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Applicability of Continuum Models for Gas Flow through Shales

Sakhaee-Pour, Ahmad 1; Kumar, Abhishek 1; Bryant, Steven L.1
1 Department of Petroleum and Geosystems Engineering, University of Texas at Austin,, Austin, TX.

A considerable volume of gas is envisaged to be stored in shales and this has recently provoked a great deal of research. Characteristic pore diameters in these rocks are extremely small. Thus efforts to model production from these rocks immediately raise the question of the appropriate physical description of gas transport. To simulate the effective or apparent permeability of gas shales, researchers have proposed different methods including molecular dynamics and diffusive transport approaches.

In this study, the feasibility of adopting continuum models to analyze the gas flow is assessed. The predicted flow rate is normalized with respect to the pressure gradient to propose an equivalent permeability. To study the possibility of a transition to grain surface dominated transport, we evaluate the equivalent permeability as a function of aperture size in pore space with several model geometries. The model geometries have a range of ratios of grain surface area to pore volume. We consider a viscous flow model with and without a slip boundary condition at the grain surface, and we compare with a diffusion model with and without a surface diffusion contribution at the grain surface. The equivalent permeability has the capability of predicting gas flow rate while using the Darcy's law for high Knudsen number.

 

AAPG Search and Discovery Article #90090©2009 AAPG Annual Convention and Exhibition, Denver, Colorado, June 7-10, 2009