Rock Mechanics and Rock Engineering

, Volume 47, Issue 6, pp 2199–2209 | Cite as

Borehole Stability in High-Temperature Formations

  • Chuanliang Yan
  • Jingen Deng
  • Baohua Yu
  • Wenliang Li
  • Zijian Chen
  • Lianbo Hu
  • Yang Li
Original Paper


In oil and gas drilling or geothermal well drilling, the temperature difference between the drilling fluid and formation will lead to an apparent temperature change around the borehole, which will influence the stress state around the borehole and tend to cause borehole instability in high geothermal gradient formations. The thermal effect is usually not considered as a factor in most of the conventional borehole stability models. In this research, in order to solve the borehole instability in high-temperature formations, a calculation model of the temperature field around the borehole during drilling is established. The effects of drilling fluid circulation, drilling fluid density, and mud displacement on the temperature field are analyzed. Besides these effects, the effect of temperature change on the stress around the borehole is analyzed based on thermoelasticity theory. In addition, the relationships between temperature and strength of four types of rocks are respectively established based on experimental results, and thermal expansion coefficients are also tested. On this basis, a borehole stability model is established considering thermal effects and the effect of temperature change on borehole stability is also analyzed. The results show that the fracture pressure and collapse pressure will both increase as the temperature of borehole rises, and vice versa. The fracture pressure is more sensitive to temperature. Temperature has different effects on collapse pressures due to different lithological characters; however, the variation of fracture pressure is unrelated to lithology. The research results can provide a reference for the design of drilling fluid density in high-temperature wells.


High temperature Thermal effect Rock mechanics Borehole stability Drilling fluid 

List of Symbols


Cross-sectional area of the annulus


Cross-sectional area of the drill string


Cohesive force of the formation


Specific heat of drilling fluid


Specific heat of the formation


Young’s modulus


Formation porosity


Heat conduction coefficient of the formation


Coefficient of heat convection of the borehole wall


Collapse pressure


Fracture pressure


Pore pressure


Radius of the borehole


Radius of the drill string


Tensile strength of the formation


Temperature of the drilling fluid in the drill string


Mud circulating time




Far-field temperature


Temperature on the borehole wall


Drilling fluid temperature in the annulus


Formation temperature


Room temperature


Coefficient of overall heat convection of the fluid–solid interface


Uniaxial compressive strength


Uniaxial compressive strength under room temperature


Poisson’s ratio


Flow velocity of fluid in the annulus


Flow velocity of fluid in the drill string


Maximum horizontal in situ stress


Minimum horizontal in situ stress


Overburden in situ stress


Radial stress around the borehole


Axial stress around the borehole


Tangential stress around the borehole


Radial thermal stress around the borehole


Axial thermal stress around the borehole


Tangential thermal stress around the borehole


Drilling fluid density


Formation density


Biot’s coefficient


Thermal expansion coefficient

\( \phi \)

Internal friction angle of the formation


Axial strain


Radial strain


Thermal expansion strain



This work is financially supported by the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (Grant no. 51221003), the National Natural Science Foundation Project of China (Grant No.51174219), and the National Oil and Gas Major Project of China (Grant Nos. 2011ZX05009-005 and 2011ZX05026-001-01).


