The impact of finite flow domain size on the statistical properties of the flow system in heterogeneous porous media

A modified covariance function of log hydraulic conductivity, accounting for a finite field size, is derived to assess the impact of finite flow domain size on the statistical properties of the flow system in heterogeneous porous media, such as the uncertainty of a large-scale mean model (variation of head fluctuations) and the effective hydraulic conductivity. This development is accomplished by applying a perturbation approximation and spectral representation to a steady three-dimensional flow field of finite extent. Closed-form expressions in a statistically isotropic porous medium indicate that the finite flow domain size has a direct effect on the head variance and the effective hydraulic conductivity. The comparison of the presented formulation for effective hydraulic conductivity is made with existing results.