Stochastic analysis of solute transport in heterogeneous, dual‐permeability media

[1] A Eulerian perturbation method is applied to study the influence of medium heterogeneity on nonreactive chemical transport in a saturated, fractured porous medium under steady state flow conditions. A dual-permeability model is used to describe the flow and solute transport in the fractured medium [, 1993a, 1993b]. The model involves two overlaying continua at the macroscopic level, a fracture pore system, and a less permeable matrix pore system. Solute advection and dispersion take place in both pore systems. A first-order mass diffusion model is used to describe the mass diffusion between fracture and matrix regions. The hydraulic conductivities in both fracture and matrix regions, Kf and Km, and the interregional mass diffusion coefficient, a, are assumed to be spatial random variables to account for heterogeneity of the medium. A closed form analytical solution for the mean concentrations in the fracture and matrix regions is explicitly given in Fourier and Laplace transforms and numerically inverted to real space via fast Fourier transform. The simulation results demonstrate the significant effects of heterogeneous distributions of Kf, Km, and a on solute transport process. Sensitivity studies show the dominant influence of heterogeneity in fracture in comparison with that in matrix. In some special scenarios of heterogeneity the dual-permeability model can be simplified to a mobile/immobile model [, 2000] or a one-domain model [, 1993]. The developed analytical solution provides a general tool to investigate the effects of various heterogeneities on solute transport in fractured porous media and to analyze the errors introduced through various model simplifications.

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