility coals is smaller, it must be allocated to relatively very few labile bridges so they become massive. The trend in MWG/MWAsimply reflects the curvature in the MWAvalues and the way that the regression values of MWG dimish monotonically with rank (seen in part 3). The probability for intact linkages of any kind, p(O), is constant for ranks through lv bituminous and then grows to its theoretical maximum for anthracites. The rank dependence of the labile bridge fraction was discussed in connection with Figure 3. Those for (O/C)B and (O/H)Bare illustrated in Figure 4. The large variations in V B are primarily responsible for the sample-to-sample variability in predicted devolatilization behavior. For the subset of hv bituminous coals, the variability of MWMON, MWA,and CAis inconsequential, but differences among the values of P(O),(O/C)B, and (O/H)B are definitely large enough to affect their devolatilization behavior. Reactivity parameters are collected in Table 4, except for the scission selectivity coefficient shown in Figure 6 and also in Table 3. All parameters that stay the same for all coal types appear in Table 4, which includes the mean energy for bridge conversion, rate parameters for recombination and peripheral group elimination, and the constants in the metaplast vapor pressure. Values in Table 4 are the same as in the original FLASHCHAIN data correlation^.^ The regressions for the two other constants in the bridge conversion rate are log A B = 6.764(O/C)B + 8.438 (6) u, kJ/mol = 61.63(0/C),
+ 9.38
(7)
General Guidelines for the Data Evaluations The 11 laboratory studies selected for this model evaluation depict ultimate total and tar yields for atmospheric pyrolysis throughout the entire rank spectrum. Nominal heating rates are at least several hundred K/s. We consider only the data for reaction temperatures and reaction times that are high enough to ensure that ultimate, asymptotic values are achieved. (Transientdata from the same studies are considered in part 5.) Reported yields were converted to the dry-ash-free (daf) basis using the reported moisture and ash contents. With one exception, wire-grid heaters in which the sample was dispersed in a layer only a few particles deep were used in all cases. In these cases, process temperatures were determined with fine-wire thermocouples and are regarded as the actual reaction temperature. (Thermocouple errors are inconsequential in evaluations with ultimate yields such as this anyway.) Freihaut and Proscia’s experiments impose nominal heating rates of 735 K/s and a 10-sreaction period at temperatures between 880 and 1000 K; Xu and Tomita heated their samples at about 3000 K/s to 1193 K and then maintained temperature for 4 s. Chen and Niksa used their new radiant coal flow reactorle operated in its mode that eliminates secondary pyrolysis of the volatiles. This entrained flow furnace heats coal suspensions with (16) Chen, J. C.; Niksa, S. Rev. Sci. Instrum. 1992, 63 (3), 2073.
Niksa
666 Energy & Fuels, Vol. 8, No. 3, 1994 Table 3. Structural Model Parameters F1443 XTMW C1488 XTSB C1493 F1493 XTWD F1499 XTHV C1451 XTLD F1451 XTNV F1516 CCBM C1516 XTKS (21521 C1508 XTHG F1468
354 353 345 337 329 329 317 312 311 305 302 300 300 291 290 288 285 285 284 274 273
124 126 136 147 155 160 169 174 175 179 178 175 175 152 157 150 146 150 143 130
MFNG MOHS MSBG LNBY PSOC-102 ARPIT PSOC-1099 BRC
320 309 311 307 308 302 302 299
122
9.7 10.1 10.8 11.6 12.2 12.6 13.4 13.6 13.7 14.0 13.9 13.7 13.8 12.0 12.2 11.7 11.4 11.7 11.3 10.4 9.9
1.862 1.806 1.536 1.315 1.172 1.107 0.952 0.894 0.873 0.847 0.874 0.930 0.933 1.467 1.371 1.546 1.647 1.560 1.734 2.192 2.480
167 171 175 176 176 176 177 167
13.1 13.5 13.7 13.8 13.9 13.8 13.8 13.1
HvA Bituminous Subset 0.992 0.148 0.140 0.969 0.134 0.875 0.132 0.867 0.866 0.131 0.126 0.889 0.125 0.895 0.125 1.128
Table 4. Reaction Rate Parameters for All Coal Types. reaction bridge dissociation recombination peripheral group elimination 'PAT(T,MW),MPA = 3 X
A factor, s-l
see eq 6 6 X 10l6 1 X 1015
E., kJ/mol 167 (see eq 7 for u ) 217 230
lo4 exp (-200 MW0.6/2').
