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Lost Circulation
Poor Hole Cleaning
Hole Caving /Collapse
WELLBORE
STABILITY
WELLBORE
STABILITY
Formation
Mud
TensileFailure Active
Tectonics
ShearFailure
PorePressure
STABLE
UNSTABLE
Rock StrengthRock Stress
Hole Enlargement
Drill String Fatigue
Tight hole /Stuck Pipe
Drilling Handbook
1.0 INTRODUCTION
2.0 BEFORE THE WELLBORE
3.0 AFTER THE WELLBORE
4.0 PROVIDING A STABLE WELLBORE
APPENDIX
1.1 Wellbore Stability Mission 21.2 Drilling Handbook Objectives 3
2.1 Conditions 12.2 Earth Stress 42.3 Effective Stress 52.4 Rock Strength 6
3.1 Near Wellbore Stress-State 13.2 Mechanical Stability 43.3 Chemical Stability 11
4.1 Planning a Stable Wellbore 14.2 Warning Signs/Corrective Actions 3
A-1 Leak-off TestsA-2 Lithology Factor (k)A-3 Wellbore Stress EquationsA-4 Nomenclature
In Situ
In Situ
Wellbore Stability
CONTENTS
StartStart
Introduction
Formation
Mud
TensileFailure Active
Tectonics
ShearFailure
PorePressure
STABLE
UNSTABLE
Rock StrengthRock Stress
SandMWHigh
MWLow Reaming
TripSpeed
ECD MobileSalt
Shale StrikeSlip
TensileFailure
HoleCleaning
ReverseFault
TimeExposed
- Wellbore Stability -Maintaining the Balance of
Rock Stress and Rock Strength
SECTION 1
1.1 Wellbore Stability Mission
1.2 Drilling Handbook Objectives
StartStart TOCTOC
Wellbore Stability
Page - 1Section 1
1.0 INTRODUCTION
Wellbore stability
600 million to 1 billion dollars
is the prevention of brittle failure or plastic deformationof the rock surrounding the wellbore due to mechanical stress or chemicalimbalance.
Prior to drilling, the mechanical stresses in the formation are less than thestrength of the rock. The chemical action is also balanced, or occurring at arate relative to geologic time (millions of years). Rocks under this balancedor near-balanced state are stable.
After drilling, the rock surrounding the wellbore undergoes changes intension, compression, and shear loads as the rock forming the core of thehole is removed. Chemical reactions also occur with exposure to thedrilling fluid.
Under these conditions, the rock surrounding the wellbore can becomeunstable, begin to deform, fracture, and cave into the wellbore or dissolveinto the drilling fluid.
Excessive rock stress can collapse the hole resulting in stuck pipe. Hole-squeezing mobile formations produce tight hole problems and stuck pipe.Cavings from failing formation makes hole cleaning more difficult andincreases mud and cementing costs.
Estimated cost to the drilling industry for hole stability problems rangefrom annually.
StuckPipe
HoleProblems
Loss OfCirculation
WellControl
Relative Costs Of Unscheduled EventsCaused By Wellbore Stability Problems
StartStart TOCTOC Section 1TOC
Section 1TOC
Wellbore Stability
Page - 2Section 1
1.1 Wellbore Stability Mission
The mission of the Wellbore Stability Team is twofold.
Minimize the "learningcurve" when developingnew reservoirs so thatoptimal well costs areobtained early on.
Identify potential drillingproblems during the wellplanning stage so thatprevention and operationalplanning can be developedto minimize costs associatedwith wellbore stabilityproblems.
Chemical Instability Mechanical Instability
Tensile Shear
FracturesLoss of Circulation
CavingsTight HoleStuck Pipe
Reactive Shale Overburden StressedGeopressured
Hydro-PressuredUnconsolidated
FracturedTectonics
Failure Mechanisms
Wellbore Stability Problems
StartStart TOCTOC Section 1TOC
Section 1TOC
Wellbore Stability
Page - 3Section 1
Understanding the conditions that cause stability problems provides for:
More effective planning.
Earlier and easier detection of warning signs.
Contingency plans to avoid the progression of the problem.
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!
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GENERAL CAUSES OFSTABILITY PROBLEMS
STABILITY PROLEMS
COST TO OPERATION
RESULTING CONDITIONS
IncorrectMud
IncorrectWell Trajectory
Poor Drilling
PracticesPoor W
ellPlan
Reactiveshale
Reactiveshale
ExcessiveW
ellborePressure
ExcessiveW
ellborePressure Excessiv
e
Rock StressExcessiv
e
Rock Stress
Hol
eCl
eani
ng
Hol
eCl
eani
ng
Hole
Enlargement
Hole
Enlargement
Hole
Collapse
Hole
Collapse
Well ControlWell Control
Lost CirculationLost Circulation
Poor logsPoor logs
Cementing Problems
Cementing ProblemsStuck PipeStuck Pipe
Drill String FatigueDrill String Fatigue
1.2 Handbook Objectives
!
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Identify and define wellbore stability problems.
Suggest consistent terminology.
Associate warning signs with stability problem.
Suggest corrective actions.
Provide the background for preventive planning.
StartStart TOCTOC Section 1TOC
Section 1TOC
SECTION 2
Before The Wellbore
2.1 Conditions
2.2 Earth Stress
2.3 Effective Stress
2.4 Rock Strength
In Situ
In Situ
StartStart TOCTOC
2. 0 BEFORE THE WELLBORE
2.1 ConditionsIn Situ
Porosity
Porosity is the percent of void space within the rock.
The rocks of sedimentary basins always exhibit some porosity. As porosityincreases, the percent of fluid volume increases while the rock matrixvolume decreases. Increasing porosity weakens the rock. Shale, forexample, will change from brittle rock to ductile clay with sufficient watercontent. The figure below shows typical porosity change with depth due tocompaction and cementation.
Wellbore Stability
Page - 1Section 2
Permeability
Permeability is the ability of a rock to flow fluids; measured in units ofdarcies.
Permeability acts to weaken the rock as the loss of water base mud filtratedissolves the grain-to-grain cement bond. Also, hydrostatic overbalanceforces water filtrate to penetrate the pores of the rock; which also weakensthe rock.
Shale
Fluid FilledPores
RockMatrix
0
5
10
15
20
25
10 20 30 40 50 60
Porosity (%)
Dep
th(f
t)
StartStart TOCTOC Section 2TOC
Section 2TOC
Wellbore Stability
Page - 2Section 2
The figure below shows typical permeability changes relative to depth forshale and sandstone. Shales may have high porosity, but have very littlepermeability.
