Characterization of macro-scale heterogeneity and homogeneity of porous media employing fractal geometry

Previous study in fractal geometry has demonstrated that porous media can be characterized in terms of a fractal exponent, β. It is found that for β −100, the porous media approaches homogeneity. Increasing values of β up to −1 infer increasingly heterogeneous porous media. β can be obtained by a type curve matching procedure. This is accomplished by plotting the dimensionless concentration against dimensionless time and then compared with the curves from the approximate analytical solution to obtain the best fit curve. From this work, it has been verified that the assumption of constant dispersion coefficient is only valid for porous media that exhibits very small values of β (approaching homogeneity). In this work, the concentration profile of invading fluids is consistent with previous investigation by Ogata and Banks when β −100 or K(tD) 0.010. It also supports the work of Ogata and Banks when tD is relatively long for smaller range of fractal exponent.