Two-Stage Kinetic Model of Primary Coal Liquefaction | Energy & Fuels

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Energy & Fuels 1996, 10, 1115-1127

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Two-Stage Kinetic Model of Primary Coal Liquefaction Bin Xu† and Rafael Kandiyoti* Department of Chemical Engineering and Chemical Technology, Imperial College University of London, London SW7 2BY, United Kingdom Received February 16, 1996. Revised Manuscript Received June 10, 1996X

A mathematical model enabling the calculation of reaction rate parameters for coal weight loss during liquefaction has been formulated. The model explicitly accounts for (i) product release during heatup as well as during holding at peak experimental temperature and (ii) stages of the process prior to and following the onset of extensive covalent bond scission (around 350 °C); the procedure thus allows the calculation of distinct activation energies for the two stages. In the initial phase of the calculation, both stage A processes (prior to the onset of extensive bond cleavage) and stage B processes (following the onset of extensive bond cleavage) have been modeled as single, irreversible, first-order processes. In the fully developed model, both stage A and stage B were considered to proceed by means of multiple parallel, independent, irreversible, first-order reactions with a Gaussian distribution of activation energies. Calculations were matched with liquefaction experiments in tetralin, carried out in a flowing-solvent reactor using seven Argonne PCSP coals and Point of Ayr (U.K.) coal. For stage A processes, the single-reaction model gave activation energies between 35 and 80 kJ mol-1. Energies of activation for the higher temperature range stage B processes (about 350-450 °C) were found to be significantly higher, between 124 and 238 kJ mol-1. This result confirms the validity and necessity of describing coal liquefaction in terms of a two-stage process. For stage A, the multiple parallel independent reaction model gave mean activation energies that were only slightly larger than those calculated from the singlereaction model. Activation energies for stage B processes, however, were greater, between 160 and 275 kJ mol-1, indicating that the single-reaction model significantly underestimates energies of activation for coal thermal breakdown. For individual coals, the standard deviation of the distribution of activation energies progressively decreased with increasing coal rank, apparently reflecting increasing structural uniformity and possibly also increasing degrees of cross-linking accompanying coal maturation. Activation energies reported in the literature for the liquefaction of coal, mostly based on isothermal kinetics, range from 18 to 358 kJ mol-1. Qualitative agreement has been found between values from the present work and results from a multiple, parallel independent reaction scheme fitted to data from the pyrolysis of the Argonne PCSP coals.

Introduction The present paper describes a mathematical model and experimental procedures used to calculate kinetic parameters for the liquefaction of a rank-ordered set of coals. The calculation scheme was designed to take into account a number of features specific to coal liquefaction; these include the effect of reactor configuration on sample weight loss, the distinct nature of predominant mass loss mechanisms prior to and following the onset of extensive covalent bond scission, and nonisothermal mass loss during heatup. Activation energies reported in the literature for the liquefaction of coal cover a wide spectrum of values, ranging from 18 kJ mol-1 (ref 1) to 358 kJ mol-1 (ref 2). It seems difficult to relate some of these valuess particularly those at the extremes of the rangeswith thermal breakdown processes normally associated with coal liquefaction. While differences in coal samples and the nature of experimental procedures might, at least in part, explain some of these variations, a re-examination of elements necessary for matching liquefaction data to kinetic models would appear to be useful. * Author to whom correspondence should be addressed. † Present address: Computational Engineering Group, Daresbury Laboratory, Keckwick Lane, Daresbury, Warrington WA4 4AD, Cheshire, U.K. X Abstract published in Advance ACS Abstracts, July 15, 1996.

(A) Reactor-Related Effects. Numerous reaction schemes, many of them based on solubility classes (oils, asphaltenes, etc.), have been proposed for analyzing batch reactor results and arriving at kinetic expressions describing the dissolution of the coal sample, as well as accounting for the multiplicity of reaction pathways available to material already released from the coal (cf. ref 3 for a brief review). As reaction schemes attempt to take into account the complexities of extraparticle processes in progressively greater detail, however, the reliability of kinetic constants accounting for rates of postulated individual reaction pathways inevitably diminish. A measure of clarity can be achieved by distinguishing between coal mass loss and subsequent reactions of coal extracts. In earlier work4 we compared conversions and product characteristics obtained from liquefaction in a minibomb and a flowing-solvent reactor; the latter (described below) allows products released from coal to be rapidly and continuously removed from the reaction zone. When using tetralin as vehicle, nearly comparable coal conversions were obtained in the two reactors, although significant differences in extract structure were found: size exclusion chromatography derived molecular mass distributions provided direct (but not unexpected) evidence for extensive cracking of dissolved extracts in the minibomb. However, very different outcomes were

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observed between these two reactors in the presence of a poor H-donor solvent, 1-methylnaphthalene (1-MN). At 450 °C, conversions in the flowing-solvent reactor increased monotonically with time (also see ref 5), while in the minibomb, the already considerably lower conversion at 100 s was reversed, thereafter giving a net increase in solid products. Smaller extents of retrogressive char formation in 1-MN have been reported in other work using batch microautoclaves at lower temperatures.1 Reaction pathways as well as rates of processes taking place during coal liquefaction depend, therefore, to some degree on interrelationships between the role of the reactor configuration and that of the solvent/ vehicle. Apparatus with specialized configurations such as the flowing-solvent reactor described below are not absolutely necessary for determining coal dissolution (conversions) independent of subsequent “secondary” reactions. Similarities between coal mass loss in the flowing-solvent and the minibomb reactors, when using tetralin as vehicle, suggest that it may be possible to calculate coal dissolution (conversions) from batch reactor data, so long as an efficient H-donor solvent is used in sufficient abundance.4 In tetralin, solvent-to-coal ratios of about 4:1, or higher, would appear to provide the abundance of H-donor required for suppressing large-scale recombination reactions between coal-derived free radicals to the same extent as in the flowingsolvent reactor. Ratios as high as 1:8 have been suggested.2 Such conversion data could be considered relatively free of reactor-related effects. However, in batch reactors, it is still possible that the rates of liquefaction would be affected by changing rates of diffusion of extract molecules out of coal particles, against a continuously rising concentration of extract molecules in the reaction mixture surrounding the particles. For Point of Ayr coal, 10-min extractions in minibombs gave about 15% lower conversions than the flowing-solvent reactor (where coal was exposed to temperature for somewhat less than 500 s), while 60min extraction results were comparable with conversions in the flowing-solvent reactor. In the latter reactor, the diffusion of extract molecules out of coal particles takes place against virtually zero concentration of dissolved coal extracts in the surrounding solvent phase, due to the continuous flow of fresh solvent; this reactor configuration therefore allows the calculation of kinetic constants independently of external diffusion resistance effects. It is important to note, finally, that in the absence of abundant H-donor solvent (e.g. in the presence of a poor donor solvent such as 1-MN), kinetic expressions describing coal liquefaction processes in batch reactors would need to reflect product loss through retrogressive radical recombination reactions, char formation, etc. In the flowing-solvent reactor, such retrogressive reactions would be minimized (but probably not totally elimi-

