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Compressive and tensile failure in verticalCompressive and tensile failure in verticalwellswells
Stress around circular cavityStress around circular cavity
© Cambridge University Press (Fig. 6.1, pp. 169)Zoback, Reservoir Geomechanics
Kirsch solutionKirsch solution
σrr
σθθ
σrθ
σzz
= (1 − ) + (1 − 4 + 3 ) cos 2θ+σHmax σhmin
2
a2
r2
−σHmax σhmin
2
a2
r2
a4
r4
+ ( − )( )Pw Pp
a2
r2
= (1 + ) − (1 + 3 ) cos 2θ − ( − )( )+σHmax σhmin
2
a2
r2
−σHmax σhmin
2
a4
r4Pw Pp
a2
r2
= (1 + 2 − 3 ) − sin 2θ−σHmax σhmin
2
a2
r2
a4
r4
= − 2ν( − )( ) cos 2θσv σHmax σhmina2
r2
ExampleExample
© Cambridge University Press (Fig. 6.2a, pp. 171)
SHmax
Sv
Shmin
Pp
Pw
= 90MPa
= 88.2MPa
= 51.5MPa
= 31.5MPa
= 31.5MPa
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Along azimuth of Along azimuth of
© Cambridge University Press (Fig. 6.2b,c, pp. 171)
SHmax Shmin
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Variation of wellbore stressesVariation of wellbore stresses
© Cambridge University Press (Fig. 6.3a, pp. 173)Zoback, Reservoir Geomechanics
Wellbore breakout regionWellbore breakout region
© Cambridge University Press (Fig. 6.3b,c, pp. 173)Zoback, Reservoir Geomechanics
Mudweight stabilizationMudweight stabilizationAs increases, decreases and increases.
© Cambridge University Press (Fig. 6.3b, pp. 173 and Fig. 6.5a,pp. 177)
ΔP σθθ σrr
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Breakouts as indicators of far-�eld stressesBreakouts as indicators of far-�eld stressesSimplify Kirsch equations at wellbore wall , soa = r
σrr
σθθ
σzz
= ( − ) = ΔPPw Pp
= + − 2( − ) cos 2θ − ΔPσHmax σhmin σHmax σhmin
= − 2ν( − ) cos 2θσv σHmax σhmin
has min at 0 and 180σθθ∘ ∘
σminθθ
= 3 − − ΔPσHmin σHmax
has min at 90 and 270 , soσθθ∘ ∘
σmaxθθ
= 3 − − ΔPσHmax σhmin
so
−σmaxθθ
σminθθ
= 4( − )σHmax σhmin
Tensile induced fracturesTensile induced fractures
© Cambridge University Press (Fig. 6.5a, pp. 177)Zoback, Reservoir Geomechanics
Safe drilling mud windowSafe drilling mud window
Mud weight too low
Breakouts
Mud weight too high
Tensile induced fractures leading to lost circulation
Imaging breakoutsImaging breakouts
Ultrasonic -wave Electrical resistivity Breakout cross-section
© Cambridge University Press (Fig. 6.4a,b,c, pp. 176)
P
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Four-arm caliper dataFour-arm caliper data
Caliper data Breakout indication Examples ofvariations
Thermal e�ects on wellbore stressThermal e�ects on wellbore stress
Strongly time dependent
strongly depenendent of the silica content of the rock.
Under steady-state conditions,
= T∂T
∂tαT∇
2
α →
Δ =σTθθ
EΔTαT
1 − ν
Time-temperature e�ectsTime-temperature e�ects
© Cambridge University Press (Fig. 6.14a,b pp. 194)
ΔT =
ΔP =
C25∘
6 MPa
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Stability through cooling?Stability through cooling?
Cooling Reference
© Cambridge University Press (Fig. 6.14c pp. 194 and Fig. 6.3pp. 173)
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Rock strength anisotropyRock strength anisotropy
© Cambridge University Press (Fig. 4.12, pp. 106)
=σ1 σ32( + )Sw μwσ3
(1 − cot ) sin 2βμw βw
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Rock strength anisotropy e�ects onRock strength anisotropy e�ects onbreakoutsbreakouts
© Cambridge University Press (Fig. 6.16a,b pp. 199)Zoback, Reservoir Geomechanics
Two mechanismsTwo mechanisms
Stresses exceed intact rock strength
Stresses activate slip on weak bedding planes
© Cambridge University Press (Fig. 6.16c pp. 199)Zoback, Reservoir Geomechanics
Chemical e�ectsChemical e�ectsWater Activity ( ) can to increased pore pressure∼Aw
1
salinity
from breakout data from breakout dataSHmax
=SHmax
( + 2 + ΔP + Δ ) − (1 + 2 cos(π − )C0 Pp σTShmin wbo
1 − 2 cos(π − )wbo
ExampleExample
© Cambridge University Press (Fig. 7.7 pp. 223)Zoback, Reservoir Geomechanics
Wellbore stabilityWellbore stability
De�ning a "stable" wellboreDe�ning a "stable" wellbore
© Cambridge University Press (Fig. 10.1a,b pp. 304)Zoback, Reservoir Geomechanics
Emperical model: Emperical model: Maximum 90Maximum 90 breakouts breakouts
© Cambridge University Press (Fig. 10.2a,b pp. 305)
∘
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Comprehensive modelComprehensive model
i.e. why your studying geomechanicsi.e. why your studying geomechanics