Reservoir Geomechanics - Amazon S3€¦ · Reservoir Geomechanics In situ stress and rock mechanics...

Reservoir Geomechanics

In situ stress and rock mechanics applied to reservoir processes ��

Week 4 – Lecture 8 Stress Concentrations/Vertical Wells – Chapter 6

Mark D. Zoback Professor of Geophysics

Section 1 •  Stress Concentration Around Vertical Wells

Section 2 •  Wellbore Breakouts (Compressive Wall Failures) Section 3 •  Drilling Induced Tensile Failures (Tensile Wall

Failures)

Section 4 •  Other Factors Affecting Breakouts

Stanford|ONLINE gp202.class.stanford.edu

2

Outline

After Kirsch (1898)

Local stress field perturbed due to the borehole

Figure 6.1 – pg. 169


3

θτ

θνσ

σθσ

θσ

θ

θθ

2sin)321)((21

2cos)(2

2cos)31)((21)1)(2(

21

2cos)341)((21)1)(2(

21

4

4

2

2

minr

2

2

min

2

20

4

4

min2

2

0min

2

20

4

4

2

2

min2

2

0min

max

max

maxmax

maxmax

rR

rRSS

RrSSS

rRP

rRSS

rRPSS

rRP

rR

rRSS

rRPSS

h

hvzz

Thh

hhrr

H

H

HH

HH

−+−=

−−=

−−+−−+−+=

++−−+−−=

Δ

−

Kirsch Eqns. –Vertical Well, Stress Field (SHmax, Shmin) Internal Pressure P0, Θ measured from SHmax

R – Wellbore radius r – radial distance from center

Equations 6.1 - 6.3 – pg. 170


4

Parameters for Figures 6.2, 6.3, & 6.5

MPa5.31 MPa5.51

3213m) (depth MPa 2.88west)-(east EN90 is norientatio

MPa90

min

max

max

==

=

=

=

mudp

h

v

H

H

PPSSSS

Example Parameters – pg. 170


5

Figure 6.2 a,b,c – pg. 171 Stanford|ONLINE gp202.class.stanford.edu

6

Concentration of Hoop Stress

Stress Concentration at the Wall of a Vertical Well

Compressive and tensile wellbore failure is a direct result of the stress concentration around the wellbore that results from drilling a well into an already-stressed rock mass. In a homogeneous and isotropic elastic material in which one principal stress acts parallel to the wellbore axis, the effective hoop stress and radial stress at the wall of a cylindrical, vertical wellbore (overburden stress, Sv is a principal stress acting parallel to the wellbore axis) is given by the following equation:

σθθ = Shmin + SHmax - 2(SHmax - Shmin) cos2θ - 2P0 - ΔP – σΔT

σrr = ΔP where θ is an angle measured from the azimuth of the maximum horizontal stress, SHmax,

Shmin is the minimum horizontal stress, P0 is the pore pressure, ΔP is the difference between the wellbore pressure (mud weight) and the pore pressure, and σΔT is the thermal stress induced by the cooling of the wellbore by ΔT.

The effective stress acting parallel to the wellbore axis is:

σzz = SV - 2ν(SHmax - Shmin) cos2θ – P0 - σΔT where ν is Poisson's ratio.

Equations 6.4 - 6.6 – pg. 174 Stanford|ONLINE gp202.class.stanford.edu

7



Failures)



8

Outline

Stress Concentration Around a Vertical Well


9

wBO

SHmax


10

Wellbore Failures

Compressional Wellbore Failures

Stress-induced wellbore breakouts form due to compressive wellbore failure that occurs within the region of maximum compressive stress around a wellbore. In a vertical well, the zone of compressive failure is centered at the azimuth of minimum horizontal far-field compression, as this is where the compressive hoop stress is greatest.

•  Wellbore breakouts were first identified using 4-arm magnetically-oriented caliper logs associated with Schlumberger dip meters. Careful analysis yields reliable stress orientations.

•  Clear identification of breakouts requires the use of acoustic televiewer data (UBI, CBIL, CAST).

•  6-arm dip meter data (Baker Hughes and Halliburton) require especially careful analysis to distinguish breakouts from tool eccentricity, key seating, etc.

•  The caliper data from 4- and 6- arm electrical image data (FMI, STAR, or EMI) cannot be used to detect small wellbore breakouts because of the large pad widths of these tools.