nated) as observed in experiments with 1-MN, quinoline, and mixtures of quinoline and phenanthrene, for which conversions very close to those observed in tetralin have been obtained.4,6 (B) Processes preceding and following the Onset of Extensive Covalent Bond Scission. It is possible to distinguish between coal mass loss taking place prior to and following the onset of extensive covalent bond scission. Data from electron spin resonance spectroscopy7-9 suggest that when coal is heated, spin concentrations of stable free radicals increase rapidly only after about 350 °C, providingsindirectsevidence for the onset of extensive bond scission at and above this temperature. In view of experimental uncertainties8 and the likely distributions of bond strengths within complex coal structures, 350 °C cannot, however, be treated as a precise dividing line; results presented below suggest that the characteristic temperature band may shift by several tens of degrees as a function of individual coal properties. Within this framework, the voluminous data on coal extraction obtained at boiling points of common solvents (e.g. chloroform, pyridine) may be safely viewed as reflecting dissolution in the absence of extensive covalent bond scissionswithout necessary reference to the precise origins of such extracts or the nature of processes involved in their release. In coal liquefaction, the dissolution of products at temperatures below the characteristic band around 350 °C may also be reasonably considered as taking place prior to extensive covalent bond scission. The proportions of coal extracted at temperatures up to 350 °C are not inconsiderable: in tetralin, mass loss from the set of samples selected for the present study showed a variation between 30 and 58% (w/w daf coal; heating at 5 K s-1 to 350 °C with a 1600-s hold). The foregoing has immediate implications for the evaluation of procedures used in the calculation of kinetic parameters for coal liquefaction processes. It was recognized early-on2,10 that activation energies of processes taking place prior to the onset of extensive bond scission in coals are significantly lower than those taking place after the “onset” temperature band has been reached. Descriptions of coal dissolution in terms of single activation energies spanning the entire temperature range from ambient to a peak temperature above 350 °C would appear, therefore, to mask a significant and (at least qualitatively) well recognized stage of the overall process, leading to the calculation of ill-defined activation energies. It must be noted that the foregoing does not pretend to contribute to debates on the description of coal structure in terms of a mobile and a macromolecular phase. Cumulative extract yields at temperatures up to 350 °C change significantly depending on the nature of the solvent: in the flowing-solvent reactor, with a 400-s hold at 350 °C, the weight loss from Point of Ayr

(1) Shin, S. C.; Baldwin, R. M.; Miller, R. L. Energy Fuels 1989, 3, 193. (2) Hill, G. R.; Hariri, H.; Reed, R. I.; Anderson, L. L. In Coal Science; Gould, R. F., Ed.; Advances in Chemistry Series 55; American Chemical Society: Washington, DC, 1966; p 427. (3) Anderson, L. L. Coal Liquefaction Kinetics. In New Trends in Coal Sciences; Yu¨ru¨m, Y., Ed.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1988; p 339. (4) Gibbins, J. R.; Kimber, G.; Gaines, A. F.; Kandiyoti, R. Fuel 1991, 70, 380.

(5) Xu, B.; Dix, M.; Kandiyoti, R. Rev. Sci. Instrum. 1995, 66 (7), 3966. (6) Xu, B.; Madrali, E. S.; Wu, F.; Li, C-Z.; Herod, A. A.; Kandiyoti, R. Energy Fuels 1994, 8, 1360. (7) Fowler, T. G.; Bartle, K. D.; Kandiyoti, R. Fuel 1988, 67, 173. (8) Fowler, T. G.; Kandiyoti, R.; Bartle, K. D.; Snape, C. E. Carbon 1989, 27, 197. (9) Fowler, T. G.; Bartle, K. D.; Kandiyoti, R. Energy Fuels 1989, 3, 515. (10) Han, K. W.; Wen, C. Y. Fuel 1979, 58, 779.

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Kinetic Model of Primary Liquefaction

coal changed from 24.6% in tetralin to 39.5% in quinoline.6 Multistep extraction,11 or the use of more powerful solvents, such as 1-methyl-2-pyrrolidinone (NMP),12 is likely to give higher extract yields prior to the onset of extensive covalent bond scission. It does not appear possible to distinguish clearly between presumed distinct phases in coals. (C) Nonisothermal Mass Loss during Heatup. When coal is pyrolyzed, sample weight loss during heatup is extensive, even when rapid heating is applied: 13 during experiments using a heating rate of 1000 °C s-1 to 700 °C in a wire-mesh reactor, almost all measurable volatile release was found to have taken place during heatup.14 In coal liquefaction, lower temperatures are used and smaller proportions of total possible products are released during heatup; the proportion of extracts released during heatup is, however, significant. In the flowingsolvent reactor, where rapid cooling is made possible by allowing a flow of cold solvent to wash over the fixed bed of sample, experiments conducted in tetralin at 5 °C s-1 to 450 °C with a “0-s” hold at peak temperature gave about 20% weight loss for Pocahontas No. 3 coal and about 30% weight loss for Point of Ayr coal.6,15 For most bomb reactors, average heating rates over the temperature interval are usually of the order of 2-5 °C s-1, i.e. similar to that of experiments carried out in the present study. Using an autoclave with a heatup period of 1.5-2 h, Hill et al.2 reported that “80% of the total possible extraction” was achieved “before the system reached the reaction temperature”. Clearly, sample weight loss during heatup takes place in nonisothermal mode, at rates that continuously change with rising temperature; its neglect in the calculation of kinetic constants for coal liquefaction processes is not therefore warranted, irrespective of the duration of the heatup period. It must be noted in this connection that the use of higher heating rates would not significantly alter the amount of extract released during heatup. We have previously reported16 on the relative insensitivity of liquefaction conversions to changes in heating rates between 0.1 and 10 °C s-1, in the presence of the efficient H-donor tetralin. Mechanisms underlying changes in yields with changes in heating rates appear to involve competition between recombination reactions and quenching of coal-derived free radicals by locally available hydrogen.17 In atmospheric pressure pyrolysis, the use of higher heating rates appears to lead to the release, in the form of volatiles, of some material which would otherwise have recondensed, leading to a repolymerized residue char.14,18 The high conversions and the absence of a heating rate effect during coal liquefaction in the presence of an efficient H-donor suggest that competition between recombination reactions and product release is not a predominant effect. In any case, changes in yields with increasing heating (11) Nishioka, M. Fuel 1991, 70, 1413. (12) Takanohashi, T.; Iino, M. Energy Fuels 1990, 4, 452. (13) Howard, J. B. In Chemistry of Coal Utilization; Elliott, M. A., Ed.; Wiley: New York, 1981; 2nd Suppl. Vol., p 665. (14) Gibbins-Matham J. R.; Kandiyoti, R. Energy Fuels 1988, 2, 505. (15) Xu, B. Ph.D. Thesis, University of London, U.K., 1995. (16) Gibbins, J. R.; Kandiyoti, R. Fuel 1991, 70, 909. (17) Li, C-Z.; Madrali, E. S.; Wu, F.; Xu, B.; Cai, H-Y.; Gu¨ell, A. J.; Kandiyoti, R. Fuel 1994, 73, 851. (18) Li, C-Z.; Bartle, K. D.; Kandiyoti, R. Fuel 1993, 72, 3.

Energy & Fuels, Vol. 10, No. 5, 1996 1117 Table 1. Elemental Analysis of the Argonne (APCS) Coals19 and Point of Ayr (U.K.) Coal15 C H N S O ash (daf) (daf) (daf) (daf) (by diff) (dry basis)

sample Beulah-Zap Wyodak Anderson Illinois No. 6 Blind Canyon Pittsburgh No. 8 Upper Freeport Pocahontas No. 3 Point of Ayr (U.K.)

