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Parameters Affecting the Proppant Distribution in Multiple Growing Hydraulic Fractures.

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Title: Parameters Affecting the Proppant Distribution in Multiple Growing Hydraulic Fractures.
Authors: Cheng, Shaoyi1,2,3 (AUTHOR), Wu, Bisheng1,2,3 (AUTHOR) wu046@mail.tsinghua.edu.cn, Wang, Guangjin4 (AUTHOR), Chen, Zhaowei5 (AUTHOR), Zhao, Yang1,2,3 (AUTHOR) yangzhao2021@mail.tsinghua.edu.cn, Ma, Tianshou6 (AUTHOR)
Source: Rock Mechanics & Rock Engineering. May2026, Vol. 59 Issue 5, p5543-5560. 18p.
Subject Terms: *Hydraulic fracturing, *Dimensionless numbers, *Crack propagation, *Strains & stresses (Mechanics), *Computer simulation
Abstract: The uniformity of the proppant distribution among multiple hydraulic fractures is of great importance in the production period after hydraulic fracturing treatments. To facilitate the understanding of the proppant transport along multiple hydraulic fractures, we present a numerical model predicting the proppant transport inside multiple growing hydraulic fractures. The model incorporates an empirical formula for the slurry and proppant transport to a fully coupled in-house hydraulic fracturing simulator, i.e. DeepFrac, based on the dual boundary element method and finite volume method. This model focuses on the propagation and interaction of multiple 2D plane strain fractures driven by mixture of fluid and proppant and neglects the perforation friction and proppant inertia. A bifurcation analysis is carried out to identify the dimensionless parameters that control the competitive growth of multiple hydraulic fractures. A dimensional analysis indicates that the propagation of multiple fractures and the proppant transport in these fractures are controlled by five dimensionless parameters, i.e. the dimensionless toughness, dimensionless proppant size, dimensionless time when proppant is injected, dimensionless time of gravitational settling and injected proppant concentration. The effectiveness of these dimensionless groups is verified first by numerical simulations. Then a parametric study of each dimensionless parameter is carried out to reveal their roles in the proppant distribution. The results show a strong dependence of proppant distribution on the stress interaction between fractures, which highlights the importance of the time when proppant is injected. A wider window period for the proppant entering each fracture can be obtained when K ′ < 0.4 . The ratio of two time scales is found to control the settling behavior of proppant. Severe gravitational settling of proppant can lead to an uneven proppant distribution among multiple hydraulic fractures. Highlights: A numerical model predicting the proppant transport in multiple simultaneously growing hydraulic fractures is developed. Five dimensionless parameters controlling the proppant transport behavior in multiple hydraulic fractures are deduced. The impact of the stress shadow effect, proppant size, proppant injection timing, proppant settling and proppant injection concentration on the proppant distribution is revealed. [ABSTRACT FROM AUTHOR]
Database: Energy & Power Source
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  Label: Title
  Group: Ti
  Data: Parameters Affecting the Proppant Distribution in Multiple Growing Hydraulic Fractures.
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  Label: Authors
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  Data: &lt;searchLink fieldCode=&quot;AR&quot; term=&quot;%22Cheng%2C+Shaoyi%22&quot;&gt;Cheng, Shaoyi&lt;/searchLink&gt;&lt;relatesTo&gt;1,2,3&lt;/relatesTo&gt; (AUTHOR)&lt;br /&gt;&lt;searchLink fieldCode=&quot;AR&quot; term=&quot;%22Wu%2C+Bisheng%22&quot;&gt;Wu, Bisheng&lt;/searchLink&gt;&lt;relatesTo&gt;1,2,3&lt;/relatesTo&gt; (AUTHOR)&lt;i&gt; wu046@mail.tsinghua.edu.cn&lt;/i&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;AR&quot; term=&quot;%22Wang%2C+Guangjin%22&quot;&gt;Wang, Guangjin&lt;/searchLink&gt;&lt;relatesTo&gt;4&lt;/relatesTo&gt; (AUTHOR)&lt;br /&gt;&lt;searchLink fieldCode=&quot;AR&quot; term=&quot;%22Chen%2C+Zhaowei%22&quot;&gt;Chen, Zhaowei&lt;/searchLink&gt;&lt;relatesTo&gt;5&lt;/relatesTo&gt; (AUTHOR)&lt;br /&gt;&lt;searchLink fieldCode=&quot;AR&quot; term=&quot;%22Zhao%2C+Yang%22&quot;&gt;Zhao, Yang&lt;/searchLink&gt;&lt;relatesTo&gt;1,2,3&lt;/relatesTo&gt; (AUTHOR)&lt;i&gt; yangzhao2021@mail.tsinghua.edu.cn&lt;/i&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;AR&quot; term=&quot;%22Ma%2C+Tianshou%22&quot;&gt;Ma, Tianshou&lt;/searchLink&gt;&lt;relatesTo&gt;6&lt;/relatesTo&gt; (AUTHOR)
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  Data: &lt;searchLink fieldCode=&quot;JN&quot; term=&quot;%22Rock+Mechanics+%26+Rock+Engineering%22&quot;&gt;Rock Mechanics &amp; Rock Engineering&lt;/searchLink&gt;. May2026, Vol. 59 Issue 5, p5543-5560. 18p.
