Uncertainty Analysis in a Mechanistic Model of Bacterial Regrowth in Distribution Systems

The first generation of mechanistic models of bacterial regrowth in distribution systems (DS) provides insight into cause-and-effect relationships. However, the state of knowledge about the processes included in these models is insufficient to warrant deterministic predictions. Even if the process descriptions are reasonable, the uncertainty in values of key system constants limits predictions of bacterial growth. A new mechanistic model was developed to incorporate the accepted knowledge of physical, chemical, and biological processes with the hydraulic features in order to capture the unsteady state behavior of the DS. Sensitivity testing showed that the extent of bacterial regrowth was affected mainly by the rate constants for chlorine decay reactions in bulk water and on the pipe wall and by the maximum growth rate constant of attached bacteria. A simple hypothetical network was used to evaluate the effects of uncertainty in these three system constants by running 100 Monte Carlo simulations. Cumulative probability plots showed a wide range of predictions for concentrations of bacteria and chlorine in bulk water at various nodes in the DS. The magnitude of these concentrations and the range of values were greatly affected by water residence time to each node. Once the chlorine residual is depleted, bacterial growth is mainly influenced by the amount of substrate available. However, high values of the coefficients for the maximum growth rate of attached bacteria, the chlorine decay in bulk water, and the chlorine decay by wall reaction did not necessarily lead to the maximum bacterial growth at a given location.