72.9 75.0 77.7 80.7 83.2 85.5 91.0 84.5

4.8 5.4 5.0 5.8 5.3 4.7 4.4 5.4

1.2 1.1 1.4 1.6 1.6 1.6 1.3 1.8

0.7 0.5 2.4 0.4 0.9 0.7 0.5 1.5

20.4 18.0 13.5 11.5 9.0 7.5 2.8 6.8

9.7 8.8 15.5 4.7 9.3 13.2 4.7 9.6

rates are not large: when during a pyrolysis experiment, the heating rate is increased from 1 to 1000 °C s-1, parallel increases in tar and total volatile yields rarely exceed 6-7% (w/w daf coal).18 In liquefaction, therefore, if significantly faster heating rates than those normally available to bomb reactors are used, it would be expected that at “zero-holding” the amount of extractables released from coal up to the peak temperature could change as a function of heating rate, possibly increasing by a small amount in the case of a nondonor solvent (due to reduced time for retrogressive reactions) and showing small reductions (due to less time available for reaction) in the case of a good H-donor vehicle.16 It is, therefore, unlikely that very significant changes in product release can be achieved during heatup by changing the heating rate: in the flowing-solvent reactor, by the time the sample reaches 450 °C in a stream of tetralin, depending on the type of coal, anywhere between 20 and 40% of a middle-rank coal may be expected to have already gone into solution. In coal liquefaction at temperatures up to 420-450 °C, events during heatup thus encompass (i) stages of the process with different activation energies and (ii) significant levels of product release during heatup, taking place over a range of temperatures, at progressively increasing rates. In this paper, we have described a set of equations enabling the calculation of reaction rate parameters for coal weight loss during coal liquefaction. The model explicitly accounts for product release during heatup, both before and after the onset of extensive covalent bond scission (around 350 °C), leading to the calculation of different activation energies for the two stages. The calculations were based on a set of coal conversion data from the flowing-solvent reactor; tetralin was used as vehicle. Experimental Section Coal Samples. Table 1 presents elemental analyses of the set of samples. Liquefaction experiments were carried out with Point of Ayr (U.K.) and seven of the Argonne PCSP19 coals: Beulah-Zap, Wyodak-Anderson, Illinois No. 6, Pittsburgh No. 8, Blind Canyon, Upper Freeport, and Pocahontas No. 3. Samples were ground, sieved, and stored under nitrogen; 100-150-µm fractions were used in the experiments. To study the effect of coal particle size on liquefaction yields, 250-500-µm fractions of Point of Ayr were used in separate experiments. Liquefaction Experiments. Details of the reactor assembly, the revised power control system, and the experimental procedure have been described elsewhere.5,16,20 Briefly, the upper section of a tubular reactor was packed with a mixture of about 200 mg of coal and 2800 mg of acid-washed sand (19) Vorres, K. S. Energy Fuels 1990, 4, 420. (20) Gibbins, J. R.; Kandiyoti, R. Rev. Sci. Instrum. 1991, 62 (9), 2234.

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Figure 1. Typical power and temperature control histories during a single experiment. The run was carried out by heating the reactor at 5 K s-1, from ambient to 450 °C with a 400-s hold. Solvent flow rate was maintained at 0.9 mL s-1 at 70 bar (g). (particle size: 106-150 µm) mounted between wire mesh plugs. Solvent was forced from a pressurized reservoir (0.9 mL s-1 at 70 bar) through a filter, a surge check valve, and a flow meter into the lower section of the reactor tube, which served as the solvent preheater. The control of this (lower) section was set for delivering solvent to the reactor (upper) section at the temperature of the latter; unless otherwise stated, samples were heated at 5 °C s-1 to the peak temperature and held for 400 s (Figure 1). Power to the two sections of the reactor was supplied by direct electrical heating and controlled separately; at the end of an experiment, the reactor was cooled by passage of cold solvent. No gaseous hydrogen was used in these experiments, where a large excess of tetralin (600-1000 mL of tetralin vs about 200 mg of coal) passed through the sample bed, continuously forcing products released from coal out of the reaction zone (6-10-s residence time) into a cooler/heat exchanger. Sample weight loss was determined by weighing the reactor and its contents following solvent (4:1 chloroform/methanol) washing and drying. Most data points given in this paper were averaged from two determinations; the repeatability of sample weight loss data was usually better than (1.5%.

Rate Equations (A) Assumptions. (1) The process was assumed to take place in two stages. (1a) Stage A Processes: Sample Weight Loss prior to the Onset of Extensive Covalent Bond Rupture, Taking Place between Ambient Temperature and ∼350 °C. The model was formulated without explicit reference to the nature of physical and chemical phenomena occurring in this temperature interval. It is thought, however, that these processes include ordinary dissolution of more soluble (smaller molecular mass and/or less polar) species possibly occluded or held by weak interactions such as hydrogen bonding and van der Waals forces. In what follows, stage A will be modeled, first, as a single activation energy, irreversible, first-order process and, second, as a set of parallel independent first-order processes with a Gaussian distribution of activation energies,13 characterised by a standard deviation, σA. In the latter case, a common pre-exponential constant is used to characterize the set of parallel, independent reactions.13 (1b) Stage B Processes: Weight Loss following the Onset of Covalent Bond Scission, Broadly Corresponding to Coal Weight Loss above ∼350 °C. Once again, no explicit reference has been made to the nature of chemical and physical phenomena occurring in this temperature interval. However, above ∼350 °C,

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extensive covalent bond rupture is known to contribute significantly to the release of material from coal particles. Changes in structural characteristics of extract fractions released from coals6,21 will not be addressed in this work. Stage B will also be modeled, first, as a single, irreversible, first-order process and, second, as a set of parallel independent first-order chemical reactions with a Gaussian distribution of activation energies,13 characterized by a standard deviation, σB. In the latter case, a common pre-exponential constant is used to characterize the set of parallel, independent reactions.13 (2) The coal is considered to behave as a homogeneous material. For ease of calculation, a single temperature is selected to distinguish between stages A and B, defined as Td: while this value was set at 350 °C for most coals, in calculations on Point of Ayr, Upper Freeport, and Pocahontas No. 3 coals, 375 °C was found to be a more appropriate value (see below). (3) The effect of intraparticle mass transport as a significant resistance or rate-determining step has been neglected. This assumption is treated as a first approximation and facilitates development of the present model. The following experiments suggest that internal diffusion may, in the first instance, be neglected, at least for some coals: a set of parallel liquefaction experiments were carried out using a sample of larger particle size (250-500 µm) Point of Ayr (U.K.) coal over the 300450 °C range. Compared to data obtained using 106150-µm particles, differences in weight loss were found to be within experimental error.15 In particular, no experimentally significant differences could be observed between the behavior of different sized particles at temperatures below the onset of extensive covalent bond scission. The evidence presented here is not thought to be conclusive; a separate study of the effect of intraparticle diffusion effects is in progress. (4) For both stage A and stage B processes, the concentration driving force in all first-order reaction terms has been expressed in terms of an “ultimate” (equilibrium) weight loss value. For stage A, equilibrium values have been estimated from sample weight loss determined by heating at 5 °C s-1 to 350 °C (or 375 °Csdepending on the coal; see below) with a 1600-s hold, followed by washing the solid residue with 4:1 chloroform/methanol at ambient temperature. Ultimate conversions at 450 °C were similarly determined after a 1600-s hold at peak temperature. Clearly, ultimate (equilibrium) weight loss may assume different values if the coal, the vehicle, or the solid residue washing procedure is changed. (B) Description of the Two-Stage Single-Reaction Model. Figure 2 presents a schematic diagram describing the two-stage single-reaction model. Both stage A and stage B are modeled as single activation energy, irreversible, first-order processes. xA(t) is defined as the time-dependent weight loss variable for stage A; this variable has an experimentally determined ultimate (equilibrium) value of xmA as defined above (1600 s at Td). As outlined below, kinetic constants for stage A processes at up to the temperature Td were calculated first. It may be noted that when the coal is heated to temperatures above Td, the available reaction time at (21) Li, C-Z.; Wu, F.; Xu, B.; Kandiyoti, R. Fuel 1995, 74, 37-45.

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Energy & Fuels, Vol. 10, No. 5, 1996 1119

as well as the holding phase of the experiment. With the initial (ambient) temperature defined as T0 and the heating rate during the heatup period as kh, the temperature T at any time can be calculated from T ) T0 + kht. The total weight loss x at any time thus includes weight loss during heatup and during the subsequent holding period. For a single run:

( )

dx

Figure 2. Two-stage single-reaction model of coal primary decomposition in a specific solvent system.

