Influence of the effective stress coefficient and sorption-induced strain on the evolution of coal permeability: Model development and analysis

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Abstract

A series of coal permeability experiments was conducted for coal samples infiltrated both with non-adsorbing and adsorbing gases – all under conditions of constant pressure difference between the confining stress and the pore pressure. The experimental results show that even under controlled stress conditions, coal permeability decreases with respect to pore pressure during the injection of adsorbing gases. This conclusion is apparently not congruent with our conceptual understanding: when coal samples are free to swell/shrink then no effect of swelling/shrinkage strain should be apparent on the permeability under controlled stress conditions. In this study, we developed a phenomenological permeability model to explain this enigmatic behavior of coal permeability evolution under the influence of gas sorption by combining the effect of swelling strain with that of the mechanical effective stress. For the mechanical effective stress effect, we use the concept of natural strain to define its impact on the change in fracture aperture; for the swelling strain effect, we introduce a partition ratio to define the contribution of swelling strain to the fracture aperture reduction. The resulting coal permeability model is defined as a function of both the effective stress and the swelling strain. Compared to other commonly used models under specific boundary conditions, such as Palmer–Mansoori (P–M), Shi–Durucan (S–D) and Cui–Bustin (C–B) models, our model results match the experimental measurements quite well. We match the experimental data with the model results for the correct reason, i.e. the model conditions are consistent with the experimental conditions (both are stress-controlled), while other models only match the data for a different reason (the model condition is uniaxial strain but the experimental condition is stress-controlled). We have also implemented our permeability model into a fully coupled coal deformation and gas transport finite element model to recover the important non-linear responses due to the effective stress effects where mechanical influences are rigorously coupled with the gas transport system.

Highlights

► A new coal permeability model under variable stresses is developed. ► The model explains why coal permeability reduces under free swelling conditions. ► The model is implemented into a fully coupled FE model of deformation and flow. ► The FE model recovers the effect of effective stresses on coal permeability.

Introduction

Coal Bed Methane (CBM) is naturally occurring methane gas (CH4) in coal seams. Methane was long considered a major problem in underground coal mining but now CBM is recognized as a valuable resource. Australia has vast reserves of coal-bed methane (about 310–410 trillion m3) (White et al., 2005) and has attracted billions of dollars in foreign investment to develop this resource. CBM recovery triggers a series of coal–gas interactions. For gas production, the reduction of gas pressure increases effective stress which in turn closes fracture aperture and reduces the permeability (McKee et al., 1988, Seidle and Huitt, 1995, Palmer and Mansoori, 1996). As gas pressure reduces below the desorption point, methane is released from coal matrix to the fracture network and coal matrix shrinks. As a direct consequence of this matrix shrinkage the fractures dilate and fracture permeability correspondingly increases (Harpalani and Schraufnagel, 1990). Thus a rapid initial reduction in fracture permeability (due to change in effective stress) is supplanted by a slow increase in permeability (with matrix shrinkage). Whether the ultimate, long-term, permeability is greater or less than the initial permeability depends on the net influence of these dual competing mechanisms (Shi and Durucan, 2004, Chen et al., 2008, Connell, 2009). Therefore, understanding the transient characteristics of permeability evolution in fractured coals is of fundamental importance to the CBM recovery and CO2 storage in coal, which has dual and complementary benefits: the enhanced production of methane and concurrent long-term storage of CO2.

A broad variety of models have evolved to represent the effects of sorption, swelling and effective stresses on the dynamic evolution of permeability over last few decades. In the latest review (Liu et al., 2011), these models are classified into two groups: permeability models under conditions of uniaxial strain and permeability models under conditions of variable stress.

Somerton et al. (1975) investigated the permeability of fractured coal to methane and presented a correlation equation in the prediction of permeability with mean stress. Gray (1987) considered the changes in the cleat permeability as a function of the prevailing effective horizontal stresses, and firstly incorporated the influence of matrix shrinkage into a permeability model. Seidle and Huitt (1995) developed a conceptual matchstick model to explain coal permeability decrease with increasing effective stress. Other stress-based coal permeability models include Harpalani and Chen (1997), Gilman and Beckie (2000), Shi and Durucan (S–D) (2004), and Cui and Bustin (C–B) (2005). Based on cubic geometry, Robertson and Christiansen (2006) described the derivation of a new equation that can be used to model the permeability behavior of a fractured, sorptive-elastic medium, such as coal, under variable stress conditions. Ma et al. (2011) proposed a permeability model based on the volumetric balance between the bulk coal, solid grains and pores, using the constant volume theory proposed by Massarotto et al. (2009).

