A Novel Orthogonal Microscope Image Analysis Method for Evaluating

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Energy & Fuels 1998, 12, 881-890

881

A Novel Orthogonal Microscope Image Analysis Method for Evaluating Solvent-Swelling Behavior of Single Coal Particles Hong Gao, Levent Artok, Koh Kidena, Satoru Murata, Masahiro Miura, and Masakatsu Nomura* Department of Applied Chemistry, Faculty of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan Received December 10, 1997. Revised Manuscript Received May 27, 1998

A novel orthogonal microscope image analysis method was developed to observe and evaluate quantitatively the dynamic solvent-swelling behavior and characteristics of coal particles separated using density gradient centrifugation technique. The important results obtained using the new method are as follows: (1) The maximum statistic probability of anisotropic swelling ratio from 1.1 to 1.3 measured in this work agrees very well with the data measured by Cody et al.; in addition, the samples with high vitrinite concentrate and high swelling ratios seem to have high anisotropic swelling feature. (2) The existence of a characteristic distribution of volumetric swelling ratio in the vitrinite concentrates strongly suggests the existence of a characteristic distribution of the molecular weight between cross-link points. (3) The average volumetric swelling ratios measured using the new method are comparable to that measured by the traditional packed bed method. (4) The simulated results using modified Painter’s disinterspersion model based on the measured characteristic swelling ratios suggest that each cluster has aromatic and hydroaromatic rings from 1 to 3 in PDC-HV coal and from 1 to 5 in Witbank coal. Moreover, the relatively short average virtual bond length per carbon atom and the random walk of the chains are the main features of the coals in pyridine. (5) Although the case II and super-case II are dominant as for diffusion of pyridine in the coal particles, a few cases of Fickian and anomalous diffusion are also existing for two kinds of coal. In addition, because the value of diffusion exponents, n, of some PDC-HV coal samples changes from 0.22 to 0.39, which does not match to any classical diffusion mechanism, it seems to be the reflection of one diffusion mechanism.

Introduction Coal is a complex and heterogeneous material. This heterogeneity leads to difficulties in accurately characterizing its structure, and there is no universally accepted model for the molecular structure of coal. However, it appears to have been generally accepted that coal consists of alkyl chain substituted aromatic and hydroaromatic units linked by covalent bonds and noncovalent bonds such as hydrogen bonding and van der Waals interactions, with entanglements of skeletal chain structure to form a three-dimensional network structure.1-4 Apart from its three-dimensional crosslinked macromolecular structure, coal is viscoelastic and partially dissolves in, and swells when exposed to, some solvents (pyridine, quinoline, 2-methylpyrrolidinone or in combination with carbon disulfide, and so on). The extent of swelling is thought to be controlled by the cross-link density and the magnitude of interaction of coal macromolecule with the solvent.5-7 (1) Van Krevelen, D. W. Coal; Elsevier: Amsterdam, 1994. (2) Lucht, L. M.; Peppas, N. A. Fuel 1989, 66, 803. (3) Vahrman, M. Fuel 1970, 49, 5. (4) Spence, J. A.; Vahrman, M. Fuel 1970, 49, 395. (5) Sanada, Y.; Honda, H. Fuel 1966, 45, 295. (6) Marzec, A.; Kisielow, W. Fuel 1983, 62, 971.

The density of cross-link and the relative abundance of each type of cross-link may influence the behavior of coal in conversion processes, such as liquefaction, carbonization, and pyrolysis. An understanding of the knowledge about the nature and density of cross-link is important for effective utilization of coal resource. In general, cross-link density is evaluated in terms of volumetric swelling ratio (Qv), defined simply as the swollen sample volume divided by the unswollen sample volume. Four kinds of measurement methods have been adopted in the evaluation of coal swelling: (1) volumetric measurement based on packed bed,8-11 (2) gravimetric measurement using solvent sorption from the vapor phase,12 (3) a microscopic observation coupled with image analysis,13-18 and (4) Malvern laser diffrac(7) Mastral, A. N.; Izquierdo, M. T.; Rubio, B. Fuel 1990, 69, 892. (8) Liotta, R.; Brons G.; Isaacs, J. Fuel 1983, 62, 781. (9) Larsen, J. W.; Green, T. K. Fuel 1984, 63, 1538. (10) Ndaji, F. E.; Thomas, K. M. Fuel 1993, 72, 1525. (11) Aida, T.; Squires, T. G. Prepr. Pap.sAm. Chem. Soc., Div. Fuel Chem. 1985, 30, 95. (12) Hsieh, S. T.; Duda, J. L. Fuel 1987, 66, 170. (13) Shibaoka, M., Stephens, J. F., Russell, N. J. Fuel 1979, 58, 515. (14) Brenner, D. Fuel 1984, 63, 1324. (15) Brenner, D. Fuel 1985, 64, 167. (16) Cody, G. D.; Larsen, J. W.; Siskin, M. Energy Fuels 1988, 2, 340.

