FLASHCHAIN theory for rapid coal devolatilization ... - ACS Publications

Energy & Fuels 1991,5, 647-665

cf,"H = 0.65) for the densest fraction. This degree of aromatic carbon substitution for the inertinite fraction reveals that the aromatic structure is not highly condensed. A comparison of the aromatic to aliphatic proton ratio determined by FTIR and NMR for the density fractions can be used to observe the change in infrared extinction coefficient ratio for aromatic and aliphatic C-H bonds. At

647

low density the ratio is approximately 7 but falls to a value of about 1.5 for the densest fractions.

Acknowledgment. The National Energy Research Development and DemonstrationCouncil of Australia and the Australian Research Council are acknowledged for partial funding of this research.

FLASHCHAIN Theory for Rapid Coal Devolatilization Kinetics. 1. Formulation Stephen Niksa* High Temperature Gasdynamics Laboratory, Mechanical Engineering Department, Stanford University, Stanford, California 94305

Alan R. Kerstein Combustion Research Facility, Sandia National Laboratories, Livermore, California 94550 Received February 7, 1991. Revised Manuscript Received June 24, 1991

This theory invokes a new model of coal's chemical constitution, a four-step reaction mechanism, chain statistics, and the flash distillation analogy to explain the devolatilization of various coal types. It is called FLASHCHAIN. The constitution submodel segregates the elements into only four pseudocomponents using the ultimate analysis, the carbon aromaticity and aromatic cluster size from 13C NMR analysis, the proton aromaticity, and the extract yield in pyridine. No functional groups appear. 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. Labile bridges comprise all aliphatic and oxygen functionalities in the coal and are the key reaction centers. 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 low-volatility coals suppresses gas yields; these coals also have too few labile bridges for extensive fragmentation, 80 their tar yields are also relatively low. Charring establishes the gas flow which sweeps away tar vapor but also suppresses the subsequent fragmentation of coal macromolecules into additional tar precursors. This scheme delivers reliable yields of gas and tar and molecular weight distributions of tar for any coal a t any condition, yet it requires only a few minutes per simulation on a personal microcomputer. The theory is introduced in three parts. Part 1 describes its phenomenological basis, the formulation of rate equations, and assignments of model parameters, while parts 2 and 3 are devoted to performance evaluations. In part 2, the theory's representation of broad ranges of temperature,.time, heating rate, pressure, and particle size is evaluated against the extensive data base for high-volatile bituminous coals. In part 3, model predictions demonstrate that this theory depicts all of the continuous trends in the yield structure from coals across the rank spectrum.

Introduction Coal devolatilization is the thermal conversion of most of the organic mass, hydrogen, oxygen, nitrogen, and sulfur in coal into gases. Volatiles consist of noncondensible gases with high heating value, light oils suitable as fuels and feedstocks, and high-boiling tars for subsequent refining. The major noncondensibles are methane and C2-C4 hydrocarbons, hydrogen and, especially in low-rank coals, water, and the oxides of carbon. Tar is operationally defined as the volatile5 that condense at room temperature. It is a mixture of aromatic compounds of molecular weights from 100 to more than lO00, having an average chemical constitution similar to the parent coal's with somewhat more hydrogen, particularly for tars from low-rank coals.

There is always a highly porous solid carbon residue called char containing most of the original mineral matter. Taken together, the available rate and yield data on coal devolatilization characterize the influences of all of the important operating conditions. Raising the temperature or reducing the pressure increases total yields,'s especially for high-volatile bituminous samples, and also generates a heavier tar.*' Product evolution rates are very sensitive (1) Howard, J. B. In Chemistry of Coal Utilization, 2nd Suppl. Vol.; A,, Ed.; Wiley-Interscience: New York, 1981; Chapter 12. Elliot, M. A., Xu, W.-C.; Tomita, A. Fuel 1987,66(5), 632. (2) x (3) Suuberg, Suuberl E. N.; Unger, P. E.; Lilly, W. D. Fuel 19815, 64, 966. (4) re1 1984,63,606. 191 (4) Unger, P. E.; Suuberg, E. M. Fuel ((5) 5 ) Oh, Oh, M. S.; Petere, W. A,; Howard, :d, J. B. AIChE J. 1989, 36,776.

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Niksa and Kerstein

to temperature, suggesting a major role for chemical ki-

netics, but devolatilization rates are very insensitive to p r e s s ~ r e . ~T*ot~al and tar yields are enhanced by faster heating, especially at reduced preasures.~1*12 For particles smaller than about 1 mm, yields and product distributions are independent of particle size.13 Ultimate yields are remarkably constant a t about 50 wt '?% for lignites, subbituminous, and high-volatile bituminous coals, then diminish for coals of higher rank.14 But the proportions of gases and tar vary widely with coal rank; tar yields are greatest for high-volatile bituminous coals, reaching 40 w t '?% at reduced p r e s s u r e ~ . ~The ~ J ~yields of water and the oxides of carbon diminish for parent coals of higher rank, while yields of noncondensible hydrocarbons and oils follow the tar yields." Tars become less aromatic for parent coals of lower rank>ls and molecular weights of tar tend to decrease slightly for parent coals of high rank.31617 Considering coal's heterogeneous chemical constitution, its irregular macromolecular confiiation, and its complex physical structure, one can imagine that tens, if not hundreds, of chemical and transport mechanisms are potentially important in devolatilization. So it is not surprising that diverse points of view have been synthesized into very dissimilar models. Generally speaking,they fall into either of two primary categories, classical theory and the more recent depolymerization schemes. Classical devolatilization theory began with the pioneering work of Howard and co-workers at MIT and has been reviewed recently by Howard' and Suuberg.17 Its essential ingredient is secondary redeposition of released volatiles into residues which remain in the char on a time scale set by the transport mechanism for volatiles escape. Consequently, factors which promote secondary redeposition chemistry, such as the higher vapor concentrations at elevated pressures or the longer transport times in larger particles, are purported to lower yields. Transport mechanisms such as escape by either continuum or Knudsen diffusion, continuum diffusion of liquids through a melt, bulk flow through macropores, film-diffusion-limited evaporation from a melt, and bubble rupture and growth in a viscous melt have been analyzed. Several of these models can correlate total weight loss and tar yields versus temperature or pressure, but tar molecular weight distributions (MWDs) have not yet been addressed. As elaborated elsewhere,13from a mechanistic standpoint, all of these models are contradicted by the observed absence of a size dependence, and several other inconsistencies with observed behavior remain unresolved. In the second modeling category, coal is recognized as a cross-linked macromolecular solid, and devolatilization is explicitly analyzed as a bona fide depolymerization. (6) Freihaut, J. D.;Proecia, W. M.; Seery, D. J. Energy Fuels 1989,3, 692.

( 7 ) Solomon, P. R.; Serio, M. A,; Deshpande, G. V.; Kroo, E. Energy Fuels 1990, 4, 42. (8) Nikaa, S.: Russel. W. B.: Saville. D. A. Sv m .n (Int.) Combust.. [Proc.],29 1982, 1151. (9) Heyd, L. E. Weight Loss Behuuior of Coal During Rapid Pyrolysis of Chemical Eneineerinn. and HvdroDvrolvsh. M.S.Thesis.IDeoartment . -. Princ~~n,'Uni;ereity, 1982. (10) Niksa, S.; Heyd, L. E.; Ruseel, W. G.; Saville, D. A. Symp. (Int.) Combust., [Proc.],20 1984, 1445. (11) Gibbins-Maltham, J.; Kandiyoti, R. Energy Fuels 1988,2, 505. (12) Gibbins, J.; Kandiyoti, R. Energy Fuels 1989,3,670. (13) Niksa, 5.AZChE J. 1988,34,790. (14) Xu, W.-C.; Tomita, A. Fuel 1987,66(5), 627. (15) Freihaut, J. D.; Zabielski, M. F.; Seery, D. J. Symp. (Znt.) Combust., [Proc.], 19 1982, 1159. (16) Fletcher, T. H.; Solum, M. S.; Grant, D. M.; Critchfield, S.; Pugmire, R. J. Symp. (Znt.) Combust., [Proc.],23 1991, 1231. (17) Suuberg, E. M. In Chemistry of Coal Conversion; Schloeberg, R. H., Ed.;Plenum: New York, 1985; Chapter 4.

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Hence, these models necessarily include a postulated submodel for coal structure and constitution. Ultimately they are intended to explain the behavior of various coal types in terms of systematic variations in initial coal structure. Gavalas et al.18Jgintroduced this approach by incorporating probability functions for the disintegration of a honeycomb network into their product evolution scheme. In contrast to the rudimentary chemistry in all other models, this one also features detailed elementary chain reaction mechanisms among many functionalities. Because of its complexity, its primary utility has been to guide simpler modeling. In DISCHAIN,20~21 Niksa and Kerstein reverted to the straight chain configurational model and a rudimentary reaction scheme to focus on the qualitative impact of macromolecular configuration. Tar formation is envisioned as a competition between (1) depolymerization of the chains, yielding monomer units which subsequently fragment into species small enough to evaporate rapidly and escape as tar, and (2) reattachment of monomers onto larger fragments, as a coarse representation of the reintegration of potential tar precursors into char via cross-linking. Chain statistics determine the instantaneous probability that a bridge scission will generate a monomer, and the number of sites available for reattachment. These modeling studies show that yield enhancements due to faster heating are consistent with coal's macromolecular structure. The model also correlates weight loss and tar yields for diverse thermal histories:l$z but only when an unreasonably high fraction of the original units in the coal structure become monomers at some stage of pyrolysis. And monomers are not size-distributed, so tar molecular weight distributions (MWDs) are ignored. No scheme is included for pressure effects. In DISARAY,23,24the same scheme is applied to the Bethe lattice, a two-dimensional structure of nodes interconnected by an arbitrarily specified number of links. Even though the Bethe lattice seems like a more appealing analog for coal's three-dimensional network, the qualitative features of DISCHAIN and DISARAY are the same. This extension did show that attempts to use model evaluations against devolatilization yields to identify the correct configurational model of coal would be submerged by uncertainties in the dissociation energies of bridges. An extension of this approachB36 invokes a description of tar formation based on Fisher and Essa"sn percolation statistics for the complete size distribution of depolymerization fragments from a Bethe lattice. In this chemical percolation devolatiliition (CPD) model, tar forms solely by dissociation of fragments from the nominally infinite lattice and is presumed to escape without further transformation. Char forms by the spontaneous conversion of labile bridges into refractory links, which diminishes the likelihood of subsequent fragmentations and keeps the infinite lattice intact. While several parameters are assigned by data regressions, at least one parameter is as(18) Gavalae, G. R.; Cheong, P. H.; Jain,R. Ind. Eng. Chem. Fundam. 1981,20, 113. (19) Gavalae, G. R.; Jain, R.; Cheong, P. H. Ind. Eng. Chem. Fundam. 1981, 20, 122. (20) Niksa, S.; Kerstein, A. R. Combust. Flame 1986,66, 95. (21) Niksa, S. Combust. Flame 1986, 66, 110. (22) Niksa, S.; Kerstein, A. R.; Fletcher, T. F. Combust. Flame 1987, 69, 221. (23) Niksa, 5.;Kerstein, A. R. Fuel 1987,66, 1389. (24) Kerstein, A. R.; Niksa, S. Macromolecules 1987,20, 1811. (25) Grant, D. M.; Pugmire, R. J.; Fletcher, T. H.; Keretein, A. R. Energy Fuels 1989, 3, 175. (26) Fletcher, T. H.; Kerstein, A. R.; Pugmire, R. J.; Grant, D. M. Energy Fuels 1990,4,54. (27) Fisher, M. E.; Essam, J. W . J. Math. Phys. 1961,2, 609.

