Swelling of Coals by Supercritical Gases and Its Relationship to

Mar 16, 2010 - St. George , J. D.; Barakat , M. A. The change in effective stress associated with shrinkage from gas desorption in coal Int. J. Coal G...
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Energy Fuels 2010, 24, 2777–2783 Published on Web 03/16/2010

: DOI:10.1021/ef901588h

Swelling of Coals by Supercritical Gases and Its Relationship to Sorption Stuart Day,* Robyn Fry, Richard Sakurovs, and Steve Weir Commonwealth Scientific and Industrial Research Organisation (CSIRO) Energy Technology, Post Office Box 330, Newcastle, New South Wales 2300, Australia

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Received December 23, 2009. Revised Manuscript Received March 5, 2010

If CO2 can be sequestered in coal seams while simultaneously displacing coalbed methane [enhanced coalbed methane (ECBM)], some of the sequestration costs can be recovered through the production of methane. One potential difficulty with ECBM is that CO2 is known to swell coal, which may reduce its permeability. Coals also swell in other gases, although not to the same extent. Here, we report on the swelling of sub-bituminous and bituminous coals in CO2, CH4, N2, CF4, ethane, and various noble gases. Helium and Ne induced negligible swelling; all other gases swelled the coals to varying degrees. The maximum swelling was proportional to the critical temperature of the gas, except for CF4, which is attributed to its greater size, preventing it from penetrating the coal as completely as the other gases. This indicates that swelling of these coals by all of these gases has a similar basic mechanism; CO2 is only different in the extent to which it swells coal. All coals swelled more in the direction perpendicular to the bedding plane than parallel to it, with the ratio of the swelling in each direction independent of pressure or gas type. Gas sorption and swelling in coal were found to be related according to a simple quadratic polynomial expression. The same relationship held for all of the coals and all gases investigated here. This means that swelling can be accurately predicted from the condensed volume of the gas adsorbed, regardless of the type of coal or gas.

suggested that, for brown coals at least, the presence of CO2 will mechanically weaken the coal and thus create cracks that will increase its permeability.6 Whatever the effect of CO2 injection, it is important to understand how swelling will affect the in situ coal properties, especially in relation to gas flow, to enable accurate reservoir modeling. Recent reservoir models have explicitly included the effects of swelling, with swelling assumed to be a linear function of gas adsorption.7 Although there is some experimental evidence to support this proposition at lower pressures,8,9 recent work indicates that the relationship may not be linear over the full range of pressures likely to be encountered in ECBM and sequestration applications.2,4,10 Coals also swell in gases other than CO2, although to differing extents. Methane, for example, swells coal, but its effect is less than CO2.2,8 However, because CH4 is displaced during ECBM, its swelling behavior must be considered. Other gases, such as H2S, which may be present in flue gas ultimately injected underground, have been shown to swell coal more than CO2.9 Water in the coal has also been found to significantly affect coal swelling by gases.3 The mechanism of coal swelling and its relationship to sorption (i.e., adsorption and absorption) is still incompletely

1. Introduction The storage of CO2 in deep, unmineable coal seams is being actively investigated in Australia and elsewhere as an option to reduce CO2 emissions to the atmosphere. Coal is an attractive storage medium because of its ability to adsorb CO2; some coals are capable of sorbing over 10% by weight of CO2.1 A further advantage of CO2 injection into coal seams over other geological options is that it affords the prospect of enhanced coalbed methane (ECBM) production, which may partially offset the cost of sequestration. One potential difficulty with sequestration and therefore ECBM is that many coal seams have low permeability. This means that practical injection rates in these seams are low. Moreover, CO2 is known to swell coal,2-4 which may reduce its permeability further by blocking cleats in the coal. This effect has already been observed in large-scale field trials of CO2 injection into coal seams.5 However, it has also been *To whom correspondence should be addressed. E-mail: stuart. [email protected]. (1) Day, S.; Duffy, G.; Sakurovs, R.; Weir, S. Effect of coal properties on CO2 sorption capacity under supercritical conditions. Int. J. Greenhouse Gas Control 2008, 2, 342–352. (2) Kelemen, S. R.; Kwiatek, L. M. Physical properties of selected block Argonne Premium bituminous coal related to CO2, CH4 and N2 adsorption. Int. J. Coal Geol. 2009, 77, 2–9. (3) van Bergen, F.; Spiers, C.; Floor, G.; Bots, P. Strain development in unconfined coals exposed to CO2, CH4 and Ar: Effect of moisture. Int. J. Coal Geol. 2009, 77, 43–53. (4) Day, S.; Fry, R.; Sakurovs, R. Swelling of Australian coals in supercritical CO2. Int. J. Coal Geol. 2008, 74, 41–52. (5) van Bergen, F.; Pagnier, H.; Krzystolik, P. Field experiment of enhanced coalbed methane-CO2 in the upper Silesian basin of Poland. Environ. Geosci. 2006, 13, 201–224. (6) Viete, D. R.; Ranjith, P. G. The effect of CO2 on the geochemical and permeability behaviour of brown coal: Implications for coal seam CO2 sequestration. Int. J. Coal Geol. 2006, 66, 204–216. r 2010 American Chemical Society

