Anisotropic coal permeability estimation by determining cleat compressibility using mercury intrusion porosimetry and stress–strain measurements
Introduction
The anisotropic elastic behaviour of coal has been discussed in coal literature for several decades, for example, Szwilski (1984) reported anisotropic elastic moduli of coal measured in two mutually perpendicular directions, reporting values as high as 9.50 GPa and 3.61 GPa. However, most of the commonly used models to predict permeability in coal (e.g., Palmer and Mansoori (1998), Seidle et al. (1992), and Shi and Durucan (2005)) apply uniform modulus of elasticity, and often also uniform cleat compressibility, using the same value in all directions and neglecting the anisotropic nature of the mechanical properties of the coal. Palmer and Mansoori (1998) found that permeability, as calculated with their model, is strongly dependent on the modulus of elasticity (E), and this was found to lie in the range E = 0.85 GPa to E = 3.0 GPa (E = 1.24 × 105 to 4.35 × 105 psi). In this and many other research papers, the modulus of elasticity and cleat compressibility are assumed to be constant and independent of the effective stress applied to the coal (Liu et al., 2012). Experimental evidence, e.g., as presented by Connell and colleagues (Connell et al., 2016; Zheng et al., 2012) suggests this assumption is not representative of coal behaviour.
Most of the coal permeability models include several key parameters to describe the physical and mechanical properties of the coal, including typically Poisson's ratio (ν), modulus of elasticity (E), porosity (ϕ), swelling and strain coefficients (εL and β), and cleat compressibility (Cf). Commonly, the cleat compressibility is found by regression of the model to measured permeability data (k) (Connell et al., 2016; Peng et al., 2017; Zheng et al., 2012). A more useful approach would be to determine cleat compressibility independently since a primary objective in many cases is to predict permeability, rather than use it as a measured value to extract coal properties. The sensitivity of the permeability to the input cleat compressibility values has been documented for the common models by Zheng et al. (2012).
It has been argued that cleat compressibility is hard to measure directly and that cleat compressibility tests are costly, lengthy, and often yield uncertain results (Seidle et al., 1992); and that it is actually easiest to obtain by fitting to permeability data (Zheng et al., 2012). However, a rigorous experimental program to measure the anisotropic permeability of coal across a relevant range of stress and pore pressure conditions is also a costly exercise.
In this paper, a new method to determine both the anisotropic elastic moduli and cleat compressibility of coal is presented, without the need to make permeability measurements and tested to show that it can be applied to reasonably predict the coal permeability.
Section snippets
Mechanistic approach
The method proceeds by assuming the measured bulk strain of a coal sample is essentially all taken up as cleat/fracture strain since the coal matrix is very stiff and the cleats/fracture comparatively soft. This assumption is supported by the literature which shows the matrix compressibility is three to four orders of magnitude lower than cleat compressibility: hence matrix strain can be assumed negligible under all but the most severe stresses. For example, Guo et al. (2014) reported the
Coal sample preparation
Industrial partner supplied a coal core collected from the ‘Lower Jundah’ formation of Surat Basin at a depth of 178.32 m to 178.50 m. The dimensions of the received core, as shown in Fig. 1(a), were ~180 mm length and 63.5 mm diameter. The core was cut into two pieces each about 90 mm long and then machined into 40 mm cubes as shown in Fig. 1(b). Because this coal is relatively brittle, the cutting broke some edges of the coal cubes, which were rebuilt using plastic bond (Selleys Plasti bond).
Stress–strain (σ–ε) measurement
Fig. 6 shows the strain response of the coal sample across the face cleat (εF), butt cleat (εB), and bedding-plane (εV) directions through 25 hydrodynamic loading-unloading cycles at a loading rate of 0 .1MPa/min from effective stresses of σeff = 0.5 MPa to σeff = 4.0 MPa. The maximum loading stress of 4.0 MPa was selected as this is well below the uniaxial compressive strength of Surat Basin coal (UCS ~18 MPa from Fig. 7 by Minaeian and Rasouli (2011)), well inside the elastic limits, as
A novel method to calculate the cleat compressibility (Cf) using MIP and stress–strain measurements
The anisotropic cleat compressibility of the coal sample in the face cleat (CfF) and the butt cleat (CfB) directions may be determined from the stress–strain data (Fig. 6) together with pore size data from mercury porosimetry (MIP) (Fig. 3). The main idea is to assign the measured bulk strain of the sample (Fig. 6) to the cleat/crack strain only, with the assumption that the coal matrix virtually incompressible as compared to cleats/cracks. This assumption is based on the knowledge that the
Cleat compressibility validation
The permeability of naturally fracture reservoirs can be described by a nine-component permeability tensor (Crosdale et al., 1998; Faiz et al., 2007), commonly simplified for coals (Wang et al., 2009) to include permeability only in mutually perpendicular directions. In this study, these mutually perpendicular directions represent the face cleat and butt cleat directions (i.e. k = [kFkB]T). Permeability changes may thus be used to validate the calculated cleat compressibility. Seidle's
Conclusions
An inexpensive, simple and time effective method to estimate the anisotropic permeability coal and its change with net stress, is outlined based on estimating cleat compressibility from two easy measurements: stress–strain data and mercury intrusion porosimetry. The method provides a straightforward way to estimate cleat compressibility and avoids the normal and much more difficult way this is normally obtained, that is, deduced from changes in field or laboratory measured permeability.
Acknowledgements
The authors gratefully acknowledge the funding and support from Centre for Coal Seam Gas at the University of Queensland and its industry members (Arrow Energy, APLNG, Shell Australia (QGC) and Santos). The authors also thank Shell Australia (QGC) for the provision of the core used in this study. The work was partly supported by ARCDP160103896.
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