Formation Pore Pressure - p
Formation pore pressure is the pressure of the naturally occurring fluid(s) inthe pores of the rock.
As long as the increase in overburden load from the rate of deposition doesnot exceed the rate at which fluid can escape from the pore, a fluidconnection exists from surface to the depth of interest. Pore pressure is thenequal to the hydrostatic pressure of formation water (normal pressure).
is equal to the hydrostatic pressure offormation water at a vertical depth of interest.Normal formation pressure
Permeability (Darcies)
Sandstone
Fluid FilledPores
ConnectedPorosity
RockMatrix
0
5
10
15
20
25
1 2 3 4
SandstoneShale
Dep
th(f
t)
Transition Shale
Formation WaterMigrating to Surface
Dep
th
Pressure
.465
psi/ft A
verag
e
8,000'
3720 psi
StartStart TOCTOC Section 2TOC
Section 2TOC
Wellbore Stability
Page - 3Section 2
Pore pressure of a permeable formation can be depleted below normal byproduction operations (subnormal pressure).
is less than normal for the vertical depthof interest.Subnormal formation pressure
If the fluid cannot escape the pore, pore pressure begins to increase at afaster-than-normal rate (abnormal pressure).
is greater than normal for the vertical depthof interest.Abnormal formation pressure
Dep
th
Pressure
Transition Shale
Depleted Zone
AbnormalPressure
Sub normalPressure
Normal TrendLineFormation Water
Migrating to Sand
8,000'
3720 psi
Estimating Formation Pore Pressure
Formation pore pressure prediction is a highly specialized process. Prior todrilling, qualitative geophysical methods are available to qualify thepresence of abnormal pressure at an approximate depth. Offset logs alsohelp estimate pore pressure.
Enhancements in geophysical interpretations have recently been made toquantify the value of abnormal pressure prior to spudding the well. Beforedevelopment of this quantitative method, only qualitative information waspossible prior to drilling.
While drilling, several MWD/LWD logs provide real time evaluation offormation pore pressure. "D" exponent plots can also indicate changes inpore pressure.
Higher than normal porosity and sonic travel time ( t ) indicate abnormal
pore pressure.
∆ c
StartStart TOCTOC Section 2TOC
Section 2TOC
Wellbore Stability
Page - 4Section 2
Weight of overlying rocks &water appliesstress to therock layer at avertical depthof interest
STRESSESHORIZONTAL
OVER
BURDENSTRESS
OVER
BURDENSTRESS
Most formations are formed from a sedimentation/compaction geologichistory. Formations may vary significantly from the earth's surface to anydepth of interest. Shallow shales will be more porous and less dense thanshales at great depths.
Typically a value of 1 psi/ft is attributed to the overburden gradient, but atshallow depths the actual value is much less and at greater depthssomewhat higher.
A density log can be used to determine the weight of the overburden. In theabsence of a density log, the overburden stress may be estimated fromalternatives such as Eaton's variable density curve or the Wylie timeaverage equation using sonic travel time, bulk density and porosity.
Estimating Overburden Stress
2.2 Earth Stress
- s
In Situ
Prior to drilling, subsurface rocks are exposed to a balanced or nearbalanced stress environment. The naturally occurring stress in place iscalled the stress. stress is normally compressive due to theweight of the overburden. For this reason, in rock mechanics compressivestress is defined to be positive.
Overburden stress is the pressure exerted on a formation at a given depthdue to the total weight of the rocks and fluids above that depth.
in situ In situ
Overburden Stress v
StartStart TOCTOC Section 2TOC
Section 2TOC
Wellbore Stability
Page - 5Section 2
As the overburden squeezes the rock vertically, it pushes horizontally.Constraint by surrounding rock creates horizontal stress.
In most drilling areas, the horizontal stresses are equal. When drillingnear massive structures such as salt domes or in tectonic areas, thehorizontal stresses will differ and are described as a minimum (s ) and a
maximum (s ).
The minimum horizontal stress (s ) is normally determined from leak-off
tests. It is difficult to determine the maximum horizontal stress from fieldmeasurements. Its value can be estimated using rock mechanicsequations.
Horizontal Stress - s sh , H
h
H
h
Estimating Horizontal Stress
2.3 Effective Stress
The rock matrix does not support the full load of overburden and horizontalstress. Part of the load is supported by the fluid in the pore (pore pressure).The net stress is the effective stress felt by the rock matrix. Effective stressis used in rock mechanics to determine the stability of the wellbore.
The overburden stress that effectively stresses the rock matrix.
= s -
Effective Overburden Stress - σv
Effective Overburden Stress = Total Overburden Stress - Pore Pressure
σv v p
Much like air pressure in a cartire supports the weight of thecar, fluid pressure in the poresupports a portion of theoverburden load.
The remaining portion of over-burden stress is the loadeffectively stressing the rockmatrix.
ROCKMATRIXROCK
MATRIX
5000 PSIPore Pressure
EffectiveOBS
EffectiveOBS
4000psi
4000psi
9000 PSIOVERBURDEN
9000 PSIOVERBURDEN
StartStart TOCTOC Section 2TOC
Section 2TOC
Wellbore Stability
Page - 6Section 2
Effective Horizontal Stress - ,σ σh H
Similarly, the effective horizontal stresses can be determined. Usually thehorizontal stresses are equal and the effective horizontal stress is equal tothe effective overburden stress times a lithology factor, . The lithologyfactor ( ) is equal to 1 for fluids but is less than 1 for more rigid materialsuch as formation rock.
= = x
kk
kσ σ σh H v
2.4 Rock Strength
Rock mechanics mechanical
stress
strain
elastic deformation
is the study of the behavior of subsurfacerocks.
Core samples (removed from conditions) are usually tested incompression with specialized laboratory equipment. To better simulatesubsurface conditions, core samples tested are also subjected to a confiningpressure ( ). The rock responds to the stress by changing in volume orform (deformation) or both. The change in the rock volume or form due tothe applied stress is called .
Rocks subjected to compressive (+) or tensile (-) stress can go through threestages of strain deformation. In , the rock deforms asstress is applied but returns to its original shape as stress is relieved. Inelastic deformation, the strain is proportional to the stress (Hooke's Law).
in situ
In tectonically active areas, the horizontal stresses are not equal. Themaximum horizontal stresses will be higher, or lower depending on tectonicmovements, by the additional tectonic stresses, In these areas, the
effective horizontal stresses are described by a maximum and minimumvalue.
= x + and = x +
In extreme tectonic environments, may be sufficient to make the
horizontal stress higher than the vertical stress.
t and t .
k t k t
t
h H
h H
H
σ σ σ σh v H v
1000 psi 900 psi 500 psi
Water Putty RockNoncompressiblefluids like waterhave a k factor of 1.
