Solute transport in heterogeneous media: The impact of anisotropy and non-ergodicity in risk assessment

Conceptual model selection is a key issue in risk assessment studies. We an alyze the effect of a number of conceptual aspects related to solute transp ort in two-dimensional heterogeneous media. The main issues addressed are n on-ergodicity, anisotropy in the correlation structure of the transmissivit y field, and dispersion at the local scale. In particular, we study the dev elopment of a solute plume when mean flow is oriented at an angle with resp ect to the principal directions of anisotropy. The study is carried out in a Lagrangian framework using Monte Carlo analysis. Of special interest is the evolution of individual plumes. A number of aspe cts are analyzed, namely the location of the center of mass for each plume and the different ways to compute the angles that the main axes of the plum e develop with respect to the direction of the mean flow. Stochastic theori es based upon ergodicity conclude that the plume gets oriented in the mean flow direction. In our non-ergodic simulations, the mean of the offset angl es, for each individual plume in each particular realization, is offset fro m the mean flow direction towards the direction of maximum anisotropy. If, instead, the analysis is performed on the ensemble plume (superposition of all different simulations), it is then found oriented closer to the directi on of the mean flow than the average offset angle for the different plumes considered separately. This last result adds an extra word of caution to th e use of ensemble averaged values in solute transport studies. Serious implications for risk assessment follow from the conceptual model a dopted. First, in any single realization there will a large uncertainty in locating the plume at any given time; second, real dilution would be less t han what would be expected if the macrodispersion values obtained for ergod ic conditions were applied; third, the volume that is affected by a non-zer o concentration is smaller than that predicted from macrodispersion concept s; fourth, the orientation of the plume does not correspond to that of the mean flow; and fifth, accounting for local dispersion helps reducing uncert ainty.