Temperature Dependence of Solvent Swelling and Diffusion

Kinetic Modeling of Coal Swelling in Solvent ... Industrial & Engineering Chemistry Research 2011 50 (5), 2562-2568 ... Sorption and Swelling in a Con...
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Energy & Fuels 1997, 11, 1155-1164


Temperature Dependence of Solvent Swelling and Diffusion Processes in Coals Yoshinobu Otake and Eric M. Suuberg* Division of Engineering, Brown University, Providence, Rhode Island 02912 Received January 31, 1997. Revised Manuscript Received August 22, 1997X

The rates of solvent swelling of the Argonne Premium Sample coals have been measured in various organic solvents at various temperatures. The results show that the extents of swelling, when experiments are carried out in liquid solvents, are independent of the temperature, within the temperature range studied here (10-60 °C). Thermodynamically, this requires that equilibrium swelling should occur with a near-zero enthalpy, as generally required for absence of a temperature effect on equilibrium. This conclusion is consistent with a number of other recently published results. The rates of swelling of the coals do not correlate with rank. The nature of the swelling process varies from relaxation controlled to Fickian diffusion controlled. The activation energies for the kinetics of swelling are consistent with other recently published values, but again, a correlation with rank could not be substantiated. The activation energies all fall in the range from 20 to 60 kJ/mol, suggesting that the activation barrier may be associated with the breakage of internal electron donor-acceptor (e.g., hydrogen bonding) interactions. Thermal pretreatment of some of the coals to 350 °C had significant effects on their swelling behaviors. The effect was generally to increase the rate of swelling, and in some cases, the extent of swelling. The activation energies for swelling were, however, unaffected. This is interpreted as consistent with the hypothesis that the activation energy barrier is determined by donoracceptor interactions which are unaffected by pretreatment but that other thermally dissociable coal-coal interactions may serve to stiffen its structure.

Introduction Diffusional limitations are of concern in virtually all types of coal processing. It is generally necessary to diffuse reactants into coals, and/or products or moisture out of coal particles at some point in any process. Often, there has been interest in diffusing organic solvents into coal, as in direct liquefaction or as part of some pretreatment step. As a result, over the past decade there have been a number of studies of the factors that influence diffusion in solid coals.1-25 The cited studies * To whom correspondence should be addressed. X Abstract published in Advance ACS Abstracts, October 1, 1997. (1) Ritger, P. L.; Peppas, N. A. Fuel 1987, 66, 1379. (2) Ritger, P. L.; Peppas, N. A. Fuel 1987, 66, 815. (3) Peppas, N. A.; Lucht, L. M. Chem. Eng. Commun. 1985, 37, 333. (4) Barr-Howell, B. D.; Peppas, N. A.; Winslow, D. Chem. Eng. Commun. 1986, 43, 301. (5) Olivares, J. M.; Peppas, N. A. Prepr. Pap.sAm. Chem. Soc., Div. Fuel Chem. 1990, 35(2), 292. (6) Barr-Howell, B. D.; Howell, J. M.; Peppas, N. A. Thermochim. Acta 1987, 116, 153. (7) Aida, T.; Squires, T. G. Prepr. Pap.sAm. Chem. Soc., Div. Fuel Chem. 1985, 30(1), 95. (8) Aida, T.; Fuku, K.; Fujii, M.; Yoshihara, M.; Maeshima, T.; Squires, T. G. Energy Fuels 1991, 5, 79. (9) Larsen, J. W.; Lee, D. Fuel 1983, 62, 1351. (10) Hsieh, S. T.; Duda, J. L. Fuel 1987, 66, 170. (11) Brenner, D.; Hagan, P. S. Prepr. Pap.sAm. Chem. Soc., Div. Fuel Chem. 1985, 30(1), 71. Also: Brenner, D. Prepr. Pap.sAm. Chem. Soc., Div. Fuel Chem. 1985, 30(1), 83. (12) Matturro, M. G.; Liotta, R.; Isaacs, J. J. J. Org. Chem. 1985, 50, 5560. (13) Green, T. K.; Kovac, J.; Brenner, D.; Larsen, J. W., Coal Structure; Meyers, R., Ed. Academic Press: New York, 1982; Chapter 6. (14) Green, T. K.; Ball, J. E.; Conkright, K. Energy Fuels 1991, 5, 609. (15) Hall, P. J.; Thomas, K. M.; Marsh, H. Fuel 1992, 72, 1271. (16) Cody, G. D.; Botto, R. E. Energy Fuels 1993, 7, 561. (17) Otake, Y.; Suuberg, E. M. Fuel 1989, 68, 1609.

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have been mostly concerned with transport of organic solvents. Others have been concerned with the transport of gases, such as methane, but these are not considered here. The studies of organic liquid diffusion have generally indicated that diffusion in coals is similar in many respects to the diffusion of solvents through glassy polymers. The process of relaxation of coal structure by the solvents plays an important role in determining how fast the coal can take up additional solvent. The rates of solvent uptake are strongly influenced by factors such as the nature of the coal, the size of the coal particles,1 the strength of the solvent,15,17,18 the size and shape of the solvent molecules,7,8,24 the temperature,5,6,17-19,23 the moisture content of the coal,19 and other features of its pretreatment.9,10,14,19-21 It is now well established that the kinetics of the solvent swelling process may be governed by either Fickian diffusion of the solvent through the coal structure, or the relaxation of the coal structure under socalled “Case II” conditions. These will be further described below. Therefore, swelling of coal occurs by processes that have been well documented for other macromolecular (polymeric) systems. (18) Otake, Y.; Suuberg, E. M. Proc. 1989 Int. Conf. Coal Sci. 1989, 1, 17. (19) Suuberg, E. M.; Otake, Y.; Yun, Y.; Deevi, S. C. Energy Fuels 1993, 7, 384. (20) Yun, Y.; Suuberg, E. M. Energy Fuels 1992, 6, 328. (21) Yun, Y.; Suuberg, E. M. Fuel 1993, 72, 1245. (22) Cody, G. D.; French, D. C.; Botto, R. E. Prepr. Pap.sAm. Chem. Soc., Div. Fuel Chem. 1994, 39 (1), 59. (23) Ndaji, F. E.; Thomas, K. M. Fuel 1993, 72, 1525 and 1531. (24) Ndaji, F. E.; Thomas, K. M. Fuel 1995, 74, 842. (25) Cody, G. D.; Botto, R. E., Macromolecules 1994, 27, 2607.

