CRACK-PROPAGATION MODELS FOR ROCK FRACTURE IN A GEOTHERMAL-ENERGY RESERVOIR

The propagation of a one-dimensional, fluid-filled crack in a hot dry rock geothermal energy reservoir (HDRGER) is discussed. In previous st udies a number of different relationships between the normal stress on the crack, the fluid pressure, and the crack height (so-called crack laws) have been used, as have different ''flow laws'' to determine the relationship between flow rate and crack geometry. Here it is shown t hat the choice of submodel may have profound implications for the math ematical structure of the problem. In particular, two crack laws (a li near law and a hyperbolic law) are considered as well as two flow laws (a cubic law and a linear law). The model contains a dimensionless pa rameter that measures the relative importance of stresses due to local deformation of asperities and the long-range deformation of the crack surface. The case is considered where the former is the dominant mech anism. A perturbation analysis is performed, and it is found that for some combinations of laws a strained-coordinate analysis is required, whilst for others a matched asymptotic approach is needed. In the latt er case the problem may be reduced to that of solving a linear, nonhom ogeneous singular integrodifferential equation to determine the behavi our in the boundary layer. This problem is solved, and some conclusion s are drawn regarding the relevance of various laws to flow in HDRGERs .