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Methane adsorption-induced coal swelling measured with an optical method
International Journal of Mining Science and Technology 25 (2015) 949–953
Contents lists available at ScienceDirect
International Journal of Mining Science and Technology journal homepage: www.elsevier.com/locate/ijmst
Methane adsorption-induced coal swelling measured with an optical method Tang Shuheng a,⇑, Wan Yi a, Duan Lijiang b, Xia Zhaohui b, Zhang Songhang a a b
School of Energy Resources, China University of Geosciences, Beijing 100083, China Asia-Pacific Department, PetroChina Research Institute of Petroleum Exploration & Development, Beijing 100083, China
a r t i c l e
i n f o
Article history: Received 21 February 2015 Received in revised form 27 March 2015 Accepted 13 May 2015 Available online 3 November 2015 Keywords: Coal Adsorption Methane Swelling Permeability
a b s t r a c t In order to quantify the effect of matrix shrinkage on reservoir permeability during coalbed methane production, coal samples from Huozhou, Changzhi and Jincheng areas in Shanxi province (classified as high-volatile bituminous coal, low-volatile bituminous coal and anthracite, respectively) were collected, and adsorption-induced coal swelling in methane were determined by an optical method at 40 °C and pressure up to 12 MPa. All three coals showed similar behavior-that swelling increased as a function of pressure up to about 10 MPa but thereafter no further increase in swelling was observed. Swelling in the direction perpendicular to the bedding plane is greater than that parallel to the bedding plane, and the differences are about 7.77–8.33%. The maximum volumetric swelling ranges from 2.73% to 3.21%-increasing with increasing coal rank. The swelling data can be described by a modified DR model. In addition, swelling increases with the amount of adsorption. However, the increase shows a relatively slower stage followed by a relatively faster stage instead of a linear increase. Based on the assumption that sorption-induced swelling/shrinkage of coal in methane is reversible, the permeability increases induced by coal shrinkage during methane desorption was analyzed, and the results indicate that the permeability change is larger for higher rank coal in the same unit of pressure depletion. Ó 2015 Published by Elsevier B.V. on behalf of China University of Mining & Technology.
1. Introduction During coalbed methane production, there are two well-known distinct phenomena associated with reservoir pressure depletion. The first is the effective stress increase with the fluid pressure reduction, and the other is the shrinkage of the coal with gas desorption. Reducing fluid pressure tends to close the cleats, reducing permeability, while shrinkage tends to open them, increasing permeability [1]. As to the former issue, much research has been conducted, and the conclusions are consistent [2–4]. However, as to the latter issue, few data could be attained in published articles owing to the difficulty of the measurement. Furthermore, shrinkage is also influenced by other factors such as petrologic composition, sample size and experimental procedure. Coal swelling is usually determined by strain gauge, and the adopted sample is usually a lump with strain gauges adhered to its smooth surface. By this method, Maffat and Weale found that swelling in methane increased with pressure up to a maximum at 15.2 MPa [5]. Significant anisotropy was also observed, i.e.
greater swelling in the direction perpendicular than parallel to the bedding plane. Lin and Zhou found that the increase in swelling with pressure is similar to the shape of the Langmuir curve, and the swelling in two directions is similar [6]. Harpalani and Schraufnagel found that swelling increased linearly with pressure, but shrinkage was nonlinear in the process of pressure dropping [7]. Levine observed that the relationship between swelling and pressure was of a similar expression to the Langmuir equation [8]. St. George and Barakat reported a volumetric shrinkage in coal up to 0.5% when releasing the pressure from 4 MPa to atmospheric pressure in a coal sample previously saturated with methane [9]. Chikatamarla et al. showed that swelling and pressure can be described using a Langmuir-like equation and that the swelling is approximately proportional to the amount of gas adsorbed [10]. By comparing swelling/shrinkage of coal in methane over three cycles of adsorption/desorption, Majewska and Zie˛tek found that swelling is anisotropic in two directions perpendicular and parallel to the bedding plane. In addition, maximum swelling in the first cycle is higher than that in the second and third [11]. Using coal specimens in the shape of 15 mm 15 mm 5 mm plates, Zare˛bska and Celarska-Stefan´ska observed that the swelling at
⇑ Corresponding author. Tel.: +86 10 82320601. E-mail address: [email protected] (S. Tang). http://dx.doi.org/10.1016/j.ijmst.2015.09.011 2095-2686/Ó 2015 Published by Elsevier B.V. on behalf of China University of Mining & Technology.
