How sorption-induced matrix deformation affects gas flow in coal seams: A new FE model

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Abstract

The influence of sorption-induced coal matrix deformation on the evolution of porosity and permeability of fractured coal seams is evaluated, together with its influence on gas recovery rates. The porosity-based model considers factors such as the volume occupied by the free-phase gas, the volume occupied by the adsorbed phase gas, the deformation-induced pore volume change, and the sorption-induced coal pore volume change. More importantly, these factors are quantified under in situ stress conditions. A cubic relation between coal porosity and permeability is introduced to relate the coal storage capability (changing porosity) to the coal transport property (changing permeability). A general porosity and permeability model is then implemented into a coupled gas flow and coal deformation finite element model. The new FE model was used to compare the performance of the new model with that of the Palmer–Mansoori model. It is found that the Palmer–Mansoori model may produce significant errors if loading conditions deviate from the assumptions of the uniaxial strain condition and infinite bulk modulus of the grains. The FE model was also applied to quantify the net change in permeability, the gas flow, and the resultant deformation in a coal seam. Model results demonstrate that the evolution of porosity and of permeability is controlled by the competing influences of effective stresses and sorption-based volume changes. The resulting sense of permeability change is controlled by the dominant mechanism.

Introduction

Methane in coal seams is an important natural energy resource, although ignition and the resulting explosion hazard remain a major problem during coal mining. Degassing seams is an important method to mitigate this hazard, and results in the beneficial recovery of a clean-burning and low-carbon fuel resource. The injection of carbon dioxide to preferentially dissociate methane has been an effective measure used after primary recovery by depressurization. Recently, carbon dioxide (CO2) sequestration in deep coal seams has attracted more attention as a method of reducing the output of greenhouse gases to the atmosphere [1].

Gas flow within coal seams is quite different from that of conventional reservoirs. Detailed studies have examined the storage and transport mechanisms of gas in coal seams. In situ and laboratory data indicate that the storage and flow of gas in coal seams is associated with the matrix structure of coal and the absorption or desorption of gas. Coal is a naturally fractured dual-porosity reservoir [2], consisting of micro-porous matrix and cleats. Most of the gas is initially stored within micro-pores in the absorbed state [3]. When gas recovery begins, the gas desorbs and diffuses from matrix to cleats due to the concentration gradient. The gas flowing through the cleats is considered to be gas seepage controlled by the permeability of the coal seam [4]. Experimental results have shown that gas sorption generally follows a Langmuir isotherm [5], [6]. Desorption plays an important role in both defining the longevity and rate of the gas supply, and in controlling the related deformation of the solid matter comprising the seam.

A variety of experiments have investigated sorption characteristics under isothermal conditions [4], [7], [8], [9], [10] with supporting models representing isothermal response [8], [9], [11], [12], [13]. These studies have also noted the dependency of volumetric strain of the coal matrix as a non-linear function of gas pressure, driven by gas desorption. There is an approximately linear relationship between the sorption-induced volumetric strain and the absorbed gas volume [7], [9], [10]. This relation holds both during uptake, described as sorption, and in discharge, described as desorption, of gases from the surfaces of the coal matrix. Because of the dual-porosity structure of coal seams (i.e., micro-porous matrix and macro-porous cleat/fracture network), the coal matrix represents the main reservoir for the gas, and the cleats the main fracture pathways. When the pore pressure declines during methane production, methane desorbs from the coal matrix and the desorbed gas flows through the cleats to the producing well. The decline of pore pressure results in a concomitant increase in effective stress. The increase in effective stress reduces the stress-sensitive permeability of the cleat system. In contrast, the desorption-induced shrinkage of the coal matrix widens the cleats and enhances permeability. The net change in permeability accompanying gas production is thus controlled by the competitive effects of declining pore pressure decreasing permeability, and the shrinking coal matrix increasing permeability. The net effect, of permeability loss or permeability gain, is dependent on the mechanical boundary conditions applied to the system.

