Multiple well systems with non-Darcy flow

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velocity increases, the nonlinear losses become important in the near-well region and the principle of superposition is no longer valid.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.