Analysis of uncertainty in optimal groundwater contaminant capture design

Abstract

A three‐dimensional groundwater management model is developed for a shallow, unconfined sandy aquifer at a Superfund site at which a vinyl chloride plume is migrating toward Lake Michigan. We use nonlinear simulation‐regression applied to a transient groundwater flow model to estimate parameter values and their uncertainties and use steady state flow path analyses to confirm the model's consistency with the location of contaminants. Parameter uncertainty is translated into flow model prediction uncertainty using a first‐order Taylor series approximation. Optimal minimum‐pumping strategies for steady state hydraulic containment of the plume are designed, and model prediction uncertainty is accounted for with stochastic programming. It is impossible to achieve a reliability level higher than 60% using only two pumping wells. For the 10‐well case, pumping rates must increase about 40% to extend reliability from 50 to 90%. Monte Carlo analyses indicate that for the 10‐well 90% reliability formulation, the first‐order method of propagating uncertainty results in a solution with accurate performance reliabilities. We find that the coefficient of variation in hydraulic gradient dictates whether the probabilistic constraints are obeyed. Comparison of the probabilistic constraint and “safety factor” approaches to overcoming model uncertainty reveals that the ability of probabilistic constraints to accommodate local variations in model prediction uncertainty is highly important. Postoptimization solute transport studies show that increased reliability levels for hydraulic containment do not necessarily translate into faster plume cleanup times.

Recent advances in modeling of well hydraulics

“…Numerical simulations can take into account the effects of complex boundary conditions as well as heterogeneity, recharge/discharge, etc., and are therefore broadly used for studying vertical well capture zones [306,307]. Shafer [308] adopted a finitedifference groundwater flow model to simulate 2-D steady state head distribution and used a fourth-order Runge-Kutta scheme to determine the flow pathlines for a time-related capture zone around extraction wells.…”

Methods for Exploring Uncertainty in Groundwater Management Predictions

“…Instead, conservative estimates can be used that can inform decisions regarding margins of safety (e.g. in Bredehoeft 1983;Tiedeman and Gorelick 1993). In practice, the best one can hope for is to identify models that bracket the true value (Doherty 2011), from which safety factors can be derived from model results even if deliberately overand under-estimated (Guillaume et al 2012).…”

Review: Simulation-optimization models for the management and monitoring of coastal aquifers

“…Different stochastic optimization techniques have been used in the past for optimal decision making under uncertainty for other groundwater management applications (Wagner and Gorelick 1987;Tiedeman and Gorelick 1993;McPhee and Yeh 2006). The main goal of a stochastic simulationoptimization model is to identify reliable optimal solutions for groundwater management.…”