Viscous-Fingering Function for Unstable Immiscible Flows

Abstract

Summary Displacement of viscous oils often involves unstable immiscible flow. Viscous instability and its influence on relative permeability were studied in this work at different viscosity ratios, injection rates, and domain widths. Micromodels and pore-scale models were used to visually inspect the interplay of viscous and capillary forces in the viscous-dominated regime. A new dimensionless scaling parameter, NI=(vwμwσow)(μoμw)2(D2/K), was developed that is useful in predicting the recoveries of unstable displacements at various viscosity ratios and injection rates. The scaling parameter showed excellent fit with experimental data of 68 corefloods. A lumped finger model was developed to modify multiphase flow equations and to yield pseudorelative permeability functions that account for viscous fingering. The parameters of the lumped model can be estimated from the new dimensionless number, NI. This pseudorelative permeability function could be applied at each gridblock on the basis of the local NI to simulate large-scale unstable floods in water-wet porous media.