S0887-0624(97)00224-7 CCC: $15.00 © 1998 American Chemical Society Published on Web 07/28/1998

882 Energy & Fuels, Vol. 12, No. 5, 1998

tion method based on the measurement of particle size distribution (PSD).18,19 On the other hand, many researchers addressed questions to the coal structures associated with the coal macromolecular network and its interactions with particular solvents by using proton NMR,20 proton NMR microscopy,21 NMR imaging and NMR spectroscopy,22,23 3D NMR microscopic imaging,24 1H spin-echo NMR,25 1H and 2H NMR,26 small-angle neutron scattering (SANS),27 and C-NEXAFS microanalysis and scanning X-ray microscopy.28 In addition, there are some researchers addressing the analysis of the coal macromolecular network structure, kinetics of coal solvent swelling, and mechanisms of solvent diffusion by using traditional volumetric techniques.10,45-57 Each method proposed for the evaluation of swelling behavior of coals in solvent is subject to inherent limitations. For example, there is an implicit assump(17) Gao, H.; Nomura, M.; Murata, S. Prepr. Pap.sAm. Chem. Soc., Div. Fuel Chem. 1997, 298. (18) Turpin, M.; Rand, B.; Ellis, B. Fuel 1996, 75, 107. (19) Milligan, J. B.; Thomas, K., M.; Crelling, J. C. Energy Fuels 1997, 11, 364. (20) Lynch, L. J.; Sakurovs, R.; Webster, D. S.; Redlich, P. J. Fuel 1988, 67, 1036. (21) Hatcher, P. G.; Hou, L.; Gravina, S. J.; Mattingly, M. A. Fuel 1992, 71, 1203. (22) Cody, G. D.; Botto, R. E. Energy Fuels 1993, 7, 561. (23) Hou, L.; Cody, G. D.; French, D. C.; Botto, R. E.; Hatcher, P. G. Energy Fuels 1995, 9, 84. (24) French, D. C.; Dieckman, S. L.; Botto, R. E. Energy Fuels 1993, 7, 90. (25) Xiaolin, Y.; Larsen, J. W.; Silbernagel, B. G. Energy Fuels 1993, 7, 439. (26) Xiaolin, Y.; Silbernagel, B. G.; Larsen, J. W. Energy Fuels 1994, 8, 266. (27) Cody, G. D.; Thiyagarajan, P.; Botto, R. E.; Hunt, J. E.; Winans, R. E. Energy Fuels 1994, 8, 1370. (28) Cody, G. D.; Botto, R. E.; Ade, H.; Behal, S.; Disko, M.; Wirick, S. Energy Fuels 1995, 9, 75. (29) Larsen, J. W., Green, T. K.; Kovac, J. J. Org. Chem. 1985, 50, 4729. (30) Nishioka, M.; Larsen, J. W. Energy Fuels 1990, 4, 100. (31) Liotta, R.; Brons, G.; Isaacs, J. Fuel 1983, 62, 781. (32) Green, T. K.; Kovac, J.; Larsen, J. W. Fuel 1984, 63, 935. (33) Otake, Y.; Suuberg, E. M. Fuel 1989, 68, 1609. (34) Cody, G. D.; Davis, A.; Hatcher, P. G. Energy Fuels 1993, 7, 463. (35) Cody, G. D.; Davis, A.; Hatcher, P. G. Energy Fuels 1993, 7, 455. (36) Green, T. K.; Larsen, J. W. Fuel 1984, 63, 1538. (37) Larsen, J. W.; Flowers, R. A.; Hall, P. J.; Carlson, G. Energy Fuels 1997, 11, 998. (38) Painter, P. C.; Graf, J.; Colemen, M. M. Energy Fuels 1990, 4, 379. (39) Painter, P. C.; Park, Y.; Sobkowiak, M.; Colemen, M. M. Energy Fuels 1990, 4, 384. (40) Painter, P. C.; Graf, J.; Colemen, M. M. Energy Fuels 1990, 4, 393. (41) Faulon, I. L. Energy Fuels 1994, 8, 1020. (42) Suuberg, Eric M.; Otake, Y.; Langer, M. J.; Leung, K. T.; Milosavljevic, I. Energy Fuels 1990, 4, 393. (43) Solum, M. A.; Pugmire, R, J.; Grant, D. M. Energy Fuels 1989, 3, 187. (44) Dryden, I. G. C. Fuel 1951, 30, 39. (45) Motsegood, A. G. W.; Clarkson, R. B. Fuel 1993, 72, 1235-1237. (46) Green, T. K.; Kovac, J.; Brenner, D.; Larsen, J. W. In Coal Structure; Meyer, R. A., Ed.; Academic Press: New York, 1982. (47) Lynch, L. J.; Peppas, Nikolaos A. Fuel 1987, 66, 803. (48) Ritger, Philip L.; Peppas, Nikolaos A. Fuel 1987, 66, 815. (49) Hall, Peter J.; Thomas, K. M.;. Marsh, H. Fuel 1988, 67, 863. (50) Ritger, Philip L.; Peppas, Nikolaos A. Fuel 1987, 66, 1379. (51) Barton, W. A.; Lynch, L. J. Energy Fuels 1989, 3, 402. (52) Barton, W. A.; Lynch, L. J. In 1989 International Conference on Coal Science; NEDO: Tokyo, 1989; pp 13-16. (53) Sakurovs, R.; Lynch, L. J.; Barton, W. A.; In Coal Science II; Schobert, H. H., Bartle, K. D., Lynch, L. J., Eds.; Symposium Series 461; American Chemical Society: Washington, DC, 1991; p 111. (54) Hall, P. J.; Thomas, K. M.; Marsh, H. Fuel 1992, 72, 1271. (55) Ndaji, Francis E.; Thomas, K. M. Fuel 1992, 72, 1531. (56) Suuberg, E. M.; Otake, Y.; Langner, M. J.; Leung, K. T.; Milosavljevic, I. Energy Fuels 1994, 8, 1247. (57) Ndaji, F. E.; Thomas, K. M. Fuel 1995, 74, 842.

