Numerical characterization of contaminant transport in nested two-scale porous media

Natural hydrogeologic properties (e.g., log hydraulic conductivity ) may include many scales of variability. This paper investigates transport in multi-scale media by numerically simulating solute plumes in nested two-scale velocity fields that have a typical scale disparity on the order of 10 [Adams and Gelhar, 1992; Hess et. al., 1992]. Two-scale velocity fields with specified covariance properties are generated from a multi-variate Fast Fourier Transform algorithm. Two dimensional solute plumes are accurately derived from a spline-based Eulerian-Lagrangian transport solver. The plumes are simulated over a travel distance on the order of hundreds of large log k scales and thousands of small log k scales. The initial size of the solute plume is close to that of the large log k scale, and the large time plume size is much larger than this scale. Spatial second moments are computed and compared to theoretical predictions. The spatial structure of the plumes is examined through the use of the dilution index and mean-square measure of concentration variability. Time histories of these measures illustrate distinctive evolutionary features of solute plumes traveling in a small-scale, a large-scale and a two-scale medium. Our results indicate that the large-scale and the two-scale plumes do not reach asymptotic state after a long travel distance. We conclude by discussing the important implication in performing two-scale solute plume simulation.