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    Fractal and multifractal characterization of stochastic fracture networks and real outcrops

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    Type
    Article
    Authors
    Zhu, Weiwei cc
    Lei, Gang cc
    He, Xupeng cc
    Patzek, Tadeusz cc
    Wang, Moran
    KAUST Department
    Energy Resources & Petroleum Engineering
    Physical Science and Engineering (PSE) Division
    Energy Resources and Petroleum Engineering Program
    Ali I. Al-Naimi Petroleum Engineering Research Center (ANPERC)
    Date
    2022-01
    Submitted Date
    2021-05-13
    Permanent link to this record
    http://hdl.handle.net/10754/675030
    
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    Abstract
    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.2021.104508
    Sponsors
    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 BV
    Journal
    Journal of Structural Geology
    DOI
    10.1016/j.jsg.2021.104508
    10.1002/essoar.10508400.1
    Additional Links
    https://linkinghub.elsevier.com/retrieve/pii/S0191814121002327
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.jsg.2021.104508
    Scopus Count
    Collections
    Articles; Energy Resources and Petroleum Engineering Program; Ali I. Al-Naimi Petroleum Engineering Research Center (ANPERC); Physical Science and Engineering (PSE) Division

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