radiant fluxes as large as 60 W/cm2,for which calculated particle heatingrates exceed lo4K/s. These dataare taken to represent uniform heating at 1.5 X lo4 K/s to 1550 K with no isothermal reaction period. Whereas uncertain thermal histories are inconsequential in this evaluation, two other potentially confusing aspects of product analysis and recovery must be resolved. Data for the C- and X-subsets include direct determinations of the yields of oils. In the evaluation, they are combined with the reported tar yields because both pairs of investigators determined that the oils are monoring aromatic compounds, which therefore evolve from nuclei rather than labile bridges. Data for the F-subset does not include this information. Against their tar yields alone, FLASHCHAIN'S predicted tar yields may be too high by as much as 5-7 wt 5% for hvA bituminous coals but not by nearly as much for all other ranks.14 The second potential complication pertains only to the lowest-rank coals. Freihaut and Proscia observed substantial amounts of char fragments in some of their tar samples, especially from a subbituminous C coal from Wyoming. These data are not included in their subset here. Their lignite data that are included (sample F1443) may be affected, although probably not by very much. Since this complication arises because low-rank chars can be friable enough to make fragments than can pass through wire grid reactors, it might have also affected some of the data in the X-subset, although Xu and Tomita did not report any char fragments in their tars. The hv bituminous subset is a compilation of eight
0.213 0.211 0.194 0.180 0.169 0.160 0.144 0.136 0.134 0.126 0.124 0.125 0.124 0.134 0.129 0.132 0.132 0.129 0.134 0.134 0.140
0.911 0.911 0.911 0.911 0.911 0.911 0.911 0.911 0.911 0.911 0.911 0.911 0.911 0.911 0.911 0.920 0.948 0.937 0.943 0.999 0.999
LOO0 LOO0 0.994 0.980 0.937 0.919 0.848 0.792 0.775 0.668 0.588 0.548 0.543 0.255 0.249 0.200 0.185 0.178 0.170 0.103 0.100
0.581 0.606 0.567 0.475 0.352 0.362 0.436 0.402 0.397 0.306 0.319 0.560 0.352 0.192 0.208 0.116 0.182 0.174 0.217 0.140 0.406
0.382 0.412 0.385 0.335 0.231 0.247 0.225 0.212 0.228 0.147 0.153 0.281 0.177 0.088 0.080 0.046 0.077 0.066 0.084 0.047 0.210
0.198 0.182 0.194 0.228 0.308 0.290 0.316 0.328 0.313 0.467 0.420 0.126 0.370 0.692 0.710 0.740 0.714 0.730 0.705 0.740 0.332
0.911 0.911 0.911 0.911 0.911 0.911 0.911 0.911
0.857 0.810 0.770 0.747 0.740 0.610 0.596 0.400
0.273 0.319 0.331 0.352 0.338 0.277 0.289 0.315
0.168 0.178 0.168 0.187 0.182 0.137 0.132 0.129
0.392 0.380 0.392 0.360 0.370 0.520 0.540 0.557
different wire grid s t ~ d i e s . l ~Heating - ~ ~ rates from 500 to 3300 K/s, temperatures from 910 to 1225K, reaction times from 0 to 2 s, and pressures from 0.0985 to 0.18 MPa are represented. (See Table 5, below, for the case-by-case with no isothermal reaction conditions.) Two cases18~24 period imposed slow cooling at 100-200 K/s, which is accounted for in the simulations. Oils (aka hydrocarbon liquids) were monitored in only one case,19 To prepare the forthcoming FLASHCHAIN predictions, the operating conditions of temperature, heating rate, time, and/or pressure were varied to match those in the experiments, while the input data in Table 2 was applied for the various coal samples to assign the structural model parameters in Table 3. The reactivity parameters in Table 4 were used for all coal samples, while sample-specific values of AB and u were specified with eqs 6 and 7, respectively. Sample-specific values of V B were assigned according to the relation in Figure 6a. A simulation of each thermal history requires less than three minutes on a 20-MHz, 386-type personal microcomputer. Results
BehavioroftheThreePrimary Subsets. Parityplots for the ultimate total and tar yields for the three primary subsets appear in Figure 7a and b, respectively. For this broad range of rank, the predicted weight loss ranges from 6 to 60 wt 74 daf, consistent with the observed range of (17) Fong, W. S.; Peters, W. A.; Howard, J. B. Fuel 1986, 65, 251. 118) Oh, M.-S.; Peters, W. A,; Howard, J. B., AIChE J. 1989,35,775. Combust., (19) Suubera,E.M.;Peters, W. A.;Howard, J. B.Symp. . - (Znt.)
