Imbibition in fractally permeable media

Fractal features of permeable (e.g., porous or/and fractured) medium strongly affect the imbibition behavior in the Lucas-Washburn-like scaling regime. Mapping a spontaneous imbibition in a fractally permeable medium onto a fractal continuum flow allows us to establish the relations between the imbibition exponents and the fractal attributes of the pore-fracture network. In this way we found that the mass imbibition exponent is determined by the network topology, whereas the imbibition length exponent depends also on the geodesic metric along the imbibition streamlines. Our findings allow for the estimation of fractal attributes of natural reservoirs from the data of imbibition experiments and/or field observations, or vice versa.