[Solved] Reservoir Geomechanics Homework No. 6 Constraining the Maximum Horizontal Stress from Wellbore Failure

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(wbo)2Pp (Pm Pp)=Co Eqn. 2

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

S1 Pp 2 +1) +)2 =( (

^{S3 Pp} Eqn. 3

in which S_hmin is a minimum horizontal stress, S_Hmax is a maximum horizontal stress, P_p is a pore pressure, P_m is a mud pressure, T_o is a tensile strength, w_bo is a breakout width, C_o is an unconfined compressive strength, S₁ is a maximum principal stress, S₃ is a minimum principal stress, and is a coefficient of sliding friction.

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

1. 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 C_o line represents a breakout, and a T_o 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