The development of a stimulated volume during hydraulic fracturing in a naturally fractured rock mass is singularly challenging to simulate mathematically. At the discrete level there are strong fabric issues (oriented joint sets, perhaps faults, weak bedding planes), different joint properties, Biot coupling, advective-conductive heat transfer, and flow in joint arrays with changing apertures. Complex discrete interaction laws for joints involve sliding Mohr-Coulomb friction with joint dilation (i.e. aperture increase), cohesion loss related to sliding and to extensional displacements across joints, strongly non-linear block contact stiffness behavior that deviates from Hertzian behavior, and loss of contacts during hydraulic fracturing when some natural fractures become open. Furthermore, the rock blocks delineated by the joints in the stimulated volume may anisotropic properties, and large-scale heterogeneity also exists. A novel upscaled HF model for stimulated volume simulation in a naturally fractured rock mass has been developed using a typical Galerkin Finite Element Method approach with full Biot coupling, but using a non-local plasticity formulation with dilation to track the evolution of bulk stiffness and fluid transmission properties. First, the evolution of the stimulated volume is quantified for an example of 3D hydraulic fracturing propagation in a naturally fractured rock. After creation of a sufficiently large stimulated volume, the well is shut-in and pressure is allowed to fall-off. We use the pressure decline analysis to relate the post shut-in behavior of the stimulated volume to the geomechanics of fracturing. Preliminary results are promising: we present interesting results that show this approach should be highly useful in analyzing hydraulic fracturing data and incorporating damage mechanics approaches into geomechanical design in naturally fractured rock masses.
It is generally understood that Hydraulic Fracturing (HF) in Naturally Fractured Rock masses (NFRs) does not lead to creation of a single fracture. Rather, it creates a Stimulated Volume (SV) with enhanced permeability through opening of pre-existing natural fractures, tensile fracturing, irreversible plastic deformation through shearing, and general damaging of a volume of the rock mass (Cipolla et al., 2010; Mayerhofer et al., 2010). However, mathematical simulation of the evolution of the SV is an intricate task because of considerable uncertainty with respect to the shape, size, and conductivity of the SV, as these characteristics are strongly dependent upon the distribution of natural fractures, in situ stresses, and other reservoir and fluid parameters.
