Upload
ahmad-waisul-qorni
View
222
Download
1
Embed Size (px)
Citation preview
7/23/2019 Modelling of Borehole Stability
1/17
Borehole stability and shale mechanics
2nd lecture:
Borehole stability modelling
Dag kland, 03.03.2000 1
7/23/2019 Modelling of Borehole Stability
2/17
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
7/23/2019 Modelling of Borehole Stability
3/17
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
7/23/2019 Modelling of Borehole Stability
4/17
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
7/23/2019 Modelling of Borehole Stability
5/17
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
7/23/2019 Modelling of Borehole Stability
6/17
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
7/23/2019 Modelling of Borehole Stability
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
7/23/2019 Modelling of Borehole Stability
8/17
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
7/23/2019 Modelling of Borehole Stability
9/17
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
7/23/2019 Modelling of Borehole Stability
10/17
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
7/23/2019 Modelling of Borehole Stability
11/17
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
7/23/2019 Modelling of Borehole Stability
12/17
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
7/23/2019 Modelling of Borehole Stability
13/17
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
7/23/2019 Modelling of Borehole Stability
14/17
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
7/23/2019 Modelling of Borehole Stability
15/17
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
7/23/2019 Modelling of Borehole Stability
16/17
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
16
7/23/2019 Modelling of Borehole Stability
17/17
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-)
17