Uncertainty Quantification Working Group
May 16, 11:30 AM, CNLS Conf. Room, TA-3, Bldg. 1690

Nonstationary stochastic theories and applications to subsurface flow and transport

Don Zhang, EES-6


It has now been well recognized that flow and transport in porous media are strongly influenced by spatial variabilities in the medium and is subject to uncertainties. Since such a situation cannot be accurately modeled deterministically without considering the uncertainties, it has become quite common to approach the subsurface flow and transport problem stochastically. Many researchers have developed and applied stochastic theories to subsurface flow and transport problems since the late 1970s. This field of research has led to fundamental understandings for flow and transport in random porous media, uncertainty propagation in such media, effective parameters, and scale dependent coefficients. However, its applications to real-world problems have been limited because of a number of simplifying assumptions and treatments such as stationary (statistically homogeneous) medium properties, uniform mean flow, and unbounded domains. This presentation will discuss some recently developed nonstationary stochastic flow and transport theories, which account for nonstationary, multiscale medium features, non-uniform mean flow (including fluid pumping/injecting), and finite domain boundaries. In these theories, general equations governing the statistical moments of flow and transport variables are derived from the original stochastic equations. Owing to the spatial nonstationarities in both the independent and dependent variables, the moment equations must generally be solved by numerical techniques, whose strategies can differ significantly from those in solving the original equations. Some computational examples and results will be shown and future research directions will be discussed.