[ P r o ~ . 18 ] 1980, 117. (20) Gibbons, J.; Kandiyoti, R. Energy Fuels 1989, 3, 670. (21) Niksa, S.; Russel, W. B.; Saville, D. A. S y m p.. (Znt.)C o n b u t . [Proc.] 19 1982, 1151. (22) Gibbons-Maltham, J.; Kandiyoti, R. Energy Fueki 1988,34,790. (23) Bautista, J. R.; Russel. W. B.; Saville, D. A. Ind. Ena. Chen. Fundam. 1986,25, 536. (24) Unger, P. E.; Suuberg, E. M. Fuel 1984, 63, 606.
Flashchain Theory
Energy & Fuels, Vol. 8, No. 3, 1994 667 Table 5. An Evaluation for HvA Bituminous Coals
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hence artificially high weight loss, could be responsible for the apparent underpredictions. In any case, the quantitative reliability of the predictions is validated for the range of yields associated with the entire rank spectrum. The evaluation of predicted tar yields in Figure 7b is satisfied to within about the same accuracy: The extreme values of 3 and 40 wt % are reliably predicted. Predicted tar yields are within 4 wt 96 of the observed values in 16 of 21 cases. There is no consistent connection to any particular rank among the discrepancies, although predicted tar yields for the F-subsets are overestimations in four of the five cases with substantial tar yields, as expected because oils are omitted from these measured values.
Niksa
668 Energy & Fuels, Vol. 8, No. 3, 1994 I
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Figure 9. An evaluation of ultimate weight loss and tar yields for the hv bituminous subset defined in Table 5. For all coals, the FLASHCHAIN predictions are indicated by (0) connected by the solid curve for weight loss and by the dashed curve for tar yields. In either case, the two pairs of different symbols at each carbon content are directly comparableas predicted and observed values.
a low-volatility sample, so there is no systematic defect for any particular coal type. The predicted sample-tosample variability of the tar yields is substantially better, being correct in 19 of 21 cases. The erratic relation between V B and carbon content in Figure 6b is primarily responsible for the high degree of sample-to-sample variability in the predictions. Resolution of Hv Bituminous Behavior. A finer resolution of FLASHCHAIN’Sability to represent sampleto-sample variability appears in Figure 9, which evaluates predicted ultimate weight loss and tar yields for the hv bituminous subset plus the coals from the other three subsets that fall within this range of carbon content. There are 15 coals in all. The specific operating conditions and numerical values for each case in this comparison are collected in Table 5. All samples in this subset have similar nominal ranks. Yet their ultimate total yields vary from 40 to 60 wt % ,and tar yields vary from 20 to 40 w t 9%. The extreme values in both of these ranges are predicted within experimental uncertainty. Predicted weight loss is within 4 wt ?4 of the observed value in 11 of 15 cases. The same tolerance is satisfied in 10 of 13 tar yields. The sampleto-sample variations are correctly predicted for all of the weight loss values except for the three samples with the largest carbon contents. The predicted sample-to-sample variations in the tar yields are correct in all but two cases. Predicted yields for bituminous coals are especially sensitive to small variations in their amounts of both oxygen and carbon, because these properties are in ranges where V B is a very steep function of (O/H)B(in Figure 6a), and where P(0)is a very steep function of 9% C (in Figure 3).
Discussion
Labile bridges are the key reaction centers in FLASHCHAIN. Their conversion governs the evolution rates and yields of both gas and tar. In this theory they are recognized as groups of several aliphatic, alicyclic, and heteroatomic functionalities, not groupings of any particular chemical bond. The theory does not resolve them from the other aliphatic functionalities in coal on the basis of chemical constitution. Rather, the pool of all aliphatic
hydrocarbon elements and all oxygen is allocated to the population of labile bridges and then apportioned to the aromatic nuclei according to the absolute number of intact linkages and the relative amounts of labile bridges and char links. FLASHCHAINs extended submodel for its reactivity parameters also assigns the elemental compositions of bridges and all its other structural components. First and foremost, this approach reveals that the elemental compositions of whole coals are very poor indicators of the compositions of their reaction centers. Most striking of all, (H/C)B actually increases with increasing carbon content, whereas the whole coal ratio diminishes. All three atom ratios, (H/C)B, (O/C)B,and (O/H)B,exhibit a far stronger rank dependence that their analogs for the whole coal with very much more sampleto-sample variability. And bridge-values are much higher than the whole-coal values, usually more than double. Obviously such large variations in the elemental compositions of bridges with rank will affect bridge conversion chemistry. According to FLASHCHAIN, bridge conversions are concerted chemical processes involving numerous steps and many reaction species,not unimolecular scissions.The details of this chemistry have never been elaborated as part of the formulation, but others have discussed representative reaction mechanisms. The