Optimization of booster chlorination for water distribution system under dual uncertainties

Chlorine is generally used as disinfectant to sustain water quality in water distribution system (WDS). To prevent the occurrence of disinfectant by-product as well as control the growth of microorganism, the residual chlorine concentration in WDS should be kept between acceptable intervals. However, the chlorine concentration was uncertain due to chlorine decay, imprecise measure, hydraulic and topological conditions. In addition, nodal response coefficients to unit disinfectant mass in the left-hand-side of the constraints were also uncertain, which is affected by uncertain pipe diameter, roughness coefficients, nodal demand, bulk decay coefficient, and wall decay coefficient, etc. Therefore, in this paper a fuzzy chance-constrained optimization model under dual uncertainties was proposed and applied to optimize the chlorine injection mass to maintain chlorine in WDS distributed uniformly with consideration of randomness of chlorine concentration limits as well as uncertainty in response coefficient. The total injection mass decreases with the uncertainty level under possibility of dominance and necessity of dominance indices, while increases with the uncertainty level under possibility of strict dominance and necessity of strict dominance indices, which is effective in chlorine injection management.