Chance-Constrained Optimal Monitoring Network Design for Pollutants in Ground Water

Abstract

A mathematical model for designing a ground-water-quality monitoring network is developed that links a ground-water pollution-transport simulation model and an optimization model. Tritium is considered as the (radioactive) pollutant. The model is formulated using chance constraints and solved by using a mixed-integer programming algorithm. It incorporates uncertainties in the prediction of pollutant movement in the saturated zone. Nonlinearities due to the inclusion of cumulative distribution functions (CDFs) of actual spatial concentrations are accommodated in the optimization model through a piecewise linearization scheme. The design of the optimal monitoring network is based on the solution of two mathematical models: a simulation model for the prediction of radioactive pollutant transport in the saturated zone, and an optimization model. Constraints of the optimization model are formulated by incorporating results from the prediction-simulation model. The simulation model provides information about pollution transport with respect to time and space. The chance-constrained optimization model solution specifies the optimal location of the monitoring wells subject to the maximum limit on the number of such wells. Performance evaluation of the developed model demonstrates potential applicability of this model for designing ground-water-quality monitoring networks.