© 1997 American Chemical Society

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The present paper presents results that shed further light on the role of temperature in determining the rates of diffusion and in solvent swelling processes generally. It is important to note at the outset that the diffusional processes that are of concern in this study involve movement of molecules of solvent through molecular scale openings in the coal. Thus, we are not concerned with bulk diffusion or convective flow in the macropores of coal, which would generally involve much faster processes than those of interest here. Experimental Section The main experimental method that is applied in this study is liquid solvent swelling of coal. This method has been applied in earlier studies of diffusion in coals.7,8,15,17-21,23,24 To be useful, this technique requires working with coal-solvent pairs that strongly interact, and that the coal measurably swell. This limits such a study to solvents that are moderate-to-strong electron donors.26 The use of nondonors as swelling agents is possible only insofar as they are mixed with a donor, or if the coal has been pretreated to remove key electron acceptor sites, especially hydrogen-bonding sites (e.g., hydroxyl functionalities). In our particular application of the solvent swelling technique, measurements of the extent of swelling were made manually. This limited the study to systems that did not swell on a time scale faster than a few minutes. The time scale of experiments could be adjusted by variation of temperature. This limited the experimental matrix that could be conveniently studied, but a broad range of conditions was still available, as will be apparent below. It should be noted that automated techniques for measuring swelling rates7,8,15,23,24 were considered but felt to pose certain problems with respect to heat transfer and maintenance of constant packing. The vapor sorption techniques also were rejected because, according to some workers, these require preextraction and corrections for pore filling3,4,27,28 which would have made them unattractive for present purposes. Extraction should only really be an issue when solvent activity reaches unity, and a liquid is condensed, but here the desire to work at unit activity made this an important consideration. Most data were obtained on the coals from the Argonne Premium Coal Sample Program.29 Since the composition and properties of these coals have been carefully tabulated elsewhere, the information will not be repeated here. The full suite of eight samples was examined and therefore covers the range of ranks from lignite to low-volatile bituminous. In a few experiments which will be explicitly identified below, another sample of Beulah lignite was employed. This coal has been described in an earlier paper17 and is generally very similar to the Beulah-Zap sample of the Argonne Premium Coal Sample bank. To assure uniformity among samples, all were dried for 3 h at 373 K in vacua. As we have noted before, the effects of drying can be quite significant.19 Studies of dried coals are nevertheless relevant, both because in practical applications coals are first dried and because the fundamental phenomena of interest here are not changed in basic nature by the drying procedure (even if the kinetics are affected). It was learned early in this study that particle size has a significant effect upon the results obtained. The major reason is that if a broad range of particle sizes is employed, packing of fine particles into the interstices between larger particles can cause significant changes in the packing density of the (26) Suuberg, E. M.; Otake, Y.; Langner, M.; Leung, K. T.; Milosavljevic, I. Energy Fuels 1994, 8, 1247. (27) Nelson, J. R.; Mahajan, O. P.; Walker, P. L., Jr. Fuel 1980, 59, 831. (28) Nelson, J. R. Fuel 1983, 62, 112. (29) Vorres, K. Energy Fuels 1990, 4, 420.

Otake and Suuberg particles during the course of an experiment, and this leads to artifacts in the volumetric swelling measurements. Thus, efforts were made to always work with relatively well-defined particle size fractions. The swelling experiments were performed as described in an earlier paper.17 The technique involved immersion of the prepared coal samples in pure, reagent grade solvents. The measurements were performed in constant diameter glass tubes of 3 mm inner diameter and about 5 cm in length. After a 30-100 mg sample was placed in the tube, it was centrifuged at 7500 rpm for 3 min in a 30 cm diameter horizontal rotor centrifuge, to permit accurate measurement of an initial dry packed height of coal. Solvent, prewarmed or precooled as necessary to the experimental temperature, was then added to the tube, and the contents were vigorously stirred with a thin rod. Such stirring is important to prevent the coal from rapidly swelling and forming a solid plug in the tube. The tube was then placed in a thermostated water bath, for the desired time, and was agitated as noted during this immersion. The temperature of the water bath was controlled to about 0.1 K. The coal was then allowed to swell for the desired time and then was removed from the bath and placed in an ice bath to slow the swelling to a negligible rate. Then the sample was again centrifuged as above, and the height of the column of coal remeasured. The ratio of the swollen height to the initial height is what is reported here as the volumetric swelling ratio. In cases in which the swelling was rapid, several different samples were employed to determine the extent of swelling as a function of time. The amounts of coal added to a measurement tube were adjusted to give a conveniently measurable change in height; coals which swelled less were added in greater quantity. The height of the coal column in the tube could be measured to fractions of a millimeter. The volumetric swelling ratio, Q, is defined by

Q ) h/hinitial


where h refers to the height of the coal in the tube at the time of measurement and hinitial is the same quantity prior to addition of solvent. Using this method, the uncertainty in Q values was seen in the second decimal place and was at most about 0.05, though typically the reproducibility was better than this. It was often necessary during the course of the swelling measurements to change the solvents, as they became visibly extract-laden. This was done by carefully decanting the extract-containing solvents and replacing with fresh solvents. Again, no attempt was made to preextract the coals prior to these measurements, since it was desired that the diffusion rates be studied in what was as close to the virgin coal state as possible, except that the coals were dried. Thus the final swelling ratio results may be viewed as being relative to a pure solvent state. A reviewer of this manuscript raised a concern that the processes of swelling and diffusion might be very different in extracted and unextracted coals. On the basis of what is known already, there can be little doubt that the rates will be different. The presently observed final extents of swelling are, however, very similar to others reported in the literature for extracted coals. It is also expected that the nature of the ratelimiting step should be the same in extracted and unextracted coals and that the activation energies will thus also be similar. This has been confirmed in at least in one case, and the results will be presented below.

