A Mathematical Model for Variable Chlorine Decay Rates in Water Distribution Systems

Abstract

A model for relating the time-dependent variable rate of reaction to the decay of chlorine residual in water is developed based on the initial chlorine dose, molar concentrations of reactants, and the rate constant itself. The mathematical model, while retaining its second order nature, simplifies the solution as the residual chlorine and aggregate parameters such as molar concentration of reactants can be estimated. The model is based on molar-averaged reaction rates involving arithmetic and harmonic means of reactants that eliminate the individual reaction rates that are difficult to determine. Part of the mathematical assumption used in the derivation of the equations using molar averaging is tested for its validity through theoretical as well as Monte Carlo simulation of the error term over wide ranges of assumed reaction rates and molar concentration of reactants. The second-order variation of the rate of reaction with respect to the initial chlorine concentration has been verified through experimental tests of bulk chlorine decay carried out at different chlorine doses.

Influence of physical and water quality parameters on residual chlorine decay in water distribution network

“…Physical water parameters are pipe length [ 2 , 7 ], pipe diameter [ [7] , [8] , [9] ], pipe roughness [ 2 , 9 ], pipe age [ 2 , 9 ] and pipe material [ 10 ]. Water quality parameters include initial chlorine concentration [ 2 , 7 , 9 , [11] , [12] , [13] , [14] , [15] , [16] ], pH [ 4 , 7 , 12 , 15 , [17] , [18] , [19] , [20] , [21] , [22] ] and turbidity [ 2 , 4 , 7 , [11] , [12] , [13] , [14] , [15] , [16] , [18] , [19] , [20] , [21] , [22] ]. However, turbidity which is commonly used by water utilities as an indicator proxy surrogate for initial chlorine dosage for suspended and colloidal organic and inorganic impurities in water [ 16 , 21 ].…”

Quality Assessment of Sokoto Water Distribution Networks

“…The problem related to the maintenance of residual chlorine is increased by water supply interruptions that lead to the formation of stagnant water, which, during the resumption of supply, may be drawn with no chlorine residual left as the water reaches the consumers. Old water supply systems with pipes that have deteriorated linings encourage microbial growth in the distribution pipe, which in turn results in rapid loss of chlorine due to the wall decay reaction [4].…”

Chlorine Concentration Modelling and Supervision in Water Distribution Systems

“…The absence of robust models for predicting chlorine behavior in WDNs is fundamentally due to two aspects: (1) the complexity of modelling the hydraulics of the WDNs and (2) the need for on-line quality data. Although authors report good results in chlorine prediction in full-scale networks in some studies [ 6 ], the predictions become less accurate when the environmental conditions or the water composition change from those of the calibration. Such a situation is very common in WDNs fed with treated surface water.…”

“…Regarding the second aspect, it is mandatory to obtain information on water quality in the effluent of the drinking water treatment plant and the relevant points in the WDNs in order to predict the behavior of chlorine. Several studies [ 6 , 9 ] base their decay models on parameters that are easily measured on-line, such as temperature, pH, redox potential, conductivity, turbidity, and chlorine concentration. Nevertheless, the calibration and maintenance of these models for their on-line use is seldom performed.…”

“…Common models for chlorine modelling in WDNs are first-order linear differential equations [ 10 ] such as: where K b is a constant that contains the different parameters and physicochemical phenomena that may affect chlorine decay, such as natural organic matter, inorganic compounds, or temperature [ 6 ]. More sophisticated models have also been studied, including second-order models [ 11 ].…”