Stiffer materialslike putty have alower k factor (.7 -.9 for example.)
Very stiffmaterials likeformation rockhave a muchlower k factor(.37 is commonfor shale.)
StartStart TOCTOC Section 2TOC
Section 2TOC
Wellbore Stability
Page - 7Section 2
When applied stress reaches the elastic limit, the rock begins to exhibit. In plastic deformation, the rock only partially returns
to its original shape as stress is relieved. If continued stress is applied,fractures develop and the rock fails ( ).
Rocks can fail in a brittle manner, usually under low confining stress, or in aductile manner under higher confining stress.
Under compression rocks actually fail in - it is easier to slide rockgrains past each other than to crush them.
plastic deformation
ultimate failure
shear
Shear Strength and Shear Failure
Stress(xpsi)1000
10 2 3 4
AxialLoad
ElasticLimit
ElasticDeformation
PlasticDeformation
Ultimate
Failure
Ultimate Strength
Strain (% of Deformation)
0
10
20
30
40
50
AxialLoad
(CompressiveStress)
ConfiningPressure
Axial Load (psi)
ConfiningPressure
Shear PlaneShearFailure
High confining pressure resists sliding on the shear plane and the rockappears stronger. If the confining pressure and axial load were equal, therewould be no shear stress on the rock and no shear failure.
Equal stresses promote stability and unequal stresses promote shearstress and possible shear failure.
StartStart TOCTOC Section 2TOC
Section 2TOC
Wellbore Stability
Page - 8Section 2
It is not possible to accurately reproduce the effects of pore pressure onrock strength when testing core samples from the field. In actual boreholeconditions, pore pressure exerts a force that tends to push the rock grainsapart. This is why the effective stress is used in rock mechanics whenapplied to wellbore stability studies.
Cohesive StrengthBonded Grains (Cement)
OverburdenStress (s )v
Increased Pore PressureReduces the Effective Stress
PorePressure
HorizontalStress (s )h
HorizontalStress (s )H
Mean Effective Stress =σ σ σv h H+ +
3
Rock mechanics uses failure models to predict wellbore stability. One suchmodel considers all three effective stresses to calculate the resultant shearstress. The "mean" effective stress is used by this model to describe thestress state of the rock.
The failure model used in the illustrations (Mohr-Coulomb) neglects theintermediate stress and considers only the and effectivestress.The greatest shear stress on the rock occurs on the two-dimensionalplane consisting of the greatest and least stress. The greatest/and or leaststress could be any of the three depending on environment and wellconditions.
greatest least
in situ
Greatest Effective
Stress ( , , or )σ σ σv h H
Greatest Effective
Stress ( , , or )σ σ σv h H
Least Effective
Stress ( , , or )σ σ σv h H
(Intermediate stress actsperpendicular to the figure)
StartStart TOCTOC Section 2TOC
Section 2TOC
Wellbore Stability
Page - 9Section 2
Shear
Stress ( )τ
S0
ConfiningPressure ( )σc
CompressionPressure (Stress)That Fails Core
Sample ( )σf
Failure ShearStress From Test 1
Failure ShearStress From Test 2 & 3
< = φ< = φ
Stress-State 1Stress-State 2
Stress-State 3
Effective Compressive Stress (σ)
The is defined as the shear stress that fails the rock. Thecoefficient of friction is also expressed in terms of an
.
= tan
The cohesive strength (S ) and the angle of internal friction ( ) are
obtained from conducting compression tests on core samples (orestimated from logs) from the field. Several tests on cores are necessaryto determine these values.
The shaded area shown below indicates the "stress-state" of one such
core sample at failure. The compression stress ( ) that fails the core
sample (greatest stress) is plotted on the horzontal axis along with the
confining pressure ( ) used for that test (least stress).
shear strengthangle of internal
friction ( )φµ φ
φ
σ
σ
0
f
c
The shear stress that fails the rock must overcome the(bonding together of the grains), and the frictional resistance between
the grains ( The frictional resistance between the grains is the product
of the and the effective compressive stress ( ).
cohesive strength,S
coefficient of friction ( )
0
µσ).µ σ
Shear Stress = Cohesive Strength + Frictional Resistance
τ µσ= S +0
StartStart TOCTOC Section 2TOC
Section 2TOC
Wellbore Stability
Page - 10Section 2
The , thenecessary to fail the sample. Several tests at increasing confiningpressures produce successive stress-states of increasing shear strength.
The " " is approximated by the line giving the best fitto the maximum shear stress points on the failure plane from severalsuch tests. The equation for this line is given below.
= S + tan
A "shear strength line" or failure envelope shown below is producedfrom such core tests (a similar stability chart is used when considering
the mean effective stress, ( + + ) / 3).
The greatest and least effective stress on the wellbore are also calculatedusing stress, pore pressure, hole inclination, etc., and indicated onthe chart. If the stress-state produces a shear stress that falls beneath theshear strength line, the wellbore is stable.
If the shear stress falls outside the stability envelope, the wellbore isunstable and formation failure will occur.
higher the confining pressure greater the compressive stress
in situ
shear strength line
τ σ φ
σ σ σ
0
v h H
Shear
Stress, τStabilityEnvelope
Failure
S0
Effective Compressive Stress, σ
Shear Strength Line
LeastEffective Stress
GreatestEffective Stress
Stress-State
StartStart TOCTOC Section 2TOC
Section 2TOC
Wellbore Stability
Page - 11Section 2
Time
Geological processes have great lengths of time in which to operate.Although geologic time is impossible to duplicate in a laboratory, it ispossible from experiments to make some deductions concerning theinfluence of time.
One analysis of special interest to drilling operations is that of .Creep is a slow continuous deformation of rock with the passage of time,even though the stress may be above or below the elastic limit.
creep
Tensile Failure
Tensile Failure results from stresses that tend to pull the rock apart (tensilestress). Rocks exhibit very low tensile strength.
TensileStress
Tensile Stress Exceedsthe Tensile Strength and the Rock Fails
StartStart TOCTOC Section 2TOC
Section 2TOC
SECTION 3
After The Wellbore
3.1 Near Wellbore Stress-State
3.2 Mechanical Stability
3.3 Chemical Stability
StartStart TOCTOC
Wellbore Stability
Page - 1Section 3
OVER
BURDENSTRESSOVER
BURDENSTRESS
STRESSES
STRESSES
HORIZONTAL
HORIZONTAL
BeforeDrillingBeforeDrilling
AfterDrillingAfterDrilling
HYDRO
STATICPRESSURE
HYDRO
STATICPRESSURE
Radial
Stress - σr
Radial
Stress - σr
Axial
Stress - σz
Axial
Stress - σz
Hoop
Stress - σθ
Hoop
Stress - σθ
HSP
As the hole is drilled, the support provided by the rock is removed andreplaced by hydrostatic pressure. This change alters the stresses. Thestress at any point on or near the wellbore can now be described in terms of:radial stress acting along the radius of the wellbore; hoop stress actingaround the circumference of the wellbore (tangential); axial stress acting
parallel to the well path. These stresses are designated by ( , , ) and the
additional shear stress components designated by ( , , ).
