Aspects of forced convective heat transfer in geothermal systems

Abstract

A knowledge of convective heat transfer is essential to understanding geothermal systems and other systems of moving groundwater. A simple, kinematic approach toward convective heat transfer is taken here. Concern is not with the cause of the groundwater motion but only with the fact that the water is moving and transferring heat. The mathematical basis of convective heat transfer is the energy equation which is a statement of the first law of thermodynamics. The general solution of this equation for a specific model of groundwater flow has to be done numerically. The numerical algorithm used here employs a finite difference approximation to the energy equation that uses central differences for the heat conduction terms and one-sided differences for the heat convection terms. Gauss--Seidel iteration is then used to solve the finite difference equation at each node of a non-uniform mesh. The Monroe and Red Hill hot springs, a small hydrothermal system in central Utah, provide an example to illustrate the application of convective heat transfer theory to a geophysical problem. Two important conclusions regarding small geothermal systems follow immediately from the results of this application. First, the most rapid temperature rise in the convecting part of a geothermal system ismore » near the surface. Below this initially rapid temperature increase the temperature increases very slowly, and thus temperatures extrapolated from shallow boreholes can be seriously in error. Second, the temperatures and heat flows observed at Monroe and Red Hill, and probably at many other small geothermal areas, can easily result from moderate vertical groundwater velocities in faults and fracture zones in an area of normal heat flow.« less

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