Impact of micro-scale heterogeneity on gas diffusivity of organic-rich shale matrix

The micro-scale heterogeneity of shale matrix may significantly impact the diffusivity of shale gas and further affect the shale gas production of a fractured horizontal well. However, the impact of shale matrix heterogeneity on the gas diffusivity is still unclear. This study investigates the impact of the heterogeneity of shale matrix microstructure on gas diffusivity through a reconstructed shale matrix model. Firstly, shale matrix is composed of organic and inorganic matrices, whose pores are distributed at nano- and micro-scales and form slit-like or tube-like channels for gas flow. The magnitude of pore sizes within the organic matrix is one or two order smaller than that within the inorganic matrix. The distribution of shale pore sizes is described by a fractal theory. Secondly, shale gas is only adsorbed on the pore surface of organic matter and the inorganic matrix provides storage space and transport paths of free shale gas. Particularly, the transport properties of slit-like and tube-like channels are discussed and their mass flow rates are validated with three sets of experimental data. Thirdly, a microstructure of shale matrix is reconstructed by a quartet structure generation set (QSGS) and the homogenized diffusivity of this microstructure of shale matrix is obtained by a homogenization method at different volume fractions. Finally, sensitivity analysis is conducted to explore the mechanisms of gas flow including viscous flow with slip boundary, molecular diffusion (i.e. molecular self-diffusion), Knudsen diffusion, and surface diffusion in organic matter and viscous flow with slippage boundary, molecular diffusion and Knudsen diffusion in inorganic matrix. It is found that higher total organic content corresponds to smaller gas diffusivity. Gas desorption can only increase the pore space in organic matter due to gas pressure depletion. The homogenized diffusivity is mainly controlled by the pore channel in inorganic matrix but organic matter provides gas source and changes gas transport mechanisms. These results show that the heterogeneity of shale matrix has significant impacts on the diffusivity and cannot be ignorable in the analysis of shale gas production.