Buoyancy Induced Boundary Layer Flows in Geothermal Reservoirs

Abstract

Most of the theoretical study on heat and mass transfer in geothermal reservoirs has been based on numerical method. Recently at the 1975 NSF Workshop on Geothermal Reservoir Engineering, Cheng presented a number of analytical solutions based on boundary layer approximations which are valid for porous media at high Rayleigh numbers. according to various estimates the Rayleigh number for the Wairakei geothermal field in New Zealand is in the range of 1000-5000, which is typical for a viable geothermal field consisting of a highly permeable formation and a heat source at sufficiently high temperature. The basic assumption of boundary layer theory is that heat convective heat transfer takes place in a thin porous layer adjacent to heated or cooled surfaces. Indeed, numerical solutions suggest that temperature and velocity boundary layers do exist in porous media at high Rayleigh numbers. It is worth mentioning that the large velocity gradient existing near the heated or cooled surfaces is not due to viscosity but is induced by the buoyancy effects. The present paper is a summary of the work that we have done on the analytical solutions of heat and mass transfer in a porous medium based on the boundary layer approximations since the 1975 Workshop. As in the classical convective heat transfer theory, boundary layer approximations in porous layer flows can result in analytical solutions. Mathematically, the approximations are the first-order terms of an asymptotic expansion which is valid for high Rayleigh numbers. Comparison with experimental data and numerical solutions show that the approximations are also accurate at moderate values of Rayleigh numbers. For problems with low Rayleigh numbers where boundary layer is thick, higher-order approximations must be used. 9 refs., 5 figs.