Skip to main content
SpringerLink
Log in

Finite element analysis for wellbore stability of transversely isotropic rock with hydraulic-mechanical-damage coupling

  • Article
  • Published:
Science China Technological Sciences Aims and scope Submit manuscript

Abstract

The finite element analysis (FEA) technology by hydraulic-mechanical-damage (HMD) coupling is proposed in this paper for wellbore stability analysis of transversely isotropic rock, developed basing on the recently established FEA technology for isotropic rock. The finite element (FE) solutions of numerical wellbore model, damage tensor calculation and Pariseau strength criterion for transversely isotropic rock are developed for researching the wellbore failure characteristics and computing the collapse and fracture pressure of laminated rock as shale reservoirs. The classic Biot constitutive for rock as porous medium is introduced to establish a set of FE equations coupling with elastic solid deformation and seepage flow. To be in accord with the inclined wellbore situation, the coordinate transformation for global, wellbore, in-situ stress and transversely isotropic formation coordinate systems is established for describing the in-situ stress field and the results in laminated rock. To be in accord with the practical situation, a three-dimensional FE model is developed, in which several other auxiliary technologies are comprehensively utilized, e.g., the typical Weibull distribution function for heterogeneous material description and adaptive technology for mesh refinement. The damage tensor calculation technology for transversely isotropic rock are realized from the well-developed continuum damage variable of isotropic rock. The rock is subsequently developed into a novel conceptual and practical model considering the stress and permeability with the damage. The proposed method utilizing Pariseau strength criterion fully reflects the strength parameters parallel or perpendicular to bedding of the transversely isotropic rock. To this end, an effective and reliable numerically three-step FEA strategy is well established. Numerical examples are given to show that the proposed method can establish efficient and applicable FE model and be suitable for analyzing the state of pore pressure and stress surrounding wellbore, furthermore to demonstrate the effectiveness and reliability of the instability analysis of wellbore failure region and the safe mud weight computation for collapse and fracture pressure of transversely isotropic rock.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Zhuang Z, Liu Z L, Wang Y L. Fundamental theory and key mechanical problems of shale oil gas effective extraction (in Chinese). Chin Quart Mech, 2015, 33: 8–17

    Google Scholar 

  2. Lo T, Coyner K B, Toksöz M N. Experimental determination of elastic anisotropy of Berea sandstone, Chicopee shale, and Chelmsford granite. Geophys, 1986, 51: 164–171

    Article  Google Scholar 

  3. Abousleiman Y N, Hoang S K, Tran M H. Mechanical characterization of small shale samples subjected to fluid exposure using the inclined direct shear testing device. Int J Rock Mech Min Sci, 2010, 47: 355–367

    Article  Google Scholar 

  4. Yang H L, Shen R C, Fu L. Composition and mechanical properties of gas shale (in Chinese). Pet Drill Tech, 2013, 41: 31–35

    Google Scholar 

  5. Bažant Z P, Salviato M, Chau V T, et al. Why fracking works. J Appl Mech, 2014, 81: 1–10

    Google Scholar 

  6. Wu Y, Liu J, Elsworth D, et al. Dual poroelastic response of a coal seam to CO2 injection. Inter J Greenhouse Gas Control, 2010, 4: 668–678

    Article  Google Scholar 

  7. Zhang H, Liu J, Elsworth D. How sorption-induced matrix deformation affects gas flow in coal seams: A new FE model. Int J Rock Mech Min Sci, 2008, 45: 1226–1236

    Article  Google Scholar 

  8. Abousleiman Y N, Nguyen V X. Poromechanics response of inclined wellbore geometry in fractured porous media. J Eng Mech, 2005, 131: 1170–1183

    Article  Google Scholar 

  9. Nguyen V X, Abousleiman Y N. Naturally fractured reservoir three-dimensional analytical modeling: Theory and case study. In: SPE Annual Technical Conference and Exhibition. New Orleans: Society of Petroleum Engineers, 2009

    Google Scholar 

  10. Chen S L, Abousleiman Y N. Stress analysis of borehole subjected to fluid injection in transversely isotropic poroelastic medium. Mech Res Commun, 2016, 73: 63–75

