Numerical simulations of fluid flow through a single rough walled fracture

Abstract

The morphological properties of rock fractures may have a significant influence on their hydromechanical behaviour. Fracture surface roughness could change the fluid flow regime from laminar to turbulent, while it causes the flow properties to deviate from cubic law for smooth channels due to a change in fracture equivalent hydraulic aperture. Different empirical (including the well known Joint Roughness Coefficient, JRC) and statistical methods have been proposed for surface roughness characterisation in an attempt to link them to the hydromechanical behaviour of fractures.This thesis aims to investigate the potential for assessment of fluid behaviour by studying its surface geometrical properties. D[subscript]R[subscript]1 and D[subscript]R[subscript]2, the 2D and 3D roughness parameters developed recently using Riemannian geometry, were used to correlate fracture geometry to its flow behaviour. Also, the 2D Riemannian isotropy parameter (I[subscript]R[subscript]2) was used to correlate surface roughness anisotropy with directionality in fluid flow behaviour along different directions.Numerical simulations in both 2D and 3D were performed assuming the laminar flow regime using FLUENT software. This assumption is, to a large extent, acceptable for situations where the height to length ratios of a fracture is very small. 2D analysis of synthetic profiles with different geometries demonstrated how a change in profile roughness can affect flow response, for example, the pressure drop. JRC flow channels developed in this work as combinations of pairs of JRC profiles were simulated numerically. The analysis results indicated that channels with a similar JRC average for the upper and lower walls but a different JRC profile number responded differently when they were subjected to fluid flow. Therefore, assuming special fluid properties, correlations developed using the pressure drop of a fracture can be estimated by its analogy to JRC flow channels.3D simulations of a corrugated plane were performed assuming different asperity height distributions, for fluid travelling along different directions with respect to surface geometry and at different shear displacements. No asperity contact and failure is assumed in the analysis performed in this work. D[subscript]R[subscript]2 analysis results of the corrugated plane indicated how fluid flow could be related to surface geometry. For instance, it was observed that the pressure drop was maximised along the direction of maximum roughness and reduced to its minimum along a perpendicular direction which shows anisotropy in fluid flow behaviour. Significant changes in pressure drop due to shear offset indicated the importance of fracture wall displacements with respect to each other. A detailed analysis of one synthetically generated surface, and also five surfaces with identical statistical parameters except their correlation distances being different, further confirmed the above concepts. This was followed by analysing a real rock like fracture which was studied elsewhere for fracture shear tests in the lab. Simulation of this surface was performed with particular interest in identifying the locations where the velocity magnitude reduced to nearly zero after the fracture was subjected to a shear offset corresponding to maximum shear stress. These areas were found to be very similar to the locations of asperity degradations as observed through lab experiments. The roughness analysis of the surface was in agreement with the correlation found between the mechanical and hydraulic behaviour of the surface.The results of this research demonstrate how detailed analysis of surface geometry could provide valuable information with respect to surface flow behaviour. Detailed discussions and interpretations of the results will be presented and various conclusions will be made.