Hawaii Geothermal Project: Steady State Free Convection in an Unconfined Geothermal Reservoir

Abstract

The problem of steady state free convection in an unconfined coastal aquifer with non-isothermal geothermal heating from below is investigated in this paper. The governing non-linear partial differential equations with non-linear boundary conditions are approximated by a set of linear sub-problems on the basis of the perturbation method. The equations for the zero-order and first-order approximations are of the elliptic type that can be solved numerically by the finite difference method. Numerical results, accurate to the first-order approximations, are obtained for temperature, pressure and stream function as well as for the shape of the water table. The influence of the location and the size of the heat source as well as various parameters on heat transfer and fluid flow characteristics in a rectangular geothermal aquifer is discussed.