Lecture 8

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Lecture 8

Ch. 6 Compressive and tensile failures in vertical wells (part 1)

(27 April 2020)

Ki-Bok Min, PhD

Professor

Department of Energy Resources Engineering Seoul National University

Reservoir Geomechanics, Fall, 2020

(2)

Compressive and tensile failures in vertical wells Introduction

• Importance

– Wellbore stability

– Observation from the wellbore provide much information – including in situ stress – Borehole breakout

 Stress orientation, and (to some extent) magnitude

– Drilling induced tensile fracture

 Shmin is the minimum principal stress

 Large difference between SHmax and Shmin

 High mud weight

 Cooling effect

– Hydraulic fracturing

 different from drilling induced tensile fracture

 Away from the borehole

(3)

• Stresses in cylindrical coordinates

반경방향응력

접선응력

Dusseault, 2012

Stresses concentration around a cylindrical

hole and wellbore failure

(4)

• Concept of “Stress Redistribution”

Dusseault, 2012

Stresses concentration around a cylindrical

hole and wellbore failure

(5)

Stress concentration

Loading condition in (reservoir) geomechanics

Side view

…

1

2

4 1

2 4

2

3

4 Civil structural problems:

Mechanics of “Addition”, “Uniaxial”

Underground Geomechanics problems:

Mechanics of “Removal”, “polyaxial”

Before

drilling/excavation

Start of

drilling/excavation

Further advance of

drilling/excavation Monitoring points

stress

strain

3

Nature of Underground Geomechanics

(6)

Stresses concentration around a cylindrical hole and wellbore failure

Zoback MD, 2007, Reservoir Geomechanics, Cambridge University Press

(7)

σ_θ σ_r

τ_rθ

S_h,min

S_H,max R

• Kirsch solution

– Problem of stress distribution around a circular borehole was solved by Kirsch (1898)

– Homogeneous, isotropic and elastic rock under plane strain condition within elastic range

Stresses concentration around a cylindrical

hole and wellbore failure

(8)

R: radius of well

r: radial distance from the center of the well

θ: measured from S_H,max

S_H,max and S_H,max: maximum and minimum horizontal insitu stress

2 2 4

max min max min

2 2 4

4 3

1 1 cos 2

2 2

H h H h

r

S S R S S R R

r r r

  ^ ^  ^ ^ ^   ^ 

2 4

max min max min

2 4

1 1 3 cos 2

2 2

H h H h

S S R S S R

r r

  ^ ^  ^ ^ ^  ^ 

   

2 4

max min

2 4

2 3

1 sin 2

2

H h

r

S S R R

r r

   ^ ^   ^ 

σ_θ σ_r

τ_rθ

S_h,min

S_H,max R

Stresses concentration around a cylindrical hole and wellbore failure

Kirsch solution

(9)

• Kirsch solution - Uniaxial boundary stress

– Stress concentration factor due to uniaxial stress is ‘3’.

– Influence of borehole is within 2~3 times of radius

Stresses concentration around a cylindrical

hole and wellbore failure

(10)

• Kirsch solution - Biaxial boundary stress

σ_y

σ_y -σ_y

3σ_y σ_x

3σ_x

-σ_x σ_x

σ_x

-σ_y+3σ_x

3σ_y-σ_x

σ_x σ_y

σ_y

+

In a uniaxial stress field, the

=

maximum stress concentration is 3 (compressive) and

minimum is -1 (tensile)

By superimposing two cases, we can obtain stress

concentration under biaxial stress field.

Stresses concentration around a cylindrical

hole and wellbore failure

(11)

• Kirsch solution - Uniaxial boundary stress

– At boundaries (by putting R=r)

r 0

 

 

max min 2 max min cos 2

H h H h

S S S S

     

r 0

 

2 4

max min max min

2 4

1 1 3 cos 2

2 2

H h H h

S S R S S R

r r

          

max min

0, _ S_H 3S_h

     

max min

90, _ 3S_H S_h

    

σ_{θ, θ=0} σ_{θ, θ=90}

S_H,max

S_h,min

Stresses concentration around a cylindrical

hole and wellbore failure

(12)

• Isotropic boundary stress

Stresses concentration around a cylindrical

hole and wellbore failure

(13)

Stresses concentration around a cylindrical hole and wellbore failure

• Anisotropic boundary stress

(14)

Stresses concentration around a cylindrical hole and wellbore failure

• Increase of internal mud/hydraulic pressure

– Water pressure – Mud pressure

– Injection pressure

2 r w 2

P a

  r

2 w 2

P a

 r

   p_w Tangential

stress 접선응력

r 0

 

2

w r

u P a

  G r 0 v_ 

a:radius

r: distance from the center

(15)

• Increase of internal mud/hydraulic pressure

p_w 접선응력

Stresses concentration around a cylindrical

hole and wellbore failure

(16)

• Isotropic boundary stress + internal pressure (0.5)

0.

