Experiments and Analysis of Multiscale Viscous Fingering During Forced Imbibition

Summary Immiscible displacement of one fluid by another in porous media has practical applications when viscous oil is produced by water injection. A greater understanding of the flow patterns that evolve during such unstable displacements yields insights into improving predictive capability and increasing oil recovery. Immiscible multiphase displacement exhibits a wide range of behaviors depending on the relative magnitude of viscous, capillary, and gravity forces. Using flow-visualization images from forced-imbibition experiments carried out in etched-silicon micromodels, we show that the conventional Darcy-type modeling of fluid flux is not predictive under unstable, immiscible, forced-imbibition conditions at the scale of interest. When a less viscous fluid displaces a more viscous fluid at low capillary numbers, the displacement patterns show viscous instabilities in the form of fingers and local capillary control of interface movement. We show that such complex displacement patterns are well modeled using statistical theories. We derive a scaling model to describe quantitatively the functional forms for saturation, fractional flow, and capillary dispersion profiles using the self-similar characteristics inherent in the displacement patterns. For the specific range of flow rates (Nc ~ 10−7) and oil/water viscosity ratios (M ~ 8–400) considered in our experiments, both capillary and viscous forces are important, and the displacement pattern indicates fractal features. Results show that functional relations of the scaling model are in considerable agreement with our experimental data.