Optimizing pumping rate in pipe networks supplied by groundwater sources

Abstract

In the present paper, an analytical solution has been reached for determining the optimum pumping rate in a pipe network supplied from a ground water source by means of water wells. The solution depends on the use of the gradient technique which requires the derivatives of the studied cost functions and is based on the maximum economic benefit from the produced water. The solution is examined on a predetermined optimal water distribution system, and gives values for optimum pumping rates which are in good agreement with those obtained using the graphical solutions, indicating the reliability of the analytical solution. The effect of the initial cost on the optimum pumping rate and its bearing on the unit price of water has been also studied. This reflects the importance of choosing the proper unit water price that makes the water return covers the global cost and satisfies the maximum economic benefit from the produced water. Studying the effect of unit price of water on the water return or different pumping rates shows that, whether ignoring or including the initial cost, the water return increases with increase of pumping rate till reaching a turning point, often which the water return begin to drop slightly. Hence, this point determines the optimum pumping rate in the pipe network as well as the maximum economic benefit satisfied. Finally within the scope of the present study, it is concluded that, the identity or good agreement found in the results of optimum pumping rates, indicates the validity of the developed analytical solution and the employed graphical solutions.