E

∫0t xmA -A xA ) ∫0t k0A exp - RTA ∫TT

h

0

or near Td is far shorter than the 1600 s used for determining the ultimate level of “simple” dissolution, xmA. During an experiment with the peak temperature set above Td, therefore, not all weight loss due to stage A processes is completed when the sample temperature reaches and increases past Td. Above Td, the model assumes continued release of material by simple dissolution up to the value xmA, through stage A processes (i.e. with activation energy EA), the instantaneous rate being governed by sample temperature at time t. Therefore, in the calculation of sample weight loss at temperatures above Td, when stage B processes (activation energy EB) are initiated, weight loss due to stage B processes is overlaid on weight loss due to stage A processes (also see eq 5). Sample weight loss due to stage B processes is defined as xB(t); overall conversion at any time t during the liquefaction process is defined as x(t) ) xA(t) + xB(t). Th is defined as the holding (i.e. peak experimental) temperature. The overall ultimate (equilibrium) conversion for stage B processes can be written in terms of the equation xm ) xmA + xmB, and xm experimentally determined as the total weight loss obtained by heating samples at 5 °C s-1 to 450 °C and holding for 1600 s; clearly

xmB ) xm - xmA where xmA is also experimentally determined (weight loss for 1600 s at Td). Equations arising from the model may be written as follows:

Stage A (T e Td) dxA/dt ) kA(xmA - xA) ) k0A exp(-EA/RT)(xmA - xA) (1a) t ) 0,

T ) T0,

t f ∞, T ) Th,

xA ) 0

(1b)

xA f xmA (for Th g Td)

(1c)

Stage B (T g Td) dxB/dt ) kB(xmB - xB) ) k0B exp(-EB/RT)(xmB - xB) (2a) t ) 0, t f ∞,

T ) T0,

T ) Th

{

xB ) 0

(2b)

xB ) 0 (Th e Td) xB f xmB (Th g Td)

(2c)

To account for weight loss during heatup, it is necessary to integrate mass loss over the heatup period

dt )

( )

( )

k0A EA EA dT + k0Ath exp (3) exp kh RTh RT holding heat-up

Therefore, when the holding temperature Th e Td, total sample weight loss is given by

[

[∫

x ) xmA 1 - exp

Th

T0

( )

k0A EA exp dT + kh RT

( )]]

k0Ath exp -

EA RTh

(4)

When Th g Td

[

k0A EA exp dT + kh RT EA k0Ath exp + xmB 1 RTh EB EB Th k0B exp dT + k0Bth exp T0 k RT RT h h

[∫

exp

( ) ( )]] [ ( ) ( )]]

[∫

x ) xmA 1 - exp

Th

T0

(5)

A set of three kinetic parameters (xm, k0, E) must be determined for both stage A (e.g. xmA, k0A, EA) and stage B (e.g. xmB, k0B, EB) processes. Of these, xm and xmA are determined experimentally; xmB is determined by the difference: xmB ) xm - xmA. The first step of the calculation (i.e. for stage A parameters) makes use of sample weight loss vs temperature data at up to Td. k0 and EA values were calculated using a two-dimensional surface-fitting nonlinear regression algorithm. Initially, a pair of values was arbitrarily selected, and the next set of approximations for the two parameters was calculated from i 0 0 ) k0A + ∆k0A (1 + cos θi) k0A

(6a)

i 0 0 E0A ) E0A + ∆E0A (1 + sin θi)

(6b)

0 ) k0A/N1 and ∆E0A ) E0A/N2 were the where ∆k0A searching step lengths adjusted by changing the values of N1 and N2. Initially N1 ) 10 and N2 ) 10; θi ) i(2π/ N) (i ) 1, 2, . . ., N) is the searching direction; e.g. N ) 8 represents the eight points surrounding the reference point . Figure 3 presents the co-ordinate axes used for this procedure. For each pair of kinetic parameters i , EiA), the simulated conversion data (weight loss) (k0A at any reaction condition (determined by specifying the heating rate, holding temperature, and holding time) can be obtained from eq 4. The search for the bestfitting kinetic parameters is performed by computing the standard error for each pair of kinetic parameters:

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Xu and Kandiyoti

Figure 3. Schematic nonlinear regression algorithm for twodimensional surface-fitting.

δi )

x

M

(xj - xj*) ∑ j)1

2

M

(7)

where xj is the simulated weight loss calculated by eq i 4, using kinetic parameters (k0A , EiA), xj* is the corresponding experimental weight loss data, M is the number of experimental data points, and δi is the i statistical least-squares standard error for (k0A , EiA). The iteration process was continued until a point on the surface in Figure 3 was found which gave the smallest standard error, δ. The searching step lengths of ∆k0A and ∆EA were then reduced by doubling the N1 and N2 values, and the search loop was repeated. Using this algorithm, the ultimate best fits for k0A and EA corresponding to the minimum overall value δ were not considered to have been reached until the search step lengths of ∆k0A and ∆EA were reduced by doubling the N1 and N2 values 10 successive times. Once the calculation for step A was completed, the same algorithm was used to search for the best fitting k0B and EB values for stage B, by fitting to pseudoexperimental data calculated from xB* ) x* - xA, where x* denotes experimental weight loss data obtained through stage B processes above 350 °C (up to 450 °C) and xA denotes the simulated weight loss by stage A mechanisms, at the corresponding reaction conditions, calculated by eq 4 using the already available values of xmA, k0A, and EA. The values of the starting parameters have not been found to influence the final values obtained in these calculations or in the multiple-reaction model calculations described below. (C) Description of the Two-Stage Multiple-Reaction Model. Early work by Jungten and van Heek22 on the pyrolytic behavior of coals has shown that when a process consisting of multiple parallel independent reactions is modeled in terms of a single reaction, the apparent activation energy turns out to be lower than the activation energies of the individual reaction path(22) Jungten, G.; van Heek, K. H. Reaktion-ablaufe unter nichtisothermen Bedingungen; Fortschritte der chemischen Forschung; Springer-Verlag: Berlin, 1970; Vol. 13, pp 601-699; translated by Belov and Associates, Denver, CO, APTICTR-0776; quoted in ref 13.

Figure 4. Two-stage multiple-reaction model of coal primary decomposition in a specific solvent system.

ways. To test the relevance of this proposition to coal liquefaction, both stage A and stage B of the liquefaction process were considered to proceed by means of multiple parallel independent irreversible first-order processes (Figure 4). The approach is adopted from the work of Howard and co-workers on volatile release during coal pyrolysis.13 Within this framework, the kinetic expression for any single process “i” is given by

dxi/dt ) ki(xmi - x) ) k0i exp(-Ei/RT)(xmi - xi)

(8)

and

(xmi - xi)/xmi )

∫0tk0i exp(-Ei/RT) dt

(9)

The model assumes that k0i ) k0 ) constant for all i. The distribution function for the energies of activation is introduced by the equation

dxmi ) xmif(E) dE

(10)

∫0∞f(E) dE ) 1

(11)

with

and the cumulative total weight loss x can be calculated from

xm - x ) xm

[

( ) ] E

∫0∞ exp ∫0t-k0 exp - RTi

dt f(E) d(E) (12)

where f(E) is considered to be a Gaussian distribution function with mean activation energy E0 and standard deviation σ:

f(E) )

[

(E - E0) 1 exp 2σ2 σ x2π

]

2

(13)

Thus, the cumulative weight loss from the set of parallel independent processes can be calculated from

+

+


xm - x 1 ) xm x σ 2π

∫0

∞

exp

[∫


( )

t

-k0 exp 0

E dt RT

]

(E - E0)2 2σ2

dE (14)

The weight loss during a particular experiment includes weight loss occurring during heatup as well as the holding period. Weight loss during the rapid cooling period has been neglected.

when Th e Td

[

x ) xmA 1 -

1 σA x2π

[(

∫0∞ exp ∫TT

( )

h

-

0

)

( )

k0A EA E exp dT + k0Ath exp - A kh RT RT (holding) (heat-up)

] ]

(EA - E0A)2 2σA2 for Th g Td

[

x ) xmA 1 -

)

1 σA x2π

[( ( )) ∫ [( ∫ ( ))

