Chemical and Process Engineering Research www.iiste.org ISSN 2224-7467 (Paper) ISSN 2225-0913 (Online) Vol.45, 2016 1 Groundwater Flows in the Vicinity of Two Well Systems with Finite Element Method using FEniCs Software Dejene Gizaw Kidane Department of Mathematics, Hawassa University, Hawassa, Ethiopia Abstract Groundwater is available in usable quantities only in aquifers. An aquifer is a geological formation which contains water and permits significant amounts of water to move through it under ordinary field conditions. Aquifer can be categorized depending on the hydraulic conductivity as: isotropic vs. anisotropic, homogeneous vs. nonhomogeneous, etc. In this paper effort is made to see the flow of ground water in aquifer in the vicinity of two well systems, pumping and recharging wells, in some rectangular shaped domain in two dimensions where the pumping well is located at point   = (−  , 0) while the recharging well is located at point   = (  , 0),   > 0. No flow condition is assumed on the boundaries of the domain, while Dirichlet boundary condition is imposed on the boundary of the pumping well and inhomogeneous normal Neumann boundary condition is imposed on the boundary of the recharging well. Numerical experiment is made at both homogeneous and inhomogeneous isotropic aquifer cases. And in each of the aquifer cases, stationary and non-stationary cases are also considered. Finite Element Method is used for the purpose of analysis, where finite element mesh is generated using an external free 3D finite element mesh generator called Gmsh. Numerical experiment is performed using free software package called FEniCs. Based on the results of the numerical experiment all the cases exhibit the same phenomena. Meaning that, the draw-down in the water level is higher near the pumping well and decrease radially outward creating a feature called the cone of depression. This happens because of a pattern of radially converging flow to the well from the surrounding aquifer which causes the lowering of the water level (the piezometric surface) extending outward from the well. And the build-up in the water level is higher near the recharging well but decrease radially inward creating a feature called the cone of impression. This happens due to a pattern of radially diverging flow from the recharging well made to produce a buildup in the water level (or the piezometric surface). Keywords: Finite Element Methods, Groundwater, Well, FEniCs, Gmsh 1. Introduction to Groundwater Flow The term groundwater refers to water found beneath the surface of the ground. Groundwater occurs in two separated zones, the saturated zone and the unsaturated zone. The two zones are separated by surface known as water table. The saturated zone is the one which is below the water table while the unsaturated zone is found above the water table. In the saturated zone, water completely fills the void space of the considered porous medium. Groundwater is found everywhere. But it is available in usable quantities only in aquifers. An aquifer is a geological (or a group of) formation which contains water and permits significant amounts of water to move through it under ordinary field conditions. Aquifers can be classified as confined or unconfined depending on the absence or presence of a water table. Confined aquifers are bounded between two layers of impervious formation (lower permeability materials) while unconfined aquifer is one in which water table (or phreatic surface) serves as its upper boundary. It is impossible to determine the exact direction of groundwater flow based on surface features alone. However, we know that water in the aquifer near a pumping well will flow toward the well to result in a draw-down near the well. Pumping well is a well through which water is extracted from an aquifer. And the flow of ground water near the recharging well (a recharging well is a well through which water is added to an aquifer) is the reverse of pumping well. The groundwater flows away from the well resulting build-up near the well. In this paper the nature of the flow of ground water near the two well(pumping and recharging well ) system in a confined aquifer will be observed using finite element method by using FEniCs software by considering different cases in two dimensional situation. 2. Groundwater Flow in a Confined Aquifer The fundamental continuity equation for the flow through a confined aquifer of thickness B as shown in the figure (1) is given by: ∇. (. ∇ℎ) +  =    (1) , where h = piezometric head; S = storativity coefficient; N=volumetric flux per unit volume representing source/sink terms; t = time; T = BK, transmissivity; B= the aquifer thickness; K= hydraulic conductivity