Quantifying the Effect of Pore-Size Dependent Wettability on Relative Permeability Using Capillary Bundle Model

Relative permeability is a key parameter for characterizing the multiphase flow dynamics in porous media at macroscopic scale while it can be significantly impacted by wettability. Recently, it has been reported in microfluidic experiments that wettability is dependent on the pore size (Van Rooijen et al., 2022). To investigate the effect of pore-size-dependent wettability on relative permeability, we propose a theoretical framework informed by digital core samples to quantify the deviation of relative permeability curves due to wettability change. We find that the significance of impact is highly dependent on two factors: (i) the function between contact angle and pore size (ii) overall pore size distribution. Under linear function, this impact can be significant for tight porous media with a maximum deviation of 1,000%. Relative permeability is an important feature for multiphase flow at the reservoir scale. It can be highly dependent on wettability, which is an interfacial property at the pore scale. Recent experimental evidence suggests that wettability is dependent on the pore size, but the impact of the pore-size-dependent wettability on relative permeability still remains unknown. In this study, we propose a theoretical model to investigate the effect of pore-size-dependent wettability on relative permeability. The pore size distribution is informed by the pore images. We find that the impact can be significant for low-permeability porous media under certain conditions. The results imply that this effect is not always neglible when modeling two-phase flow. A theoretical framework is proposed to quantify the impact of pore-size dependent wettability on relative permeability The maximum impact on relative permeability can be as significant as 1,000%