From the local to the regional scale. What is the effect of missing vertical heterogeneity moving from fully 3-D to 2-D depth averaged dispersion models?

The plume evolution in natural porous formations is strongly affected by the erratic variability of the hydraulic conductivity K that exhibits a three-dimensional correlation structure. In regional domains, the effect of the vertical heterogeneity combines itself with that one due to the horizontal variability of K, and when the plume has travelled a large number of (horizontal) integral scales, under the hypothesis that the transmissivity spatial distribution prevails, its evolution can be analyzed by two-dimensional models. Until this limit is reached, the vertical and horizontal variability of K are combined to give a fully three-dimensional dispersion process and the application of depth averaged models may gives erroneous results. In order to analyze the effects on trasport deriving from this simplification, we present the results of some numerical experiments that compare the three-dimensional plume evolution with two-dimensional simulations developed by tacking into account different hydraulic conductivity spatial distributions. The comparison between results of numerical simulations and theoretical considerations based on first order solution suggests a possible way to take into account the vertical variability of K in a depth averaged model