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

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