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Statistical Analysis of Fracture-Length Distribution Sampled Under the Truncation and Censoring Effects

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Abstract

The present paper addresses statistical analysis and estimation of fracture-length distributions at scales influenced by the truncation and censoring effects. The computational method employed here uses fracture-length distributions of a given set of measurements and information about observational constraints (i.e., window of observation) to estimate the probability density of the truncated and censored parts of fracture data sets. The results are benchmarked against power-law based maximal likelihood estimations commonly used for the same purpose. The relationship between the accuracy of estimates and size of the window of observation is studied. The utility of employing statistical models with arbitrary probability distributions of fracture lengths in order to provide a valid statistical model approximation is also considered. A verification of the suggested approximation using the Kolmogorov–Smirnov test applied to truncated and censored data is proposed. Numerical computations show that the proposed method can represent an essential improvement compared to other commonly employed techniques.

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Acknowledgments

The financial support from Statoil-VISTA, research cooperation between the Norwegian Academy of Science and Letters and Statoil is acknowledged. The research was carried out as part of the Impact of Fault Envelope Architecture on Reservoir Fluid Flow Project at Centre for Integrated Petroleum Research (Uni CIPR), Uni Research. We acknowledge partial support from RFBR (grant no. 14-05-93090 Norv_a ) and NORRUSS programme of the Norwegian Research Council. The authors are grateful to two anonymous reviewers for their constructive comments on the earlier version of the manuscript.

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Correspondence to Dmitriy Kolyukhin.

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Kolyukhin, D., Tveranger, J. Statistical Analysis of Fracture-Length Distribution Sampled Under the Truncation and Censoring Effects. Math Geosci 46, 733–746 (2014). https://doi.org/10.1007/s11004-013-9517-7

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  • DOI: https://doi.org/10.1007/s11004-013-9517-7

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