Developing and operating deep geothermal projects require a comprehensive understanding of the hydraulic properties of the reservoir. Structural features such as fractures have a crucial impact on hydraulic conductivity and thus on the geothermal reservoir sustainability. Therefore, reliable quantification of fluid flow through fractures is of high interest for reservoir engineering, especially for deep geothermal applications.
From a geometrical point of view, fractures are void spaces constraint by rough and sheared rock surfaces. The quantification of the relationship between pressure loss and flow rate for the flow along rough surfaces is a complex task and computationally expensive, particularly if it is considered on large scale and in three dimensions. Typically, Darcy-based 2D-local cubic law (LCL) simulations are used to reduce computational time. By increasing flow rates, the inertial forces, typically occurring near the borehole, have a significant effect on the pressure drop and cannot be neglected. In order to obtain realistic results for such systems, the flow has to be expressed in terms of Navier-Stokes equations. In this study, we compare widely spread LCL-based approaches and also present initial steps towards 3D-Navier-Stokes (NS) calculations on a single fracture scale.
For the application of the LCL, whose validity for small flow rates has already been confirmed, a defined fracture aperture is required. This aperture is often assumed to be the distance between the two fracture surfaces in the vertical direction, while shear effects, such as anisotropy, tortuosity and roughness, are neglected. It could be shown that this assumption leads to large uncertainties and that instead the fracture aperture should be described by an effective aperture determined by the measurement of the distance along surface normals. For higher flow rates, it could be shown that this simplification is no longer permissible and non-parallel flow and inertial effects must also be considered. In order to quantify the non-linear fluid flow, the Navier-Stokes equations must be applied to a three-dimensional fracture geometry representing the real fracture topology. A comparison of the LCL with NS shows that differences in anisotropy and channeling have to be expected even at low flow rates. These differences in anisotropy and channeling rise by increasing the flow rate.
The comparison of both approaches presented herein leads to valuable evidence to which extend LCL quantifications on rough surfaces provide results with tolerable uncertainties, and in which configurations (flow velocities, tortuosity, channeling, etc.) inertial forces have to be considered using Navier-Stokes.