Skip to main content
Log in

Uncertainties in the estimation of in situ stresses: effects of heterogeneity and thermal perturbation

  • Original Article
  • Published:
Geomechanics and Geophysics for Geo-Energy and Geo-Resources Aims and scope Submit manuscript

Abstract

In situ stress directions and magnitudes in subsurface are commonly estimated using two different methods: (1) borehole break-out—drilling-induced fracture interpretation complemented by extended leak-off tests; (2) stress estimation from acoustic measurements using advanced wireline tools. Both methods use stress perturbations around boreholes to estimate far field stresses employing Kirsch’s equations, which are only valid for boreholes aligned with one of the principal stresses, linear elastic deformation and homogeneous isotropic materials. Furthermore, the original stress state may have been altered by drilling-mud-circulation induced temperature changes. Using heuristic models including heterogeneity, this study investigates potential errors in the estimation of far-field stress due to (a) the generalisation of Kirsch’s equations to heterogeneous media and (b) plausible temperature perturbations. First, errors due to uncertainties in measuring wave slowness are analysed for an idealised homogeneous material. Second, errors due to application of Kirsch’s equations are investigated considering potential effects of frictional interfaces between layers, pore pressure in the rock matrix and thermal perturbations induced by drilling for example cases. To analyse stress in these complex scenarios finite element analysis was used, revealing strong effects of lithological and thermal variations. Stress magnitude was amplified by stiff layers and was attenuated by soft ones. At layer interfaces, substantial changes in stress orientation occurred. Kirsch’s equations for the considered cases resulted in errors in far field stresses as large as 44% in the magnitude and 90° in orientations. An uncertainty propagation analysis indicated a high accuracy of acoustic estimates for homogenous materials. However, a dramatic impact of small-scale heterogeneity may not be resolved by the logging process.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24

Similar content being viewed by others

Abbreviations

d b :

Borehole diameter (M)

E :

Young’s modulus (GPa)

f :

Vector of body forces (N)

G :

Shear modulus (GPa)

K :

Thermal conductivity [W/(mK)]

p p :

Pore pressure (MPa)

p w :

Wellbore pressure (MPa)

q :

Heat flux (W/m2)

S11 :

Radial stress in a cylindrical coordinate system with its origin set to the wellbore centre

S22:

Hoop stress in a cylindrical coordinate system with its origin set to the wellbore centre

NT11:

Temperature in bedrock

T :

Temperature (K)

V c :

Compressive wave velocity (m/s)

V s :

Shear wave velocity (m/s)

V s1 :

Fast shear wave (m/s)

V s2 :

Slow shear wave (m/s)

V Stoneley :

Stoneley wave velocity (m/s)

u,v,w :

Displacements in x, y, and z directions (m)

α :

Biot coefficient

β :

Thermal expansivity (1/K)

σ H :

Maximum principal horizontal total far-field stress (MPa)

σ h :

Minimum principal horizontal total far-field stress (MPa)

σ v :

Vertical total stress (MPa)

σ θmin :

Minimum hoop stress around wellbore (MPa)

σ θmax :

Maximum hoop stress around wellbore (MPa)

σ′:

Effective stress (MPa)

ε :

Strain

θ :

Angle measured from the major horizontal stress (°)

μ :

Coefficient of internal friction

ν :

Poisson’s ratio

ρ :

Rock density (kg/m3)

References

  • Abousleiman Y, Ekbote S (2005) Solutions for the inclined borehole in a porothermoelastic transversely isotropic medium. J Appl Mech 72:102–114. doi:10.1115/1.1825433

    Article  MATH  Google Scholar 

  • Al-Tahini A, Abousleiman Y (2008) Acoustic measurement and calibration of in situ stress anisotropy around a wellbore. 1 Jan 2008

  • Anderson EM (1951) The dynamics of faulting and dyke formation with applications to Britain. Oliver and Boyd, Edinburgh

    Google Scholar 

  • Barber JR (2010) Elasticity. Springer, New York

    Book  MATH  Google Scholar 

  • Barton CA, Zoback MD (1994) Stress perturbations associated with active faults penetrated by boreholes: possible evidence for near-complete stress drop and a new technique for stress magnitude measurement. J Geophys Res Solid Earth 99:9373–9390. doi:10.1029/93JB03359

    Article  Google Scholar 

  • Barton CA, Moos D, Peska P, Zoback MD (1997) Utilizing wellbore image data to determine the complete stress tensor: application to permeability anisotropy and wellbore stability. Log Anal 38(6):21–33

    Google Scholar 

  • Boness NL, Zoback MD (2004) Stress-induced seismic velocity anisotropy and physical properties in the SAFOD Pilot Hole in Parkfield. Geophys Res Lett, CA. doi:10.1029/2003GL019020

    Google Scholar 

  • Brandas LT, Fjær E, Tokle K, Tronvoll J (2012) Relating acoustic wave velocities to formation mechanical properties. 1 Jan 2012

  • Byerlee JD (1978) Friction of rock. Pure appl Geophys 116:615–626

    Article  Google Scholar 

  • Chang C, Zoback MD, Khaksar A (2006) Empirical relations between rock strength and physical properties in sedimentary rocks. J Petrol Sci Eng 51:223–237. doi:10.1016/j.petrol.2006.01.003

    Article  Google Scholar 

  • Coulomb CA (1773) Sur une application des regles de maximums et minimums a quelques problemes de statistique relatifs a larchitesture. Acad R Sci Mem Mech Min Sci 7:343–382