coal pyrolysis mechanisms developed by Gavalas and ~o-workers~~9~6 are especially relevant because they emphasize concerted chemistry and a multitude of mechanistic interactions among all of the aliphatic material in coal, including constituents initially present in both bridges and peripheral groups. A pool of H, CH3, and C2H5 radicals develops from numerous abstraction reactions and @-scissionsof peripheral groups and simultaneously attacks a diverse assortment of bridge structures and aryl radicals to fragment the original coal lattice. Many other studies in the literature elaborate additional mechanistic detail for model coal systems as in, for example, refs 27 and 28 . Although FLASHCHAIN does not incorporate free radical chain mechanisms directly, the theory explicitly recognizes that the population of functionalities that determines a coal’s devolatilization behavior is its entire aliphatic portion regardless whether, in actuality, the material appears in bridges or peripheral groups. This approach omits the potentially confounding contributions for the aromatic constituents, either nuclei or char links, because aromatic components are refractory. We have no indications that any of the material in condensed aromatic ring structures in coal is reformulated into volatiles to an appreciable extent during devolatilization or, for that matter, any other coal utilization process. To the contrary, aromatic rings become more numerous during pyrolysis.29 Consequently, the best regression variables and guidelines are those unaffected by characteristics of the aromatic constituents, and the atomic ratios for bridges from FLASHCHAIN appear to be ideal. Given their compelling chemical implications and large degree of sample-tosample variability, these elemental ratios should also be (25) Gavalas, G. R.;Cheong,P. H.-K.;Jain,R.Znd.Eng. Chem.Fundam. 1981, 20, 113. (26) Gavalas, G. R.;Jain,R.;Cheong,P.H.-K.2nd.Eng.Chem. Fundam. 1981, 20, 122. (27) Allen, D. T.; Gavalas, G. R. Fuel 1984,63, 586. (28) Mahesay, S. R.;Nardin, R.; Stock, L. M.; Zabransky,R. F. Energy Fuels 1987, 1,65. (29) Miknis, F. P.; Turner, T. F.; Ennen, L. W.; Netzel, D. A. Fuel 1988,67, 1568.
Flashchain Theory
useful for interpreting yields from many other coal conversion schemes. By factoring away the contributions from a sample’s refractory material, we arrive a t an unmistakable conclusion: Elemental compositionsof the reaction centers in coal are grossly different among different coal types, so the bridges in different coal types cannot possibly have the same conversion rates. In lieu of detailed chain radical reaction mechanisms, FLASHCHAIN invokes a single distributed energy rate law to represent bridge conversion. So the pertinent corollary of this conclusion is that the rate parameters for bridge conversion cannot possibly be rank-independent. The (O/C)Bratio is the best regression variable for the rate constants because, among the more abundant organic elements in coals, oxygen is the most effective promoter of pyrolytic decompositions. The (0/ H)Bratio is best for the selectivity between scission and condensation into char links because oxygen promotes crosslinking but hydrogen addition to broken bridge fragments stabilizes them. These hypotheses and the high degree of sample-to-sample variability of both of these bridge-based atomic ratios are primarily responsible for the accuracy of predicted ultimate devolatilization yields from coals across the rank spectrum. The very close agreement seen in Figures 8 and 9 could not be achieved by relating the reactivity parameters to any of the coalbased atomic ratios. Additional support for this approach is presented in part 5 in evaluations against transient yields. Whereas the most important implications of the rank dependences of the assigned values for (O/C)Band (0/ H)Bare obvious, it is impossible to validate the absolute magnitudes of the values assigned from this theory. We have no analytical technique that can identify the chemical compositions of all functionalities that interconnect nuclei to objectively define the populations of bridges and char links and their rankdependences. So the relation between labile bridge fraction and carbon content in Figure 3 is plausible, but impossible to validate. We have no method that can resolve peripheral groups from labile bridges in coals either, which limits how precisely the chemical compositions of the reaction centers can be assigned. FLASHCHAIN delivers several useful hypotheses regarding coal structure, particularly the labile bridge fractions in Figure 3 and the bridge-based atomic ratios in Figure 4, but advances in coal characterization will be needed to validate them in any absolute sense. Of course, performance is the central issue in applications and the data evaluations in this paper set a new standard for quantitative accuracy. Predictions are within experimental uncertainty in more than four out of five cases with a database that truly represents the entire rank spectrum. Moreover, FLASHCHAIN depicts sample-to-sample variability with uncanny accuracy even for groups of samples with similar nominal properties. This performance provides one clear basis to distinguish FLASHCHAIN from the other two depolymerization models for coal devolatilization. Another basis is the required input data. FLASHCHAIN and CPD have comparable numbers of input parameters, but structural data from 13C NMR analyses is required for every sample with CPD. Whereas FLASHCHAIN entails no laboratory tests whatsoever, FG-DVC has grown into a framework for extensive laboratory work involving state-of-the-art experimental fa~ilities.~ Since they require such specialized input, neither CPD nor FG-DVC can be used to make
