Chapter 09 - FracturePressure

Chapter Nine:Chapter Nine: Fracture PressureFracture Pressure

TopicsLeak-off TestsLost CirculationDrilling Into Depleted ReservoirsIncreasing Mud Weights Above the Least Principal Stress

© 2005 GeoMechanics International2

Chapter Objectives

Be able to determine the least principal stressBe able to explain the effect of depletion in a reservoir and calculate the fracture gradientBe able to determine drilling directions that are likely to increase the fracture gradient above the least principal stress

LeakLeak--off Testsoff Tests


Least Principal Stress (Shmin) from XLOT

(after Gaarenstroom et al., 1993)volume


Typical Extended Leak-off Test

Shut-in


Hydraulic Fracturing

• For an impermeable rock a sharp peak pressure (i.e., fracture breakdown) is often seen.

• For a permeable formation wellbore fluids can continuously percolate into the formation, hence, making a sharp peak pressure difficult to develop. Usually, a gradual inflection point is seen, which may be interpreted as fracture initiation.

• In a permeable formation a step-rate test may be preferred.


Timor Sea Extended Leak-Off Tests

0

500

1000

1500

2000

2500

0

0.5

1

1.5

2

0:00 15:00 30:00 45:00 60:00 75:00 90:00 105:00 120:00 135:00

Elapsed Time (min)

Pressure

Flowrate

Shut-in

10 bbls 15 bbls

Shut-in

Shut-in Shut-in


Shut-In Pressure – S3 ≅ 1,940 psi

1700

1750

1800

1850

1900

1950

2000

2050

0 5 10 15 20 25 30

First Cycle

time after shut in

ISIP

1700

1750

1800

1850

1900

1950

2000

2050

0 5 10 15 20 25 30

Second Cycle

ISIP


Determining Fracture Closure From Pressure Decline as a Function of SQRT Time

(after Nolte)

PC: Fracture closure pressure [MPa]pW: Wellbore pressure [MPa]


Fracture Closure Pressure – S3 ≅ 1900 psi

1750

1800

1850

1900

1950

2000

2050

0 1 2 3 4 5 6 7 8

Cycle 2

Sqrt time

Closure Pressure

1700

1750

1800

1850

1900

1950

2000

2050

0 1 2 3 4 5 6 7 8

First Cycle

Sqrt time (min)

Closure Pressure


Plot of Shmin From Leak-Off Tests

Leak-off tests provide accurate and consistent measurements if performed and analyzed consistently.

Lost CirculationLost Circulation


Traditional Fracture Pressure Calculations

• Stress Ratio Methods

• Poisson's Ratio Methods

• Empirical Methods

• Tectonic Stress Methods

• Porosity Methods

• Frictional Equilibrium Methods


Fracture Pressure Prediction Methods

The ratio of the minimum horizontal effective stress to vertical stress (k) is defined as:

k = (S3-Pp)/(Sv-Pp)

Rearranging for S3

S3 = (k)(Sv-Pp) + Pp


Stress Ratio, k

k has been estimated using several approaches:

Empirical k = (0.039)(D-W/4-A)0.33

Uniaxial Strain k = (ν)/(1- ν)Plastic k = 1Solidity k = (1-φ)Hoop Stress k = (2 ν)/(1- ν)Failure k = 1/[(μ2+1)0.5+ μ]2Fault Angle k = 1/tan2θ

Where ν is Poisson’s ratio, φ is fractional porosity, μ is the coefficient of sliding friction, and θ is the dip angle of faults measured from the horizontal


Hubbert & Willis (1957)

S3 = 0.3 (Sv – Pp) + Pp

Where 0.3 is an estimate of the maximum ratio of horizontal to vertical stress. A later amendment increased the ratio coefficient to 0.5

Sv is the Overburden and Pp is the Pore Pressure

Results tend to be on the low side


Matthews and Kelly (1967)(Most Generic Method)

