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

Zoback, Reservoir Geomechanics

Along azimuth of Along azimuth of

© Cambridge University Press (Fig. 6.2b,c, pp. 171)

SHmax Shmin

Zoback, Reservoir Geomechanics

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

Zoback, Reservoir Geomechanics

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

Zoback, Reservoir Geomechanics

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

Zoback, Reservoir Geomechanics

Stability through cooling?Stability through cooling?

Cooling Reference

© Cambridge University Press (Fig. 6.14c pp. 194 and Fig. 6.3pp. 173)

Zoback, Reservoir Geomechanics

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

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)

∘

Zoback, Reservoir Geomechanics

Comprehensive modelComprehensive model

i.e. why your studying geomechanicsi.e. why your studying geomechanics