In-Stream water quality modelling and optimisation by mixed-integer programming : simulation and application in actual system

Abstract

Water scarcity has become a global problem due to diminishing water resource and pollution of the remaining resources. The problems arising fromwater scarcity are exacerbated rapid urbanisation and industrialisation. Water quality management systems are introduced. Numerous water management methods exist some of which, if applied e ectively, can remedy these problems. In South Africa, water management systems are urgently needed to start addressing issues around the longterm sustainability of our limited water resource. Water quality modelling is one of the tools employed to assist in validating decisions made during the planning phase of a water quality management system. It also provides a means of exploring viable options to be considered when these decisions are to be made. A range of management options exist and implementing all of them may prove costly, therefore optimisation techniques are utilised to narrow down options to the most e ective and least costly among the available choices. Commonly, water quality models are used to predict concentrations in the river from which constraint equations are generated. The constraint equations are used in optimisation models to generate feasible solutions by either maximising or minimising the objective function. In this case the objective function is wastewater treatment cost. Constraints equations are based on the set in-stream water quality standard at selected theoretical measuring stations (checkpoints) in the stream and a feasible solution is one that suggests a treatment method that will ensure water quality standards are met at the lowest regional treatment cost. This study focused on the Upper Olifants river catchment near Witbank in Mpumalanga province. This catchment is subjected to extensive wastewater e uents from various mining operations and wastewater treatment plants. The aim here was to develop a water quality model for predicting dissolved oxygen (DO) concentration in the river, and to use a modelling approach to generate constraint equations for the system. A Streeter-Phelps stream simulation model was employed to predict DO concentration in the river. A mixed-integer programming technique was then used to evaluate the impact of nine wastewater treatment facilities discharging e uent into the river. Treatment levels were varied to test model reliability. The coupled stream simulation and optimisation model produced feasible solutions under 2 minutes, with each solution suggesting a range of treatment levels which ensured that the critical DO concentration was above 5 mg/L and the most stringent DO concentration the system could manage without violations anywhere else in the stream was obtained to be 7mg/L.