Groundwater Flows in the Vicinity of Two Well Systems with Finite Element Method using FEniCs Software

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  while the recharging well is located at point 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