Results and Discussion A. Effect of Particle Size on Swelling Behavior. It was noted that particle size had an effect on the observed swelling behavior of coals, due to artifacts

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equilibrium extent of swelling.26 If the free energy change upon swelling may be represented as ∆Gs, then regardless of the details of the process, the GibbsHelmholtz equation requires that

(∂[∆Gs/T]/∂[1/T])p ) -∆Hs

Figure 1. Effect of particle size on swelling of Beulah lignite in pyridine at 46.7 °C or 46.8 °C. Particle size range 150-212 µm (solid squares) 212-300 µm (triangles), and 300-600 µm (open squares).

associated with particle packing. This effect is attributable to particle size distribution, rather than the actual size of the particles (small particles tend to pack into the interstitial spaces between larger). This was observed to lead to irreproducible results when samples of a broad range of particle size were examined. Consequently, all experiments presented here have been performed with narrow size distribution samples. Figure 1 shows the data obtained from swelling the Beulah lignite which is similar to but not identical with the Argonne Premium sample. The experiments were conducted in pyridine at a temperature of 46.7 or 46.8 °C. These results, obtained with narrow particle size distributions, show little influence of the particle size, in the range from 150 to 600 µm on either kinetics or final extent of swelling. The final equilibrium swelling ratio for all the samples was 1.87 ( 0.01. The same conclusion was reached from experiments conducted at all temperatures of relevance. Thus there was no significant effect of particle size on the kinetics of the swelling process, at least with this sample whose characteristic time scale for swelling was measured in tens of minutes. This conclusion strongly suggests that for particulate samples such as used here, the characteristic length scale for diffusion was not the particle diameter itself but may have been determined by the existence of a network of pores within the particle. The fundamental length scale would be determined by the distance between such pores. This aspect of the swelling process was not studied in more detail. It should not be concluded on the basis of these results that the same behavior will necessarily be seen with other coals or samples with much larger dimensions. The remainder of the experiments were all carried out with particles of similar diameters, either in the range 212-300 µm or in the range 150-212 µm, so they will be directly comparable. B. Effect of Temperature on the Extent of Swelling of Coals. There are two potential effects of temperature on the swelling behavior of coals. Temperature may influence both the ultimate extent of swelling as well as the rate of swelling. Several workers have noted the insensitivity of ultimate swelling ratio to temperature.17,23,30 In the present experiments, we have again confirmed that there is no significant effect of temperature on the extent of swelling, at least in the range from 10 to 60 °C. The absence of temperature dependence is understood in terms a near zero enthalpy of swelling near the (30) Cody, G. D.; Eser, S.; Hatcher, P. G.; Davis, A.; Sobkowiak, M.; Shenoy, S.; Painter, P. C. Energy Fuels 1992, 6, 716.


A change in the amount of solvent uptake by the coal would result in a change in free energy of the system, including a contribution of elastic expansion.26 This change would necessarily be tied to the enthalpy change during swelling. The fact that there is no change in uptake, and thus in ∆Gs, necessarily implies that ∆Hs must also be zero. This should not be misinterpreted as implying that the free energy itself does not change with temperature; it does by virtue of a (-T∆Ss) contribution. It is the (net positive) entropy change upon swelling (∆Ss) that drives the process to final equilibrium.26,31 There may be concern raised about the above conclusion on the basis of many well-known results showing that the immersion of coals in electron donors is not thermoneutral (e.g., ref 32). The resolution of the apparent paradox is seen in the fact that the largest heat effects are generally observed early during the swelling or immersion process.26,32 The reports of high heats of immersion generally come from situations in which “free” electron acceptor sites are probably filled first.26,33 This means that the final equilibrium swelling occurs under a condition of near thermoneutrality. It is not the overall enthalpy of the swelling process which is of relevance but rather the enthalpy near the end stages. The final swelling can involve breakage of strong noncovalent interactions within the coal, substituting coal-solvent interactions in a net near-thermoneutral process.26 It has also been argued that the weak dependence of the extent of equilibrium coal swelling on temperature could be a consequence of a rather special form of the equation describing the partial molar Gibbs free energy of elastic deformation;30 in this case, the partial molar free energy of coal elastic deformation must be temperature independent. The recognized need for inclusion of the combinatorial entropy of mixing raised questions about the validity of this theory, however, since this reintroduces the temperature dependence to the expression governing equilibrium. It should also be noted that there are some reports of great sensitivity of the swelling ratio to temperature.1,34 The experiments in question were conducted by allowing solvent uptake from a vapor phase, as opposed to the liquid phase, as in the other cited studies. In this one case, there is always a significant (exothermic) enthalpy of solvent condensation from the vapor which must be included as part of ∆Gs. In this case, the ∆Hs is not zero, meaning that swelling would be less extensive the higher the temperature, as was observed.1 Thus the “difference” in this case was merely attributable to a difference in experimental conditions. The same expla(31) Larsen, J. W.; Gurevich, I.; Glass, A.; Stevenson, D. S. Energy Fuels 1996, 10, 1269. (32) Gumkowski, M.; Liu, Q.; Arnett, E. M. Energy Fuels 1988, 2, 295. (33) Suuberg, E. M. Energy Fuels 1997, 11, 1103. (34) Lucht, L. M.; Peppas, N. A. Fuel 1987, 66, 803.

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nation cannot be applied in the case of other data obtained by the same group,34 in which the opposite trend was observed. C. Solvent Swelling Kinetics in Pyridine. The diffusion of solvents into coals, as governs their swelling, has often been noted to be highly non-Fickian in nature. The behavior is often similar to that observed in glassy polymers and involves “Case II” diffusion, as defined by Alfrey et al.35 The Case II situation involves a solvent uptake process whose rate 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 the coal. To the extent that solvent swelling is linearly related to mass uptake, it is possible to relate the two quantities via

M/M∞ ) (Q - 1)/(Q∞ - 1)


where M refers to mass uptake of solvent by the coal and the subscript ∞ refers to the final equilibrium values. The error associated with the neglect of small amounts of empty voidage is generally negligible. Analysis of the nature of the diffusional process has been greatly aided by a simple empirical approach, which relates M/M∞ to time:2

M/M∞ ) ktn

Figure 2. Swelling of Beulah-Zap lignite in pyridine at 25.8 °C (solid squares), 45.8 °C (triangles), and 59.5 °C (open squares).