(7) Pan, Z. J.; Connell, L. D. A theoretical model for gas adsorptioninduced coal swelling. Int. J. Coal Geol. 2007, 69, 243–252. (8) Levine, J. R. Model study of the influence of matrix shrinkage on absolute permeability of coal bed reservoirs. Coalbed Methane and Coal Geology; The Geological Society: London, U.K., 1996; Special Publication 109, pp 197-212. (9) Cui, X.; Bustin, R. M.; Chikatamarla, L. Adsorption-induced coal swelling stress: Implications for methane production and acid gas sequestration into coal seams. J. Geophys. Res. 2007, 112, No. B10202. (10) Majewska, Z.; Ceglarska-Stefa nska, G.; Majewski, S.; Zie-tek, J. Binary gas sorption/desorption experiments on a bituminous coal: Simultaneous measurements on sorption kinetics, volumetric strain and acoustic emission. Int. J. Coal Geol. 2009, 77, 90–102.

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understood. It has been suggested that CO2 is a special case and that it can dissolve into the organic matrix of the coal, thus softening the coal, in effect acting as a plasticizer.11 Irreversible changes in coal after exposure to CO2 have been reported for some experimental studies,10,12 yet other studies show no such changes.4 It has been found that exposure to supercritical CO2 can extract small quantities of hydrocarbons from coals.13 However, results from our laboratory have shown that any effect on swelling by the removal of this material is negligible; multiple exposures result in the same degree of swelling with no sign of hysteresis.4 Recently, Sakurovs et al. reported that, in relation to sorption on coal, CO2 is not fundamentally different to other gases.14 They found that, for a wide range of gases, the maximum sorption capacity (expressed on a volume basis) increased linearly with an increasing critical temperature of the gas. On a more fundamental basis, they contend that the strength of the sorption of the gas to the coal is approximately proportional to the strength of the attractive forces between the gas molecules. While gas sorption and swelling in coal are widely recognized as being related, it is only relatively recently that the relationship has begun to be investigated in detail.2,4,9 The renewed interest in the subject reflects its importance to CO2 sequestration and ECBM. In this paper, we present the results of a study that extends the work of Sakurovs et al.14 to investigate the swelling effects of various gases on several Australian coals. Also considered is the relationship between swelling and sorption at pressures and temperatures that may be typical of ECBM applications.

Table 1. Properties of the Gases Used in the Swelling and Sorption Measurementsa gas

van der Waals van der Waals MW Tc (K) Pc (MPa) density (kg m-3) volume (m3 mol-1)

44.0 304.2 CO2 CH4 16.0 190.5 N2 28.0 126.2 He 4.0 5.2 Ne 20.2 44.4 Ar 40.0 150.9 Kr 83.8 209.4 Xe 131.3 289.7 CF4 88.0 227.7 C2H6 30.1 305.4

7.38 4.60 3.40 0.23 2.76 4.90 5.50 5.84 3.74 4.88

4.28  10-5 4.31  10-5 3.86  10-5 2.38  10-5 1.67  10-5 3.20  10-5 3.96  10-5 5.16  10-5 6.32  10-5 6.50  10-5

1028 372 726 168 1205 1248 2119 2546 1392 463

a MW, molecular weight of the gas; Tc, critical temperature; Pc, critical pressure.