5

Stresses concentration around a cylindrical

hole and wellbore failure

(17)

• Isotropic boundary stress + internal pressure (0.8)

0.

8

Stresses concentration around a cylindrical

hole and wellbore failure

(18)

• Isotropic boundary stress + internal pressure (2 or 4)

• Hydraulic fracturing occur when internal pressure is large.

• The location of the initiation of fracture can be decided depending on the boundary stress

2 or 4

Stresses concentration around a cylindrical

hole and wellbore failure

(19)

• Effect of temperature change - thermal stress

– Thermally induced hoop stress at the wall of cylindrical borehole

r 0

 

 0

1 ^w

E T T

 

  



r 0

 

α: linear thermal expansion coefficient E: Elastic Modulus

T_w: well temperature T₀: reservoir temperature

T_w T₀

Stresses concentration around a cylindrical

hole and wellbore failure

(20)

• Thermal stress due to cold mud/water injection is important for geothermal project

– Ex) Injecting water T = 25°C, reservoir T = 75°C, Elastic modulus

= 50 GPa, ν=0.25, α = 1x10^-5/°C  hoop stress = 33 MPa  big influence!!!

Stresses concentration around a cylindrical hole and wellbore failure

Effect of temperature change - thermal stress

(21)

Stresses concentration around a cylindrical hole and wellbore failure

• Stresses distribution around a borehole with;

– Principal in situ stress boundary

– Internal pore pressure (could be mud pressure) – Temperature change

2 2 4

max min max min

2 2 4

2 2

4 3

1 1 cos 2

2 2

H h H h

w r

S S R S S R R

r r

P R

r r

  ^ ^  ^ ^ ^   ^  

 

2 4

max min max min

2 4 0

2 2

1 1 3 co

s 2 1

2 2

H h

w

H h

w

S S R S S R

r r

P R T

r

E T

  



   

 

        

 

 

2 4

max min

2 4

2 3

1 sin 2

2

H h

r

S S R R

r r

  ^ ^   ^ 

(22)

Stresses concentration around a cylindrical hole and wellbore failure

• Some insights

• Stresses distribution around a borehole is

– independent of size of radius

– independent of Elastic modulus of rocks

– Poisson’s ratio has some influence on vertical stress distribution (in vertical hole)

(23)

max

SH min

Sh

max

SH

min

Sh

Tensile stress/

hydraulic fracturing

Borehole breakout Borehole breakout

Tensile stress/

hydraulic fracturing

borehole breakout vs. hydraulic fracturing

Stresses concentration around a cylindrical

hole and wellbore failure

(24)

• Kirsch solution with pore pressure in porous medium Stresses concentration around a cylindrical

hole and wellbore failure

σ_θ σ_r

τ_rθ

S_h,min

S_H,max R

Missing in the ebook

(25)

Stresses concentration around a cylindrical hole and wellbore failure

(26)

Stresses concentration around a cylindrical hole and wellbore failure

(27)

Stresses concentration around a cylindrical hole and wellbore failure

(28)

• Borehole breakout

– When stress exceed the rock strength near the borehole

r=R,

Borehole Breakout

or or at r=R …

compare

(29)

Borehole Breakout

• Location

– Perpendicular to maximum principal stress

Occur in pairs in opposite direction

– Opening angle of Borehole Breakout: W_BO – Comprehensive analysis of borehole

breakout yields profiles of stress orientation

• Characterization through logging:

– Ultrasonic image log:

Fracture in dark area (low amplitude)

Travel time increase when radius is increased

– Electrical image log:(e.g., FMI)

out of focus area (due to poor contact of

electrode at breakout) ^maximum

principal stress Ultrasonic

televiewer image

Electrical image

(30)

Borehole Breakout

• Borehole stabilize with mud weight increase

– Zone of failure gets smaller – Principle of mud weigtht control

ΔP=0 MPa  ΔP=10 MPa

(31)

Borehole Breakout progression of failure

• Some observations:

– BB tends to deepen (instead of widening)

