Impact of Viscous Fingering on the Prediction of Optimum WAG Ratio

Abstract In miscible flooding, injection of solvent is often combined with water in an attempt to reduce the mobility contrast between injected and displaced fluids, and control the degree of fingering. Using traditional fractional flow theory, Stalkup estimated the optimum water-solvent ratio (or WAG ratio) when viscous fingering effects are ignored, by imposing that the solvent and water fronts travel at the same speed. Here we study how the displacement efficiency and the mobility ratio across the solvent front vary with the WAG ratio, when fingering is included in the analysis. We do so by computing analytical solutions to a one-dimensional model of two-phase, three-component, first-contact miscible flow that includes the macroscopic effects of viscous fingering. The macroscopic model, originally proposed by Blunt and Christie, employs an extension of the Koval fingering model to multiphase flows. The premise is that the only parameter of the model —the effective mobility ratio— must be calibrated dynamically until self-consistency is achieved between the input value and the mobility contrast across the solvent front. This model has been extensively validated by means of high-resolution simulations that capture the details of viscous fingering and carefully-designed laboratory experiments. The results of this paper suggest that, while the prediction of the optimum WAG ratio does not change dramatically by incorporating the effects of viscous fingering, it is beneficial to inject more solvent than estimated by Stalkup's method. We show that, in this case, both the PVI for complete oil recovery and thedegreeof fingering are minimized.