Reliable aquifer remediation in the presence of spatially variable hydraulic conductivity: From data to design

Abstract

Most optimization models for groundwater quality management have ignored the effects of uncertainty due to spatial variability of hydraulic conductivity. Here we explicitly incorporate this uncertainty into a procedure for the optimal design of aquifer remediation strategies. Local hydraulic conductivity and head data are used to quantify the uncertainty which is traced through to target a reliable remediation design. The management procedure is based on the stochastic approach to groundwater flow and contaminant transport modeling, in which the log‐hydraulic conductivity is represented as a random field. The remediation design procedure has two steps. The first is solution of the stochastic inverse model. Maximum likelihood and Gaussian conditional mean estimation are used to characterize the random conductivity field based on the hydraulic conductivity and hydraulic head measurements. Based on this statistical characterization, conditional simulation is used to generate numerous realizations (maps) of spatially variable hydraulic conductivity that honor the head and conductivity data. The second step is solution of the groundwater quality management model. Two management model formulations are presented. The first, termed the multiple realization management model, simultaneously solves the nonlinear simulation‐optimization problem for a sampling of hydraulic conductivity realizations. It is shown that reclamation design based on as few as 30 conductivity realizations can provide reliable (over 90%) remediation strategies. The second model, termed the Monte Carlo management model, solves the nonlinear simulation‐optimization problem individually for a sampling of hydraulic conductivity realizations. This provides a relationship between pumping (cost) and reliability. Each of the management models is linked with the stochastic inverse model, and each is demonstrated for two cases: (1) the available data are limited to hydraulic conductivity measurements and (2) both hydraulic conductivity and hydraulic head measurements are used.