Gao et al.

tion in the standard packed bed method that the fractional void of the swollen bed is the same as that of the dry bed. As was pointed out by Turpin et al.,18 in the dry bed the particles are hard and glassy and are suspended in a large contrast density. During centrifugation, compacting is aided by the high force but is impeded by the hard, glassy, and unyielding nature of the particles. In the swollen coal, the particles are probably rubbery14 and are suspended in a relatively low density contrast. The compacting force is therefore much reduced, but compacting is aided by the rubbery and yielding nature of the particles. A more important problem existing in volumetric techniques is the evaluation of the cross-link density of the macromolecular level with a packed bed in which the topological features of particles and interactions among the particles are not yet clear. Another problem with volumetric techniques is that the soluble fraction is present in coals. When the solvent is introduced into the coal sample bed, a significant amount of dissolution occurs, resulting in reduction of solvent activity. This problem is not yet solved well. Therefore, it is clear that there is a need for a more reasonable and more precise method for the measurement of coal swelling in solvent on the real macromolecule level. One microscope coupled with an image analysis13-18 and PSD measurement using the Malvern laser diffraction method18,19 were used for evaluating the coal swelling in solvent. The important problem using one microscope is associated with its inability for detecting three-dimensionally the anisotropic swelling nature of coal particles. The PSD method offers a significant advantage over the volumetric method, since the ambiguity of the packing of the particle bed is removed, and the method can employ a concentration of coal particles which is sufficiently low for solubilization not to remarkably affect the solvent activity. However, two implicit assumptions were made in this approach: particles of all sizes swell to the same average extent, and the particles must not fracture or agglomerate during swelling. In our recent work, we have observed clearly that some coals fracture during the solventswelling procedure and the coal particles do not swell to the same extent.17 Another shortcoming of the PSD method is that the kinetics data of coal swelling in solvent cannot be obtained easily. On the other hand, except for the works by Cody et al.16 and Milligan et al.,19 all studies mentioned above that used any of techniques given above are average methods and neglect the heterogeneous nature of coals by making the assumption that all coal particles swell to the same extent. However, it may not be the case as was observed by Cody et al.16 It is also not the case implied by Milligan and Thomas et al.,19 since they observed skewed function from the solvent-swelling measurement of maceral concentrates by the PSD method. There is no explicit evidence for this phenomenon, and this ambiguity can be eliminated by microscopically observing the swelling behavior of single particles from multiple directions. Herein, we propose a novel orthogonal microscope image analysis method to improve the measurement of the real volumetric swelling ratio and swelling kinetics of coal particles in organic solvent, and we evaluate the swelling behavior of coal particles having different

