Finite volume method for modelling gas flow in shale

Gas flow in shale is a complex phenomenon and is currently being investigated using a variety of modelling and experimental approaches. A range of flow mechanisms need to be taken into account when describing gas flow in shale including continuum, slip, transitional flow and Knudsen diffusion. A finite volume method (FVM) is presented to mathematically model these flow mechanisms. The approach incorporates the Knudsen number as well as the gas adsorption isotherm, allowing different flow mechanisms to be taken into account as well as methane sorption on organic matter. The approach is applicable to non-linear diffusion problems, in which the permeability and fluid density both depend on the scalar variable, the pressure. The FVM is fully conservative, as it obeys exact conservation laws in a discrete sense integrated over finite volumes. The method is validated first on unsteady-state problems for which analytical or numerical solutions are available. The approach is then applied for solving pressure-pulse decay tests and a comparison with an alternative finite element numerical solution is made. Results for practical laboratory pressure-pulse decay tests of samples with very low permeability are also presented.