mpwe - advanced drilling practices - form fract gradc

8/10/2019 mpwe - advanced drilling practices - form fract gradc

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Master of Petroleum Well EngineeringMaster of Petroleum Well Engineering dvanced Drilling Practices

dvanced Drilling Practices

AprilApril20052005

Assoc. Prof. SampaioAssoc. Prof. [email protected]@peteng.curtin.edu.au

FORMATION FRACTURE GRADIENT


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Formation Fracture GradientFormation Fracture Gradient

May be predicted from:May be predicted from:

Pore pressure (vs. depth)Pore pressure (vs. depth)

Effective stressEffective stress

Overburden stressOverburden stress

Formation strengthFormation strength


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Rock MechanicsRock Mechanics

HowHow a rock reacts to an imposeda rock reacts to an imposedstress, is important in determiningstress, is important in determining

FormationFormation drillabilitydrillability

Perforating gun performancePerforating gun performance

Control of sand productionControl of sand production

Effect of compaction on reservoir performanceEffect of compaction on reservoir performance

Creating a fracture by applying a pressure to aCreating a fracture by applying a pressure to a

wellborewellbore


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Elastic Properties of RockElastic Properties of Rock


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Elastic Properties of RockElastic Properties of Rockcontcontdd


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Elastic Properties of RockElastic Properties of Rockcontcontdd

The vertical stressThe vertical stressat any point can beat any point can be

calculated by:calculated by:

a

F

A

=

The axial and transverse strains are:The axial and transverse strains are:

2 1 2 1

1 1a tr

L L d d

L d

= =


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A

B C

D

StressStressStrain DiagramStrain Diagram


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HookeHookess andand PiossonPiossonss

E =

HookeHookess Law forLaw for UniaxialUniaxial Loading:Loading:

PoissonPoissons Ratios Ratio

a

tr

=

EEis called Modulus of Elasticityis called Modulus of Elasticity

or Youngor Youngs Moduluss Modulus


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Typical Elastic Properties of RockTypical Elastic Properties of Rock


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GeneralizedGeneralized HookeHookess LawLaw

( )

( )

( )

1

1

1

xyx x y z xy

yz

y x y z yz

zx

z x y z zx

E G

E G

E G

= =

= + =

= + =


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Modulus 0f RigidityModulus 0f Rigidity

G is called Modulus or Rigidity or Shear ModulusG is called Modulus or Rigidity or Shear ModulusIt can be shown thatIt can be shown that

12E

G = +


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Volumetric StrainVolumetric Strain

f i

V

i

V V

V =


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Bulk ModulusBulk Modulus

For small StrainsFor small Strains

ForFor xx== yy== zz== (hydrostatic stress state)(hydrostatic stress state)

V x y z = + +

( )

( )

3 1 2

3 1 2

V

V

V

E

E

k

=

=

=

kkis calledis called

Bulk ModulusBulk Modulus


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Bulk ModulusBulk Moduluscontcontdd

CompressibilityCompressibility

Incompressible material:Incompressible material: c = 0c = 0

1c k=

( )3 1 21 0 0.5ck E

= = = =


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General Elastic Relations:General Elastic Relations:

( )

( )

( )

12

3 1 2

3 1 2

2 1

EG

Ek

G

k

= +

=

=

+


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InIn--situ stressessitu stresses

Vertical Equilibrium in a rock element:Vertical Equilibrium in a rock element:

ob p zp = +


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InIn--situ stressessitu stressescontcontdd

With increasing depthWith increasing depth pore pressure increases approximately 0.445pore pressure increases approximately 0.445

psipsi/ft/ft

overburden stress increases betweenoverburden stress increases between0.850.85 psipsi/ft to 1.1/ft to 1.1 psipsi/ft/ft

ThenThen

matrix stress increases betweenmatrix stress increases between0.4050.405 psipsi/ft to 0.665/ft to 0.665 psipsi/ft/ft

ob p zp = +


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Te increase in matrix stress is theTe increase in matrix stress is theprimary responsible for the decreaseprimary responsible for the decrease

in the porosity with depth.in the porosity with depth.


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Sedimentary rockSedimentary rock is the result ofis the result ofmillions of years of continuingmillions of years of continuing

deposition of sediments that deepensdeposition of sediments that deepens

and compact.and compact.

As depth increases, grain to grainAs depth increases, grain to grain

stresses increase.stresses increase.


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Due to theDue to the zz, a tendency exists to the, a tendency exists to theformation to expand laterallyformation to expand laterally(Poisson(Poissons ratio).s ratio).