FLASHCHAIN Theory for Coal Devolatilization

signed from the skeletal characteristics inferred from 13C NMR analyses. Total and tar yields from three coals at diverse thermal histories have been correlated with this model; no tar MWDs or pressure effects have yet been reported. Niksa's FLASHTWO t h e ~ r y ' ~is* ~the ~ first depolymerization-type model to satisfactorilydepict pressure effects. Strictly speaking, it is not in the same category as the others because it does not include any fragment or network statistics; instead, the broad distribution of fragment sizes formed in a depolymerization is represented with a distribution function specified a priori by fitting the observed MWDs of vacuum tar. The details of the depolymerization are suppressed to highlight FLASHTWOS novel scheme for pressure effects. A phase equilibrium among like-sized constituents of the primary fragments in the vapor and condensed phases is represented with Raoult's law for continuous mixtures. This equilibrium stipulates the instantaneous mole fraction of tar in a binary mixture with noncondensible gases. The evolution rate of tar, and hence its yield, is related to the chemical production rate of noncondensibles;consequently, internal and ambient pressures are equal and all transport resistances are deemed negligible. This scheme remains the only one to correctly depict all facets of the pressure effect without any size dependence. It also correlates tar MWDs for broad temperature and pressure ranges. More generally, FLASHTWO demonstrates that the influences of all of the important operating conditions on total and tar yields and tar MWDs can be understood in terms of only three mechanisms: (1)the disintegration of the coal macromolecule into primary fragments which are widely distributed in size: (2) their partitioning into volatile and condensed species according to a phase equilibrium for continuous mixtures; and (3) char formation in the condensed phase with the concurrent evolution of noncondensible gases, as a mechanism for reducing the availability of tar precursors. This model depicts coal type effects only with heuristic parameter adjustments. Like FLASHTWO, the FG-DVC model of Solomon et is related to the purer depolymerization models in some respects. Coal is represented as a two-dimensional array constructed from a Gaussian distribution of oligomers, with random cross-links among selected monomers, two kinds of bridges, and various sites for subsequent cross-linking. Roughly a dozen adjustable parameters are used to characterize the initial coal structure and chemical composition. The depolymerization and reintegration of the coal lattice is realized in Monte Carlo simulations involving a detailed set of chemical and transport mechanisms. At least 10 mechanisms are invoked, including several conjectural ones, such as extraloose, loose, tight, and extratight precursors for the same noncondensible gas, and assignments of the MWD of char. Yields and M W D s of tar are determined along with the evolution rates of noncondensibles as molecular species, based on about 100 adjustable parameters. Obviously, assigning values to so many parameters is a daunting challenge, and an independent evaluation suggested that optimal values have not yet been identified,s2 even for a single coal type. Mass transport mechanisms are also emphasized by these (28) N i b , S. Symp. (Int.) Combust., [ h o c . ] 22 1988,105. (29) Solomon, P. R.; Hamblen, D. G.;Carangelo, R. M.; Serio, M. A,; Deahpande, G. V. Combwt. Flame 1988, 71, 137. (30) Solomon, P. R.; Hamblen, D. G.;Carangelo, R. M.; Serio, M. A.; Deahpande, G.V. Energy Fueb 1988,2,405. (31) Solomon,P. R.; Hamblen, D. G.; Yu, Z. Z.;Serio, M.A. Fuel 1990, 69,764. (32) KO,G.H.; Petere, W. A.; Howard, J. B. Energy f i e b 1988,2,567.

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workers, both intraparticle and external, 80 FGDVC might seem more akin to classical models. Actually, FG-DVC does not contain any mathematical representation of any transport mechanism. Whereas transport does, in actuality, determine the internal pressure, in this model it is regarded as an adjustable parameter. In the reported data correlations, the pressure drop to the surroundings, denoted as AP,,was adjusted from 0.02 to l MPa to match thermal history effects, pressure effects, and data for two different coals. In summary, the devolatilization models developed during the past five years depart from classical theory in two important respects: (1) no recent model includes secondary redeposition of released volatile8 into solid residues within the char; instead, char formation is treated as the reintegration of potential tar precursors in the condensed phase, and (2) explicit submodels of coal structure and constitution are the basis for bona fide depolymerization and crosslinking/reattachment mechanisms. For the most part, but not completely, mass transport resistances for pulverized coals have also been neglected. These models' performance clearly surpasses earlier milestones. For any particular coal type, the dominant processing influences-pressure, temperature, heating rate, reaction time, and particle size-can be correlated with depolymerization models. And beyond yields and lumped product distributions, reliable correlations of tar MWDs are available. A coherent theory for coal type effects is the principal remaining imperative for the characterization of devolatilization rates and yields. The theory formulated in this paper invokes a new model of coal constitution, chemical kinetics, chain statistics, and flash distillation to explain the devolatilization of various coal types. It is called FLASHCHAIN. Like DISCHAIN and DISARAY, it comprises simplified kinetic mechanisms and analytical expressions for chain statistics and their time evolution. And like FLASHTWO, this theory invokes the flash distillation analogy to rationalize the pressure dependence. However, the fragment size distribution is now calculated from population balances without constraining its functional form, whereas the functional form of the fragment distribution in FLASHTWO is specified a priori. The submodel of coal's chemical constitution rests on the premise that the partitioning of the elements among aliphatic, heteroatomic, and aromatic constituents largely determines the devolatilization behavior of any coal type. This segregation is implemented with only four pseudocomponents, yet remains firmly connected to measured characteristics. The theory incorporates the ultimate analysis, the carbon aromaticity and aromatic cluster size from 13CNMR analysis, the proton aromaticity, and the extract yield in pyridine. No functional groups appear. The model is introduced in three parts. Part 1 is devoted to its mathematical formulation, without any performance evaluations. First the premises behind the coal submodel and reaction mechanisms are corroborated from a phenomenologicalpoint of view. Then definitions of the state variables pave the way to mathematical expressions for the chemical reaction rates and chain statistics. Finally, these joint influences are synthesized into species conservation laws. The summary in part 1 emphasizes the assignments of model parameters. Performance evaluations appear in both parts 2 and 3. In part 2, the extensive data base for high-volatile bituminous coals is brought to bear against the theory's representation of diverse operating conditions. Data correlations over broad ranges of temperature, time, heating

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650 Energy & Fuels, Vol. 5, No. 5,1991

rate, pressure, and particle size establish FLASHCHAINs quantitative performance. Part 3 is devoted entirely to coal rank effects. Model predictions bsed on the properties of the eight samples in the Argonne Premium Coal Samples Bank (APCSB) demonstrate that this theory depicts all of the continuous trends in the yield structure from coals across the rank spectrum. Ultimately, predictions based on only the ultimate analysis and linear regressions of all other input data are shown to be as reliable as those based on the complete set of input data.

Overview of Coal Structure and Constitution and the Reaction Mechanisms According to this theory, the devolatilization behavior of any coal type is determined by the proportions of aromatic, heteroatomic, and aliphatic constituents. Being refractory, condensed-ring aromatic nuclei are not reactants in the chemical mechanisms, but they constitute most of the mass of tar and char, and their total amount increases during devolatili~ation.~~ Oxygen, the most abundant heteroatom, is often a major constituent of noncondensible gases which make up the convective flow that sweeps away tar vapor. Oxygen is also implicated as an inhibitor to tar formation, since COz evolution histories have been clearly related to cross-link densities throughout pyrolysis.M Aliphatics are important as precursors to noncondensible gases. Even at this cursory level, such factors have clear implications for modeling coal rank effects. Being refractory, aromatic components can only be released as parts of tar molecules, but heteroatomic and aliphatic components are both precursors to noncondensibles and components of tar. Since low-rank coals have relatively less aromatic carbon, their product distributions are dominated by noncondensible gases. Their abundant oxygen promotes cross-linking, which suppresses tar formation. High-rank coals have low volatility because aliphatics and heteroatoms are scarce. Tar is their major pyrolysis product because the absence of oxygen suppresses charring. Tar is the major product from high-volatile bituminous coals because oxygen is scarce, but noncondensible yields remain significant, because aliphatics are plentiful. The constitution submodel in FLASHCHAIN emphasizes these phenomenological aspects without incorporating functional group distributions. Coal is modeled as a mixture of chain fragments ranging in size from a monomer to the nominally infinite chain. Fragments are composed of identical aromatic nuclei interconnected pairwise by two different typea of linkages, with peripheral groups on some of the fragment ends. Fragments are composed of only four structural components aromatic nuclei, labile bridges, char links, and peripheral groups. All structural components of a given kind are identical-all labile bridges have the same molecular weight and elemental composition, etc. Aromatic nuclei are the immutable units, having the characteristics of the hypothetical aromatic cluster based on 13NMRanalysis. They also contain all of the coal nitrogen. Nuclei are interconnected by two typesof linkages, labile bridges or char links. Neither linkage is a chemical bond. Rather, labile bridges are groups of several aliphatic, alicyclic, and heteroatomic functionalities. They contain no aromatic constituents, but are apportioned all of the oxygen, sulfur, and nonaromatic carbon in coal. Being the charred remains of labile bridges, char links are much

Table I. Structural Parameters for Different Coal Types bridge compoeition labile %C, MWA, MWB, wt wt fraction sample daf g/mol g/mol % C % 0 P(0) N.D. Lignite 72.9 101 57 188 35 0.88 75.0 152 284 59 Wyd. subb. 32 0.81 Ill. No.6 77.7 166 179 52 32 0.73 Utah hvB 80.7 154 63 236 26 0.65 82.6 153 58 145 28 0.63 Stock hvB 83.2 154 Pit. No.8 63 176 24 0.60 Fre. B 85.5 57 195 153 28 0.53 71 91.1 216 14 0.37 Poc. LVB 132

lighter, without any heteroatoms, and completely aromatic. Peripheral groups are the remnants of broken bridges, having the same composition but only one-half the weight. The macromolecular fragment in Figure 1A proposed by Ladne9 exhibits the condensed nuclei, hydroaromatic bridges, and diverse set of peripheral groups common to all postulated coal macromolecules. At 82.8 w t 3' % carbon, its constitution is representative of hv bituminous samples. The FLASHCHAIN analogue appears in Figure 1B. Each aromatic nucleus contains 10 carbons, although the low N/C (-0.02) implies that relatively few contain nitrogen. Each labile bridge contains 11 carbons, pictured as hydroaromatic rings with methylene chain substituents. The three oxygen atoms appear as ether, in heteroatomic rings, and as methoxy. Only one char link is shown, comprising eight carbons in two condensed rings. The broken bridge remnant on the far right end contains one-half of its original atoms. Note that the labile bridges in FLASHCHAIN are much more massive than actual bridge structures in coal, because only two linkages per nucleus are allowed in chain fragments, and peripheral groups appear only on fragment ends. To illustrate rank variations in the constitution parameters, the size characteristics of model nuclei and bridges for the eight APCSB coals appear in Table I. Nuclei become more massive with increasing rank, although their size is uniform for the most heavily utilized coals, subbituminous through hvA bituminous. The weights of bridges vary widely but still exhibit the tendency to lower values for coals of higher rank. The proportion of oxygen in bridges exhibits the most definite tendency to diminish with increasing coal rank. The balance of the bridge mass is due largely to hydrogen, except for high sulfur coals such as the Illinois No. 6. Char links are also present initially in this coal analogue, in amounts which are consistent with the carbon and hydrogen aromaticities of the actual coal sample. In principle, the fraction of labile bridges could range from unity for highly aliphatic naphthalene polymers to zero for a fully graphitized material. The fractions of intact bridges which are labile, P(0)in Table I, decrease for coals of higher rank, consistent with the view that coalification is essentially a graphitization process. As noted earlier, coal's cross-linked, three-dimensional macromolecular configuration is rendered simply as a mixture of linear chain fragments in this model. This approach is motivated by our earlier studies**%based on branched networks, which showed that chain fragments retain the relevant qualitative features of more complex configurations, especially in view of uncertainties in the decomposition energies of labile bridges. Like the branched network, the mixture of linear fragments provides a means to vary the connectedness of the initial

(33) Miknie, F. P.; Turner,T. F.; Ennen, L. W.; Netzel, D. A. Fuel

1988, 67, 1568.

