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Research Papers

Crack Tunneling in Cement Sheath of Hydrocarbon Well

[+] Author and Article Information
Zhengjin Wang

State Key Laboratory for Strength and
Vibration of Mechanical Structures,
International Center for Applied Mechanics,
School of Aerospace Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China;
School of Engineering and Applied Sciences,
Kavli Institute for Nanobio Science and Technology,
Harvard University,
Cambridge, MA 02138

Yucun Lou

Schlumberger-Doll Research,
One Hampshire Street,
Cambridge, MA 02139

Zhigang Suo

School of Engineering and Applied Sciences,
Kavli Institute for Nanobio
Science and Technology,
Harvard University,
Cambridge, MA 02138
e-mail: suo@seas.harvard.edu

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received September 17, 2015; final manuscript received September 21, 2015; published online October 8, 2015. Editor: Yonggang Huang.

J. Appl. Mech 83(1), 011002 (Oct 08, 2015) (7 pages) Paper No: JAM-15-1504; doi: 10.1115/1.4031649 History: Received September 17, 2015; Revised September 21, 2015

In a hydrocarbon well, cement fills the annular gap between two steel casings or between a steel casing and rock formation, forming a sheath that isolates fluids in different zones of the well. For a well as long as several kilometers, the cement sheath covers a large area and inevitably contains small cracks. The cement sheath fails when a small crack grows and tunnels through the length of the well. We calculate the energy release rate at a steady-state tunneling front as a function of the width of the tunnel. So long as the maximum energy release rate is below the fracture energy of the cement, tunnels of any width will not form. This failsafe condition requires no measurement of small cracks, but depends on material properties and loading conditions. We further show that the critical load for tunneling reduces significantly if the cement/casing and cement/formation interfaces slide.

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Figures

Grahic Jump Location
Fig. 1

A crack tunnel in a cement sheath. (a) A cross section along the length of a well. A cement sheath fills the gap between a steel casing and rock formation. A crack tunnel in the cement sheath. (b) A cross section normal to the well, far ahead the tunnel front. The pressure inside the steel casing causes a stress field in the cement sheath. (c) A cross section normal to the well, far behind the tunnel front. The pressure inside the steel casing causes the crack to open in the cement.

Grahic Jump Location
Fig. 2

The energy release rate of a steady-state tunneling crack is a function of the width of the tunnel, G(h). (a) In some cases, the energy release rate reaches maximum Gmax when the width of the tunnel is less than the thickness of the cement sheath. (b) In other cases, the energy release rate monotonically increases with the width of the tunnel.

Grahic Jump Location
Fig. 3

The normalized energy release rate as a function of the normalized width of the tunnel: (a) νc=0.2 and (b) νc=0.4

Grahic Jump Location
Fig. 4

Two regions exist on the plane with axes of the normalized Young's modulus and normalized fracture energy of the cement: (a) νc = 0.2 and (b) νc = 0.4

Grahic Jump Location
Fig. 5

The correlation between the fracture energy and elasticmodulus of cement. The constant coefficient values arespecified as νc = 0.2, Ef = 20 GPa, νf = 0.2, Rc = 80 mm, and Rb = 100 mm.

Grahic Jump Location
Fig. 6

The effect of interfacial sliding on energy release rate. (a) Four interfacial conditions. Each interface is either well-bonded or capable of frictionless sliding. The energy release rates as functions of Young's modulus of the cement for the four interfacial conditions for (b) νc = 0.2 and (c) νc = 0.4.

Grahic Jump Location
Fig. 7

The effect of friction on the energy release rate. The modulus ratio of cement Ec/Ef = 0.5. Poisson's ratios for the cement are chosen as: (a) νc=0.2 and (b) νc=0.4.

Grahic Jump Location
Fig. 8

The hoop stress, σθ, in the cement sheath when p = 50 MPa, Ef = 20 GPa, νf = 0.2, Rc = 80 mm, ts = 10 mm, and Rb = 100 mm: (a) νc = 0.2 and (b) νc = 0.4

Grahic Jump Location
Fig. 9

Finite-element model for cement sheath: (a) meshed symmetric model, (b) refined mesh near the crack, and (c) characteristic of the contour integrals around the crack tip

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