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S. Tang et al. / International Journal of Mining Science and Technology 25 (2015) 949–953
3.6 MPa was 0.4% and 0.3% in the two directions, perpendicular and parallel to the bedding plane respectively [12]. Optical methods have been adopting for swelling measurement in recent years. Ottiger et al. and Pini et al. used a coal disc of about 22 mm in diameter to measure swelling, and found that swelling isotherms could be effectively described by Langmuir-like equations until the pressure reached 11.6 MPa [13,14]. Van Bergen et al. found the linear swelling is 0.65% at 8 MPa for a cube-like sample 1.0–1.5 mm3 in volume, and the sample returned to its original size after gas release [15]. Because the strain gauge may not deform homogeneously with the coal, leading to greater error, an optical method has an obvious advantage. However, it should be pointed out that the equilibrium time (about 2 days at each pressure step) is long and the assumption of isotropic swelling is not accurate in the experiments conducted by Ottiger et al. and Pini et al. [13,14]. The error (about 0.3%) is obvious in the experiments conducted by Van Bergen et al. in determining the linear expansion [15]. Furthermore, all three experiments mentioned above used dry samples, which are not consistent with reservoir conditions. In this study, water equilibrium coal pieces were adopted, which can both assure a short equilibrium time and high measuring precision. 2. Experimental 2.1. Samples In this study, three lumps of coal were collected from Xinzhi mine of Huozhou, Changcun mine of Changzhi and Sihe mine of Jincheng area in Shanxi province. The maceral composition of the three coals is shown in Table 1. Coal test pieces were cut from each of the three lumps of coal. 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. The dimensions of the perpendicular and parallel blocks were nominally 20 mm 5 mm 2 mm. Prior to the measurements, all of the six specimens were stored in a sealed chamber containing a saturated solution of potassium sulphate to maintain a constant relative humidity of 96%. 2.2. Apparatus A schematic diagram of the swelling apparatus is shown in Fig. 1. The heart of the system is a high pressure sight cell with transparent glass windows on opposite sides through which the samples could be directly observed. In the experiment, the cell is heated with a thermocouple and can be maintained at a constant temperature to within ±0.5 °C of the set point. The volume of the cell is about 200 mL, and the maximum permissible pressure of the system is about 20 MPa. A digital photo camera (Sony, model DSC-T90 12MP CCD) is used to collect images through the transparent glass window of the cell. In order to minimize the relative error, all of the results used in this study are based on the measurements made along the length (the longer dimension) of each sample block. Initial trials of the apparatus indicated that, particularly at higher pressures, the change in the refractive index of the methane
Pressure transducer
P
Camera
Coal
Ro,max
Vitrinite
Fusinite
Liptinite
Minerals
Huozhou Changzhi Jincheng
0.85 1.89 2.89
74.35 91.88 94.07
19.73 1.62 0.54
1.85
4.01 6.48 5.29
T
P Cell Transparent glass window
CH 4 Sample PC
Steel wire
Thermocouple
Fig. 1. Schematic diagram of the apparatus for measuring coal swelling.
in the cell was sufficient to affect the apparent length measured by the cameras. To overcome this problem, the apparent length of each sample was normalized to the apparent length of a reference thin steel wire. The steel wire was hung parallel to the coal specimen in the cell with a similar length as the samples. Because the steel wire is non-reactive with methane and the thermal expansion can be ignored at the constant temperature, it is assumed that there is no dimension change of the steel wire during the experiment. The collected image of steel wire and coal specimen was transferred into a PC, and then opened by ACD See-10 image analysis software. The image was amplified and analyzed by MB-ruler software. In each measurement, the apparent length of the sample, L1, and the steel wire, L2, on the photo were recorded simultaneously. On the hypothesis that the length of the steel wire, d, does not change, the true length of the sample, L, can be obtained from the Eq. (1):
L ¼ ðd L2 Þ=L1
ð1Þ
An average length of each specimen was obtained by 4 measurements along its length at 4 points. With this correction, the overall sensitivity of the apparatus is less than about 0.01 mm. 2.3. Procedures Both the sample and the steel wire were clamped on the top with a clip (to keep the top sealable), then hung in the cell inner top (with the steel wire placed between the sample and camera as was shown in Fig. 1). After sealing the sample cell, the system was heated and kept at about 40 °C. First, samples were degassed under vacuum for about 24 h, and then the length of the sample and steel wire were measured and calculated every 30 min. When the values of the three consecutive tests remained stable, equilibrium was considered to be established in the system, and the length of the sample and the pressure in the cell were recorded. The equilibrium time is about 5 h at different pressures. Afterwards, the pressure was increased to the next set point and the procedure repeated, as described above. In this experiment, a total of seven pressure points were set up for every sample, i.e. 1, 2, 4, 6, 8, 10 and 12 MPa. After measurement, the pressure was reduced to atmospheric. For every sample, the length and the volume obtained under the vacuum condition was referred to the reference length. The axial strain, e, for each sample is given by Eq. (2):
e¼
Table 1 Details of the three coal samples (%).
Vent and vacuum
Li L0 L0
ð2Þ
where Li and L0 are the sample length at the set point of pressure and vacuum, respectively. Volumetric swelling for each sample was calculated by assuming that expansion in the two parallel dimensions was equal;
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thus the volumetric expansion per volume at each pressure step is given by Eq. (3):
1.0
Length change (%)
DV ¼ ð1 þ e1 Þ2 ð1 þ e2 Þ 1 V0
1.2
ð3Þ
where DV and V0 are the swelling volume by gas adsorption and the reference volume of the sample, respectively; e1 and e2 are the length changes of the parallel and perpendicular samples.
0.8 0.6 Parallel
0.4
Perpendicular 0.2 0
2
4
3. Results
6
8
10
12
14
Pressure (MPa)
Fig. 3. Linear expansion of Changzhi sample as a function of methane pressure.
1.2
Length change (%)
1.0 0.8 0.6 Parallel
0.4
Perpendicular
0.2
0
2
4
6
8
10
12
14
Pressure (MPa)
Fig. 4. Linear expansion of Jincheng sample as a function of methane pressure.
