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

Data on hydrocarbon reservoir attributes (e.g., permeability, porosity) are only available at a set of sparse locations, thus resulting in an at best incomplete knowledge of spatial heterogeneity of the system. This lack of information propagates to uncertainty in our evaluations of reservoir performance and as the resulting oil recovery. In this context, a variety of stochastic analyses have been performed for single phase fluid flow and transport (e.g., Dagan, 1989; Dagan and Neuman, 1997; Gelhar, 1993; Zhang, 2001; Sanchez-Vila et al., 2006). Here, we consider a two-phase flow setting taking place in randomly heterogeneous (correlated) permeability field and study competitive effects on fractional flow due to viscous, capillary and gravity forces by way of a suite of detailed computational experiments. Zhang and Tchelepi (1999) consider immiscible two-phase displacement as described through the Buckley-Leverett approach to estimate the saturation field and the associated uncertainty in random media. These authors ground their analysis on an extension of (statistical) moment equations of single phase fully saturated subsurface flow (see, e.g., Guadagnini and Neuman, 1999; Zhang, 2002; Ye et al., 2004; Zhang and Lu, 2004) to encompass two-phase flow. This approach entails approximating otherwise exact moment equations through a perturbative technique. Analyses of heterogeneity effects within the context of the Buckley-Leverett approach with focus on saturation displacement front are illustrated by Noetinger et al. (2006) and Teodorovich et al. (2011). To the best of our knowledge, an assessment of the feedback between viscous and gravity forces and random spatial heterogeneity of permeability fields is still unexplored. This is precisely the aim of our study, which is set in a numerical Monte Carlo context and is targeted to characterize oil recovery predictions uncertainty under the scenario above described.