Stochastic Analysis of Reactive Solute Transport in Heterogeneous, Fractured Porous Media: A Dual-Permeability Approach

Abstract

A nonlocal, first-order, Eulerian stochastic theory is developed for reactive chemical transport in a heterogeneous, fractured porous medium. A dual-permeability model is adopted to describe the flow and transport in the medium, where the solute convection and dispersion in the matrix are considered. The chemical is under linear nonequilibrium sorption and first-order degradation. The hydraulic conductivities, sorption coefficients, degradation rates in both fracture and matrix regions, and interregional mass transfer coefficient are all assumed to be random variables. The resultant theory for mean concentrations in both regions is nonlocal in space and time. Under spatial Fourier and temporal Laplace transforms, the mean concentrations are explicitly expressed. The transformed results are then numerically inverted to the real space via Fast Fourier Transform method. The theory developed in this study generalizes the stochastic studies for a reactive chemical transport in a one-domain flow field (Hu et al., 1997a) and in a mobile/immobile flow field (Huang and Hu, 2001). In comparison with one-domain transport, the dual-permeability model predicts a larger second moment in the longitudinal direction, but smaller one in the transverse direction. In addition, various simplification assumptions have been made based on the general solution. The validity of these assumptions has been tested via the spatial moments of the mean concentration in both fracture and matrix regions.