These stresses are perpendicular to each other and for mathematicalconvenience, are used as a borehole coordinate system.
in situ
σ σ σσ σ σ
r z
r rz z
θ
θ θ
3.0 AFTER THE WELLBORE
3.1 Near Wellbore Stress-State
Before drilling, rock stress is described by the stresses; effectiveoverburden stress, effective minimum horizontal stress, and the effectivemaximum horizontal stress. These stresses are designated by ( , , ).
in situ
σ σ σv h H
StartStart TOCTOC Section 3TOC
Section 3TOC
Wellbore Stability
Page - 2Section 3
Hoop Stress - σθ
Hoop stress is dependent upon wellbore pressure ( ), stress
magnitude and orientation, pore pressure, and hole inclination anddirection. Wellbore pressure ( ) is directly related to mud weight/ECD.
= [ & well parameters] - -
For a vertical wellbore with equal horizontal stresses, hoop stress isdependent upon the mud weight and the magnitude of the horizontalstresses and is equally distributed around the wellbore.
p in situ
p
in situ p p
w
w
σθ w
EqualHorizontal
Stresses
A deviated well creates of hoop stress around thewellbore due to the redistribution of the horizontal and vertical stresses.Hoop stress acting on a cross-section of the wellbore is maximum at thesides of the wellbore perpendicular to the maximum stress.
The same is true when drilling a vertical well in an environment ofunequal horizontal stress. Hoop stress is maximum at the side of thewellbore perpendicular to the maximum horizontal stress.
unequal distribution
in situ
Low Side of Hole
High Side of HoleAdditional Components
Of Stress From OverburdenAnd Horizontal Stresses
MinimumHoop Stress
MaximumHoop Stress
StartStart TOCTOC Section 3TOC
Section 3TOC
Wellbore Stability
Page - 3Section 3
Axial Stress - σz
Axial stress is oriented along the wellbore path and can be unequallydistributed around the wellbore. Axial stress is dependent upon;stress magnitude and orientation, pore pressure, and hole inclination anddirection. Axial stress is not directly affected by mud weight.
= [ & well parameters] -
For a vertical well with equal horizontal stress (s = s ), axial and vertical
stress are the same. Axial stress in a deviated well is the resolution of theoverburden and horizontal stresses.
in situ
in situ pσz
h H
Vertical Well -Equal Horizontal
Stresses
Axial Stress isOnly the Overburden
Axial Stress isThe Resolution of
Overburden and HorizontalStresses
Deviated Well -Equal or Unequal
Horizontal
Radial Stress - σr
Radial stress is the difference in wellbore pressure and pore pressure andacts along the radius of the wellbore.
Since wellbore and pore pressures both stem from fluid pressure actingequally in all directions, this pressure difference is acting perpendicular tothe wellbore wall, along the hole radius.
= -
Radial Stress = Wellbore Pressure - Pore Pressure
σr wp p
StartStart TOCTOC Section 3TOC
Section 3TOC
Wellbore Stability
Page - 4Section 3
3.2 Mechanical Stability
Hoop ( ), radial ( ), and axial ( ) stress describe the near wellbore
stress-state of the rock. is the of thesestresses in an effort to prevent shear or tensile rock failure.
Normally the stresses are compressive and create shear stress within therock. The more equal these stresses, the more stable the rock.
σ σ σθ r z
Mechanical stability management
Axial - σz
Hoop - σθ
Radial - σr
Hoop
Radial
ShearStress
As shown by the right side drawing above, the radial stress is resistingshear caused by the hoop stress.
Hoop, axial, and radial stress can be calculated and the greatest and leastof the three indicated by a stress-state semicircle on the stability chart.
Shear failure occurs if the stress-state falls outside of the stability envelop.Tensile failure occurs if the stress-state falls to the left of the shear stressaxis and exceeds the tensile strength of the rock.
S0
Shear Strength Line
StabilityEnvelope
Failure
LeastStress
GreatestStress
ShearStress
Effective Compressive Stress
Stress-State
StartStart TOCTOC Section 3TOC
Section 3TOC
Mechanical stability is achieved by controlling the parameters that affecthoop, axial, and radial stress.
MW/ECDMud Filter CakeWell Path - Inclination and AzimuthDrilling/Tripping Practices
Unfavorable ConditionsAdverse FormationsConstrained Wellbore Trajectory
Mechanical stability of the well is also impacted by drillingfluid/formation interaction. Chemical instability eventually results inmechanical failure of the rock in shear or tension.
is also an important consideration. The longer the formation isexposed to the drilling mud, the more near-wellbore pore pressureincreases. The rock looses support provided by the mud weight.
Controllable parameters:
Uncontrollable parameters:
Time
!
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!
!
!
!
!
In Situ
Page - 5Section 3
Wellbore Stability
Whenever hoop or radial stress become tensile (negative), the rock isprone to fail in tension. Many unscheduled rig events are due to loss ofcirculation caused by tensile failure.
Tensile Failure Due toNegative Hoop Stress
StartStart TOCTOC Section 3TOC
Section 3TOC
S0
Shear Strength Line
StabilityEnvelope
FailureEnvelope
RadialStress
HoopStress
ShearStress
Stress-State BeforeMW Decrease
Stress-State AfterMW Decrease
MW Decrease
Wellbore Stability
Page - 6Section 3
Effect of Mud Weight/ECD
Mud weight, ECD, and pressure surges on the wellbore directly effecthoop and radial stress. An increase in MW decreases hoop stress andincreases radial stress. Similarly, a decrease in MW increases hoop stressand decreases radial stress. The result on wellbore stability is dependentupon the magnitude of the mud weight increase/decrease.
Shear Strength Line
StabilityEnvelope
Failure
Radial Stress Hoop Stress
ShearStress Stress-State Before
MW Increase
Stress-State AfterMW Increase
Increase in MW
Excessive Increase in MW
Shear Strength Line
StabilityEnvelope
Failure
New Radial StressNew Hoop Stress
ShearStress Stress-State Before
MW Increase
Stress-State AfterMW Increase
StartStart TOCTOC Section 3TOC
Section 3TOC
Wellbore Stability
Page - 7Section 3
Mud Filter Cake and Permeable Formations
The filter cake plays an important role in stabilizing permeable formations.An ideal filter cake isolates the wellbore fluids from the pore fluids next tothe wellbore. This is important for hole stability and helps preventdifferential sticking as well.
