Uncertainty Analysis and Calibration of Water Distribution Quality Models

Abstract

Water distribution system modeling can be used as a basis of planning and operation decisions. However, model accuracy and uncertainty will impact the model based decisions. Model prediction uncertainty results from uncertainty in model parameters that are determined through calibration or are based upon modeler judgment. The focus of this dissertation is the effect of uncertainties on water quality model estimates and calibration. The dissertation is centered around three journal articles and a technical note.In the first paper, the effect of parameter uncertainty on water quality in a distribution system under steady and unsteady conditions was analyzed by Monte Carlo simulation (MCS). Sources of uncertainties for water quality include decay coefficients, pipe diameter and roughness, and nodal spatial and temporal demands. The effect of individual parameter is discussed, as well as the combined effect of the parameters. It also describes the effect of flow patterns.A general calibration model is developed in the second paper for identifying wall decay coefficients. The problem is solved using the SFLA optimization algorithm that is coupled with hydraulic and water quality simulation models using the EPANET toolkit. The methodology is applied on two application networks. The study presents the effect of different field conditions such as the network with or without tanks, altering disinfectant injection policies, changing measurement locations, and varying the number of global wall decay coefficient on the estimated parameters. The numerical study also discusses whether the complexity of the system can be captured with fewer than the actual number of field parameters and if the number of the measurement locations is sufficient.The third paper conducts a study that considers a full calibration assessment for a water quality model in the distribution systems. The calibration process begins with estimating the the best fit wall decay coefficients. Next, the uncertainties involved with estimated parameters are calculated. Finally, the study assesses the model prediction uncertainties for critical demand conditions due to the parameter uncertainties. Various conditions are evaluated including the effects of different measurement errors and different measurement conditions on the uncertainty levels of estimated parameters as well as on the model predictions.Fourth paper presents study in which a booster disinfectant is introduced within a distribution system to maintain disinfectant residuals and avoid high dosages at water sources. Assuming that first order reaction kinetics apply to chlorine decay, an integer linear programming optimization problem is posed to booster locations and their injection rates. The formulation avoids long water quality simulations by adding constraints requiring the concentrations at the beginning and end of the design period to be the same. The optimization problem is divided into two levels. The upper level selects the booster locations using a genetic algorithm, if more than a few boosters are included, or enumeration, if the number of boosters and/or potential locations is relatively small. Given a set of boosters from the upper level, the lower level minimizes the chlorine mass to be injected to maintain required residuals. The approach is applied to the Brushy Plains system for alternative numbers of allowable boosters.