S3 = Ki (Sv – Pp) + Pp

Where Ki = σh/ σv

Empirical regional values of Ki are needed tobe established from LOT calibrations


Eaton (1969)

Fp = (ν /1- ν)(Sv – Pp) + Pp

Where ν = Poissons Ratio

Eaton Replaced Ki with a value calculated from Poisson's Ratio

Empirical regional values of ν are needed tobe established from LOT calibrations


Anderson et al. (1973)

Fp = (Sv(2ν/1-ν))+((1-2ν/1-ν)(αPp))

Where α = 1-(1-φD)n

And ν is related to the lithology where theShaliness = (φS- φD)/ φS and

φS is the sonic and φD is the density porosity

Attributes fracture gradient variationsTo changes in lithology

Empirical regional values of α and ν are needed tobe established from LOT calibrations


Cesaroni et al. (1981)Formations with elastic behavior (sandstones)

Fp = ((2ν/1-ν)(SV – Pp)) + Pp

Elastic formations with deep invasion (unconsolidated sands)

Fp = 2ν(SV – Pp) + Pp

Plastic formations (shale, marl, salt, etc)

Fp = SV

Where ν is 0.25 for clean sands and unfractured carbonates at shallow depth and 0.28 for shaly sands, carbonates and sandstones at greater depth.


Daines (1982)

Fp = (ν/1- ν)(SV – Pp) + Pp + αt

Daines added a superimposed tectonic Stress αt to Eaton’s relationship

αt is calibrated to LOTs

Daines also applied varyingvalues of ν to different lithologies

e.g. Shale 0.14, Sandstone 0.06


Pilkington (1978)

Fp = Ka (Sv – Pp) + Pp

Where Ka represents the statistical meanof the values of Ki and ν/1- ν used by previous authors

Ka substitutes Ki in Matthews and Kelly’srelationship


Breckels & Van Eekelen (1981)(Only Valid in Areas with Established Relationships)

Empirical Relationship

Gulf Coast Relationship

Fp = 0.053 Z1.145 + 0.46(P – Pn)For Z < 3500m

Fp = 0.264 Z –317 + 0.46(P – Pn)For Z > 3500m

Where Z is the depth and Pn is the normalPore pressure

Also established relationships for N.Sea,Venezuela and Brunei


Bryant (1983)

Fp = Ki (SV – Pp) + Pp

Modifies Ki in Matthews and Kelly relationship to take into account the contribution of pore pressure to the the mechanical properties of the matrix

If Pp < 1.4Pn, (low to moderate overpressure), Matthews and Kelly relationship is used

If Pp > 1.4Pn, (moderate to high overpressure), Ki is obtained from Ki = P/S


Holbrook (1990)

(Use Only Recommended in Actively Compacting Formations in Tectonically Inactive

Areas)

Fp = ((1-φ)(SV – Pp)) + Pp

Replaces Ki or Poisson's ratio with a porosity term


Important Limitations/Problems of Traditional Methods

• Most commonly used fracture gradient prediction methods assume the absence of tectonic stresses. (Applicable in GOM, Nile Delta, but not many other places)

• Poisson’s ratio methods are based on erroneous assumptions.

How to Determine S3?

• If S3 measurements are available (from LOT, minifrac, step rate test, circulation losses, ballooning), then use Matthews and Kelly(S3 = Ki (Sv – Pp) + Pp)Ki is calculated at depth(s) of S3 measurement(s).

• If no S3 measurements are available ⇒


Zoback (1990)

Frictional Faulting theory where μ is coefficient of sliding friction, typically 0.6 in crystalline rocks but maybe as low as 0.3 in plastic formations.

