Theoretical Estimation of Disinfectant Mass Balance Components in Drinking Water Distribution Systems

The water quality audit concept is an important feature in assessing the loss of disinfectant mass in drinking water distribution systems. Based on this concept, the loss can be divided into the loss of disinfectant mass through water losses ($M_l$) and the decay of disinfectant mass due to chemical reactions ($M_r$). When an audit focuses on the effect of water losses on the loss of disinfectant mass, the decay of disinfectant mass by chemical reactions with the ideal condition of no water losses ($M_{ro}$) has to be estimated; thus, the disinfectant mass associated with water losses ($M_{WL}=M_l+M_r-M_{ro}$) can be assessed. Generally, the computation of these components ($M_l$, $M_r,$ and $M_{WL}$) needs hydraulic and water quality modeling. In this study, we propose a novel method based on a simple theoretical analysis to evaluate these components using only two parameters: the ratio of water losses ($p$) and the ratio of disinfectant concentrations at the critical pressure point and the network inlet ($C_p^{*}$). The coefficients of our theoretical $M_l$, $M_r$, and $M_{WL}$ were estimated using 20 real network models, with $p$ between 2.8% and 54.9% and $C_p^{*}$ between 18.4% and 91.9%. The results showed that our equations were effective at assessing the loss of disinfectant mass in drinking water distribution networks for the top-down auditing approach.