3.5 Volumetric expansion (%)
The length of each sample increased with increasing methane pressure as shown in Figs. 2–4. After an initial rapid increase in length, a maximum value was reached at about 10 MPa. Further increase in pressure had little or no effect on the swelling. In all cases, the maximum expansions in the direction perpendicular to the bedding plane are greater than that in the parallel plane, and the differences are about 7.77% to 8.33%. Volumetric swelling for each coal as a function of pressure is plotted in Fig. 5. Obviously, the maximum swelling of each sample increased with coal rank as shown in Table 2. Coal swelling is usually described by Langmuir-like equations, which indicate that swelling increases with pressure increase. However, in this study the swelling shows decreasing trends after the maximum swelling was observed at relatively high pressure, which is consistent with the results of Maffat and Weale [5]. Pan and Connell further explained that the matrix compression, as a result of pore pressure increase, dominates the dimension changes of sample instead of adsorption-induced swelling at high pressure [16]. The maximum swelling did not occur in the measurements of Ottiger et al. and Pini et al., which may be due to the difference in experimental procedure, petrologic composition of samples, and so on [13,14]. Day et al. used a modified DR model, in which a maximum swelling was included, to fit CO2-induced coal swelling, and the results fitted extremely well at pressures up to 15 MPa [17]. In this study, this model was adopted, and is shown in Eq. (4):
3.0 2.5 2.0 1.5
Huozhou coal Changzhi coal Jincheng coal
1.0 0.5
S ¼ Smax eD½lnðqa =qg Þ þ kqg 2
ð4Þ 0
where Smax is the maximum swelling of the coal, qg is the density of the gas at the temperature and pressure, qa is the density of the adsorbed phase (taken to be 420 kg/m3)[18], k is a constant related to the solubility of methane into the coal, and D is an empirical curve fitting parameter. This model was applied to the swelling data measured on all the three samples and the fits were found to be good, as shown by the line plots in Fig. 6 and Table 3. Though the maximum swelling, Smax, determined by this model is slight higher than the measured value, this model is better than the Langumir-like model as discussed above. In addition, Smax increases with coal rank, which is consistent with measured results.
Length change (%)
1.0
2
4
6
8
10
12
14
Pressure (MPa)
Fig. 5. Volumetric swelling of samples from three mine areas as a function of methane pressure.
Table 2 Maximum length and volume changes in the three coals (%). Coal
Huozhou Changzhi Jincheng
Maximum length change Perpendicular
Parallel
0.95 1.04 1.11
0.88 0.96 1.03
Maximum volume change
2.73 2.98 3.21
4. Discussion
0.8 0.6 Parallel
0.4
Perpendicular 0.2
0
2
4
6
8
10
12
14
Pressure (MPa)
Fig. 2. Linear expansion of Huozhou sample as a function of methane pressure.
Because the relationship between swelling and pressure is similar to the Langmuir model in former experiments, many scholars have proposed that swelling is proportional to gas adsorption [10,16,19]. Combining the data from a previous study where the methane adsorption capacities of coals from the same areas were measured at 40 °C up to 12 MPa [20], both the volumetric swelling and the amount of methane adsorbed were plotted in the same figure as shown in Fig. 7. The results indicate that swelling increases with adsorption, and the tendency seems to be slower at the first stage and faster at the second stage.
S. Tang et al. / International Journal of Mining Science and Technology 25 (2015) 949–953 3.5
3.5
3.0
3.0
Volumetric expansion (%)
Volumetric expansion (%)
952
2.5 2.0
Huozhou coal measured Huozhou coal model Changzhi coal measured Changzhi coal model Jincheng coal measured Jincheng coal model
1.5 1.0 0.5 0
20
40
60
80
2.5 2.0 1.5 Huozhou coal Changzhi coal Jincheng coal
1.0 0.5 0
100
5
10
Gas density (kg/m3 )
15
20
25
30
Adsorption (m3/t)
Fig. 6. Volumetric swelling of samples from three areas attained by measuring and model.
Fig. 7. Volumetric swelling of samples from three mine areas as a function of sorption.
Usually, swelling is interpreted as adsorption inducing a change in the coal specific surface energy, which can be compensated by the elastic energy change associated to the volume change [16,21]. At low pressure, methane molecules adsorbed on coal surfaces mainly in the form of a monolayer, which may be the reason for the linear relationship between swelling and amount adsorbed. However, at high pressure the swelling characteristic, which is nonlinear, cannot be explained by this theory. It is proposed that with increasing pressure, gas molecules penetrate into the coal matrix, i.e. absorption, which may destroy the interconnections in the coal network, and make it expand outwards. The increase in sorption (mainly as absorption) is small at this stage but results in larger swelling. Lin and Zhou found that the maximum swelling of middle-rank coal is lower than that of low-rank and high-rank coal [6]. Chikatamarla et al. found that strain increased with coal maturity in rank from lignite to bituminous coal [10]. In this study, the maximum swelling increased with rank, consistent with the change in the amount of gas adsorbed. It is proposed that micropores abound in higher rank coal, which leads to more adsorption and absorption and thus, larger swelling. Because the number of samples used in this experiment were limited and the impacts of maceral composition on coal swelling are unknown, further study should be carried out to probe the relationship between swelling and coal rank. Coal swelling in methane is anisotropic, which is also often observed in organic solvents. As in the latter case, two explanations have been proposed to explain this effect; the preferential orientation of cross-links in the macromolecular network in coal, and ‘‘locked in” strain derived from overburden pressure gradients [22–25]. These two explanations may, in essence, be the same because the macromolecular network in coal may be compressed during coalification, so the strain is stored. As to the former case, Zare˛bska and Celarska-Stefan´ska proposed that methane molecules penetrating the carbon matter in the direction perpendicular to the bedding plane have to overcome smaller energy resistance than those entering the structure in the direction parallel to the bedding plane, hence greater swelling occurs as the inter-molecular distances are larger than those between particular high-molecular elements [12]. However, this needs further evidence. So, the anisotropic swelling might be attributable to the different degree of recovery of strain in two planes exposed to methane.
