Publisher Summary This chapter discusses the mathematical formulation of the problems of convective heat transfer in geothermal systems. Geothermal reservoirs may have numerous near-vertical faults and relatively impermeable intrusive interspersed in the aquifers. Both theoretical and experimental investigations of heat transfer in geothermal systems are reviewed. A qualitative understanding of the large-scale convection processes in a geothermal reservoir and the prediction of reservoir behavior under production can be obtained by idealizing it as a saturated porous medium. The identification of a viable geothermal reservoir and the estimation of its capacity remain major problems in the utilization of geothermal resources. Thermal anomalies in geothermal areas can be detected by surface manifestations, aerial infrared surveys, geochemical analyses, or exploratory drillings. Many of the analyses are applicable to a wide range of engineering problems whenever they can be idealized as convection in a porous medium. These include the problems of the secondary recovery of oil by thermal methods, the use of fibrous materials for thermal insulations, the design of aquifers as an energy storage system, and the deposition of mineral ore in the subsurface formation. Results from short-duration well testing are used to determine reservoir characteristics.

Heat Transfer in Geothermal Systems

Possible similarity solutions for free convection boundary layers adjacent to flat plates in porous media

The hydrogeology of Kilauea volcano

A reappraisal of the international heat flow database has been carried out and the corrected data set was employed in spherical harmonic analysis of the conductive component of global heat flow. Procedures used prior to harmonic analysis include analysis of the heat flow data and determination of representative mean values for a set of discretized area elements of the surface of the earth. Estimated heat flow values were assigned to area elements for which experimental data are not available. However, no corrections were made to account for the hypothetical effects of regional-scale convection heat transfer in areas of oceanic crust. New sets of coefficients for 12° spherical harmonic expansion were calculated on the basis of the revised and homogenized data set. Maps derived on the basis of these coefficients reveal several new features in the global heat flow distribution. The magnitudes of heat flow anomalies of the ocean ridge segments are found to have mean values of less than 150 mW/m2. Also, the mean global heat flow values for the raw and binned data are found to fall in the range of 56–67 mW/m2, down by nearly 25% compared to the previous estimate of 1993, but similar to earlier assessments based on raw data alone. To improve the spatial resolution of the heat flow anomalies, the spherical harmonic expansions have been extended to higher degrees. Maps derived using coefficients for 36° harmonic expansion have allowed identification of new features in regional heat flow fields of several oceanic and continental segments. For example, lateral extensions of heat flow anomalies of active spreading centers have been outlined with better resolution than was possible in earlier studies. Also, the characteristics of heat flow variations in oceanic crust away from ridge systems are found to be typical of conductive cooling of the lithosphere, there being little need to invoke the hypothesis of unconfined hydrothermal circulation on regional scales. Calculations of global conductive heat loss, compatible with the observational data set, are found to fall in the range of 29–34 TW, nearly 25% less than the 1993 estimate, which rely on one-dimensional conductive cooling models.

Spherical harmonic analysis of earth’s conductive heat flow

Superconvecting geothermal zones

The problem of steady state free convection in an unconfined aquifer bounded by ocean on the sides with geothermal heating from below is investigated in this paper. The governing nonlinear partial differential equations with nonlinear boundary conditions are approximated by a set of linear subproblems on the basis of perturbation method. The equations for the zero- 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.

Steady state free convection in an unconfined geothermal reservoir

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Steady state free convection in an unconfined geothermal reservoir