Lateral expansion is prevented fromLateral expansion is prevented from

occurring by the surrounding rock,occurring by the surrounding rock,

This generates horizontal matrixThis generates horizontal matrixstresses (stresses (xx andand yy).).


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Simplifying Assumptions:Simplifying Assumptions:1. The rock behaves as an elastic material,

2. The horizontal stresses are equal

(x = y = H),

3. No horizontal strain (x = y = 0), and

4. Rock properties are constant withdepth.


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Using GeneralizedUsing Generalized HookeHookess LawLaw

( ) ( )

( ) ( )

1 10

1 10

x x y z H H z

y x y z H H z

E E

E E

= =

= + = +

1H z

=


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Pressure Required to

Fracture a Formation

To hydraulically fracture a formation,To hydraulically fracture a formation,the pressure of fluid in a cavity of thethe pressure of fluid in a cavity of the

formationformation

Must overcome the cohesive strength ofMust overcome the cohesive strength of

the grains PLUSthe grains PLUS

The matrix stress (and any stressThe matrix stress (and any stressconcentration) at the cavity wall PLUSconcentration) at the cavity wall PLUS

The fluid pressure in the pores of theThe fluid pressure in the pores of the

rock.rock.


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Pressure Required to Fracture

a Formation contd

For formation deep enough, theFor formation deep enough, thecohesive stresses are much less thancohesive stresses are much less than

the matrix stresses and are, thereforethe matrix stresses and are, therefore

neglected.neglected.

The same is not true for shallowThe same is not true for shallow

formations.formations.Too shallow (or young) formations areToo shallow (or young) formations are

normally unconsolidated.normally unconsolidated.


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a Formation contd

A typical circularA typical circular

hole in an infinitehole in an infiniteplate subjectedplate subjectedto anto an uniaxialuniaxialstress causes astress causes astressstress

concentration ofconcentration ofmagnitudemagnitude 33 ononthe wall of thethe wall of the

hole.hole.

3


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a Formation contd

This means thatThis means that

to initiate ato initiate afracture, thefracture, thematrix stressmatrix stressthat must bethat must beovercame is 3overcame is 3

times larger thantimes larger thanthe originalthe originalundisturbedundisturbed

matrix stress.matrix stress.

3


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a Formation contd

However at aHowever at a

short distanceshort distance

from the wall offrom the wall of

the hole, thethe hole, thematrix stressmatrix stress

reduces rapidlyreduces rapidly

to theto the

undisturbedundisturbed

matrix stressmatrix stress

3

Pl f F tPl f F t


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Plane of FracturePlane of Fracture

The plane of fracture is perpendicularThe plane of fracture is perpendicularto the direction of the least principalto the direction of the least principal

matrix stress.matrix stress.

In a geologically relaxed regionIn a geologically relaxed region

fractures tend to be horizontal.fractures tend to be horizontal.

In regions subjected to tectonicIn regions subjected to tectonicforces, things may be much moreforces, things may be much more

complicated.complicated.

Pl f F tPl f F t ttdd


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Plane of FracturePlane of Fracturecontcontdd

Rock propertiesRock properties

assumedassumed

constant withconstant withdepthdepth

Pl f F tPl f F t ttdd


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obob

is the max.is the max.

principalprincipal

stressstress

Failure occursFailure occursperpendicular toperpendicular to

the leastthe least

principal stressprincipal stress

Pl f F tPlane of Fracture tcontdd


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HH >>

obob can becan be

created bycreated byTectonic forcesTectonic forces

PostPost--depositionaldepositionalerosionerosion

Glacial action orGlacial action or

melting of glaciermelting of glacier

Plane of FracturePlane of Fracture contcontdd


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Effect ofEffect of

tectonictectonic

stresses onstresses onfracture planefracture plane

directiondirection

Plane of FracturePlane of Fracture contcontdd


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Effect ofEffect of

topographtopography ony on obob

Formation Fracture PressureFormation Fracture Pressure


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Fracture Pressure:Fracture Pressure:

Least Matrix Stress:Least Matrix Stress:

Horizontal MatrixHorizontal Matrix

StrtessStrtess::

minff pp p = +

1H z

=

min H =



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CombiningCombining

Matrix Stress:Matrix Stress:

contcontdd

1ff p zp p

= +

z ob pp =



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contcontdd

Combining againCombining again

oror

1 2

1 1ff ob pp p

= +

1 21

ff ob zp

= +

FromationFromation Fracture GradientFracture Gradient


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FromationFromation Fracture GradientFracture Gradient

Gradient at a given depthGradient at a given depth DD

(psi/ft)

19.25 (lb/gal)

ff

ff

ffff

p

p D

pp

D

=

=

Rock PoissonRock Poissons Ratios Ratio


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Rock PoissonRock Poisson s Ratios Ratio

This is a key parameter.This is a key parameter.PoissonPoissons Ratio is depth dependents Ratio is depth dependent

A great deal of data from hydraulicA great deal of data from hydraulicfracturing treatments and leakfracturing treatments and leak--of testof test

in nearby areas are needed to obtainin nearby areas are needed to obtain

accurate values ofaccurate values of

Rock PoissonRock Poissonss


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RatioRatio

contcont

dd

ExampleExample


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ExampleExample

Calculate the formation fracturegradient at 10,000 ft depth for the datain Example 7 in Pore Pressure.