Figure 3. Swelling of Illinois No. 6 bituminous coal in pyridine at 11.9 °C (solid squares), 24.0 °C (triangles), and 44.7 °C (open squares).


where k is a proportionality constant related to the rate of swelling and n is a number that crudely indicates the nature of the diffusion. For nearly spherical particles and for mass uptakes up to about 60% of the equilibrium value, n ) 0.43 for Fickian diffusion, and n ) 0.85 for Case II diffusion. Values above n ) 0.85 are possible and are termed “super-Case II”.2 It is very important to note that the cited work showed that the expected values of n are sensitive to the assumed particle shape. For an infinite plane sheet, the values would be 0.5 and 1.0 for Fickian and pure Case II, respectively, and in the case of an infinite cylinder, 0.45 and 0.89, respectively. Since real coal particles will involve shapes that approximate all of these values, it is impossible to interpret the results for n unequivocally. Moreover, as the results on the different particle size fractions demonstrated, it is not the geometrical surface of the particle which is the swelling surface. There is probably penetration of solvent into the particle interior, through pores. Finally, there may be differences in the swelling behavior of different sections of the coal. Thus the values of n can be used only as a rough guide as to the nature of the process. For example, it would be difficult to argue that a value of unity for n indicates super-Case II as opposed to Case II kinetics. Typical results obtained in this study are shown in Figures 2-5. All are for swelling of the dried Argonne coals in pyridine. Figure 2 shows results for the lowest rank coal studied, the Beulah-Zap lignite. This coal required a day to reach its final equilibrium swelling ratio of Q∞ ) 2.33. Figure 2 shows only the kinetic data for the early stages of swelling. It is seen that near room temperature, the coal reached the 50% swelling (35) Alfrey, T.; Gurnee, E. F.; Lloyd, W. G. J. Polym. Sci. 1966, C2, 249.

Figure 4. Swelling of Pittsburgh No. 8 bituminous coal in pyridine at 11.7 °C (solid squares), 24.1 °C (triangles), and 41.0 °C (open squares).

point in about 230 min. This coal was the slowest swelling of all those studied. The results for swelling of Illinois No. 6 high-volatile bituminous coal are shown in Figure 3. In contrast to the slow-swelling lignite, this coal was unexpectedly the fastest swelling coal of the group. At room temperature, it reached an extent of 50% of final swelling ratio in less than 2 min. Figure 4 shows the results for Pittsburgh No. 8 high-volatile bituminous coal. It swells at a rate between those for the Illinois No. 6 and lignite samples, requiring 30 min to achieve 50% of its final swelling value at room temperature. The near linearity of swelling ratio with time may be also noted from the figure. Figure 5 shows the results for another low-rank coal, the Wyodak subbituminous sample. It swells at a rate between those of the Pittsburgh No. 8 and Illinois No. 6 samples, requiring about 12 min to reach the 50% criterion at room temperature. It is seen that there is no obvious correlation of swelling rate with rank (or with the geographic region from which the coal was mined). In order to analyze the kinetics of swelling, the value of the exponent n in eq 4 had to be determined.

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Energy & Fuels, Vol. 11, No. 6, 1997 1159 Table 1. Summary of Swelling Results on Argonne Premium Coal Samples in Pyridine coal


T t50 (°C) (min)

Beulah-Zap lignite

Figure 5. Swelling of Wyodak subbituminous coal in pyridine at 11.9 °C (solid squares), 24.2 °C (triangles), and 42.1 °C (open squares).


2.33 25.8 230.0 0.67 45.8 35.5 0.68 59.5 11.3 0.69 Wyodak subbita 2.42 11.9 47.0 0.64 24.2 12.8 0.72 42.1 5.1 0.46 Illinois No. 6 hvba 2.23 11.9 4.5 0.53 24.0 1.7 0.43 44.7 0.7 0.50 Blind Canyon hvba 2.22 11.9 92.0 0.72 24.3 30.0 0.69 42.1 7.3 0.68 Lewiston-Stockton hvb 1.94 20.0 41.0 0.70 40.7 9.4 0.70 50.9 5.3 0.74 Pittsburgh No. 8 hvb 2.14 11.7 90.0 0.97 24.1 30.5 0.85 41.0 8.5 0.69 a

E k × 103 (kJ/mol) 12.7 42.6 91.6 42.2 77.7 233.2 206.9 378.6 588.0 18.8 48.4 129.7 37.3 100.7 144.6 6.4 26.6 112.7

51 (48) 36 (43) 20 (23) 44 (48) 37 (35) 52 (73)

Particle size: 212-300 µm.

Figure 6. Analysis of the swelling data of Figure 1, for Beulah-Zap lignite, using eq 5. The symbols are as in Figure 1.

Appropriate plots were constructed by equating (3) with (4) and taking the natural log of both sides of the resulting equation:

ln [(Q - 1)/(Q∞ - 1)] ) ln k + n ln t


It is important to keep in mind the restriction on allowable values of (Q - 1)/(Q∞ - 1) for comparing the values of n to the theoretical values from the Fickian and Case II values, i.e., when (Q - 1)/(Q∞ - 1) ) 0.6, then ln [(Q - 1)/(Q∞ - 1)] ) -0.51. Consequently, curve fits to (5) were restricted to this range, except for the case of Illinois No. 6, which gave linear plots even slightly beyond this range. Figure 6 shows the fit obtained to the data on BeulahZap lignite. Good straight line fits are obtained at all three temperatures. The results from the correlation are given in Table 1. It is seen that the value of n implies a process somewhere between the limits of Fickian diffusion and Case II relaxation. The uncertainty in the value of n, at a confidence level of 0.9, is in the range (0.04 to (0.05 for all of the results of Figure 6. These uncertainties are typical of all of the results shown in Table 1. Figure 7 shows a similar plot for the data on Pittsburgh No. 8 coal. The values of the exponent n are seen (Table 1) to be somewhat more temperature dependent than in the previous case, and the values show a trend that appears strongly relaxation controlled at the lowest temperature to a value more like that for Beulah-Zap at the highest temperature. It is also important to recall that the k values obtained from (5) and also shown in Table 1 may only be viewed as proportionality constants in the empirical rate law (4) and do not cleanly represent either the diffusion coefficient or the relaxation constant for the coal. This is why no units are shown for k in Table 1, since the units will depend upon the value of n (but the values

Figure 7. Analysis of the swelling data of Figure 3, for Pittsburgh No. 8 coal, using eq 5. The symbols are as in Figure 3.

