Numerical simulations of incompressible fluid flow in synthetic fractures using lattice Boltzmann method

Abstract

The effect of the geometrical complexity on the fluid flow through single fractures is the subject of this study. Synthetic self-affine fractures with different waviness and local roughness are generated by SynFrac. Several fracture profiles were sliced from the generated fractures for 2D simulations. An incompressible lattice Boltzmann method with non-equilibrium extrapolation method was used to simulate the fluid flow through the generated rough fractures by solving the full Navier-Stokes equations. The results indicate that the scaling irregular nature has a great influence on the fluid flow through single fractures. The tortuosity and the randomly distributed stagnated areas had been confirmed as the reasons for the deviation from local cubic law both theoretically and numerically. The tortuosity tends to have a linear relationship with the standard deviations which represent the amplitude of the waviness on the large scale, and a second-order dependence on the fractal dimensions which presents the degree of local roughness. The recirculation zones were formed in the troughs of rough fractures even when the flow was a creeping one with the Reynolds number below 1. These stagnated areas were observed to have an intuitive influence on the local effective advective aperture. An effective volume ratio was defined to quantify this effect of eddies on the hydraulic aperture which had been related to the local roughness of the fractures. The tortuosity of the fluid flow and eddies formed along the fractures combined together to make the permeability deviate from the local cubic law.