Linking gas-sorption induced changes in coal permeability to directional strains through a modulus reduction ratio
Introduction
Knowledge of changes in coal permeability due to gas sorption-induced effective stress is crucially important for the evaluation of both primary gas production from coalbed reservoirs and for CO2-enhanced coalbed methane recovery (ECBM) (RECOPOL Workshop, 2005).
For primary gas production, as the gas pressure reduces below the desorption point, methane is released from the coal matrix to the fracture network and the coal matrix shrinks. As a direct consequence of this matrix shrinkage the fractures dilate and fracture permeability correspondingly increases. Thus, a rapid initial reduction of 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. ECBM involves the injection of CO2 into a coal seam to promote the desorption of coalbed methane (CBM) while simultaneously sequestering CO2 in the coal seam. This process exploits the greater affinity of carbon dioxide (CO2) to adsorb onto coal relative to methane (CH4), resulting in the net desorption of methane and its potential recovery as a low-carbon fuel. Laboratory isotherm measurements for pure gases have demonstrated that coal can adsorb approximately twice (or more) as much CO2 (in moles) by volume as methane (White et al., 2005). Correspondingly, CO2 injection with concurrent production of methane can cause differential swelling of the coalbed particularly in the near wellbore area. This may play an important role in determining the resulting deformation of the coal matrix, the related permeability change and its impact on both gas diffusion to the cleats and gas flow along the cleat network. Thus, the influence of these distinct but connected changes in deformation, due to both effective stresses and to gas-sorption-induced swelling, are key to unravelling the transient response to gas injection and recovery. The complexity of the response is further increased by the overprinted effects of bedding plane and cleat orientations, which together with directional stresses or displacement restraints impart a further directional heterogeneity to the transient evolution of permeability. Thus understanding the transient and anisotropic characteristics of permeability evolution in fractured coals is of fundamental importance to the recovery of methane from CBM reservoirs and equally important for CO2 storage using ECBM.
The potential impacts of the coal sorption and related swelling characteristics of coals have been investigated experimentally. The effects of water content on swelling and sorption have been explored for CO2 uptake at 298 K (Ceglarska-Stefanska and Czaplinski, 1993) using a gas-flame coal, a gas-coking coal and an anthracite and indicate a reduction in swelling strain for “dry” coal versus “pre-wetted” samples (Ceglarska-Stefanska and Brzoska, 1998). Rates of swelling are controlled largely by diffusive length scales imparted by the cleats. A surrogate of this case is powdered coals where for powdered high volatile bituminous Pennsylvanian coals the adsorption rate decreases with increasing grain size for all experimental conditions (Busch et al., 2004). Similarly, coal type and rank (Robertson and Christiansen, 2007, Prusty, 2007) influences the preferential sorption behavior and the evolution of permeability with these changes is linked to macromolecular structure (Mazumder and Wolf, 2008). Adsorption kinetics may also be determined for various gases (e.g. for CO2 and CH4) using confining cells to apply desired pressures and temperatures (Charrière et al., 2010) and using X-ray CT methods to determine the resulting sorption isotherms (Jikich et al., 2009). These experiments have focused on the isotropic characteristics of intact or powdered coals.
Nevertheless, some experiments have focused on the anisotropic characteristic of coal. Water transmission characteristics have been shown to be significantly different Gash et al., 1993) under confining pressures when measured perpendicular to either face cleats, butt cleats, or bedding planes. Directional flow experiments on isotropically compressed samples have similarly confirmed the anisotropy of permeability for gas flows (Li et al., 2004). These results are congruent with optical measurements of coal swelling under in CO2 and other gases where swelling in the plane perpendicular to the bedding plane was always substantially higher than parallel to the bedding plane (Day et al., 2008). This phenomenon has also been observed in the field well tests in the Warrior Basin (USA) where the anisotropy ratio of permeability in the direction of the bedding plane was as high as 17:1 (Koenig and Stubbs, 1986).
Based on experimental observations, a variety of models have been formulated to quantify the evolution of permeability during coal swelling/shrinkage. Gray (1987) firstly attempted to quantify the role of stresses on the evolution of coal-reservoir permeability, in which permeability was computed as a function of reservoir pressure-induced coal-matrix shrinkage assumed directly proportional to changes in the equivalent sorption pressure. Since then, a number of theoretical and empirical permeability models have been proposed (Seidle and Huitt, 1995, Palmer and Mansoori, 1996, Pekot and Reeves, 2002, Shi and Durucan, 2004). However, most of these studies are under the assumption of either an invariant total stress or uniaxial strain conditions. These critical and limiting assumptions have been relaxed in new models rigorously incorporating in-situ stress conditions (Zhang et al., 2008, Palmer, 2009, Connell, 2009) and are extended to rigorously incorporate CO2–CH4 coal–gas interaction relevant to CO2–ECBM (Connell and Detournay, 2009, Chen et al., 2010).