Figure 8. Analysis of the swelling data of Figure 2, for Illinois No. 6 coal, using eq 5. The symbols are as in Figure 2.

are consistent with t in minutes). Thus values of k obtained at two different temperatures cannot be directly compared unless the values of n are the same at the two temperatures. The better comparison of swelling rates is provided by the data at a constant 50% of final swelling t50. Figure 8 shows the results for Illinois No. 6, plotted according to eq 5. Table 1 shows that the values of the exponent n all cluster nearer the values for pure Fickian diffusion control than the values for relaxation control. This was surprising, insofar as there is little doubt that the Illinois No. 6 coal is in the glassy state prior to swelling and achieves the rubbery state during swelling. It has thus normally been assumed that the swelling process in coal is governed by relaxation rather than diffusion.25 Still, the unusually fast diffusion observed

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with this coal does set it apart from most others we have observed, and only the Wyodak subbituminous coal at 42.1 °C begins to show similar rates and a tendency toward a low value of n. The remaining coals all exhibit behaviors that are consistent with those already given in one of these other cases. The values are summarized in Table 1. Generally speaking, the values of n are reasonably constant with temperature, though in two cases they showed a significant decrease with temperature above 40 °C. Again, the values of n indicate a range of behaviors ranging from likely Fickian in Illinois No. 6 to relaxation-controlled in Pittsburgh No. 8. This range of behaviors is precisely the same as has been recently reported for a suite of British coals.23 It should be noted that we provide no values for two Premium Sample Coals (Pocahontas and Upper Freeport), because as has been noted earlier, these coals swell to a negligible degree until thermally relaxed at much higher temperatures.21 These two coals will be further discussed below. Given the values of n from Table 1, it is possible to evaluate activation energies for the swelling process. Consider eq 5 for any particular extent of swelling Qr:

ln[(Qr - 1)/(Q∞ - 1)] ) ln k + n ln tr


In this case, an activation energy may be defined as

d ln k/d(1/T) ) -E/R


E ) -nR[d(ln 1/tr)/d(1/T)]


from which

where E is the activation energy, R is the gas constant, and tr refers to the time at a fixed extent of swelling. This definition of activation energy is based upon the rate law (4) and is slightly different from that which we used earlier.17,18 The values from (8) are more directly comparable with other values recently published.23 The legitimacy of this definition of an activation energy hinges upon the value of n being relatively constant over the temperature range of interest. In such a case, the value of k is proportional to the square root of ordinary diffusivity in the Fickian limit and to the relaxation constant in the Case II limit.2 It is naturally more complicated to analyze cases in which the value of n varies with temperature or to interpret the activation energy in cases which do not correspond to either the Fickian or Case II limit. The results of the activation energy calculations are also shown in Table 1. The values have been computed for extents of swelling between 20 and 60% of the total and are generally quite constant over this range. It should be noted that these values have been calculated as implied by eq 8, as opposed to using the values of k in Table 1. It is important to recall that the value of activation energy cannot generally be obtained by simple calculation from the values of k as a function of temperature, if there is a change of n with temperature. Since the values of n did not change very dramatically in this study, the activation energies could also be estimated from the k’s. The values in parentheses are the values calculated from the k values directly, using eq 7. The two estimates of activation energy are in fair

agreement, except where there is a significant variation of n with temperature. Thus clearly the variation of n with temperature needs to be taken into account, and the value of activation energy from (8), using an average value of n, is probably the better estimate. The more formal correction of the calculation, based upon eq 6, allowing n to be a function of temperature as well, results in a further correction of only a few kJ/mol. The values of the apparent activation energies for swelling calculated from eq 8 range from about 20 to 50 kJ/mol. It may be noted that the coals with the higher rates of swelling (indicated by the time to achieve 50% swelling, t50) generally exhibit lower activation energies for swelling. It is logical to associate a lower energy barrier to swelling with a higher rate. Swelling of the coal showing the lowest activation energy, Illinois No. 6, was apparently limited by ordinary Fickian diffusion, given the n value for this case. The activation energy of 20 kJ/mol should arguably be doubled for comparison with values from relaxationlimited cases, since as noted above, k is proportional to the square root of diffusivity in the Fickian limit. This would give 40 kJ/mol in the present case, and then virtually all of the swelling processes would have an activation energy barrier of comparable height, of around 40-50 kJ/mol, regardless of the nature of the limiting process. For consistency, “corrections” should of course also be applied to all of the apparent activation energies for coals that fall between Fickian and Case II, though it is not clear how to do this. Presumably the corrections would be of lesser magnitude, because the processes are already somewhat toward the relaxation-control regime, and the general conclusion would not be altered much. The apparent activation energies are all in a range that could easily be associated with a need to break a single hydrogen-bonding type of interaction, as also noted by others.23 The very central role of such bonding interactions in determining the extent of swelling has been recently discussed.26,31 It is therefore not at all implausible that the rate-determining step for the swelling could be associated with the same feature in the coals. This hypothesis will be considered further below, in light of other data. Earlier, we reported that low-rank coals generally exhibit higher activation energies for swelling than do higher rank coals.18 The opposite conclusion was more recently presented by another group,23 but they examined a somewhat narrower range of rank. Here, we again see a low-rank coal show a high activation energy, but now there is no clear trend with rank. The conclusion is that there is no definite trend of activation energy with rank. The actual rates of swelling were also earlier reported to show no correlation with rank.18,23 Again, this is seen to be the case here as well. Solvent diffusion experiments may offer an alternative way in which to determine the maximum hydrogen bond strength in coals. These bond strengths have been determined by other means36,37 and yield results of roughly comparable magnitude to the activation energies determined here. The results from these studies (36) Miura, K.; Mae, K.; Takebe, S.; Wakiyasu, H.; Hashimoto, K. Energy Fuels 1994, 8, 874. (37) Miura, K.; Mae, K.; Morozumi, F. Prepr. Pap.sAm. Chem. Soc., Div. Fuel Chem. 1997, 42, 209.

