Research Papers: Petroleum Engineering

An Analytical Solution for Microannulus Cracks Developed Around a Wellbore

[+] Author and Article Information
Arash Dahi Taleghani

Craft and Hawkins Department of
Petroleum Engineering,
Louisiana State University,
Baton Rouge, LA 70808
e-mail: a_dahi@lsu.edu

Denis Klimenko

Craft and Hawkins Department of
Petroleum Engineering,
Louisiana State University
Baton Rouge, LA 70808

1Corresponding author.

Contributed by the Petroleum Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received January 15, 2015; final manuscript received May 5, 2015; published online June 2, 2015. Editor: Hameed Metghalchi.

J. Energy Resour. Technol 137(6), 062901 (Nov 01, 2015) (8 pages) Paper No: JERT-15-1018; doi: 10.1115/1.4030627 History: Received January 15, 2015; Revised May 05, 2015; Online June 02, 2015

In situations like blowout or hydraulic fracturing, excessive fluid pressure may cause leaking in the casing in shallower parts of the formation. The resulting high pressure may form a cylindrical crack around the wellbore. An analytical solution for stress distribution and displacement along a cylindrical crack formed between the casing and the formation is provided in this paper. The crack is assumed to be opened by uniform fluid pressure exerted on both sides of the crack. This solution has a wide range of applications from failure analysis of fibers in manufacturing composite materials to wellbore integrity in petroleum and subsurface engineering problems.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Benson, S. M., and Cole, D. R., 2008, “CO2 Sequestration in Deep Sedimentary Formations,” Elements, 4(5), pp. 325–331. [CrossRef]
Dahi Taleghani, A., 2013, “An Improved Closed-Loop Heat Extraction Method From Geothermal Resources,” ASME J. Energy Resour. Technol., 135(4), p. 042904. [CrossRef]
Crow, W. L., Anderson, E. P., and Minugh, E., 1985, “Subsurface Venting of Hydrocarbon Vapors From an Underground Aquifer: Final Report,” American Petroleum Institute, Washington, DC, Publication No. 4410.
Shojaei, A., Dahi Taleghani, A., and Li, G., 2014, “A Continuum Damage Failure Model for Hydraulic Fracturing of Porous Rocks,” Int. J. Plast., 59, pp. 199–212. [CrossRef]
Wang, W., and Dahi Taleghani, A., 2014, “Cement Sheath Integrity During Hydraulic Fracturing; an Integrated Modeling Approach,” SPE Hydraulic Fracturing Technology Conference, The Woodlands, TX, Feb. 4–6, Paper No. SPE-168642-MS. [CrossRef]
Grace, R. D., 2003, Blowout and Well Control Handbook, Elsevier Science.
Ekbote, S., Abousleiman, Y., Cui, L., and Zaman, M., 2004, “Analyses of Inclined Boreholes in Poroelastic Media,” Int. J. Geomech., 4(3), pp. 178–190. [CrossRef]
Chen, S., Abousleiman, Y., and Muraleetharan, K., 2012, “Closed-Form Elastoplastic Solution for the Wellbore Problem in Strain Hardening/Softening Rock Formations,” Int. J. Geomech., 12(4), pp. 494–507. [CrossRef]
Thorsen, K., 2013, “Analytical Failure Prediction of Inclined Boreholes,” Int. J. Geomech., 13(3), pp. 318–325. [CrossRef]
Wang, W., and Dahi Taleghani, A., 2014, “Three-Dimensional Analysis of Cement Sheath Integrity Around Wellbores,” J. Pet. Sci. Eng., 121, pp. 38–51. [CrossRef]
Goodwin, K. J., and Crook, R. J., 1992, “Cement Sheath Stress Failure,” SPE Drill. Eng., 7(4), pp. 291–296. [CrossRef]
Kutchko, B. G., Strazisar, B. R., Dzombak, D. A., Lowry, G. V., and Thaulow, N., 2007, “Degradation of Well Cement by CO2 Under Geologic Sequestration Conditions,” Environ. Sci. Technol., 41(13), pp. 4787–4792. [CrossRef] [PubMed]
Van der Kuip, M. D. C., Benedictus, T., Wildgust, N., and Aiken, T., 2011, “High-Level Integrity Assessment of Abandoned Wells,” Energy Procedia, 4, pp. 5320–5326. [CrossRef]
Bois, A. P., Garnier, A., Rodot, F., Saint-Marc, J., and Aimard, N., 2011, “How to Prevent Loss of Zonal Isolation Through a Comprehensive Analysis of Microannulus Formation,” SPE Drill. Completion, 26(1), pp. 13–31. [CrossRef]
Ozbek, T., and Erdogan, F., 1969, “Some Elasticity Problems in Fiber-Reinforced Composites With Imperfect Bonds,” Int. J. Eng. Sci., 7(9), pp. 931–946. [CrossRef]
Erdogan, F., and Ozbek, T., 1969, “Stresses in Fiber-Reinforced Composites With Imperfect Bonding,” ASME J. Appl. Mech., 36(4), pp. 865–869. [CrossRef]
Martynenko, M. A., and Ulitko, A. F., 1982, “Solution of the Axisymmetric Problem for Elastic Body With a Cylindrical Crack,” Akademiia Nauk Ukrains'koi RSR, Dopovida Seriia A—Fiskio-Matematichni ta Tekhnichni Nauk10, pp. 43–46.
