Dynamic capillary pressure curves from pore-scale modeling in mixed-wet-rock images

In reservoir multiphase-flow processes with high flow rates, both viscous and capillary forces determine the pore-scale fluid configurations, and significant dynamic effects could appear in the capillary pressure/saturation relation. We simulate dynamic and quasistatic capillary pressure curves for drainage and imbibition directly in scanning-electron-microscope (SEM) images of Bentheim sandstone at mixed-wet conditions by treating the identified pore spaces as tube cross sections. The phase pressures vary with length positions along the tube length 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 crosssectional fluid configurations are computed accurately at any capillary pressure and wetting condition by combining free-energy minimization 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 with volume-averaged phase pressures, and dynamic capillary coefficients are obtained by computing the time derivative of saturation and the difference between the dynamic and static capillary pressure. Consistent with previously reported measurements, our results demonstrate that, for a given water saturation, simulated dynamic capillary pressure curves are at a higher capillary level than the static capillary pressure during drainage, but at a lower level during imbibition, regardless of the wetting state of the porous medium. The difference between dynamic and static capillary pressure becomes larger as the pressure step applied in the simulations is increased. The model predicts that the dynamic capillary coefficient is a function of saturation and is independent of the incremental pressure step, which is consistent with results reported in previous studies. The dynamic capillary coefficient increases with decreasing water saturation at water-wet conditions, whereas, for mixed- to oil-wet conditions, it increases with increasing water saturation. The imbibition simulations performed at mixed- to oil-wet conditions also indicate that the dynamic capillary coefficient increases with decreasing initial water saturation. The proposed modeling procedure provides insights into the extent of dynamic effects in capillary pressure curves for realistic mixed-wet pore spaces, which could contribute to the improved interpretation of core-scale experiments. The simulated capillary pressure curves obtained with the pore-scale model could also be applied in reservoir-simulation models to assess dynamic porescale effects on the Darcy scale.