Samples usually remained in the system between runs and were degassed in situ at 55 °C for at least 48 h. A total of 10 gases were used in these experiments, details of which are summarized in Table 1. The change in volume of the coal blocks at each pressure step, V þ ΔV, was calculated from eq 1 V þ ΔV ¼ ðlper þ Δlper Þðlpar þ Δlpar Þ2

ð1Þ

where lper and lpar are the lengths of the perpendicular and parallel samples, respectively. For all of the experiments, the volumetric swelling data were fitted to a modified Dubinin-Radushkevich isotherm model, in which gas density is used instead of pressure. This model has been found to fit sorption data extremely well over a wide range of experimental conditions15 and has also been applied to coal swelling.4 In this model, the volumetric swelling, Q, is given by eq 2 2

2. Experimental Section

Q ¼ Qmax e-D½lnðFL =Fg Þ

Gas-induced swelling of coal was measured using an optical technique, which has been described in detail previously.4 Briefly, dimensional changes of machined test specimens of coal (nominally 30  9  9 mm) contained within a high-pressure cell with transparent glass windows are observed with digital cameras. A steel block with the same dimensions as the test pieces (which does not swell) is used as a reference to avoid any artifacts caused by the changing refractive index of the gas within the cell. Coal test pieces were cut from fresh core samples or lumps of coal using a diamond saw. Two test pieces were made from each sample, one with the long axis perpendicular to the bedding plane and the other with the long axis parallel to the bedding plane. Prior to measuring swelling, the coal samples were dried under vacuum at 60 °C for 48 h. The dimensions of the perpendicular and parallel blocks were measured with a micrometer and then placed in the sample cell along with the steel reference block. After the sample cell was sealed, the system was heated in an oven and maintained at a temperature of 55 °C. Samples were degassed under vacuum for at least 24 h prior to beginning the measurements. Experiments were run by increasing the pressure in a series of steps up to a maximum of 16 MPa. The system was maintained at each pressure step for at least several hours after swelling had ceased, typically about 24 h or more, depending upon the gas.

where Qmax is the maximum swelling of the coal, Fg is the density of the gas at the temperature and pressure, FL is the density of the condensed gas, and D is a constant. The condensed gas density, FL, has often been assumed to be that of the liquid adsorbate at its boiling point at 1 atm, but there are some problems with this assumption. For instance, CO2 does not form a liquid at 1 atm, and in any case, under supercritical conditions, gases do not condense to liquids. Recently, Sakurovs et al. adopted the “van der Waals” density (Table 1) as the condensed gas density and found that this was a better approach in relation to sorption of gases onto coal.14 We have therefore also used the van der Waals density for FL when applying the Dubinin-Radushkevich model to the swelling results. The density of the gas in the sample cell at a given temperature and pressure (Fg) was determined using the online calculator available from the U.S. National Institute of Standards and Technology (NIST) Chemistry WebBook.16 Gas sorption measurements were made using a gravimetric apparatus that has been described previously.1 Adorption isotherms were measured on about 200 g of dry crushed and sized coal (0.5-1 mm particles) from the same batch of material used to prepare the swelling samples. Measurements were made at 55 °C for a range of gases, and the results were fitted to a modified Dubinin-Radushkevich model. Complete details of the sorption measurements and data analysis are provided by Sakurovs et al.14 In this study, three Australian coals were examined: bituminous and sub-bituminous coals from the Bowen Basin in Queensland

(11) Larsen, J. W. The effects of dissolved CO2 on coal structure and properties. Int. J. Coal Geol. 2004, 57, 63–70. (12) Walker, P. L.; Verma, S. K.; Rivera-Utrilla, J.; Khan, M. R. A direct measurement of expansion in coals and macerals induced by carbon dioxide and methanol. Fuel 1988, 67, 719–726. (13) Kolack, J. J.; Burruss, R. C. Geological investigation of the potential for mobilizing non-methane hydrocarbons during carbon dioxide storage in deep coal beds. Energy Fuels 2006, 20, 566–574. (14) Sakurovs, R.; Day, S.; Weir, S. Maximum sorption capacity of coals for different gases. Energy Fuels 2010, DOI: 10.1021/ef901238c.

