Inertia Dominant and Transient Flow in Fractures - Beyond the Cubic Law

There are many applications which require a fracture flow model that accounts for variations in aperture beyond surface roughness. Large-scale models and simulations of fluid flow through fractures are almost exclusively based on the cubic law (Poiseuille flow) for steady-state flow through rigid parallel plates. When the fracture aperture is time and/or spatially varying, flow is transient, and/or flow rates are modest (Re≥1), cubic law predictions can deviate substantially from true fluid behaviour. In this paper, we present a new Reduced Dimension Fracture Flow (RDFF) model which more accurately predicts transient flow for incompressible fluids with modest Reynolds numbers through fractures with time and/or spatially varying aperture. The RDFF model is derived from the two-dimensional Navier-Stokes equations and yields a two-field model (fluid flux and pressure) governed by the conservation of mass and momentum. The RDFF model is shown to conserve energy in spatially varying fractures where the cubic law does not. We demonstrate that the RDFF model captures complex transient and inertial behaviours not previously captured for flows with modest Reynolds numbers (1≤Re≤100) and demonstrates up to 400% improvements in error over the cubic law in steady-state flow conditions through fractures with sinusoidally varying aperture.