Numerical Simulations of Fluid Flow in a Single Fracture under Loading and Unloading Conditions

Hydraulic aperture is one of the most important parameters to describe fluid flow in fractured rocks. Hydraulic apertures are typically determined indirectly by fluid flow experiments or hydraulic field tests based on the cubic law. Alternatively, there are different equations approximating an empirical relation between mechanical and hydraulic aperture. However, these methods most widely neglect mechanisms such as stress changes, where increasing stresses decrease the mechanical aperture and, therefore, also the effective hydraulic aperture. Hence, the objective of the present study is to simulate fluid flow in a single fracture under loading/unloading conditions and validate the results with core flooding experiments. Core flooding data and X-ray CT scans (voxel size 0.5 x 0.5 x 1 mm) of a sandstone sample with a single fracture (measured mean aperture of around 0.1 mm) were obtained by laboratory experiments. The fluid flow simulations are performed by solving the incompressible Navier-Stokes equation by using a finite volume method. Input data are given by experimental flow rates, pressures, applied stress levels and CT images of the fracture. In addition, an error analysis is performed to establish confidence in results. Results of the validation exhibit significant effects of stress on aperture distribution such as channeling and stress-dependent fracture permeability. A significant stress sensitivity of hydraulic aperture compared to the mechanical aperture was found, which can be explained by roughness changes resulting from loading. Observations indicate that with increasing stress, changes in mechanical aperture are small, while changes in hydraulic aperture can be very large. Since previous equations for hydraulic aperture do not consider changes in normal stress, a modification of these equations is proposed, including the stress-dependency of mechanical apertures to provide a better approximation to the observed hydraulic apertures.