PermeableSand
Pores
WellboreWellbore
Wellbore
FilterCake
pw p
Ideal Filter Cake
If there is no filter cake, the pore pressure near the wellbore increases tothe hydrostatic pressure; the effective radial stress is zero. Thesimultaneous decrease in effective hoop stress causes the stress-state tomove left in the stability envelope; decreasing the stability of theformation. An ideal filter cake helps provide for a stable wellbore.
S0
Shear Strength Line
StabilityEnvelope
FailureEnvelope
RadialStress
σr = 0
HoopStress
σθ
ShearStress Stress-State After
Filter Cake Failure
Example of a Poor Filter Cake
Stress-StateWith Good Filter Cake
The chemical composition of the mud and permeability of the formationcontrol the filter cake quality and the time it takes to form.
StrongThin
FlexibleImpermeable
Effective Compressive Stress
StartStart TOCTOC Section 3TOC
Section 3TOC
Wellbore Stability
Page - 8
S0
Shear Strength Line
StabilityEnvelope
Failure
MinimumHoop Stress
ShearStress
Stress-State in VerticalHole Section
Stress-State in HorizontalHole Section
RadialStress
MaximumHoop Stress
Drilling a Horizontal Well
Section 3
Hole Inclination and Direction
The inclination and direction of the wellbore greatly impacts the stabilityof the well. Unequal distribution of hoop and axial stress around thecircumference of the well tends to make the wellbore less stable.
MinimumHoop Stress
MaximumHoop Stress
Increased Vertical Stressof the Overburden
For Equal Horizontal Stress
Drilling a horizontal well causes thehoop and axial stress distributionaround the wellbore to change.
Before drilling from vertical, thehoop stress is equally distributed. Asangle increases to horizontal, thehoop stress on the high and low sideof the wellbore decreases, but thehoop increases greatly on theperpendicular sides.
The change in the stress-state at the wellbore wall is shown below. Theradial stress remains fixed but the increasing hoop stress increases thestress-state.
StartStart TOCTOC Section 3TOC
Section 3TOC
Wellbore Stability
Page - 9Section 3
Bottom-hole Temperature
High bottom-hole-temperature wells can experience stability problems ashoop stress changes because of temperature differences between the mudand formation.
If the mud is cooler than the formatio, it reduces the hoop stress as theformation is cooled. This reduction in hoop stress can prevent shear failureand stabilize the hole, if the hoop stress were high due to low mud weight.On the other hand, if the mud weight is too high and close to the fracturegradient, excessive cooling can lower the hoop stress and make it tensile.This could cause tensile failure or fracturing as it effectively lowers thefracture gradient.
If the mud is hotter than the formation, exactly the opposite occurs as hoopstress is increased. This could promote spalling or shear failure.
Consider what happens during a typical round-trip on a deep hightemperature well. During the trip, formation temperature returns to itsambient value. This causes the hoop stress to increase. When back onbottom and circulation resumes, the cooler mud traveling down thedrillstring reduces the temperature of the nearby formation, causing hoopstress to decrease.
As the hot bottoms-up mud circulates past formations at shallower depths,hoop stress increases as the mud heats up the formations.
These variations in hoop stress have the same effect as pressure surgesassociated with swabbing and surging and can cause both tensile and shearfailure downhole.
Variations in Hoop Stress in a High Temperature Well
S0
Shear Strength Line
StabilityEnvelope
Failure
ShearStress
RadialStress
Changes in ShearStress on Formation
Increased Hoop Stress While POOH
Hoop Stress Prior to Trip
Decrease in Hoop Stress While Circulating Bottoms-Up
StartStart TOCTOC Section 3TOC
Section 3TOC
Wellbore Stability
Page - 10Section 3
Impact of Mechanical Stability on the Wellbore
Mechanical stability problems directly account for many unscheduled rigevents. Stability problems also effect overall drilling efficiency by alteringthe shape of the hole being drilled.
Severe hole deformation occurs when extreme stress environmentsare penetrated. The drawing below is indicative of such drilling. Thedrawing is only a slice of the actual wellbore. Consider the path of a typicalwell, and consider this deformation over several thousand feet of open hole;it is easy to see the impact of such a wellbore on operations.
in situ
Maximum HorizontalStress Orientation
Shear FailureZone (Breakouts)
Tensile FailureZone
Cavity
OriginalHole Size
Encroachment ofBrittle Sands
Resulting Operational Problems Include:
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!
Stuck pipe, casing, logging tools, etc.
Ineffective hole cleaning.
Ledges and breakouts.
High torque and severe slip-stick.
Drillstring failures.
StartStart TOCTOC Section 3TOC
Section 3TOC
Wellbore Stability
Page - 11Section 3
3.3 Chemical Stability
is the control of the drilling fluid/rock interaction;usually most problematic when drilling shales.
are fine grain sedimentary rocks with very low permeability andcomposed primarily of clay minerals (gumbo to shaly siltstone).
Chemical stability
Shales
Clay platelets (2 micronsand less) settling to themud line.
Mud at mud line, 60 - 90%porosity. Clay plateletsmaintain a water envelopeafter burial. Mud readilydeforms (much likepudding).
Compaction drives porewater back to the sea.Platelets begin to contactforming pliable clay (muchlike putty).
Further compaction,geologic time, andtemperature cements theclay platelets into shale(less than 20% porosity).
Mud
Clay
Shale
MuddyWater
One factor that distinguishes shale from other rock is it's sensitivity to thewater component of drilling fluids. With time, shale/water interaction willdecrease the strength of the shale; making it more prone to mechanicalstability failure.
StartStart TOCTOC Section 3TOC
Section 3TOC
Wellbore Stability
Page - 12Section 3
As shale is drilled, a sequence of events take place that can lead to thestressing, weakening, and eventual failure of the shale. Several parameters,described below, contribute to the chemical stability of shale.
is the transport of fluid through shale due to pressuredifferential. Typically, wellbore hydrostatic pressure is greater thanformation fluid pressure. When exposed to a permeable formation, theliquid phase of the mud is "pushed" into the pore openings by the pressuredifferential.
In a highly permeable sand, the flow rate of fluid loss is sufficient to form afilter cake that controls fluid loss. With shales, however, the filter cakecannot develop, since the permeability of a typical shale is much less thanthat of any filter cake. Also, the particle size of a typical filter cake is toolarge to plug the pore throats of shale (much like trying to plug a shakerscreen with beach balls).