Fu et al. analyzed the permeability increase induced by coal shrinkage during methane desorption [26,27]. However, the strain data were derived from a CO2-induced coal swelling experiment and because CO2 can induce more coal swelling than methane, the results of Fu et al. are not accurate [6,8–10,13,14]. Gray stated that unconstrained (stress-free) strain data is appropriate for use in his coal permeability model and several scholars have also adopted the unconstrained strain data in their permeability models [1,28–30]. In this study, unconstrained strain data was also used to calculate permeability. It is assumed that the adsorption-induced swelling is equal to desorption-induced shrinkage, so the measured swelling values could be acting as shrinkage during pressure depletion. 10 MPa corresponds to the pressure at about 1000 m below ground, which is the current maximum depth of economic coalbed methane development in China, so the impact of matrix shrinkage on permeability was analyzed for conditions below this pressure point. The increment of permeability induced by matrix shrinkage, DKe, is given by Eq. (5):
Coal Huozhou Changzhi Jincheng
Smax (%) 2.947326 3.587185 3.811353
D 0.0447874 0.0542836 0.0475446
k 0.0010962 0.0017025 0.0023360
R2 (%) 99.27537 99.44247 99.13374
" # Deji 3 1þ 1 100%
ð5Þ
ui
where K i and K j are the permeability at initial pressure pi and current pressure pj , Deji is the matrix shrinkage from pi to pj , and ui is the porosity at pi [8]. Based on the porosity of coal in the Huozhou, Changzhi and Jincheng areas (which are 13.8%, 3.27% and 2.56% respectively), the increase in permeability at each pressure relative to 10 MPa could be calculated. As shown in Fig. 8, the permeability change is larger for higher rank coal in the same unit of pressure depletion. The initial permeability is low in higher rank coal for a tight matrix, which results in
300
Permeability increment (%)
Table 3 Modified DR parameters when applied to swelling data.
Kj Ki DK e ¼ 100% ¼ Ki
Huozhou coal Changzhi coal Jincheng coal
250 200 150 100 50
0
2
4
6
8
10
Pressure (MPa)
Fig. 8. Permeability increment of samples from three areas during pressure depletion.
S. Tang et al. / International Journal of Mining Science and Technology 25 (2015) 949–953
weak leakage and slow pressure expansion, so the permeability increment for higher rank coal is not obvious in coalbed methane development. 5. Conclusions With increasing methane pressure, coal size change can be divided into three stages; rapid increase, slow increase and decrease. The swelling is nonlinear to gas sorption, which may be because it is controlled by adsorption-induced swelling, absorption-induced breakage and expansion of interconnections in the coal network, and matrix compression as a result of pore pressure. Anisotropic swelling, which is greater perpendicular to the bedding plane than parallel to it, was observed in this study, which might be attributable to the different degree of recovery of strain in two planes. Higher rank coal has the largest capacity for adsorption and absorption, and thus has larger swelling. Based on the assumption that sorption-induced swelling/shrinkage of coal in methane is reversible, the permeability increase induced by coal shrinkage during methane desorption was analyzed, and the results indicate that the permeability change is larger for higher rank coal in the same unit of pressure depletion. Acknowledgments This research is funded by the National Key Technology Support Program of China (No. 2014BAC18B02), and the National Natural Science Foundation of China (Nos. 41272176 and 41202116). References [1] Gray I. Reservoir engineering in coal seams: Part 1-the physical process of gas storage and movement in coal seams. SPE Reserv Eng 1987;2:28–34. [2] Seidle JP. Application of matchstick geometry to stress dependent permeability in coals. In: SPE rocky mountain regional meeting, Wyoming; 1992. p. 433–45. [3] Enever RE, Hennig A. The relationship between permeability and effective stress for Australian. In: The 1997 international coalbed methane symposium, Alabama. p. 13–22. [4] Connolly P, Cosgrove J. Prediction of fracture-induced permeability and fluid flow in the crust using experimental stress data. AAPG Bull 1999;83 (5):757–77. [5] Moffat DH, Weale KE. Sorption by coal of methane at high pressures. Fuel 1955;34:449–62. [6] Lin BQ, Zhou SN. Experimental investigation on the deformation law of coal body with methane. J China Coll Min Technol 1986;3:9–16. [7] Harpalani S, Schraufnagel RA. Shrinkage of coal matrix with release of gas and its impact on permeability of coal. Fuel 1990;69:551–6.
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[8] Levine JR. Model study of the influence of matrix shrinkage on absolute permeability of coal bed reservoirs. In: Geological Society Special Publication, London; 1996. p. 197–212. [9] St. George JD, Barakat MA. The change in effective stress associated with shrinkage from gas desorption in coal. Int J Coal Geol 2001;69(6):105–13. [10] Chikatamarla L, Cui X, Bustin RM. Implications of volumetric swelling/ shrinkage of coal in sequestration of acid gases. In: 2004 International coalbed methane symposium proceedings, Alabama. p. 435. [11] Majewska S, Zie˛tek J. Change of acoustic emission and strain in hard coal during gas sorption-desorption cycles. Int J Coal Geol 2007;70:305–12. [12] Zare˛bska K, Celarska-Stefan´ska G. The change in effective stress associated with swelling during carbon dioxide sequestration on natural gas recovery. Int J Coal Geol 2008;74:167–74. [13] Ottiger S, Pini R, Storti G, Mazzotti M. Competitive adsorption equilibria of CO2 and CH4 on a dry coal. Asorption 2008;14:539–56. [14] Pini R, Ottiger S, Burlini L, Storti G, Mazzotti M. CO2 storage through ECBM recovery: an experimental and modeling study. Energy Proc 2009;1:1711–7. [15] 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. [16] Pan Z, Connell LD. A theoretical model for gas adsorption-induced coal swelling. Int J Coal Geol 2007;69:243–52. [17] Day S, Fry R, Sakurovs R. Swelling of Australian coals in supercritical CO2. Int J Coal Geol 2008;74:41–52. [18] Sudibandriyo M, Pan Z, Fitzgerald JE, Robinson RL, Gasem KAM. Adsorption of methane, nitrogen, carbon dioxide and their binary mixtures on dry activated carbon at 318.2 K and pressures up to 13.6 MPa. Langmuir 2003;19:5323–31. [19] Cui X, Bustin RM. Volumetric strain associated with methane desorption and its impact on coalbed gas production from deep coal seams. AAPG Bull 2005;89:1181–202. [20] Tang SH. Multi-component gas