Fluid Injection into Fractured Rock: Hydro-Mechanical Concepts for Numerical Modeling

For many years, the determination of the geometrical and hydraulic properties of conduits relevant for subsurface fluid flow has been performed by means of pumping experiments in boreholes and wells. The transient pressure response due to sequences of injection or production from a borehole into the surrounding rock represents the information gained from such tests. Traditionally, emphasis is put on constraining the transport property associated to the fluid flow, i.e. transmissivity, permeability, but storage properties representing fluid compressibility and conduit deformability received less attention. Diffusion equations have proven to be valuable in analyzing pressure records. Yet, some phenomena cannot be explained relying on diffusion equations with locally ascribed, constant hydraulic properties. Despite the substantial number of previous approaches, it is in fact questionable to which extent the non-local character of deformation associated with pressure transients is appropriately captured. In particular, the coupling effects have to be accounted for in reservoirs containing natural or stimulated fractures. We propose and investigate modeling approaches which include non-constant hydraulic properties and fracture deformation. Small displacements of the fracture surface greatly affect the hydraulic conductivity of the fracture and, therefore, the fluid flow. Furthermore, injection at one point causes finite displacements everywhere along the fracture, i.e., storage capacity becomes strongly non-local. Due to the coupled nature of the problem, conceptually and technically different strategies can be applied to solve the resulting hydro-mechanical system. On the one hand, we rely on Biot's quasi-static poroelastic equations and model the fracture domain as well as the surrounding rock as porous materials. On the other hand, rather than relying on a heuristic formulation of an associated diffusion equation, we present a model which is derived from physically-based conservation conditions, avoiding most of the frequently used approximations. We investigate fluid injection and production into and from a single fracture as the basic model for the coupled hydro-mechanical problem. We apply the models to field data in order to estimate effective hydraulic properties of a single fracture behaving hydraulically in the same way as the real subsurface. The presented approaches capture phenomena that cannot be addressed by diffusion equations and, thereby, better explain the experimental data than conventional approaches. The effects of fracture deformation strongly affect the pressure transient along the fracture, indicating that the relevant hydraulic properties, e.g. fracture storage capacity, are scalar functions and cannot be simplified to a single effective property describing the entire fracture. The proposed models represent a comprehensive tool which allows constraining critical geometrical properties of fractured rock formations, such as effective fracture aperture and fracture length.