modelling of borehole stability

7/23/2019 Modelling of Borehole Stability

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Borehole stability and shale mechanics

2nd lecture:

Borehole stability modelling

Dag kland, 03.03.2000 1


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Tertiary

Quat.

Made by: D

DEPTH(mRKB)

TVD

Stratigraphy

Seabed

Date:03.03.00

PL nnn, WELL: xx/xx-2

Water Depth: 300 m MSL

RKB - Sea: 23,5 m

System

Group

1911

aland

1450

Nord

land

mRKB

Casing

30"

380,5m

Lithology

20"

810m

320

0

100

200

300400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700

1800

1900

2000

12-1 12-1kv.3 12-1FIT 11-2 11-2kv3 11-2sst 12/7 12-7FIT 12/9s 12-9s FITsst 12/10

12-10FIT 12/6 11-4sFIT 11-4s 0 15 30 45 60 75 90

Fm.

Nau

st

Kai

ge

*

0 H V

--P (PP) --Pk --LOTk (FG) -- (HS) -- (OB)

STABIL AnalysisDummy Field


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Base case for modelling(Dummy Field, 2350 m depth)

Stresses and pressures Stress / Pressure[MPa]

Gradient[g/cm3]

v (vertical stress) 47.5 2.06

H (max. horizontal stress) 44.2 1.92

h (min. horizontal stress) 44.2 1.92

p0 (pore pressure) 38.0 1.65

pw (well pressure) 42.2 1.83

Borehole orientation

Borehole inclination 45

Rock strength

C0 (uniaxial compr. strength) 4.0 0.17

Angle of internal friction 12

(unless otherwise specified) 3


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Borehole stresses are a function of:

in si tustresses (1 , , 2 , 3)

pore pressure (p0)

borehole orientation (inclination, azimuth)Poisson's ratio (to a very small degree)

well pressure (pw)

In inclined wells (well axis non-parallel with in si tu

principal stress axis), stresses are calculated thus:Transform in situ stresses to well coordinates (x, y, z)

Use formulas from Bradley (1979)

Borehole stresses(linear elastic solution)

4


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Assumptions:linear elasticity

impermeable borehole wall

plane strain (no displacement in z-direction parallel toborehole axis)

Effective stresses on the borehole wall:

r= pw - p0

= (x + y - pw) - 2(x - y)cos2 - 4xysin2 - p0

z = zz -[2(x - y)cos2 + 4xysin2] - p0

r = 0z = 2(-xzsin + yzcos) (NB! Misprint in Bradley's article)

rz = 0

Borehole stresses(after Bradley, 1979)

(Bradley, W.B. (1979) Failure of Incl ined Boreholes. J Energy Res. Tech.; Trans ASME 101, 1482 - 1498) 5


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Borehole stressesbase case

0 90 180 270 360

Angle along well circumference [ from high side]

-5

0

5

10

15

20

Effectivestress

es[MPa]

Sigma theta

Sigma z

Sigma r

Tau th-z

Sigma 1

Sigma 2

6


7/17

Borehole stresses2 = 45.9 MPa (1.99 g/cm3)

azimuth = 30 (clockwise from 1)

0 90 180 270 360

Angle along well circumference [ clockwise from high side]

-5

0

5

10

15

20

Effectivestress

es[MPa]

Sigma theta

Sigma z

Sigma r

Tau th-z

Sigma 1

Sigma 2

7


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Borehole failure

Shear failure:Compressive stressanisotropy causes shearstresses in excess of rockstrength

Fragments (cavings) arecreated on the borehole

wallDirectional borehole

enlargement (breakout)

Tensile failure:Tensile stress exceedstensile rock strength

Hydraulic fracture initiationon borehole wall

Lost circulation if fracturepropagates

8


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Shear failure criteria

Mohr-Coulomb (conservative)

1 = C0+ q3

Drucker-Prager (may overestimate influence of 2)

(1 - 2)2 + (1 - 3)2 + (2 - 3)2 = C(1 + 2 + 3 + A)2

Stassi-d'Alia (a bit weird)

(1 - 2)2 + (1 - 3)2 + (2 - 3)2 = 2(C0-T0)(1 + 2 + 3) + 2T0C0

Statoil version: T0 = 0

9


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Comparison of failure criteriabase case

0 30 60 90

Borehole inclination [ from vertical]

1.65

1.7

1.75

1.8

1.85

1.9

1.95

2

Minimums

tablemuddensity[g/cc]

Mohr-Coulomb

Drucker-Prager

Stassi-d'Alia

sigma hmin

10


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What simplifications have we made?

1. Impermeable borehole wall; unchanged pore pressure

2. Linear elasticity3. Biot's coefficient = 1

4. Elasto-brittle failure5. Failure = shear fracture initiation6. Chemically inert mud

7. Well pressure = hydrostatic mud pressure8. No thermal stresses

11


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1.Pore pressure in formationPressure changes immediately after drillout

in response to elastic volumetric strains

Plot created with B OSS-APF from PUC-Rio 12


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1.ConsolidationPressure changes with time due to consolidation.

10 nD permeability assumed for this plot.

Plot created with B OSS-APF from PUC-Rio 13


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1.Yielded zone (red) increasesdue to consolidation

Plots created with BOSS-APF from PUC-Rio

15.8 minutes

623 years14.6 days2.15 days

14.2 hours2.37 hours

4.77 days

14


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2.Pressure-dependent elasticity

Santarelli et al (1986) proposed a Young's moduluswhich depends on the confining pressure;

E(r) = E0ra ; 0 < a < 1

Supported by laboratory observations

Tangential stress is reduced when computed with thismethod

(Santarelli, F.J. et al. (1986) Analysis of Bo rehole Stresses Using Pressu re-Dependent Linear Elast ic i ty.

Int. J. Rock Mech. Sci. & Geomech. Abstr., 23, 445 - 449) 15


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2.and 4.Elasto-plasticity

Real rock displays plastic yield and can sustainconsiderable plastid deformation before critical failure.

May be modelled with Finite Element Method (FEM)models.

Failure

Failure?

Residual

strength

Elasto-brittle Elasto-plastic

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Other comments to simplifications

3. Biot's coefficient = 1

< 1 in deep formations; affects effective stresses

5. Failure = shear fracture initiationConservative; some researchers have proposed a"break-out span"; a critical angular breakout extent

6. Chemically inert mudHydration / dehydration and ionic alteration in shalemay lead to volumetric deformations

7. Well pressure = hydrostatic mud pressureSurge / swab and ECD effects may give transient well

pressures above or below hydrostatic pressure

8. No thermal stresses

= T*E*T/(1-)

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modelling of borehole stability

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