Calibration of Hazen–Williams coefficients in pipe networks using tracers

Abstract

A model that directly estimates HW coefficients for pipe networks by making tracer concentration measurements at selected nodes is developed utilizing the inverse method. The model considers even-, over- and under-determined cases, depending on the number of measurements and estimated parameters. For the purpose of model verification, tracer concentrations obtained by forward simulation are considered as measurements. Results showed that the model made accurate determinations of the unknown HW coefficients for both even- and over-determined cases for some scenarios and less accurate determinations for other scenarios. The under-determined case made reasonable estimates of the unknown HW coefficient for most of the scenarios considered. Error analysis showed that errors are introduced into the determined HW coefficient as a result of measurement errors and as a result of making the measurements at low sensitive nodes. Error analysis also showed that the determined HW coefficient is more sensitive to the measurement location (sensitivity) than to the measurement error. Both conservative and non-conservative tracers may be used. However, conservative tracers are expected to make better estimation of HW coefficients as they produce larger sensitivities.