Represents the stress to cause optimally oriented fractures and faults to slip. (Faults limit differential stress within the earth)

In normal faulting stress states: [ ] ppv P

PSS +

++

−≥ 2

23

1 μμ

≤


Travis Peak Stress State is Consistent with a Crust in Frictional Equilibrium

12.3PS

PS

pminh

pv =−

−


Impact of Water Depth on Fracture Gradient3,000 ft water depthonshore 6,000 ft water depth

Pore pressure (hydrostatic)

Frac gradient

Overburden (based on a constant density of 2.1 g/cm3)

Increasing water depth reduces the fracture gradient due to the difference between density of rock vs water (approx 9 ppg). The problem gets acute in ultra deepwater when the fracture gradient cannot support columns of mud even slightly heavier than water.

sea floor

sea floorMud Window becomes very narrow near the sea floor, which requires additional casing strings.


Fracture Gradient in Weak, Unconsolidated Sediments (1)

Because of their viscous nature, weak and unconsolidated sediments cannot support any differential stress over a long period of time.

Wilmington Sand Stress Relaxation


Fracture Gradient in Weak, Unconsolidated Sediments (2)

Weak, unconsolidated sediments cannot support any differential stress over a long period of time.

As a result, no difference exists between S3 and Sv in unconsolidated sediments.

=> S3 and therefore the fracture pressure is very close to the overburden in unconsolidated sediments.

Unconsolidated sediments

PressureD

epth

Overburden

Pore pressure

Least principal stress


How to Determine S3 Versus Depth Profiles

• If S3 measurements are available (from LOT, minifrac, step rate test, circulation losses, ballooning), then use Matthews and Kelly(S3 = Ki (Sv – Pp) + Pp)Ki is calculated at depth(s) of S3 measurement(s).

• If no S3 measurements are available

– Look for measurements in offset fields

– Tectonic regime from active geologic structures(determine whether S3 << Sv or S3 ~ Sv)

– Use lower bound on S3 from Frictional Faulting Theory (next slide)

– In viscoelastic/viscoplastic formations (shaley, poorly consolidated) S3 ~ Sv

Drilling Into Depleted ReservoirsDrilling Into Depleted Reservoirs


Poro-Elastic Response to a Change of Pp

Using instantaneous application of force and pressure with no lateral strain:

( )pvpH PSPS Δ−Δ⎟⎠⎞

⎜⎝⎛

−=Δ−Δ

ννα

1

( )( ) pH P1

21S Δν−ν−

α=Δ

Pp32SH Δ=Δ1,25.0 == ανif

g

b

KK

−=1α

Sv

SH

0L: Length (lateral extent) of reservoir [m]H: Height (thickness) of reservoir [m]ΔPP: Change in pore pressure [MPa]ΔSH: Change in horizontal stresses [MPa]SH ≡ Shmin ≡ SHmax

ν: Poisson’s ratioα: Biot’s coefficient

Kb: Bulk modulus of rock [GPa]Kg: Bulk modulus of individual grains [GPa]


Ekofisk Field


Elastic Solution:A=α(1-2ν)/(1-ν)

Α: Stress path parameter [ ]A ≡ ΔSH/ΔPp

Fault Reactivation Due to Poroelasticity


Mud Window Size

Depleted sand

In some cases it may be necessary to case off the depleted sand to avoid circulation losses.

Does a Depleted Sand Increase the Risk for Lost Circulation? (Example from the GOM)


Drilling Depleted Reservoirs –Planning Ahead

Time

Pre

ssur

e

Sv

Pp

Shmin

Collapse MW in shalesECD

Constant lossesNo losses Few losseswith careful ECD control

ECD: Equivalent circulating density

Increasing Mud Weights AboveIncreasing Mud Weights AboveThe Least Principal StressThe Least Principal Stress


Lost Circulation Occurs if all of the Following Three Conditions are True

1. The borehole pressure is large enough to initiate a tensile fracture at the wellbore wall (or a pre-existing fracture is present).

• Borehole pressure necessary to initiate a tensile fracture depends on in-situ stress state, Pp, borehole orientation, (and tensile strength).

2. Fractures at the wellbore wall can be “linked up” to form one large, pervasive fracture through which significant quantities of fluid can escape.

