Heat Extraction from a Hydraulically Fractured Penny-Shaped Crack in Hot Dry Rock

Abstract

Heat extraction from a penny-shaped crack having both inlet and outlet holes is investigated analytically by considering the hydraulic and thermal growth of the crack when fluid is injected at a constant flow rate. The rock mass is assumed to be infinitely extended, homogeneous, and isotropic. The equations for fluid flow are derived and solved to determine the flow pattern in the crack. Temperature distributions in both rock and fluid are also determined. The crack width change due to thermal contraction and the corresponding flow rate increase are discussed. Some numerical calculations of outlet temperature, thermal power extraction, and crack opening displacement due to thermal contraction of rocks are presented for cracks after they attain stationary states for given inlet flow rate and outlet suction pressure. The present paper is a further development of the previous works of Bodvarsson (1969), Gringarten et al. (1975), Lowell (1976), Harlow and Pracht (1972), McFarland (1975), among others, and considers the two dimensional rather than the one-dimensional crack. Furthermore, the crack radius and width are quantities to be determined rather than given a priori.