Applicability of the ‘cubic law’ for non-Darcian fracture flow

The influence of inertial effects on the flow of fluids through fractured media is a topic of interest for a number of engineering applications, particularly within the energy sector (e.g. production from gas and oil reservoirs, heat extraction from enhanced geothermal systems, coal-bed methane production). The ‘cubic law’ can provide a simple relationship between the hydraulic aperture of a fracture and its permeability, for Darcian flow of a given fluid. At significant flow velocities, fracture flow becomes non-Darcian, the velocity–permeability relationship becomes non-linear and the cubic law becomes invalid. However, for transitional flow, which retains a component of linearity, the cubic law may still be applicable for initial determination of superficial velocities from flow rate data. Here, the results of fluid flow experiments carried out for air flow through a fractured granite sample under various pressures of confinement are presented. Analysis of the flow data using the cubic law produced valid results for non-Darcian flow cases where inertial effects were modest. The cubic law appears to be applicable for flow cases that, following analysis using the cubic law, return a Forcheimer number < 1.30.

► We investigate the applicability of the ‘cubic law’ for non-Darcian fracture flow. ► Data was collected from flow experiments on fractured rock under triaxial conditions. ► The cubic law was used to analyse non-Darcian flow cases and the results verified. ► Results suggest the cubic law gives accurate values if inertial effects are limited. ► We recommend such analysis only where fracture flow has Forcheimer number < 1.30.