Pore-Scale Modelling of Water Flooding in Mixed-Wet Rock Images: Effects of Initial Saturation and Wettability

Abstract

Abstract We simulate transient behaviour of viscous- and capillary-dominated water invasion at mixed-wet conditions directly in SEM images of Bentheim sandstone by treating the pore spaces as cross-sections of straight tubes. Initial conditions are established by drainage and wettability alteration. Constant rate or differential pressure is imposed between tube inlet and outlet. The phase pressures vary with positions along the tube length but remain unique in each cross-section, consistent with one-dimensional core-scale models. This leads to a nonlinear system of equations that are solved for the interface positions as a function of time. The cross-sectional fluid configurations are computed accurately at any capillary pressure and wetting condition by combining free energy minimisation with a menisci-determining procedure that identifies the intersections of two circles moving in opposite directions along the pore boundary. Circle rotation at pinned contact lines accounts for mixed-wet conditions. The fluid conductances are estimated by new explicit expressions that are shown to be in agreement with numerical computations performed directly in the cross-sectional fluid configurations. An SEM image of Bentheim sandstone is taken as input to the developed model for simulating the evolution of saturation profiles during water floods for different flow rates and several mixed-wet conditions, which are established with different initial water saturations and contact angles. It is demonstrated that the simulated saturation profiles depend strongly on initial water saturation at mixed-wet conditions. The saturation profiles exhibit increasingly gradual behaviour in time as the contact angle, defined on the oil-wet solid surfaces, increases or the initial water saturation decreases. Front menisci associated with positive capillary pressures promote oil displacement by water, whereas for large and negative capillary pressures at small flow rates oil displaces water because the associated front menisci retract. This results in the development of pronounced gradual saturation fronts at mixed-wet conditions. The water floods simulated at conditions established with a large initial water saturation and small contact angle on the oil-wet solid surfaces, exhibit steep Buckley-Leverett saturation profiles for high flow rates because the capillary pressure is small and less important. The shape of the saturation profiles are interpreted based on the simulated capillary pressure curves and the corresponding fluid configurations occurring in the rock image.