Dispersion in heterogeneous porous media: 2. Predictions for stratified and two-dimensional spatially periodic systems


  • O. A. Plumb,

  • S. Whitaker


The closure scheme which is presented in part 1 (Plumb and Whitaker, this issue) is solved for a stratified system and for a two-dimensional spatially periodic system. By this we mean that the ω and η regions, which make up the heterogeneous media, are distributed in a spatially periodic manner. The solution to the closure problem yields the information necessary to determine the large-scale dispersion tensor and the other coefficients that appear in the large-scale dispersion equation. The theoretical results for the stratified system exhibit an increase in the longitudinal dispersion coefficient of several orders of magnitude over that which would be predicted using established correlations based on laboratory experiments with seemingly homogeneous porous media. For the cases studied, the coefficient of the mixed space-time derivative appears to be significant and this coefficient increases for those conditions which yield increasing longitudinal dispersion coefficients. The results for the two-dimensional spatially periodic system are in qualitative agreement with experimental observations, and we found that both the size of the heterogeneity and the difference in the hydraulic conductivity between the two regions had an important influence on the large-scale dispersion tensor. As in the case of a stratified medium, the predicted values of the coefficient of the mixed space-time derivative (the skewness vector) indicate that this term could be a significant factor in the prediction of mass transport in heterogeneous porous media.