(34)Suuberg, E. M.; Lee, D.; Larsen, J. W.Fuel 1985,64, 1668.

(35)

Gibson, J. J . Imt. Fuel 1978,51, 67.

FLASHCHAIN Theory for Coal Devolatilization A.


Y< CHz

0 4 - \

CHz

/

1

\

\ -brldg.

B.

\

onF\cH;ICn\o~cHZ L ‘ cH3 Figure 1. Ladner’s proposed molecular model of an 82% C vitrinite (A) with H/C = 0.77,0/C = 0.09,and N/C = 0.02. Carbon and proton aromaticities are 0.62 and 0.17, respectively. Its analogue in FLASHCHAIN (B)maintains these characteristics, and also has C, = 12 carbons, p ( 0 ) = 0.91, and p(0)= 0.63, so that @ = 0.056. These latter values are consistent with this rank, as seen in part 3.

structure, which is another important aspect of coal rank. In FLASHCHAIN, the initial coal configuration is specified by the proportions of broken bridges and intact links, where the latter encompass both labile and refractory types. Fragment size is expressed in terms of the number of linked nuclei, so that the fraction of broken bridges determines the initial fragment size distribution. This distribution is empirically related to extract yields in pyridine. Qualitatively, fragment distributions skewed toward smaller sizes correspond to coals with substantial amounts of readily extractable material, so there is a firm connection to the rank dependence of the proposed mobile phase in The initial proportion of intact labile bridges is especially important because bridges are the key reaction centers. A labile bridge can either dissociate during pyrolysis or spontaneously condense into a char link. Consequently, 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 char link accompanied by the immediate release of the associated peripheral groups, forming noncondensible gases. Chemically, spontaneous condensation represents an internal rearrangement into more extensive aromatic domains with the simultaneous expulsion of small radicals, and their immediate stabilization into noncondensibles. Grant et al. included the same concept in the CPD model% and, in a similar vein, Gavalas et al. invoked the deacti(36)Given, P. H.; Marzec, A.; Barton, W. A.; Lynch, L. J.; Cerstein, B. C. Fuel 1986,65,155.

vation of ethylene bridges into refractory links.18 Bridge scissions represent all bond ruptures which are rapidly stabilized before extensive aromatization can occur, so it seems reasonable that the remnants retain their high reactivity as gas precursors. Note that bridge conversion either reduces the fragment size or generates volatile product. Scissions reduce the average fragment size and create additional peripheral groups which are not volatile. Spontaneous condensation does neither, but does cause the immediate release of noncondensible gases. Also, as char links accumulate the likelihood of subsequent fragmentation diminishes, especially into the smaller size classes, so spontaneous condensation suppresses the production of tar precursors. Additional char links and gases may also form by bimolecular recombination between the ends of the smallest fragments. Recombination always adds new char links but releases gases only if at least one of the participating ends has a peripheral group. Finally, the direct conversion of peripheral groups on fragment ends into noncondensible gases is modeled as a first-order reaction. According to this scheme, bridges in the coal are the primary source of gas precursors, since the initial mass fraction of peripheral groups is very small because so few ends are present initially among long chains. This reaction mechanism retains the connection between char formation and gas evolution introduced in FLASHTWO13 and that between bridge scission and peripheral group formation in DISCHAIN. Whereas char links form only by bimolecular recombination in DISCHAIN, most of the char links in this model form by

652 Energy & Fuels, Vol. 5, No. 5, 1991 FLASHCHAIN

Niksa and Kerstein Gufranspon~a Mndeawdooof bridges

1

G u f” spmMMur

; c t a f bridges bridne

convected away in s v e ~ ofl g u

Figure 2. A schematic illustration of the mechanisms in FLASHCHAIN.

spontaneous condensation. Of course, the relative roles of scission, condensation, and recombination are very sensitive to the initial proportion of intact labile bridges, which varies widely for coals of different rank. Moreover, the selectivity between scission and spontaneous condensation is prescribed by a stoichiometric coefficient which is inversely proportional to the oxygen content of the coal, to incorporate the propensity of oxygen functionalities to cross-link. The abundance of labile bridges in lignites promotes their extensive conversion to noncondensibles, but their oxygen promotes spontaneous condensation, thereby inhibiting fragmentation. Conversely,the paucity of labile linkages in low-volatility coals suppresses gas yields; these coals also have too few labile bridges for extensive fragmentation, so their tar yields are also relatively low. Chemical and configurational transformations among fragments in the condensed phase strongly influence tar formation. This theory incorporates the flash distillation analogy,**in which a phase equilibrium relates the instantaneous mole fractions of like-size fragments in the tar vapor and condensed phase. Representing the equilibrium with Raoult’s law for continuous mixturesm* characterizes the impact of fragment size on the phase change. The total evolution rate of volatiles is based on the chemical production rate of noncondensibles. No finite mass transport rates appear, because all volatile8 are presumed to escape by a convective flow process, so that the evolution rate of tar is proportional to that for noncondensibles when weighted by the ratio of their respective mole fractions. In keeping with the lack of firm experimental evidence,20 the contribution of finite-rate hydrogen abstraction to tar stabilization is omitted. The entire reaction scheme appears schematically in Figure 2, where it can be seen that the condensed species have been categorized further. For several reasons, initially and throughout pyrolysis, fragments in the condensed phase are subdivided into reactant, intermediate, and metaplast lumps. Metaplast fragments are the smallest, comprising all potential tar species. Recent measurements of the saturated vapor pressures of synthetic liquids confirm a strong size dependence which dominates over all so tar formation is restricted to only structural those species which are light enough to evaporate under conditions of interest. The parameter J* is the maximum degree of polymerization of metaplast, specified to be at (37)Cottarman, R. L.; Prausnitz, J. M. Ind. Eng. Chem. Process Des. Dev. ISM,24,434. (38)Cotterman, R. L.; Bender, R.; Prauenitz, J. M.Ind. Eng. Chem. Rocerr Der. Dev. 1985,24,194. (39)Hlutounian, H.; Allen, D.T. Fuel 1989,68,480. (40)Vajdi, L. E.; Allen, D. T. Fuel 1989,68,1388.

least as large as that for the largest fragment which evaporates. The smallest fragments are also distinguished by two other features. Their relatively small size presumably imparts greater mobility, and their abundance during the reactive transient allocates to them a majority of the potential sites for bimolecular recombination. With both of these features in mind, we restrict bimolecular recombination to metaplast species only. Metaplast fragments are present initially, in amounts prescribed by the proportion of broken links in the coal, and are formed in abundance as scissions fragment the other lumps. Metaplast may be present in the chars at low to moderate extents of devolatilization, but it eventually vanishes as the production mechanism winds down due to the depletion of labile bridges available for scission and the conversion of metaplast into intermediate fragments by bimolecular recombination. Tar forms only if metaplast is present. Reactant species comprise the upper portion of the size distribution, extending to nominally infinite chain lengths. Initially, most of the coal mass is in the reactant but, ultimately, the char mass is distributed between reactant and intermediate. Within these lumps, evaporation is negligible, and bimolecular recombination is suppressed due to the paucity of fragment ends. (The fragment end population varies inversely with fragment size.) Hence, the reactant decomposes into metaplast and intermediate fragments at a rate governed by the bridge scission proceas. As labile bridges are depleted due to scission and the competing process of spontaneous condensation, the cascade to smaller fragment sizes is suppressed. Gases are expelled from reactant species as long as labile bridges are available for spontaneous condensation or peripheral groups are replenished by bridge scission for their subsequent elimination. Intermediate species have sizes between those of the metaplast and reactant; no special reactivity is implied by their name. In fact, they are subject to the same mechanisms as the reactant species: scission and spontaneous Condensation but no evaporation or recombination. The minimum degree of polymerization in this size range is assigned to ensure negligible volatility, because intermediate fragments are not tar precursors. Intermediate fragments do not participate in bimolecular recombination either, because there are relatively few fragment ends in this lump. However, metaplast species can be transformed into the intermediate size range via bimolecular recombination. As seen clearly in this ensuing mathematical formulation, this is the only distinction between intermediates and reactants. Species in the gas phase can be seen coarsely as a mixture of tar and noncondensible gases, with the tar constituents distributed in size over the same range as metaplast. The tar MWD shifts with changes in the operating conditions and in the state of the mixture in the condensed phase. Tar constitution also varies with extent of conversion as volatile fragments with high proportions of labile bridges and ends that have peripheral groups give way during the later stages to fragments with higher proportions of char links and open ends. Noncondensibles are treated as a single lump because, as illustrated below, the average molecular weight of gases from virtually any coal is about the same. Model Formulation In the following sections, the above ideas are rendered into a mathematical model. First, state variables are defined to track the changing chemical constitution and fragment size distributions. Then, they are related to the


FLASHCHAIN Theory for Coal Deuolatilization

species

Table 11. Definitions of the Concentration Variables and Probabilitiesa constitution intact labile aggregate size range fragment linkages bridges

peripheral groups

reactant

intermediate

metaplast

M

l5j5J*

tar

T

lljlJ*

BT

tj

PT'J.

+ CT

Citj

j-1

noncondensible gases a

G

pTb =

BT J.

Xiti

j=1

pTe

=

ST J'

2Etj j=1

N/A

B, C, and S denote the molar concentrations of labile bridges, char links, and peripheral groups, respectively.

ultimate analysis and average structural parameters from '3c NMR to assign the molecular weights of nuclei, bridges, char links, and peripheral groups in the original coal. Coal configuration is stipulated further by relating the initial amounts of reactant, intermediate, and metaplast to the initial fragment size distribution. The next sections are devoted to the rate equations. After rate laws for individual reactions are discussed, they are implemented in population balances which describe the fragment size distributions and constitution a t all stages of devolatilization. Finally, the state variables are related to the yields and MWDs of the primary products.

