PREDICTIONS OF SOLUTE TRANSPORT IN FRACTURED MEDIA USING OPERATOR-STABLE DENSITIES AND FRACTURE NETWORK STATISTICS

This research explores the convergence of ensemble plumes in fractured media to the analytical solutions of fractional-order advection dispersion equations. The multiscaling fractional advection-dispersion equation (MFADE) is a multidimensional solute transport model that accounts for different rates of power-law particle motion in multiple directions. Solutions to the MFADE are operator-stable densities. Operator-stable densities (which include the classical multi-Gaussian as a subset) are typically characterized by power-law leading edge concentration profiles and super-Fickian plume growth. The use of the MFADE for solute transport predictions in fractured media relies on defining the relationship between quantifiable properties of a fractured rock mass and the parameters within the equation.

Synthetic plumes are produced using numerical simulations of fluid flow and solute transport through large scale (2.5km by 2.5km), randomly generated fracture networks. These two-dimensional networks are generated according to the statistics obtained from field studies of fracture length, transmissivity, density and orientation. For low to moderate fracture densities and fracture length exponent values, ensemble particle motions converge to operator-stable densities with power-law leading edge concentration profiles and super-Fickian growth rates, while densely fracture networks with high fracture length exponent values lead to multi-Gaussian densities and roughly Fickian growth. Dominant plume growth directions for the operator-stable scaling matrix are modeled by eigenvectors that correspond to primary fracture set orientations, while the eigenvalues describe rates of plume scaling and depend on the distributional properties of fracture transmissivity and length. The convergence of particle motion to a multi-Gaussian at high fracture densities indicates that a threshold exists where the truncation of pathways satisfies the traditional central limit theorem, leading to Fickian scaling rates along orthogonal plume growth directions, consistent with the classical advection-dispersion equation for solute transport.