A natural gradient experiment on solute transport in a sand aquifer: Spatial variability of hydraulic conductivity and its role in the dispersion process

TLDR

Permeability measurements on cores taken along two cross sections in the Borden aquifer quantified the spatial variability of hydraulic conductivity for a long‑term tracer test. The tracer test revealed that the aquifer consists of thin, discontinuous hydraulic‑conductivity lenses with an exponential covariance (variance 0.29, horizontal correlation ≈ 2.8 m, vertical ≈ 0.12 m), yielding macrodispersivities of 0.6 m (3‑D) and 0.45 m (2‑D) that, when applied to stochastic transport equations, accurately predicted the observed longitudinal and transverse tracer spread and suggest the theory can estimate effective transport parameters in similarly complex aquifers.

Abstract

The spatial variability of hydraulic conductivity at the site of a long‐term tracer test performed in the Borden aquifer was examined in great detail by conducting permeability measurements on a series of cores taken along two cross sections, one along and the other transverse to the mean flow direction. Along the two cross sections, a regular‐spaced grid of hydraulic conductivity data with 0.05 m vertical and 1.0 m horizontal spatial discretization revealed that the aquifer is comprised of numerous thin, discontinuous lenses of contrasting hydraulic conductivity. Estimation of the three‐dimensional covariance structure of the aquifer from the log‐transformed data indicates that an exponential covariance model with a variance equal to 0.29, an isotropic horizontal correlation length equal to about 2.8 m, and a vertical correlation length equal to 0.12 m is representative. A value for the longitudinal macrodispersivity calculated from these statistical parameters using three‐dimensional stochastic transport theory developed by L. W. Gelhar and C. Axness (1983) is about 0.6 m. For the vertically averaged case, the two‐dimensional theory developed by G. Dagan (1982, 1984) yields a longitudinal djspersivity equal to 0.45 m. Use of the estimated statistical parameters describing the ln ( K ) variability in Dagan's transient equations closely predicted the observed longitudinal and horizontal transverse spread of the tracer with time. Weak vertical and horizontal dispersion that is controlled essentially by local‐scale dispersion was obtained from the analysis. Because the dispersion predicted independently from the statistical description of the Borden aquifer is consistent with the spread of the injected tracer, it is felt that the theory holds promise for providing meaningful estimates of effective transport parameters in other complex‐structured aquifers.