INVERSE ESTIMATION OF SURFACE FRACTAL DIMENSION AND APERTURE WIDTH FOR ROCK FRACTURES FROM SPONTANEOUS IMBIBITION MEASUREMENTS

Spontaneous imbibition has been shown to be markedly faster in fractured porous media than in the surrounding matrix. Differences in fracture imbibition rates are influenced by the fracture width and overall roughness of the fracture surface. Fractal dimensions are an excellent way to characterize surface roughness across multiple scales. In the present study, we derive a theoretical model for early-time spontaneous imbibition (i.e., ignoring gravity) of a wetting fluid that allows for the inverse estimation of fracture surface fractal dimensions and mean aperture widths. The model was tested using previously published data for the spontaneous imbibition of water into four initially dry fractured Berea sandstone cores of varying permeability. The data were collected using dynamic neutron radiography at ORNL’s Neutron Imaging Facility (beam line CG-1D, HFIR). The theoretical model was fitted to the experimental data using non-linear least squares regression. Analyses for three of the four cores investigated yielded surface fractal dimensions with values between two and three, providing plausible characterization of multi-scale fracture surface roughness. The estimated mean fracture aperture widths compared favorably with independent measurements from image analysis. The proposed model is physically-based and could be useful in applications as diverse as the deep disposal of hazardous wastes, caprock integrity, and leak-off in hydraulic fracturing operations.