Geomechanics: stress around a vertical wellbore

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Modeling the stress state around a borehole, a tunnel or other underground excavations and using it to verify the failure criteria is one of the main challenging goals of geomechanics and geotechnics. This tool provides a solution to a very basic problem of a vertical well located in an isotropic elastic formation subjected to a farfield vertical stress σV and maximum and minimum horizontal stresses, σHmax and σhmin, respectively. The borehole wall is assumed to be impermeable (due to a perfect cake) and Terzaghi's effective stress is considered (Biot's coefficient equal to 1). The plane strain condition on the horizontal plane is assumed. Analytical solutions to that problem was derived by Kirsch (1898) which are also annexed in many petrophysical handbooks (e.g. Fjaer et al., 2008; Sayers, 2010, Cui et al., 1997).

Fjaer, E., Horsrud, P., Raaen, A. M., Risnes, R., & Holt, R. M. (1992). Petroleum related rock mechanics (Vol. 33). Elsevier.
Sayers, C. M. (2010). Geophysics under stress: Geomechanical applications of seismic and borehole acoustic waves. Society of Exploration Geophysicists and European Association of Geoscientists and Engineers.
Cui, L., Cheng, A. H., & Abousleiman, Y. (1997). Poroelastic solution for an inclined borehole. Journal of applied mechanics, 64(1), 32-38.
Kirsch, E. G. (1898). Die Theorie der Elastizit t und die Bed rfnisse der Festigkeitslehre. Zeitshrift des Vereines deutscher Ingenieure, 42, 797-807.

Horizontal plane of a borehole.
Horizontal plane of a vertical well.

Input the farfield in-situ stresses, pore pressure, mud pressure and the Poisson ratio of rock then click the Compute button to run the simulation.

Maximum horizontal stress σHmax (MPa)

Minimum horizontal stress σhmin (MPa)

Vertical stress σV (MPa)

Mud pressure Pmud (MPa)

Pore pressure Ppore (MPa)

Poisson ratio of rock

Note: on the charts below, the direction of the vertical stress is perpendicular to the plane. The vertical axis coincides with the direction of the maximum horizontal stress and the horizontal axis coincides with the direction of the minimum horizontal stress.

View the wellbore stresses along a direction that makes an angle θ to the vertical axis (the direction of the maximum horizontal stress).

θ (°)

Use the slider below to smoothly modify the directional angle θ (Note: this option works on most internet navigators except some Internet Explorer versions):

Output data