Theory study of gas-water relative permeability in roughened fractures

It has been shown that gas-water relative permeability in fracture or fractured porous media plays an important role in determination of flow characteristics for gas-water two-phase flow. The accurate prediction of gas-water two-phase flow in fracture or fractured media is hence highly important. In most recent analytical models for gas-water relative permeability in fracture, the fracture is conceptualized as smooth wall. Reliable characterization of roughened fracture surface is severely limited. The analytical models for gas-water two-phase relative permeability in roughened fracture are scarce, thus, it is desirable to develop an analytical model for gas-water relative permeability in fracture with roughened surface. The goal of this work is to present an analytical model for gas-water relative permeability in roughened fracture. The rough surface topography of roughened fracture can be addressed by fractal theory. In addition, the proposed model is modified by considering the influence of tortuosity to study the gas-water relative permeability in fractured porous media. The proposed gas-water relative permeability is found to be a function of the structural parameters of roughened fracture. The predictions of relative permeability by the proposed model have similar variation trend with available experimental data, which verifies the theoretical models. We also conduct several sensitivity studies. These proposed analytical models provides a more realistic representation of gas-water two-phase flow in roughened fracture and fractured porous media, and gives rise to more reliable gas-water relative permeability curves that can be used for analyzing gas-water two-phase flow characteristic in fractured reservoirs.