Recall: Recall: State of stress surrounding anState of stress surrounding anarbitrarily deviated wellarbitrarily deviated well

© Cambridge University Press (Fig. 8.1b, pp. 237)Zoback, Reservoir Geomechanics

Stresses in the wellbore coordinate systemStresses in the wellbore coordinate system

=RB

⎡

⎣⎢⎢

cos δ cosϕ

− sin δ

cos δ sinϕ

sin δ cosϕ

cos δ

sin δ sinϕ

− sinϕ

0

cosϕ

⎤

⎦⎥⎥

=SB RBSGRTB

= ( S )SB RB RTG RG R

TB

Stress at wellbore wallStress at wellbore wall

σzz

σθθ

τθz

σrr

= − 2ν( − ) cos 2θ − 4ν sin 2θσ33 σ11 σ22 σ12

= + − 2( − ) cos 2θ − 4 sin 2θ − ΔPσ11 σ22 σ11 σ22 σ12

= 2( cos θ − sin θ)σ23 σ13

= ΔP

Principal e�ective stresses around thePrincipal e�ective stresses around thewellborewellbore

σtmax

σtmin

= ( + + )1

2σzz σθθ ( − + 4σzz σθθ)2 τ2

θz‾ ‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√

= ( + − )1

2σzz σθθ ( − + 4σzz σθθ)2 τ2

θz‾ ‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√

Example: Reverse faultingExample: Reverse faulting

Find the minimum and maximum tangential stress for an open hole well that is oriented from North and deviated from vertical at a depth of km. Assume a hydrostatic porepressure gradient, a Poisson ration of , and a balanced drilling operation.

S =

⎡

⎣⎢⎢

30

0

0

0

25

0

0

0

20

⎤

⎦⎥⎥

α

β

γ

= 90∘

= 0∘

= 0∘

Azimuth of SHmax

=S1 SHmax

=S2 Shmin

20∘

20∘ 2

0.2

© Cambridge University Press (Fig. 8.1a, pp. 237)Zoback, Reservoir Geomechanics

Lower hemisphere projectionLower hemisphere projection

© Cambridge University Press (Fig. 8.1a, pp. 237)Zoback, Reservoir Geomechanics

ExampleExample

Examples: Breakout initiationExamples: Breakout initiation

Normal Strike-slip Reverse

© Cambridge University Press (Fig. 8.2a,b,c, pp. 240)Zoback, Reservoir Geomechanics

Examples: Drilling induced tensile fractureExamples: Drilling induced tensile fracture

Normal Strike-slip Reverse

© Cambridge University Press (Fig. 8.3a,b,c, pp. 240)Zoback, Reservoir Geomechanics