A Hele-Shaw Model of Heat Convection i n Porous Media under Geothermal Conditions

Abstract

Evidence from New Zealand indicates that geothermal fields occur at reasonably regular intervals of about 15 kilometers apart. Investigators have speculated that these regular intervals may be indications of the scale of the heat convection cells.

Wooding (1975) has described the four well-known approaches to solve the equations of continuity, motion and heat transport for heat convection in porous media. Unfortunately, to date, none of thew methods has provided solutions for all geothermal conditions with a Rayleigh number up to the order of 1000 and also allowed the viscosity to vary. the permeability is in the order of 3 x 10-11 cm2, the change of density Ap is 0.2 gm/cm3, the length scale L p is 0.001 to 0.01 poise (depending on the temperature of the fluid) and the In New Zealand, is about 5 x 105 cm, the dynamic viscosity thermal diffusivity k is 0.003 cm 9 /sec. The range of Rayleigh number would be from 100- 1000.

The Stuart-Watson method has been applied to small viscosity change the critical value for neutral stability ). The Galerkin method and low Rayleigh number (R * Rc For high Rayleigh number the method is not applicable. has been applied to two-dimensional constant viscosity cases. The variational method has been applied to three-dimensional constant viscosity cases with R-500. The methods of numerical solution have been applied to both constant and variable viscosity cases. Due to the great cost involved in computer solution, a relatively large mesh was used at R = 5010. The accuracy of these results is questionable.