Aquifer remediation design under uncertainty using a new chance constrained programming technique

Abstract

A new technique, called the mixed-integer-chance-constrained programming (MICCP) method is developed in this research. This technique considers uncertainty in all linear programming constraint coefficients and does not require a priori knowledge of the distribution. A groundwater remediation problem serves as an example. The method is developed to find the globally optimal trade-off curve for maximum reliability versus a minimum pumping objective. As the fields became more heterogeneous, the pumping rate of a reliable solution increases. Four simple "rule of thumb" methods are compared to the MICCP technique. In general, the performance of such methods decreases as the heterogeneity of the hydraulic conductivity field increases. by constructing engineered impervious barriers, (2) physical removal of the contaminated water and soil, (3) in situ treatment of contaminants in the aquifer, or (4) removal of the polluted water by hydraulic means.While the potential of the first three approaches is recognized, only the latter approach is considered in the research reported here. Such techniques consist of selectively pumped extraction and injection wells that flush the polluted water from the aquifer and bring it to the surface for treatment to a quality acceptable for surface discharge or reinjection.Designing such a flushing and extraction system, which consists of determining the least cost well locations and extraction or withdrawal rates, is especially challenging due to the great deal of hydrogeological uncertainty. Certain basic information about the aquifer must be known, for example, aquifer thickness, hydraulic conductivity, storativity, permeability of overlying and underlying strata, the hydraulic head, effects of evapotranspiration and infiltration, and porosity. Quite often, however, these parameters are not adequately known throughout the region of interest to predict the aquifer respon.se to pumping with a degree of accuracy sufficient for the design of the remediation system. Because of the heterogeneous and uncertain nature of most aquifers, the errors involved in predictions of solute transport can be considerable.The degree to which the hydraulic gradient is changed by injection or withdrawal of water into the aquifer is dependent upon the hydraulic conductivity of the aquifer. The hydraulic conductivity (K) of the aquifer can vary spatially by orders of magnitude. This spatial variability implies that K at any point is uncertain and ideally this uncertainty should be incorporated into the optimal design. The main goal of this paper is the development of a new chance constrained programming technique to perform that optimal design. This technique is used to develop a tradeoff curve between cost and reliability in the containment of a contaminant in a groundwater aquifer. The effect of different degrees of heterogeneity of the parameters in the aquifer will be studied. PREVIOUS WORK In a series of early papers, Charnes et al. [1958] and Charnes and Cooper [1963] studied chance constrained programming....

Reliable groundwater management in hydroecologically sensitive areas

“…Morgan et al [1993] presented a mixed-integer chance-constrained programming (MICCP) method to find the optimal trade-off curve for maximum reliability versus a minimum pumping objective in a groundwater remediation problem in the presence of aquifer heterogeneity. In their formulation of the hydraulic gradient constraints an integer indicator flagged constraint sets in which violations occurred.…”

“…Realizations can be generated that are conditioned on local conductivity values, such as those at the pumping centers. Optimal groundwater planning that accounts for uncertainty in hydraulic conductivity is based on a stochastic simulation-optimization method known as the multiplerealization or stacking approach [Gorelick, 1987;Wagner and Gorelick, 1989;Morgan et al, 1993;Chan, 1993]. In the approach a large number of realizations are included in the optimization formulation, and a large simulation-optimization involving simultaneous simulations based on each conductivity realization is solved.…”

“…We evaluate the sensitivity of optimal groundwater allocation to the level of reliability of meeting the water level constraints, to the innate variability in the spatial statistics of hydraulic conductivity, to the number of conditioning data, and to boundary conditions employed in the aquifer model. Our analysis begins with a stochastic simulation-optimization formulation known as the multiplerealization approach [Gorelick, 1987;Wagner and Gorelick, 1989;Morgan et al, 1993;Chan, 1993]. This is a simulation-optimization technique in which numerous realizations of uncertain model parameters are considered simultaneously in a single optimization formulation that simulates a collection of statistical aquifers, constraining the water levels in each aquifer model.…”

A hydro-economic modeling framework for optimal management of groundwater nitrate pollution from agriculture

“…A third approach was presented by Morgan et al (1993), which combined the advantages of the simulation-optimization models with those of the chance-constrained models. Again, the designer can select the degree of reliability, which is accomplished by allowing a certain number of the Monte Carlo realizations to fail.…”

“…predefined reliability Morgan et al (1993) introduced a mixed-integer approach to solve an optimization model to find an optimal remediation design with certain reliability. The approach combines the advantages of the simulation-optimization models with those of the chance-constrained models.…”