Abstract—In this paper, the velocity potential and stream function of capture zone for a well field in an aquifer bounded by two parallel streams with or without a uniform regional flow of any directions are presented. The well field includes any number of extraction or injection wells or a combination of both types with any pumping rates. To delineate the capture envelope, the potential and streamlines equations are derived by conformal mapping method. This method can help us to release constrains of other methods. The equations can be applied as useful tools to design in-situ groundwater remediation systems, to evaluate the surface–subsurface water interaction and to manage the water resources. Keywords—Complex potential, conformal mapping, groundwater remediation, image well theory, Laplace’s equation, superposition principle. I. INTRODUCTION HE capture zone of an aquifer is the region from which water is withdrawn by one or more pumping wells under steady state conditions [1]. After pumping is initiated, the capture zone grows and reaches its maximum size at steady state. The capture zone (also termed the capture envelope [2]) is a key factor in aquifer management, and provides basic understanding for different applications such as groundwater remediation projects (e.g., pump-and-treat, plume containment, bioremediation and chemical oxidation), surface- subsurface water interactions, well head protection, water rights, and transboundary aquifer management. For over- exploited aquifers (where extraction exceeds recharge), delineation of capture zones underpins optimal pumping plans to recover and sustain the depleted storage. Capture zone determination for confined aquifers is long established in groundwater engineering [3]-[8]. For instance, a 2D pump-and-treat system was presented in [5], including type curves to determine the number and pumping rate of wells to contain a contamination plume. Capture zones in 3D [9] accounted for both horizontal drains and vertical wells in homogeneous, anisotropic aquifers. In [10], analytical and S. Nagheli is with Department of Earth Sciences, Shiraz University, Shiraz 71454, Iran and Laboratoire de technologie écologique (ECOL), Institut des sciences et technologies de l’environnement (IIE), Faculté de l’environnement naturel, architectural et construit (ENAC), Ecole polytechnique fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland (e-mail: setareh.nagheli@epfl.ch). N. Samani is with Department of Earth Sciences, Shiraz University, Shiraz 71454, Iran (e-mail: samanin@shirazu.ac.ir). D. A. Barry is with Laboratoire de technologie écologique (ECOL), Institut des sciences et technologies de l’environnement (IIE), Faculté de l’environnement naturel, architectural et construit (ENAC), Ecole polytechnique fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland (e- mail: Andrew.barry@epfl.ch). semi-analytical expressions for multiple wells and extraction rates and locations based on complex potential theory and superposition were presented. This was extended in [11] to the computation of stagnation point locations in a multi-well system. Despite the utility of these results, the abovementioned studies focused on simple aquifer geometries and did not account for different boundary configurations or unconfined flow. Efforts to extend analytical results include the case of a multi-well system in rectangular [2] and wedge- shaped confined and unconfined aquifers [12]. Capture zones for multi-well systems in peninsula-shaped aquifers are also available [13], also for confined and unconfined aquifers. The approach most commonly used to obtain analytical results is the image well method in conjunction with the governing Laplace equation. For complex boundary conditions, the number of imaginary wells is numerous, and the method can become unwieldy. In this situation, however, conformal mapping can be used, since the number of imaginary wells is then limited. Conformal mapping was used in [14] to obtain analytical results for flow to a well between two parallel rivers or rivers that are at a fixed angle. Our purpose here is to derive a general solution for the capture zone of a multi-well system in a layered aquifer with or without uniform regional flow. The well system includes any number of arbitrarily located extraction or injection wells. Conformal mapping and the Schwarz-Christoffel transformation are applied to determine the complex potential, complex velocity and streamline equations for determining the capture envelope. Based on the results, the effects of number, position and type of wells and regional flow rate on the capture envelope are investigated. II. CONCEPTUAL MODEL Fig. 1 (a) shows a plan view of the conceptual model of a confined aquifer with a fully penetrating well bounded by two long parallel boundaries that are a distance d apart. The aquifer is isotropic and homogeneous with uniform thickness. Steady, 2D flow is considered. In Fig. 1, the boundaries are fully penetrating streams with zero longitudinal gradient and ߶ ଴ potential head, and that have no hydraulic resistance with the aquifer. An extraction or injection well is located at ( ݔ ଴ , ݕ ଴ ). III. MATHEMATICAL FORMULATION We consider a single well first, followed by multiple wells. The Schwarz-Christoffel transformation is applied. This transforms the conceptual model from the ݖ-plane to the ߞ- plane. For this conceptual model, a well is located between Capture Zone of a Well Field in an Aquifer Bounded by Two Parallel Streams S. Nagheli, N. Samani, D. A. Barry T World Academy of Science, Engineering and Technology International Journal of Civil and Environmental Engineering Vol:12, No:1, 2018 67 International Scholarly and Scientific Research & Innovation 12(1) 2018 ISNI:0000000091950263 Open Science Index, Civil and Environmental Engineering Vol:12, No:1, 2018 publications.waset.org/10008848/pdf