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 quasi-static 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. 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 cross-sectional 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 using 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 located at a higher capillary level than the static capillary pressure during drainage, but at a lower level during imbibition, regardless 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 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 modelling procedure provides insights into the extent of dynamic effects in capillary pressure curves for realistic mixed-wet pore spaces, which could contribute to 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 pore-scale effects on the Darcy scale.