• depends on in-situ stress state, and borehole orientation.

3. A fracture is propagated into the formation.

• Requires that fluid pressure at fracture tip exceeds the minimum horizontal stress

• Depends on Shmin and mud properties (mud invasion factor)


Fracture Initiation - Stress Concentration Around a Vertical Well

A fracture is initiated when σθθmin drops below the tensile

strength of the formation

P0: Pore pressure [MPa]σθθ: Circumferential stress [MPa]σzz: Axial stress [MPa]


Example for Occurrence of Drilling-Induced Tensile Fractures

Hypothetical Stress States, Hydrostatic

Pore Pressure

Normal Faulting

Normal/Strike-Slip Faulting

For comparison: Shmin = 12.95 ppg


Inclined Tensile Cracks – Geothermal Well, Japan (Introduction to Fracture Link-Up)


Modeling Inclined Tensile Fractures


Example of Modeling the Occurrence of Lost Circulation Events

Hypothetical Stress States, Hydrostatic

Pore Pressure

Normal Faulting

Normal/Strike-Slip Faulting

For comparison: Shmin = 12.95 ppg

Fracture Initiation Fracture Link Up


Propagation of a Mode I Fracture

Pp: Pore pressure [MPa]

S3: Minimum stress [MPa]

L: Fracture length [m]

Ki: Stress Intensity Factor


Step Rate

Propagation pressure is negligible at higher flow rates because of low tensile strength and high stress intensity factor


Definition of the Invaded Zone

PgrowPpPp

S3

S3

Mud plug

Penny shapedfracture

2R1

2R

Definition of the invaded zone (2R1) where the internal pressure is Pgrow and the non-invaded zone (R – R1) where the internal pressure is Ppduring fracture growth.

Pgrow − S3

S3 − Pp

=1

1 − 1 −R1

R⎛ ⎝ ⎜

⎞ ⎠ ⎟

21 −

R1

R⎛ ⎝ ⎜

⎞ ⎠ ⎟

2

+π

4 RK IC

S3 − Pp

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟


Fracture Propagation

Neglecting KIC once the fractures have propagated away from the well, leads to:

Pgrow

S3

=1 −

PpS3

⎛ ⎝ ⎜

⎞ ⎠ ⎟ 1 − R1

R⎛ ⎝ ⎜ ⎞

⎠ ⎟ 2

1 − 1 − R1R

⎛ ⎝ ⎜ ⎞

⎠ ⎟ 2


Lost Circulation Occurs if all of the Following Three Conditions are True

1. Borehole pressure exceeds fracture Initiation pressure

⇒ Should only be used with caution as upper bound!

2. Borehole pressure is large enough for fractures to link up

⇒ Good upper bound if stress field is well known

3. A fracture is propagated into the formation.

⇒ Most conservative upper bound. Can be constrained with extended leak off test.

Case Study:Case Study:Deep Water Gulf of Mexico Deep Water Gulf of Mexico –– Maximizing Maximizing

Fracture GradientFracture Gradient


Overcoming Near Wellbore Stresses


Increasing Fracture Pressure


Increasing Fracture Pressure in a Deviated Well


Further Reading

Hubbert, M. K., and D. G. Willis, 1957. Mechanics of hydraulic fracturing, AIME Trans., 210, 153–163.Ito, T., M. D. Zoback, and P. Peska, 2001. Utilization of mud weights in excess of the least principal stress in extreme drilling environments, SPE Drilling and Completion, December 2001, SPE 57007.Nolte, K. G. and M. J. Economides, 1989, Fracturing diagnosis using pressure analysis, in Reservoir Simulation, M. J. Economides and K. G. Nolte, eds., Prentice Hall: Englewood Cliffs, N.J.Ward, C. D., and M. Beique, 1999. How to identify Lost Circulation Problems with Realtime Pressure Measurement: Downhole Pressure Sensing heads off Deepwater Challenge, Offshore, August 29.

Chapter 09 - FracturePressure

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