Abstract
In this paper we present the equation of capture zone of a multi-well system in wedge-shaped confined and unconfined aquifers. Three wedge boundary configurations: barrier–barrier wedge, barrier–constant head wedge and constant head–constant head wedge are considered. The well system may be consisted of any number of production or injection wells or a combination of both with various flow rates. Method of image wells is used in the wedge-shaped domain and an appropriate complex function is formulated to find the capture zone. The stream function and velocity potential are derived from the imaginary part and real part of the complex function, respectively. Solutions are provided for the wedge domains with and without a uniform regional flow and can also be used for aquifers of infinite extent. The presented equations are of general character and have removed the limitations of the previous equations in regards to well numbers, positions and types, extraction/injection rate, and regional flow rate and direction. Capture envelopes are presented in dimensionless form which can be used as tools in real engineering practices to plan pump-and-treat operations, groundwater remediation projects or well-head protection plans. It is also demonstrated that the equations may also be used for the verification of numerical models. The developed equations are constrained by the image well theory limitations.
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