Title: An efficient distribution method for nonlinear two-phase flow in highly heterogeneous multidimensional stochastic porous media,
Abstract: In the context of stochastic two-phase flow in porous media, we introduce a
novel and efficient method to estimate the probability distribution of the
wetting saturation field under uncertain rock properties in highly
heterogeneous porous systems, where streamline patterns are dominated by
permeability heterogeneity, and for slow displacement processes (viscosity
ratio close to unity). Our method, referred to as the frozen streamline
distribution method (FROST), is based on a physical understanding of the
stochastic problem. Indeed, we identify key random fields that guide the
wetting saturation variability, namely fluid particle times of flight and
injection times. By comparing saturation statistics against full-physics Monte
Carlo simulations, we illustrate how this simple, yet accurate FROST method
performs under the preliminary approximation of frozen streamlines. Further, we
inspect the performance of an accelerated FROST variant that relies on a
simplification about injection time statistics. Finally, we introduce how
quantiles of saturation can be efficiently computed within the FROST framework,
hence leading to robust uncertainty assessment.