Numerical assessment of 3D macrodispersion in heterogeneous porous media

Abstract

Hydrodynamic dispersion is a key controlling factor of solute transport in heterogeneous porous media. It critically depends on dimensionality. The asymptotic macrodispersion, transverse to the mean velocity direction, vanishes only in 2D and not in 3D. Using the classical Gaussian correlated permeability fields with a lognormal distribution of variance σY 2 , the longitudinal and transverse dispersivities are determined numerically as a function of heterogeneity and dimensionality. We show that the transverse macrodispersion steeply increases with σY 2 underlying the essential role of flow lines braiding, a mechanism specific to 3D systems. The transverse macrodispersion remains however at least two orders of magnitude smaller than the longitudinal macrodispersion, which increases even more steeply with σY 2 . At moderate to high levels of heterogeneity, the transverse macrodispersion also converges much faster to its asymptotic regime than do the longitudinal macrodispersion. Braiding cannot be thus taken as the sole mechanism responsible for the high longitudinal macrodispersions. It could be either supplemented or superseded by stronger velocity correlations in 3D than in 2D. This assumption is supported by the much larger longitudinal macrodispersions obtained in 3D than in 2D, up to a factor of 7 for σY 2 = 7.56.