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Numerical Monte Carlo analysis of the influence of pore‐scale dispersion on macrodispersion in 2‐D heterogeneous porous media
Author(s) -
Beaudoin Anthony,
de Dreuzy JeanRaynald,
Erhel Jocelyne
Publication year - 2010
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2010wr009576
Subject(s) - dispersion (optics) , permeability (electromagnetism) , transverse plane , isotropy , porous medium , mechanics , materials science , porosity , physics , chemistry , composite material , optics , structural engineering , engineering , membrane , biochemistry
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 σ 2 . Macrodispersion is evaluated numerically by using parallel simulations on grids of characteristic size ranging from 200 λ to 1600 λ . We note α L and α T the pore‐scale longitudinal and transversal dispersivities. For α L / λ < 10 −2 and α T / 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 ( α L / λ ≥ 10 −2 or α T / λ ≥ 10 −3 ) induce larger effects than those obtained by the semianalytical expression of Salandin and Fiorotto (1998) for σ 2 > 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 σ 2 > 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 σ 2 ≥ 2.25.