Antipov, Y. A., 2001, “Solution by Quadratures of the Problem of a Cylindrical Crack by the Method of Matrix Factorization,” IMA J. Appl. Math., 66(6), pp. 591–619. [CrossRef]
Budyansky, B., Hutchinson, J. W., and Evans, A. G., 1986, “Matrix Fracture in Fibre-Reinforced Ceramics,” J. Mech. Phys. Solids, 34(2), pp. 167–189. [CrossRef]
Farris, T. N., Kokini, K., and Demir, I., 1989, “The Cylindrical Crack,” ASME J. Appl. Mech., 56(4), pp. 981–983. [CrossRef]
Freund, L. B., 1992, “The Axial Force Needed to Slide a Circular Fiber Along a Hole in an Elastic Material and Implications for Fiber Pull-Out,” Eur. J. Mech. A/Solids, 11(1), pp. 1–19.
Antipov, Y. A., Movchan, A. B., and Movchan, N. V., 2000, “Frictional Contact of a Fibre and an Elastic Solid,” J. Mech. Phys. Solids, 48(6–7), pp. 1413–1439. [CrossRef]
Green, A. E., 1949, “On Boussinesq's Problem and Penny-Shaped Cracks,” Proc. Cambridge Phil. Soc., 45(2), pp. 251–257. [CrossRef]
Sneddon, I. N., 1965, “A Note on the Problem of the Penny-Shaped Crack,” Proc. Cambridge Phil. Soc., 61(2), pp. 609–611. [CrossRef]
Wang, X. Y., Li, L. K. Y., Mai, Y. W., and Shen, Y. G., 2008, “Theoretical Analysis of Hertzian Contact Fracture: Ring Crack,” Eng. Fract. Mech., 75(14), pp. 4247–4256. [CrossRef]
Gordeliy, E., Piccinin, R., Napier, J. A., and Detournay, E., 2013, “Axisymmetric Benchmark Solutions in Fracture Mechanics,” Eng. Fract. Mech., 102, pp. 348–357. [CrossRef]
Itou, S., 1990, “Stresses Around a Cylindrical Interface Crack Under Shear,” Eng. Fract. Mech., 36(4), pp. 631–638. [CrossRef]
Han, X. L., and Wang, D., 1996, “The Crack Problem of a Fiber–Matrix Composite With a Nonhomogeneous Interfacial Zone Under Torsional Loading—Part I. A Cylindrical Crack in the Interfacial Zone,” Eng. Fract. Mech., 54(1), pp. 63–69. [CrossRef]
Itou, S., and Shima, Y., 1999, “Stress Intensity Factors Around a Cylindrical Crack in an Interfacial Zone in Composite Materials,” Int. J. Solid Struct., 36(5), pp. 586–698. [CrossRef]
Itou, S., 2005, “Stress Intensity Factors for a Moving Cylindrical Crack in a Nonhomogeneous Cylindrical Layer in Composite Materials,” Arch. Appl. Mech., 75(1), pp. 18–30. [CrossRef]
Korsunsky, A. M., 1994, “The Solution of Axisymmetric Crack Problems in Inhomogeneous Media,” Ph.D. thesis, University of Oxford, Oxford, UK.
Korsunsky, A. M., 1995, “Fundamental Eigenstrain Solutions for Axisymmetric Crack Problems,” J. Mech. Phys. Solids, 43(8), pp. 1221–1241. [CrossRef]
Cotterell, B., and Rice, J. R., 1980, “Slightly Curved or Kinked Cracks,” Int. J. Fract., 16(2), pp. 155–169. [CrossRef]
Gao, H., 1992, “Three-Dimensional Slightly Nonplanar Cracks,” ASME J. Appl. Mech., 59(2), pp. 335–343. [CrossRef]
Movchan, A. B., Gao, H., and Willis, J. R., 1998, “On Perturbations of Plane Cracks,” Int. J. Solids Struct., 35(26–27), pp. 3419–3453. [CrossRef]
Obrezanova, O., Movchan, A. B., and Willis, J. R., 2002, “Dynamic Stability of a Propagating Crack,” J. Mech. Phys. Solids, 50(12), pp. 2637–2668. [CrossRef]
Sneddon, I. N., 1995, Fourier Transforms, Courier Dover Publications, New York.
Sokolnikoff, I. S., 1956, A Treatise on the Mathematical Theory of Elasticity, (English translation by N. M. Queen, Overseas Publisher Association, Amsterdam) McGraw-Hill Publishing Company, New York.
Prudnikov, A. P., Brychkov, I. A., and Maričev, O. I., 1986, Integrals and Series: Special Functions, Vol. 2, Taylor & Francis.
Yau, W. F., 1967, “Axisymmetric Slipless Indentation of an Infinite, Elastic Cylinder,” SIAM J. Appl. Math., 15(1), pp. 219–227. [CrossRef]


Grahic Jump Location
Fig. 1

A schematic picture of fluid migration outside the casing is shown in the right picture. Left pictures show different mechanisms for failure initiation in small scale: (a) radial cracking, (b) debonding or delamination crack between cement and casing, (c) delamination crack between casing and cement, and (d) channelization inside cement is marked in thick lines.

Grahic Jump Location
Fig. 2

The cylindrical crack is located at distance R from the tube centerline with the length equal to 2a

Grahic Jump Location
Fig. 3

Radial (a) and vertical (b) displacements calculated using the provided solution are compared with finite element solutions shown by dots

Grahic Jump Location
Fig. 4

Radial and vertical displacements for two cylindrical cracks (short and long) are demonstrated




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In