Percolation theory for solute transport in realistic porous media

Abstract:

Starting in 2008 (Hunt and Skinner), percolation concepts have been applied to an initial delta-function solute pulse to obtain solute arrival time distributions a distance x downstream, or spatial solute distributions at an arbitrary time. Specific application has been to monomodal local conductance distributions and a single scale of heterogeneity. The treatment generalizes the concept of critical path analysis to find the probability that two sides of an arbitrary volume, a separation x apart, are connected by an interconnected cluster of arbitrary minimal, or cut-off, conductance value. Then it uses the topology of the backbone and the relevant resistance distribution (on the cluster!) to calculate the time required for solutes to cross such a cluster. Tests in over 50 separate cases have found its results to predictive, while its predicted envelope of dispersivity values as a function of length scale is verified through comparison with 2200 experimental values from length scales of a few microns to 100km. Tackling such a wide range of space and time scales (10 order of magnitude of space and as many as 19 orders of magnitude of time scale) is unprecedented in this field of endeavor.

The theoretical results for conservative solute transport can be used to predict reactive solute transport, i.e., the temporal scaling of chemical reaction rates in porous media. The precise predictions of the solute transport distance match thicknesses of weathering rinds and of soils, while the derivative of the transport distance generates the reaction rate.