Modelling of anisotropic coal swelling and its impact on permeability behaviour for primary and enhanced coalbed methane recovery
Research Highlights
► A theoretical model for anisotropic coal swelling induced by gas sorption. ► An anisotropic coal permeability model incorporate anisotropic coal swelling. ► Significant permeability difference between applying anisotropic and isotropic coal swelling.
Introduction
Coal swelling/shrinkage due to gas adsorption/desorption is a well-known phenomenon and is regarded as a key component for coal reservoir permeability behaviour during primary and enhanced coalbed methane (CBM) recovery (Palmer and Mansoori, 1998, Shi and Durucan, 2005). Laboratory measurements of coal swelling in gas have been conducted by various researchers (Chikatamarla et al., 2004, Day et al., 2008, Levine, 1996, Moffat and Weale, 1955, Pan et al., 2010a, Pan et al., 2010b, Reucroft and Patel, 1986, Reucroft and Sethuraman, 1987, Robertson and Christiansen, 2005, St. George and Barakat, 2001). However most of the swelling measurements have only considered one axis or direction. Nevertheless, there are a few studies where coal swelling has been measured along more than one axis. Levine (1996) presented coal swelling measurements for two high-volatile C bituminous coal samples from Illinios, USA in both methane and CO2. The results show that one coal sample swelled about 10% more in the direction perpendicular to the bedding than that parallel to the bedding in both methane and CO2 with pressure up to 800 psi (or 5.5 MPa). For the second coal sample the magnitude of the swelling was similar in both directions in methane but in CO2 there was 25% more swelling in the direction perpendicular to the bedding for pressures up to 500 Psi (or 3.4 MPa). More recently, Day et al. (2008) measured directional coal swelling in CO2 for pressures up to 14 MPa; these measurements found that the expansion in the direction perpendicular to the bedding plane is about 70% greater than that parallel to the bedding plane for two coal samples from the Hunter Valley and Bowen Basin, Australia, and about 30% greater for a coal sample from Illawarra, Australia. The coal sample from the Illawarra is higher rank with a mean Vitrinite Reflectance of 1.29% and the mean Vitrinite Reflectance is 0.89% and 0.95% for coal samples from the Hunter Valley and Bowen Basin, respectively. Their results indicate that lower rank coal tends to show stronger anisotropic swelling. X-ray CT was used to study coal swelling under confined conditions and it was found that the coal swelling is anisotropic and also heterogeneous (Karacan, 2003, Karacan, 2007, Pone et al., 2009). Although strong anisotropic swelling is observed for some coals, how swelling anisotropy would affect reservoir permeability and then gas flow is not well understood.
In order to evaluate the impact of coal swelling on permeability, a swelling model needs to be integrated into the coal permeability model. Gray (1987) applied a linear relationship between the swelling/shrinkage strain and pressure in his permeability model. Levine (1996) found that the linear relationship would overestimate the impact from swelling/shrinkage, especially at high pressures and used a Langmuir-like equation to describe the swelling behaviour based on experimental observations. This approach of Langmuir-like equation to describe swelling strain has been widely applied (e.g., Palmer and Mansoori, 1998, Seidle and Huitt, 1995, Shi and Durucan, 2004). In order to describe swelling induced by mixed-gas adsorption, an extended Langmuir-like equation is applied by some researchers (e.g., Connell, 2009, Connell and Detournay, 2009, Cui and Bustin, 2005, Mitra and Harpalani, 2007). Sawyer et al. (1990) and others (e.g., Shi and Durucan, 2005) apply a linear relationship between the swelling strain and total adsorbed amount. However, all these approaches to describe swelling strain are empirical and can only be applied in a certain pressure range. They may also lead to large errors when describing mixed-gas adsorption induced coal swelling (Mitra and Harpalani, 2007).
To more accurately describe the swelling strain induced by gas adsorption, the key is to understand the interactions between gas and coal that cause the swelling. Larsen (2004) proposed that CO2 has the same effect on coal swelling behaviour as liquids known to dissolve in and to swell coals. He concluded that CO2 also dissolves in coal and acts as a plasticiser enabling rearrangements in the coal physical structure that swells the coal. However, Day et al. (2008) found that swelling is completely elastic even after the coal had been subject to multiple exposures to CO2 and they find no evidence of CO2 acting as a plasticiser of coal. Moreover, other measurements from the literature show that CO2 swelling has the same magnitude as other gases, such as methane, for the same adsorbed amount (e.g., Levine, 1996, Pan et al., 2010a). This may suggest that the mechanism for CO2 swelling is similar to that of other gases, instead being like a liquid. These measurements do not show coal swelling in CO2 at high pressure is increasing as would have been suggested by the dissolution assumption. Furthermore, CO2 adsorption in coal is found within the typical range for physical adsorption, as indicated by heat of adsorption (e.g., Ozdemir et al., 2004). Since physical adsorption means gas interaction with and on the adsorbent surface, the cause of adsorption-induced coal swelling must be the force induced by the gas molecules adsorbed on the surface.
