Numerical Investigation of Boundary Effects, Fluid Mobility, and Viscous Coupling in 2D Spontaneous Imbibition

Summary Spontaneous imbibition (SI) occurs in water-wet and mixed-wet porous media when capillary forces displace oil by water. In this work, we compare conventional modeling (using relative permeabilities) with application of a generalized model that includes viscous coupling (interphase drag) to investigate 2D matrix block imbibition. Boundary conditions were varied by opening surfaces to water or oil, and fluid viscosities were also adjusted. We report the oil recovery factor (RF) profiles and where the oil was produced, either from the water-exposed sides (countercurrent production) or oil-exposed sides (cocurrent production). Previous studies have not explored viscous coupling, mobilities, and their interplay with boundary conditions on production profiles, their distribution, and scaling. For water-wet cases, the imbibition rate increased as more matrix boundaries were opened to water or oil. Cocurrent imbibition was less efficient than countercurrent imbibition (0% oil area fraction) at early time (RF < 0.35), as higher water area fraction increased recovery (for same total open area). For intermediate mobility ratios, late time recovery (RF = 0.95) was achieved faster with cocurrent imbibition than countercurrent imbibition for an optimal oil area fraction of ~25%. However, at oil area fractions higher than 40% (45% for the generalized model), cocurrent imbibition took more time than countercurrent imbibition. At an unfavorable mobility ratio, the imbibition time was similar as for countercurrent imbibition up to 75% oil area. Favorable mobility ratio cases showed similar imbibition time up to 25% oil area, while higher oil area rapidly increased imbibition time. In the generalized model, viscous coupling increased the imbibition time when more of the production was countercurrent. For cases with the same open area and same areas exposed to water and oil, a more concentrated oil exposure gave slower recovery. Recovery scaled (increased) by water area for favorable mobility ratios and by total open area for unfavorable mobility ratios. Countercurrent production increased with higher mobility ratio and higher water area fraction; at high (unfavorable) mobility ratio, oil was produced equally from all open sides, and at low mobility ratio, oil was produced only from oil-exposed sides. More oil-wet cases had lower recovery, and the oil was produced more equally from all sides due to maintaining high oil mobility. Because water had low mobility for such states, the imbibition time increased when less open area was exposed to water (i.e., covering the full block with water was optimal).