Stochastic study of solute flux in nonstationary flow field conditioning on measured data

Abstract

It has been well recognized that natural media are generally heterogeneous, and groundwater flow and solute transport through the media is significantly influenced by the heterogeneity. The stochastic perturbation approach is the most commonly used method to study groundwater flow and solute transport in heterogeneous media, and many theories have been developed. The unconditional stochastic studies on groundwater flow and solute flux in a nonstationary conductivity field show that the standard deviations of the hydraulic head and solute flux are very large in comparison with their mean values. In this study, we develop a numerical method of moments conditioning on measured data to reduce the variances of the head and the solute flux. For the numerical method of moments, a Lagrangian perturbation method is applied to develop the framework for solute flux in a nonstationary flow field. The solute flux is described as a space-time process, where time refers to the solute flux breakthrough through a control plane (CP) at some distance downstream of the solute source and space refers to the transverse displacement distribution at the CP. Instead of using an unconditional conductivity field as an input to calculate groundwater velocity, we combine a geostatistical method and a method of moment for flow to conditionally simulate the distributions of head and velocity based on the measurements of hydraulic conductivity and head at some points. The developed theory has been applied in several case studies to investigate the influences of the measurements of hydraulic conductivity and/or the hydraulic head on the variances of the predictive head and the solute flux in nonstationary flow fields. The study results show that the conditional calculation will significantly reduce the head variance. Due to the hydraulic head, measurement points are treated as the interior boundary (Dirichlet boundary) conditions in our method, conditioning on both the hydraulic conductivity and the head measurements is much better than conditioning only on conductivity measurements for reduction of head variance. However, for solute flux, variance reduction by the conditional study is not so significant.