Optimum allocation of monitoring wells around a solid-waste landfill site using precursor indicators and fuzzy utility functions

Abstract

An optimum monitoring well network (number of wells and their locations) is proposed which enables rapid, redundant and economical detection of contaminants in groundwater around a solid-waste landfill site. The procedure also guarantees detection of the contaminants given data on the probability of detection at different points in the saturated zone. The well selection is accomplished using a two-step procedure: 1. (1) A Monte Carlo simulation of contaminant transport in the unconsolidated shallow saturated zone is conducted. In this zone hydrogeological parameters are variable but their stochastic distributions are known. Three governing equations are solved numerically using the finite-difference method to obtain the travel time distribution of each contaminant: the two-dimensional steady-state groundwater flow equation; the two-dimensional transient convective-dispersion equation for sorptive contaminants; and the sorptive-desorptive isotherm equation. 2. (2) The procedure utilizes “fuzzy” theory, comprising of a set of newly developed mathematical techniques to deal with uncertainty in a wide range of man-machine interface issues, to assist in the design of a monitoring well network. The procedure requires a mathematical description of a four-attribute design problem using fuzzy utility functions and fuzzy weights. An optimum monitoring well network is then defined as the network having maximum total utility, which is evaluated as a fuzzy expectation of weighted arithmetic sums of the four utilities. One result of the simulation is the definition of relationships between the contaminant of interest and precursor materials. The precursor material can then serve as an “indicator” for faster detection of contaminant leaked from solid-waste landfill site. The procedures are applied to a hypothetical solid-waste landfill site under appropriate conditions to obtain the optimum monitoring well network for detection of precursor indicators. Sensitivity analysis of the optimum network was conducted by considering changes in components of the mathematical description of the design problem. Components which were changed include total utility evaluation, quality of uncertainty in weight factor and utility evaluation, weigth level determination, delay time requirement, well number limitation and perfect detection constraint.