State Variables The model is formulated in terms of scaled molar concentrations, in units of moles per volume of coal present initially. All species concentrations are scaled with respect to the initial concentration of aromatic nuclei, A@ The aggregate amounts of reactant, intermediate, metaplast, tar, and gas are denoted by R, N , M,T , and G , respectively. For the lumps which are distributed in size, the concentrations of fragments of degree of polymerization j (i.e., j linked nuclei) are denoted by rj, nj, mj,and tjl respectively. As seen in the collection of these definitions in Table 11, J* is the degree of polymerization of the largest metaplast specie. Intermediate fragments can be up to twice as long as metaplast whereas the size range of reactant fragments extends to infinity. The chemical constitution of the fragments is expressed in terms of four structural elements: bridges (B),char links (C), peripheral groups (S),and aromatic nuclei (A). Even though all nuclei are identical initially and remain the same, the fragments are not composed of identical monomeric units. In the model, a monomeric unit within a fragment comprises an aromatic nucleus plus, if intact, both of ita linkages or, if on a fragment end, its linkage and peripheral group, if there is any. Fragments cannot be resolved for accounting purposes into identical monomeric units because linkages within these units can be either char links or labile bridges, even initially. Various probabilities describe the proportions of each kind of link and of fragment ends having peripheral groups versus open ends, in the coal initially and throughout, pyrolysis. On a mass basis, each labile bridge is further resolved into a char link and two gas precursors; similarly, peripheral groups are

resolved into one-half char link plus one gas precursor. Consequently, a half-link is permanently attached to each chain end, but the associated gas precursors are transitory. Furthermore, the chemical constitution differs among the different lumps for several reasons. There are proportionally more ends among the shortest fragments so metaplast fragments tend to be more aliphatic initially, when all ends have peripheral groups. As devohtilization proceeds, the metaplast and intermediates tend to become relatively enriched in char links, because only these classes are affected by bimolecular recombination. Since all tar fragments devolve from metaplast, it is clear that the chemical constitution of tar changes throughout devolatilization. Instantaneous probabilities are used to describe the average chemical constitution of fragments of a particular size, and of each aggregate lump. Three probabilities are required for each lump: p I ( t ) ,the instantaneous fraction of all potential links which are intact; p&), the fraction of all potential links which are labile bridges; and p f ( t ) , the fraction of all fragment ends which have a peripheral group. Here the subscript I is the generic index for lumps denoted by R, N, and M, respectively. As seen in Table 11, denominators in the expressions for p~ and p t are the number of potential links in lump I, which is C j x j , where x is any of the four fragment lumps (r, n, m, t). The summation extends over all fragment sizes within the lump. Since the half-bridges on all chain ends are included in the population of potential linkages, the number of potential linkages equals the number of nuclei. The denominator for p t is simply twice the number of chains, 2Cxj. We will also apply these three probabilities to the population of all species in the condensed phase; the same symbols are used but without subscripts, according to p ( t )= (B + C)/?jxj 1'1

pb(t)= B / b j

(1)

1'1 li)

p"t) = S / 2 C X j j=l

where x = r, n, or m, depending on the range of j . Here


Niksa and Kerstein

and in Table 11, B, C, and S denote the concentrations of labile bridges, char links, and peripheral groups. It will be convenient also to express the proportion of labile bridges on the basis of the number of intact linkages, rather than the number of potential linkages. This ratio, denoted as F?, is expressed in terms of pI and pIbas

loo^

~ " " ~ ' ~ " ~ " " l " " 1 " " 1 " " ~

-

i3 8

c

0 0 0

0 0

-

.-g eo/Y

-I -I

t

Here also, the unsubscripted symbol P represents the ratio B / ( B + C) = p b / p for intact linkages in the entire condensed phase. P

A

V A

0 " " 1 " " 1 " " ~ " " 1 " " 1 " ' 6 65 70 75 80

Coal Constitution

Two modeling principles constrain any characterization of the chemical constitution of coal. First, only the grossest features of coal structure can be represented with a tractable number of parameters. Second, as many of the modeling parameters as possible should be assigned from readily available measurements. FLASHCHAIN incorporates the atomic ratios H/C, O/C, N/C, and organic S/C into the definition of the molecular weight of the average monomer unit. Presumably these values come from the ultimate analysis. To further resolve the constitution, the monomer is segregated into a nucleus and labile bridges and/or char links using f,', the carbon aromaticity based on carbon atom fraction contained in condensed rings; Hfl, the proton aromaticity; and AC/Cl, the number of aromatic carbons per cluster. In what follows f,' and AC/Cl are evaluated from recent 13C NMR analyses, although ways to assign them from alternative analyses will be discussed in part 3. Since these analytical data apply to the aggregate sample, they define the characteristics of the average monomeric unit within a fragment in this model. All such monomers are not identical, however, so properties of the average monomer within a fragment are determined by the characteristics of nuclei, bridges, and char links, as well as the proportions of bridges and char links in the whole coal initially. Relations in this section express the analytical data in terms of the chemical constitution and sizes of bridges, char links, peripheral groups, and nuclei, weighted for the proportions of bridges and char links. First, the weighting factors are developed as follows: The initial concentration pb(0)of labile bridges in the coal, as a fraction of the number of nuclei, may be expressed as p ( 0 ) P(0);similarly, the fraction of char links is p ( 0 ) (1 - P(0)).The fraction of intact linkages,p(O),is specified to match the initial mass fractions of monomer and intermediate to the solvent extract yield in pyridine, as illustrated below. The initial labile bridge fraction, P(O), is an adjustable parameter which is found to be linearly proportional to the carbon content, as demonstrated in part 3. These probabilities enable the average properties of the coal to be expressed in terms of those of the constituents in this model. Since all fragment ends are assumed to have peripheral groups initially, the constituents of two ends on a fragment are the same as the constituents of a single labile bridge, so that dissociated links in the coal are equivalent to bridges for accounting purposes. Hcnce, the population weighting for labile bridges plus peripheral based groups in the aggregate sam le is 1- p(0) (1- P(O)), on the weighting p(0) (1- (0))for char links. Therefore, any chemical property of the unreacted coal can be expressed as a sum of the properties of the nucleus, wei hted by unity, of the bridges, weighted by 1 - p(0) (1 - (0)), and of the char, weighted by p(0) (1- P(0)).For example,

&

A

85

90

,

95

Carbon Content, % daf

Figure 3. Oxygen distribution among volatiles. Oxygen content of tar is based on a correlation of (S + 0) for tar reported by Freihaut et using Xu and Tomita's2 (v)and Freihaut et al.'s (A)tar yields. Noncondensible fractions ( 0 )comprise CO, COP, HZO, and phenol, from Xu and Tomih2 The total yield of oxygen in volatiles measured by Xu and Tomita also appear ( 0 ) .

the number of carbon atoms allocated to the average monomeric unit within a fragment is expressed as CT = CA + (1 - 8)CB + flc, where CT is the total number of carbon atoms in a monomer, CAthe number of carbon atoms in a nucleus, CB the number of carbon atoms in a labile bridge, Cc the number of carbon atoms in a char link, and p = p ( 0 ) (1 - w3). As this illustrates, a monomeric unit is operationally defined as a nucleus plus a prorated portion of linkage material. It is useful to adopt CT as a scale for the other contributions, and to express the carbon balance in nondimensional form, as 1 = C A + (1 - p)cB + pCC (3)

ci

where = Ci/CP CT is evaluated from the aromatic carbons per cluster, AC/Cl, according to CT = (AC/Cl)/f,'. Values of AC/C1 have recently been inferred from 13C NMR analysis of the Argonne Premium Coal Samples by Solum et al.41 Since peripheral groups are regarded as purely aliphatic, the carbon aromaticity is assumed to represent only the nuclei and char links in the sample; in fact, the latter components are assumed to contain only aromatic carbon, so that (4) f,' = C A + pCC Similar reasoning defines the molecular weights of the structural components, once the distribution of heteroatoms among nuclei, bridges, and char has been specified. In lieu of definitive functional group identifications for the heteroatoms, we rely on the connections between the pyrolysis product distribution and their precursors in this model. In the model, all noncondensible gas products come from labile bridges or peripheral groups. Since the initial population of peripheral groups is small for long linear fragments, labile bridges constitute the largest repository of potential precursors to noncondensibles. Since only two linkages per nucleus are permitted in the model and peripheral groups appear only on chain ends, each model bridge is allocated more mass than is present in actual bridges (cf. Figure 1). But this feature does not adversely (41) Solum, M. S.;Pugmire, R. J.; Grant, D.M.Energy Fuels 1989, 3, 187.


affect the predicted molar evolution rates of gases, as explained below. According to this hypothesis, heteroatoms which appear primarily in noncondensible products are assigned to bridges. The distribution of fuel oxygen among noncondensibles and tar in Figure 3 indicate that oxygen belongs in this category. In Figure 3, the oxygen content of noncondensibles from 17 coals reported by Xu and TomitaI4 is plotted as a fraction of the oxygen content of the parent coal. Also plotted is the oxygen content of tar based on tar yields reported by Xu and Tomita" and the oxygen content of tar reported by Freihaut et al.6 for coals containing 71-90% carbon. Note that the oxygen contents of tar based on Freihaut et al.'s tar yields are indistinguishable from those estimated by difference from Xu and Tomita's data for yields of noncondensibles and total volatiles. Although the scatter is considerable, on average, 90% of the oxygen in coal is dispersed among noncondensibles and tar, with three-fourths evolved as noncondensible gases and one-sixth as tar. The only rank dependences in this data are the reduced amounts of tar oxygen for very low and very high rank coals, which are neglected at this stage. These results indicate that oxygen in any coal is completely expelled during primary devolatilization, to good approximation. Consequently, all of the oxygen is apportioned to labile bridges, as the precursors to both tar 0 and gas 0. Tar 0 is presumed to reside in labile bridges between oxygen-free aromatic nuclei. Gas 0 also devolves from the oxygen in labile bridges, by two pathways. Spontaneous charring of bridges induces intermediate gas release, and bridge scissions create peripheral groups which subsequently dissociate into gas. Being determined by the rates of three processes, the proportions of oxygen in tar and noncondensibles will vary for different pyrolysis conditions. Nitrogen in coal is assigned entirely to aromatic nuclei for two reasons. First, nitrogen in coal is almost entirely heterocyclic, with five-membered rings predominating over six-membered rings except for ranks above the low-volatile b i t u m i n o u ~ . ~Second, ~ the evolution of fuel N during pyrolysis is consistent with the view that tar is the primary nitrogen shuttle while gas N, particularly HCN, is a product of secondary tar pyrolysis.l6ta According to this hypothesis, the partitioning of volatile N and char N is determined by the partitioning of aromatic nuclei between tar and char. Organic sulfur is found in both aliphatic functionalities and so its assignment is not clear-cut. Aliphatic forms predominate in low-rank coals, but heterocycles become more important for higher rank coals; the sulfur is evenly distributed between these two forms for high-sulfur bituminous coals.'b Notwithstanding this complexity, organic sulfur is a minor species in the mass partitioning of all but a few eastern bituminous coals. To rough approximation, it is assigned as an element of labile bridges, consistent with the conversion of organic sulfur into noncondensibles, especially H2S. Of course carbon and hydrogen are dispersed among all constituents. They are partitioned to match the carbon and proton aromaticities, assuming that only aromatic forms appear in the char and nuclei and only aliphatics appear in bridges. Furthermore, aromatic hydrogen is partitioned in proportion to aromatic carbon. (42) Burchill, P.; Welch, L. 5.Fuel 1989,68, 100.