Solvent Swelling and Diffusion in Coals

Energy & Fuels, Vol. 11, No. 6, 1997 1161

Table 2. Swelling of Pittsburgh No. 8 Coal in Various Solvents solvent


pyridine (80.9)a


butylamine (98.8)a


hexylamine (132.1)a


THF (81.0)a pyridine (heat treated)b THF (heat treated)b

1.41 2.18 1.76

T (°C)

t50 (min)


k × 103

11.7 24.1 41.0 25.3 35.5 46.7 25.3 35.5 46.7 24.2 34.9 15.5 24.1 19.1 24.2 34.9 40.0

90.0 30.5 8.5 16.2 10.5 8.1 117.0 62.0 35.2 143.0 80.0 35.0 15.4 16.2 8.9 4.6 3.0

1.04 0.81 0.68 0.82 0.90 0.85 1.09 1.31 1.23 0.92 0.94 0.79 0.94 0.67 0.86 ND ND

5.0 30.1 113.4 36.6 43.1 58.8 2.6 2.3 6.4 5.6 8.7 32.2 39.0 96.1 81.1 ND ND

E (kJ/mol) 52 22 55 39 48 39

a Molar volume of solvent, in cm3/mol. b Samples heat treated at 8 °C/min to 350 °C, then quenched.

are, however, not consistent with the known enthalpies of hydrogen bonding between pyridine and phenolic hydroxyls (31 kJ/mol) or between THF and phenolic hydroxyls (24 kJ/mol, see the next section).38 It is thus possible that the strongest electron donor-acceptor interactions, those thought to be responsible for controlling relaxation during swelling, are not those involving phenolic hydroxyls as electron acceptors. However, the involvement of phenolic groups need not be ruled out, in light of some new results. Measurements of noncovalent bond strengths in coals by differential scanning calorimetry have suggested a distribution of bond strengths ranging from 0 to 100 kJ/mol.36 More recently, the same group used infrared and DSC methods to suggest a resolution of the apparent discrepancy between typical hydrogen bond enthalpies and the high values cited above.37 The enthalpy of hydrogen bonding was noted to be in the same range as given in the classical calorimetric determinations (i.e., below 40 kJ/ mol). The difference between this value and the higher measured values comes from the distinction between the enthalpy of the interaction and the actual hydrogen bond strength; the former includes a contribution of the change in the phenolic OH bond strength due to a change in the length of the O-H bond. If this contribution is included, the distribution of actual hydrogen bond strengths may reach above 100 kJ/mol, and was calculated to have a peak between 40 and 70 kJ/mol.37 In view of this hypothesis, and awaiting its further substantiation, the solvent swelling activation energies of the present study appear to be consistent with an energy barrier associated with breaking a hydrogen bond. D. Solvent Swelling Kinetics in Other Solvents. There is a strong dependence of activation energy on the nature of the solvent. The results obtained using various solvents to swell the Pittsburgh No. 8 sample are shown in Table 2. It has been earlier concluded that the degree of coal swelling is strongly correlated with the electron donor strength of the swelling solvent,26 or equivalently, the basicity of the solvent.23 It was also earlier reported that the basicity is an important factor only during initial swelling, prior to initial relaxation of the coal structure.23 In the case of raw coals it was (38) Glass, A. S.; Larsen, J. W. Energy Fuels 1994, 8, 284.

suggested that the stronger the base, the faster the initial swelling. The results of Table 2 show that there is no correlation of activation energy for swelling of raw coals with basicity alone. Butyl- and hexylamines are stronger bases than is pyridine, which is stronger than THF. The values of activation energy show no such ordering. This is consistent with the earlier reported dependence of activation energy on what were termed “steric” factors, in addition to base strength.24 These steric factors depend upon both the size and shape of the diffusing molecule. The variation of activation energy of solvent swelling was addressed in similar experiments with alkylamines, in which it was shown that activation energy increases with the size of the amine, reaching a nearly constant value above a certain size.24 The same trend is also seen in Table 2, for the two alkylamines diffusing in Pittsburgh No. 8 coal, especially noting that the activation energy for hexylamine is close to that for pyridine just as in the previously reported study. In both cases these two solvents give nearly the same values near the maximum for the alkylamine series. What the above results indicate is that below a certain critical amine size, the swelling of the coal has a lower activation energy barrier than observed for pyridine or larger amines. The molar volume of the butylamine is actually larger than that of pyridine, but the linear nature of the butylamine allows it easier access to the coal structure than the pyridine ring. These results can be rationalized in terms of a model in which reference is made to the critical role played by hydrogen bond breakage, using this as an example of the electron donor-acceptor interactions that exist between different parts of the coal in the dry state (and between coal and solvent in the swollen state). If it is postulated that the activation energy for swelling in pyridine or hexylamine is determined by a need to first fully break a coal-coal hydrogen-bonding interaction in order to accommodate a solvent molecule that will form a new coal-solvent hydrogen bond, then the activation energy barrier will be commensurate with the coal-coal hydrogen bond strength. On the other hand, in the case of a solvent molecule that is able to more easily penetrate the structure, the coal-coal hydrogen-bonding interaction may not need to be fully broken prior to the time that the solvent molecule begins to contribute to the hydrogenbonding interaction. This would effectively lower the activation barrier. The present results cannot be offered as firm proof of such a hypothesis, but they are not inconsistent with such a scenario. The much weaker electron donor THF exhibits an activation energy intermediate between the much larger and stronger bases butylamine and hexylamine (see Table 2), but as discussed above, direct comparison is made difficult because of the very different sizes and shapes of the molecules. The value for THF is also lower than that for the similar size and shape pyridine. By the same arguments as advanced above, it may be hypothesized that tetrahydrofuran is dissociating the strongest hydrogen-bonding interactions for which it can substitute, subject to limitations imposed by the enthalpy. The difference between the values of activation energy between pyridine and THF is about 13 kJ/mol, which is larger than the difference between the hydrogenbonding enthalpies of these two solvents with phenolic

1162 Energy & Fuels, Vol. 11, No. 6, 1997

Otake and Suuberg

Table 3. Activation Energies for Swelling Various Coalsa in Pyridine and THF pyridine




E (kJ/mol)


E (kJ/mol)

Beulah lignite Montana suubit Bruceton hv bit Powhatan hv bit

0.83 0.93 0.80 0.62

55 70 49 31

0.93 ND 0.81 0.92

44 ND 25 34

a Elemental analyses for these coals are given in ref 17. b ND, not determined.

