In this paper, the gas-water two-phase flow characteristics of rock media are studied based on fractal theory and the relative roughness model, and the analytical model of gas-water relative permeability of rock pores with relative roughness is derived. Through numerical simulation, it is found that the maximum flow velocity in the rough microchannel is greater than the maximum flow velocity in the smooth microchannel, but the average flow velocity in the rough microchannel is less than the average flow velocity in the smooth microchannel. The theoretical model results show that the dimensionless permeability of gas-water two-phase flow is inversely proportional to the fractal dimension of relative roughness and tortuosity, and the relative permeability of gas-water two-phase flow is inversely proportional to the relative roughness. The correctness of the model is verified by comparing it with the relevant experimental data.

本文基于分形理论和相对粗糙度模型研究岩石介质气水两相流动特性，推导了相对粗糙度岩石孔隙气水相对渗透率解析模型。通过数值模拟发现，粗糙微通道中的最大流速大于光滑微通道中的最大流速，但粗糙微通道中的平均流速小于光滑微通道中的平均流速。理论模型结果表明，气水两相流的无量纲渗透率与相对粗糙度和曲折度的分形维数成反比，气水两相流的相对渗透率与相对粗糙度成反比。通过与相关实验数据的比较验证了模型的正确性。