A Mathematical Model of Coupled Gas Flow and Coal Deformation with Gas Diffusion and Klinkenberg Effects

Abstract

The influence of gas diffusion behavior on gas flow and permeability evolution in coal seams is evaluated in this paper. Coalbed methane (CBM) reservoirs differ from conventional porous media and fractured gas reservoirs due to certain unique features, which lead to two distinct gas pressures: one in fractures and the other in the coal matrix. The latter pressure, also known as the sorption pressure, will be used in calculating sorption-based volume changes. The effective stress laws for single-porosity media is not suitable for CBM reservoirs, and the effective stress laws for multi-porosity media need to be applied. The realization of the above two points is based on the study of the two-phase state of gas migration (involving Fickian diffusion and Darcy flow) in a coal seam. Then, a general porosity and permeability model based on the P-M model is proposed to fit this phenomenon. Moreover, the Klinkenberg effect has been taken into account and set as a reference object. Finally, a coupled gas flow and coal deformation model is proposed and solved by using a finite element method. The numerical results indicate that the effects of gas diffusion behavior and Klinkenberg behavior can have a critical influence on the gas pressure, residual gas content, and permeability evolution during the entire methane degasification period, and the impacts of the two effects are of the same order of magnitude. Without considering the gas diffusion effect, the gas pressure and residual gas content will be underestimated, and the permeability will be overestimated.