Time-Dependent Closure and Permeability of a Small-Scale Hydraulic Fracture Under Constant Normal Stress

Abstract

The permeability of a hydraulic fracture, which acts as an artificial heat exchanger in HDR geothermal energy extraction, may decrease with time due to time-dependent closure under compressive in-situ stresses. The decrease depends on the topography of the fracture surfaces and the rheological properties of rock. In this study, a hydraulic fracture was created in a block of granite in the laboratory. Specimens of a hollow cylinder, which contained a hydraulic fracture perpendicular to the axis, were taken from the block, and height distributions of the fracture surfaces were measured along matched paths to determine two-dimensional aperture distributions of the fracture. The power spectral density of the aperture showed that the fractures used in this study had the surfaces strongly correlated to each other. The changes in the permeability and closure of the fracture with time under constant normal stress were measured for normal stresses up to 25 MPa. The fracture permeability was given as a hydraulic aperture, which is equivalent to the aperture required by a parallel-plate model to give the same flow rate. Timedependent closure was very small and approached a constant value. The ultimate time-dependent closure did not depend on normal stress. A fundamental mechanism of this independence was considered to lie in that the increase rate in contact area with respect to time-dependent closure of the fracture increases with normal stress. The hydraulic aperture was also very small and decreased with time to approach a constant value. Using an empirical formula between normalized hydraulic aperture and normalized mean aperture, obtained by a simulation for water flow through a hydraulic fracture in granite, the mean aperture of the fracture during time-dependent closure was estimated. The time-dependent hydraulic aperture of the fractures used in this study was less than 10 % of the mean aperture. Thus, the permeability of a hydraulic fracture never obeys the Darcyís law in the entire process of closure.