Ensemble Results of Solute Transport in 2D Operator-Stable Random Fields

As it moves through an aquifer, a dissolved solute plume will evolve according to the complex heterogeneities that are present at many scales. Some statistical model must account for the aquifer structure. A fractional Brownian motion (fBm) model has been shown to create the long-range correlation that can produce continually faster-than-Fickian plume growth. Previous fBm models have assumed isotropic scaling (defined by a scalar Hurst coefficient). Motivated by field measurements, recent techniques were developed to handle anisotropic scaling, in which the scaling, or self-similarity parameter, is defined by a matrix. Ensemble numerical results are analyzed for solute transport through some of these 2D operator-stable fBm fields. Both the longitudinal and transverse Hurst coefficients are important in solute transport. Smaller Hurst coefficients in the transverse direction lead to more stretching of the convolution kernel in the direction of transport. This stretching creates a more stratified aquifer, with more continuity in high and low values in hydraulic conductivity (K). The result is faster-than-Fickian growth rates, and a longer tail in the breakthrough curve.