Numerical assessment of 3-D macrodispersion in heterogeneous porous media

Hydrodynamic dispersion is a key controlling factor of solute transport in heterogeneous porous media that critically depends on dimensionality. The transverse macrodispersion (asymptotic dispersion transverse to the mean velocity direction) is known to vanish only in 2-D and not in 3-D. Using classical Gaussian correlated permeability fields with a lognormal distribution of variance sigma(2)(Y), we determine numerically the longitudinal and transverse dispersivities as functions of heterogeneity and dimensionality. We show that the transverse macrodispersion steeply increases with sigma(2)(Y) underlying the essential role of flow lines braiding, a mechanism specific to 3-D systems that we qualitatively characterize by the increasing expansion of the flow lines transversally to the flow direction. The transverse macrodispersion remains however at least two orders of magnitude smaller than the longitudinal macrodispersion, which increases even more steeply with sigma(2)(Y). At moderate to high levels of heterogeneity, the transverse dispersion also converges much faster to its asymptotic regime than do the longitudinal dispersion. 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 It could be either supplemented or superseded by stronger velocity correlations in 3-D than in 2-D. This assumption is supported by the much larger longitudinal macrodispersions obtained in 3-D than in 2-D, up to a factor of 5 for sigma(2)(Y)=6.25.