ð2Þ

(15) Sakurovs, R.; Day, S.; Weir, S.; Duffy, G. Application of a modified Dubinin-Radushkevich equation to adsorption of gases by coals under supercritical conditions. Energy Fuels 2007, 21, 992–997. (16) National Institute of Standards and Technology (NIST). Thermochemical properties of fluid systems. 2008 (http://webbook.nist.gov/ chemistry/fluid/).

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Table 2. Analytical Data for the Three Coalsa moisture (%, ad) ash (%, db) volatile matter (%, daf) carbon (%, daf) hydrogen (%, daf) mean vitrinite reflectance Rmax (%) vitrinite (vol %, mf) inertinite (vol %, mf) liptinite (vol %, mf) density (g mL-1) a

coal A

coal B

coal C

1.1 16.9 21.7 88.9 4.61 1.40 30.3 69.7 0.0 1.484

8.5 7.7 31.7 83.0 6.08 0.69 29.7 66.4 3.9 1.422

9.3 20.3 31.2 80.7 4.17 0.62 23.9 74.5 1.6 1.637

The maceral composition is reported on a “mineral-free” basis.

and a bituminous coal from the Illawarra coalfield in New South Wales. Analytical data for the 0.5-1 mm particle size fraction of the three coals are listed in Table 2.

3. Results and Discussion 3.1. Gas-Induced Swelling. All three coal samples swelled in the presence of all of the gases, except for helium and neon, which caused the coals to contract slightly. This contraction was probably a result of physical compression of the coal. In He, the reduction in coal volume at 16 MPa ranged from 0.17% for both coals A and C to 0.15% for coal B. In all cases, the decrease in the coal volume was proportional to the applied pressure. It has been suggested that He does not adsorb on coal and hence will not induce swelling.17 Results in our laboratory also indicate that at 55 °C and pressures up to 20 MPa, there is virtually no sorption. Neon, on the other hand, would be expected to adsorb, albeit to only a very small amount, and therefore cause some swelling.14 However, the amount of Ne-induced swelling is apparently so low that its contribution is overshadowed by compression. We attempted to remove the effects of compression by subtracting the volumetric He compression results from the Ne swelling data. After this correction was applied, the Ne results showed that there was in fact a slight swelling in this gas (about 0.01%). The scatter in the data was high, however, because of the fact that the change in the length was about the same as the detection limits of the apparatus. Although compression in all coals was measurable, its effect was small. To simplify data analysis and allow for a comparison to sorption data (which were not corrected for compression), all of the swelling results reported here refer to uncorrected measurements. The maximum pressure achieved for the Xe runs was about 12 MPa compared to about 16 MPa for the other gases. This was because the density of the Xe at higher pressures was more than the density of the coal, and hence, the sample blocks floated in the test cell preventing further measurements from being made. Figure 1a shows the volumetric swelling of coal C in each gas as a function of pressure; the behavior of the other coals was similar, although the extent of swelling varied between coals. Coal A, which was the highest rank coal in this study (88.9% C daf) showed the least swelling, whereas coal C with the lowest rank (80.7% C daf) had the highest. Other studies

Figure 1. Volumetric swelling of coal C in various gases as a function of (a) pressure and (b) gas density. Solid lines in b represent modeled curves.