A number of coal permeability models were developed based on strains. McKee et al. (1988) developed a theoretical permeability model using matrix compressibility as a fundamental property, but did not include the effect of sorption-induced strain on permeability change. Sawyer et al. (1990) proposed a permeability model assuming that fracture porosity (to which permeability can be directly related) is a linear function of changes in gas pressure and concentration. Palmer and Mansoori (P–M) (1996) presented a theoretical model for calculating pore volume compressibility and permeability in coals as a function of effective stress and matrix shrinkage. The P–M model was updated in Palmer et al. (2007). Similarly, the Advanced Resources International (ARI) group developed another permeability model (Pekot and Reeves, 2002). This model does not have a geomechanics framework, but instead extracts matrix strain changes from a Langmuir curve type of strain versus reservoir pressure, which is assumed to be proportional to the gas concentration curve. Zhang et al. (2008) developed a permeability model under variable stress conditions, and was extended to CO2–ECBM conditions by (Chen et al., 2009, Chen et al., 2010). Connell et al. (2010) presented two analytical permeability models for tri-axial strain and stress conditions.

Pan and Connell (2007) developed a theoretical model for sorption-induced strain and applied to single-component adsorption/strain experimental data. Clarkson (2008) expanded this theoretical model to calculate the sorption-strain component of the P–M model. Pan and Connell (2011a) developed an anisotropic swelling model based on their swelling model (Pan and Connell, 2007). The dependence of coal permeability on pore volume compressibility was also investigated (Shi and Durucan, 2010, Tonnsen and Miskimins, 2010).

As reviewed above, there are a large collection of coal permeability models from empirical ones to theoretical ones. These models normally have a set of common assumptions: (1) the overburden stress remains constant; (2) coal deforms under the uniaxial strain condition; (3) the effective stress coefficient is assumed as one; and (4) the sorption-induced strain is totally counteracted by the closure of the fracture aperture. These assumptions have limited their applicability as Liu et al. (2011) concluded that current models have so far failed to explain the results from stress-controlled shrinkage/swelling laboratory tests and have only achieved some limited success in explaining and matching in situ data. Liu et al. (2011) considered the main reason for these failures is the impact of coal matrix-fracture compartment interactions has not yet been understood well and further improvements are necessary as demonstrated in latest studies (Connell et al., 2010, Liu and Rutqvist, 2010, Izadi et al., 2011). In this study, a coal permeability model based on coal matrix-fracture interaction was developed and then implemented into a fully coupled coal deformation and gas transport finite element model to recover the important non-linear responses due to the effective stress effects.

Section snippets

Permeability model development

Previous work of Chen et al. (2011) has reported the findings of a series of experiments conducted for coal samples infiltrated both with non-adsorbing and adsorbing gases – all under conditions of constant pressure difference between the confining stress and the pore pressure. Observations have demonstrated that even under controlled stress conditions the injection of adsorbing gases actually does reduce coal permeability. The swelling strain effect has also been separated from the effective

Permeability model evaluation

A series of gas flow-through experiments have been carried out all under constant pressure difference conditions (Chen et al., 2011), which were defined as the difference between confining stress and pore pressure. First, the effective stress coefficient is measured for the non-adsorbing gas (helium) flow-through experiments. In these experiments, the impact of gas sorption is null and any permeability alteration is considered to be due to the variation in the effective stress coefficient.

Model implementation

In our previous studies (Zhang et al., 2008, Chen et al., 2009, Chen et al., 2010, Liu et al., 2010a, Liu et al., 2010b, Wu et al., 2010, Wu et al., 2011), a series of single poroelastic, equivalent poroelastic, and dual poroelastic models were developed to simulate the interactions of multiple processes triggered by the injection or production of both single gas and binary gas. Many studies have also been carried out by other researchers (Cui et al., 2007, Bustin et al., 2008). In order to

Conclusions

Coal permeability models are required to define the transient characteristics of permeability evolution in fractured coals. A broad variety of models have evolved to represent the effects of sorption, swelling and stresses on the dynamic evolution of permeability. These models can be classified into two groups: permeability models under conditions of uniaxial strain such as Palmer–Mansoori (P–M), Shi–Durucan (S–D) and Cui–Bustin (C–B) models, and permeability models under conditions of variable

Acknowledgments

This work was supported by WA:ERA, the Western Australia CSIRO-University Postgraduate Research Scholarship, National Research Flagship Energy Transformed Top-up Scholarship, and by NIOSH under contract 200-2008-25702. These supports are gratefully acknowledged.

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