  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.
