| Summary: | 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 (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>M</mi><mi>l</mi></msub></mrow></semantics></math></inline-formula>) and the decay of disinfectant mass due to chemical reactions (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>M</mi><mi>r</mi></msub></mrow></semantics></math></inline-formula>). 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 (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>M</mi><mrow><mi>r</mi><mi>o</mi></mrow></msub></mrow></semantics></math></inline-formula>) has to be estimated; thus, the disinfectant mass associated with water losses (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>M</mi><mrow><mi>W</mi><mi>L</mi></mrow></msub><mo>=</mo><msub><mi>M</mi><mi>l</mi></msub><mo>+</mo><msub><mi>M</mi><mi>r</mi></msub><mo>−</mo><msub><mi>M</mi><mrow><mi>r</mi><mi>o</mi></mrow></msub></mrow></semantics></math></inline-formula>) can be assessed. Generally, the computation of these components (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>M</mi><mi>l</mi></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>M</mi><mi>r</mi></msub><mo>,</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>M</mi><mrow><mi>W</mi><mi>L</mi></mrow></msub></mrow></semantics></math></inline-formula>) 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 (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>p</mi></semantics></math></inline-formula>) and the ratio of disinfectant concentrations at the critical pressure point and the network inlet (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>C</mi><mi>p</mi><mo>*</mo></msubsup></mrow></semantics></math></inline-formula>). The coefficients of our theoretical <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>M</mi><mi>l</mi></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>M</mi><mi>r</mi></msub></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>M</mi><mrow><mi>W</mi><mi>L</mi></mrow></msub></mrow></semantics></math></inline-formula> were estimated using 20 real network models, with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>p</mi></semantics></math></inline-formula> between 2.8% and 54.9% and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>C</mi><mi>p</mi><mo>*</mo></msubsup></mrow></semantics></math></inline-formula> 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.
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