Fractal aspects of miscible displacement in rough fractures: An experimental approach

Experiments were performed to study the effect of fracture surface roughness on fluid distribution during miscible displacement. The transparent replicas of single fractures obtained from seven different rocks were prepared and the surface roughness of each sample was described by fractal dimensions using the variogram, power spectral, and triangular prism (TP) techniques. Then, the effect of flow rate and viscosity on the geometry of the displacement front during miscible radial injection was investigated experimentally. The fractal dimensions of the fronts were obtained using box counting fractal analysis at different time lapses. The fractal values of invasion front varied from lithology to lithology, due to different surface roughnesses controlled by the lithology of the rocks. Although fluctuations of fractal values were observed during the growth of the front, fractal dimensions typically yielded an increasing trend. Fractal dimension became more stable with increasing flow rate and developed modestly with increasing viscosity. Finally, relationships between the fractal dimensions of displacement fronts and fracture surfaces were quantitatively analyzed and correlated in order to improve the prediction of fluid distribution within a single fracture during miscible displacement. Overall, correlations were observed between the surface characteristics and front fractal dimension values with some exceptions. In summary, to determine the probable distribution of miscible fluid and development of the front, all parameters except power spectral density (PSD) fractal dimension can be applied in the case of high viscosity ratios. In the case of low injection rates, TP could be applicable. No fractal behavior was present at extreme injection and low viscosity ratios, thus no correlation can be determined for the miscible displacement.