Homogenization and effective parameters for the Henry problem in heterogeneous formations

摘要

General upscaling of density-dependent flow is investigated for the classical two-dimensional Henry problem of saltwater intrusion in coastal aquifers. Combined theoretical and numerical results are here presented. Effective flow and transport parameters for saline intrusions could be derived for statistically isotropic and anisotropic heterogeneous permeability fields by use of homogenization theory, applying also to the preasymptotic regime. Our numerical results indicate that heterogeneities in permeability affect foremost the transient evolution of saltwater intrusion, whereas the steady state saltwater distribution is less sensitive to spatially varying permeabilities and longitudinal dispersion. For the isotropic media the effective permeability is found to correspond to the geometric mean, as under conditions without fluid density contrast. The extension of results to anisotropic media requires nontrivial corrections for the effective permeability, which include the variance of log(k) and the directional correlation lengths. The appropriate dispersion coefficients for the problem correspond to the local dispersion coefficients, rather than macrodispersion coefficients. These results are discussed in light of the specific flow configuration posed in the Henry problem.