Advection
Advection
4500 psi
Wellbore
5000psi
Wellbore
5000psi
PoreThroat
PoreFluid
Shale
PoreSpaces
WellboreWellbore
Wellbore
Capillary Effects
Drilling fluid must overcome capillary pressure to enter the pore throats ofshale. Capillary pressure, developed at the drilling fluid /pore fluidinterface, is dependent on several factors; pore throat radius, interfacialtension, and contact angle.
When drilling water-wet shales with water base mud; surface tensionbetween the mud's water phase and the pore fluid is very low. Underfavorable salinity conditions, the water phase enters the pore throat.
StartStart TOCTOC Section 3TOC
Section 3TOC
Wellbore Stability
Page - 13Section 3
Osmosis
Pressure Diffusion
Osmosis is caused by the imbalance of salt concentration between the mud'swater phase and the pore water. The salinity imbalance is separated byshale which acts as a semi-permeable membrane that allows the transport ofwater only. Water moves from low salinity to high salinity until the salinitydifference (chemical activity) is balanced.
If the mud salinity is too low, water moves into the shale increasing the porepressure. As pore pressure increases, it has an adverse effect on stability.
If the mud salinity is too high, pore water flows into the mud systemdehydrating the shale. As pore pressure decreases, effective hoop stressincreases also promoting shear failure.
is the change in near-wellbore pore pressure relative totime. This occurs as overbalance and osmotic pressures drive the pressurefront through the pore throat, increasing pore fluid pressure away from thewall of the hole. This pore pressure penetration leads to a less stablecondition at and near the wellbore wall.
Pressure diffusion
4500 psi
WBM
5000psi
WBM
5000psi
PoreThroat
PoreFluid
4500 psi
OBM
5000psi
OBM
5000psi
PoreThroat
PoreFluid
SurfaceTension
When drilling water-wet shales with oil base mud, the capillary pressure isvery high (i.e., 8000 to 10,000 psi) due to the large interfacial tension andextremely small pore throat radius. The high capillary pressure preventsentry of the oil phase as overbalance pressures are very low in comparison.However, if the salinity of the mud's water phase is not balanced with shalesalinity, water transfer through osmosis can still occur.
StartStart TOCTOC Section 3TOC
Section 3TOC
Wellbore Stability
Page - 14Section 3
As pressure diffusion increases pore pressure near the wellbore, shearstrength of the rock is reduced. The time for pressure diffusion to impactshale may result in failure of a shale section exposed for several days.
Time required for the pressure front to penetrate a given depth dependsprimarily on the permeability of the shale (connectivity of the pores) andthe pressure differential between the wellbore ( ) and pore pressure
( ).
p in situ
pw
Swelling /Hydration
Over geologic time, mud/clay solidifies into shale as overburden stressdrives off the water envelope (dehydration) and cements the platelets withthe minerals left behind after dehydration.
After drilling, water enters the shale by advection and osmosis. Negativelycharged clay ions attract and hold the polar water. The increasing volumeof attached water produces a swelling stress that "wedges" the clay plateletsapart.
Distance From Wellbore (Hole Diameters)
Pre
ssure
p
pw
0 1 2
Day 1
Day 3
Day 2
Fluid Front
Pore Channel
Pressure Front
In Situp
Pressure( )
( )pw
5000 psi
Pore Throat
4500 psi
StartStart TOCTOC Section 3TOC
Section 3TOC
Wellbore Stability
Page - 15Section 3
The swelling pressure and behavior of shales are directly related to thetype and amount of clay minerals contained in the shale. Shales withhigh concentrations of negatively charged ions can produce very highswelling pressure (50,000 psi plus).
Swelling pressure decreases the strength of the shale by destroying thenatural cement bond between the clay platelets. Brittle shale becomesductile and is pushed into the wellbore by the compressive hoop stressand the swelling stress.
OVERBURDEN LOADOVERBURDEN LOAD
PoreWater
NaturalCement
ShaleClay
ClayPlatelets
OVERBURDEN LOADOVERBURDEN LOAD
OVERBURDEN LOADOVERBURDEN LOAD
OVERBURDEN LOADOVERBURDEN LOAD
ShaleWellbore(1 hour)
Adsorbedwater
SwellingStress
Wellbore(1 Day)
StartStart TOCTOC Section 3TOC
Section 3TOC
SECTION 4
Providing A Stable Wellbore
G
4.1 Planning A Stable Wellbore
4.2 Warning Signs /Corrective Action
StartStart TOCTOC
Wellbore Stability
Page - 1Section 4
.
4.0 PROVIDING A STABLE WELLBORE
4.1 Planning A Stable Wellbore
σσσ
1
2
3
= Greatest effective stress
= Intermediate effective stress
= Least effective stress
σ σv 1=
σ σh 3=
σ σH 2=
NormalFault
σ σv = 3
σ σH 1=
σ σh = 2
ReverseFault
1. Potential Stability Indicators
If the answer to any of the questions below is "yes", preventive measuresshould be taken.
σ σv 2=
σ σH 1=
σ σh 3=
Strike-slipFault
Indications of tectonic activity in the area?
Sudden pressure transition zones expected?o
Adverse formations expected (reactive shale, unconsolidated or fracturedformations, abnormal or subnormally pressured zones, plastic formations?
Is wellbore inclination greater than 30 ?o
3. Determine Magnitude of In Situ Condition (s s s )
Obtained from density logs of offset wells.
Estimated by seismic and logs.
Determined by LOT and/or logs.
v , h , H
Overburden - s
Formation Pore Pressure -
Minimum Horizontal Stress - s
v
h
p
2. Identify Stress Regime
StartStart TOCTOC Section 4TOC
Section 4TOC
Wellbore Stability
Page - 2Section 4
..
5. Research Offset Wells for Indications of Stability Problems
Offset well data is invaluable information for identification of stabilityproblems in the field.
Identify hole sections with stability symptoms.List the conditions that caused the stability problem.Identify similar problems in offset wells occurring at the same verticaldepth. Look for similarity in the conditions that caused the problem.List the drilling parameters effecting the problem (i.e., mud type andweight, hole angle, adverse formations, unusual drilling practices).
