Numerical calculation method of aperture function for rough rock fracture flow

Abstract

Fracture is the main path of rock seepage and plays a decisive role in the permeability of rock masses. The method of solving Navier-Stokes (NS) equation directly to study the fracture seepage flow has high accuracy and can well reflect the nonlinear flow characteristics in the fracture, but there is also the problem of excessive calculation. In this paper, the fracture aperture spatial data is substituted into the local cubic law as an aperture function to form a numerical calculation method for seepage in rough rock fractures, namely, the aperture function method(AFM). After comparing with the experimental calculation results of fracture seepage, it is found that the AFM calculation results are in good agreement. Using the method of solving the NS equation, the seepage calculations were performed for two typical fracture models with multiple boundary conditions. After comparison and analysis, a) the nonlinear term in the rough fracture flow mainly originates from the local pressure drop (LPD), and the generation of the recirculation zone(RZ) is the main reason for the formation of the LPD. b)The AFM calculation results are compared with the NS method under low hydraulic gradient conditions and its error is not significant (i. e., 0.21%, 0.81%). AFM is an excellent numerical calculation method when the condition of neglecting the effect of nonlinear items in fracture flow is allowed. c) The main advantage of AFM is that it has a very high numerical calculation efficiency, which makes the method available for seepage calculations in large-scale rough fractures.