Groundwater flow simulations and management under imprecise parameters

Abstract

This dissertation considers modeling groundwater flow under imprecisely known parameters and managing a plume of contaminant. A new approach has been developed to study the effects of parameters uncertainty on the dependent variable, here the head. The proposed approach is developed based on fuzzy set theory combined with interval analysis. The kind of uncertainty modeled here is the imprecision associated with model parameters as a result of machine or human imprecision or lack of information. In this technique each parameter is described by a membership function. The fuzzy inputs into the model are in the form of intervals so are the outputs. The resulting head interval represents the change in the output due to interval inputs of model parameters. The proposed technique is illustrated using a two dimensional flow problem solved with a finite element technique. Three different cases are studied: homogeneous, mildly heterogeneous and highly heterogeneous transmissivity field. The groundwater flow problem analysis requires interval input values for the parameters, the output may be presented in terms of mean value, upper and lower bounds of the hydraulic head. The width of the resulting head interval can be used as a measure of uncertainty due to imprecise inputs. The degree of uncertainty associated with the predicted hydraulic head is found to increase as the width of the input parameters interval increases. Compared to Monte Carlo simulation approach, the proposed technique requires less computer storage and CPU time, however at this stage autocorrelation and crosscorolation are not configured in the presented formulation. In the plume containment problem two formulations are presented using the hydraulic gradient technique to control the movement of the contaminants. The first one is based on multiobjective analysis and the second, on fuzzy set theory. Multiobjective analysis yields a set of alternative strategies each of which satisfies the multiple objectives to a certain degree. Three different techniques have been used to choose a compromise strategy. Although they follow different principles, the same preferred strategies are selected. It is also noticed that rapid restoration results in a large pumping volumes and high costs. Using a fuzzy formulation for plume containment yields the optimum pumping rates and locations in addition to the membership function at each pumping location. The resulting membership functions at these pumping locations can be used to study the sensitivity of each location to a change in objective function and constraints bounds. Overall, both the fuzzy and multiobjective methodologies, presented in this dissertation, provide new and encouraging approaches to groundwater quality management.