Darcy-Scale Simulation of Boundary-Condition Effects During Capillary-Dominated Flow in High-Permeability Systems

We present numerical interpretations of two experimental sets of spontaneous-imbibition tests with combined cocurrent/countercurrent flow in high-permeability, unconsolidated sandpacks. The experiments were conducted using the two-ends-open free-spontaneous-imbibition (TEOFSI) boundary condition, in which one end face was in contact with the wetting (W) phase and the other with the nonwetting (NW) phase. The simulations quantified the impact from boundary-condition effects during capillary imbibition in the low-capillary sandpacks; the flow resistance in the outlet filter controlled imbibition rates, end recovery, and countercurrent production in tests with high NW-phase viscosity. A hydrostatic water column of a few centimeters at the W-phase end face also affected the imbibition process. Numerical and analytical solutions provided insight into when such boundary effects become important. In particular, the observed linear recovery with time and variations in time scale could not be explained by conventional modeling, but were captured by incorporating a thin, low-permeability filter into the models. For high-viscosity NW-phase tests with a low-permeability filter, countercurrent production is strongly enhanced and controlled by the capillary backpressure (CBP).