A Novel Method for Evaluating Solvent Swelling

Energy & Fuels, Vol. 12, No. 5, 1998 883

Table 1. Petrographic, Ultimate, and Proximate Analyses of the Coals and Their DGC Samples

coal Witbank (W)

PDC-HV (PH)

a

sample W0 W1 W2 W3 W4 PH0 PH1 PH2 PH3 PH4

density, g cm-3 nmg

>1.38 1.30-1.38 1.25-1.30 1.38 1.30-1.38 1.25-1.30 liptinite > inertinite. To quantitatively describe the solvent-swelling behavior of very heterogeneous coal on the macromolecule level, it is not sufficient to use only the average value

886 Energy & Fuels, Vol. 12, No. 5, 1998

Figure 5. Characteristic distributions of the volumetric swelling ratio of PDC-HV coal samples in pyridine at ambient temperature.

of raw coal. In the present work, the statistical distribution characteristics of the equilibrium swelling ratio of eight DGC samples from two kinds of coal were measured and are shown in Figures 5 and 6. The general feature of the statistical probability distributions of the volumetric swelling ratio is the existence of characteristic multimodal distribution in all samples. In addition, except for W4, the maximum peaks of the distributions shift to high swelling ratio with the increase of vitrinite concentration. In the cases of PH coal, the statistical probability distribution of the equilibrium swelling ratio can be divided into five characteristic zones according to the swelling ratio and statistical probability: (1) with swelling ratio from 1.0 to 1.4, (2) with swelling ratio from 1.4 to 2.2, (3) with swelling ratio from 2.2 to 2.8, (4) with swelling ratio from 2.8 to 3.4, and (5) with swelling ratio from 3.4 to 3.8. The samples with lower density (higher vitrinite concentration) had the zones with higher swelling ratio and high probability. As shown in Figure 5, the distribution of PH1 samples consists of the first three zones from 1 to 3, but zone 2 is dominant. The distribution of PH2 consists of the first four zones, but zones 2 and 3 are dominant. Those of PH3 and PH4 samples consist of zones from 2 to 5, but zone 3 is dominant and the area of zone 2 for PH4 is much smaller than that of PH3.

Gao et al.

Figure 6. Characteristic distributions of the volumetric swelling ratio of Witbank coal samples in pyridine at ambient temperature.

In the cases of W coal, the distribution curves of the equilibrium swelling ratios can also be divided into five characteristic zones according to the swelling ratio and statistical probability: (1) with swelling ratio from 1.0 to 1.6, (2) with swelling ratio from 1.6 to 2.22, (3) with swelling ratio from 2.22 to 2.8, (4) with swelling ratio from 2.8 to 3.4, and (5) with swelling ratio from 3.4 to 3.8. The distributions of swelling ratios are different for some W samples compared to those of PH samples: the zone 1 of W3 samples is wider than that of PH samples. W3 samples with the highest vitrinite content (93.4%) and W4 samples still contain all four characteristic zones, and the probability of zone 1 is still rather high. On the other hand, the multinomial regression was also used to fit distributional swelling ratios. The statistically characteristic distributions of the volumetric swelling ratios of eight kinds of DGC coal samples can be expressed by multinomials with relatively high correlation coefficients (R2 ) 0.78-0.90 for PDC-HV and R2 ) 0.74-0.98 for Witbank). The characteristic peaks and their shift feature can also be clearly seen in these regression curves. It should be noted that the distributions of the equilibrium swelling ratio may be affected by the orientation of the anisotropic swelling with respect to a known frame of reference which is not measured using

