Theoretical study of hydraulically fractured penny-shaped cracks in hot,dry rocks

A simple and analytical method of solving the problem of heat extraction from a penny-shaped crack having both inlet and outlet holes is developed by using a two-dimensional flow model when fluid is injected at a constant flow rate. Temperature distributions in both rock and fluid are obtained by taking into account the hydraulic and thermal growth of the crack. The outlet fluid temperature and energy extraction rate versus time are shown by some illustrative examples. Although the effect of thermal, contraction of rock upon the crack width is large, its influence upon flow rate and crack tip stress intensity factor is sufficiently small within the first several years so that the crack radius can be determined mainly by the mechanical deformation of, the rock.