hydroxyl groups (about 7 kJ/mol),38 but as discussed above, hydrogen-bonding enthalpies may not be as relevant as hydrogen bond strengths. Earlier we reported values of activation energies for diffusion of pyridine and THF in a number of other coals.17 These values have been recomputed for consistency with the present values, using eq 8, and are shown in Table 3. The recomputations involved using the mean values of the earlier reported values of n and the activation energies measured between 20 and 50% extents of swelling. The Beulah sample in Table 3 is the same coal as that in Figure 1. Once again, Table 3 shows that there is no simple relationship between the activation energy values for THF and pyridine. In two cases, the values for pyridine are again significantly higher than those for THF. In the third case, the values are quite close. These results imply that there is a high degree of sensitivity to the details of the coal’s structure, and, again, that there is no simple correlation with rank. E. Effects of Heat Treatment on Solvent Swelling Kinetics. We have earlier shown that this Pittsburgh No. 8 coal can be thermally relaxed by heating to 350 °C at 8 °C/min.20,21 We explored the swelling kinetics of samples treated in this manner. The results are shown in Table 2. These results show that the activation energies for swelling are only slightly decreased by the thermal pretreatment, while the rates of swelling are increased. Thus the nature of the activation energy barrier to swelling is not significantly affected by prepyrolytic thermal treatments. The fact that hydrogen bond strength distribution is only be modestly affected by such heat treatment in this temperature range37 is consistent with these results. It has also been earlier noted that the ultimate extent of swelling of Pittsburgh No. 8 coal in pyridine is unaffected by this kind of heat treatment,20,21 so the basic nature of the macromolecular structure does not appear to be very much altered, even if it is somewhat loosened. In THF, both the apparent ultimate extent and rate of swelling are significantly increased by heat pretreatment. The true ultimate extent of swelling in THF is actually higher than indicated for the untreated coal because the value given in Table 2 is the usual one-day apparent equilibrium value. We have shown that in the untreated coal swelling continues at very low rates for almost a week and achieves values almost the same as those for the thermally treated samples.21 Thus the apparent differences in ultimate extents of swelling are only a manifestation of the very different time scales of swelling of the treated and untreated samples. The oneday apparent value of THF swelling equilibrium is given in Table 2, rather than the week-long value, because we believe that the latter value is determined by processes other than hydrogen bond cleavage, and to

normalize kinetics with respect to that value would be to combine two unlike processes. The nature of the rate-determining step in swelling of the Pittsburgh No. 8 coal in THF warrants further discussion. The observed (prepyrolytic) heat pretreatment effects are a result of thermally induced relaxation of the coal structure.20,21 The effects of this relaxation are only weakly observed in the case of pyridine swelling because pyridine is a strong enough solvent so that it can induce the same relaxation itself, whereas the THF is unable to do so. It has been suggested that coals are not, in fact, in a fully relaxed state in an as-mined and/ or dried condition.26,39 The nature of the thermally induced relaxation is not clearly established, but it has also been shown to have a dramatic effect on the swellability of the Pocahontas and Upper Freeport samples from the Argonne Sample bank.21 Without such thermal pretreatment, these samples cannot swell much, even in pyridine (Q is about 1.1). Following thermal treatment, the swelling ratio increases to over 2 for the Upper Freeport sample and to about 1.7 for the Pocahontas sample. These changes are accompanied by only a small amount of mass loss (a percent or two) associated with loss of “guest” molecules. The temperatures of the thermal relaxation events have been established by differential scanning calorimetry and shown to increase with increase in rank. The relaxation has therefore been hypothesized to be associated with interactions between the aromatic structures in coals.21 Thus it may be the relaxation of aromatic-aromatic interactions that determines the time scale of ultimate swelling of Pittsburgh No. 8 in THF. That process has been earlier shown to involve an activation energy of over 200 kJ/mol.21 The fact that this relaxation may be induced by the strong solvent (pyridine) confirms a thermodynamically different situation in this solvent than in THF. In light of the above, the suggestion is that the activation energy barrier of interest here is determined by the dissociation of hydrogen-bonding interactions, which remain unaltered by heat pretreatment (since there is no pyrolytic loss of functional groups). The actual rate of the swelling process is affected by the stiffness of the coal network structure, which is higher prior to thermal relaxation, due to the presence of more noncovalent cross-links of an aromatic-aromatic nature. Again, the fact that THF does not appear to swell to as great an extent prior to thermal relaxation is a kinetic artifact, associated with the slow room-temperature dissociation of these other kinds of noncovalent cross-links. These results also appear to suggest that the activation energies for (initial) solvent swelling are determined by a process which is distinct from the thermally induced relaxation. The role of thermal relaxation is in some respects quite similar to the role of water as a “plasticizing” agent in the coal. It was previously reported that in the case of the Beulah lignite of Table 3, the presence of small amounts of moisture significantly enhanced the rate of swelling.19 It is presumed that the water acts by solvating some of the coal-coal hydrogen-bonding interactions which are otherwise present in the dry coal. This “loosens” the structure for transport of the organic (39) Cody, G. D.; Larsen, J. W.; Siskin, M. Energy Fuels 1988, 2, 340.

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Energy & Fuels, Vol. 11, No. 6, 1997 1163

Figure 9. A comparison of the swelling behavior of dried, raw Beulah lignite in pyridine (open squares) with the swelling behavior of dried, pyridine preextracted Beulah lignite in pyridine (solid squares). All data taken at approximately 35.6 °C. Table 4. Swelling Results on Raw and Pyridine-Extracted Beulah Lignite coal


Beulah lignite


extracted Beulah lignite


T (°C)

t50 (min)


k × 103

25.2 35.7 46.7 57.8 27.2 35.5 42.9

469 216 76.0 35.6 57.5 22.0 12.0

1.02 0.79 0.75 0.75 0.70 0.63 0.83

0.94 6.96 19.2 33.9 28.7 69.2 37.1

E (kJ/mol) 55


solvent. In the case of the water-enhanced transport, it was reported that the activation energy of the basic process did not change.19 Calculated by the current method using eq 8, the activation energy was determined to be constant at approximately 54 kJ/mol, for transport in samples containing 0%, 6.6%, and 11.2% by mass of water (these samples differed slightly from the sample of Table 3 in preparation, which explains the small difference in zero moisture values). The transport was near relaxation control (n g 0.7) for all temperature and moisture levels, except tending toward Fickian diffusion control at high temperatures (T >35.7 °C) and moisture levels (11.2%), for which n < 0.6. This is again strong evidence to support the view that the rate-limiting factor in solvent swelling is hydrogen-bond cross-link dissociation, since otherwise a rate enhancement due to water is difficult to understand. F. Effects of Preextraction on Swelling Kinetics. It has been noted in an earlier study23 that pyridine extraction can significantly affect the kinetics of coal swelling. This issue was also briefly explored in this study. Some typical results are shown in Figure 9, for the non-Argonne Beulah lignite. The data compare the swelling behavior of the dried, raw Beulah lignite with that of the pyridine preextracted, dried coal. These results confirm that the pyridine-extracted coal is indeed much more quickly swollen by the pyridine than is the raw coal. The kinetics of swelling the extracted and raw coal are summarized in Table 4. Comparison of the results for the raw and pyridine extracted Beulah lignite shows that the increase in rate of swelling (by about an order of magnitude) is not accompanied by an increase in the activation energy of the process. The relaxation-controlled swelling behavior at room temperature also appears to be modified by the pre-extraction, as indicated by the change in the value of n. The reason for the dramatic increase in swelling rate, due to extraction, is not yet firmly established. It is well-known that removing pyridine from coal, after

