An efficient distribution method for nonlinear two-phase flow in highly heterogeneous multidimensional stochastic porous media

摘要

In the context of stochastic two-phase flow in porous media, we introduce anovel and efficient method to estimate the probability distribution of thewetting saturation field under uncertain rock properties in highlyheterogeneous porous systems, where streamline patterns are dominated bypermeability heterogeneity, and for slow displacement processes (viscosityratio close to unity). Our method, referred to as the frozen streamlinedistribution method (FROST), is based on a physical understanding of thestochastic problem. Indeed, we identify key random fields that guide thewetting saturation variability, namely fluid particle times of flight andinjection times. By comparing saturation statistics against full-physics MonteCarlo simulations, we illustrate how this simple, yet accurate FROST methodperforms under the preliminary approximation of frozen streamlines. Further, weinspect the performance of an accelerated FROST variant that relies on asimplification about injection time statistics. Finally, we introduce howquantiles of saturation can be efficiently computed within the FROST framework,hence leading to robust uncertainty assessment.