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Abstract <p>The mathematical statement and efficient high-speed algorithm for solving the inverse problem of interpreting tracer studies of the lengths of fractures of multistage hydraulic fracturing (MHF) are given. The case of fractures of infinite permeability is considered. Solving the forward problem requires numerical modeling a multicomponent flow. To reduce computational costs, the spatial problem is decomposed into a set of problems of reduced dimension along the stream’s tubes. At a high level of accuracy, such a model reduces the computer calculation time by two orders of magnitude. A stable algorithm for solving the inverse problem is presented. An evaluation of the sensitivity of the quasi-solution of the problem to measurement error is given.</p>

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Determination of the Length of Fractures in Multistage Hydraulic Fracturing Using the Streamtube Model

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • K. A. Potashev,
  • A. A. Uraimov,
  • A. B. Mazo

摘要

Abstract

The mathematical statement and efficient high-speed algorithm for solving the inverse problem of interpreting tracer studies of the lengths of fractures of multistage hydraulic fracturing (MHF) are given. The case of fractures of infinite permeability is considered. Solving the forward problem requires numerical modeling a multicomponent flow. To reduce computational costs, the spatial problem is decomposed into a set of problems of reduced dimension along the stream’s tubes. At a high level of accuracy, such a model reduces the computer calculation time by two orders of magnitude. A stable algorithm for solving the inverse problem is presented. An evaluation of the sensitivity of the quasi-solution of the problem to measurement error is given.