Linking gas-sorption induced changes in coal permeability to directional strains through a modulus reduction ratio

Abstract

Although coal–gas interactions have been comprehensively investigated, most prior studies have focused on one or more component processes of effective stress or sorption-induced deformation and for resulting isotropic changes in coal permeability. In this study a permeability model is developed to define the evolution of gas sorption-induced permeability anisotropy under the full spectrum of mechanical conditions spanning prescribed in-situ stresses through constrained displacement. In the model, gas sorption-induced coal directional permeabilities are linked into directional strains through an elastic modulus reduction ratio, Rm. It defines the ratio of coal bulk elastic modulus to coal matrix modulus (0 < Rm < 1) and represents the partitioning of total strain for an equivalent porous coal medium between the fracture system and the matrix. Where bulk coal permeability is dominated by the cleat system, the portioned fracture strains may be used to define the evolution of the fracture permeability, and hence the response of the bulk aggregate. The coal modulus reduction ratio provides a straightforward index to link anisotropy in deformability characteristics to the evolution of directional permeabilities. Constitutive models incorporating this concept are implemented in a finite element model to represent the complex interactions of effective stress and sorption under in-situ conditions. The validity of the model is evaluated against benchmark cases for uniaxial swelling and for constant volume reservoirs then applied to match changes in permeability observed in a field production test within a coalbed reservoir.