Estimating the Effect of Fractal Dimension on Representative Elementary Volume of Randomly Distributed Rock Fracture Networks

The effect of fractal dimension (D-f ) on the determination of representative elementary volume (REV) was investigated through numerical experimentations, in which a new method was adopted to extract submodels that have different length-width ratios from original discrete facture networks (DFNs). Fluid flow in 1610 DFNs with different geometric characteristics of fractures and length-width ratios was simulated, and the equivalent permeability was calculated. The results show that the average equivalent permeability (K-REv ) at the REV size for DFNs increases with the increase in D-f . The K-REv shows a downward trend with increasing length-width ratio of the submodel. A strong exponent functional relationship is found between the REV size and D-f . The REV size decreases with increasing D-f . With the increment of the length-width ratio of submodels, the REV size shows a decreasing trend. The effects of length-width ratio and D f on the REV size can he negligible when D-f >= 1.5, but are significant when D-f < 1.5.