adsorption-desorption of coal from Jincheng, Shanxi, China. Beijing: China University of Mining & Technology; 2001. [21] Scherer GW. Dilatation of porous-glass. J Am Ceram Soc 1986;69:473–80. [22] Cody GD, Larsen JW, Siskin M. Anisotropic solvent swelling of coals. Energy Fuels 1988;2:340–4. [23] Hou L, Hatcher PG, Botto RE. Diffusion of pyridine in Illinois No.6 coal: measuring the swelling and deswelling characteristics by combined methods of nuclear magnetic resonance (NMRI) and nuclear resonance imaging (NMRI). Int J Coal Geol 1996;32:167–89. [24] Hall PJ, Larsen JW. Use of Einstein specific heat models to elucidate coal structure and changes in coal structure following solvent extraction. Energy Fuels 1993;7:42–51. [25] Larsen JW, Flowers RA, Hall PJ. Structural rearrangement of strained coals. Energy Fuels 1997;11:998–1002. [26] Fu XH, Qin Y, Zhang WH. Coupling correlation between high-rank coal matrix mechanic effect and coal reservoir permeability. Geol J China Univ 2003;9 (3):373–7. [27] Fu XH, Qin Y, Jiang B. Study on the ‘‘bottle-neck” problem of coalbed methane productivity of high-rank coal reservoirs. Geol Rev 2004;50(5):507–13. [28] Palmer I, Mansoori J. How permeability depends on stress and pore pressure in coalbeds: a new model. SPE 1998;1(6):539–44. [29] Pekot LJ, Reeves SR. Modeling the effects of matrix shrinkage and differential swelling on coalbed methane recovery and carbon sequestration. In: 2003 International coalbed methane symposium, Alabama; 2003. [30] Shi JQ, Durucan S. Changes in permeability in coalbeds during primary recovery-Part 1: model formulation and analysis. In: 2003 International coalbed methane symposium, University of Alabama, Alabama; 2003. p. 341.
Contents lists available at ScienceDirect
International Journal of Mining Science and Technology journal homepage: www.elsevier.com/locate/ijmst
Methane adsorption-induced coal swelling measured with an optical method Tang Shuheng a,⇑, Wan Yi a, Duan Lijiang b, Xia Zhaohui b, Zhang Songhang a a b
School of Energy Resources, China University of Geosciences, Beijing 100083, China Asia-Pacific Department, PetroChina Research Institute of Petroleum Exploration & Development, Beijing 100083, China
a r t i c l e
i n f o
Article history: Received 21 February 2015 Received in revised form 27 March 2015 Accepted 13 May 2015 Available online 3 November 2015 Keywords: Coal Adsorption Methane Swelling Permeability
a b s t r a c t In order to quantify the effect of matrix shrinkage on reservoir permeability during coalbed methane production, coal samples from Huozhou, Changzhi and Jincheng areas in Shanxi province (classified as high-volatile bituminous coal, low-volatile bituminous coal and anthracite, respectively) were collected, and adsorption-induced coal swelling in methane were determined by an optical method at 40 °C and pressure up to 12 MPa. All three coals showed similar behavior-that swelling increased as a function of pressure up to about 10 MPa but thereafter no further increase in swelling was observed. Swelling in the direction perpendicular to the bedding plane is greater than that parallel to the bedding plane, and the differences are about 7.77–8.33%. The maximum volumetric swelling ranges from 2.73% to 3.21%-increasing with increasing coal rank. The swelling data can be described by a modified DR model. In addition, swelling increases with the amount of adsorption. However, the increase shows a relatively slower stage followed by a relatively faster stage instead of a linear increase. Based on the assumption that sorption-induced swelling/shrinkage of coal in methane is reversible, the permeability increases induced by coal shrinkage during methane desorption was analyzed, and the results indicate that the permeability change is larger for higher rank coal in the same unit of pressure depletion. Ó 2015 Published by Elsevier B.V. on behalf of China University of Mining & Technology.
1. Introduction During coalbed methane production, there are two well-known distinct phenomena associated with reservoir pressure depletion. The first is the effective stress increase with the fluid pressure reduction, and the other is the shrinkage of the coal with gas desorption. Reducing fluid pressure tends to close the cleats, reducing permeability, while shrinkage tends to open them, increasing permeability [1]. As to the former issue, much research has been conducted, and the conclusions are consistent [2–4]. However, as to the latter issue, few data could be attained in published articles owing to the difficulty of the measurement. Furthermore, shrinkage is also influenced by other factors such as petrologic composition, sample size and experimental procedure. Coal swelling is usually determined by strain gauge, and the adopted sample is usually a lump with strain gauges adhered to its smooth surface. By this method, Maffat and Weale found that swelling in methane increased with pressure up to a maximum at 15.2 MPa [5]. Significant anisotropy was also observed, i.e.
greater swelling in the direction perpendicular than parallel to the bedding plane. Lin and Zhou found that the increase in swelling with pressure is similar to the shape of the Langmuir curve, and the swelling in two directions is similar [6]. Harpalani and Schraufnagel found that swelling increased linearly with pressure, but shrinkage was nonlinear in the process of pressure dropping [7]. Levine observed that the relationship between swelling and pressure was of a similar expression to the Langmuir equation [8]. St. George and Barakat reported a volumetric shrinkage in coal up to 0.5% when releasing the pressure from 4 MPa to atmospheric pressure in a coal sample previously saturated with methane [9]. Chikatamarla et al. showed that swelling and pressure can be described using a Langmuir-like equation and that the swelling is approximately proportional to the amount of gas adsorbed [10]. By comparing swelling/shrinkage of coal in methane over three cycles of adsorption/desorption, Majewska and Zie˛tek found that swelling is anisotropic in two directions perpendicular and parallel to the bedding plane. In addition, maximum swelling in the first cycle is higher than that in the second and third [11]. Using coal specimens in the shape of 15 mm 15 mm 5 mm plates, Zare˛bska and Celarska-Stefan´ska observed that the swelling at
⇑ Corresponding author. Tel.: +86 10 82320601. E-mail address: [email protected] (S. Tang). http://dx.doi.org/10.1016/j.ijmst.2015.09.011 2095-2686/Ó 2015 Published by Elsevier B.V. on behalf of China University of Mining & Technology.