– Name: Subject
  Label: Subject Terms
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  Data: *&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Hydraulic+fracturing%22&quot;&gt;Hydraulic fracturing&lt;/searchLink&gt;&lt;br /&gt;*&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Dimensionless+numbers%22&quot;&gt;Dimensionless numbers&lt;/searchLink&gt;&lt;br /&gt;*&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Crack+propagation%22&quot;&gt;Crack propagation&lt;/searchLink&gt;&lt;br /&gt;*&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Strains+%26+stresses+%28Mechanics%29%22&quot;&gt;Strains &amp; stresses (Mechanics)&lt;/searchLink&gt;&lt;br /&gt;*&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Computer+simulation%22&quot;&gt;Computer simulation&lt;/searchLink&gt;
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: The uniformity of the proppant distribution among multiple hydraulic fractures is of great importance in the production period after hydraulic fracturing treatments. To facilitate the understanding of the proppant transport along multiple hydraulic fractures, we present a numerical model predicting the proppant transport inside multiple growing hydraulic fractures. The model incorporates an empirical formula for the slurry and proppant transport to a fully coupled in-house hydraulic fracturing simulator, i.e. DeepFrac, based on the dual boundary element method and finite volume method. This model focuses on the propagation and interaction of multiple 2D plane strain fractures driven by mixture of fluid and proppant and neglects the perforation friction and proppant inertia. A bifurcation analysis is carried out to identify the dimensionless parameters that control the competitive growth of multiple hydraulic fractures. A dimensional analysis indicates that the propagation of multiple fractures and the proppant transport in these fractures are controlled by five dimensionless parameters, i.e. the dimensionless toughness, dimensionless proppant size, dimensionless time when proppant is injected, dimensionless time of gravitational settling and injected proppant concentration. The effectiveness of these dimensionless groups is verified first by numerical simulations. Then a parametric study of each dimensionless parameter is carried out to reveal their roles in the proppant distribution. The results show a strong dependence of proppant distribution on the stress interaction between fractures, which highlights the importance of the time when proppant is injected. A wider window period for the proppant entering each fracture can be obtained when K ′ &lt; 0.4 . The ratio of two time scales is found to control the settling behavior of proppant. Severe gravitational settling of proppant can lead to an uneven proppant distribution among multiple hydraulic fractures. Highlights: A numerical model predicting the proppant transport in multiple simultaneously growing hydraulic fractures is developed. Five dimensionless parameters controlling the proppant transport behavior in multiple hydraulic fractures are deduced. The impact of the stress shadow effect, proppant size, proppant injection timing, proppant settling and proppant injection concentration on the proppant distribution is revealed. [ABSTRACT FROM AUTHOR]
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1007/s00603-024-03872-z
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 18
        StartPage: 5543
    Subjects:
      – SubjectFull: Hydraulic fracturing
        Type: general
      – SubjectFull: Dimensionless numbers
        Type: general
      – SubjectFull: Crack propagation
        Type: general
      – SubjectFull: Strains & stresses (Mechanics)
        Type: general
      – SubjectFull: Computer simulation
        Type: general
    Titles:
      – TitleFull: Parameters Affecting the Proppant Distribution in Multiple Growing Hydraulic Fractures.
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          Name:
            NameFull: Cheng, Shaoyi
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            NameFull: Wu, Bisheng
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            NameFull: Wang, Guangjin
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            NameFull: Chen, Zhaowei
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            NameFull: Zhao, Yang
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            NameFull: Ma, Tianshou
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          Dates:
            – D: 01
              M: 05
              Text: May2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 07232632
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              Value: 59
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              Value: 5
          Titles:
            – TitleFull: Rock Mechanics & Rock Engineering
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