(43) Chen, J.;Caetagnoli, C.; N h 5.Paper prewnted at the WSS/Cl 1990 Fall Meeting, University of California, San Diego, October, 1990;

-Peaer _ r - - No. 90-48. --

(44)Stock, L. M.; Wolny, R.; Bal, B. Energy Fuek 1989,9, 651. (46) Calkins, W. H. Energy Fuek 1987, 1,5B.


Based on these hypotheses, the nondimensional molecular weights of the constituents defined with respect to weight of the carbon atoms are given by

MWc = MWC = &I1 12CT

-(-)-I

+ 121 Hc

( c9 )12(1l6 P)

'f,' f,'

(6)

+(") c 1 2 032- P ) (7)

Balances for hydrogen and the total molecular weight of the monomer can also be written, but they are satisfied identically by eqs 3-7. An application of these rules was seen earlier in Table I. Equations 3-7 are five independent relations among seven unknowns: the three carbon numbers and three molecular weights for nuclei, bridges, and char links, and 0. The submodel is closed by assigning MWc and 8. Our strategy specifies the molecular weight of a char link as a fixed fraction of that of a labile bridge, independent of coal type. As seen in part 3, this stipulation is consistent with the partitioning of carbon from bridges into noncondensibles for various coal types. The parameter 0 is determined by the values of p ( 0 ) and P(0).There is no analytical method to distinguish the labile linkages among nuclei in coal from refractory ones, so P(0)is taken to be an adjustable parameter which correlates with carbon content, as expected from the view that coalification is essentially a graphitization process (see part 3). The probability p ( 0 ) for intact links in the coal is assigned to match the solvent extract yields in pyridine, as developed below. In summary, FLASHCHAIN'S submodel for coal structure and constitution involves eight parameters: three carbon numbers, three molecular weights for bridges, char links, and nuclei, and two structural values, P(0)and p(0). The carbon numbers of the structural elements and the molecular weights of a nucleus and of a labile bridge are specified from independent analyses of carbon and proton aromaticities, the H/C, O/C,N/C, and S/C ratios associated with the ultimate analysis, and the molecular weight and aromatic carbon number of the hypothetical cluster unit from 13CNMR. The probability for intact linkages, p(O), is specified from extract yields in pyridine. Thus, this submodel includes only two parameters which cannot be assigned independently. One, the char molecular weight, is assigned as a constant fraction of the weight of a labile bridge for all coal types; it is not readjustable for each coal. The second, P(O),is taken to be linearly proportional to carbon content. This dependence is based on a data correlation presented in part 3, consistent with the view that coalification is a graphitization process. Macromolecular Configuration Coal is widely regarded as a covalently cross-linked macromolecule which includes a substantial portion of smaller trapped molecules, called the mobile phase. Even the amount of mobile phase is controversial,a so little can be said of its chemical properties. Nevertheless, it is fre(46) Given, P. H.In Coal Science; Gorbaty, M. L.; Lareen, J. W.; Wender, I., Me.; Academic Prese: Orlando, FL, lBW, Vol. 3, p 65.

Niksa and Kerstein


quently invoked in the contexts of solvent extraction, swelling, and viscoelasticity. The mobile phase may be viewed as the lighest end of a continuous size distribution of macromolecules extending to the nominally infinite, cross-linked, coal lattice. As such it provides an indication of the connectedness among the macromolecules and thus has implications for devolatilization rates and yields. Furthermore, the mobile phase is absent in coals of higher rank, indicating that connectedness is also coal-rank dependent. We find that it is an important element of devolatilization modeling for various coals. Only straight-chain fragments are considered in FLASHCHAIN, so pairwise connectedness of nuclei is the only aspect of macromolecular configurationin this model. In this respect, the chemical nature of the links is irrelevant; only the fraction of intact links matters. The proportion p(0) of intact linkages among all potential linkages determines the fragment size distributions and proportions of each of the fragment lumps in the whole coal. Intuitively, fewer intact links implies more metaplast and less reactant and intermediate, although no analytical method to quantitatively measure the fragment distribution in coal is available. In FLASHCHAIN, a rudimentary model of the initial fragment distribution is assigned by fitting the extract yields in pyridine to the initial amounts of metaplast and intermediate, using the relations in this section. The simplest form for the distribution of fragments in coal is based on random scissions among nominally infinite chains (the ‘theory of runs”; see discussion of eq 31), and is given by xj = p(O)j-1(1 - p(0))Z (8) where xi is the number of j-mers divided by the number of nuclei. A j-mer is recognized as a sequence of j - 1 intact links, with a broken half-link on each end. The mer-size distribution specified by eq 8 is applied to the three fragment lumps within the size ranges defined in Table 11. To evaluate fragment size distributions, intact links must be allocated among the fragment lumps in accordance with the parametrization of coal constitution shown in Table 11. For example, to evaluate the definition of pR(0) in Table 11, note that the normalized population of intact linkages within reactant mers obeys m

so that oD

C

j=W*+l

jrj

C jrj

j=W*+l

The identities

5

j=W*+l

p(O)i-l(l -

As explained in the derivation of eq 37 below, the fraction of intact links in the reactant lump for all time is given by eq 9 by using the instantaneous value of p in place of ita initial value. Applying similar manipulations to the intermediate and metaplast distributions yields PN(0) = (1 - P(0))(1 - P W * ) 1(10) J*(1 - p ( 0 ) ) + 1 - p(0)J0(2J*(1- p ( 0 ) ) + 1) pM(0)

1-

(1 - p(O))(1 - P(0)”) 1 - p(O)J’(J*(l - p ( 0 ) ) 1)

+

(11)

Relating these distributions to mass fractions closes the connection to extract yields. Unlike the size distribution, the fragment mass does depend on the proportions of bridges and char links. Since the size disrtibutions are based on random scissions, it is reasonable to assume that the fraction of bridges among the intact links in a particular lump is the same as in the whole coal, and specified as P(0).Consequently, the bridge fractions for each lump are evaluated from PIYO) = PI@) (12) The probabilities pI(0),pIb(0),and pf(0) determine the mass of the average monomeric unit of mers within each lump. When weighted by the mer-size distributions, the monomer mass determines the mass fraction of the entire lump. The mass of the average monomer in a specified range of fragment sizes is the mass of a nucleus, plus weighted contributions for peripheral groups, bridges, and char links. It is defined as a function of pI(0),p&O), and pIe(0),according to

mo)

Note that eq 13 is valid initially and throughout devolatilization because the probabilities implicitly depend on time. For the original coal, it is evaluated with the initial values. The total mass of a particular lump is simply the product of the average monomer mass and the number of monomers, which is assigned from the size distributions as Cjxj evaluated over the appropriate range of j . It is also convenient to express these amounts as mass fractions of original coal, using the mass density = A,( MW) (P(O),P~(O),P~(O))

(14) On this basis, the mass fractions of reactant, intermediate, and metaplast fragment lumps are given by PO

= P(O)W*(l- p ( 0 ) )

and oD

yield the expression (25* - 1)(1 - p(0)i’) pR(o) = 2J*(1 - p ( 0 ) ) 1

+

Note also that initial mass fractions are obtained by evaluating (MW) in the numerators with initial values of the species-specific probabilitiesdefined by eqs s 1 2 . Also, for the initial values only, the total number of nuclei in all fragments in the lump can be expressed in terms of the


FLASHCHAIN Theory for Coal Deuolatilization lWL'

-i

6o

i .G L

U

I

I

I

I

I

B

I

I

,

I

I

I

I

,

I

I

I

I

I

I

I

t

I

,

1

I

1

'

4

Reactant

are simple monotonic functions of p(0). This trend demonstrates that connectedness governs the initial size distribution of the macromolecules and also suggests an empirical connection to both the mobile phase and solvent extract yields. Since metaplast and intermediate fragments are restricted to fixed ranges of molecular weights, by definition, a value of p(0) can be assigned by matching their mass fractions to measured extract yields. Note, however, that the mass fractions of these lumps is not a function of p ( 0 ) only, as suggested by the behavior in Figure 4. The weight fractions of the fragment l u m p also vary with different values of J*, the largest degree of polymerization of metaplast. As explained earlier, the value of J* must segregate volatile fragments from nonvolatile ones, and short, mobile fragments from stationary ones which do not participate in bimolecular recombination. Another stipulation is that the nominal molecular weight of the largest intermediate fragment, the 2J*-mer, should equal the extent of the MWD of the extract associated with the assigned value of p(0). For the results in Figure 4, J* is 5, so the largest intermediate is a 10-mer. As explsined in part 3, the average molecular weight of monomer typically ranges from 275 to 400, so metaplast weights can be as large as 1400-2000 and intermediate weights can be as large as 2800-4000. Even though the molecular weights of solvent extracts are highly uncertain, we can be reasonably sure that they fall within these upper limits. Hence, the value of p(0)is assigned by matching the initial amount of metaplast plus intermediate to the solvent extract yield in pyridine. Equations 21-24 were also evaluated to determine the relative contribution of peripheral group as gas precursors. Their contribution is about 12% for p ( 0 ) = 0.88 and vanishes at p ( 0 ) = 1. For lower values of P(O),their contribution increases. However, no case for an actual coal sample was found to have more than 15% of the gas precursors as peripheral groups in the coal.