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S. Tang et al. / International Journal of Mining Science and Technology 25 (2015) 949–953
3.6 MPa was 0.4% and 0.3% in the two directions, perpendicular and parallel to the bedding plane respectively [12]. Optical methods have been adopting for swelling measurement in recent years. Ottiger et al. and Pini et al. used a coal disc of about 22 mm in diameter to measure swelling, and found that swelling isotherms could be effectively described by Langmuir-like equations until the pressure reached 11.6 MPa [13,14]. Van Bergen et al. found the linear swelling is 0.65% at 8 MPa for a cube-like sample 1.0–1.5 mm3 in volume, and the sample returned to its original size after gas release [15]. Because the strain gauge may not deform homogeneously with the coal, leading to greater error, an optical method has an obvious advantage. However, it should be pointed out that the equilibrium time (about 2 days at each pressure step) is long and the assumption of isotropic swelling is not accurate in the experiments conducted by Ottiger et al. and Pini et al. [13,14]. The error (about 0.3%) is obvious in the experiments conducted by Van Bergen et al. in determining the linear expansion [15]. Furthermore, all three experiments mentioned above used dry samples, which are not consistent with reservoir conditions. In this study, water equilibrium coal pieces were adopted, which can both assure a short equilibrium time and high measuring precision. 2. Experimental 2.1. Samples In this study, three lumps of coal were collected from Xinzhi mine of Huozhou, Changcun mine of Changzhi and Sihe mine of Jincheng area in Shanxi province. The maceral composition of the three coals is shown in Table 1. Coal test pieces were cut from each of the three lumps of coal. 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. The dimensions of the perpendicular and parallel blocks were nominally 20 mm 5 mm 2 mm. Prior to the measurements, all of the six specimens were stored in a sealed chamber containing a saturated solution of potassium sulphate to maintain a constant relative humidity of 96%. 2.2. Apparatus A schematic diagram of the swelling apparatus is shown in Fig. 1. The heart of the system is a high pressure sight cell with transparent glass windows on opposite sides through which the samples could be directly observed. In the experiment, the cell is heated with a thermocouple and can be maintained at a constant temperature to within ±0.5 °C of the set point. The volume of the cell is about 200 mL, and the maximum permissible pressure of the system is about 20 MPa. A digital photo camera (Sony, model DSC-T90 12MP CCD) is used to collect images through the transparent glass window of the cell. In order to minimize the relative error, all of the results used in this study are based on the measurements made along the length (the longer dimension) of each sample block. Initial trials of the apparatus indicated that, particularly at higher pressures, the change in the refractive index of the methane
Pressure transducer
P
Camera
Coal
Ro,max
Vitrinite
Fusinite
Liptinite
Minerals
Huozhou Changzhi Jincheng
0.85 1.89 2.89
74.35 91.88 94.07
19.73 1.62 0.54
1.85
4.01 6.48 5.29
T
P Cell Transparent glass window
CH 4 Sample PC
Steel wire
Thermocouple
Fig. 1. Schematic diagram of the apparatus for measuring coal swelling.
in the cell was sufficient to affect the apparent length measured by the cameras. To overcome this problem, the apparent length of each sample was normalized to the apparent length of a reference thin steel wire. The steel wire was hung parallel to the coal specimen in the cell with a similar length as the samples. Because the steel wire is non-reactive with methane and the thermal expansion can be ignored at the constant temperature, it is assumed that there is no dimension change of the steel wire during the experiment. The collected image of steel wire and coal specimen was transferred into a PC, and then opened by ACD See-10 image analysis software. The image was amplified and analyzed by MB-ruler software. In each measurement, the apparent length of the sample, L1, and the steel wire, L2, on the photo were recorded simultaneously. On the hypothesis that the length of the steel wire, d, does not change, the true length of the sample, L, can be obtained from the Eq. (1):
L ¼ ðd L2 Þ=L1
ð1Þ
An average length of each specimen was obtained by 4 measurements along its length at 4 points. With this correction, the overall sensitivity of the apparatus is less than about 0.01 mm. 2.3. Procedures Both the sample and the steel wire were clamped on the top with a clip (to keep the top sealable), then hung in the cell inner top (with the steel wire placed between the sample and camera as was shown in Fig. 1). After sealing the sample cell, the system was heated and kept at about 40 °C. First, samples were degassed under vacuum for about 24 h, and then the length of the sample and steel wire were measured and calculated every 30 min. When the values of the three consecutive tests remained stable, equilibrium was considered to be established in the system, and the length of the sample and the pressure in the cell were recorded. The equilibrium time is about 5 h at different pressures. Afterwards, the pressure was increased to the next set point and the procedure repeated, as described above. In this experiment, a total of seven pressure points were set up for every sample, i.e. 1, 2, 4, 6, 8, 10 and 12 MPa. After measurement, the pressure was reduced to atmospheric. For every sample, the length and the volume obtained under the vacuum condition was referred to the reference length. The axial strain, e, for each sample is given by Eq. (2):
e¼
Table 1 Details of the three coal samples (%).
