An Analytical Relative Permeability Model Considering Flow Path Structural Characteristics for Gas-Liquid Two-Phase Flow in Shale Fracture

Relative permeability models are essential in describing the multiphase fluid flow in reservoir rocks. Literature work has shown that the existing theoretical models of relative permeability cannot perfectly describe the two- phase flow experimental data in fractures because those models are mostly developed for porous media (such as sandstone) or proposed without fully taking the specific characteristics of two- phase flow into consideration. In this paper, we propose a theoretical two- phase flow relative permeability model based on the tortuous flow channels, considering the structural characteristics of two- phase flow in the fractures. This model considers that the gas and liquid flow through different channels of different shapes and sizes at the same time. The formula for two- phase relative permeability was derived from cubic law in fracture and Darcy's law, with the influence of the slip effect of the gas phase also considered. The results from different models were compared using several series of experimental data. The model proposed in this paper has a better fit than the others for the raw experimental data. This study demonstrates that it is crucial to take the flow paths and distribution of the two phases into consideration to model the two- phase flow in fracture accurately. This work also found that the tortuosity of the gas channel at the irreducible liquid saturation has a negative effect on gas relative permeability but positive to liquid relative permeability. Moreover, the model demonstrates that the decrease in aperture leads to an increase in the gas relative permeability due to gas slippage, while the impact of gas slippage reduces under high pressure.