A Novel Method for Evaluating Solvent Swelling

the orthogonal microscope technique proposed in this work. This problem will be solved by the development of a real three-dimensional microscope technique or a holographic microscope technique. On the other hand, the existence of a characteristic distribution of the equilibrium swelling ratio is partly due to the presence of other maceral constituents, but wide distribution of swelling ratios, even for high vitrinite concentrates, cannot be accounted for by maceral contamination. Eventually these findings strongly suggest the existence of, on average, a characteristic distribution of the molecular weight between cross-link points. Analysis of the Average Number of Carbons per Cluster and Average Number of Carbons between Cross-Link Points Using Modified Painter’s Disinterspersion Model. One of the goals of coal swelling studies is to obtain data that can be used to calculate intermolecular interaction parameters and the molecular weight between cross-link points, thus providing fundamental insight into coal structure. The swelling of coals by solvents has been extensively examined in recent years. However, there are a number of experimental difficulties and also questions concerning the degree of validity of the models that have so far been employed. Painter et al.38,39 considered the thermodynamics of mixing coals with solvent, extending the application of the Flory lattice model so as to include the effect of hydrogen bonding. Painter et al.40 indicated that the relatively stiff and presumably short nature of the chains present in coal precludes an application of any ideal network theory and proposed a model for coal swelling based on a process called “disinterspersion” to calculate “molecular weight” or the number of aromatic “clusters” between cross-link points under the assumption that rigid chains swell with little or no change in average conformation up to a limit imposed by the geometry of the network. An expression between the number of statistical aromatic units and the volume fraction of the swollen network is obtained, regarding the volume of chains present in a sphere surrounding a particular branch point. Faulon41 modified Painter’s disinterspersion model based on graph theory and the formula of Euler applied to polymer networks. Faulon’s corrections change the concept of average repeat unit to average repeat connecting link, which gives higher values of chain lengths, more in accord with results from the classical thermodynamic approach to swelling phenomenon. Recently, Suuberg et al.56 deeply discussed the implications of linear alkylamine swelling results for standard solvent-swelling theories, evidence for specific interaction sites in coals, correlation of swelling with heats of immersion, and effect of solvent activity on swelling, proposing a modified thermodynamics model for solvent swelling in specifically interacting media. To calculate the average molecular weight between crosslink points (Mc), both its initial value (Mc0) and the fraction of imbibed solvent molecules, which act to actually dissociate noncovalent cross-links, must be known. It is not yet possible to say what those values are without further information. In the same paper, Suuberg et al.56 indicated that

Energy & Fuels, Vol. 12, No. 5, 1998 887

Painter’s disinterspersion model is a very different type of swelling model recently having been advanced, although in adopting this different theoretical viewpoint, the need to have a solvent being able to replace coal-coal interactions with coal-solvent interactions remains. We observed that the most of coal particles measured seem to have a tendency to maintain their initial shape during swelling. These macroscopic phenomena seem to be a reflection of limited flexibility of cross-linked macromolecular networks. Therefore, to discuss simply the cluster sizes and cross-link nature using swelling data measured with new orthogonal microscope method, in this work we tentatively applied the modified Painter’s disinterspersion model, which is shown in eqs 7 and 8, for obtaining the knowledge of the relationship between the average number of carbons in aromatic and hydroaromatic clusters and the average number of carbons between cross-link points in the coals studied.

[

]

3fQv,eVc 1 ) nc 4πac3

1/(3v-1)

Nc(1-3v)/[3(v-1)] +

(2/f) - 1 (7) Nc

where nc is the average number of carbon atoms per average repeat aromatic unit, and f is the functionality of the cross-link points, on the order of 3 or 4 (here we assume f ) 3 as the number of bridges and loops in each aromatic cluster based on the 13C NMR measurement made by Solum et al.43). Qv,e is the characteristically distributed equilibrium swelling ratio in pyridine, and Vc is the molar volume of the nonswollen coal per carbon atom, which is given by eq 81

