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Compressive and tensile failure in verticalCompressive and tensile failure in verticalwellswells
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Stress around circular cavityStress around circular cavity
© Cambridge University Press (Fig. 6.1, pp. 169)Zoback, Reservoir Geomechanics
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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
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ExampleExample
© Cambridge University Press (Fig. 6.2a, pp. 171)
SHmax
Sv
Shmin
Pp
Pw
= 90MPa
= 88.2MPa
= 51.5MPa
= 31.5MPa
= 31.5MPa
Zoback, Reservoir Geomechanics
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Along azimuth of Along azimuth of
© Cambridge University Press (Fig. 6.2b,c, pp. 171)
SHmax Shmin
Zoback, Reservoir Geomechanics
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Variation of wellbore stressesVariation of wellbore stresses
© Cambridge University Press (Fig. 6.3a, pp. 173)Zoback, Reservoir Geomechanics
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Wellbore breakout regionWellbore breakout region
© Cambridge University Press (Fig. 6.3b,c, pp. 173)Zoback, Reservoir Geomechanics
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Mudweight stabilizationMudweight stabilizationAs increases, decreases and increases.
© Cambridge University Press (Fig. 6.3b, pp. 173 and Fig. 6.5a,pp. 177)
ΔP σθθ σrr
Zoback, Reservoir Geomechanics
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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
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Tensile induced fracturesTensile induced fractures
© Cambridge University Press (Fig. 6.5a, pp. 177)Zoback, Reservoir Geomechanics
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Safe drilling mud windowSafe drilling mud window
Mud weight too low
Breakouts
Mud weight too high
Tensile induced fractures leading to lost circulation
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Imaging breakoutsImaging breakouts
Ultrasonic -wave Electrical resistivity Breakout cross-section
© Cambridge University Press (Fig. 6.4a,b,c, pp. 176)
P
Zoback, Reservoir Geomechanics
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Four-arm caliper dataFour-arm caliper data
Caliper data Breakout indication Examples ofvariations
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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
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Time-temperature e�ectsTime-temperature e�ects
© Cambridge University Press (Fig. 6.14a,b pp. 194)
ΔT =
ΔP =
C25∘
6 MPa
Zoback, Reservoir Geomechanics
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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)
Zoback, Reservoir Geomechanics
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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
Zoback, Reservoir Geomechanics
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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
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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
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Chemical e�ectsChemical e�ectsWater Activity ( ) can to increased pore pressure∼Aw
1
salinity
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from breakout data from breakout dataSHmax
=SHmax
( + 2 + ΔP + Δ ) − (1 + 2 cos(π − )C0 Pp σTShmin wbo
1 − 2 cos(π − )wbo
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ExampleExample
© Cambridge University Press (Fig. 7.7 pp. 223)Zoback, Reservoir Geomechanics
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Wellbore stabilityWellbore stability
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De�ning a "stable" wellboreDe�ning a "stable" wellbore
© Cambridge University Press (Fig. 10.1a,b pp. 304)Zoback, Reservoir Geomechanics
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Emperical model: Emperical model: Maximum 90Maximum 90 breakouts breakouts
© Cambridge University Press (Fig. 10.2a,b pp. 305)
∘
Zoback, Reservoir Geomechanics
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Comprehensive modelComprehensive model
i.e. why your studying geomechanicsi.e. why your studying geomechanics