  1. Aadnoy BS, Chenevert ME (1987) Stability of highly inclined boreholes (includes associated papers 18596 and 18736). SPE Drill Eng 2(4):364–374CrossRefGoogle Scholar
  2. Aadnoy BS, Larson K (1989) Method for fracture-gradient prediction for vertical and inclined boreholes. SPE Drill Eng 4(2):99–103CrossRefGoogle Scholar
  3. Aadnoy BS, Ong S (2003) Introduction to special issue on borehole stability. J Petrol Sci Eng 38:79–82CrossRefGoogle Scholar
  4. Adamson K, Birch G, Gao E, Hand S, Macdonald C, Mack D, Quadri A (1993) High-pressure, high-temperature well construction. Oilfield Rev 5(2/3):15–32Google Scholar
  5. Al-Ajmi AM, Zimmerman RW (2006) Stability analysis of vertical boreholes using the Mogi–Coulomb failure criterion. Int J Rock Mech Min Sci 43:1200–1211CrossRefGoogle Scholar
  6. Al-Saeed A, Chandra R, Al-Mai N, Al-Awadi M, Dashti Q (2012) Corrosion monitoring, root cause analysis and selection criteria for future well completion design in deep HPHT sour wells. In: Proceedings of the SPE international conference and exhibition on oilfield corrosion, Aberdeen, UK, May 2012Google Scholar
  7. Boas BMV (1990) Temperature profile of a fluid flowing within a well. In: Proceedings of the SPE Latin America petroleum engineering conference, Rio de Janeiro, Brazil, October 1990Google Scholar
  8. Bradley WB (1979) Mathematical concept—Stress Cloud—can predict borehole failure. Oil Gas J 77(8):92–102Google Scholar
  9. Carbajal D, Burress C, Shumway W, Zhang Y (2009) Combining proven anti-sag technologies for HPHT North Sea applications: clay-free oil-based fluid and synthetic, sub-micron weight material. In Proceedings of the SPE/IADC drilling conference and exhibition, Amsterdam, the Netherlands, March 2009Google Scholar
  10. Chen M (2004) Review of study on rock mechanics at great depth and its applications to petroleum engineering of China. Chin J Rock Mech Eng 23(14):2455–2462Google Scholar
  11. Chen GZ, Ewy R (2005) Thermoporoelastic effect on wellbore stability. SPE J 10(2):121–129CrossRefGoogle Scholar
  12. Chen YM, Chenevert ME, Sharma MM (2003) Chemical-mechanical wellbore instability model in shale. J Pet Sci Technol 38(34):167–176Google Scholar
  13. Chen LJ, Zhao HB, Liu XL, Huang XG (2008a) Experimental research on heat swelling power of sandstone and limestone. J China Univ Min Technol 37(5):670–674Google Scholar
  14. Chen M, Jin Y, Zhang GQ (2008b) Petroleum related rock mechanics. Science Press, BeijingGoogle Scholar
  15. Chenevert ME, Sharma AK (1993) Permeability and effective pore pressure of shales. SPE Drill Complet 8(1):28–34CrossRefGoogle Scholar
  16. Closmann PJ, Bradley WB (1979) The effect of temperature on tensile and compressive strengths and Young’s modulus of oil shale. Old SPE J 19(5):301–312Google Scholar
  17. Corre B, Eymard R, Guenot A (1984) Numerical computation of temperature distribution in a wellbore while drilling. In: Proceedings of the SPE annual technical conference and exhibition, Houston, Texas, USA, September 1984Google Scholar
  18. Detournay E, Cheng AD (1988) Poroelastic response of a borehole in a non-hydrostatic stress field. Int J Rock Mech Min Sci Geomech Abstr 25(3):171–182CrossRefGoogle Scholar
  19. Dodson J, Dodson T, Schmidt V (2004) Gulf of Mexico ‘trouble time’ creates major drilling expenses: use of cost-effective technologies needed. Offshore 64(1):46–48Google Scholar
  20. Duan YS (1999) Well Ya 21-1-3 drilling techniques. Nat Gas Ind 19(1):79–82Google Scholar
  21. Espinosa-Paredes G, García-Gutierrez A (2004) Thermal behaviour of geothermal wells using mud and air–water mixtures as drilling fluids. Energy Convers Manage 45(9–10):1513–1527CrossRefGoogle Scholar
