Research on the influence of geometry on nonlinear flow in constructed rough fractures by lattice Boltzmann simulation

Abstract

The fluid flow behavior in widespread rough fractures has important impacts on the utilization and protection of groundwater resources, the development of oil and gas resources, and waste treatment. However, it is hard to describe and numerically construct the complex geometry of a real rough fracture. The influence of fracture geometry on the nonlinear flow within a fracture needs further illustration. This paper provides a new simple method for constructing a 2D single rough fracture. Fracture roughness is considered to consist of rough elements and large-scale waviness. The rough element size distribution was proven to be a Gaussian distribution through laser scanning and wavelet analysis. Circles whose radii satisfy the Gaussian distribution within an STD (standard deviation) were used to construct the rough elements, which are convexities when the radii are greater than 0 mm and concave pits when the radii are less than 0 mm. The circular rough elements are tangentially arranged, and their centers are located on the large-scale waviness. A sine function with random periods was adopted to control the large-scale waviness. To research the flow nonlinearity in rough fractures, 32 rough fractures with different STDs, apertures, and tortuosity values were constructed, and the LBM (lattice Boltzmann method) was adopted to simulate the water flow in the constructed fractures under different driving pressure gradients. Through 256 simulations, the pressure field, velocity field, streamlines, and vorticity field were qualitatively and comparatively analyzed. It was found that when the driving pressure gradient is constant, nonlinearity may increase first and then decrease as the element size distribution STD or aperture increases instead of always increasing. Nonlinearity is the combined result of the fracture aperture, element size distribution STD, driving pressure gradient, and fracture tortuosity, and the main influencing factor varies by situation. The results may enhance our understanding of nonlinear flow in rough fractures.