Fluid flow through a rough fracture can be affected by several geometrical parameters such as aperture, roughness, and contact area. Of these, eddy flow can occur around contact areas and change streamline patterns. Fluid flow behavior through a 10 cm × 10 cm square fracture was numerically analyzed with different contact shapes and distributions. The basic shape of the contact area is assumed to be square with a 1 cm2 area. The squares as contact areas through fractures were distorted with different ratios, rotations, and relocations. The total contact area and the physical aperture in all models were 25 cm2 and 1 mm, respectively. The flow rates through the fractures were computed with 5 different water pressures. The Forchheimer equation was adopted to analyze results. The calculations highlight the importance of the parameter β in the Forchheimer equation, which reflects the impact of fracture surface geometry on fluid flow.
Evaluation of fluid flow rate through a fracture is important due to its great influence on oil and gas production, safety of nuclear waste repositories, carbon dioxide sequestration, and water resource management. The flow rate and hydraulic aperture of a fracture are controlled by different variables such as geometrical properties of fractures, hydraulic gradients, and stress states. Geometrical properties of fractures, such as physical aperture, roughness, and contact areas, can change under different normal and shear stress regimes.
Many efforts have been made to understand the effect of geometrical properties of fractures such as physical aperture (Chen et al. 2021), roughness (Brown 1987), and contact areas (Walsh 1981), on flow rate and distribution in discontinuities. Among the others, contact areas can play a crucial role on fluid flow. Variations in size and shape of contact areas can affect fluid flow by blocking potential void spaces. For example, an increase in normal stress could increase contact areas, and consequently, it decreases flow rate and increase/decrease violation in flow pathways. Contact ratio is used to define contact areas through a fracture (Equation 1);
(Equation)
where Scontact is the contact area and Stotal is the fracture surface area (Chen et al. 2017).