2ok ;, >, 40

, ,

, , ~,

i

\

Metaplast

n 6.88

0.90

0.92

0.94

0.96

0.98

1.OC

Initial Link Probability, p(0)

Figure 4. Uese fractions of reactant, intermediate, and metaplaat versus the initial link probability, p ( 0 )for p(0)= 0.9 and J* = 5.

aggregate probability for intact links, p(O), as in the derivation of eqs 9-11. The final forms for the initial mass distribution are

(20)

These final forms reveal that the initial amount of nuclei, AB does not have to be specified, and that molecular weight ratios, not absolute values, are the relevant parameters. Both these features were introduced in DISCHAIN. The development of eqs 18-20 is also the way to define the mass fractions of bridges, char links, peripheral groups, and nuclei in each lump, according to

Chemical Reaction Mechanisms Four distinct chemical reactions represent the disintegration of the coal macromolecule during devolatilization: bridge scission, spontaneous condensation, bimolecular recombination, and peripheral group elimination. Rates of these reactions only partially determine rates of product evolution, because of the independent influence of macromolecular configuration. Chemical reaction rates are defined in this section, and chain statistics are developed in the next. Bridge scission may be diagrammed as a spontaneous dissociation Xj-k-Xk

W,*(O)=

Cjxj Po AOMWA

where each I is associated with a range of j. All summations can be expressed in p(O),as before. Also, the molecular weights of bridges, char links, and nuclei have already been defined, and MWE will be defined below in terms of the average weight of noncondensibles; it is not an adjustable parameter. In Figure 4, the initial mass distribution of metaplast, intermediate, and reactant fragments appear for the relevant range of p(0). These calculations are based on P(0) = 0.9, although those for P(0)= 0.3 are virtually identical. Note that the amounta of both metaplast and intermediate

-

'Xj-k

+ *Xk

The reactant is the labile bridge (-) between segments x and x k of a j-mer. Its scission generates two s m a l c fragments, a 0' - k)-mer and a k-mer, with one-half of a char link and a peripheral group on each of the newly created ends (represented by the dots). Since there are no noncondensible products, bridge scission does not change the mass in the condensed phase, but if a product fragment is in the metaplast range, it may later vaporize into tar. A continuous distribution of activation energies, f ( E ) , is deemed adequate to represent the very broad thermal response of the varied bridge structures in coal. As in DISCHAIN, the conventional derivation of the bridge scission rate yields

Niksa and Kerstein


where

A B is a fmed frequency factor for all bridge decompositions, E B the mean activation energy in f ( E ) ,and u the standard

deviation about EB in f(E). This decomposition rate applies to all intact labile bridges, but does not explicitly resolve the temperature and concentration dependences as they would be, for example, in nth-order reactions. Such complexity is incompatible with the chain statistics, which are based on a scission rate per bridge. As described elsewhere:' the pseudo-first-order rate which is exactly equivalent to the rate from eq 25 is defined by

1-I

bIOL k

t

0

65

" " 1 " " 1 " " " " " " " 1 " " 70 75

80

85

90

95

Carbon Content, Yodaf

Figure 5. Average molecular weight of noncondensibles based on Xu and Tomita's product distributions? except that only one-fourth of the hydrogen yield is included.

where

Unlike an ordinary rate constant for a fmt-order reaction, kB changes in time. In the simulations, it is evaluated as the numerical derivative of a cubic spline fit to the argument of the logarithm. Since the same energy distribution pertains to scission and spontaneous condensation, the stoichiometric coefficient VB specifies the selectivity of bridge scission versus spontaneous condensation, and is therefore bounded between zero and unity. Spontaneous condensation likewise transforms a labile bridge between segmenta of a chain fragment, but without affecting the fragment size, and converts part of the bridge material into noncondensibles, according to xj-k-xk ---* xj-k'xk + VcG where (=) denotes the newly refractory link and vc is a stoichiometric coefficient. This process is governed by the same energy distribution and selectivity coefficient as bridge scission, in the following rate law:

Spontaneous condensation does not introduce any additional rate parameters. The conversion of bridges into noncondensible gases is based on the stoichiometric coefficient, VC, defined as MWB - MWc vc = (28) MWG While MWBand MWc have been defined, eq 28 brings in the average molecular weight of noncondensibles, MWc. Values based on Xu and Tomita's product distributions appear in Figure 5. They are based on total yields of all reported noncondensible species except that, for hydrogen, only one-fourth of the reported yield was considered. This basis for MWo segregates products formed on disparate time scales, in keeping with observations214 that most hydrogen is evolved after primary devolatilization when the char graphitizes very slowly. Based on a least-squares regression of the values of MWGin Figure 5, vc is evaluated from eq 28; it is not an adjustable parameter. This procedure also ensures that the molar evolution rates of (47) Nikaa, S.; Lau, C.-W. Combuut. Flame, submitted for publication. (48) Bautista, J. R.; R w e l , W. B.; Saville, D. A. Ind. Eng. Chem. Fundam. 1986,26,536.

noncondensibles are reliably predicted, even though the bridges in this model are longer than the actual bridges in coal. The third reaction is bimolecular recombination. Each recombination event involves the formation of a char link connecting a pair of metaplast fragments, making a larger fragment and releasing any gas precursor a t the linkage point, as in mi + mk mj+k(or nj+k)+ vcG

-

The products of bimolecular recombination are either larger metaplast or intermediates, depending on the degrees of polymerization of the reactants. Its chemical reaction rate is second order overall and introduces an Arrhenius rate coefficient in terms of A R and E& The stoichiometry for gas evolution as written above is based on peripheral groups on both of the participating fragment ends, so vc again appears. Peripheral groups are not necessarily present on the reactants; alternative cases are incorporated based on weighting factors defined in Table 11, without any additional adjustable parameters. Noncondensibles are also formed by peripheral group release, depicted as x,-S ~j + vEG

-

where VE

= vC/2

Here, (-) denotes a half-bridge from which a peripheral group, S, is released. This process is represented with a single first-order reaction which introduces two Arrhenius rate parameters, AG and EG, in the following rate law: dSi/dt = -kGSi (29) Note that the stoichiometry is also expressed in terms of vc. Based on mass conservation and the value of vc defined in eq 28, the molecular weight of peripheral groups, MWE, is given by (MWB - MWc)/2MW~. In summary, the four chemical reaction mechanisms in FLASHCHAIN involve one distributed-energy rate (AB, EB, and u), one single fmt-order reaction (AG and EG), and one bimolecular reaction with a single rate constant (AR and E R ) . The same energy distribution describes the thermal response of both bridge scission and spontaneous condensation, and a stoichiometriccoefficient, yg, specifies the selectivity. All of these parameters are adjustable. The remaining stoichiometriccoefficient for gas production, uC, is not; it is assigned from measured values of the average molecular weights of noncondensibles.



Species Conservation Laws In a depolymerization such as coal devolatilization, there are large families of reactants with members of various degrees of polymerization, rather than a handful of pure components. Even for chemical processes that are unaffected by the size of the participants, as assumed here, the time evolution of the size distributions are governed by the entire species population. Population statistics describe the likelihood that specific reactants participate in a chemical process that changes the concentration of those and other reactants. The population statistics incorporate the joint influences of chain statistics and chemical reaction rates in the framework of a set of conservation laws for individual species. Derivation of the population balances is initiated by treating the reactant fragments. For this lump, labile bridge scission is the principal consideration. The treatment for metaplast, presented next, is considerably more complex due to the addition of bimolecular recombination. Next, the number distributions of intermediate fragments are described. Finally, flash distillation and various mechanisms of gas production are incorporated into the tar production rate. In reactant chains, bridges decompose either by scission or condensation, although only scission changes the fragment size. (Recall that size in this context refers to the number of linked aromatic nuclei comprising the fragment.) Fragments of a certain size may also form when a bridge cleaves in a larger fragment. Consequently, two distinct rates govern the concentration of a reactant j-mer:

the theory of runs; viz., rj = $-l(l - pI2 satisfies eq 30 identically for all time, provided that p evolves in time according to dp/dt = -VBkgb (31) Since this is precisely the rate equation governing the postulated bridge-scission process, the theory-of-runs expression for rj is confirmed. pbappears in eq 31 because the scission rate of labile bridges governs the total link probability, whereas spontaneous condensation is irrelevant. However, both spontaneous condensation and scission affect the labile bridge probability, according to dpb/dt = - k g b (32) It is important to realize that eqs 31 and 32 and the size distribution in eq 8 replace eq 30, thereby eliminating the intractable number of ODES,at least when the entire size range is considered. This analysis also applies to reactant chains, for the following reasons. It is true that scissions remove fragments from the restricted size range, 2J* + 1 to infinity. But the conversion of rj into nj and m, cannot affect the size distribution in the reactant, because scission can only reduce the fragment sizes. Moreover, there are no mechanisms by which metaplast or intermediates grow into the reactant range. The size distribution of reactant is entirely governed by scission. Therefore eq 8, as a solution to eq 30, is the correct size distribution for reactant fragments, as noted above, it is expressed in terms of the total link probability from eq 31 as follows: rj = (1 -~)~ppl-'

where 2J*

+ 1 Ij

I

The first rate represents the depletion of rj by scissions of its own labile bridges. This expression is the product of the rate of scission per bridge, uBkg, and the total number of labile bridges in r.*of the (j- 1) links in the fragment, only a fraction p R b T p R are labile. The second rate in eq 30 represents the formation of rj by scissions in larger fragments. This rate depends on the concentrations of all larger fragments, given by CE-j+lrk and the scission rate per bridge, uBkB. The remaining factors account for the fraction of labile bridges and the fact that, among ( k - 1 ) links, there are two whose scission would yield an rj, provided that lz f 2j. For the special case of k = 2j, two r, form if the central bond breaks, so this case is also correctly represented. The time-evolution of pRand p R b must be described as an aspect of the solutions of eq 30. But a much more troublesome observation is that the range of j in eq 30, from W *+ 1 to infinity, implies an infinite number of ordinary differential equations. Both of these difficulties are circumvented by recognizing an analogy between the population balance for reactants and the classical statistical theory of runs.4g ("Runs" are sets of consecutive like outcomes of random, statistically independent binary decisions like coin tosses.) For the time being, we consider the size distribution defined by eq 30 for the expanded size range from one to infinity and therefore drop the subscript R. Scission among all fragment sizes is described by the fragment distribution, eq 8, postulated for the initial coal based on (49) Wilkn, S. 5. Mathematical Statistics; Wiley: New York, 1962; p 144.

(33)

The probabilities for the reactant, pR(t) and h b ( t ) ,must also be defined. Instead of a separate equation for pR,eq 31 is solved for p(t), which specifies p~ from eq 9 when initial values are replaced by instantaneous values. To define pRb,the labile bridge concentration BR in the reactant is determined from instantaneous values of the state variables, and the definition

is applied. The evolution of BR depends on scissions and spontaneous condensations, and the scission-induced transfer of labile-bridge-containing fragments to the intermediate and metaplast lumps. Thus,the concentration evolves as

-U =R dt

(34) where dn./dt)R = generation rate of nj from scission of reactant iragments and dm./dt)R = generation rate of mj from scission of reactant tragments. Depletion due to scissions and condensations are lumped into the pseudofirst-order reaction. In the remaining terms, (j- l ) p R b / p R specifies the number of labile bridges in a j-mer. In defining the generation of metaplast by reactant scission, it is useful to realize that the formation rate is the same for fragments of any size, because there are two ways to form any size metaplast fragment from any r j The formation rate is (35)

Niksa and Kerstein


based on considerations similar to those involved in the derivation of the last term of eq 30. Since the rates are independent of j, the cumulative rate for all metaplaat sizes is

istics. The following development of the balances for metaplast emphasizes recombination and relegates flash distillation to the tar formation scheme, below. The net evolution rate of the concentration of any mi is given by dmj

-- -

(36)

In the latter form the distribution function from eq 33 was used to evaluate the summation. A similar analysis of the formation of intermediates by reactant scission leads to an identical expression for dnj/dtIa. (In this instance the special case of k = 2j is treated as in the derivation of eq 30.) Both expressions are then substituted into eq 34. All of the summations in eq 34 can now be evaluated as functions of p. Several such manipulations bring the evolution equation for labile reactant bridges into final form, which is

