The mixed-order chlorine decay model with an analytical solution and corresponding trihalomethane generation model in drinking water

Ensuring effective drinking water disinfection, remaining a certain amount of residual chlorine, and controlling disinfection by-product formation were very important for guarantying water quality safety and protecting public health; thus, the chlorine decay model and corresponding disinfection by-product formation model were necessary. This paper proposed a mixed-order chlorine bulk decay model (two parameters) based on Taylor's formula and derived its analytical solution. The accuracy of the mixed-order model was evaluated by comparing it with the nth-order model. To optimize the model and reduce the number of parameters required to be calibrated, the relationship of parameters with temperature, initial chlorine concentration, TOC and inorganic substance (ammonia nitrogen and iodide ion) was explored. The result proved that one of the parameters could be regarded as temperature dependent only. Meanwhile, the temperature equation of the model parameters was established by the Arrhenius formula. Subsequently, this paper selected trihalomethane as the target and study the linear relationship between chlorine consumption and trihalomethane formation. The results indicated that the liner slope had little correlation with initial chlorine concentration and temperature. On this basis, the corresponding trihalomethane model was built and its performance was proven to be good. The modeling developed in this work could be applied to drinking water distribution systems for residual chlorine and trihalomethane prediction, and provided a reference for the decision involving water quality.