Vc ) 1200/%CdmmfF

(8)

where F is physical density. ac is average virtual bond length per carbon atom, ac ) 0.5-0.6 Å; υ is an exponent statistical factor which has values of 0.5 for a chain following random walk statistics, 0.6 for a self-avoiding walk, and 1 for an extended rigid rod; and Nc is the number of carbon atoms between cross-link points. The results calculated using the measured independent variables Qv,e, %Cdaf, and F are shown in Figures 7 (parts a-c) and 8 (parts a-c). Although we now do not have the data of the average number of carbons between the cross-link point for the samples with the characteristic distributed swelling ratio, using the calculated relations between nc and Nc we can obtain some important information about the DGC samples from two kinds of coal. As shown in the figures, the cluster size increases with the decreasing of equilibrium swelling ratio for the two kinds of coal. These results suggest that, for the same carbon atoms between cross-link point, the small clusters have higher potential for topological reorganization. Assuming f ) 3, ac ) 0.5, υ ) 0.5, and Nc ) 60 (Figures 7a and 8a), the cluster sizes are with 6-15 carbons for the typically characteristic swelling ratio of PH coal and 8-25 carbons for W coal. These results seem to be reasonable. Assuming f ) 3, ac ) 0.6, υ ) 0.6, and Nc ) 10 (Figures 7b and 8b), the average number of carbons per cluster is 2-5 for the typically characteristic swelling ratio of PH coal and 4-8 for W coal. These results seem not to be reasonable.

888 Energy & Fuels, Vol. 12, No. 5, 1998

Figure 7. Plots of the average number of carbon atoms per cluster (nc) versus the average number of carbon atoms between cross-link points (Nc) of PH samples (Cdaf ) 84.95, F ) 1.25 g/cm3).

Assuming f ) 3, ac ) 0.5, υ ) 0.6, and Nc ) 10 (Figures 7c and 8c), the average number of carbons per cluster for the typically characteristic swelling ratios of PH coal and W coal is smaller than 5 for PH coal and W coal. It is clear that they are not the real case for the coals. Painter et al.40 indicated that a value of ac close to 0.6 would appear to be the most probable. However, it seems not to be suitable for the coals studied in the present work. The results obtained suggest that each cluster seems to have aromatic and hydroaromatic rings from 1 to 3 in PDC-HV coal and from 1 to 5 in W coal. Moreover, the relatively short (ac ) 0.5) average virtual bond length per carbon atom and the random chains walk (υ ) 0.5) seem to be the main features of the coals studied. Kinetics of Solvent Diffusion in the DGC Samples. Another goal of coal swelling studies is to obtain kinetic swelling data that can be used to analyze the interaction between coal macromolecules and solvents and the solvent diffusion mechanism in coal macromolecules. Diffusion limitations are of concern in virtually all aspects of coal utilization. Over the past few years there have been quite a few of studies about the factors that influence diffusion.44-57 These studies have been mostly concerned with the transport of solvent through coals based on measurements of the packed bed. The diffusion of solvent into coals, as governs their swelling, has been noted by virtually all workers to be highly non-

Gao et al.

Figure 8. Plots of the average number of carbon atoms per cluster (nc) versus the average number of carbon atoms between cross-link points (Nc) of W samples (Cdaf ) 81.49, F ) 1.25 g/cm3).

Fickian in nature. Solvent uptake follows the generalized simple semiempirical expression (eq 9).48

Mt/Me ) ktn

(9)

Since the extent of solvent swelling is linearly related to mass uptake (eq 10), it is possible to relate the two quantities into eq 11.54

Mt/Me ) (Qv,t -1)/(Qv,e - 1)

(10)

(Qv,t - 1)/(Qv,e - 1) ) ktn

(11)

where Mt and Qv,t are the mass uptake of solvent and volumetric swelling ratio at time t, Me and Qv,e are the mass of solvent uptake and swelling ratio at equilibrium state, n is the diffusion exponent which is indicative of the solvent transport mechanism, and k is the relaxation constant. The initial values of n and k can then be obtained. Ritger and Peppas48 determined that for a spherical geometry, Fickian diffusion (which is dependent upon the diffusion coefficient across a concentration gradient), has n ) 0.43. Case II diffusion has n ) 0.85, in which a solvent uptake process is controlled by the relaxation of the macromolecular network structure, as opposed to diffusion itself. It is characterized by a sharp front separating the swollen and unswollen regions of

A Novel Method for Evaluating Solvent Swelling

Energy & Fuels, Vol. 12, No. 5, 1998 889

Table 3. Swelling Ratios (Qv,e), Diffusion Exponents (n), and Rate Constants (k) of PH Coal Samples in Pyridine at Ambient Temperature PH1

PH2

PH3

PH4

Qv,e

n

k(s-1 × 105)

Qv,e

n

k(s-1 × 105)

Qv,e

n

k(s-1 × 105)

Qv,e

n

k(s-1 × 105)

