NUMERICAL STUDY OF GEOMETRICAL DISPERSION IN SELF-AFFINE ROUGH FRACTURES

We report a numerical study of passive tracer dispersion in fractures with rough walls modeled as the space between two complementary self-a ffine surfaces rigidly translated with respect to each other. Geometri cal dispersion due to the disorder of the velocity distribution is com puted using the lubrication approximation. Using a spectral perturbati ve scheme to solve the flow problem and a mapping coordinate method to compute dispersion, we perform extensive ensemble averaged simulation s to test theoretical predictions on the dispersion dependence on simp le geometrical parameters. We observe the expected quadratic dispersio n coefficient dependence on both the mean aperture and the relative sh ift of the crack as of well as the anomalous dispersion dependence on tracer traveling distance. We also characterize the anisotropy of the dispersion front, which progressively wrinkles into a self-affine curv e whose exponent is equal to that of the fracture surface.