Modeling transient variations of permeability in coal seams at the reservoir scale

Abstract

Production of fluid from or injection of fluid into a coal seam leads to variations of permeability of the seam, resulting from adsorption of fluid in the coal matrix in particular. One subtle effect is that, if the fluid pressure in the cleat increases, after an immediate opening of the cleat, one expects the cleat aperture (and hence the permeability) to decrease for a transient time, as a consequence of the fluid diffusion from the cleat to the coal matrix. In this work, we aim to model such transient variations of permeability by proposing constitutive equations at the fractured coal scale. Permeability depends on the complete history of pressures over time. The constitutive equations rely on Boltzmann's superposition principle, which requires kernels as inputs. One can identify the kernels with finite-element simulations of the response of an individual cleat subjected to a history of fluid pressure. We also propose approximate versions of those kernels, which only depend on a few parameters with a physical meaning. Examples of fluid injection simulations into a coal seam making use of the constitutive equations here derived are presented.