Navier-Stokes flow and transport simulations using real fractures shows heavy tailing due to eddies

Two-dimensional Navier-Stokes flow and transport simulations are conducted for a 15-cm long fracture mapped via X-ray computed tomography. (1) The actual fracture with irregular aperture, (2) a truncated fracture where the largest aperture area is excluded from the domain, (3) the truncated fracture with further thinning of other large aperture areas, and (4) a fracture with uniform vertical aperture equal to the actual fracture's mean aperture, are subjected to the same pressure gradient. Slight variations in fracture characteristics result in significantly different flow and transport behavior. Flux is much larger for the uniform-aperture fracture compared to the actual fracture. A pronounced eddy is present at the largest aperture zone of the actual fracture resulting in a power-law tail absent in other cases. The uniform aperture fracture has the largest effective dispersion coefficient estimated via inversion of a 1D analytical model. The analytical model fit to the other cases is not as robust as in the uniform aperture case.