Mathematical Model for Urban Water Supply and Waste Disposal Systems

Most urban areas are facing an ever increasing demand for fresh water due to population and industrial growth. This paper proposes an integrated approach for optimal design of urban water supply and waste disposal systems. A network model is presented for evaluating alternatives for supplying water from different sources – treated fresh water, ground-water, desalinated seawater and renovated water – to satisfy future demands for domestic, industrial and public use at minimum cost. This model carries out optimization on the basis of estimated cost functions for various processes including water development, conveyance and treatment. Design of optimal water transmission network is a complex problem due to pressure and flow constraints at various nodes of the network and merits consideration on its own. This involves the network and merits consideration on its own. This involves choice of pipe diameters and lengths in a given water transmission network to minimise discounted total cost of installation and operation of the system. A Linear Programme model is presented for the solution of this problem for branched networks. Before deciding on a waste disposal plan, the effect on the quality of the receiving waters of wastewater discharges after treatment, in any, must be analysed. A water quality model for predicting pollutant concentrations from hydrological and waste discharge data is presented for this purpose. An iterative solution approach using the network model for land based processes and facilities and the water quality model is suggested for designing an optimal water supply/waste disposal system which will meet all water demands while maintaining the receiving waters at acceptable quality levels. The detailed design of the water transmission network is obtained by the application of the Linear Programming model using optimal solution from the Network Model as input giving quantities available at various sources and the layout of the network supplying demand quantities at the distribution zones. Thus design of an optimal system for water supply and wastewater disposal involves interactions between the three given models.