Path-dependent approach to estimate chlorine wall demand coefficient in water distribution system

A novel approach to calibrate pipe wall demand coefficients for chlorine decay using an input-output model framework is proposed. The input-output model of water quality in water distribution system developed in this research is presented as a particle (water parcel) backtracking algorithm, which provides information that is not available using traditional simulation approaches: the various paths that water takes between a particular input source and output node, and their associated time delays and impact on output node water quality. Such information constitutes a complete description of the input-output behavior under typical assumption of first-order chemical decay or production reactions. Therefore the chlorine concentration at "downstream" locations can be expressed explicitly as a function of concentration at "upstream" locations, and pipe wall demand coefficients. This not only expedites the computational efficiency of the parameter estimation algorithm, but frees the field study to consider chlorine concentration sampling at any location in a network. Chlorine measurement and hydraulic model errors will cause uncertainty in wall demand coefficient estimates and this should be taken into consideration in sampling design. In this research, sensitivity-based method is developed to select chlorine measurement locations for the purpose of getting reliable estimates of wall demand coefficients. The impact of hydraulic error on wall demand coefficient estimation of different designs is compared using a heuristic representing the sensitivity of modeled chlorine concentration to hydraulic error. Chlorine measurement errors are also considered and a D-optimal design algorithm is applied to select chlorine measurement locations. This proposed approach is suboptimal, yet efficient and practical, and considers both hydraulic and chlorine measurement errors. A field study is conducted in a southern U.S. utility as an application of the parameter estimation approach. A tracer study is implemented and the conductivity measurements are used to calibrate an existing hydraulic model through a manual approach. Chlorine concentrations are monitored continuously both at water source and within the distribution system. The wall demand coefficient is calibrated, assuming all pipes have the same demand coefficient.