have also reported an inverse relationship between gasinduced swelling and rank.2,18 The maximum volumetric swelling of the sub-bituminous coal C in CO2 was over 5%, which is not unusual for sub-bituminous coals.7 The maximum swelling observed for coal A (1.8%) is typical of bituminous coals4 and is far less than either coal B or C. With the exception of He and Ne, the volumetric swelling of the coals could be fitted accurately by the modified Dubinin-Radushkevich isotherm (eq 2). For He and Ne, which compressed the samples, the induced volume reduction was proportional to pressure. In the case of Ne with the effects of compression removed, there was too much scatter in the data to enable accurate fitting by the model. The modeled data are represented as lines plotted in Figure 1b. In all cases, the root-mean-squared (rms) residuals were less than 1% of the maximum swelling, Qmax. A summary of Qmax and the corresponding D values calculated from the model for all runs is provided in Table 3. The maximum compression in He and Ne measured at 16 MPa is also shown in Table 3. Comparing the amount of swelling at a given pressure relative to the maximum swelling, Qmax, shows that for CO2, Xe, CF4, and C2H6 swelling was essentially complete by about 16 MPa (i.e., more than 95% of swelling had occurred). For the other gases, CH4, N2, Ar, and Kr, only about 70-80% of the calculated maximum swelling had occurred by 16 MPa (Figure 1a).

(17) St. George, J. D.; Barakat, M. A. The change in effective stress associated with shrinkage from gas desorption in coal. Int. J. Coal Geol. 2001, 45, 105–113. (18) Ceglarska-Stefa nska, G.; Czapli nski, A. Correlation between sorption and dilatometric processes in hard coals. Fuel 1993, 72, 413– 417.

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Table 3. Swelling Parameters for the Three Coals Calculated Using eq 2,a coal A

coal B

Maximum Swelling, Qmax (vol %) 1.81 4.41 CO2 1.17 2.46 CH4 0.54 1.19 N2 Ar 0.78 Kr 1.33 Xe 4.34 1.39 CF4 4.25 C2H6 He (compression at 16 MPa) 0.17 0.15 Ne (compression at 16 MPa) 0.08 CO2 CH4 N2 Ar Kr Xe CF4 C2H6

D parameter 0.062 0.090 0.127 0.121 0.086

0.068 0.107 0.136 0.067 0.077 0.080

here for a Polish bituminous coal in CO2, CH4, and various mixtures, whereas results reported for three Australian coals (different from those in the current study) in CO2 showed that swelling in the perpendicular plane was between 30 and 70% more than in the parallel plane.4 Levine also reported that, for a U.S. coal, swelling was about 10% higher in the perpendicular plane in CO2 but much less pronounced in CH4.8 In a study using a core sample of Pittsburgh No. 8 coal, substantial differences in the CO2-induced strains (including both compression and swelling) in the x, y, and z directions were noted.20 However, in another recent study of several Argonne Premium coals, it was found that there was no statistically significant difference in the strains measured in the perpendicular and parallel planes.2 An explanation of the anisotropy of coal swelling was proposed by Larsen et al.21 They suggested that the compression applied to the coal seam by overlying strata forces the coal to creep or flow in a direction parallel to the bedding plane. The induced strain is retained by the coal because the structure is sufficiently rigid to prevent molecular rearrangement. Unlike some liquid solvents, exposure to the gases examined here does not impart enough molecular mobility to allow for relaxation of the structure. Thus, the coals remain elastic, and the swelling process is reversible. Assuming that the explanation of swelling by Larsen et al.21 is correct, higher rank coals, having been subjected to a more severe stress history, should in general exhibit more anisotropy than low-rank coals. Although the highest rank coal (coal A) showed the highest ratio (Figure 2), the results of the three coals examined here are too close to make meaningful comparisons. The variability of results reported in other studies also suggests that the relationship between swelling anisotropy and rank is not straightforward. Other factors, such as mineral matter content, may also need to be considered. The results show that the swelling of all three coals was unaffected even by multiple exposures to the various gases. Rerunning the samples at the end of the experimental series in CO2 gave identical results to the initial CO2 runs on fresh coal. Even if, as has been suggested, very small amounts of hydrocarbons or other material are extracted by exposure to supercritical CO2,13 there is no measurable effect on the swelling behavior of the coal. This indicates that such extraction, if it occurs, does not significantly alter the basic structure of the coal. Although we did not find any irreversible effects in these coals, it should be remembered that the samples were dry. In a recent investigation that included moist coals, samples that swelled in high-pressure CO2 were found to shrink relative to their initial size when the CO2 pressure was reduced.3 Because coal seams are normally saturated with water, the effect of moisture on coal-swelling properties is an important area for further research. 3.2. Relationship between Swelling and Critical Temperature. Recently, it has been observed that the maximum sorption capacity of coal is related to the critical temperature, Tc, of the gas.14 The results presented here show that the maximum swelling is also strongly correlated with the critical temperature of the gas. The maximum swelling, Qmax, is

coal C 5.14 2.70 1.03 1.45 2.73 4.91 1.58 4.49 0.17 0.17 0.090 0.127 0.116 0.127 0.109 0.070 0.091 0.087

a Note that the values shown for He and Ne are the compression measured at 16 MPa.