extraction, is very difficult, and therefore one possible reason for the increased rate of swelling is that some pyridine remained after drying. This would be particularly important if the pyridine remained in very strong binding sites, since by removing such sites from participation in coal-coal interactions, the structure may be considerably “loosened”. Again, this relates to the role of hydrogen-bonding solvents in “plasticizing” coals, as discussed above. There was no evidence of significant pyridine retention by the extracted coal of this study, though it was difficult to quantify to better than a percent by weight. The present results, which imply that the activation energy does not change with extraction, contradict other published results which showed a decrease in activation energy with pyridine extraction.23 At the present time, there is also no definite explanation for the discrepancy. It is easy to rationalize the present observation that activation energy does not change, since if the activation energy barrier involves mainly the dissociation of electron donor-acceptor interactions in the coal, then these should not be altered by the removal of some extractable materials from the coal. A lowered activation energy barrier, as observed elsewhere,23 cannot be explained by pyridine retention, since this contradicts the results obtained with water addition. Alternatively, it is possible that the coal structure was unable to relax to its minimum energy state following extraction. In this case, strong coal-coal electron donor-acceptor bonds may not be reformed. The difference in postextraction activation energies between the two studies might therefore be found in how the samples were dried following extraction. Our drying procedure, 3 h at 100 °C, was considerably more severe than the pentane extraction combined with roomtemperature drying employed in the other study.23 The more severe drying procedure could have resulted in the more complete relaxation of the structure back to a preextraction-like configuration. This configuration would involve formation of the same types of electron donoracceptor (hydrogen bonding) interactions as existed prior to extraction. The significant effects of 100 °C thermal treatments on the swelling behavior of low-rank coals has been noted before.19 It was observed in that case that heat pretreatment in the range of temperatures of interest here slowed and limited the extent of swelling. The role of preextraction may also be better understood by reference to the results of swelling experiments on other coals. If the swelling rate of the Wyodak subbituminous coal (Table 1) is compared with those of the raw Beulah-Zap (Table 1) and Beulah lignites (Table 4), it is seen that the raw lignites swell much more slowly at any given temperature. This means that the structures of the raw lignites are in some way much stiffer. It is not likely that the contents of polar functional groups in these three coals are very different. The difference in swelling rates arises from other structural features. Interestingly, following pyridine preextraction of the Beulah lignite, the kinetics of swelling of this coal are much more comparable with that of the Wyodak coal. There are thus other factors, not yet identified, which determine the observed large differences in swelling rate between coals. These factors can be influenced by

1164 Energy & Fuels, Vol. 11, No. 6, 1997

physical treatments of the coal. They have not yet been characterized, nor do they appear characterizable in terms of rank. Entanglements could be playing some role, and the presence of entanglements would not be reflected in the kinds of characterizations that go with rank. The distribution of ion-exchanged cations could also be playing some role. Alternatively, there could be some coal-coal interactions in the raw coal which are not correlated with rank and which are determined by the geological conditions under which the coal was formed or deposited. Again, coals are not in a fully relaxed state relative to laboratory conditions in either an as-mined or a dried state.26,39 The dramatic increase in swelling rate that the Beulah lignite experiences following pyridine extraction could suggest disruption of such interactions (which may be of the aromaticaromatic type) during the initial swelling cycle that accompanies pyridine extraction. These structural changes could occur without modifying the activation energy barrier, if dissociation of the hydrogen-bonding interactions remains the rate-determining step in swelling. Conclusions The swelling kinetics of several raw and thermally pretreated coals have been examined in various solvents at various temperatures. The ultimate extent of swelling was not a strong function of temperature, which implies that the swelling process was essentially thermoneutral in character. This implies a process that is driven by entropy, to the extent permitted by cleavage of coal-coal electron donor-acceptor interactions by the solvents. There was generally an enormous variability in diffusional/swelling rates, which did not correlate well with coal rank. In some coals, the process of swelling was characterized by Case II relaxation control, while in others Fickian diffusion appeared to control. In a few cases, the nature of the process changed with

Otake and Suuberg

temperature. These data have been examined in terms of apparent activation energies. Both size and shape of the solvent molecules appear to play a role in determining the activation energies, as does the electron donor strength of the solvent. The overall rates of diffusion were naturally lower, the bigger the solvent. Activation energies for diffusion however appeared to reach an upper limit for large, strong electron donors. The nature of this limit will be discussed in a future publication. The activation energies determined for the swelling processes were generally consistent with cleavage of coal-coal electron donor-acceptor interactions (possibly hydrogen bonding). In cases in which the solvent molecules were small enough (and/or of the correct shape) the activation energy barrier was reduced, perhaps because the solvent itself could participate in the cleaving of the interactions. Thermal pretreatment of the coals below the temperatures of pyrolysis could affect some aspects of the swelling process. The activation energy for the swelling process was largely unaffected, meaning that the same critical step played a role before or after pretreatment. It appears that the thermal pretreatments relax certain kinds of coal-coal bonding interactions which are not at equilibrium with respect to laboratory conditions. These have been speculated to be aromatic-aromatic interactions. This has the effect of reducing the stiffness of the network and permitting the solvent swelling to occur more readily. Preextraction of a coal did not influence observed activation energies, though observed rates of swelling were much higher following extraction. Acknowledgment. We gratefully acknowledge the financial support of this work by the U.S. Department of Energy, through Contract DE-AC22-91PC91027 and Grant DE-FG22-90PC90308. EF970020V