Homework No. 6 – Constraining the Maximum Horizontal Stress from Wellbore Failure Solved

The condition for a tensile fracture forming in the wellbore wall in a vertical well when a thermal stress is ignored is (Zoback, 2007),

 

Shmin +SH max −2(SH max −Shmin )−2Pp −(Pm −Pp)=To                                                                      Eqn. 1

 

It may be assumed that at the maximum angle of a breakout initiation, a circumferential stress is equal to the unconfined compressive rock strength (Barton et al., 1988),

 

Shmin +SH max −2(SH max −Shmin )cos(π−wbo)−2Pp −(Pm −Pp)=Co                                                    Eqn. 2

 

If faults are in frictional equilibrium (Zoback, 2007),

 

S1 −Pp 2 +1) +µ)2 =( (µ

S3 −Pp                                                                                                                                                                        Eqn. 3

 

in which Shmin is a minimum horizontal stress, SHmax is a maximum horizontal stress, Pp is a pore pressure, Pm is a mud pressure, To is a tensile strength, wbo is a breakout width, Co is an unconfined compressive strength, S1 is a maximum principal stress, S3 is a minimum principal stress, and µ is a coefficient of sliding friction.

 

Use the following unit in your calculation: ‘psi’ for maximum horizontal stress and minimum horizontal stress

 

        I.          Answer the questions on the page below

 

In a vertical well, assuming a pore pressure of 4400 psi, an overburden stress of 11000 psi, a coefficient of sliding friction of 0.6, a mud pressure of 5900 psi, a tensile strength of 0 psi, a

breakout width of 0°, and an unconfined compressive strength of 14000 psi, calculate values of the minimum horizontal stress and the maximum horizontal stress at points 1, 2, 3, 4, and 5 in Figure 1.

 

 

Figure 1. A stress polygon assuming a pore pressure of 4400 psi, an overburden stress of 11000 psi, a coefficient of sliding friction of 0.6, a mud pressure of 5900 psi, a tensile strength of 0 psi, a breakout width of 0°, and an unconfined compressive strength of 14000 psi. A Co line represents a breakout, and a To line represents a drilling induced tensile fracture.

 

Please do not write a unit in an answer, just write a number.

 

 

Zoback, M. (2007). Reservoir Geomechaincs. Cambridge: Cambridge University Press.

doi:10.1017/CBO9780511586477

 

Barton, C. A., Zoback, M. D., and Burns, K. L. (1988). In-situ stress orientation and magnitude at the Fenton

Geothermal Site, New Mexico, determined from wellbore breakouts. Geophysical Research Letters, Volume 15,

Issue 5, doi: 10.1029/GL015i005p00467