•  Breakouts can sometimes be seen as out-of-focus zones on the image data


11

A Simple View of Wellbore Stability

σ1

σ2

σ3


12

Regional Stress Field in the Timor Sea


13

Why Wellbore Failure So Effectively Samples the Stress Field

At the point of minimum compression around the wellbore (i.e, at θ = 0, parallel to SHmax), Equation (1) reduces to

σθθ

min = 3Shmin - SHmax - 2P0 - ΔP - σΔT

Whereas, at the point of maximum stress concentration around the

wellbore (i.e, at θ = 90°, parallel to Shmin),

σθθmax = 3SHmax - Shmin - 2P0 - ΔP - σΔT

σθθ

max - σθθmin = 4 (SHmax- Shmin)

Equations 6.7 - 6.9 – pg. 174


14

Raising Mud Weight Increases Wellbore Stability


15


16

Breakout Width

Figure 6.5 a,b – pg. 177


17

Raising Mud Weight

Wellbore Stress Concentration – Same Depth, Different Stress States


18

Figure 6.8 a,b – pg. 182 Stanford|ONLINE gp202.class.stanford.edu

19

Regional Stress Fields

Figure 6.10 – pg. 184 Stanford|ONLINE gp202.class.stanford.edu

20

Complex Stress Field

4-Arm Dipmeter Tool Schematic


21


22

Analyzing 4-Arm Caliper Log

“Elongation” Directions in the Visund Field


23

Keyseats in Bore Hole Televiewer (BHTV)

tan 2° x 1000ft = 35 ft Stanford|ONLINE gp202.class.stanford.edu

24

Figure 6.11a,b,c – pg. 185 Stanford|ONLINE gp202.class.stanford.edu

25

6-Arm Caliper Data

Figure 6.12a,b,c – pg. 186


26

Comparison of Analysis Techniques

Quality Ranking System (Zoback and Zoback)

A B C D Earthquake Focal Mechanisms

Average P-axis or formal inversion of four or more single-event solutions in close geographic proximity (at least one event M ≥ 4.0, other events M ≥ 3.0)

Well-constrained single-event solution (M ≥ 4.5) or average of two well-constrained single-event solutions (M ≥ 3.5) determined from first motions and other methods (e.g., moment tensor wave-form modeling, or inversion)

Single-event solution (constrained by first motions only, often based on author's quality assignment) (M ≥2.5) Average of several well-constrained composites (M ≥ 2.0)

Single composite solution Poorly constrained single-event solution Single-event solution for M < 2.5 event

Wellbore Breakouts Ten or more distinct breakout zones in a single well with S.D. ≤ 12o and/or combined length > 300 m Average of breakouts in two or more wells in close geographic proximity with combined length > 300 m and S.D. ≤ 12o

At least six distinct breakout zones in a single well with S.D. ≤ 20o and/or combined length > 100 m

At least four distinct breakouts with S.D. < 25o and/or combined length > 30 m

Less than four consistently oriented breakout or > 30 m combined length in a single well Breakouts in a single well with S.D. ≥ 25o

Drilling-Induced Tensile Fractures

Ten or more distinct tensile fractures in a single well with S.D. ≤ 12o and encompassing a vertical depth of 300m, or more

At least six distinct tensile fractures in a single well with S.D. ≤ 20o and encompassing a combined length > 100 m

At least four distinct tensile fractures with S.D. < 25o and encompassing a combined length > 30 m

Less than four consistently oriented tensile fractures with < 30 m combined length in a single well . Tensile fracture orientations in a single well with S.D. ≥ 25o

Hydraulic Fractures Four or more hydrostatic orientations in a single well with S.D. ≤ 12o depth > 300 m Average of hydrofrac orientations for two or more wells in close geographic proximity, S.D. ≤ 12o

Three or more hydrofrac orientations in a single well with S.D. <20o. Hydrofrac orientations in a single well with 20o.< S.D. <25o

Hydrofac orientations in a single well with 20o < S.D. <25o Distinct hydrofrac orientation change with depth, deepest measurements assumed valid One or two hydrofrac orientations in a single well

Single hydrofrac measurements at < 100 m depth

Table 6.1 – pg. 189 Stanford|ONLINE gp202.class.stanford.edu

27

Statistics of Azimuthal Data

ksd

RNNk

lmmlR

R

mm

R

llml

m

n

ii

n

ii

n

ii

n

ii

iiii

81 ; 1

tan ;

and ; sin and cos

1

11

2

11

=−−

=

⎟⎠

⎞⎜⎝

⎛=+=

====

−

==

==

∑∑

∑∑

θ

θθ


28

Drilling Induced Tensile Fractures A drilling-induced tensile wall fracture will be induced when

σθθmin = 3Shmin – SHmax – 2Pp – ΔP – σΔT

Ignoring σΔT (for the moment) and assuming To ~ 0, a tensile fracture will from at the wellbore wall when:

Pmud = 3Shmin – SHmax – Pp ≈ 0

This is the same equation for inducing a hydraulic fracture. What distinguishes a drilling-induced tensile fracture from a hydraulic fracture are:

•  Drilling-induced tensile fractures form when the mud weight is comparable, or slightly greater than the pore pressure (but is not comparable to S3). This only occurs for certain stress states and well orientations.

