Gas flow in shale is a poorly understood and potentially complex phenomenon.It is currently being investigated using a variety of techniques including the analysis of transient experiments conducted on full core and crushed shale using a range of gases.A range of gas flow mechanisms may operate including continuum flow,slippage,transitional flow and Knudsen diffusion.These processes,as well as gas sorption,need to be taken into account when interpreting experimental data and extrapolating the results to the subsurface.Several models have been published that attempt to account for these different processes.Unfortunately,these have a large number of unknown parameters and few studies have assessed the extent to which transient experiments may be used to invert for the key unknowns or the errors that are associated.Here we present a methodology in which various inversion techniques are applied to assess the viability of deriving key unknowns which control gas flow in shale from transient experiments with a range of noise.A finite volume method is developed based on the model of Civan(2010,2011a,b)to mathematically model the transient gas flow in shale.The model is applicable to non-linear diffusion problems,in which the permeability and fluid density both depend on the scalar variable,pressure.The governing equation incorporates the Knudsen number,allowing different flow mechanisms to be addressed,as well as the gas adsorption isotherm. The method is validated for unsteady-state problems for which analytical or numerical solutions are available.The method is then applied for solving a pressure-pulse decay test.An inverse numerical formulation is generated,using a minimisation iterative algorithm,to estimate different number of unknown parameters.Both numerically simulated noisy and experimental data are input into the formulation of the inverse problem.Error analysis is undertaken to investigate the accuracy of results.A good agreement between inverted and exact parameter values is obtained for several parameters.However,it was found that the strong correlation between intrinsic permeability and tortuosity meant that it was not possible to accurately invert simultaneously for these two parameters.The workflow presented here can be readily applied to other gas flow models to assess the extent to which they can be applied to invert experimental data.
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