ON IMPROVING THE LOCAL CUBIC LAW FOR FRACTURE FLOW MODELING BY KEEPING IMPACTS OF FLUID INERTIA AND IRREGULAR BOUNDARIES

Local cubic law (LCL) has been widely used for fracture flow modeling; however, its reliability is still subject to debate. In this paper the basic assumptions of LCL were revisited to take into account the impacts of variable boundaries and inertial forces. The vertical distributions and magnitudes of the flow velocities through variable apertures were improved by solving a semiempirically simplified nonlinear Navier-Stokes (N-S) equation. Nonlinear relationships were established between pressure gradients and local flow rates based on these solutions of velocities, and these relationships were regarded as conductivities for the revised LCL models. The following improvements are achieved: (1) the impacts of variable geometries and inertial forces were retained to accommodate the nonlinearity of N-S flow; (2) variations of both the vertical and horizontal velocities were taken into account. The revised LCL models were validated by analytical solutions of transmissivities through sinusoidally walled channels. Results suggest that these revised LCL models show significant improvement. The revised LCL models can also provide a more accurate prediction of pressure distributions, with a good representation of the nonlinearity of N-S flow as well. Meanwhile, the revised LCL model still keeps the advantage of the original LCL method for the convenience in boundary condition treatment.