Stochastic analysis of transient saturated flow through heterogeneous fractured porous media: A double-permeability approach

In this paper we use a double-porosity/double-permeability approach to stud y transient, saturated flow in heterogeneous, fractured porous media. The s patial variabilities in both the fracture and matrix continua motivate us t o treat some of the fracture and matrix medium properties as stochastic pro cesses. Hence flow through heterogeneous, fractured porous media is also am enable to stochastic analysis. In particular, we develop a moment equation- based stochastic theory for flow in fractured porous media. We derive gener al equations governing the statistical moments of the pressure heads in suc h media by perturbation expansions. The solutions of these moment equations are the first two moments of the pressure heads. These may be used to cons truct the confidence intervals of the fracture and matrix pressure heads, w hich are measures of uncertainties caused by incomplete knowledge of the fr acture and matrix medium heterogeneities. The resulting moment equations of pressure heads are coupled and need to be solved sequentially in an iterat ive manner. The two-dimensional version of the equations is implemented num erically and illustrated with some examples.