Figure 2. Ratio of the linear strain in the perpendicular direction to the parallel direction for the three coals. The plot is a composite of all gases.

All samples exhibited anisotropic strains in all of the gases that caused swelling, with the strain always greater in the direction perpendicular to the bedding plane. Similarly, for He and Ne, which compressed the coals, the effect was always greater in the perpendicular plane. In Figure 2, the ratio of perpendicular/parallel strain is plotted as a function of pressure for all gases that induced swelling for all three coals. Despite the substantial differences in swelling between gases and coals, the perpendicular strain was always about 10-30% higher than in the parallel plane under all conditions of pressure and gas type. Coal B appeared to have a slightly lower ratio compared to the other two coals (Figure 2) but the difference was small and close to the experimental uncertainty of the measurements. Anisotropy is characteristic of most gas-induced coalswelling measurements, although the reported swelling ratios between the parallel and perpendicular planes vary considerably. For instance, Zare- bska and CeglarskaStefa nska19 measured strain ratios similar to those reported

(20) Pone, J. D. N.; Hile, M.; Halleck, P. M.; Mathews, J. P. Threedimensional carbon dioxide-induced strain distribution within a confined bituminous coal. Int. J. Coal Geol. 2009, 77, 103–108. (21) Larsen, J. W.; Flowers, R. A.; Hall, P. J.; Carlson, G. Structural rearrangement of strained coals. Energy Fuels 1997, 11, 998–1002.

(19) Zare-bska, K.; Ceglarska-Stefa nska, G. The change in effective stress associated with swelling during carbon dioxide sequestration on natural gas recovery. Int. J. Coal Geol. 2008, 74, 167–174.

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Day et al. Table 4. Maximum Sorption Capacity, W0, for the Three Coals in Each Gas maximum sorption capacity, W0 (vol %)

CO2 CH4 N2 Ar Kr Xe CF4 C2H6

coal A

coal B

coal C

7.95 5.45 2.88 3.71 5.93

15.1 7.05

16.5 9.10 4.98 14.2 6.66 14.3

It is also important to process data to eliminate the effects of measurement errors, which may lead to artifacts. Results obtained in this laboratory have shown that sorption measurements made at high pressures are particularly sensitive to uncertainties in the volume of the sample cells of the sorption apparatus.22 These uncertainties lead to disproportionately large errors in the sorption isotherm at high pressures. To account for these errors and minimize their effects on the values of maximum sorption capacity, W0, and heat of adsorption calculated from experimental data, the modified Dubinin-Radushkevich model proposed by Sakurovs et al. includes an additional term, k, that is proportional to gas density.15 This k term compensates for the volume errors but also includes the effects of any absorption of the gas by the coal. Because, in this study, coal expansion is directly observed optically, the cell volume is not required to calculate swelling. Accordingly, the modified Dubinin-Radushkevich equation when used in relation to swelling is not affected by errors in cell volume, and the k term is correspondingly lower than in sorption measurements. Absorption, however, may still be apparent, but recent data suggest that this component, if any, is very low and does not appear to affect swelling.14 The k term, therefore, can be neglected, so that for swelling, the modified Dubinin-Radushkevich equation reduces to eq 2. Sorption isotherms were measured for a range of gases on the three coals and fitted to the modified DubininRadushkevich adsorption model.14 The maximum sorption capacity, W0, of each gas and coal combination determined by Sakurovs et al.14 is shown in Table 4. To enable a direct comparison to the swelling data, the maximum sorption capacity has been expressed volumetrically, i.e., m3 of condensed gas (using the van der Waals density) per m3 of coal multiplied by 100 (i.e., volume %). Plotting Qmax versus maximum sorption capacity, W0 (Figure 4), shows that, while the two are highly correlated, they are not exactly proportional. A more detailed relationship is shown in Figure 5, where the volumetric swelling of coal C in each gas has been plotted as a function of absolute sorption (in volume %). In this case, the swelling data are the measured points (at all pressures); the absolute sorption data were calculated for the corresponding pressures using the modified Dubinin-Radushkevich model. Although there is some scatter in the data, the results follow a remarkably similar form, with all plots lying on essentially the same curve. Similar results were obtained for

