The complexity of fluid flow modeling through a single rough walled fracture is due to its tortuous paths followed by the fluid particles and presence of uneven walls. Flow of fluid can take place through a single fracture, fault, or a network of fractures. Large body of numerical and simple analytical solutions has been proposed to study the fluid flow in a single fracture. The main difficulty in all these models is how appropriately incorporating the effect of fracture morphology, which has a significant influence on fluid flow behavior. Pressure drop and velocity magnitudes of synthetic and real rock profiles were estimated using FLUENT software. Pressure drop showed a good correlation with a new surface roughness parameter (DR1) already developed based on the amount of dispersion for distribution of normal vectors to a surface. The results indicated that the larger is profile's DR1 (i.e. rougher profile) the higher would be pressure drop along the fracture. However, it was demonstrated that the existence of extremely reduced size openings against fluid path could be more influencing on flow behavior than fracture geometry.


The fluid flow behavior in a rock mass is usually governed by fluid properties, void geometry, and the fluid pressure at the joint boundary [1]. Analysis of fluid flow in natural fractures is an important subject in many fields of engineering such as hydrogeology, geology, mining and petroleum. The irregular and uneven geometry of fracture surfaces makes the analysis of fluid flow in natural fractures a challenging subject [2]. The common approach in studying fluid flow in a single rough walled fracture is to use Cubic Law formula which is a simplified version of the Navier-Stokes equation [3, 4]. Presence of roughness can be considered as an effective parameter in fluid flow characteristics in a real fracture with rough geometries, such as its effect on fracture transmisivity [5]. This effect in natural fractures causes deviation from the cubic law concept and therefore the need to modify this formula [2, 3]. One of the first comprehensive works on flow analysis through fractures was presented by Lomize [6]. Later on, several numerical studies were developed to investigate fluid flow characteristics in real rough walled fractures [2, 7]. These studies also suggest the need to modify the cubic law to account for the tortuosity or the area of surface contact of a rough walled fracture. Patir and Cheng (1978) showed that the flow rate can be different for isotropic roughness than the surface with a strong roughness with directional fabric. Barton et al. (1977) employed the joint roughness coefficient (JRC) as a roughness parameter to consider the effect of roughness in fluid flow analysis of real fractures. In this study numerical analyses of synthetic symmetric triangular profiles as well as some real rock fractures were carried out using FLUENT software. Pressure drop and velocity magnitudes were estimated for these profiles and the effect of different geometrical and hydraulic properties on pressure drop were studied.

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