∫0∞ exp ∫TT

h

EA EA dT + k0Ath exp RT RT

[

xmB 1 -

)

1 σB x2π

-

0

∞

0

dEA (15)

( ] ] ( ] ]

k0A exp kh

(EA - E0A)2

-

exp

EB EB dT + k0Bth exp RT RT

2σA2 Th

T0

-

-

-

dEA +

k0B exp kh

(EB - E0B)2 2σB2

dEB

(16)

In the multiple-reaction model, in addition to the preexponential term and the mean activation energy, the standard deviation of the distribution (of activation energies) must also be calculated. As before, stage A parameters (k0A, E0A, and σA) were calculated first, using weight loss data obtained between ambient and Td for the particular coal. To reduce the three-dimensional nonlinear regression problem to a two-dimensional search, the third variable σA was preset at a series of fixed values (E0A/10, E0A/ 25, E0A/50, E0A/100, and E0A/200) and the (k0A, E0A) values corresponding to the best fit were calculated using the same two-dimensional surface-fitting algorithm described above. Among these sets of parameters, the overall best-fitting set of K0A, EA, and σA was determined by minimizing δ as defined in eq 6. Interpolation between preset σA values did not appear to improve the fit and reduce δ significantly; in such cases, improvements in the fit of simulated values to experimental data turned out to be within experimental error. As before, when the peak experimental temperature Th exceeds Td, weight loss due to stage B processes is added to that due to stage A processes (eq 16). A similar algorithm was then used for calculating values of k0B,

E0B, and σB. A detailed description of the codes has been given elsewhere.15 Calculations were executed in FORTRAN-77 on a DEC Alpha 3000 workstation; calculation of k0 and E values corresponding to the best fit for the singlereaction model required several minutes. For the multiple-reaction model, however, several hours were required to calculate the kinetic parameters corresponding to the best fit. Results and Discussion Liquefaction Conversions. Table 2 presents experimental coal weight loss data as a function of temperature. As can be seen from a comparison of the results between 350 °C (1600-s hold) and 375 °C (400-s hold), all samples except Point of Ayr (U.K.), Upper Freeport, and Pocahontas No. 3 coals gave significant increases in weight loss over the interval, suggesting that for these three coals Td may be somewhat higher than 350 °C: for these three coals, 375 °C was used as Td to delineate stage A and stage B in the kinetic models. The large conversions of Upper Freeport coal at relatively low temperatures (Table 2) are consistent with the 59.4% extraction yield of this coal in a mixture of CS2 and 1-methyl-2-pyrrolidinone at room temperature;12 in that series of experiments, the next largest extraction yield was reported as 39.2% for Pittsburgh No. 8 coal. It may also be noted that while conversion of most coals at 450 °C (400-s hold) was close to the “ultimate” conversion obtained at the same temperature with a 1600-s hold, the conversion of Pocahontas No. 3 coal increased quite substantially during holding between 400 and 1600 s. Longer holding time experiments may eventually be required for this coal. Figure 5 presents the development of sample weight loss profiles for the set of samples as a function of elemental carbon content and increasing reaction temperature and time. Conversions under the most intense reaction conditions (400- and 1600-s hold at 450 °C) traced the expected (e.g. cf. ref 16) maximum near the middle of the coal rank range. However, patterns observed under conditions of intermediate reaction intensity appeared to owe much to individual variations between the coals. It would be reasonable to expect interrelationships between pore structure evolution with temperature and the intrinsic reactivity and solubility of the original coal mass to affect the temperature dependence of liquefaction yields for particular coals. The anomalous behavior of Upper Freeport and Pocahontas coals in this respect may reflect no more than differences in the morphological characteristics of the two coals, the first with an open initial pore structure and the latter with pores that dilate mostly upon exposure to relatively high temperatures for relatively long times. However, the present data, and model, do not allow one to distinguish between the effects due to intrinsic reactivity and the development of pore structure with changing reaction conditions. Kinetic Parameters. Table 3 presents kinetic parameters calculated using the single-reaction model (eqs 4 and 5); activation energy values for stage A processes, EA, were found to be considerably smaller than those for stage B processes, EB.

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Xu and Kandiyoti

Table 2. Primary Liquefaction Yields of a Set of Rank-Ordered Coal Samples in the Flowing-Solvent Reactora wt loss (w/w, %, daf) coal sample Beulah-Zap Wyodak-Anderson Illinois No. 6 Blind Canyon Pittsburgh No. 8 Point of Ayr (U.K.) Upper Freeport Pocahontas No. 3

holding temp (°C): holding time (s):

300 400

350 400

350 1600

375 400

400 400

425 400

450 400

450 1600

17.4 25.0 24.6 22.9 26.6 17.0 39.7 9.0

31.1 35.0 47.3 35.4 41.5 24.6 51.9 24.0

40.6 38.6 54.7 37.9 55.2 36.0 57.9 29.8

46.7 45.2 61.6 48.6 56.4 27.0 58.7 27.3

55.2 62.0 79.8 73.0 71.6 47.0 67.0 32.7

68.3 73.1 89.0 84.4 84.7 72.5 75.0 39.8

75.0 82.0 90.0 91.0 84.2 82.5 81.8 43.5

84.0 88.6 94.7 92.0 89.0 84.0 86.0 70.0

a Samples were heated in tetralin at 5 K s-1 to the holding temperatures and held for 400 s (except where indicated); solvent flow rate was maintained at 0.9 mL s-1 at 70 bar (g).

Figure 5. Liquefaction yields (weight loss) as a function of elemental carbon content at different liquefaction conditions (Table 2).

With the exception of Pocahontas No. 3 coal, EA values in Table 3 were found to vary within a relatively narrow band with no discernible pattern, suggesting a degree of similarity between rate-limiting steps in this temperature range. Most of the actual EA values appear somewhat low, even for diffusion-limited processes. These energies of activation may be attributable to processes involving desorption and dissolution of smaller molecular mass and/or less polar materials within the coal mass. It may be noted, however, that the lowest EA value in Table 3 was found for Point of Ayr coal, the sample for which conversions were found not to change when the particle size was more than doubled (see above). Similar diffusional resistance checks on coals with higher EA values may lead to different conclusions concerning diffusion limitations, particularly for the highest rank sample in the present set. Energies of activation for the higher temperature range (Td up to 450 °C) stage B processes, during which extensive covalent bond scission is expected to contribute to the dissolution of the coal mass, were found to lie between 124 and 238 kJ mol-1. The sharp difference between the ranges of EA and EB values found in these calculations confirm the validity and indeed the necessity of the added complications involved in introducing a two-stage model. Descriptions of coal liquefaction in terms of a single activation energy, which is expected to span the range of processes taking place between ambient and peak temperature, would appear to conceal at least one distinct and important transition. Nevertheless, values at the lower end of the EB range were smaller than would have been expected compared to values of bond dissociation energies and

