Minimization of Transient Groundwater Pumping Cost - Analytical and Practical Solutions

In this paper, we study pumping cost minimization for any number and layout of wells under transient groundwater flow conditions in infinite confined aquifers and semi-infinite ones, to which the method of images applies. Moreover, we take into account additional steady-state flow, which is independent of the well system and results in non-horizontal initial hydraulic head level distribution. We prove analytically that, at any time, the instant pumping cost is minimum, when the following condition holds: the observed at that instant differences between hydraulic head values at the locations of the wells are equal to the half of the initial ones, which are due to the additional steady-state flow. Based on this proof, an analytical calculation procedure of the time-dependent optimal distribution of the required total flow rate to the individual wells is also presented. Moreover, as well flow rates usually remain constant over the pumping period, an approximate calculation of the optimal constant well flow rate distribution is outlined, based again on an analytical procedure.