A Critical Analysis of the Relationship Between Statistical- and Fractal-Fracture-Network Characteristics and Effective Fracture-Network Permeability

Abstract

Summary Estimation of effective fracture-network permeability (EFNP) is an essential part of modeling transport processes in naturally fractured reservoirs. A practical way of doing this is to use correlations that consider the statistical and physical characteristics of the networks. Thus, selection of the proper parameters to be characterized and/or measured that are highly correlative to the network permeability is critical. In this study, we analyzed fractal-based correlations previously developed by Jafari and Babadagli (2011a, 2011b) to clarify the physical relationship among network properties and the correlation parameters. It was shown that the connectivity index is a more-powerful parameter to rely on in permeability estimation, especially at percolation ranges far from the threshold. Also, it was of high interest to inspect the effect of physical parameters of a fracture network on different fractal dimensions as well as their positive/negative correlation with permeability to make a distinction between the mathematical and physical contributions of variables. We explained the earlier observation of Jafari and Babadagli (2009) regarding the method to determine fractal dimensions and their observed differences, which were found to be related to the computational scheme. That is why the box-counting fractal dimension gives the highest correlation compared with other fractal dimensions, especially the sandbox fractal dimension. The conditions of a strong correlation among different fractal dimensions and the scale-dependency of correlations in natural and synthetic patterns were also addressed.