A New Geometrical Model of Fluid Flow in Rock Fractures for Valid Application of the Cubic Law

Abstract

The cubic law (CL) is one of the most commonly applied physical laws for flow through rock fractures and fractured media, but many studies indicate that the CL is often not adequate. We investigate the establishment conditions of valid applying the “cubic law” to flow in fractures. A dimensional analysis of the N-S equations yields three conditions for the applicability of cubic law, as a leading order approximation in a local fracture segment with parallel walls. These conditions may not be met in many natural rock fractures as whole and demonstrate that the “cubic law” should be exactly applied in local segments (local cubic law, LCL). In this way, a new 2D discrete equivalent model for natural rough fractures is introduced, and its equivalent aperture and flow formulation are derived. By comparing the developed model and experimental results of different fractures, good accuracy was found, and the model was validated. The model could be useful for theory studies of flows through real rock fractures.