Shale-Gas Permeability and Diffusivity Inferred by Improved Formulation of Relevant Retention and Transport Mechanisms

A theoretically improved model incorporating the relevant mechanisms of gas retention and transport in gas-bearing shale formations is presented for determination of intrinsic gas permeability and diffusivity. This is accomplished by considering the various flow regimes according to a unified Hagen-Poiseuille-type equation, fully compressible treatment of gas and shale properties, and numerical solution of the non-linear pressure equation. The present model can accommodate a wide range of fundamental flow mechanisms, such as continuum, slip, transition, and free molecular flow, depending on the prevailing flow conditions characterized by the Knudsen number. The model indicates that rigorous determination of shale-gas permeability and diffusivity requires the characterization of various important parameters included in the present phenomenological modeling approach, many of which are not considered in previous studies. It is demonstrated that the improved model matches a set of experimental data better than a previous attempt. It is concluded that the improved model provides a more accurate means of analysis and interpretation of the pressure-pulse decay tests than the previous models which inherently consider a Darcian flow and neglect the variation of parameters with pressure.