  22. Espinosa-Paredes G, Morales-Díaz A, Olea-González U, Ambriz-Garcia JJ (2009) Application of a proportional-integral control for the estimation of static formation temperatures in oil wells. Mar Pet Geol 26(2):259–268CrossRefGoogle Scholar
  23. Fjær E, Holt RM, Horsrud P, Raaen AM, Risnes R (2008) Petroleum related rock mechanics, 2nd edn. Elsevier, AmsterdamGoogle Scholar
  24. Hasan AR, Kabir CS (1994) Static reservoir temperature determination from transient data after mud circulation. SPE Drill Complet 9(1):7–24CrossRefGoogle Scholar
  25. Honore RS Jr, Tarr BA, Howard JA, Lang NK (1993) Cementing temperature predictions based on both downhole measurements and computer predictions: a case history. In: Proceedings of the SPE production operations symposium, Oklahoma City, Oklahoma, USA, March 1993Google Scholar
  26. Huang BJ, Xiao XM, Dong WL (2002) Multiphase natural gas migration and accumulation and its relationship to diapir structures in the DF1-1 gas field, South China Sea. Mar Pet Geol 19(7):861–872CrossRefGoogle Scholar
  27. Keller HH, Couch EJ, Berry PM (1973) Temperature distribution in circulating mud columns. Old SPE J 13(1):23–30Google Scholar
  28. Li SG (2004) The study on HT/HP wellbore stability. Doctoral dissertation, China University of Petroleum, Beijing, ChinaGoogle Scholar
  29. Li L, Lin LZ, Liu KM, Lao BH (1990) Microscopic study on the strength, deformation and fracture characteristics of rocks after heated. Rock Soil Mech 11(4):51–61Google Scholar
  30. Li SG, Deng JG, Yu BH, Yu LJ (2005) Formation fracture pressure calculation in high temperatures wells. Chin J Rock Mech Eng 24(S2):5669–5673Google Scholar
  31. Marshall DW, Bentsen RG (1982) A computer model to determine the temperature distributions in a wellbore. J Can Pet Technol 21(1):63–75CrossRefGoogle Scholar
  32. Maury V, Guenot A (1995) Practical advantages of mud cooling systems for drilling. SPE Drill Complet 10(1):42–48CrossRefGoogle Scholar
  33. Mody FK, Hale AH (1993) Borehole-stability model to couple the mechanics and chemistry of drilling-fluid/shale interactions. J Petrol Technol 45(11):1093–1101CrossRefGoogle Scholar
  34. Nawrocki PA, Dusseault MB, Bratli RK, Xu G (1998) Assessment of some semi-analytical models for non-linear modelling of borehole stresses. Int J Rock Mech Min Sci 35(4–5):522–531CrossRefGoogle Scholar
  35. Ong SH (1994) Borehole stability. Doctoral dissertation, University of Oklahoma, Norman, OklahomaGoogle Scholar
  36. Qin BD, Luo YJ, Men YM (2011) Experimental research on swelling properties of limestone and sandstone at high temperature. Rock Soil Mech 32(2):417–422Google Scholar
  37. Raymond LR (1969) Temperature distribution in a circulating drilling fluid. J Pet Technol 21(3):333–341CrossRefGoogle Scholar
  38. Richter D, Simmons G (1974) Thermal expansion behavior of igneous rocks. Int J Rock Mech Min Sci Geomech Abstr 11(10):403–411CrossRefGoogle Scholar
  39. Romero-Juárez A (1979) A simplified method for calculating temperature changes in deep wells. J Petrol Technol 31(6):763–768CrossRefGoogle Scholar
  40. Roshan H, Fahad M (2012) Chemo-poroplastic analysis of a borehole drilled in a naturally fractured chemically active formation. Int J Rock Mech Min Sci 52:82–91CrossRefGoogle Scholar
  41. Sofianos AI, Nomikos PP (2006) Equivalent Mohr–Coulomb and generalized Hoek–Brown strength parameters for supported axisymmetric tunnels in plastic or brittle rock. Int J Rock Mech Min Sci 43(5):683–704CrossRefGoogle Scholar
  42. Su C, Guo W, Li X (2008) Experimental research on mechanical properties of coarse sandstone after high temperatures. Chin J Rock Mech Eng 27(6):1162–1170Google Scholar