Vent and vacuum
Li L0 L0
ð2Þ
where Li and L0 are the sample length at the set point of pressure and vacuum, respectively. Volumetric swelling for each sample was calculated by assuming that expansion in the two parallel dimensions was equal;
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thus the volumetric expansion per volume at each pressure step is given by Eq. (3):
1.0
Length change (%)
DV ¼ ð1 þ e1 Þ2 ð1 þ e2 Þ 1 V0
1.2
ð3Þ
where DV and V0 are the swelling volume by gas adsorption and the reference volume of the sample, respectively; e1 and e2 are the length changes of the parallel and perpendicular samples.
0.8 0.6 Parallel
0.4
Perpendicular 0.2 0
2
4
3. Results
6
8
10
12
14
Pressure (MPa)
Fig. 3. Linear expansion of Changzhi sample as a function of methane pressure.
1.2
Length change (%)
1.0 0.8 0.6 Parallel
0.4
Perpendicular
0.2
0
2
4
6
8
10
12
14
Pressure (MPa)
Fig. 4. Linear expansion of Jincheng sample as a function of methane pressure.
3.5 Volumetric expansion (%)
The length of each sample increased with increasing methane pressure as shown in Figs. 2–4. After an initial rapid increase in length, a maximum value was reached at about 10 MPa. Further increase in pressure had little or no effect on the swelling. In all cases, the maximum expansions in the direction perpendicular to the bedding plane are greater than that in the parallel plane, and the differences are about 7.77% to 8.33%. Volumetric swelling for each coal as a function of pressure is plotted in Fig. 5. Obviously, the maximum swelling of each sample increased with coal rank as shown in Table 2. Coal swelling is usually described by Langmuir-like equations, which indicate that swelling increases with pressure increase. However, in this study the swelling shows decreasing trends after the maximum swelling was observed at relatively high pressure, which is consistent with the results of Maffat and Weale [5]. Pan and Connell further explained that the matrix compression, as a result of pore pressure increase, dominates the dimension changes of sample instead of adsorption-induced swelling at high pressure [16]. The maximum swelling did not occur in the measurements of Ottiger et al. and Pini et al., which may be due to the difference in experimental procedure, petrologic composition of samples, and so on [13,14]. Day et al. used a modified DR model, in which a maximum swelling was included, to fit CO2-induced coal swelling, and the results fitted extremely well at pressures up to 15 MPa [17]. In this study, this model was adopted, and is shown in Eq. (4):
3.0 2.5 2.0 1.5
Huozhou coal Changzhi coal Jincheng coal
1.0 0.5
S ¼ Smax eD½lnðqa =qg Þ þ kqg 2
ð4Þ 0
where Smax is the maximum swelling of the coal, qg is the density of the gas at the temperature and pressure, qa is the density of the adsorbed phase (taken to be 420 kg/m3)[18], k is a constant related to the solubility of methane into the coal, and D is an empirical curve fitting parameter. This model was applied to the swelling data measured on all the three samples and the fits were found to be good, as shown by the line plots in Fig. 6 and Table 3. Though the maximum swelling, Smax, determined by this model is slight higher than the measured value, this model is better than the Langumir-like model as discussed above. In addition, Smax increases with coal rank, which is consistent with measured results.
Length change (%)
1.0
2
4
6
8
10
12
14
Pressure (MPa)
Fig. 5. Volumetric swelling of samples from three mine areas as a function of methane pressure.
Table 2 Maximum length and volume changes in the three coals (%). Coal
Huozhou Changzhi Jincheng
Maximum length change Perpendicular
Parallel
0.95 1.04 1.11
0.88 0.96 1.03
Maximum volume change
2.73 2.98 3.21
4. Discussion
0.8 0.6 Parallel
0.4
Perpendicular 0.2
0
2
4
6
8
10
12
14
Pressure (MPa)
Fig. 2. Linear expansion of Huozhou sample as a function of methane pressure.
Because the relationship between swelling and pressure is similar to the Langmuir model in former experiments, many scholars have proposed that swelling is proportional to gas adsorption [10,16,19]. Combining the data from a previous study where the methane adsorption capacities of coals from the same areas were measured at 40 °C up to 12 MPa [20], both the volumetric swelling and the amount of methane adsorbed were plotted in the same figure as shown in Fig. 7. The results indicate that swelling increases with adsorption, and the tendency seems to be slower at the first stage and faster at the second stage.
S. Tang et al. / International Journal of Mining Science and Technology 25 (2015) 949–953 3.5
3.5
3.0
3.0
Volumetric expansion (%)
Volumetric expansion (%)
952
2.5 2.0
Huozhou coal measured Huozhou coal model Changzhi coal measured Changzhi coal model Jincheng coal measured Jincheng coal model
1.5 1.0 0.5 0
20
40
60
80
2.5 2.0 1.5 Huozhou coal Changzhi coal Jincheng coal
1.0 0.5 0
100
5
10
Gas density (kg/m3 )
15
20
25
30
Adsorption (m3/t)
Fig. 6. Volumetric swelling of samples from three areas attained by measuring and model.
Fig. 7. Volumetric swelling of samples from three mine areas as a function of sorption.
