Based on the KGD scheme, this paper investigates, with both analytical and numerical approaches, the propagation of a hydraulic fracture with a fluid lag in permeable rock. On the analytical aspect, the general form of normalized governing equations is first formulated to take into account both fluid lag and leak-off during the process of hydraulic fracturing. Then a new self-similar solution corresponding to the limiting case of zero dimensionless confining stress () and infinite dimensionless leak-off coefficient () is obtained. A dimensionless parameter is proposed to indicate the propagation regimes of hydraulic fracture in more general cases, where is defined as the ratio of the two time-scales related to the dimensionless confining stress and the dimensionless leak-off coefficient . In addition, a robust finite element-based KGD model has been developed to simulate the transient process from to under , and the numerical solutions converge and agree well with the self-similar solution at and . More general processes from and to and for three different values of are also simulated, which proves the effectiveness of the proposed dimensionless parameter for indicating fracture regimes.
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September 2018
Research-Article
Propagation of a Plane Strain Hydraulic Fracture With a Fluid Lag in Permeable Rock
B. Chen,
B. Chen
Energy Safety Research Institute,
College of Engineering,
Swansea University Bay Campus,
Swansea SA1 8EN, UK;
Zienkiewicz Centre for Computational
Engineering, College of Engineering,
Swansea University Bay Campus,
Swansea SA1 8EN, UK
College of Engineering,
Swansea University Bay Campus,
Swansea SA1 8EN, UK;
Zienkiewicz Centre for Computational
Engineering, College of Engineering,
Swansea University Bay Campus,
Swansea SA1 8EN, UK
Search for other works by this author on:
Andrew R. Barron,
Andrew R. Barron
Energy Safety Research Institute,
College of Engineering,
Swansea University Bay Campus,
Swansea SA1 8EN, UK;
Department of Chemistry,
Rice University,
Houston, TX 77005;
Department of Materials Science and
Nanoengineering,
Rice University,
Houston, TX 77005
College of Engineering,
Swansea University Bay Campus,
Swansea SA1 8EN, UK;
Department of Chemistry,
Rice University,
Houston, TX 77005;
Department of Materials Science and
Nanoengineering,
Rice University,
Houston, TX 77005
Search for other works by this author on:
D. R. J. Owen,
D. R. J. Owen
Zienkiewicz Centre for Computational
Engineering,
College of Engineering,
Swansea University Bay Campus,
Swansea SA1 8EN, UK
Engineering,
College of Engineering,
Swansea University Bay Campus,
Swansea SA1 8EN, UK
Search for other works by this author on:
Chen-Feng Li
Chen-Feng Li
Energy Safety Research Institute,
College of Engineering,
Swansea University Bay Campus,
Swansea SA1 8EN, UK;
Zienkiewicz Centre for Computational
Engineering, College of Engineering,
Swansea University Bay Campus,
Swansea SA1 8EN, UK;
Department of Chemistry,
Rice University,
Houston, TX 77005;
Department of Materials Science
and Nanoengineering,
Rice University,
Houston, TX 77005
e-mail: c.f.li@swansea.ac.uk
College of Engineering,
Swansea University Bay Campus,
Swansea SA1 8EN, UK;
Zienkiewicz Centre for Computational
Engineering, College of Engineering,
Swansea University Bay Campus,
Swansea SA1 8EN, UK;
Department of Chemistry,
Rice University,
Houston, TX 77005;
Department of Materials Science
and Nanoengineering,
Rice University,
Houston, TX 77005
e-mail: c.f.li@swansea.ac.uk
Search for other works by this author on:
B. Chen
Energy Safety Research Institute,
College of Engineering,
Swansea University Bay Campus,
Swansea SA1 8EN, UK;
Zienkiewicz Centre for Computational
Engineering, College of Engineering,
Swansea University Bay Campus,
Swansea SA1 8EN, UK
College of Engineering,
Swansea University Bay Campus,
Swansea SA1 8EN, UK;
Zienkiewicz Centre for Computational
Engineering, College of Engineering,
Swansea University Bay Campus,
Swansea SA1 8EN, UK
Andrew R. Barron
Energy Safety Research Institute,
College of Engineering,
Swansea University Bay Campus,
Swansea SA1 8EN, UK;
Department of Chemistry,
Rice University,
Houston, TX 77005;
Department of Materials Science and
Nanoengineering,
Rice University,
Houston, TX 77005
College of Engineering,
Swansea University Bay Campus,
Swansea SA1 8EN, UK;
Department of Chemistry,
Rice University,
Houston, TX 77005;
Department of Materials Science and
Nanoengineering,
Rice University,
Houston, TX 77005
D. R. J. Owen
Zienkiewicz Centre for Computational
Engineering,
College of Engineering,
Swansea University Bay Campus,
Swansea SA1 8EN, UK
Engineering,
College of Engineering,
Swansea University Bay Campus,
Swansea SA1 8EN, UK
Chen-Feng Li
Energy Safety Research Institute,
College of Engineering,
Swansea University Bay Campus,
Swansea SA1 8EN, UK;
Zienkiewicz Centre for Computational
Engineering, College of Engineering,
Swansea University Bay Campus,
Swansea SA1 8EN, UK;
Department of Chemistry,
Rice University,
Houston, TX 77005;
Department of Materials Science
and Nanoengineering,
Rice University,
Houston, TX 77005
e-mail: c.f.li@swansea.ac.uk
College of Engineering,
Swansea University Bay Campus,
Swansea SA1 8EN, UK;
Zienkiewicz Centre for Computational
Engineering, College of Engineering,
Swansea University Bay Campus,
Swansea SA1 8EN, UK;
Department of Chemistry,
Rice University,
Houston, TX 77005;
Department of Materials Science
and Nanoengineering,
Rice University,
Houston, TX 77005
e-mail: c.f.li@swansea.ac.uk
1Corresponding author.
Manuscript received February 22, 2018; final manuscript received May 13, 2018; published online June 14, 2018. Editor: Yonggang Huang.
J. Appl. Mech. Sep 2018, 85(9): 091003 (10 pages)
Published Online: June 14, 2018
Article history
Received:
February 22, 2018
Revised:
May 13, 2018
Citation
Chen, B., Barron, A. R., Owen, D. R. J., and Li, C. (June 14, 2018). "Propagation of a Plane Strain Hydraulic Fracture With a Fluid Lag in Permeable Rock." ASME. J. Appl. Mech. September 2018; 85(9): 091003. https://doi.org/10.1115/1.4040331
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