1.42 1.49 1.55 1.66 1.69 1.71 1.87 1.88 1.99 2.00 2.16 2.29 2.43 3.46

0.28 0.37 1.28 3.17 3.05 0.54 1.04 0.95 0.69 2.50 1.85 1.11 1.22 2.86

1547.95 1457.91 0.13 5.62 × 10-9 1.01 × 10-9 153.38 1.90 3.36 89.49 1.58 × 10-6 0.003 0.44 0.12 1.12 × 10-7

1.65 1.66 1.67 1.81 1.84 1.97 2.02 2.30 2.35 2.38 2.46 2.59 2.67 2.97

1.39 1.29 1.14 1.35 1.59 1.07 0.52 1.47 0.80 0.27 1.21 1.18 1.01 0.84

0.04 0.18 0.21 0.06 0.01 2.08 291.03 0.11 12.26 1035.80 1.92 0.54 0.72 7.88

1.65 1.75 1.99 2.05 2.20 2.30 2.35 2.39 2.44 2.55 2.78 2.86 2.96 3.10

1.21 0.30 0.89 0.65 1.11 1.62 0.69 2.19 0.91 1.47 2.07 1.66 1.33 1.98

0.37 1788.13 9.38 73.61 1.09 0.23 24.22 6.64 × 10-5 4.16 0.12 0.0001 0.004 0.098 0.0007

1.89 2.02 2.05 2.07 2.15 2.21 2.29 2.40 2.44 2.46 2.59 2.71 3.08 3.60

1.07 0.77 0.98 0.70 0.52 0.56 0.39 0.39 0.78 0.95 0.22 0.25 1.18 0.31

0.83 19.21 6.02 9.22 169.14 97.98 840.31 840.31 11.08 5.07 1586.45 1873.15 0.31 1803.71

Table 4. Swelling Ratios (Qv,e), Diffusional Exponents (n), and Rate Constants (k) of W Coal Samples in Pyridine at Ambient Temperature W1 Qv,e 1.25 1.29 1.31 1.34 1.38 1.46 1.53 1.64 1.70 1.80 2.02 2.33

n 1.01 1.08 0.65 0.82 1.28 1.31 2.72 1.89 1.05 1.70 2.69 1.91

W2 k(s-1

×

105)

12.35 6.43 295.09 70.46 61.20 645.29 8.55 × 10-6 0.003 7.81 0.02 3.70 × 10-6 0.003

Qv,e 1.37 1.42 1.51 1.55 1.56 1.60 1.61 1.77 1.82 1.83 2.00 2.85

n 2.59 0.59 1.57 2.25 2.12 2.64 2.31 2.38 3.37 3.33 5.17 1.51

W3 k(s-1

×

105)

Qv,e

n

10-5

1.27 1.29 1.38 1.44 1.63 1.74 1.92 1.96 2.10 2.12 2.36 2.39

1.20 0.84 1.09 1.15 1.48 1.12 0.58 1.98 1.09 1.14 1.05 0.54

1.40 × 460.78 0.12 0.0002 0.002 1.33 × 10-5 0.0001 8.11 × 10-5 5.49 × 10-8 7.53 × 10-8 2.66 × 10-14 0.06

the coal. Intermediate values correspond to an anomalous diffusion mechanism in which diffusion and relaxation rates are comparable. Values above n ) 0.85 are possible and are termed “super-case II”. Values of the diffusion exponent (n), obtained by analyzing the initial part of the graph of ln[(Qv,t - 1)/ (Qv,e - 1)] against ln t, and the relaxation constant (k) of the DGC coal samples with different equilibrium swelling ratios are shown in Tables 3 and 4. In the cases of PH coal samples, although case II and super-case II are dominant, a few of the Fickian and anomalous diffusions exist. In addition, the interesting result is that the value of n changes from 0.22 to 0.39 in some PH samples (especially in PH4 samples), this not matching to any classical diffusion mechanism. Moreover, the relaxation constants of these samples are much greater than those of other samples. The exponents being outside of the range previously reported seems to reflect one diffusion mechanism. This is an interesting result, and it is being investigated further now. In general, the case II and super-case II are dominant for W coal samples, although a small amount of anomalous diffusion is also existing. In addition, the values of n for some samples, especially W4 samples, are much larger than those of other samples. Their relaxation constant is very small. These results suggested that the relaxation of the macromolecular network structure for these samples is very fast and the macromolecular network structure of these samples seems to be very different from the other samples.. Ritger and Peppas48 indicated that for Fickian diffusion in a powder consisting of uniform spherical par-

