Corner flow effect on the relative permeability of two-phase flow in nano-confined porous media

Abstract

Relative permeability is a critical factor clarifying the multiphase flow behavior in nano-porous media. However, most studies have focus on the circle flow, neglecting the corner flow effect. Therefore, in this work, a comprehensive relative permeability model considering the corner flow effect is proposed. We integrated the corner flow with the immiscible flow model and the confined liquid-gas phase equilibrium with the near-miscible flow model. Then it was validated against the experimental measured data, indicating the proposed model can well describe the two-phase flow in the confined space. Subsequently, sensitivity analysis of corner number, fractal dimension, minimum radius, and viscosity ratio were conducted. Results show that the corner flow effect is noticeable when corner number is less than 8. Under the optimal pore radius of 2 × 10−5 m, the gas relative permeability increases from 0.4909 to 0.9274 with corner number raising from 4 to 10. Under critical oil phase saturation of 0.175, increase of fraction dimension, minimum radius, and viscosity ratio leads to the significant decrease of oil relative permeability and increase of gas relative permeability. In addition, nano-confinement effect and CO2 injection will reduce the interfacial tension and increase the near-miscible relative permeability. When CO2 injection increase to 100% under oil saturation of 0.4084, the increment of oil relative permeability is nearly 67.2%. Interfacial intension-based interpolation method indicates that the confined fluid is more likely to be miscible than the bulk fluid. This relative permeability model provides deeper understandings of two-phase flow in the nano-porous media, which is benefit for the better development of unconventional reservoirs.