Department of Earth Science and Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK.
Ground Water. 2013 Jul-Aug;51(4):588-96. doi: 10.1111/j.1745-6584.2012.00992.x. Epub 2012 Oct 5.
Optimization of groundwater and other subsurface resources requires analysis of multiple-well systems. The usual modeling approach is to apply a linear flow equation (e.g., Darcy's law in confined aquifers). In such conditions, the composite response of a system of wells can be determined by summating responses of the individual wells (the principle of superposition). However, if the flow velocity increases, the nonlinear losses become important in the near-well region and the principle of superposition is no longer valid. This article presents an alternative method for applying analytical solutions of non-Darcy flow for a single- to multiple-well systems. The method focuses on the response of the central injection well located in an array of equally spaced wells, as it is the well that exhibits the highest pressure change within the system. This critical well can be represented as a single well situated in the center of a closed square domain, the width of which is equal to the well spacing. It is hypothesized that a single well situated in a circular region of the equivalent plan area adequately represents such a system. A test case is presented and compared with a finite-difference solution for the original problem, assuming that the flow is governed by the nonlinear Forchheimer equation.
优化地下水和其他地下资源需要分析多井系统。常用的建模方法是应用线性流动方程（例如，承压含水层中的达西定律）。在这种条件下，可以通过加总各个井的响应来确定井系统的综合响应（叠加原理）。然而，如果流速增加，近井区域的非线性损耗变得重要，叠加原理不再有效。本文提出了一种将非达西流动的解析解应用于单井到多井系统的替代方法。该方法侧重于位于等间距井阵列中的中央注入井的响应，因为它是系统内压力变化最大的井。该关键井可以表示为位于封闭正方形域中心的单个井，该正方形域的宽度等于井间距。假设位于等效平面区域圆形区域中的单个井可以充分代表这样的系统。本文提出了一个测试案例，并与原始问题的有限差分解进行了比较，假设流动受非线性 Forchheimer 方程控制。