    Article  Google Scholar 

  11. Hoang S, Abousleiman Y N, Ewy R T. Openhole stability and solids production simulation in emerging reservoir shale using transversely isotropic thick wall cylinders. In: SPE Annual Technical Conference and Exhibition. New Orleans: Society of Petroleum Engineers, 2009

    Google Scholar 

  12. Lu Y H, Chen M, Jin Y, et al. A mechanical model of borehole stability for weak plane formation under porous floe. Pet Sci Tech, 2012, 30: 1629–1638

    Article  Google Scholar 

  13. Roberto S R, Chaitanya D, Yi K Y. Unlocking the unconventional oil and gas reservoirs: The effect of laminated heterogeneity in wellbore stability and completion of tight gas shale reservoirs. In: Offshore Technology Conference. Offshore Technology Conference, 2009

    Google Scholar 

  14. Liang Z Z, Tang C A, Li H X, et al. A numerical study on failure process of transversely isotropic rock subjected to uniaxial compression (in Chinese). Rock Soil Mech, 2005, 26: 57–62

    Google Scholar 

  15. Xiao Y, Liu H, Desai C S, et al. Effect of intermediate principal stress ratio on particle breakage of rockfill material. J Geotech Geoenviron Eng, 2016, 142: 06015017

    Article  Google Scholar 

  16. Xiao Y, Sun Y, Hanif K F. A particle-breakage critical state model for rockfill material. Sci China Tech Sci, 2015, 58: 1125–1136

    Article  Google Scholar 

  17. Warpinski N R, Mayerhofer M J, Vincent M C, et al. Stimulating unconventional reservoirs: Maximizing network growth while optimizing fracture conductivity. J Can Pet Tech, 2009, 48: 39–51

    Article  Google Scholar 

  18. Zhuang Z, Cheng B B. A novel enriched CB shell element method for simulating arbitrary crack growth in pipes. Sci China-Phys Mech Astron, 2011, 54: 1520–1531

    Article  Google Scholar 

  19. Liao J H, Zhuang Z. A consistent projection-based SUPG/PSPG XFEM for incompressible two-phase flows. Acta Mech Sinica, 2012, 28: 1309–1322

    Article  MATH  MathSciNet  Google Scholar 

  20. Lin Z J, Zhuang Z. Enriched goal-oriented error estimation for fracture problems solved by continuum-based shell extended finite element method. Appl Math Mech, 2014, 35: 33–48

    Article  MATH  MathSciNet  Google Scholar 

  21. Zeng Q L, Liu Z L, Xu D D, et al. Modeling stationary and moving cracks in shells by X-FEM with CB shell elements. Sci China Tech Sci, 2014, 57: 1276–1284

    Article  Google Scholar 

  22. Xu D D, Liu Z L, Liu X M, et al. Modeling of dynamic crack branching by enhanced extended finite element method. Comput Mech, 2014, 54: 489–502

    Article  MATH  MathSciNet  Google Scholar 

  23. Wang T, Gao Y, Liu Z L, et al. Numerical simulations of hydraulic fracturing in large objects using an extended finite element method. J Tsinghua Uni (Sci Tech), 2014, 10: 1304–1309

    Google Scholar 

  24. Krajcinovic D, Lemaitre J. Continuum Damage Mechanics Theory and Applications. New York: Springer-Verlag, 1987

    Book  MATH  Google Scholar 

  25. Zhu W C, Bruhns O T. Simulating excavation damaged zone around a circular opening under hydromechanical conditions. Inter J Rock Mech Min Sci, 2008, 45: 815–830

    Article  Google Scholar 

  26. Lu Y L, Elsworth D, Wang L G. Microcrack-based coupled damage and flow modeling of fracturing evolution in permeable brittle rocks. Comput Geotech, 2013, 49: 226–244

    Article  Google Scholar 

  27. Wang Y L, Liu Z L, Lin S C, et al. Finite element analysis of seepage in rock based on continuum damage evolution. Eng Mech, 2016, 54: 1304–1309

