Solute transport in highly heterogeneous aquifers

The paper deals with the transport of nonreactive solute in heterogeneous formations with prescribed statistical properties of the hydraulic log conductivity Y=ln K. Available solutions obtained from perturbation methods are limited to first- and second-order solutions, valid only for small values of the log conductivity variance σ2Y. Published numerical investigations give comparative results with finite values of σ2Y, but some discrepancies among the results generate doubts about the capability of numerical methods to capture high-order effects for media with large variance values. When these large σ2Y values are encountered in natural formations, the related nonlinear effects could be significant in the velocity statistics and in the overall dispersion process. The nonlinearity consequences are here investigated in two-dimensional isotropic porous media by the Monte Carlo technique coupled with a finite element analysis. The analysis includes σ2Y values from 0.05 to 4 enhancing the relevance of the nonlinear effects in the dispersion tensor solution. To dissipate the doubts related to the numerical approach, the accuracy of the solutions was defined by checking the influence of the factors which can affect the solution and by giving an estimation of the related errors. The numerical results confirm the validity of the first-order and second-order analyses when σ2Y → 0; the second-order solution captures the nonlinear effects in a small range of log conductivity variance close to zero. The nonlinear terms neglected in the first-order formulation for higher σ2Y values give (1) late travel time longitudinal dispersion values greater than the linear solution, (2) notably non-Gaussian distribution of the Lagrangian velocity and particle displacements, and (3) travel times to approach the asymptotic Fickian regime longer than those obtained using the linear solution.