Numerical modeling of steady-state flow of a non-Newtonian power-law fluid in a rough-walled fracture

Numerical simulations of power-law fluid flow in a rough fracture of regular or irregular topography were carried out using the finite-volume method under the assumptions of the lubrication theory approximation. The model was verified by comparing its results with analytical results available for regular 1D sinusoidal profiles across or along the flow. For a regular profile with sinusoidal variation of the aperture in both directions, the model confirmed that a geometric average can be used as a first approximation, as long as the variation in the profile is not too large. For all fracture topographies studied, reducing the exponent, i.e. making the fluid more shear-thinning, resulted in increasing equivalent hydraulic aperture. The normalized equivalent hydraulic aperture decreased with the normalized standard deviation of the fracture aperture for all fracture topographies studied, except a fracture with a large-scale feature representing a zone of overlap in the middle of the fracture. The validity of the assumptions made in the numerical simulations, in particular the lubrication theory approximation, is discussed and the directions for future work are outlined in conclusion.