Adsorption of gas, such as carbon dioxide, is the reverse of desorption. When the gas pressure increases, the gas adsorbs onto the coal matrix. The increase of pore pressure results in a decrease of effective stress. The reduction in effective stress enhances the coal permeability. In contrast, the adsorption-induced swelling of the coal matrix reduces the cleat apertures and decreases the permeability. The net change in permeability accompanying gas sequestration is also controlled competitively by the influence of effective stresses and matrix swelling, again controlled by the boundary conditions applied locally between the end-members of null changes in either mean stress or volume strain.

Numerical simulations of gas diffusion, gas flow, and coupled hydromechanical response have been widely applied. Finite element methods and a formulation for modeling mass transport problems in porous media have been applied, including the effects of coupled solid–gas response for gas flow in coal seams [14]. This included only the effect of gas sorption on mass storage [15]. Valliappan and Zhang developed a coupled model incorporating the effect of diffusion of adsorbed methane gas from the solid matrix to the voids [16]. A dual-porosity poroelastic model was extended and utilized in solving generalized plane strain problems [17], [18]. Gilman and Beckie proposed a simplified model of methane diffusion and transport in a coal seam and found a reference time of methane release from the coal matrix into cleats to have a critical influence on overall methane production [19]. A model for multiphase flow, coupled with heat transfer and rock deformation, was used to simulate CO2 injection into a brine formation by Rutqvist and Tsang [20]. In 2004, a non-linear coupled mathematical model of solid deformation and gas seepage was presented and the methane extraction from fractured coal seam was simulated [21]. However, the constitutive relationships between stress and strain are similar to conventional poroelastic mechanics in most of the above simulations and the effect of sorption-induced strain on matrix volumetric strain has not been taken into account although experimental data have noted its significant impact—both on total volumetric strain of the seam, and the resulting feedback on permeability.

The gas flow in coal seams is a complex physical and chemical process coupling solid deformation, gas desorption and gas movement. Although the influence of sorption-induced deformation on porosity, and on permeability has been widely studied, how this in turn affects gas flow within the seam is not well understood. This is partly because no coupled gas flow and sorption-induced coal deformation models are available for in situ stress conditions. The primary motivation of this study is to investigate how sorption-induced coal matrix deformation affects the gas flow in a coal seam through developing such a porosity-based model.

Section snippets

Governing equations

In the following, a set of field equations are defined which govern the deformation of the solid matrix, and prescribe the transport and interaction of gas flow in a similar way to poroelastic theory [22]. These derivations are based on the following assumptions: (a) coal is a homogeneous, isotropic and elastic continuum. (b) Strains are much smaller than the length scale. (c) Gas contained within the pores is ideal, and its viscosity is constant under isothermal conditions. (d) The rate of gas

Finite element implementations

The above governing equations, especially the gas flow equation incorporating the effect of desorption, are a set of non-linear partial differential equations (PDE) of second order in space and first order in time. The non-linearity appears both in the space and time domains; and therefore, these equations are difficult to solve analytically. Therefore, the complete set of coupled equations is implemented into, and solved by using COMSOL Multiphysics, a powerful PDE-based multiphysics modeling

Simulation examples

In the following, we present three simulation examples to illustrate the resultant effects of coupled gas sorption and coal deformation. These three examples are under different boundary conditions which causes different stress states. The first one is under uniaxial stress condition. The second one is under constrained plane strain condition. The last one is under unconstrained plane strain condition. We use the three examples to quantify the net change in permeability, in gas flow, and in

Conclusions

In this study, a new coupled gas flow and sorption-induced coal deformation finite element model is developed to quantify the net change in permeability, the gas flow, and the resultant deformation of the coal seam. The coupling between gas flow and coal deformation is realized through a general porosity and permeability model. The general porosity model considers the principal controlling factors, including the volume occupied by the free-phase gas, the volume occupied by the adsorbed phase

Acknowledgment

This work is supported by the Australia Research Council under Grants DP0342446 and DP0209425 and by the Australian Department of Education, Science and Training through the Australia-China Special Fund. This support is gratefully appreciated.

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