  43. Sun Q, Zhang ZZ, Xue L, Zhu SY (2013) Physico-mechanical properties variation of rock with phase transformation under high temperature. Chin J Rock Mech Eng 32(5):935–942Google Scholar
  44. Thigpen L (1979) Vertical stress distribution in oil–shale aggregate columns during retorting. Old SPE J 19(2):97–106Google Scholar
  45. Wang ZH (2011) Status and development trend of ultra-high temperature and high density drilling fluid at home and abroad. Pet Drill Tech 39(2):1–7Google Scholar
  46. Wang CH, Wang HC, Liu LP, Sun DS, Zhao WH (2012) Effects of high temperatures on mechanical performance of basaltic tuff and mechanism analysis. Chin J Geotech Eng 34(10):1827–1835Google Scholar
  47. Wong-Loya JA, Andaverde J, Santoyo E (2012) A new practical method for the determination of static formation temperatures in geothermal and petroleum wells using a numerical method based on rational polynomial functions. J Geophys Eng 9(6):711–728CrossRefGoogle Scholar
  48. Xu ZZ (1992) A discussion of factors influencing thermophysical characteristics of rocks and their mechanisms. Pet Explor Dev 19(6):85–89Google Scholar
  49. Yang M, Meng YF, Li G, Deng JM, Zhao XY (2013) A transient heat transfer model of wellbore and formation during the whole drilling process. Acta Petrolei Sinica 34(2):366–371Google Scholar
  50. Yin G, Li X, Zhao H (2009) Experimental investigation on mechanical properties of coarse sandstone after high temperature under conventional triaxial compression. Chin J Rock Mech Eng 28(3):598–604Google Scholar
  51. You MQ, Su CD, Li XS (2008) Study on relation between mechanical properties and longitudinal wave velocities for damaged rock samples. Chin J Rock Mech Eng 27(3):458–467Google Scholar
  52. Yuan JL, Deng JG, Tan Q, Yu BH, Jin XC (2013) Borehole stability analysis of horizontal drilling in shale gas reservoirs. Rock Mech Rock Eng 46(5):1157–1164CrossRefGoogle Scholar
  53. Zeuch DH (1983) The mechanical behavior of Anvil Points oil shale at elevated temperatures and confining pressures. Can Geotech J 20(2):344–352CrossRefGoogle Scholar
  54. Zeynali ME (2012) Mechanical and physico-chemical aspects of wellbore stability during drilling operations. J Petrol Sci Eng 82–83:120–124CrossRefGoogle Scholar
  55. Zhang JC, Lang J, Standifird W (2009) Stress, porosity, and failure-dependent compressional and shear velocity ratio and its application to wellbore stability. J Petrol Sci Eng 69:193–202CrossRefGoogle Scholar
  56. Zhang K, Zhang J, Dai W (2010) Drilling technology for deep & ultra-deep well in West China. Drill Prod Technol 33(1):36–40Google Scholar
  57. Zhang ZZ, Gao F, Xu XL (2011) Experimental study of temperature effect of mechanical properties of granite. Rock Soil Mech 32(8):2346–2352Google Scholar
  58. Zheng Z (1998) Integrated borehole stability analysis—against tradition. In: Proceedings of the SPE/ISRM conference on rock mechanics in petroleum engineering, Trondheim, Norway, July 1998Google Scholar
  59. Zoback MD, Pollard DD (1978) Hydraulic fracture propagation and the interpretation of pressure–time records for in-situ stress determinations. In: Proceedings of the 19th US symposium on rock mechanics (USRMS), Reno, Nevada, USA, May 1978Google Scholar

Copyright information

© Springer-Verlag Wien 2013

Authors and Affiliations

  • Chuanliang Yan
    • 1
  • Jingen Deng
    • 1
  • Baohua Yu
    • 1
  • Wenliang Li
    • 1
  • Zijian Chen
    • 1
  • Lianbo Hu
    • 1
  • Yang Li
    • 1
  1. 1.State Key Laboratory of Petroleum Resources and ProspectingChina University of Petroleum, BeijingBeijingChina

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