Non-Newtonian fluid flow in geological rough fractures: lubrication approximation versus direct 3D simulations

We simulate non-Newtonian flow in rough fractures. Random aperture fields with isotropic spatial correlations are generated using an FFT-based algorithm. We first solve the flow with a finite-difference code based on the lubrication approximation for power law and Carreau rheologies (2D approach). We then solve a modified Navier-Stokes equation incorporating both rheologies, in the 3D fracture space (3D approach). The 2D approach's efficiency to predict the flow distribution in the fracture plane depends on the fracture closure and correlation length.