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CHEMICAL(Hole Enlargement /Hole Cleaning)
CHEMICAL(Hole Enlargement /Hole Cleaning)
MECHANICAL
Reactive ShaleReactive Shale
PLASTICDEFORMATION
(Tight Hole /Casing Collapse)
PLASTICDEFORMATION
(Tight Hole /Casing Collapse)
Mobile Salt
Mobile Shale
Mobile Salt
Mobile Shale
TENSILEFAILURE
(Lost Circulation)
TENSILEFAILURE
(Lost Circulation)
ExcessiveWellborePressure
ExcessiveWellborePressure
COMPRESSIONALFAILURE
(Hole Caving /Collapse)
COMPRESSIONALFAILURE
(Hole Caving /Collapse)
Overburden Stress
Tectonic Stress
Geo-Pressured Shale
Unconsolidated Formation
Fractured Formation
Overburden Stress
Tectonic Stress
Geo-Pressured Shale
Unconsolidated Formation
Fractured Formation
WELLBORE STABILITY PROBLEMSWELLBORE STABILITY PROBLEMS
4. Use Core Tests or Logs to Determine Formation Rock Strength
Core Tests
ShearStress
StabilityEnvelope
Unstableor Failure
S0
Effective Compressive Stress
Logs
Rock strength is estimated through correlations with sonic density logssince slow sonic velocity and high porosity generally relate to lower rockstrength.
StartStart TOCTOC Section 4TOC
Section 4TOC
Wellbore Stability
Page - 3Section 4
4.2 Warning Signs and Corrective Action
7. Avoiding Stability Problems
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Select an inhibitive mud for reactive formations.Casing points should allow for mud weight windows determinedfrom stability analysis.Maintain mud weight/ECD in stability window. Use down holeECD monitoring tools in critical wells.Optimize well trajectory based on drilling days vs. stability.Plan for effective hole cleaning and stuck pipe prevention.Follow defensive drilling practices. Control ROP, surge pressures.Train drilling team members..
No single action can prevent stability problems. Wellbore stability must bemanaged by the controllable parameters.
Mud type, composition and density.Drilling practices (minimize ECD, swab /surge pressures).Wellbore angle and direction.
Chemical stability problems occur when reactive shales are drilled with anon-inhibitive drilling fluid. Chemical stability is time dependent anddifficult to quantify. The drilling fluid interaction results in shale hydrationand swelling which leads to shale falling into the wellbore causing holeenlargement and tight hole conditions.
BHA balling and slow drilling, flow line plugging, soft mushycuttings on shaker.Smooth increases in torque/dragOverpull off slips, pump pressure increasing.Increases in mud parameters (mud weight, plastic viscosity, yieldpoint, cation exchange capacity (CEC), and low gravity solids).
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Chemical Stability
Warning Signs of Chemical Stability Problems
6. Select Mud System and Determine Mud Weight Window
Stability spreadsheets and analysis tools are used to determine the mudweight window for each hole section.
StartStart TOCTOC Section 4TOC
Section 4TOC
Wellbore Stability
Page - 4Section 4
Preventive /Corrective Measures
Chemical stability problems are prevented by selecting proper mud type andcomposition. Initial corrective measures are to use suitable mud additives. Ifthe problem persists, replacing the existing mud with a more inhibitive mudmay be necessary.
Addition of various salts (K, Na, Ca) to balance water activity.Addition of glycol to reduce chemical attraction of water to shale.Addition of various "coating" polymers (PHPA, etc.) to reducewater contact with shale.Use of oil base or synthetic oil base mud to exclude water contactand entry into shale.Minimize the open hole exposure time.Plan regular wiper trips.Minimize surge/swab pressures.Ensure adequate hydraulics for bit and hole cleaning.Maintain required mud properties.Use minimum mud weight, if possible.
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Mechanical Stability
Mechanical instability is related to incorrect mud weight /ECD and/orwell trajectory. Too low mud weight can cause hole cavings or collapseresulting in stuck pipe. Too high mud weight /ECD can cause excessivefluid losses to the formation or total loss of returns.
Large size and volume of cavings over shakers.Erratic increase in torque/drag.Hole fill on connections or trips.Stuck pipe by hole pack-off /bridging.Restricted circulation /increases in pump pressure.Loss of circulation.Loss/gain due to ballooning shales.
Two indicators of mechanical stability problems are loss of circulationand increased volume of cavings. Partial or total loss of circulation maybe due to pressure induced or naturally existing fractures. The reducedhydrostatic associated with loss of circulation may cause formation cavingand collapse.
Warning Signs of Mechanical Stability Problems
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StartStart TOCTOC Section 4TOC
Section 4TOC
Wellbore Stability
Page - 5Section 4
Preventing Mechanical Stability Problems
The constraints on wellbore pressure are dictated by formation pressure onthe low end and fracture strength on the high end. Hydraulics planningmust also consider minimizing the shock load imposed to the wellbore.
Measures to prevent/correct mechanical stability problems include:
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Increase the mud weight (if possible). The mud weight valuesshould be determined using a stability analysis model and pastexperience if drilling in a known field.If drilling fractured formations, it is not recommended to increaseMW. Increase the low end rheology (< 3 RPM Fann reading).Improve hole cleaning measures. Maintain 3-rpm Fann readinggreater than 10. GPM for high-angle wells equal to 60 times thehole diameter in inches and half this value for hole angle of less
than 35 .Circulate on each connection. Use back reaming and wiper tripsonly if hole conditions dictate.Minimize surge/swab pressures.Monitor torque/drag and the size and amount of cuttings onshakers.
0
PorePress
PorePressShear
EnvelopeCollapse Caving
Partial TotalLoss Loss
HydrostaticPressureHydrostaticPressure
Break Circ
Swab
Press
Surge
Press
Circ
Press
Solids
Loading
TENSILE FAILURETENSILE FAILURESTABLESHEAR FAILURESHEAR FAILURE
Wellbore Pressure Shock
FracPressFracPress
Wel
lD
epth
StartStart TOCTOC Section 4TOC
Section 4TOC
Wellbore Stability
Page - 6Section 4
Controlling Stability Problems
The entire rig team is responsible for detecting stability problems. Oncedetected, there are many controls to consider that can provide for a stablewellbore. The drilling supervisor, with input from rig team members mustbe aware of the parameters that restore the balance between rock stress androck strength.