Figure 3. Maximum swelling, Qmax, as a function of the critical temperature of the gas for coals A and C. Note that the data points shown for He and Ne (points below 50 K) are the measured points at 16 MPa.

plotted against Tc for coals A and C in Figure 3. Coal B has been omitted from Figure 3 for the sake of clarity but was very similar to coal C. Note that, for the He and Ne results, Qmax could not be calculated using eq 2. Consequently, the points for these gases in Figure 3 are the results measured at 16 MPa. In general, for all three coals, the maximum swelling, Qmax, increased as a linear function of the critical temperature. There are, however, some exceptions, specifically, CF4. For CF4, the measured point is well below the expected point based on the critical temperature relationship. This molecule is quite large, with a molecular volume of 6.32  10-5 m3 mol-1 (Table 1). It is therefore likely that the physical size of the molecule prevents it from fully accessing the pores of the coals, thus yielding a correspondingly lower degree of swelling. Ethane has a critical temperature of 305.4 K, which is very similar to CO2 (304.2 K). The critical temperature relationship therefore predicts that C2H6 should induce about the same level of swelling as CO2. However, C2H6 also has a large molecular volume of 6.50  10-5 m3 mol-1, even higher than CF4; therefore, it may be expected that the swelling would be low. The measured swelling results (Figure 3) show that the C2H6 swelling was in fact similar to CO2. The reason for the high swelling despite the high molecular size is possibly due to C2H6 being a linear-shaped molecule, whereas CF4 is more spherical. The C2H6 is probably able to gain access to the pore structure in the end-on orientation. If this is the general trend, the relatively high swelling (and sorption) induced by CO2 compared to most other gases is only due to its higher critical temperature. Furthermore, because the relationship between the swelling and critical temperature is linear for gases below a certain molecular size, we conclude that gas accessibility in the coal is about the same for all of these gases. Thus, for example, CO2, CH4, and N2 appeared to be able to access all of the pore structure of the coals equally well. If this were not the case, the relationship would not be linear. 3.3. Relationship between Swelling and Sorption. When the interaction between swelling and sorption is considered, care must be taken to ensure that the correct quantities are compared. Thus, for example, if sorption is compared to volumetric swelling, it is necessary to ensure that absolute sorption data (rather than excess sorption) are used and that they are expressed in volumetric units.

(22) Sakurovs, R.; Day, S.; Weir, S. Causes and consequences of errors in determining sorption capacity of coals for carbon dioxide at high pressure. Int. J. Coal Geol. 2009, 77, 16–22.

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Figure 4. Relationship between the maximum swelling, Qmax, to the maximum sorption capacity, W0, for the three coals.

Figure 6. Swelling (in all gases) as a function of absolute sorption for the three coals. The line plot is the polynomial best fit to the combined data for all three coals. The Blind Canyon, Pittsburgh, and Pocahontas data are from Keleman and Kwiatek.2

