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

Abstract

Conceptual model selection is a key issue in risk assessment studies. We analyze the effect of a number of conceptual aspects related to solute transport in two-dimensional heterogeneous media. The main issues addressed are non-ergodicity, anisotropy in the correlation structure of the transmissivity field, and dispersion at the local scale. In particular, we study the development of a solute plume when mean flow is oriented at an angle with respect 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 aspects 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 plume develop with respect to the direction of the mean flow. Stochastic theories based upon ergodicity conclude that the plume gets oriented in the mean flow direction. In our non-ergodic simulations, the mean of the offset angles, for each individual plume in each particular realization, is offset from 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 direction 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 the use of ensemble averaged values in solute transport studies.

Serious implications for risk assessment follow from the conceptual model adopted. First, in any single realization there will a large uncertainty in locating the plume at any given time; second, real dilution would be less than what would be expected if the macrodispersion values obtained for ergodic conditions were applied; third, the volume that is affected by a non-zero concentration is smaller than that predicted from macrodispersion concepts; fourth, the orientation of the plume does not correspond to that of the mean flow; and fifth, accounting for local dispersion helps reducing uncertainty.