    Google Scholar 

  28. Hill R. The Mathematical Theory of Plasticity. Oxford: Oxford University Press, 1950

    MATH  Google Scholar 

  29. Pariseau W G. Plasticity theory for anisotropic rocks and soils. In: The 10th U.S. Symposium on Rock Mechanics. Austin: American Rock Mechanics Association, 1968. 267–295

    Google Scholar 

  30. Biot M A. General theory of three-dimensional consolidation. J Appl Phys, 1941, 12: 155–164

    Article  MATH  Google Scholar 

  31. Biot M A. Theory of Stress-strain relations in anisotropic viscoelasticity and relaxation phenomena. J Appl Phys, 1954, 25: 1385–1391

    Article  MATH  Google Scholar 

  32. Detourmay E, Cheng A H D. Fundamentals of Poroelasticity. Oxford: Pergamon, 1993

    Google Scholar 

  33. Cheng A H D. Material coefficients of anisotropic poroelasticity. Inter J Rock Mech Min Sci, 1997, 34: 199–205

    Article  Google Scholar 

  34. Multiphysics C. COMSOL Multiphysics user’s guide. COMSOL Inc, 2010

    Google Scholar 

  35. Jean L. Coupled elasto-plasticity and damage constitutive equations. Comput Methods Appl Mech Eng, 1985, 51: 31–49

    Article  MATH  Google Scholar 

  36. Benjamin L, Jean H. Accurate numerical solutions for Drucker-Prager elastic-plastic models. Comput Methods Appl Mech Eng, 1986, 54: 259–277

    Article  MATH  MathSciNet  Google Scholar 

  37. Jaeger J C, Cook N G W. Fundamentals of Rock Mechanics. Houston: Blackwell Publishing, 1983

    Google Scholar 

  38. Krajcinovic D. Damage mechanics: Accomplishments, trends and needs. Inter J Solids Struct, 2000, 37: 267–277

    Article  MATH  MathSciNet  Google Scholar 

  39. Zhu W C, Bruhns O T. Simulating excavation damaged zone around a circular opening under hydromechanical conditions. Inter J Rock Mech Min Sci, 2008, 45: 815–830

    Article  Google Scholar 

  40. Willson S M, Last N C, Zoback M D, et al. Drilling in south America: Stability approach for complex geological conditions. In: Latin American & Caribbean Petroleum Engineering Conference. New Orleans: Society of Petroleum Engineers, 1999. 21–23

    Google Scholar 

  41. Mastin L G, Heinemann B, Krammer A, et al. Stress orientation in the KTB pilot hole determined from wellbore breakouts. Sci Drill, 1991, 2: 1–12

    Google Scholar 

  42. Cook J M, Goldsmith G, Bailey L, et al. X-ray tomographic study of the influence of bedding plane orientation on shale swelling. In: SPE Annual Technical Conference and Exhibition. New Orleans: Society of Petroleum Engineers, 1994

    Google Scholar 

  43. Lee H, Ong S H, Azeemuddin M, et al. A wellbore stability model for formations with anisotropic rock strengths. J Pet Sci Eng, 2012, 96: 109–119

    Article  Google Scholar 

  44. Lee H, Chang C, Ong S H, et al. Effect of anisotropic borehole wall failures when estimating in situ stresses: A case study in the Nankai accretionary wedge. Mar Pet Geol, 2013, 48: 411–422

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Applied Mechanics Laboratory, School of Aerospace Engineering, Tsinghua University, Beijing, 100084, China

    YongLiang Wang, ZhanLi Liu & Zhuo Zhuang

  2. Zienkiewicz Centre for Computational Engineering & Energy Safety Research Institute, College of Engineering, Swansea University, Swansea, SA2 8PP, UK

    YongLiang Wang

  3. Drilling Research Institute, China National Petroleum Corporation, Beijing, 100195, China

    HengLin Yang

Authors
  1. YongLiang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. ZhanLi Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. HengLin Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhuo Zhuang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to YongLiang Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Y., Liu, Z., Yang, H. et al. Finite element analysis for wellbore stability of transversely isotropic rock with hydraulic-mechanical-damage coupling. Sci. China Technol. Sci. 60, 133–145 (2017). https://doi.org/10.1007/s11431-016-0007-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-016-0007-3

Keywords

Search

Navigation