Hawaii Geothermal Project: Numerical Solutions for Steady Free Convection in Island Geothermal Reservoirs

Abstract

The problem of steady free convection in an island aquifer, confined by caprock at the top and heated by an impermeable surface from below is considered. The governing non-linear partial differential equations are approximated by a set of finite difference equations, which are solved numerically by the iteration method. To guarantee convergence of the iteration process, the non-linear convective terms in the energy equation are approximated by the upwind difference scheme. The effects of thermal conditions at the caprock, the geometry of the reservoir, the variation of Rayleigh number, the length of the heating surface, and the magmatic intrusion, on fluid flow and heat transfer characteristics in island geothermal reservoirs are discussed.