Stochastic Analysis of Macrodispersive Solute Flux in Heterogeneous Aquifers With Nonstationary Random Hydraulic Conductivity Fields

Abstract This work develops a theoretical framework for modeling the large‐scale transport of inert solutes in heterogeneous aquifers, where the perturbation field of logarithmic hydraulic conductivity (ln K ) is considered nonstationary. Based on the intrinsic hypothesis for the ln K perturbation field, the variability of the ln K perturbation field can be characterized by the semivariogram. The general expressions for the concentration semivariogram and the macrodispersive flux in Fourier spectral space are derived using the Fourier‐Stieltjes spectral representation approach and the representation theorem. These solutions generalize the previous results presented in the literature on stochastic subsurface hydrology under the assumption of a stationary covariance function of the ln K perturbation field. The theories developed here are applied to the case of solute transport in heterogeneous media, where the variation of the ln K perturbation field exhibits a power‐law semivariogram. It is shown that the nonstationarity of the ln K perturbation field leads to nonstationary perturbation fields of the hydraulic head and thus of the specific discharge, which in turn results in a nonstationary perturbation field of the concentration, leading to a non‐Fickian macrodispersion. The greater the Hurst exponent, the greater the variability of the specific discharge and solute concentration perturbation fields and thus the greater the macrodispersive flux.