activation energies calculated in previousspyrolysis relatedswork.23,24 Table 4 presents kinetic parameters calculated using the multiple parallel independent reaction model for both stages of the process. From a comparison of the parameters calculated from the two models (Tables 3 and 4), it may be observed that mean activation energies for stage A processes (T < Td) calculated using the multiple parallel independent reaction model were only slightly larger than those calculated from the singlereaction model. This result suggests that the number and nature of independent pathways involved in stage A processes are indeed probably fairly limited. The spread of activation energies, characterized by the standard deviations of the distributions, σA, were found to be correspondingly narrow; the steady decline of absolute σA values with increasing coal rank (with the exception of the two low-rank samples) could be interpreted in terms of the simplification of structural features with increasing coal maturation (also see below). Activation energies for stage B processes (covering temperatures above the onset of extensive covalent bond scission: T > Td), however, differ sharply from results calculated using the single-reaction model. The mean activation energy values were found to be considerably greater, with an overall range between 160 and 275 kJ mol-1. Recalling that the activation energy for the bibenzyl cracking reaction25 has been reported as 201 kJ mol-1 (235 kJ mol-1; ref 26), the E0B values calculated for the present set of coals appear within a range that can be said to represent thermally induced bond scission.11 The initiation of radical formation by hydrogen-transfer-promoted radical activation27,28 could possibly be considered as a possible mechanism tending to lower activation energies during liquefaction in tetralin. In view of the multiplicity of parallel reaction pathways expected at temperatures above 350-375 °C, it seems physically reasonable that the single-reaction model (Table 3) should underestimate the mean energy of activation for stage B processes and that the absolute (23) Burnham A. K.; Myongsook S. Oh; Crawford, R. W.; Samoun, A. M. Energy Fuels 1989, 3, 42-55. (24) Gavalas, G. R.; Cheong, P. H-K.; Jain, R. Ind. Eng. Chem. Fundam. 1981, 20, 113-122. (25) Pullen, J. R. Solvent Extraction of Coal; IEA Coal Research: London, 1981; p 65. (26) Vernon, L. W. Fuel 1980, 59, 102; quoted in ref 25. (27) McMillen, D. F.; Malhotra, R.; Hum, G. P.; Chang, S-J. Energy Fuels 1987, 1, 193. (28) McMillen, D. F.; Malhotra, R.; Nigenda, S. E. Fuel 1989, 68, 380.

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Table 3. Comparison of Kinetic Parameters of the Set of Coal Samples (Single-Reaction Model) stage A

stage B

coal sample

Xma (w/w, daf)

xmA (w/w, daf)

K0A (s-1)

EA (kJ mol-1)

xmB (w/w, daf)

K0B (s-1)

EB (kJ mol-1)

Beulah-Zap Wyoming Illinois No. 6 Blind Canyon Pittsburgh No. 8 Upper Freeport Pocahontas No. 3 Point of Ayr (U.K.)

0.84 0.89 0.95 0.92 0.89 0.86 0.70 0.84

0.41 0.39 0.55 0.38 0.56 0.58 0.30 0.36

1.52 × 102 0.50 × 102 3.06 × 103 7.44 × 102 0.16 × 102 0.51 × 102 2.05 × 104 0.21 × 102

55.4 47.2 69.3 60.5 44.0 46.8 80.5 35.0

0.43 0.50 0.40 0.54 0.31 0.28 0.4 0.48

4.12 × 106 1.67 × 107 2.26 × 108 2.50 × 108 8.25 × 109 6.23 × 107 9.40 × 107 4.65 × 1015

124.0 130.4 142.5 142.7 161.2 139.4 150.0 238.0

a

Total mass loss after 1600 s at 450 °C. Table 4. Comparison of Kinetic Parameters of the Set of Coal Samples (Multiple-Reaction Model) parameters stage A stage B from pyrolysis experiments23 xmA Xm xmB (w/w, (w/w, (w/w, E0A (kJ σA E0B (kJ σB E0 (kJ σ (kJ daf) daf) K0A (s-1) mol-1) daf) K0B (s-1) mol-1) coal sample (kJ mol-1) (kJ mol-1) mol-1) mol-1)

Beulah-Zap Wyodak-Anderson Illinois No. 6 Blind Canyon Pittsburgh No. 8 Upper Freeport Pocahontas No. 3 Point of Ayr (U.K.) a

0.84 0.89 0.95 0.92 0.89 0.86 0.70 0.84

0.41 0.39 0.55 0.38 0.56 0.58 0.3 0.36

3.07 × 102 0.92 × 102 3.55 × 104 9.41 × 102 0.25 ×102 0.93 ×102 3.70 ×104 0.25 ×102

58.9 50.0 81.3 64.5 46.5 49.5 83.6 35.6

E0A/25 E0A/25 E0A/25 E0A/25 E0A/25 E0A/25 E0A/100 EA/25

0.43 0.50 0.40 0.54 0.31 0.28 0.40 0.48

2.23 × 1012 4.32 × 1011 2.32 ×1012 6.08 × 1013 1.97 × 1012 2.09 × 1016 4.94 × 108 1.97 × 1018

200.0 188.4 194.1 210.9 191.0 252.5 160.0 275.0

E0B/25 E0B/25 E0B/50 E0B/50 E0B/50 E0B/50 E0B/100 EB/100

232 263 210 196 205 262 222 n/aa

E0/38 E0/45 E0/45 E0/49 E0/54 E0/84 E0/57 n/a

n/a, not available.

values of σB in Table 4 should be larger than σA values. The trend of decreasing σB values (Table 4) with increasing coal rank may be viewed in terms of increasing structural uniformity and possibly increasing degrees of cross-linking accompanying coal maturation. In Table 4, the E0B value for Pocahontas No. 3 was lowest, while the value for Upper Freeport appears unexpectedly high. For these two coals, the values of E0A and E0B may not be unrelated. The greater product release from Upper Freeport coal at lower temperatures has already been mentioned; the high E0B value for Th > Td may be viewed in terms of the more difficult (more polar or more densely cross-linked or more completely occluded) fractions of the coal remaining behind to be extracted. The opposite trend may be attributed to the case of Pocahontas No. 3 coal. However, the high E0B value found for Point of Ayr coal does not fit the same pattern: this last result does reflect the consensus that this particular coal is not, after all, an “easy” one to liquefy. Provided that the kinetic procedure described in this study survives the test of time, the E0B values calculated by this method may serve to assist in investigations of coal structure as well as help to determine the suitability of individual coals for conversion by liquefaction. Simulation of Coal Weight Loss during Liquefaction. In all cases considered, the multiple parallel independent reaction scheme gave smaller matching δ values, compared to the single-reaction model, indicating smaller standard errors and closer fits. Visually, however, the fits were indistinguishable. In what follows, all diagrams were drawn using the singlereaction model. Figure 6 presents simulations of weight loss from Point of Ayr (U.K.) and Pittsburgh No. 8 coals as a function of temperature, showing the cumulative mass loss through stage A and stage B processes. It may be observed that for Point of Ayr coal, conversion through stage B processes eventually exceeded weight loss

Figure 6. Simulated liquefaction yields as a function of reaction holding temperature using the two-stage singlereaction model. The experimental data were obtained by heating the sample in tetralin at 5 K s-1, with a 400-s hold at the peak temperature. Solvent flow rate was maintained at 0.9 mL s-1 at 70 bar (g).

through stage A processes. By contrast, for Pittsburgh No. 8 coal, stage A processes gave more conversion. Comparing xmA and xmB values listed in Tables 3 and 4

+


Figure 7. Simulated liquefaction yields of Beulah-Zap as a function of reaction time using the two-stage single-reaction model. The experimental data were obtained by heating the sample in tetralin at 5 K s-1 to 450 °C with holding times up to 1600 s. Solvent flow rate was maintained at 0.9 mL s-1 at 70 bar (g).

Figure 8. Simulated liquefaction yields of Point of Ayr as a function of reaction time using the two-stage single-reaction model. The experimental data were obtained by heating the sample in tetralin at 5 K s-1 to 450 °C with holding times up to 1600 s. Solvent flow rate was maintained at 0.9 mL s-1 at 70 bar (g).

shows that, in this respect, no particular order has been found among the samples studied: stage B processes gave more product from Blind Canyon and WyodakAnderson. The greater conversion of Pocahontas No. 3 between 400 and 1600 s at 450 °C would place it in the same group, although much of it was observed to take place at long reaction times (see Figure 5). It may be recalled that xmA and xm values were obtained from experiment and that xmB ) xm - xmA. For all coals in the study, good internal agreement was obtained between simulated results and data not used in the calculation of the kinetic constants; these results have been presented in detail elsewhere.15 Figure 7 presents the simulated weight loss of Beulah Zap lignite as a function of time. The calculation assumes heating at 5 K s-1 from ambient (20 °C) to 450 °C with a 1600-s hold. A data point not used in the calculations has been plotted in the diagram (at 200 ssindicated with the arrow) as a test of the internal consistency of the model with the data. Figure 8 presents the analogous diagram for Point of Ayr (U.K.) coal weight loss as a function of time; the arrows indicate data points not used in the calculation of the kinetic constants.

