Geothermal energy extraction from hot, dry rock requires the circulation of water under pressure through a crack with a small opening (several millimeters) and a large radius (several hundred meters) at several kilometers beneath ground surface. Here we present the basic two-dimensional field equations for the fluid flow and heat transfer, by systematically integrating over the crack thickness the fundamental mass, momentum, and energy equations. The importance of various terms on physical grounds is briefly discussed, and on this basis the corresponding equations are simplified. Finally, with the aid of a finite-element approximation, typical illustrative examples are worked out. These examples reveal that a more accurate estimate for the effective conductivity between fluid and the solid must be obtained in order to more realistically estimate the basic heat extraction process. In particular, the effect of secondary cracks must be carefully examined. This and related aspects of the problem are discussed, and certain areas in need of further research are pointed out.

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