Pumping cost minimization in aquifers with regional flow and two zones of different transmissivities

In this paper we study minimization of pumping cost of a given total flow rate from any number and layout of wells. Building on previously published results, we have considered steady state flow in aquifers with two zones of different transmissivities, to which the method of images applies. Moreover, we have taken into account additional regional flow, which results in different hydraulic head values at the location of the wells, independent of their operation. We prove analytically that in this general case, pumping cost is minimized, when final differences between hydraulic head values at the locations of the wells, resulting from superposition of the regional flow and the operation of the system of the wells, are equal to the half of those, which are due to the regional flow only. Finally we present the analytical calculation procedure of the optimal distribution of the required total flow rate to the individual wells and we provide illustrative examples.