Use pore pressure calculated usingboth (a) Equivalent Matrix Stressmodel and (b) Empirical Correlationmodel

Assume Poissons ratio for

overburden gradient equal to 1.0 psi/ftin shales.

SolutionSolution


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SolutionSolution

a) Equivalent Matrix StressFrom Example 6 results

(pp)10,000 = 7,669 psi

(ob)10,000 = 10,378 psi

From graph: = 0.423

SolutionSolution contcontdd


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SolutionSolution contcontdd

1 2

1 1

ff ob pp p

= +

0.423 1 2 0.423

10,378 7,669 9,655 psi1 0.423 1 0.423

9,655 psi

10,000 ft

ff

ff

ff

p

pp

D

= + =

= =

0.966 psi/ft 18.6 lb/galffp = =


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b) Equivalent Matrix StressFrom Example 6 results

(pp)10,000 = 8,100 psi

(ob

)10,000

= 10,378 psi

= 0.423


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LeakLeak--Off TestOff Test


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LeakLeak Off TestOff Test

PurposePurpose1. Test the casing couplings sealing,

2. Test the sealing of the annular between

the casing and the cement, and betweencement and cased formations,

3. Test the resistance of the formations

below the last casing shoe (normally theformation right below the casing shoeand also the first sand below the casing

shoe).

LeakLeak--Off TestOff Test contcontdd


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LeakLeak Off TestOff Test contcontdd

Remarks:Remarks:

a) casing tests are performed before the cement isdrilled from the bottom joint.

b) the annular sealing and leak-off test areperformed simultaneously, after the formation is

drilled about 10 ft below casing shoe. A largedeparture from the expected pressure increaseline indicates a fail in the cement bonding.Cement must be squeezed in order to promote

sealing.c) fracturing the formation will not decrease the

resistance of the formation, since the stress dueto the surrounding rocks and pore pressure are

the responsible for the formation fractureresistance.

Calculation of the Leak off Pressure


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pf=frictional pressure loss (small)Gel strength may be large. track pressures in both annular and

drillstring gages noting the maximum

difference as the gel strength

LO ff fp p g D p= +

Calculation of the Leak off Pressure contd


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Circulate the fluid before the test to Homogenize the fluid,

Break the gel, and

Remove solids in suspension and

contaminants.

Pump Rates for shales in the range of0.25bbl/min to 0.5 bbl/min. For Porous

sandstones, 1.5 bbl/min.

Calculation of the


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Leak off Pressure

contd

Graph the surface

pressure vs.

injected volume.

Include theanticipated leak-off

pressure and

anticipated slope ofthe pressure line.

Slope of Pressure LineSlope of Pressure Line


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pp

Equivalent compressibility of the fluid ce

ce= cwfw+ cofo+ csfs

0.2x10-6Solids

5.0x10-6Oil

3.0x10-6Water

Compressibility

(psi-1)

Component

Slope of Pressure LineSlope of Pressure Linecontcontdd


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pp

By definitionBy definition

1e

dVc V dp=

Slope of Pressure LineSlope of Pressure Linecontcontdd


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pp

The injection if a volumeThe injection if a volume VVii into ainto a

constant well volumeconstant well volume VV00 correspondscorrespondstoto reduvereduve the volume fromthe volume from VV00+V+Vii toto VV00,,

that is a change of volume equal tothat is a change of volume equal toVVii

Therefore the anticipated slope isTherefore the anticipated slope is

0

1

i e

dp

dV c V

=

LeakLeak--Off TestOff Testcontcontdd


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After the end of the test, measure thevolume of mud that is bled from the

well. The volume should be very close

to the injected volume (the differenceis the amount of filtrate lost in the test).

If fracture occurred, or leak due to badcementing job, this difference will be

larger.

LeakLeak--Off TestOff Testcontcontdd


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Poor cementbonding in theannular betweencasing and borehole

This behavior is anindication that fluid isseeping between the

casing and cementlayer of between thecement layer and the

formation, or both.

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mpwe - advanced drilling practices - form fract gradc