Fractal and multifractal characterization of stochastic fracture networks and real outcrops
Type
ArticleKAUST Department
Energy Resources & Petroleum EngineeringPhysical Science and Engineering (PSE) Division
Energy Resources and Petroleum Engineering Program
Ali I. Al-Naimi Petroleum Engineering Research Center (ANPERC)
Date
2022-01Submitted Date
2021-05-13Permanent link to this record
http://hdl.handle.net/10754/675030
Metadata
Show full item recordAbstract
The fractal dimension and multifractal spectrum are widely used to characterize the complexity of natural fractures. However, systematic investigations, considering impacts of different fracture geometrical properties (fracture lengths, orientations, center positions) and system sizes, on the fractal and multifractal characterization of complex fracture networks are insufficient. Here, we utilize an in-house developed DFN modeling software, hatchfrac, to construct stochastic fracture networks with prescribed distributions and systematically study the impact of three geometrical properties of fractures and system sizes on the fractal and multifractal characterization. We calculate the single fractal dimension and multifractal spectrum with the box-counting method. The single fractal dimension, D, and the difference of singularity exponent, Δα, are used to represent the fractal and multifractal patterns, respectively. We find that fracture lengths, orientations and system sizes positively correlate with D and Δα, while the system size has the most significant impact among the four parameters. D is uncorrelated with fracture positions (FD), which means that a single fractal dimension cannot capture the complexity caused by clustering effects. However, Δα has a strong negative correlation with FD, implying that clustering effects make fracture networks more complex, and Δα can capture the difference. We also digitize 80 outcrop maps with a novel fracture detection algorithm and calculate their fractal dimension and multifractal spectrum. We find wide variations of D and Δα on those outcrop maps, even for outcrops at similar scales, indicating that a universal indicator for characterizing fracture networks at different scales or the same scale is almost impossible. D and Δα have negligible correlations with scales, supporting the self-similarity patterns of natural fracture networks.Citation
Zhu, W., Lei, G., He, X., Patzek, T. W., & Wang, M. (2022). Fractal and multifractal characterization of stochastic fracture networks and real outcrops. Journal of Structural Geology, 104508. doi:10.1016/j.jsg.2021.104508Sponsors
This project was supported by the National Key Research and Development Program of China (No. 2019YFA0708704). The authors would like to thank all editors and anonymous reviewers for their comments and suggestions.Publisher
Elsevier BVJournal
Journal of Structural GeologyAdditional Links
https://linkinghub.elsevier.com/retrieve/pii/S0191814121002327ae974a485f413a2113503eed53cd6c53
10.1016/j.jsg.2021.104508