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PKN Solution Revisit: 3-D Hydraulic Fracture Size and Stress Anisotropy Effects

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Abbreviations

c :

Stress anisotropy factor

D :

Reservoir depth

E :

Young’s modulus of the rock

FEM:

Finite element method

H :

Fracture height

H r :

Reservoir thickness

L :

Fracture length

p t :

Downhole treatment pressure

PKN:

Perkins and Kern fracture

R :

Hole radius

S h :

Minimum horizontal stress

S H :

Maximum horizontal stress

S V :

Vertical stress

w max :

Maximum fracture width

w max_R :

Maximum fracture width at hole radius R

\(w_{{\hbox{max} \_S_{\text{V}} }}\) :

Maximum fracture width at maximum stress S V

w 3D_max :

Maximum fracture width for 3-D PKN

ρ :

Density of the rock

ν :

Poisson’s ratio of the rock

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Acknowledgements

This work was partially supported by the Program for Innovative Research Team in University sponsored by Ministry of Education of China (IRT-17R37), National Science Foundation of China (51774136), China National Key R&D Project (2017YFC0804108) during the 13th Five-Year Plan Period and Natural Science Foundation of Hebei Province of China (D2017508099). The authors wish to thank COMSOL Inc. to provide the Multiphysics FEM software for conducting this research.

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  1. Jincai Zhang

    Present address: Sinopec Tech Houston, Houston, TX, USA

Authors and Affiliations

  1. Geomech Energy, Houston, TX, USA

    Jincai Zhang

  2. North China Institute of Science and Technology, Yanjiao, Beijing, China

    Jincai Zhang & Shangxian Yin

  3. Wanfang College of Science and Technology, Henan Polytechnic University, Jiaozuo, Henan, China

    Yushuai Zhang

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  1. Jincai Zhang
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  2. Yushuai Zhang
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Correspondence to Jincai Zhang or Shangxian Yin.

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Zhang, J., Zhang, Y. & Yin, S. PKN Solution Revisit: 3-D Hydraulic Fracture Size and Stress Anisotropy Effects. Rock Mech Rock Eng 51, 653–660 (2018). https://doi.org/10.1007/s00603-017-1346-4

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