Modeling Dispersion in Variably Saturated Porous Media

Abstract:

Modeling dispersion under variably saturated conditions is essential to study solute transport in fracture networks, rocks, and soils. Here, we propose a theoretical framework using concepts from cluster statistics of percolation, fractal scaling of percolation clusters, and critical path analysis to model dispersion in disordered porous media.

In our approach, the key influence on the variability of the dispersivity at shorter length scales is the magnitude of the medium heterogeneity. We show that our theoretical results correctly lie within the experimental range of observed dispersivities over more than 10 orders of magnitude of length scale. Our model predicts that: (1) the arrival time distribution decays slowly and approximately as a power law, and (2) the transport time is a superlinear power of the transport distance. The most important influence on these properties is the topology of the percolation backbone. In order to further evaluate our theory, we compare the arrival time distributions predicted by the proposed model with those measured on experimental columns over a range of saturations and find excellent match between theory and the measurements.