W4 k(s-1

×

105)

10.00 69.81 8.65 10.00 0.31 10.00 259.05 0.001 10.00 3.95 2.36 226.18

Qv,e

n

k(s-1 × 105)

1.32 1.51 1.45 1.47 1.68 1.79 1.93 1.95 2.09 2.18 2.43 2.72

6.75 11.96 11.66 4.47 2.07 11.60 2.26 2.77 2.53 3.71 11.75 3.63

9.02 × 10-20 2.06 × 10-38 4.94 × 10-37 9.28 × 10-12 0.001 10.00 0.0002 7.86 × 10-6 1.22 × 10-5 1.52 × 10-9 9.96 × 10-38 1.10 × 10-9

ticles a plot of Mt/M∞ versus t1/2 (time dependence of solvent uptake) is only valid for the first 10-15% of the total solvent uptake. For case II diffusion, the empirical prediction of a linear time dependence of penetrate uptake is also valid only for the first 10-15% of the total sorption process. On the other hand, the significant “overshoot”, observable as an apparent decrease in swelling, was detected after maximum swelling in this work and previous works,16,17 which was not observed using traditional or modified volumetric techniques. These observations motivated the development of a more reasonable expression for the solvent-swelling process of coal particles. It will be presented in a forthcoming publication. From the above results, by using the new orthogonal microscope video camera image analysis method, we could obtain some very important information, which will refine our understanding of solvent-swelling behavior. However, it should be noted that the problem existing in the new method proposed is still caused by the orientation of the anisotropic swelling of coal particles with respect to a known frame of reference not being measured. The modification of the present technique will be our next work. Conclusions A novel orthogonal microscope video camera system coupled with an image analysis system was developed to observe and evaluate quantitatively the dynamic swelling behavior and characteristics of DGC coal samples in solvent. Some important results using the new proposed method are as follows.

890 Energy & Fuels, Vol. 12, No. 5, 1998

The maximum statistic probability of anisotropic swelling ratio from 1.1 to 1.3 for all particle samples agrees very well with the data measured by Cody et al.16 However, the range of anisotropic swelling ratios measured in this work is much wider, suggesting that anisotropic swelling of the coal particles has distribution nature. Moreover, the analysis on the characteristic distribution of the anisotropic swelling ratio of eight kinds of DGC coal sample suggests that the samples with high vitrinite concentrate and high swelling ratios have a high anisotropic swelling feature. The existence of characteristic multiple-peak distribution of the volumetric equilibrium swelling ratio in the coal samples with high vitrinite concentrates strongly suggests the existence of a characteristic distribution of the molecular weight between cross-link points. The average volumetric swelling ratios measured using the new method are comparable to those measured by the traditional packed bed method. These results indicate that the new method is effective even in the evaluation of average parameters of solvent swelling. The average number of carbons per cluster and average number of carbons between cross-link points analyzed using modified Painter’s interspersion model based on the measured characteristic swelling ratios suggest that the each cluster has aromatic and hydroaromatic rings from 1 to 3 in PDC-HV coal, and from 1 to 5 in Witbank coal. Moreover, the relatively short average virtual bond length per carbon atom is and the

Gao et al.

random walk of the chains are the main features of the coals in pyridine. On the other hand, the analysis on the phenomenologically experienced equations for the diffusion of pyridine in the eight kinds of DGC sample with different characteristic swelling ratios indicated that although case II and super-case II are dominant, a small amount of Fickian and anomalous diffusion also exist for two kinds of coal. The interesting result is that the value of diffusion exponents (n) for some PDC-HV coal samples (especially PH4) changes from 0.22 to 0.39, which does not match to any classical diffusion mechanism, reflecting one diffusion mechanism of pyridine in the coal. In addition, the diffusion exponents of some W samples (especially W4 samples) are much larger than those of other samples. Their relaxation constants are very small. These results suggested that relaxation of the macromolecular network structure for these samples is very fast and the macromolecular network structure for these samples seems to be much different from the other samples. Acknowledgment. We thank very sincerely Mr. T. Chikada and Mr. T. Yamamoto (Division of Ironmaking Process, Multiple Technique Institute, Sumimoto Metal Industry Co., Ltd., Japan) for providing the DGC coal samples with some analytical data. EF970224B