Roughness decomposition and nonlinear fluid flow in a single rock fracture

The objective of this paper is to investigate the effects of wall surface roughness on fluid flow through rock fractures. A wavelet analysis technique was developed to define a mathematical criterion for decomposing the original wall surface roughness profiles of a fracture into a high-frequency (secondary roughness) profile and a low-frequency (primary roughness) profile, in order to examine their impacts on fluid flow, by solving the Navier-Stokes equations (NSE) without linearization, using a self-developed 2D finite volume method (FVM) code. The results indicate that the high-frequency secondary roughness is the main cause for dynamic evolution of Eddy flow regions in the fracture flow field, besides the Reynolds number (Re). In the original fracture model with the high-frequency secondary roughness, our results show that fluid flow fields are not only generally non-linear, but also with non-stop generation and motions of eddies in the boundary layer regions of rough fractures when the Re=1000 in this study, which will affect the solute transport processes in fractured rock masses. The complete NSE were solved without removing acceleration and inertial terms, so that the impacts of surface roughness on the nonlinear and dynamic flow behavior of rock fractures were calculated and visualized more accurately, which is important for modeling mass and energy transport processes in fractures and fractured rock masses.