Drainage under Nonequilibrium Conditions: Exploring Wettability and Dynamic Contact Angle Effects Using Bundle‐Of‐Tubes Simulations

Abstract

Numerical simulators often assume that equilibrium capillary pressure–saturation conditions are maintained as changes in fluid saturation are taking place; however, equilibrium conditions may not be maintained in all circumstances. An alternative approach is to describe a nonequilibrium difference between wetting and nonwetting fluid pressures as a function of the rate of change of saturation and a damping coefficient. It has been proposed that this damping coefficient may be a function of multiple fluid and porous medium properties, including wettability. This study used bundle‐of‐tubes simulations to provide insight into the potential effect of increasing equilibrium contact angle, as a measure of wettability, on the magnitude of the damping coefficient. The effect of considering the dynamic contact angle, as a function of wettability, was also investigated. Results showed that when dynamic contact angles were considered, larger damping coefficient values were predicted. These values varied nonmonotonically with equilibrium contact angle and had maximum values near an equilibrium contact angle of 60°. The results also showed that values of the damping coefficient were dependent on the type of pressure boundary condition used. A steadily increasing boundary pressure resulted in larger damping coefficient values that were a function of the equilibrium contact angle, and better represented experimental pressure–saturation observations, than simulations using a series of instantaneous steps. These results suggest that assuming equilibrium conditions may be reasonable under wettability conditions characterized by equilibrium contact angles near 90°, potentially for contact angles near 0°, but not at moderate equilibrium contact angles. Further work is necessary, however, to determine the underlying physical mechanisms that govern nonequilibrium pressure differences and the magnitude of the damping coefficient.