The results for the three Australian coals presented here are comparable to those reported by Kelemen and Kwiatek for several U.S. coals.2 In that study, swelling and sorption of CO2, CH4, and N2 were measured at pressures up to 1.8 MPa on three Argonne Premium coals of widely varying rank. They identified a nonlinear relationship between swelling and sorption but also found that the same relationship held for all gases and coals. Even significant temperature differences had little effect (their measurements were made at 30 and 75 °C). It is useful to compare the Kelemen and Kwiatek results to those for the Australian coals; however, in their study, adsorption was reported in units of mmol g-1 and linear strain was reported in ppm. To allow for a comparison to our results, it was necessary to recalculate the data in terms of volumetric swelling (assumed to be 3 times the linear strain) and volumetric sorption. The volumetric sorption was calculated using the van der Waals density for the condensed phase density, and the density of each coal was taken as 1.31 g mL-1 for Blind Canyon, 1.37 g mL-1 for Pittsburgh, and 1.38 g mL-1 for Pocahontas.23 The Kelemen and Kwiatek data are plotted in Figure 6 alongside the results for the Australian coals. Despite widely differing coals, gases, and even temperatures, all results follow the same trend. If these results are generally indicative of the swelling behavior, they are potentially very significant. They suggest that swelling can be accurately predicted entirely on the basis of the adsorption isotherm, regardless of the coal type or nature of the gas, and over a significant range of pressures and temperatures.

Figure 5. Swelling as a function of absolute sorption in various gases for coal C.

the other two coals, and indeed, the relationship between absolute sorption and swelling were virtually identical for all three coals. Figure 6 shows a plot of all of the data from the three coals; all points are closely grouped along the same curve. It is clear, however, that this relationship is not linear. At high gas sorption, the effect on swelling is proportionally greater than at low gas sorption. For example, at 5% sorption, only about 1% swelling is induced in the coal (i. e., sorption/swelling ratio of 5:1). However, between 14 and 16% sorption, the ratio reduces to 2:1. Regression analysis of the combined data showed that the best fit is a polynomial of the form Q ¼ -0:0037 þ 0:1596x þ 0:0101x2

ð3Þ

4. Conclusions An investigation of the swelling behavior has been conducted for three Australian coals in a wide range of different gases. Helium was found to induce no swelling, although the effects of mechanical compression were evident because the coals contracted slightly with increasing pressure. Neon also induced negligible swelling; however, if the effects of compression were removed, there was a very slight degree of swelling apparent. All other gases swelled the coals to varying extents.

where Q is the volumetric swelling and x is the absolute sorption (expressed volumetrically). The fit of the data to this expression was very good, with a r2 value of 0.9740. The reason for proportionally higher swelling with increasing sorption is unknown, but it could be related to a weakening of the coal, as suggested by Viete and Ranjith.6 If so, however, the effect is completely reversible because no permanent changes were observed even after repeated exposure to various gases. Further experiments with different sorbents may help to elucidate the mechanism at work.

(23) Huang, H.; Wang., K.; Bodily, D. M.; Hucka, V. J. Density measurements of Argonne Premium coal samples. Energy Fuels 1995, 9, 20–24.

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: DOI:10.1021/ef901588h

Day et al.

The amount of swelling induced in each coal could be accurately modeled using a Dubinin-Radushkevich equation, as modified by Sakurovs et al.15 In general, the maximum amount of swelling induced by a particular gas increased linearly with an increasing critical temperature of the gas. However, the swelling induced by CF4 was significantly lower than predicted from the critical temperature. Presumably, this was because the large size of the gas molecules prevented them from fully accessing the pores of the coal, thus producing less swelling. The dependence upon critical temperature suggests that, although the amount of swelling will vary from coal to coal, the maximum swelling ratio of CO2/CH4 (or any other gas that follows the relationship) will be constant. However, there is some evidence relating to sorption on coal that suggests that this ratio also depends upon the rank of coal; therefore, further work to investigate rank dependence upon swelling is warranted.14

The amount of swelling induced was found to be strongly correlated to the absolute sorption of gas according to a simple quadratic relationship. This relationship held for all of the coals and gases investigated. As well, swelling and sorption data for several U.S. coals measured by Kelemen and Kwiatek followed the same relationship.2 This suggests that there may be a single relationship, independent of coal type or the sorbate gas, that is capable of accurately predicting the swelling behavior of coal from the sorption isotherm alone. Such a relationship has the potential to improve reservoir models and may also eliminate the need to measure coal swelling if reliable isotherm data are available. Acknowledgment. The authors gratefully acknowledge the CSIRO Energy Transformed Flagship for the financial support for this research. We also thank Paul Marvig, who prepared the samples for the swelling experiments.

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