Interpreting dynamics of snap-off in a constricted capillary from the energy dissipation principle

Abstract

Snap-off usually occurs during two-phase fluid displacement in a constricted capillary, where the nonwetting phase fluid is cut into blobs or ganglia due to surface tension. Snap-off has been intensely recognized as a predominant pore-scale mechanism that may be responsible for the breakup and trapping of the nonwetting phase in complex geophysical structures. Herein, we investigated the dynamics of snap-off in a constricted pore and throat structure with a square cross-section using the volume of fluid method. Despite the geometric constraint dictated by Roof, a new judging diagram for the occurrence of snap-off was proposed as a function of Ca number and viscosity ratio. Our prediction from the numerical simulation is consistent with the analytical solution derived from the balance of capillary and hydrodynamic pressure. Furthermore, the associated transient energy balance was thoroughly studied, considering the alteration of the surface energy, kinetic energy, total input energy, and viscous dissipation during the period of snap-off. The results indicated that snap-off is always characterized by a sharp decline in the surface energy, which resulted in a surge in the kinetic energy and viscous dissipation. In addition, we observed a sharp surge in the viscous dissipation rate curve associated with such energy change, which is attributed to the redistribution of the velocity field. The sudden surge unanimously decreased while increasing the Ca number or viscosity ratio. Meanwhile, the position at which snap-off took place was shifted downstream of the throat, explaining the condition of the snap-off had become much more difficult.