Abstract: The relative permeabilities for water-air two-phase flow in rough-walled fractures of rock are significant parameters on multiphase flow and hydro-coupling analysis in fractured rock engineering. According to the capillary theory and cubic law, the rough-walled fractures are conceptualized as a large number of parallel plates of different apertures, and a relative permeability model for water-air two-phase flow in rough-walled fractures is proposed on the basis of micro structure of rough-walled fractures. The theoretical model is validated by the comparison with experimental data from two different rough-walled fractures with distinguished spatial distributions. No matter for water phase or air phase, the proposed model can satisfy the experimental data better than X model, V-C model and Corey model. In order to evaluate the feasibility of the proposed model on rough-walled fractures with different spatial distributions, a numerical approach is developed to generate the aperture distribution based on random successive addition method, and to perform water-air two-phase flow process based on the invasion percolation model, respectively. On the basis of a large number of numerical results, predictions of the proposed model are consistent with the calculated data and presents better goodness of fit than X model, V-C model and Corey model. This more reliable analytical model can be used for better understanding the multiphase flow and hydro-coupling analysis in fractured rock.

Key words: rough-walled fracture, relative permeability, saturation, numerical simulation