Modeling the Effect of Viscosity Ratio on Spontaneous Imbibition

Abstract

Summary Spontaneous-imbibition data for Berea sandstone cores, which are very strongly wetted by the aqueous phase and initially 100% saturated with mineral oil, are reported for linear, radial, and allfaces-open boundary conditions. Oil viscosities were 4, 63, and 173 cp, and aqueous-phase viscosities ranged from 1 to 495 cp. Oil-/aqueous-phase-viscosity ratios were varied by more than four orders of magnitude (0.01 to 173.1). Near-linear relationships (with slopes close to one-half), between the frontal position and imbibition time on a log-log scale, were obtained for both linear and radial countercurrent flow. Behavior is consistent, with near piston-like displacement by the imbibing aqueous phase. The results are analyzed by a new mathematical model that accounts for countercurrent spontaneous imbibition with symmetrical flow patterns. The model assumes that saturation and permeabilities to counterflowing phases behind the front are constant and that any effect of local change in interfacial curvature with distance is negligible. The results from the model are used to extend scaling to include the measured effect of viscosity ratio for linear and radial flow. For the all-faces-open boundary condition, commonly used in core-analysis studies, oil recovery vs. imbibition time is estimated by a combination of spherical and radial flow. Consistently close agreement was obtained between experiments and behavior predicted by the model.