Formation
Mud
TensileFailure Active
Tectonics
ShearFailure
PorePressure
STABLE
UNSTABLE
Rock StrengthRock Stress
SandMWHigh
MWLow Reaming
TripSpeed
ECD MobileSalt
Shale StrikeSlip
TensileFailure
HoleCleaning
ReverseFault
TimeExposed
- Wellbore Stability -Maintaining the Balance of
Rock Stress and Rock Strength
The drilling team must recognize the warning signs of an unstablewellbore and adjust the drilling program accordingly to thebalance of rock stress and rock strength.
maintain
StartStart TOCTOC Section 4TOC
Section 4TOC
APPENDIX
A - 1 Leak-Off Tests
A - 2 Lithology Factor (k)
A - 3 Wellbore Stress Equations
A - 4 Nomenclature
τmax
σ1
σ2
StartStart TOCTOC
Wellbore Stability
Appendix A-1
LOT data is necessary to determine the maximum mud weight for wellcontrol and hole stability and has a direct influence on casing design. LOTfield data is also helpful for planning future field drilling and productionoperations because it measures the minimum horizontal stress (s ). Theminimum horizontal stress is important for wellbore stability analysis.
Consistency in LOT procedure, accuracy in reading test pressures andproper data reporting all have a direct impact on the quality of thisinformation. Refer to document F96-P-24, Standardization of Leak-off TestProcedure for more detail.
Preparation is a key factor in achieving good quality LOT data. Beforetesting begins:
Check offset well leak-off data for expected leak-off test pressure, pumprates, test problems or any unusual conditions.
Check logs for exposed sands to anticipate straight or curved linepressure plot.
Check for hole washouts to anticipate problems with the cement job.
Perform a casing integrity test (CIT). Test pressure at any point not toexceed 80% of casing burst.
Construct a LOT chart.
1. Drill out the shoe, rathole and 10 to 15 feet of new hole.
2. Circulate the hole clean and condition the mud to a consistent density.
3. Pull the drillstring +/-10 feet above the shoe.
4. Rig up the cement pump on the drillstring and pressure test system.
5. Close the annular BOP and begin the leak-off test.
6. Maintain a constant pump rate during test (1/4 to 1 bbl/min maximum).
7. Plot the pressure every 1/4 barrel pumped.
h
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LOT Procedure
A - 1 Leak-off Tests
StartStart TOCTOC AppendixTOC
AppendixTOC
Wellbore Stability
Appendix A-1
10 to 15Feet
Testpsi
The initial volume pumpedresults in fluid compressionand expansion of thewellbore. After this initialphase, pressure increaseslinearly with barrels pumped.
Pres
sure
LinearIncrease
Shut-in Time(Minutes)
0
0 10 20
1 2 3 4
FluidCompression
Stop Pump
Initial Shut-in Pressure (ISIP)
Min. Horizontal Stress (s )h
Record every min for 20 minutesor until pressure stabilizes
Leak off
Barrels
Leak-off pressure (LOP)
initial shut inpressure (ISIP)
minimum horizontal stress (s )
is the first point where there is a permanentdecrease in the slope (usually equal to or greater than the minimum stresspressure). When the pump is stopped, pressure falls to the
due to the loss of friction pressure.
The is the first point after a permanent
decrease in the slope (usually equal to or less than LOP). Retest to confirmminimum stress measurement.
As the formation is either fractured naturally or fractured during the drillingoperation, leak-off test pressure should range between 1 to 1.1 times theminimum horizontal stress.
h
StartStart TOCTOC AppendixTOC
AppendixTOC
Wellbore Stability
Appendix A-2
k =s -h p
s -v pPr
essu
re
Shut-in Time(Minutes)
0
0 10 20
1 2 3 4
Stop Pump
Initial Shut-in Pressure (ISIP)
Min HorizontalStress - sh
Leak off
Barrels
The Lithology Factor ( ) Calculated from LOT Datak
A - 2 Lithology Factors
Using Poisson's Ratio ( to Calculate the Lithology Factorν)
k =ν
1 - ν
Clay .17very wet .50
Conglomerate .2
Dolomite .21
Limestone:fine, medium .28medium, calcarenitic .31porous .20stylolitic .27fossiliferous .09bedded fossils .17shaley .17
Sandstone:coarse .05coarse, cemented .10fine .03medium .06poorly sorted, clayey .24fossiliferous .01
Shale:calcereous .14dolomitic .28siliceous .12silty .17sandy .12kerogenaceous .25
Siltstone .08
Slate .13
From, Weurker H. G.:"Annotated Tables of Strength and Elastic Properties of Rocks", Drilling, reprint Series SPEDallas (1963)
Poisson's Ratio Poisson's Ratio
StartStart TOCTOC AppendixTOC
AppendixTOC
Wellbore Stability
Appendix A-3
A - 3 Wellbore Stress Equations
Stress transformation from global to wellbore coordinates:
Where is the horizontal angle (azimuth) between s and the wellbore
and is the wellbore inclination.
λα
h
For equal horizontal stresses ( s = s )h H
and for a vertical well with = = 0:λ α
Effective radial, hoop, and axial stresses at the wellbore wall:
s = ( s cos + s sin ) cos + s sinx h H v
2 2 2 2λ λ α α
s = ( s cos + s sin ) sin + s cosz h H v
2 2 2 2λ λ α α
s = s sin + s cosy h H
2 2λ λ
s = sin cos cos (s - s )xy H hλ λ α
s = sin cos sin (s - s )yz H hλ λ α
s = sin cos ( s cos + s sin - s )xz h H vα α λ λ2 2
(1)
(2)
(3)
(4)
(5)
(6)
s = s cos + s sinx h v
2 2λ α
s = s sin + s cosz h v
2 2α α
s = sy h s = sin cos ( s - s )xz h vα α
s = s = 0xy yz(7)
(8)
(9)
(10)
(11)
s = sx h s = sy h s = sz v s = s = s = 0xy yz xz(12) (13) (15)(14)
σr = -p pw
σ θ θθ = ( s + s ) - 2 ( s - s ) cos 2 - 4 s sin 2 -x y x y xy p - pw
σ ν θ θz z x y xy= s - ( 2 ( s - s ) cos 2 + 4 s sin 2 ) - p
σ σr rzθ = = 0
σ θ θθz yz xz= 2 ( s cos - s sin ) - p
(16)
(17)
(18)
(19)
(20)
StartStart TOCTOC AppendixTOC
AppendixTOC
Wellbore Stability
Appendix A- 4
A - 4 Nomenclature
pp
k
t
formation pore pressurewellbore pressure (hydrostatic/ECD)
s total overburden stress
s minimum horizontal stress
s maximum horizontal stress
effective overburden stress
effective minimum horizontal stress
effective maximum horizontal stress
lithology factor
Poisson's ratio
tectonic stress
angle of internal friction
coefficient of friction
S cohesive strength
effective radial stress
effective hoop stress
effective axial stress
greatest effective stress
intermediate effective stress
least effective stress
w
v
h
H
v
h
H
0
r
z
1
2
3
σσσ
ν
φµ
σσσ
σσσ
θ
StartStart TOCTOC AppendixTOC
AppendixTOC