Moment Differential Equations for Flow in Highly Heterogeneous Porous Media

Quantitative descriptions of flow and transport in subsurface environmentsare often hampered by uncertainty in the input parameters. Treatingsuch parameters as random fields represents a useful tool for dealingwith uncertainty. We review the state of the art of stochasticdescription of hydrogeology with an emphasis on statisticallyinhomogeneous (nonstationary) models. Our focus is on composite mediamodels that allow one to estimate uncertainties both in geometricalstructure of geological media consisting of various materials and inphysical properties of these materials.