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Mathematical Modeling of 3D Dynamic Processes near a Fracture Using the Schoenberg Fracture Model

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Abstract

Fractured media are important objects of investigation, because they accumulate oil. Hydraulic fracturing is of great practical interest. The exploration of such heterogeneities with the help of mathematical modeling methods makes it possible to examine different problem formulations with fractures of different forms, sizes, and other characteristics. The Schoenberg fracture model takes into account the characteristics of the fluid inside the fracture, which is utterly important in conducting seismic geological surveys. In this work, an algorithm for computing the medium parameters at the boundary of a fracture described by the Schoenberg model is developed using the grid-characteristic method. We present the results obtained by applying the developed algorithm to the solution of the problem of seismic monitoring of a hydraulic fracture, where the fracture-filling fluid is a necessary part of the investigation.

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Funding

This work was supported by the Russian Foundation for Basic Research, project no. 19-01-00281.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology (National Research University), 141701, Dolgoprudnyi, Moscow oblast, Russia

    I. B. Petrov, P. V. Stognii & N. I. Khokhlov

  2. Scientific Research Institute for System Analysis, Russian Academy of Sciences, 117218, Moscow, Russia

    I. B. Petrov & N. I. Khokhlov

Authors
  1. I. B. Petrov
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  2. P. V. Stognii
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  3. N. I. Khokhlov
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Corresponding authors

Correspondence to I. B. Petrov or P. V. Stognii.

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The authors declare that they have no conflicts of interest.

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Translated by I. Ruzanova

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Petrov, I.B., Stognii, P.V. & Khokhlov, N.I. Mathematical Modeling of 3D Dynamic Processes near a Fracture Using the Schoenberg Fracture Model. Dokl. Math. 104, 254–257 (2021). https://doi.org/10.1134/S1064562421050070

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  • DOI: https://doi.org/10.1134/S1064562421050070

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