A mechanistic model for permeability evolution in fractured sorbing media

A mechanistic model is presented to represent the evolution of permeability in fractured sorbing media such as coal beds and organic-rich shales. This model accommodates key competing processes of poromechanical dilation and sorption-induced swelling. We show that the significant difference in stiffness between fracture and matrix transforms the composite system from globally unconstrained to locally constrained by the development of a virtual "stiff shell" that envelops the perimeter of a representative elementary volume containing a fracture. It is this transformation that results in swelling-induced permeability reduction at low (sorbing) gas pressures and self consistently allows competitive dilation of the fracture as gas pressures are increased. Importantly, net dilation is shown to require a mismatch in the Biot coefficients of fracture and matrix with the coefficient for the fracture exceeding that for the matrix-a condition that is logically met. Permeability evolution is cast in terms of series and parallel models with the series model better replicating observational data. The model may be cast in terms of nondimensional parameters representing sorptive and poromechanical effects and modulated by the sensitivity of the fracture network to dilation or compaction of the individual fractures. This latter parameter encapsulates the effects of fracture spacing and initial permeability and scale changes in permeability driven by either sorption or poromechanical effects. This model is applied to well-controlled observational data for different ranks of coals and different gases (He, CO₂) and satisfactory agreement is obtained.