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

Abstract EN

The effect of fractal dimension (Df) 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 (KREV) at the REV size for DFNs increases with the increase in Df.

The KREV shows a downward trend with increasing length-width ratio of the submodel.

A strong exponent functional relationship is found between the REV size and Df.

The REV size decreases with increasing Df.

With the increment of the length-width ratio of submodels, the REV size shows a decreasing trend.

The effects of length-width ratio and Df on the REV size can be negligible when Df≥1.5, but are significant when Df<1.5.