Assessment of the predictive capabilities of stochastic theories in a three-dimensional laboratory test aquifer: Effective hydraulic conductivity and temporal moments of breakthrough curves

摘要

Conservative and sorptive tracer experiments were conducted in a highly heterogeneous (σ_(lnK)~2 = 1.79) and anisotropic (λ_H/λ_V = 3.52) three-dimensional test aquifer under well-controlled laboratory conditions to evaluate the effective conductivity and temporal moments predicted by stochastic theories. The spatial distribution of lnK in the test aquifer conformed to a statistically homogeneous system, thus allowing evaluation of results from stochastic theories for stationary random fields. Effective hydraulic conductivity K_(eff) in the mean flow direction for the test aquifer was compared with different stochastic theoretical expressions. Breakthrough curves (BTCs) at individual deep-penetrating observation wells and averaged breakthrough curves at control planes were examined. The mean arrival time and the travel time variance estimated using averaged BTCs from many observation wells at the same control plane for bromide and lithium were slightly overestimated by stochastic theories, yet most of the experimental data ranged within the confidence interval rendered by the uncertainty in the statistical properties of the test aquifer. A highlight of our experimental approach is that the continuous sampling procedure also permitted the evaluation of higher-order temporal moments that were analyzed to study the asymmetry and peakedness of BTCs by means of the coefficients of skewness and kurtosis, respectively. Small-perturbation analytical solutions for the coefficient of skewness and kurtosis were provided. It is seen that although stochastic theories based upon small perturbations provide reasonably good estimates of the coefficients of skewness and kurtosis associated with averaged BTCs at control planes, in general, they can largely underestimate the peakedness and tailing of BTCs observed at individual deep-penetrating observation wells.