Feedback Between Gravity and Viscous Forces in Two-phase Buckley-Leverett Flow in Randomly Heterogeneous Permeability Fields

Summary Data on hydrocarbon reservoir attributes (e.g., permeability, porosity) are only available at a set of sparse locations, thus resulting (at best) in an incomplete knowledge of spatial heterogeneity of the system. This lack of information propagates to uncertainty in our evaluations of reservoir performance and of the resulting oil recovery. We consider a two-phase flow setting taking place in a randomly heterogeneous (correlated) permeability field to assess the feedback between viscous and gravity forces in a numerical Monte Carlo context and finally characterize oil recovery estimates under uncertainty for a water flooding scenario. Our work leads to the following major conclusions: Uncertainty in the spatial distribution of permeability propagates to final oil recovery in a way that depends on the feedback between gravity and viscous forces driving the system. Uncertainty of final oil recovered (as rendered in terms of variance) is smallest for vertical flows, consistent with the observation that the gravity effect is largest in such scenarios and is dominant in controlling the flow dynamics. Uncertainty of final oil recovered tends to be higher when there is competition between the effects of gravity and viscous forces, the latter being influenced by the strength of the spatial variability of permeability.