    Google Scholar 

  • Ellis DV, Singer JM (2007) Well logging for earth scientists. Springer Science & Business Media, New York

    Book  Google Scholar 

  • Fjær E, Holt RM, Horsrud P, Raaen AM, Risnes R (2008) Petroleum related rock mechanics. Elsevier, London

    Google Scholar 

  • Gaede O, Karpfinger F, Jocker J, Prioul R (2012) Comparison between analytical and 3D finite element solutions for borehole stresses in anisotropic elastic rock. Int J Rock Mech Min Sci 51:53–63. doi:10.1016/j.ijrmms.2011.12.010

    Article  Google Scholar 

  • Gaines S, Diederichs MS, Hutchinson DJ (2012) Review of borehole. In: Situ stress measurement techniques for various ground conditions and numerical stress estimation considerations. 1 Jan 2012

  • Goodman HE, Connolly P (2007) Reconciling subsurface uncertainty with the appropriate well design using the Mechanical Earth Model (MEM) approach. 1 Jan 2007

  • Grandi S, Rao RVN, Toksoz MN (2002) Geomechanical modeling of in situ stresses around a borehole. http://hdl.handle.net/1721.1/67848

  • Hoeink T, van der Zee W, Moos D (2012) Finite element analysis of stresses induced by gravity in layered rock masses with different elastic moduli. 1 Jan 2012

  • Huang S, Burns DR, Toksoez NM (2001) The effect of stresses on the sound velocity in rocks: theory of acoustoelasticity and experimental measurements. Massachusetts Institute of Technology. Earth Resources Laboratory, http://eaps.mit.edu/erl/research/report1/pdf/huang.pdf

  • Jha B, Juanes R (2007) A locally conservative finite element framework for the simulation of coupled flow and reservoir geomechanics. Acta Geotech 2:139–153. doi:10.1007/s11440-007-0033-0

    Article  Google Scholar 

  • Kirsch EG (1898) Die Theorie der Elastizität und die Bedürfnisse der Festigkeitslehre. Z Ver Dtsch Ing 42:797–807

    Google Scholar 

  • Malvern LE (1969) Introduction to the mechanics of a continuous medium. Prentice-Hall.

  • Mavko G, Mukerji T, Dvorkin J (2003) The rock physics handbook: tools for seismic analysis of porous media. Cambridge University Press, Cambridge

    Google Scholar 

  • Padmanabhan E, Sivapriya B, Huang KH, Askury AK, Chow WS (2015) The impact of stylolites and fractures in defining critical petrophysical and geomechanical properties of some carbonate rocks. Geomech Geophys Geo Energy Geo Resour 1:55–67. doi:10.1007/s40948-015-0007-x

    Article  Google Scholar 

  • Peng S, Zhang J (2007) Engineering geology for underground rocks. Springer, Berlin

    Google Scholar 

  • Peška P, Zoback MD (1995) Compressive and tensile failure of inclined well bores and determination of in situ stress and rock strength. J Geophys Res Solid Earth 100:12791–12811. doi:10.1029/95JB00319

    Article  Google Scholar 

  • Sayers CM (2005) Sensitivity of elastic-wave velocities to stress changes in sandstones. Lead Edge 24:1262–1266. doi:10.1190/1.2149646

    Article  Google Scholar 

  • Sayers CM, Nagy Z, Adachi J, Singh V, Tagbor K, Hooyman P (2009) Determination of in situ stress and rock strength using borehole acoustic data. Paper presented at the international exposition and annual meeting—SEG, Houston

  • Schlumberger (2005) Sonic scanner. Schlumberger Marketing Communications

  • Schlumberger (2005b) Sonic scanner. Schlumberger Marketing Communications, Houston

    Google Scholar 

  • Sinha BK (2002) Determining stress parameters of formations from multi-mode velocity

  • Sinha BK et al (2008) Estimation of formation stresses using borehole sonic data. Paper presented at the SPWLA 49th annual logging symposium, May 25–28, 2008

  • Sirat M, Zhang X, Simon J, Vantala A, Povstyanova M (2014) Mechanical layering: implications for hydraulic fracturing in an unconventional tight carbonate reservoir in Abu Dhabi, UAE. 25 Feb 2014

  • Zoback MD (2007) Reservoir geomechanics. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Zoback MD, Healy JH (1984) Friction, faulting, and “in situ” stresses. Ann Geophys 2:689–698

    Google Scholar 

  • Zoback MD, Mastin L, Barton C (1986) In-situ stress measurements in deep boreholes using hydraulic fracturing, wellbore breakouts, and stonely wave polarization. In: Proceedings of the international symposium on rock stress and rock stress measurements, Stockholm, September, 1986. International Society for Rock Mechanics, ISRM

Download references

Acknowledgements

Caroline Millotte (FEI Inc., Canberra, Australia) is thanked for the generation of the more complex facies model and mesh. Their original geometries were generated with SBED, Geomodelling Technology Corp., Alberta, Canada.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hossein Agheshlui.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Agheshlui, H., Matthai, S. Uncertainties in the estimation of in situ stresses: effects of heterogeneity and thermal perturbation. Geomech. Geophys. Geo-energ. Geo-resour. 3, 415–438 (2017). https://doi.org/10.1007/s40948-017-0069-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40948-017-0069-z

Keywords

Navigation