Usually, swelling is interpreted as adsorption inducing a change in the coal specific surface energy, which can be compensated by the elastic energy change associated to the volume change [16,21]. At low pressure, methane molecules adsorbed on coal surfaces mainly in the form of a monolayer, which may be the reason for the linear relationship between swelling and amount adsorbed. However, at high pressure the swelling characteristic, which is nonlinear, cannot be explained by this theory. It is proposed that with increasing pressure, gas molecules penetrate into the coal matrix, i.e. absorption, which may destroy the interconnections in the coal network, and make it expand outwards. The increase in sorption (mainly as absorption) is small at this stage but results in larger swelling. Lin and Zhou found that the maximum swelling of middle-rank coal is lower than that of low-rank and high-rank coal [6]. Chikatamarla et al. found that strain increased with coal maturity in rank from lignite to bituminous coal [10]. In this study, the maximum swelling increased with rank, consistent with the change in the amount of gas adsorbed. It is proposed that micropores abound in higher rank coal, which leads to more adsorption and absorption and thus, larger swelling. Because the number of samples used in this experiment were limited and the impacts of maceral composition on coal swelling are unknown, further study should be carried out to probe the relationship between swelling and coal rank. Coal swelling in methane is anisotropic, which is also often observed in organic solvents. As in the latter case, two explanations have been proposed to explain this effect; the preferential orientation of cross-links in the macromolecular network in coal, and ‘‘locked in” strain derived from overburden pressure gradients [22–25]. These two explanations may, in essence, be the same because the macromolecular network in coal may be compressed during coalification, so the strain is stored. As to the former case, Zare˛bska and Celarska-Stefan´ska proposed that methane molecules penetrating the carbon matter in the direction perpendicular to the bedding plane have to overcome smaller energy resistance than those entering the structure in the direction parallel to the bedding plane, hence greater swelling occurs as the inter-molecular distances are larger than those between particular high-molecular elements [12]. However, this needs further evidence. So, the anisotropic swelling might be attributable to the different degree of recovery of strain in two planes exposed to methane.
Fu et al. analyzed the permeability increase induced by coal shrinkage during methane desorption [26,27]. However, the strain data were derived from a CO2-induced coal swelling experiment and because CO2 can induce more coal swelling than methane, the results of Fu et al. are not accurate [6,8–10,13,14]. Gray stated that unconstrained (stress-free) strain data is appropriate for use in his coal permeability model and several scholars have also adopted the unconstrained strain data in their permeability models [1,28–30]. In this study, unconstrained strain data was also used to calculate permeability. It is assumed that the adsorption-induced swelling is equal to desorption-induced shrinkage, so the measured swelling values could be acting as shrinkage during pressure depletion. 10 MPa corresponds to the pressure at about 1000 m below ground, which is the current maximum depth of economic coalbed methane development in China, so the impact of matrix shrinkage on permeability was analyzed for conditions below this pressure point. The increment of permeability induced by matrix shrinkage, DKe, is given by Eq. (5):
Coal Huozhou Changzhi Jincheng
Smax (%) 2.947326 3.587185 3.811353
D 0.0447874 0.0542836 0.0475446
k 0.0010962 0.0017025 0.0023360
R2 (%) 99.27537 99.44247 99.13374
" # Deji 3 1þ 1 100%
ð5Þ
ui
where K i and K j are the permeability at initial pressure pi and current pressure pj , Deji is the matrix shrinkage from pi to pj , and ui is the porosity at pi [8]. Based on the porosity of coal in the Huozhou, Changzhi and Jincheng areas (which are 13.8%, 3.27% and 2.56% respectively), the increase in permeability at each pressure relative to 10 MPa could be calculated. As shown in Fig. 8, the permeability change is larger for higher rank coal in the same unit of pressure depletion. The initial permeability is low in higher rank coal for a tight matrix, which results in
300
Permeability increment (%)
Table 3 Modified DR parameters when applied to swelling data.
Kj Ki DK e ¼ 100% ¼ Ki
Huozhou coal Changzhi coal Jincheng coal
250 200 150 100 50
0
2
4
6
8
10
Pressure (MPa)
Fig. 8. Permeability increment of samples from three areas during pressure depletion.
S. Tang et al. / International Journal of Mining Science and Technology 25 (2015) 949–953
weak leakage and slow pressure expansion, so the permeability increment for higher rank coal is not obvious in coalbed methane development. 5. Conclusions With increasing methane pressure, coal size change can be divided into three stages; rapid increase, slow increase and decrease. The swelling is nonlinear to gas sorption, which may be because it is controlled by adsorption-induced swelling, absorption-induced breakage and expansion of interconnections in the coal network, and matrix compression as a result of pore pressure. Anisotropic swelling, which is greater perpendicular to the bedding plane than parallel to it, was observed in this study, which might be attributable to the different degree of recovery of strain in two planes. Higher rank coal has the largest capacity for adsorption and absorption, and thus has larger swelling. Based on the assumption that sorption-induced swelling/shrinkage of coal in methane is reversible, the permeability increase induced by coal shrinkage during methane desorption was analyzed, and the results indicate that the permeability change is larger for higher rank coal in the same unit of pressure depletion. Acknowledgments This research is funded by the National Key Technology Support Program of China (No. 2014BAC18B02), and the National Natural Science Foundation of China (Nos. 41272176 and 41202116). References [1] Gray I. Reservoir engineering in coal seams: Part 1-the physical process of gas storage and movement in coal seams. SPE Reserv Eng 1987;2:28–34. [2] Seidle JP. Application of matchstick geometry to stress dependent permeability in coals. In: SPE rocky mountain regional meeting, Wyoming; 1992. p. 433–45. [3] Enever RE, Hennig A. The relationship between permeability and effective stress for Australian. In: The 1997 international coalbed methane symposium, Alabama. p. 13–22. [4] Connolly P, Cosgrove J. Prediction of fracture-induced permeability and fluid flow in the crust using experimental stress data. AAPG Bull 1999;83 (5):757–77. [5] Moffat DH, Weale KE. Sorption by coal of methane at high pressures. Fuel 1955;34:449–62. [6] Lin BQ, Zhou SN. Experimental investigation on the deformation law of coal body with methane. J China Coll Min Technol 1986;3:9–16. [7] Harpalani S, Schraufnagel RA. Shrinkage of coal matrix with release of gas and its impact on permeability of coal. Fuel 1990;69:551–6.
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