Dynamic Capillary Pressure Curves from Pore-scale Modelling in Mixed-wet Rock Images (SPE 154474)

In several reservoir multiphase flow processes, such as fracture and near well-bore flow, both viscous and capillary forces determine the pore-scale fluid configurations due to high flow rates. This gives rise to significant dynamic effects in the capillary pressure relation because the fluids are redistributed faster than the relaxation time required for transitions between capillary-equilibrium states. We simulate quasi-static and dynamic capillary pressure curves for drainage and imbibition directly in SEM images of Bentheim sandstone at mixed-wet conditions by treating the identified pore spaces as tube cross-sections. Stepwise pressure differences are imposed between inlet and outlet. The phase pressures vary with length positions but remain unique in each cross-section, which leads to a nonlinear system of equations that are solved for 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. Dynamic capillary pressure is calculated using volume-averaged phase pressures, and dynamic capillary coefficients are obtained from the rates of saturation change. The results could be applied in reservoir simulation models to assess dynamic pore-scale effects on the Darcy scale. Consistent with measurements, our results demonstrates that dynamic capillary pressure is higher than the static capillary pressure during drainage, but lower during imbibition. The dynamic capillary coefficients and rates of saturation change during imbibition depend strongly on wettability and initial water saturation. The proposed model provides insights into the extent of dynamic effects in capillary pressure curves for realistic mixed-wet pore spaces, which contributes to improved interpretation of core-scale experiments.