In this paper, we have investigated minimization of total cost to pump a given flow rate from any number (n) of wells up to a water tank, under steady-state flow conditions. Regarding groundwater flow, we have considered infinite or semi-infinite aquifers, to which the method of images applies. Additional regional groundwater flow can be taken into account, too. The pipe network connecting the wells to the tank can include junctions at the locations of the wells only. Moreover, all pumps have equal efficiency. We have derived a new analytical formula, which holds at the critical points of the total cost function. Based on this formula, we derived a system of n equations and n unknowns, to calculate the well flow rate combinations which correspond to the critical points of the total cost function. The n-1 equations are 2nd degree polynomials, while the remaining one is linear, expressing the constraint that the sum of well flow rates must be equal the required total flow rate. The solution of the system can be achieved using commercial solvers. Moreover, we have concluded that there is one feasible solution that minimizes the total cost. Finally, we present a tabulation process to facilitate the use of solvers and we provide and discuss two illustrative examples.

在本文中，我们研究了在稳态流量条件下，将给定流量从任意数量（n）的水井泵送到水箱的总成本的最小化。关于地下水流量，我们考虑了采用图像方法的无限或半无限含水层。也可以考虑额外的区域地下水流量。将井连接到储罐的管网可以仅在井的位置包括接头。此外，所有泵的效率均相等。我们得出了一个新的分析公式，该公式适用于总成本函数的关键点。基于此公式，我们推导了一个由n个方程和n个未知数组成的系统，以计算与总成本函数的临界点相对应的井流量组合。n-1个方程是二阶多项式，而其余的是线性的，表示井流量之和必须等于所需的总流量的约束。可以使用商用求解器来实现系统的解决方案。此外，我们得出的结论是，有一种可行的解决方案可将总成本降至最低。最后，我们提出了一个制表过程，以方便求解器的使用，并提供并讨论了两个说明性示例。