Research Papers

Toughness-Dominated Hydraulic Fracture in Permeable Rocks

[+] Author and Article Information
Xuelin Dong

Key Laboratory of Petroleum Engineering,
China University of Petroleum,
18# Fuxue Road,
Changping District,
Beijing 102249, China
e-mail: dongxl@cup.edu.cn

Guangqing Zhang

Key Laboratory of Petroleum Engineering,
China University of Petroleum,
18# Fuxue Road,
Changping District,
Beijing 102249, China
e-mail: zhang@263.com

Deli Gao

Key Laboratory of Petroleum Engineering,
China University of Petroleum,
18# Fuxue Road,
Changping District,
Beijing 102249, China
e-mail: gaodeli@cast.org.cn

Zhiyin Duan

Beijing Key Lab of Heating,
Gas Supply, Ventilating and
Air Conditioning Engineering,
Beijing University of
Civil Engineering and Architecture,
1# Zhanlanguan Road,
Xicheng District,
Beijing 100044, China
e-mail: duanzhiyin@bucea.edu.cn

1Corresponding author.

Manuscript received February 28, 2017; final manuscript received April 2, 2017; published online April 28, 2017. Editor: Yonggang Huang.

J. Appl. Mech 84(7), 071001 (Apr 28, 2017) (8 pages) Paper No: JAM-17-1115; doi: 10.1115/1.4036475 History: Received February 28, 2017; Revised April 02, 2017

A solution to the problem of a hydraulic fracture driven by an incompressible Newtonian fluid at a constant injection rate in a permeable rock is presented in this paper. A set of governing equations are formed to obtain the fracture half-length, crack opening, and net fluid pressure. The solution is derived under the assumptions of plane strain, zero lag between fluid front and crack tip, followed by negligible fluid viscosity. The last assumption is related to a toughness-dominated fracture propagation regime therefore leading to a uniform fluid pressure along the crack surface. Early-time and late-time asymptotic solutions are obtained, which correspond to both regimes when the fluid contains within the crack and most of the injected fluid infiltrates into the rock, respectively. It is shown that these asymptotic solutions are in a simple form when the fracture propagation is dominated by the material toughness. The transient solution for the evolution from the early time to the late time is also obtained by a numerical method.

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Fig. 1

Schematic of a hydraulic fracture propagating in a permeable rock

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Fig. 6

The treatment efficiency loss with the time deduced by the asymptotic solutions and transient solution

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Fig. 3

Fracture opening profiles at different times: (a) the storage solution and transient solution and (b) the leak-off solution and transient solution (see figure online for color)

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Fig. 4

The fracture half-length variation with time from the asymptotic solutions and transient solution

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Fig. 2

The crack half-length evolution with the leak-off parameter from the storage solution (see figure online for color)

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Fig. 5

The evolution of the net pressure from the asymptotic solutions and transient solution




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