From heterogeneity characterization to prediction of transport in highly heterogeneous aquifers (with application to MADE)

Abstract:

We consider transport of an inert solute for mean steady and uniform water flow in a heterogeneous aquifer of arbitrary logconductivity variance σ­­_Y­­². Longitudinal transport is quantified by mass arrival at control planes or spatial mass distribution, for an ergodic plume injected instantaneously in a flux proportional mode. Longitudinal spreading is governed by the advective random velocity term in the stochastic local ADE. The velocity field results from the solution of the stochastic flow equations, with the random permeability serving as input. The logconductivity is characterized by the pdf and the horizontal and vertical integral scales. For weakly heterogeneous formations (σ­­_Y­­² <1) it was found in the past that the plume is Gaussian and modeled by an upscaled ADE with constant mean velocity and a time dependent macrodispersivity. The latter tends to a constant value and asymptotically transport is Fickian. To deal with highly heterogeneous formations like MADE we have developed in the last decade an approximate model, coined as MIM-SCA, which predicts mass arrival in terms of the permeability statistics. The structure is modeled as an ensemble of blocks of independent permeability (multi indicator model) of pdf identified from field characterization. A simple semi-analytical solution is achieved by the self-consistent approximation, superposition of solutions for isolated blocks submerged in a matrix of effective properties. Comparison of prediction with the snapshots at all times of the longitudinal mass distributions of MADE plume shows good agreement, problems of mass recovery notwithstanding. Prediction is based solely on the permeability structure, characterized with the aid of the recent DPIL  technology. The emphasis of the presentation is on the physical mechanisms which explain the plumes non-Gaussian behavior in highly heterogeneous aquifers: the long tailing for the large residence times, channeling for the fast advancing front. Connection with other models of Time Domain Random Walk is discussed.