– Good correlation with theoretical prediction – Cooling make less BB – Effect of rock strength

anisotropy

– Effect of mud chemistry – Penetration of mud into

fractured rock

(32)

Borehole Breakout Rock Anisotropy

• Rock strength anisotropy can affect the shape of BB

– Due to the weak planes – double lobes are observed

• Situation of importance

– Vertical drilling through steep bedding plane

– Highly deviated well through near-horizontal bedding

(33)

Borehole Breakout

Elastic vs. Elasto-plastic analysis

• Elastic analysis with borehole breakout is a simplification

– Elasto-plastic analysis is more ideal

– Nevertheless, elastic

analysis is still fairly good – simple theory is still

powerful

(34)

• Caliper log

– continuous measurement of the size and shape of a borehole along its depth – Borehole break has to be distinguished from keyseat.

 Keyset: grooves in the side of the well caused by the rubbing of pipe (asymmetrical). When there is rapid turn of well trajectory

 Washout: enlargement of the entire wellbore (complete failure)

Determination of breakout orientation from caliper log

Rider M and Kennedy M, 2011, The geological interpretation of well logs, 3^rded., Rider French

https://www.glossary.oilfield.slb.com

(35)

Determination of breakout orientation from caliper log

• Example: Consistent stress direction mapped from caliper log

(36)

Determination of breakout orientation from caliper log

Comparison of different methods:

Borehole televiewer, six arm caliper and electrical imaging

(37)

Drilling induced tensile fracture

• Drilling induced tensile fracture

– Local tension at the wellbore wall during drilling – Will not lead to hydraulic fracturing unless mud

weights exceed the least principal stress – Wellbore image log is the only way to identify

ΔP=0 MPa  ΔP=10 MPa

Drilling induced Tensile fracture

Borehole breakout

(38)

Drilling induced tensile fracture

• Examples

– Drilling induced tensile fractures by electrical image log

– S_Hmax measured by drilling

induced tensile frature matches with S_Hmax by borehole break

(39)

Drilling induced tensile fracture

• Examples North Sea

– 1261 observations at five wells (depth

2,500 m – 5,200 m), up to ~ 20 km apart – Standard deviation:

~ 10°

– Uniform stress fields are determined from drilling induced

tensile failure

(40)

Drilling induced tensile fracture

Observation at strike-slip faulting regime

• Tensile fracture and strike-slip faulting

– At μ = 0.6

– Minimum hoop stress

When cooling, and Δp are negligible

– In, strike-slip faulting stress regime, wellbore wall will go into tension at the azimuth of SHmax even without high wellbore pressure or cooling effect

(41)

Drilling induced tensile fracture

• Condition of tensile failure in relation to stress regime

(42)

Quality ranking system for stress indicators

• Four types of stress indicators (indicated at depths)

– Earthquake focal mechanism: 3~15 km – Stress-induced wellbore breakout: 1~4 km – Drilling-induced tensile fracture

– Open hole hydraulic fracturing – usually at shallow depth (not in petroleum/geothermal)

• Quality of stress indicators: A, B, C & D (D is not acceptable)

– The greater the depth interval where wellbore observations are made

– The larger the number of observation – The smaller the standard deviation

(43)

Quality ranking system for stress indicators

(44)

Quality ranking system for stress indicators

• Mean borehole breakout direction

– Use cosine & sine (instead of direction directly, why?)

(45)

Thermal effect

• Can be important when wellbore fluid is at a significantly different than the rock

• Cooler mud pressure generate tensile stress at the wall

Transient solution

Steady state solution

(46)

• Effect of temperature change - thermal stress

– Thermally induced hoop stress at the wall of cylindrical borehole

r 0

 

 0

1 ^w

E T T

 

  



r 0

 

α: linear thermal expansion coefficient E: Elastic Modulus

T_w: well temperature T₀: reservoir temperature

T_w T₀

Thermal effect

Silica content is critical for thermal expansion coefficient

(47)

Thermal effect

• Expected time to reach steady state

min

(48)

Multiple Mode of compressive wellbore failure

• Assumption in wellbore breakout about the principal stress:

– (hoop stress is the maximum principal stress, radial stress is the least principal stress).

• Other modes can cause compressive wellbore failure

washout

σ₁ σ₂ σ₃

σ₁

σ₁ σ₃

σ₃ σ₂

σ₂

B X

Z

Fjaer E et al., 2008, Petroleum-related Rock Mechanics, 2nd Ed., Elsevier

Fjaer E et al., 2008