The only aspect of the reactant fragments remaining to be described is the concentration of peripheral groups. Peripheral groups leave the reactant lump either through release or through scission-induced transfer of peripheral-group-containing fragments to the metaplast and intermediate lumps; their number increases when the scission forms fragments that remain in the reactant lump. Therefore, the population balance is

(42) The three source terms grouped together describe growth by scission of larger metaplast and all intermediate and all reactant fragments, respectively. The next term accounts for depletion by its own scission, and is followed by terms for depletion by its own recombination with another metaplast, and for growth by the recombination of smaller fragments. In the recombination terms, the reaction rate coefficient is assumed to be independent of the sizes of the recombining mers. Note also that recombination introduces second order processes into the scheme. The final term, rj, is the loss of mi by flash distillation into tar, defined later. While the scission terms closely resemble their counterparts for the reactant in form, the terms for metaplast and intermediates introduce probabilities for labile bridges and intact links for individual mer sizes, rather than for the entire lump; e.g., (Bxj+ ex) PXj = JXj

The prefactors (1 + pRe)arise because a peripheral group must be on every newly formed fragment end, but not necessarily on the other end of the original chain; hence, pRe,the aggregate probability that ends have peripheral groups, appears. These terms can be eliminated with the definition of pRein Table 11,to bring eq 38 into final form, which is

where x = n or m. The need for this segregation is one consequence of recombination. Recombinations are more likely to involve the smaller mers due to their greater abundance. Mer sizes whose replenishment by recombination is greatest will therefore tend to have more char links, so aggregate probabilities cannot apply equally to all sizes. Analogous to earlier considerations, the sizespecific probabilities are given by PXj =

dSR -= dt

B,

j-1

j and pX: = JXj

so that Pxj B, - =PXj 0'- 1)Xj

(39)

Equations 31-33 and 38-39, and the probabilities defined in Table I1 determine the instantaneous values of labile bridges, char links, and peripheral groups in the reactant, and the size distribution. Initial values of the probabilities have already been defined, and are specified as follows for BR and SR: BR(O) ~ ~ ~P(0)''[2J*(l ( 0 1

- ~ ( 0 )+ ) 11

SR(0) = 2pe(o) p(o)w*(l- p(0))

This ratio accounts for the number of labile bridges among - 1 links in an xj. Once the concentrations of all F~have been determined, pM,the total intact-link probability in the entire lump is assigned from

j

J*

(40) (41)

These expressions follow from evaluations of the respective definitions of pRband pRe in Table I1 using the identities incorporated into the derivation of eq 9. The population balances for metaplast and intermediates also incorporate very similar expressions for the role of scission. But recombination comes into play for both lumps, and flash distillation affects metaplast character-

(43)

PM

J*

= 1 - j-1 Emj/+j 1-1

(44)

Both summations are evaluated from the concentrations of mi. It would be incorrect to assign p M from the total aggregate link Probability,p, from eq 31, using the relation for the initial coal, eq 11, because p is based only on scission. But recombination and flash distillation are reflected in the concentrations which enter into eq 44. To evaluate the p,b, the following balance for the concentration of labile $ridges for each mer size within the

Energy & Fuels, Vol. 5,No. 5, 1991 661


In succession, the source terms represent spontaneous conversion of peripheral groups to noncondensibles, their formation by scission of metaplast, intermediate, and reactant, their conversion and/or transfer to the intermediate lump when metaplast recombines, and their transfer to the tar lump. Each recombination eliminates up to four peripheral groups in the metaplast; Le., up to two are converted as the char link forms (depending on whether the participating ends have peripheral groups), and up to two are transferred on the ends of the newly formed intermediate chain (if the recombining mers are sufficiently long). Once SMis computed, pMeis evaluated from ita definition in Table 11. Based on the initial fragment distribution, eq 8, the relation in eq 43, and the expression for S M in Table 11, the initial conditions for bridges and peripheral groups in metaplast can be evaluated to obtain

metaplast lump must be solved:

k (g)nk+ 2

0’-1)

k=J*+l

The first term accounts for scission and condensation of labile bridges in j-mers. Among the four terms collected as a common factor multiplying 2VBkB, the first three represent the addition of bridges in the mj fragment class by scission of larger mers grouped as metaplast, intermediate, and reactant, respectively. The fourth accounts for bridge transfer to smaller mers as bridge scission causes j-mers to disintegrate. The overall order of these reaction rates is unity, consistent with the postulated unimolecularity of scission. But the chain statistics resolve this further (through the factors pmbgiven by eq 43) into a second-order dependence on the bridge concentration and an inverse first-order dependence on the mi concentration. The two terms collected as a common factor multiplying kR/2 account for the addition of bridges into mi via recombination of smaller fragments, and for bridge loss when an mj recombines with any metaplast fragment. In the first contribution, the mer-size dependence of the labilebridge concentration among intact linkages is reflected explicitly. Finally, bridges leave the mi in the form of tar vapor. Note that the chemical constitution of metaplast determines that of newly formed tar vapor. A tacit assumption underlying eq 45 is that the likelihood of an intact link being labile is independent of its location within the fragment. This is not strictly correct for fragments in lumps which are affected by recombination. Once the B, are determined, the labile bridge probability for the metaplast lump is determined from J’

CB / E._i m j

PMb = j = l

(46)

SM(0) = 2pe(0)(1- p(o))(1- p(o)J*)

(49)

The population balances for the intermediate do not introduce any new processes and will be stated directly. For the fragment concentrations

For the labile bridge concentrations

0’-1)0‘-2

For peripheral groups in the intermediate

-dSN - - -kr$& dt

+ ~ V B ~ B+B N

1-1

Peripheral groups in the metaplast evolve according to the following rate equation:

Based on considerations like those leading to eqs 48 and 49, the initial conditions for bridges and peripheral groups in the intermediate lump are

SN(0) = 2pe(0)p(0)”(1 - p(o)J*)(l- p(0))

J*

(54) To this point, population balances have been developed to describe the complete range of fragment sizes in the

Niksa and Kerstein


condensed phase, but product evolution has not been considered. Yet in FLASHCHAIN there are direct connections between the amounts of condensed reaction species and gas evolution rates. Tar forms only when metaplast is present, itself formed by scissions of reactant and intermediate fragments. In the model, tar's aromaticity and molecular weight distribution are determined solely by chemistry in the condensed phase because homogeneous secondary chemistry is omitted. Also, the release of noncondensibles depends on the concentrations of peripheral groups and labile bridges. In fact, in this theory absolutely no chemical or transport processes in the vapor phase enter into any aspect of the evolution rates or chemical constitution of volatile matter. This restriction is not fundamental, the computed transient volatiles yields could be used as input to a submodel for homogeneous chemistry if desired. The molar evolution rate of noncondensible gases is the sum of three contributions, according to

(57)

where G is the mole fraction of noncondensible gases, H the aggregate mole fraction of tar vapor, and tj/Ccltj the number-based instantaneous tar vapor MWD. d e ratio of the gas evolution rate to the mole fraction of noncondensibles defines the total molar escape rate, which is multiplied by the mole fraction of a ti to define r.. The mole fractions of tar fragments are deduced from two additional stipulations: (1) mole fractions sum to unity; and (2) phase equilibrium is maintained while the tar vapor is within the particle. The vapor consists of a multicomponent mixture of tar fragments and noncondensibles; the condensed phase consists of a polydisperse mixture of chains. These concentrations are related by a generalization of Raoult's law for continuous mixtures which was developed for flash calculation^.^^^^^ In this model, Raoult's law is expressed as J'

Cpj = HPo = xm,Pat(T,MWtj)

j=l

The first two sources account for spontaneous condensation of labile bridges and peripheral group elimination in any size range; the last term accounts for gas evolution when peripheral groups are expelled from the ends of recombining metaplast fragments. The solution of eq 55 specifies the molar amount of gas formed in a specified time interval, which is converted to fractional weight loss as follows:

All liberated noncondensible reaction species appear as products, neglecting any gas accumulation within the particle, and neglecting any secondary homogeneous pyrolysis within the particle. The latter assumption may restrict the model to smaller particle sizes, although there is ample e ~ i d e n c e ' supporting ~.~~ its application to sizes smaller than 1 mm for all pressures of technological interest. Based on molar evolution rates consistent with measured product molecular weights and mass loss rates, volatiles are transported into the ambience on time scales which are orders of magnitude shorter than those for secondary homogeneous pyrolysis.'l Tar formation is based on the flash distillation analogy.13 This scheme invokes a scaling which shows that accumulation of vapor species is negligible and continuum flow is the only transport mechanism which can accommodate measured product evolution ratesaw Moreover, the pressure difference for escape by continuum flow is expected to be much less than the ambient pressure, except for vacuum pyrolysis. Consequently, transport resistances are deemed negligible, and the internal and ambient pressures are equivalent (except under vacuum). To maintain a fixed internal pressure, noncondensibles escape at their rate of production by chemical reaction, as given by eq 65. Tar escape is also determined by this rate because, in any convective flow process, species transport rates are proportional to the total escape rate and their respective mole fractions. Consequently, the molar evolution rate of aj-mer of tar,rj = dYj/dt, is given by (60)R m l , W.B.;Saville, D.A.; Creene, M.I. MChE J. 1979,25,65.

(58)

where pi is the partial pressure of a t x the mole fraction of m. in the condensed phase, and b@',MWj) the saturated vapor pressure of metaplast. The latter quantity is modeled as Fat(T,MWti) = Pc ex.(

-7)

(59)

where Pc, A, and z are constants fit to tar yields and MWDs, and MW, is the instantaneous molecular weight of a tj, defined as

(60) This definition shows explicitly how the chemical constitution of tar is determined by the structure of metaplast. The above relations can be rearranged into definitions of H,the instantaneous tar MWD, and rj,as follows:

j=l

'


FLASHCHAIN Theory for Coal Deuolatilization

Finally, the total molar evolution rate of tar comprises all size-specific evolution rates, as in (64) Since the molecular weights of the tar fragments change in time, the tar yield on a fractional weight basis must be determined by integrating the instantaneous molar evolution rate, which is given by

Table 111. Structure of the Initial Value Problem for

FLASHCHAIN lump reactant intermediate

state variables

2, SR ni

B,

SN metaplast

mi

B,

SM

where (MWT,) is the instantaneous number-average MW of tar:

gas

YG

tar

YT

WT gi

wi

defining diff eqs 30 37 39 50 51 52 42,43 45 47 55 63,64 65 67 70

eq for init. valueso 8 40 41 8 53 54 8 48 49

(0) (0) (0) (0) (0)

aQuantities in parentheses are initial values.

