Microflow effects on the hydraulic aperture of single rough fractures

The understanding of flow behavior in rough fractures is essential for many engineering activities. When the aperture of a rough fracture approaches the mean free path of fluid molecules, the microflow effect, sometimes also referred to relative rarefaction effect, relative discrete effect or non-equilibrium effect, becomes pronounced. It was found often to enhance the flow rate. However, the surface roughness shows completely contrary influence. In order to clarify the influences of the two factors, a computer simulation work accompanied with theoretical analyses is conducted. Previous empirical models for hydraulic aperture which already containing roughness effect are modified with consideration of the microflow effect. Direct simulation using the lattice Boltzmann method is conducted on artificially created 2D fractures with random roughness following Gaussian distribution to reveal the competitive relationship of two effects. The simulation results also verify modified models. Among them, the one based on Rasouli and Hosseinian's model agrees with the simulation on the relationship between hydraulic aperture and mechanical aperture for both cases with very rough fractures and relatively smooth fractures. Further investigation confirms that, under various roughness, the ratio of hydraulic aperture over mechanical aperture shows quantitatively different trends as mechanical aperture decreases. This phenomenon exists on a relatively wide scale. An equilibrium point of two effects is also found through analysis of the relationship. The results reveal the mechanism of microflow in 2D rough fractures and also provide a reference for engineering problems like the transport of natural gas through microfractures.