•  Drilling-induced tensile fractures are limited to the wellbore wal.l Because the fracture does not propagate into the formation, drilling-induced tensile fractures are not associated with lost circulation or drilling problems.


29



Failures)



30

Outline


31


wBO

SHmax


32

Wellbore Failures



33

Visund Field Orientations


34

Drilling Induced Tensile Fractures — Visund Field


35

Tensile Fractures in Vertical Wells Generally Imply a Strike-Slip Faulting Environment

Earth (Strike-Slip Faulting)

( ) 1.31PSPS 2

2

pminh

pmaxH =µ++µ=−

−for µ = 0.6

SHmax = 3.1 Shmin – 2.1 Pp

SHmax = 3Shmin – 2Pp + 0.1 (Shmin – Pp)

Vertical Wellbore (Tensile Fractures)

σθθ = 3Shmin – SHmax – 2Pp = -T for T = 0

SHmax = 3Shmin – 2Pp


36

Tensile Fractures in Vertical Wells

Figure 6.13 – pg. 193 Stanford|ONLINE gp202.class.stanford.edu

37



Failures)



38

Outline

Thermoelastic Effects on Wellbore Stresses

The effect at the wellbore wall of a temperature difference ΔT between the wellbore fluid and the rock surrounding well is given by the equation:

σθθΔT = (α E ΔT)/(1-ν)

where α is the linear coefficient of thermal expansion and E is Young's modulus.

For drilling-induced tensile fractures in the Visund field in the North

Sea, a cooling of ~30° C at a depth of ~2750 m resulted in σθθΔT = 1.7 MPa based on the following: α = 2.4x10-6 °C-1 (corresponding to a rock composed of 50% quartz), E = 1.9x104 MPa (from the measured P-wave velocity) and ν = 0.2 (based on the P to S-wave velocity ratio).

Equation 6.22 – pg. 193


39

a)

b)

c)

Cooling does reduce breakout size (but not very practical) -The effect on tensile fractures is more important (but still not as important as mud weight).

Thermal Stresses and Breakout Formation


40

Tensile Fractures in Vertical Wells

Figure 6.13 a,b,c – pg. 193


41

Fixed Breakout Width After Initiation

More on Compressional Wellbore Failure


42

Breakout Shapes Under Successive Episodes of Failure – wBO is constant


43

wBO

a)

b) c)

Breakouts > 90° ?


44

Weak Bedding Planes Can Be a Source of Wellbore Instability


45

Breakouts in Sands (Isotropic Strength) Deviated Well


46

Anisotropic Strength Causes Unusual Breakouts in Shale


47

Weak Bedding Planes Can Be a Source of Wellbore Instability


48

Impact of Chemical Effects on Wellbore Stability

Mody & Hale (1993) model for chemical osmosis: (Non time-dependent)

P = Pp + β × RT/V × ln(Am/Ap)

P: Near-wellbore pore pressure [MPa] Pp: Far-field pore pressure [MPa] β: Membrane efficiency [ ], 0 ≤ β ≤ 1 (OBM has a membrane efficiency of 1) R: Gas constant, = 8.3 [J/(mol x degree Kelvin)] T: Absolute temperature [degree Kelvin] V: Partial molar volume of water [m3/mol] Am: Water activity in drilling fluid [ ] Ap: Water activity in pore fluid (an activity of 1 corresponds to fresh water) [ ]

Pore pressure in the near wellbore zone is affected by fluid transport due to differences in water molar free energies of the drilling and pore fluids (chemical osmosis).

Poroelasticity equations are explicitly correct only for zero time, just after drilling.


49

Illustration of Mody & Hale Model

•  According to the Mody & Hale model, high salinity muds stabilize the formation, because chemical osmosis causes a drop in formation pressure (increase in σrr) near the wellbore wall.

•  Conversely, a low salinity mud destabilizes the formation because chemical osmosis “charges” the formation and σrr increases near the wellbore wall.

Formation Wellbore

Pp

High PMud

Mud Activity < Formation Fluid Activity��(High Salinity Mud)

σrr

Formation Wellbore

Pp

High PMud

σrr

Mud Activity > Formation Fluid Activity��(Low Salinity Mud)

β × RT/V × ln(Am/Ap)

β × RT/V × ln(Am/Ap)


50

A Simple View of Maintaining Wellbore Stability

σ1

σ2

σ3


51


52


Reservoir Geomechanics - Amazon S3€¦ · Reservoir Geomechanics In situ stress and rock mechanics...

Documents

Transcript of Reservoir Geomechanics - Amazon S3€¦ · Reservoir Geomechanics In situ stress and rock mechanics...