Numerical Monte Carlo analysis of the influence of pore‐scale dispersion on macrodispersion in 2‐D heterogeneous porous media

Abstract

We investigate the influences of pore‐scale dispersion and of larger‐scale permeability heterogeneities on the macrodispersion without the molecular diffusion. Permeability follows a lognormal exponentially correlated distribution characterized by its correlation length λ and its lognormal variance σ2. Macrodispersion is evaluated numerically by using parallel simulations on grids of characteristic size ranging from 200λ to 1600λ. We note αL and αT the pore‐scale longitudinal and transversal dispersivities. For αL/λ < 10−2 and αT/λ < 10−3, the influence of pore‐scale dispersion on the macrodispersion is smaller than 5% of the macrodispersion due only to permeability heterogeneities. Larger dispersivities (αL/λ ≥ 10−2 or αT/λ ≥ 10−3) induce larger effects than those obtained by the semianalytical expression of Salandin and Fiorotto (1998) for σ2 > 1. The effects of local dispersion on the longitudinal macrodispersion remain limited to 25% at most of the macrodispersion due only to permeability heterogeneities. For σ2 > 1, isotropic local dispersion induces a reduction of the longitudinal macrodispersion, whereas anisotropic local dispersion lets it increase. The longitudinal and transverse local dispersions induce opposite effects on the longitudinal macrodispersion, which are respectively an increase and a reduction. The transverse macrodispersion null without local dispersion or molecular diffusion becomes strictly positive with local dispersion. Because of the velocity field heterogeneities, it is amplified by a factor of 2 to 50 from the grid scale to the macro scale. The transverse dispersion is triggered by both longitudinal and transverse local dispersions. A reduction of a factor of 2 of the transverse local dispersion at fixed longitudinal local dispersion yields only a reduction of a factor of 4 at most of the transverse macrodispersion for σ2 ≥ 2.25.