Energy & Fuels, Vol. 8,No. 3, 1994 669
predictions for the substantial backlog of experimental studies in the literature because the information needed to define their input parameters was never acquired. The underlying hypotheses about the chemistry of bridge decomposition are also substantially different among these models. FG-DVC invokes ethylene linkages as surrogates for all labile bridges in any coal type, and its creators emphasize that a single distributed energy rate law for bridge conversion is applicable to any coal. CPD does not yet contain a submodel for the partitioning of the elements among its structural components, but its creators adopt the rate constants for bridge conversion from FG-DVC and also emphasize their rank independence. It would be informative to see if the degree of quantitative accuracy achieved here with FLASHCHAIN can be demonstrated with either of these models, but the prospects are not favorable for two reasons. First, FLASHCHAIN is fully specified by the sample’s ultimate analysis alone, but the inordinate input data required with CPD and FG-DVC prevent the kind of comprehensive data evaluations that are needed to validate representations of sample-to-sample variability. Second, predicted total and tar yields from FG-DVC are still largely based on subjective adjustments of the pressure inside the coal sample, via the parameter Ap, which saps any potential mechanistic implications from its data evaluations. In broader terms, both CPD and FG-DVC attempt to incorporate far more morphological detail than FLASHCHAIN’Sstraight-chain conformation submodel. At first glance, FLASHCHAIN’S submodel seems like a needless regression to the simple phenomenology in DISCHAIN,30 which also invokes straight chains. In fact, its direct antecedent is DISARAY,31 the model that introduced Bethe lattices into devolatilization modeling. Data evaluations and parametric sensitivity studies with DISARAY show that it is impossible to infer coals’ true configuration from comparisons among predicted and observed product yields, because perturbations to the rate parameters for bridge conversion exert the same impact as variations in the coordination number in the conformational submodel. Compounding this ambiguity is the fact that none of these models really represents the molecular architecture of coal, even to the best of our knowledge. Their key deficiency is that average characteristics are applied to identical repeating units whereas, in actuality, all of a coal’s structural components are diverse groups.
Conclusions 1.FLASHCHAIN identifies the key reaction centers in coal as its structural components called labile bridges. Their elemental compositions are grossly different than the analogous whole-coalproperties, showing much stronger rank dependences and a much higher degree of sampleto-sample variability. 2. Once the characteristics of refractory aromatic constituents are eliminated, variations among the elemental compositions of the reaction centers of diverse coal types makes it inconceivable that bridge conversion rates are rank-independent. Hence the rate parameters for this process are related to (O/C)Band (O/H)B. 3. Ultimate analyses are the only sample-specific input (30) Niksa, S.;Kerstein, A. R. Combust. Flame 1986, 66, 95. (31) Niksa, S.;Kerstein, A. R. Fuel 1987,613, 1389.
670 Energy & Fuels, Vol. 8,No. 3, 1994
Niksa
data needed to accurately predict the ultimate total and t a r yields from coal samples across t h e entire rank spectrum.
measured value of the average molecular weight of noncondensibles nondimensional molecular weight of structural constituent L molecular weight of an average monomer unit measured ratio of atomic nitrogen to carbon measured ratio of atomic oxygen to carbon initial probability for intact linkages prefactor of P A T saturated vapor pressure of metaplast measured ratio of atomic organic sulfur to carbon measured extract yield in pyridine exponent in PSAT
Nomenclature constant in vapor pressure of metaplast, PSAT frequency factor for bridge decomposition frequency factor for peripheral group elimination frequency factor for bimolecular recombination measured number of aromatic carbons per cluster (monomeric unit) nondimensional number of carbons in structural component L (L = A, B, C, S) mean activation energy for bridge decomposition activation energy for peripheral group elimination activation energy for bimolecular recombination measured value of carbon aromaticity fraction of all intact linkages among aromatic units that are labile measured value of proton aromaticity measured ratio of atomic hydrogen to carbon
Greek Symbols
B VB VC
YE U
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P(O)(l selectivity for scission in the bridge decomposition rate moles of gas formed per spontaneous condensation moles of gas formed per peripheral group elimination standard deviation about& in the energy distribution for bridge conversion