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Xu and Kandiyoti

Figure 9. Simulated primary coal liquefaction processes of different coal samples in the flowing-solvent reactor using the two-stage single-reaction model.

Figure 9 presents simulated weight loss curves (5 K s-1 to 450 °C with variable hold times) for the set of samples, comparing relative speeds with which different coals achieve their ultimate (equilibrium) conversions. In this diagram, weight losses were normalized to indicate percent weight loss (daf) of the ultimate conversion (xm) value for each particular coal. Consistent with experimental data, two low-rank samples, BeulahZap lignite and Wyodak-Anderson coal, and the highrank Pocahontas No. 3 coal were found to be slowest in approaching their ultimate conversions. Comparison with Previous Studies of Coal Liquefaction Kinetics. The present calculation takes into account weight loss during heatup, distinguishes between two distinct stages in coal liquefaction with different activation energies, and shows that modeling the thermal breakdown step as a set of parallel independent reactions leads to apparently more realistic results: the latter assumption has been shown (Tables 3 and 4) to have a significant effect on calculated activation energies for stage B (thermal breakdown) processes. Clearly, a direct comparison with results of calculations from other work assuming (i) a single energy of activation and/or (ii) isothermal kinetics for the whole process is not entirely appropriate. Our findings should nonetheless be placed in the context of previous work by comparison with activation energies calculated in different investigations. Table 5 presents a short review of coal liquefaction activation energies found in the literature; the review is not meant to be exhaustive. A number of these investigations have reported Ea values that appear to be very low (e.g. refs 1 and 29-33). Differences in model formulation outlined above (i.e. modeling coal liquefaction as an isothermal process and in terms of single reactions) may help clarify some of the reasons underlying the nature of these results. However, a small number of studies, using models similar to those used in the latter studies, have reported Ea values similar to or greater than those found in the present work. These studies will be briefly reviewed. (29) Curran, G. P.; Struck, R. T.; Gorin, E. Ind. Eng. Chem. Process Des. Dev. 1967, 6, 167. (30) Brunson, R. J. Fuel 1979, 58, 203. (31) Wiser, W. H. Fuel 1968, 47, 475. (32) Cronauer, D. C.; Shah, Y. T.; Ruberto, R. G. Ind. Eng. Chem. Process Des. Dev. 1978, 17, 281. (33) Morita, M.; Sato, S.; Hashimoto, T. Prepr. Pap.sAm. Chem. Soc., Div. Fuel Chem. 1979, 24 (2), 63.

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Table 5. Summary of Some Previous Studies of Coal Dissolution Kinetics coal Utah HV

solvent/coal

temp (°C)

tetralin (10:1)

409-497 (pyrolysis) 350-450 (liquefaction) 324-387

definition of conversiona wt loss (pyrolysis) benzene solubles

activation energy (kJ mol-1)

ref

149 (2nd-order initial) 17.2 (1st-order later) 120.5 (2nd-order initial) 54.8 (1st-order later) Ea ) 125.5 (fast) Ea ) 159.0 (slow)

31

32

Pittsburgh seam (Ireland mine)

tetralin (4:1)

Belle Ayr (sub)

HAOb HPHb none

400-470

xylenol cyclohexane, benzene, cresol pentane, benzene, pyridine

400-440

benzene

coal f product E ) 70.0 (HAO) coal f product E ) 85.8 (HPH) “asphalt” hydrogen E ) 150

350-450

hexane benzene

coal f asphaltene E(calcd) ) 68.6 asphaltene oil E(calcd) ) 67.0

33

Utah Spring Canyon

recycle stream (330-380 °C), MoO3 catalyst tetralin (10:1)

350-450

benzene

2

Big Horn

process (3:2)

413-440

Makum

tetralin (1:1)

380-410

boiling ranges (heavy oil > 343 °C) benzene

Argonne PCS

1-MNb

375-425

E ) 134 from 0 to 90% reacted ∆H ) 155.6-358 coal f oil E ) 230 coal f furnace oil E ) 169.5 initial rx ) E ) 330.5 step 2 Ea ) 196.6 step 3 Ea ) 146.4 E ) 18-112 E ) 31.4-123.4

Pittsburgh seam (Bruceton mine) Miike

toluene THF

29

34, 35

36 37 1

aSolid residue washed (extracted) in stated solvent. b HAO, hydrogenated anthracene oil; HPH, hydrogenated phenanthrene; 1-MN, 1-methylnaphthalene.

Weller et al.34,35 used a rotating autoclave with a 1-h heatup time and an isothermal kinetic scheme: heating and cooling periods were assumed to add another 20 min to reaction time at peak temperature. They found that during the catalytic “hydrogenolysis” of an “anthraxylon” (vitrinite) fraction of Bruceton coal in the absence of liquid solvent, “reaction was so rapid” that “no accurate value for the activation energy. . .can be deduced”. While observing that “the simple Arrhenius relation. . .does not hold. . .”, these authors calculated an Ea value of 150 kJ mol-1 for the hydrogenation of an “asphalt” fraction, from results at 430 and 440 °C “for which the greatest accuracy in k′ was observed”. In an interesting early study, Hill et al. used a 1-L autoclave into which coal (Utah, Spring Canyon) was injected at the intended reaction temperature;2 the estimated 1-2-min heatup time quoted in their paper corresponds to a heating rate of about 3.5-7 K s-1. The authors tantalizingly state “that at the initial stage of the experiment, the reaction is under diffusion control. . .this process has a very low activation energy”. For purposes of the kinetic calculations, however, the coal was assumed to have reached the reaction temperature instantaneously; no account was taken of possible successive stages and weight loss during heatup. Nonetheless, the authors assumed a first-order dissolution process to take place in parallel with a second-order “extraction of interspersed materials” at the peak experimental temperature; activation energies of 212 and 109 kJ mol-1, respectively, were found. These results may be said to have foreshadowed findings reported in the present paper. In a second model developed within the same report,2 the “first order reaction velocity constant” was found to vary with the fraction extracted at constant temperature: a gradual increase in the “enthalpy of activation” from 156 to 358 kJ mol-1 with increasing conversion (nearly 90%) was

reported. The activation energy for the rate constant characterizing the initial rate at each temperature was found to be 134 kJ mol-1. The simpler reaction schemes and isothermal treatment of the kinetics in these authors’ work make it difficult to comment on observed changes in the reaction rate constant as a function of conversion. However, we have recently reported increasing molecular masses and increasing polynuclear aromatic ring system sizes with increasing intensity (and extent) of liquefaction at peak temperature6 (450 °C). Investigating the implications of these observations may well prove worthwhile. In modeling coal liquefaction (and subsequent reactions of extracts) in a “segmented-bed” reactor, Shah et al.36 reported a coal-to-gas Ea value of 357 kJ mol-1. It is straightforward to show that if intervening steps within a set of consecutive reactions are ignored (and provided that pre-exponential constants are of comparable magnitude), apparent energies of activation for the overall process may approach or even exceed the sum of the Ea values for the intervening reaction steps. The same study found Ea values closer to those in Table 4, of 230 and 169.5 kJ mol-1 for coal to “heavy oil” and coal to “furnace oil” conversion, respectively. In these calculations, isothermal kinetics and a single-stage coal dissolution step have been assumed; however, the results are more difficult to interpret than most since the presence of a preheater (operating at an unspecified temperature) was indicated. During their coal liquefaction experiments in tetralin, Gun et al.37 have also observed the reaction order and the energy of activation to change with time. These workers used a 2-L stirred autoclave and assumed isothermal kinetics. The order of the reaction rate was found to change from initial values of 1.0-1.2 to 2.02.2 and then to decrease to between 0.6 and 1.0; activation energies during this three-step process were

(34) Weller, S.; Pelipetz, M. G.; Friedman, S. Ind. Eng. Chem. 1951, 43, 1575. (35) Weller, S.; Pelipetz, M. G.; Friedman, S. Ind. Eng. Chem. 1951, 43, 1572.

