Stochastic evaluation of the flow regime on rough and sheared fractures

The detailed knowledge of the hydraulic properties is crucial for the assessment of geothermal reservoirs. In the case of Enhanced Geothermal Systems (EGS), fluid flow occurs along complex networks of faults and fractures that connect two or more boreholes. The geometric appearance and properties of these fractures are highly variable. They can be e.g. open or closed, altered and/or filled, smooth and rough. All these factors lead to unknown difficulties in predicting fluid pathways and quantifying flow behavior in the fractured reservoir and in the creation of numerical models.
In these numerical models, often highly simplified assumptions regarding flow behavior and geometry are used to project a fracture in 2D. The most common cubic law (CL) allows the calculation of the total fracture flow, while the local cubic law (LCL) considers the local pressure gradient as well as a local aperture. However, both flow laws pose the same problems: 1) The law is only valid for simple 2D geometries, 2) the aperture is defined and measured differently and 3) laminar Darcy flow is assumed. If these boundary conditions are no longer valid, e.g. during hydrotesting or in the vicinity of wells during production/injection, the complex and nonlinear Navier-Stokes equations must be solved.
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We present the results of flow modeling in rough and sheared fractures by solving the Navier-Stokes equations. Using thirty statistically generated tortuous fracture geometries, the effects of different pressure gradients and flow directions on the formation of preferential fluid pathways and expected flow rates are investigated. The results show a strong dependence on aperture definition and shear direction with respect to flow rates and the formation of preferential fluid pathways. The flow perpendicular to the shearing is about 45 % higher than parallel to it. First nonlinear effects are detectable for a mean Re about 1. Within the identified channels, a laminar flow field can be maintained much longer, while outside the channels, mainly due to irregular geometries, nonlinear effects occur even for Re far below 1. The LCL leads to a mean overestimation between 5 and 15 %, depending on whether the fracture is flowed through perpendicularly or parallel. These differences mainly occur outside the identified channels, while inside the channels the parabolic flow field leads to reduced deviations.