Rarefied gas transport in heterogeneous shale matrix using a practical apparent permeability model and fuzzy statistical method

Abstract

A new shale gas transport model is derived to characterize the matrix structural heterogeneity impact on the gas apparent permeability (AP). The developed analytical model is built upon two steps: first, the homogeneous AP model is formulated by assigning the Knudsen-number-parameterized weight coefficients to flow mechanisms based on the analyses of representative rarefied gas transport models; then, the homogeneous model is improved to the heterogeneous model with the help of fuzzy statistical method to assess the structural heterogeneity influences. More specifically, the homogeneous AP model incorporates the multilayer adsorption, surface diffusion, real gas effect, and pore confinement effect. The physical terms in the apparent permeability including the rarefaction coefficient and multilayer adsorption model are simplified to facilitate the large-scale simulation. Meanwhile, the heterogeneous AP model is quantified by the distribution of porosity, tortuosity, and pore size. It is demonstrated that the developed AP model can reproduce the experimental and numerical experiments for five types of gases. It is concluded that the rarefaction in nanopores could be reasonably characterized by the weighted Knudsen diffusion and viscous flow mechanisms. Moreover, it is noticed that the surface diffusion and Knudsen diffusion cannot be ignored in nanopores with radius smaller than 3 nm at low reservoir pressures. In contrast, the viscous flow plays a significant role in shale gas transport in nanopores with radius larger than 75 nm. In addition, the fuzzy statistical method in the proposed heterogenous model provides the indicators to evaluate the impact of structural heterogeneity on the AP. It is observed that the heterogeneous model can accurately predict the realistic apparent permeability as the heterogeneity increases to σ = 0.15. However, the accuracy decreases when the matrix heterogeneity increases.