Numerical Modeling of Hot Water Storage in Aquifer by Finite Element Method

Abstract

This chapter discusses numerical modeling of hot water storage in aquifer by finite element method. A three-dimensional finite element model is developed for the simulation of hot water storage in a stratified aquifer saturated by cold water. The hydrodynamic instabilities of non-isothermal flow through porous media are investigated when both density and viscosity vary with temperature. The instabilities are due to a density gradient directed upward (Rayleigh-Bénard instabilities), and to the displacement of a more viscous fluid by a less viscous one inducing fingering (Saffman-Taylor instabilities). Both instabilities may drastically affect the efficiency of hot water storage, and the purpose of this simulation is to identify the conditions for which the effects of hydrodynamic instabilities are minimized. The simulations are performed for cylindrical three-dimensional aquifers. The equations used to model the system are discretized using Q 1 finite elements in space and an Euler's semi-implicit scheme in time. The matrix system is solved by the preconditioned conjugate gradient method with Choleski's incomplete factorization.