Also since the weight of the tar fragments changes, the MWD of tar escaping from the sample at any instant is not the same aa the MWD of the accumulated tar sample evolved up to that point. As in eq 65, the characteristics of the cumulative sample are assigned by integrating those of all instantaneous contributions. The number-based MWD of the cumulative tar sample is developed from the number fractions of j-mers in the cumulative tar sample, defined as gj = yj/yT (66)

respective moles of j-mers, labile bridges, and peripheral groups in the metaplast, intermediate, and reactant lumps, the gas yield, and the molar and mass yield and the number- and mass-based size distributions of tar. Values of the state variables determine values for all probabilities, based on their definitions in Table 11. The fractional maas is determined from the molar concentration by eqs 13-24 for species and structural components in the condensedphase lumps, and by eq 56 for noncondensible gases.

where Yj is the molar yield of tar j-mer. These fractions evolve in time according to

FLASHCHAIN renders the chemical constitution of coal

&j

rj

gj

dYT

G dt

where the final form involves substitutions from eqs 57, 64, and 66. This distribution could be used to define the number-average molecular weight of the cumulative tar sample, M,,, although a simpler definition is M n = WT/YT (68) Values of M,, have been reported, but most of the reported measurements of tar MWDs are mass-based. Weight fractions of the tar sample are defined as w j = wj/wT (69) where W. and WT are the fractional mass-based cumulative yields orj-mers and of all fragment sizes of tar, respectively. These fractions evolve in time according to

In a similar way, the aromaticity of the cumulative tar sample can be expressed in terms of constituent values for bridges, char links, peripheral groups, and nuclei weighted by the changing proportions of these constituents. Since these tar characteristics will not be compared to data in parts 2 and 3, their definitions will be reported in future extensions. Finally, all state variables, differential equations, and initial values in the initial problem associated with this theory appear in Table 111. The state variables are the

Summary

in terms of a typical refractory aromatic nucleus, two linkage types (labile bridges and char links) and a typical peripheral group. Most importantly, these constituents distinguish centers of disparate reactivity. Aromatic nuclei and char links remain refractory throughout all stages of primary devolatilization. Since nuclei are massive, their partitioning between char and tar largely determines mass loss, especially for bituminous coals. Peripheral groups present initially are expelled as noncondensible gases, but only a small fraction of the total gas yield forms this way. Labile bridges are regarded as the key reaction centers, and their decomposition initiates two distinct pathways which govern both tar and gas formation: (1)Scinsions that represent ruptures which are rapidly stabilized before extensive aromatization can occur, yielding smaller fragments, with peripheral groups that are precursors for subsequent gas generation. (2)Spontaneous condensations that represent internal rearrangements into more extensive aromatic domains can take place, spawning small radicals that are instantly stabilized into noncondensibles. Such structure-reactivity hypotheses are also the basis for describing the distribution of heteroatoms and aromaticities. Elements expelled for the most part as permanent gases are derived from bridges and peripheral groups. Such atoms will also be found in tar,but only to the extent that it contains labile bridges. Oxygen clearly belongs in this category, but sulfur is treated this way only because it is not very abundant in most coals. Future extensions will treat sulfur elimination in greater detail. Elements that can be exclusively expelled with the tar under some operating conditions, such as nitrogen, are included in the nucleus. Since refractory behavior during pyrolysis is consistent with high aromaticities, all carbons and hydrogens in a nucleus or a char link are regarded as aromatic; aliphatic elements are distributed among peripheral groups and bridges. Thus, as seen in the compilation of model parameters in Table IV, measured ultimate analyses and proton and carbon aromaticities

664 Energy & Fuels, Vol. 5, No. 5, 1991 Table IV. Model Parameters parameter specification A. Coal Constitution f,', ACICl ultimate analysis, Hf.' ultimate analysis, Hf.' ultimate analysis, Hf: ultimate analysis, Hf: ultimate analysis, Hf.' assumed consiant 6action of MWB regression of data in Figui*e5 pyridine extract yields adjustable

Reaction Mechanisms adjustable adjustable adjustable measured MWc measured MWG adjustable

specify parameters in the coal submodel. The hypothetical coal reactant also contains both labile bridges and char links, consistent with the view that coalification is essentially a graphitization,but no analytical method is available to assign their relative abundance. The degree of connectedness of coal's macromolecular structure is the key configurational factor governing its thermal response. As evident from extract yields, coals of all ranks through the high-volatile bituminous have open networks with substantial amounts of trapped molecules, but higher rank coals begin to approach a fully connected state. In FLASHCHAIN the mobile phase is recognized as the lightest end of a continuous size distribution of macromolecules extending to a nominally infinite chain, which is analogous to the connected coal matrix. Size distributions for broken straight chains relate solvent extract yields to the initial proportions of intact and broken links, and the initial fragment distribution. In part 3, these ideas are evaluated against the data base for coals across the rank spectrum, following illustrations in part 2, of the reaction mechanisms and evaluations based on comparisons with the extensive data base for bituminous coals. Acknowledgment. Partial support for S.N.and the computational facilities were provided by EPRI through their Exploratory Research Program, and also by the Advanced Research and Technology Development Program administered by the U.S.Department of Energy through Pittsburgh Energy Technology Center. Support for A.R.K. was provided by the Division of Engineering and Geosciences, Office of Basic Energy Sciences, US. Department of Energy. Nomenclature Reaction Species, Probabilities, and Yields A moles of aromatic nuclei in the condensed phase B moles of labile bridges in the condensed phase aggregate moles of labile bridges in lump K BK C moles of char links in the condensed phase aggregate moles of char links in lump K FK c% fraction of intact links which are labile bridges in lump K M moles of chains in the metaplast lump moles of metaplast j-mer moles of chains in the intermediate lump moles of intermediate j-mer instantaneous fraction of intact links among all p(t) chains in the condensed phase

2

Niksa and Kerstein

instantaneous fraction of labile bridges among all chains in the condensed phase instantaneous fraction of labile bridges among chains in lump K instantaneous fraction of labile bridges among j-mers of kind x instantaneous fraction of ends having peripheral groups among all chains in the condensed phase instantaneous fraction of ends having peripheral groups among chains in lump K instantaneous fraction of intact links among chains in lump K instantaneous fraction of intact links among jmers of kind x ( x = n, m, t ) moles of chains in the reactant lump moles of reactant j-mer moles of peripheral groups in the condensed phase aggregate moles of peripheral groups in lump K moles of tar j-mer fractional mass of lump or product K moles of any condensed-phase j-mer molar gas yield molar tar yield Other Variables and Parameters constant in the exponent of Pt molar concentration of aromatic nuclei in original coal 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 constituent L (L = A, B, C, S) mean activation energy for bridge decomposition activation energy for peripheral group elimination activation energy for bimolecular recombination Gaussian distribution of activation energies for labile bridges measured value of carbon aromaticity measured value of proton aromaticity increment for tar j-mers in the number-based size distribution of accumulated tar instantaneous mole fraction of gas within the coal instantaneous mole fraction of tar within the coal measured ratio of atomic hydrogen to carbon maximum degree of polymerization of metaplast and tar instantaneous Arrhenius rate constant for scission on a per bridge basis Arrhenius rate constant for peripheral group elimination Arrhenius rate constant for bimolecular recombination number-average molecular weight of accumulated tar measured value of the average molecular weight of noncondensibles nondimensional molecular weight of structural constituent L molecular weight of an average monomer unit instantaneous molecular weight of a tar j-mer measured ratio of atomic nitrogen to carbon measured ratio of atomic oxygen to carbon ambient pressure saturated vapor pressure of metaplast

Energy & Fuels 1991,5,665-673

PC (S/ C )

prefactor of Pt measured ratio of atomic organic sulfur to carbon T temperature increment for tar j-mers in the weight-based size Wj distribution of accumulated tar mole fraction of mj among all species in the Xmj condensed phase Greek Symbols B P ( O ) ( l - mo)) molar evolution rate of tar j-mer rj selectivity for scission in the bridge decomposiVB tion rate moles of gas formed per spontaneous condensa*C tion

666

moles of gas formed per peripheral group elimination bulk density of the original coal Po a standard deviation about EB in f ( E ) Subscripts G gas I generic index for metaplast, reactant, and intermediate lumps M metaplast metaplast j-mer intermediate intermediate j-mer reactant T tar YE

ilfi 2

FLASHCHAIN Theory for Rapid Coal Devolatilization Kinetics. 2. Impact of Operating Conditions Stephen Niksa High Temperature Gasdynamics Laboratory, Mechanical Engineering Department, Stanford University, Stanford, California 94305 Received February 7,1991. Revised Manuscript Received June 24,1991

In this paper, the theory formulated in a companion paper is evaluated against the extensive data base for high-volatile bituminous coals. Thermal history effects are illustrated for heating rates from 1 to 103 K/s and temperatures to 1200 K by using transient and ultimate weight loss, tar yields, and tar molecular weight distributions (MWDs). The examination of pressure effects incorporates data from vacuum to 6.9 MPa, including gas yields and the yields and average molecular weights of tar; transient weight low showing nominally equal devolatilization rates at all pressures; and the suppression of yield enhancements by faster heating at elevated pressures. Ultimate weight loss for sizes to one millimeter is also examined. In every respect, model predictions are within the discrepancies among measurements for similar samples from different laboratories. Hence, the influences of all of the important operating conditions on the devolatilization of high-volatile bituminous coals can be understood in terms of only four mechanisms: (1)the coal macromolecule disintegrates into primary fragments which are widely distributed in size; (2) a phase equilibrium establishes the mole fraction of tar fragments in a gas stream which is convected out of the particle with no transport resistance (the flash distillation analogy); (3) reactions in the condensed phase convert labile bridges into char links and simultaneously expel noncondensible gases, establishing the convective flow and inhibiting the formation of tar precursors; and (4) recombination reactions in the condensed phase reincorporate tar precursors into char. This evaluation also spawns two distinct interpretations of processes in the condensed phase. One is reminiscent of the two-component hypothesis, in which only a fraction of the original aromatic nuclei become susceptible to tar formation at some stage of devolatilization and the rest are inert. The other envisions a thorough disintegration of the coal macromolecule into relatively small fragments. The latter scenario yields an abundance of tar precursors, so a competition between flash distillation and repolymerization into larger involatile fragments determines the tar yields.

Introduction This modeling study aims to explain the influences of all of the operating conditions on the yields, lumped product distributions, and molecular weight distributions (MWDs)of tar from high-volatile bituminous coals, using FLASHCHAIN. A mathematical formulation of the theory appears in part 1of this series, and coal type effects are considered in part 3. The available data base establishes the influences of temperature, time, heating rate, pressure, and particle size, especially for high-volatile bituminous coals. So even without coal type effects, current rate and yield data present a formidable challenge for reaction modelers. 0887-0624/91/2505-0665$02.50/0

Early laboratory studies mapped out the primary influences of temperature and pressure' on yields and product distributions, while independent roles for heating rate and particle size were ambiguous.**2 Recently, however, improved schemes to control and monitor the coal's thermal history have been developed for both wire-grid" and en(1) Howard, J. B. In Chemistry of Coal Utilization;Elliot, M. A, Ed.; Wilev-Intarscience: New York.. 1981:. Second Surmlementarv Volume. Chapter 12. (2) Nikea, S. AIChE J. 1988,34(5), 790. (3) Gibbins-Maltham,J.; Kandiyoti, R. Energy Fuels 1988, 2, 606. (4) Freihaut, J. D.; Proscia, W. M. Energy Fuels 1989,3, 626. (5) Glass, M. W.; Zygourakie, K. Reo. Sci. Inatrum. 1988,69(4), 680.

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0 1991 American Chemical Society

FLASHCHAIN theory for rapid coal devolatilization ... - ACS Publications

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