Despite the complexity of models applied to represent the evolution of coalbed methane reservoirs, few accommodate feedbacks of both anisotropy and coal–gas interaction on the evolution of permeability — including the important roles of linked stress-deformation and gas flow and adsorption/desorption processes. The effect of stress on the evolution of flow anisotropy in orthogonally fractured media (Sayers, 1990) and in deformable granular media (Du et al., 2004) has been investigated although not with the influence of gas adsorption or desorption effects. The impact of permeability anisotropy and pressure interference on CBM gas production has been investigated specifically to seek any unique performance feature that might distinguish between isotropic or anisotropic permeability of the CBM reservoir or to identify the drainage geometry (Chaianansutcharit et al., 2001). And analytical solutions have been presented for steady-state conditions with anisotropic permeability (Al-Yousef, 2005). More recently, an alternative approach has been proposed to develop an improved permeability model for CO2-ECBM recovery and CO2 geo-sequestration in coal seams, integrating the textural and mechanical properties to describe the anisotropy of gas permeability in coal reservoirs under confined stress conditions (Wang et al., 2009).
In this study, a novel permeability model is developed to define the evolution of gas sorption-induced permeability anisotropy under in-situ stress conditions. Gas sorption-induced coal directional permeabilities are linked to directional strains through the elastic modulus reduction ratio (the ratio of coal mass elastic modulus to coal matrix modulus) that represents the partition of the total strain for an equivalent porous coal medium between the fracture system and the matrix. It is assumed that only the partitioned fracture strains are responsible for the changes in directional permeabilities. These new relations are the key cross couplings that link effective stress-related and sorption-related changes in permeability to fluid pressure and gas content. These constitutive relationships are incorporated into a finite element model to represent the complex interactions of stress and chemistry under in-situ conditions and to project their impact on rates and magnitudes of gas recovery. The validity of the general model is evaluated against results for special cases representing uniaxial swelling, constant volume reservoirs, and for the case of a coalbed methane production well test. The incorporation of gas sorption-induced coal permeability anisotropy into the multiphysics simulation of coal–gas interaction represents a new and important contribution to this subject.
Section snippets
Approach
The overall approach is illustrated in Fig. 1. The evaluation of fully coupled deformation and gas transport in the fractured coal is conducted through four integrated steps: (1) Coal deformation analysis; (2) Flow equivalence analysis; (3) Permeability evolution analysis; and (4) Flow equivalence updating. These four steps are detailed in the following sections.
Uniaxial strain condition
For the case of uniaxial strain, the lateral strains, Δɛtx and Δɛty, are equal to zero. Based on Hooke's law, the relation between stress and strain increments are:
Substituting these Eqs. into Eq. (20) gives
As shown in Eqs. (30), (31), coal permeability in the x-direction is not
Displacement controlled condition
For the displacement controlled (or constant reservoir volume) case, strains in all directions, Δɛtx, Δɛty, and Δɛtz are equal to zero. Substituting zero value into Eq. (20) gives
As shown in Eq. (32), coal permeability ratio in the x- and y-directions is equal to the permeability ratio in the z-direction. All permeability ratios are determined by the swelling strain only. It is apparent that kz is equal to kx if kx0 = ky0 = kz0. In order to illustrate these
Field case
It is generally believed that the in-situ response of a coal gas reservoir to gas production (injection) can be approximated either by the uniaxial deformation-permeability model (Liu and Rutqvist, 2010) or by the constant volume-permeability model (Massarotto et al., 2009). In this section, we apply both coal permeability models to a field case.
Mavor and Vaughn (1997) reported coal permeability results of three wells in the Valencia Canyon area of the San Juan Basin, and found coal
Evaluation of coupled processes
A field scale model is used to simulate the performance of coalbed methane production under in-situ conditions. Input parameters for this simulation are identical to the parameters used in Section 5. The simulation model geometry is 200 m by 200 m with a methane production well located at the lower left corner. For the coal deformation model, all four sides are constrained in the normal direction. For the gas transport model, the coal is saturated initially with CH4 and the initial pressure is
Conclusions
A novel permeability model has been developed to define the evolution of gas sorption-induced permeability anisotropy under in-situ stress conditions. This was implemented into a fully coupled finite element model of coal deformation and gas flow and transport in a coal seam. Based on the model evaluations and the analysis of coupled processes, the model adequately and consistently reflects the conceptual assumptions:
- •
The directional permeability of coal is determined by the mechanical boundary
Acknowledgements
This work was supported by 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 various sources of support are gratefully acknowledged.
References (37)
- et al.
Methane and carbon dioxide adsorption–diffusion experiments on coal: upscaling and modeling
International Journal of Coal Geology
(2004) - et al.
The effect of coal metamorphism on methane desorption
Fuel
(1998) - et al.
Correlation between sorption and dilatometric processes in hard coals
Fuel
(1993) - et al.
Effect of pressure and temperature on diffusion of CO2 and CH4 into coal from the Lorraine basin (France)
International Journal of Coal Geology
(2010) - et al.
Impact of CO2 injection and differential deformation on CO2 injectivity under in-situ stress conditions
International Journal of Coal Geology
(2010) Coupled flow and geomechanical processes during gas production from coal seams
International Journal of Coal Geology
(2009)- et al.
Coupled flow and geomechanical processes during enhanced coal seam methane recovery through CO2 sequestration
International Journal of Coal Geology
(2009) - et al.
Swelling of Australian coals in supercritical CO2
International Journal of Coal Geology
(2008) - et al.
Linking stress-dependent effective porosity and hydraulic conductivity fields to RMR
International Journal of Rock Mechanics and Mining Sciences
(1999) - et al.
Differential swelling and permeability change of coal in response to CO2 injection for ECBM
International Journal of Coal Geology
(2008)