Rough surface heterogeneous influence on rarefied gas flow in single rock fractures

Abstract

Rarefied gas flow in rock fractures governed by Knudsen flow is employed in residual gas capture and storage. Previous studies mainly adopted the classical theory under the continuum hypothesis to describe the gas flow in fractures, and the research on the interaction between molecules and walls of rarefied gas flow in heterogeneous fracture channels was limited. The molecular flow module is established based on the equations of the kinetic theory of gases, and the mathematical particle tracking module is established based on Newton's laws of motion. 2D and 3D fracture models with different tortuosity and aperture were established to quantify the influence of surface heterogeneity on the transmission probability of rarefied gas flow. The research findings indicate that as the aperture standard deviation and tortuosity increases, the transmission probability correspondingly decreases. Furthermore, in the case of a 3D channel, the aperture standard deviation exerts a dominant influence on transmission probability, and the fitted relationship F = a − b⋅σb^c has been derived. This discovery underscores the limitations inherent in 2D models: these models exhibit anomalous molecular retention phenomena, which hinder their ability to accurately represent true three-dimensional transport mechanisms. In contrast, 3D models feature dominant channels that mitigate the impact of local surface roughness peaks. The findings offer universally applicable theoretical tools for regulating gas flow in a wide range of deep geological engineering applications, contributing to the resolution of the dual challenges of “efficient resource extraction” and “environmental risk prevention and control.”