A numerical analysis of dimensionality and heterogeneity effects on advective dispersive seawater intrusion processes

Two-dimensional (2D) and 3D numerical simulations of the dispersive Henry problem show that heterogeneity affects seawater intrusion differently in 2D and 3D. When the variance of a multi-Gaussian isotropic hydraulic conductivity field increases, the penetration of the saltwater wedge decreases in 2D while it increases in 3D. This is due to the combined influence of advective and dispersive processes which are affected differently by heterogeneity and problem dimensionality. First, the equivalent hydraulic conductivity controls the mean head gradient and therefore the position of the wedge. For an isotropic medium, increasing the variance increases the equivalent conductivity in 3D but not in 2D. Second, the macrodispersion controls the rotation of the saltwater wedge by affecting the magnitude of the density contrasts along the saltwater wedge. An increased dispersion due to heterogeneity leads to a decreasing density contrast and therefore a smaller penetration of the wedge. The relative magnitude of these two opposite effects depends on the degree of heterogeneity, anisotropy of the medium, and dimension. Investigating these effects in 3D is very heavy numerically; as an alternative, one can simulate 2D heterogeneous media that approximate the behaviour of the 3D ones, provided that their statistical distribution is rescaled.