(36) Shah, Y. T.; Cronauer, D. C.; McIlvried, G. G.; Paraskos, J. A. Ind. Eng. Chem. Process Des. Dev. 1978, 17, 288. (37) Gun, S. R.; Sama, J. K.; Chowdhury, P. B.; Mukherjee, S. K.; Mukherjee, D. K. Fuel 1979, 58, 171.

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given as 332.5, 196, and 146 kJ mol-1, respectively; Ea values were reported to decrease with increasing reaction time. In view of the large thermal inertia of their reactor and the assumption that “experimental zero time” was assigned to the time when reaction temperature had been reached, it seems difficult to comment on these results in any detail. Comparison with Kinetic Parameters Calculated from Pyrolysis Experiments. Similarities and differences between thermal breakdown in coal during the initial stages of coal pyrolysis and liquefaction have recently been discussed.17 Generally, pyrolysis yields are even more sensitive than liquefaction conversions to reactor design, and Ea values reported in the literature cover a wide spectrum.13 Total volatile yields from pyrolysis are also considerably lower than conversions normally expected from liquefaction. A comparison of energies of activation between pyrolysis and liquefaction experiments is only defensible (i) if it can be assumed that thermal breakdown constitutes the rate-limiting step in product release during pyrolysis and (ii) to the extent that stage B processes represent thermal breakdown in the liquefaction of coals. Within the present context, the first of these assumptions is not entirely justifiable: in addition to extensive recombination reactions, internal tar migration and tar release by mass transfer from external surfaces have been considered as significant resistances to product release from coal particles.38,39 Recombination reactions and diffusion limitations do not appear to affect the present liquefaction conversions, in any case not to the same extent. It may nevertheless be instructive to compare activation energies from the present liquefaction work and pyrolysis experiments from a study on similar coal samples in which a multiple parallel independent reaction model has been used. The last column of Table 4 presents energies of activation and σ values (with units adapted to the present study) from the pyrolysis of the Argonne PCSP coals; a Rock-Eval reactor was used in these experiments.23 The latter apparatus is not thought to be as free from extraparticle secondary reactions as “droptube” or “wire-mesh” (heated-grid) instruments.13,18 Comparing results with those from the present liquefaction study indicates somewhat higher pyrolysis E0 values and some individual differences, notably for Wyodak and Pocahontas No. 3 coals. The results nevertheless appear to show energies of activation to be within the same range. σ values calculated from the pyrolysis data covered a narrower range, but progressively diminished with increasing rank, in line with the trend observed from liquefaction results in the present study. Summary and Conclusions A set of equations has been formulated enabling the calculation of reaction rate parameters for coal weight loss during the liquefaction process. The model explicitly accounts for product release during heatup and stages of the process prior to (stage A) and following (38) Unger, P. E.; Suuberg, E. M. Proceedings of the 18th Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1981. (39) Suuberg, E. M. In Chemistry of Coal Conversion; Schlosberg, R. H., Ed.; Plenum: New York, 1985; p 67.

Xu and Kandiyoti

(stage B) the onset of extensive covalent bond scission, leading to the calculation of different activation energies for the two stages. Accompanying experiments have been carried out in a flowing-solvent reactor, which allows products released from coal to be rapidly and continuously removed from the reaction zone. Experiments were carried out with Point of Ayr (U.K.) coal and seven of the Argonne PCSP19 coals. In the simpler version of the present model, both stage A and stage B have been modeled as single activation energy, irreversible first-order processes. In the fully developed model, both stage A and stage B of the liquefaction process were considered to proceed by means of multiple parallel independent irreversible first-order processes with a Gaussian distribution of activation energies.13 Numerical procedures for calculating the kinetic constants have been described. Principal results and conclusions from the investigation may be summarized as follows: 1. Kinetic parameters calculated using the singlereaction model show activation energies for stage A (dissolution) processes (in the 35-80 kJ mol-1 range) to be considerably smaller than those for stage B (thermal breakdown) processes (between 124 and 238 kJ mol-1). This result indicates the validity and necessity of the added complications involved in introducing a two-stage model. Descriptions of coal dissolution in terms of single activation energies spanning the entire temperature range from ambient to peak temperature would appear to mask a distinct and important transition during the coal liquefaction process. Comparable liquefaction studies based on isothermal kinetics, single reactions, and a single-stage model of liquefaction were found to give values ranging from 18 to 358 kJ mol-1. 2. Compared to the single-reaction model, the multiple-reaction model provided improved fits with experimental data over the range of reaction conditions. Mean activation energies for stage A processes (T < Td) were only slightly larger that those calculated from the singlereaction model, suggesting that the number and nature of independent pathways involved in stage A processes are probably quite limited. The spread of activation energies, characterized by the standard deviations of the distributions, σA, were found to be correspondingly narrow. Activation energies for stage B processes (covering temperatures above the onset of extensive covalent bond scission: T > Td) calculated by the multiple-reaction model, however, were significantly greater than those calculated using the single-reaction model, with an overall range between 160 and 275 kJ mol-1. In view of the multiplicity of parallel reaction pathways expected at temperatures above 350-375 °C, it appears physically reasonable that the single-reaction model should underestimate mean energies of activation for stage B processes. The absolute values of σB (spread of activation energies) decreased with increasing coal rank, apparently reflecting increasing structural uniformity and possibly increasing degrees of cross-linking accompanying coal maturation. 3. Within the limits of the considerable differences between liquefaction and pyrolysis processes, qualitative agreement has been found with activation energies calculated for the pyrolysis of similar samples. The

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values derived from pyrolysis experiments tended to have somewhat higher values. In line with those from the present liquefaction results, the range of σ values (standard deviations of the energy of activation distributions) from the pyrolysis experiments were reported to progressively diminish with increasing rank. Nomenclature EA ) activation energy of stage A processes (kJ mol-1) E0A ) mean value of Gaussian distribution of activation energies of stage A processes EB ) activation energy of stage B processes (kJ mol-1) E0B ) mean value of Gaussian distribution of activation energies of stage B processes kA ) reaction rate constant for stage A processes k0A ) pre-exponential factor of reaction constant for stage A processes kB ) reaction rate constant of stage B processes k0B ) pre-exponential factor of reaction constant for stage B processes kh ) heating rate (K s-1) M ) number of experimental data R ) gas constant (8.314 kJ mol-1 K-1) t ) reaction time (s) T0 ) ambient (room) temperature (K) T ) reaction temperature (K), during heatup Td ) onset temperature of thermal decomposition Th ) peak experimental (holding) temperature (K)

Energy & Fuels, Vol. 10, No. 5, 1996 1127 th ) holding time at peak experimental (holding) temperature (s) X ) weight loss at reaction time t, (wt %, daf) xA ) weight loss resulting from stage A processes at reaction time t, (wt %, daf) xmA ) ultimate weight loss resulting from stage A processes (wt %, daf) xB ) weight loss resulting from stage B processes at reaction time t, (wt %, daf) xmB ) ultimate weight loss resulting from stage B processes (wt %, daf) xj ) simulated weight loss of a single coal particle calculated using kinetic parameters xj* ) corresponding experimental weight loss data point σA ) standard deviation value for Gaussian distribution of activation energies for stage A processes σB ) standard deviation value for Gaussian distribution of activation energies for stage B processes δi ) statistical least-squares standard error for data simulation using (ki0A, EiA)

Acknowledgment. We thank Raymond Chan for assistance in parts of the experimental work and G. M. Kimber for helpful discussions. Support for this work by the European Union under Research Contract ECSC 7220-EC/862 is gratefully acknowledged. EF9600265

Two-Stage Kinetic Model of Primary Coal Liquefaction | Energy & Fuels

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