Recently, Pan and Connell (2007) presented a theoretical model based on adsorption thermodynamics (Myers, 2002) and elasticity theory, using a structure model developed by Scherer (1986). This model describes gas adsorption-induced swelling by assuming that the surface energy change caused by adsorption is equal to the elastic energy change of the coal solid. The Pan and Connell swelling model is able to describe coal swelling in different gases based on one set of coal property parameters and adsorption isotherms for different gases. This model has been readily extended to describe coal swelling in mixed-gas adsorption by using the same set of coal property parameters and mixed-gas adsorption isotherms. It has been shown that the Pan and Connell model can accurately describe experimental measurements of coal swelling in mixed gas (Clarkson et al., 2010). The model has also been applied with the Palmer and Mansoori (1998) permeability model to accurately describe CBM production data from a San Juan Basin CBM well, in which a high concentration of CO2 is produced with methane (Clarkson et al., 2010). Nevertheless, the Pan and Connell model is only applicable at coal reservoir conditions and where gas is adsorbed on the coal surface. At elevated temperatures, the coal properties may change (Larsen, 2004). Thus, if the gas and coal interactions exceed physical adsorption, the mechanism of swelling becomes more complex.
However, all these approaches assume isotropic swelling as described above. For coals with little or small anisotropic swelling behaviour, assuming isotropy is a good approximation. However, for coals which show strong anisotropic swelling behaviour as shown by Day et al. (2008), assuming isotropy may not be valid and may lead to erroneous predictions of permeability behaviour. Moreover, a permeability model which includes anisotropic swelling will require anisotropic coal properties to be represented to consistently describe permeability anisotropy and its change during primary and enhanced coalbed methane recovery. A number of coal reservoir permeability models have been developed to describe the impact of coal swelling/shrinkage (Cui and Bustin, 2005, Cui et al., 2007, Gilman and Beckie, 2000, Gray, 1987, Liu et al., 2010, Palmer and Mansoori, 1998, Pekot and Reeves, 2003, Pekot, 2003, Seidle and Huitt, 1995, Shi and Durucan, 2004, Shi and Durucan, 2005). However, these assume isotropic coal properties and swelling behaviour. Recently, Wang et al., 2009, Wu et al., 2010 developed models to describe permeability anisotropy that incorporated anisotropic coal properties. However, isotropic swelling is still assumed in their work. Thus, the integration of an anisotropic coal swelling model with an anisotropic permeability model would provide a means of more accurately describing permeability behaviour under conditions known to occur for many coals.
In this work, we develop an anisotropic swelling model based on the Pan and Connell (2007) swelling model, incorporating anisotropic coal properties. Then we present swelling measurements on an Australian coal sample in gases including N2, CH4 and CO2. The coal sample is a bituminous coal from New South Wales, Australia. The experimental results show strong anisotropic swelling in all three gases. The developed anisotropic coal swelling model is then applied to describe the experimental data from this work and other data from literature. Then the anisotropic swelling model is incorporated a permeability model and permeability behaviour during CBM and ECBM process are investigated.
Section snippets
Model development
Coal is highly heterogeneous and sample dependent, thus extremely difficult to describe with a simple structural model. Part of this heterogeneity can be attributed to coal layering (Mahajan, 1984) and its crosslinked nature (Larsen, 2004). Pan and Connell (2007) applied a structure model developed by Scherer (1986) and successfully used it to describe gas adsorption-induced coal swelling based on assuming isotropy. Thus, in this work, we apply a similar approach but assuming anisotropy in coal
Experimental work and results
Directional swelling strains and adsorption on one bituminous coal sample from the Hunter Valley, New South Wales, Australia were measured. The apparatus used for the measurements is a triaxial permeability cell, which measures gas adsorption and permeability under hydrostatic conditions. Radial and axial displacements are measured at each adsorption step to obtain swelling strain. The detailed experimental procedures are described elsewhere (Pan et al., 2010a). The coal sample was 60.8 mm in
Case 1: results for the Hunter Valley swelling measurements
The experimental results show that the swelling strains in the two directions parallel to the bedding are almost identical. Thus in the modelling, the coal mechanical properties and structure are assumed equal in the x and y directions, which represent two directions parallel to the bedding. The anisotropic swelling is mainly between the directions perpendicular and parallel to the bedding.
In order to reduce the parameter requirements for the model it is assumed that the Poisson's ratio is
Anisotropic permeability change
To evaluate the impact of anisotropic coal swelling on the permeability change, an anisotropic permeability model incorporating anisotropic coal swelling is required. As mentioned above, most previous studies have been focused on applying an isotropic permeability model with isotropic coal swelling. In order to evaluate anisotropic permeability change, a starting point is the constitutive equation for anisotropic poroelastic media with orthorhombic symmetry (Jaeger and Cook, 1969) and
Conclusions
This paper has presented a theoretical model to describe the gas adsorption-induced anisotropic coal swelling from a consideration of coal's anisotropic mechanical properties and structure. In testing of the developed model it was fitted to experimental observations of swelling and was found to be in close agreement. More importantly, the model is able to describe the coal swelling induced by different gas species using a common set of the coal property and structure parameters. However, these
Acknowledgements
The financial support from CSIRO Advanced Coal Technology Portfolio is gratefully acknowledged. The authors are also grateful to Mr Michael Camilleri and Mrs Deasy Heryanto for performing the experimental work and analysing the experimental data.
Glossary
- a
- Cylinder radius in the coal structure model
- B
- Langmuir constant (Pa−1)
- c
- Pore structure model constant (1.200)
- C
- Number of components (–)
- cf
- Cleat compressibility (Pa−1)
- E
- Elastic modulus (Pa)
- k
- Permeability, (mD)
- l
- Length in the coal structure model
- L
- Langmuir constant (mole/kg)
- P
- Pressure (Pa)
- R
- Gas constant (8.314 J mol−1 K−1)
- S
- Specific surface area (m2/kg)
- s
- Compliances (Pa−1)
- Sc
- Acting area of the cylinder in the coal structure model (m2)
- T
- Temperature (K)
- V0
- Specific volume (m3/kg)
- Vc
- Volume of the cylinder in the coal
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