Advective Transport in Heterogeneous Formations: The Impact of Spatial Anisotropy on the Breakthrough Curve

Abstract

Water flow and solute transport take place in formations of spatially variable conductivity K. The logconductivity Y = ln K is modeled as a random stationary space function, of normal univariate pdf (of mean In KG and variance \({\sigma_{Y}^{2}}\)) and of axisymmetric autocorrelation of integral scales Ih,Iv (anisotropy ratio f = Iv/Ih 1 }\) , which is of interest for many aquifers and is more difficult to solve either numerically or by approximations. We approach the three dimensional problem by modeling the structure as an ensemble of densely packed oblate spheroids of semi-major and semi-minor axis R and f R, respectively, and independent lognormal K, submerged in a matrix of uniform conductivity Kef, the effective conductivity of the ensemble. The detailed numerical simulations of transport show that the BTC is insensitive to the value of the anisotropy ratio f, i.e., μ (t, x) Ih/U depends only on \({\sigma _{Y}^{2}}\) (except for small differences in the tail). This important result implies that transport, as quantified by BTCs or spatial longitudinal mass distributions, can be modeled accurately by the much simpler solutions developed in the past for isotropic media, like e.g., the semi-analytical self-consistent approximation.