A Modified Cubic Law for single-phase saturated laminar flow in rough rock fractures

Abstract

The purpose of the study presented was to develop a Modified Cubic Law (MCL) for single-phase saturated laminar flow in rough rock fractures. Based on the fundamental assumptions made for the Cubic Law (CL), the proposed MCL incorporates modifications to the aperture field by considering flow tortuosity, aperture variation and local roughness effects. We assess the performance of the MCL by applying it to synthetic fractures with different surface roughness and varying aperture and compare the outputs to numerical simulation results from solving the Navier-Stokes Equations and results from previous versions of CL-based models. In general, the MCL performs well in predicting the volumetric flow rate in synthetic fractures with deviations (D) from simulation results ranging from −11.1% to 8.4% and an average effective deviation of 4.7%. The proposed model retains the simplicity of CL models and improves the accuracy of flow prediction in terms of single-phase saturated laminar flow in rough rock fractures and it can be extended to analyse other hydro-related problems.