Pore-Scale Modeling of the Effect of Wettability on Two-Phase Flow Properties for Newtonian and Non-Newtonian Fluids

The Darcy-scale properties of reservoir rocks, such as capillary pressure and relative permeability, are controlled by multiphase flow properties at the pore scale. In the present paper, we implement a volume of fluid (VOF) method coupled with a physically based dynamic contact angle to perform pore-scale simulation of two-phase flow within a porous medium. The numerical model is based on the resolution of the Navier-Stokes equations as well as a phase fraction equation incorporating a dynamic contact angle model with wetting hysteresis effect. After the model is validated for a single phase, a two-phase flow simulation is performed on both a Newtonian and a non-Newtonian fluid; the latter consists of a polymer solution displaying a shear-thinning power law viscosity. To investigate the effects of contact angle hysteresis and the non-Newtonian nature of the fluid, simulations of both drainage and imbibition are carried out in order to analyze water and oil saturation-particularly critical parameters such as initial water saturation (Swi) and residual oil saturation (Sor) are assessed in terms of wettability. Additionally, the model sensitivities to the consistency factor (χ), the flow behavior index ( ), and the advancing and receding contact angles are tested. Interestingly, the model correctly retrieves the variation in Sor and wettability and predicts behavior over a wide range of contact angles that are difficult to probe experimentally.