Effects of inertia and directionality on flow and transport in a rough asymmetric fracture

Two-dimensional flow and transport simulations are conducted for a 15-cm-long fracture mapped via X-ray computed tomography. The simulations consider either Navier-Stokes equation (NSE) based flow or Stokes equation (SE) based flow and are run for opposing directions. NSE and SE solutions deviate at larger bulk velocity, and the errors are sensitive to fracture geometry. Transport in all cases is non-Fickian, owing mainly to the presence of a large eddy, and exhibits power law residence time distributions (RTDs). The tailing is more persistent at higher Reynolds numbers (Re), with the exponents of the power law RTDs related to Re via a power function, and becomes asymptotic at higher Re. The late-time portion of the RTD changes with flow direction and is also sensitive to whether the flow is represented by the NSE or the SE. The sensitivity of transport to flow direction and formulation is primarily driven by varying eddy geometry under the different conditions. Our study opens the path to developing robust and mechanistic continuum-scale models of solute transport in fractured geologic media.