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A realistic transport model with pressure dependent parameters for gas flow in tight porous media with application to determining shale rock properties

Shale gas recovery has seen a major boom in recent years due to the increasing global energy demands; but the extraction technologies are very expensive. It is therefore important to develop realistic transport modelling and simulation methods, for porous rocks and porous media, that can compliment the field work. Here, a new nonlinear transport model for single phase gas flow in tight porous media is derived, incorporating many important physical processes that occur in such porous systems: continuous flow, transition flow, slip flow, Knudsen diffusion, adsorption and desorption in to and out of the rock material, and a correction for high flow rates (turbulence). This produces a nonlinear advection-diffusion type of partial differential equation (PDE) with pressure dependent model parameters and associated compressibility coefficients, and highly nonlinear apparent convective flux (velocity) and apparent diffusivity. An important application is to the determination of shale rock properties, such as porosity and permeability, by history matching of the the simulation results to data from pressure-pulse decay tests in a shale rock core sample [Pong K., Ho C., Liu J., Tai Y. Non-linear pressure distribution in uniform microchannels. ASME Fluids Eng. Div. (FED) Vol. 197, 51--56, (1994)]. The estimates of the rock porosity and the permeability from our model simulations are realistic of shale rocks, more realistic than obtained from previous models, and illustrates the potential of the modelling strategy presented here in producing accurate simulations of shale gas flow in tight reservoirs.