An anisotropic damage–permeability model for hydraulic fracturing in hard rock

Hydraulic fracturing is the most efficient method to exploit valued geothermal energy trapped in low-permeable hard rock, e.g. granite. Most research on the hydraulic fracturing has focused on its application in shale gas and oil. However, the hydraulic fracturing performs differently in geothermal reservoir, as the rock properties are quite different. In this work, an anisotropic damage–permeability model is developed on the fundament of continuum theory to study the hydraulic fracturing of hard rock in geothermal reservoir. The plastic-hardening and damage-softening behaviours are considered in this model. A cubic law is adopted to characterize the damage enhanced permeability. Its directional information is converted from damage tensor, while the effect of compression stress on permeability is isotropic and characterized by an impact factor. The newly developed model is calibrated and validated by a series of stress–strain curve, damage and axial permeability from triaxial tests on granite. In the application to cyclic fracturing test at Aspö Hard Rock Laboratory, the capacity of newly developed model is proven by good matching of measured injection pressure, permeability, etc. The results show clearly that the fracture is mostly activated by tensile failure in this case. Moreover, the stimulated fracture will be closed during flow back and re-activated in subsequent re-fracturing. If the fracture from previous fracturing is not re-activated completely, no new fractures will be created in current re-fracturing, and the damage amasses continuously due to repeated re-activation of closed fracture during re-fracturing.