Experimental study of miscible displacement fronts in rough self-affine fractures

Miscible fluid displacements are studied experimentally in a radial flow between two complementary replica of a self-affine rough granite fracture surface. The displacement front between a dyed fluid and a transparent (but otherwise identical) one is followed optically through one face of the cell. The evolution of its geometry is studied as a function of time, flow-rate, and normal and lateral relative displacements between the two surfaces. For a purely normal displacement, the front is globally smooth, due to the constant local distance between surfaces. For a finite lateral displacement, the front is rough due to spatial variations of this distance; its geometry is fractal and its dimension is directly related to the Hurst exponent H approximately 0.8 of the surface. The fractal regime is observed only above a lower cut-off scale that depends on the normal spacing of the surfaces and an upper one that increases with the injected volume and with the amplitude of the lateral displacement.