A Novel Model of the Gas–Water Relative Permeability of Gas Reservoirs Under High-Temperature and High-Pressure Conditions

Currently, there are numerous studies on the gas–water relative permeability model. However two key mechanisms are often overlooked: including water film thickness as a function of driving pressures, and the gas slippage effect, which can be neglected under high-temperature and high-pressure conditions. To address this gap, a mathematical model for relative permeability based on fractal theory is proposed, explicitly accounting for the effect of water film thickness as a function of driving pressure. The validity of the proposed model is verified through comparison with laboratory experimental results, followed by a sensitivity analysis. The findings indicate that under elevated pressure and temperature conditions, gas viscosity increases, which reduces the flow capacity of the gas phase. Consequently, gas’ relative permeability decreases, while water’s relative permeability increases correspondingly. The pore fractal dimension exhibits a negligible impact on relative permeability. As the displacement pressure gradient decreases, water’s relative permeability declines, and gas’ relative permeability rises correspondingly. This work has significant implications for the development of gas reservoirs under high-temperature and high-pressure conditions.