Doctoral Dissertation
Characterizing the Full In-Situ
Stress Tensor and Its Applications for
Petroleum Activities
Department of Energy and Resources Engineering
Graduate School, Chonnam National University
Do Quang Khanh
August 2013
Characterizing the Full In-Situ
Stress Tensor and lts Applications
for Petroleum Activities
Department of Energy and Resources Engineering
Graduate School. Chonnam National Universitv
Do Quang Khanh
Supervised by Professor YANG, Hyung-Sik
A dissertation submitted in partial fulfillment of the requirements for the Doctor of
Philosophy in Energy and Resources Engineering.
Committee in Charge
Dr.
:
So-Keul
GAM)
Prof. Tam T
Prof. Jeong-Flwan Lee
Prol-. Piyush Rai
(CNU)
ilffi"4--
(BHU, India)
Prof. Hyung-Sik Yans
(CNU)
August 2013
)z
4
-3-
CONTENTS
Characterizing the Full In-Situ Stress Tensor
and Its Applications for Petroleum Activities
Contents
i
List of figures and tables
iv
Nomenclature of symbols
viii
Abstract
x
CHAPTER 1: INTRODUCTION
1
1.1. Project rationale
1
1.2. Project philosophy and purposes
2
1.3. Review
3
1.4. Outline of thesis
7
CHAPTER 2: IN-SITU STRESS TENSOR
AND ITS RELATING CONCEPTS
9
2.1. Introduction
9
2.2. In-situ stress tensor
9
2.3. State of in-situ stress
13
2.4. Pore pressure and effective stress
14
2.5. Frictional limits to stress
15
2.6. Stresses and rock failure
17
CHAPTER 3: STRESS AND FAILURE ANALYSIS FOR WELLBORES
22
3.1. Introduction
22
3.2. Stress and failure analysis for a vertical cylindrical wellbore
22
3.2.1. Stresses around a vertical cylindrical wellbore
22
3.2.2. Failure analysis for a vertical wellbore
26
3.3. Stress and failure analysis for an arbitrarily deviated wellbore
28
3.3.1. Stresses around an arbitrarily deviated wellbore
28
3.3.2. Failure analysis for an arbitrary deviated wellbore
33
i
CHAPTER 4: METHODS FOR DETERMINING IN-SITU STRESS
35
4.1. In-situ stress measurements in drilling boreholes
35
4.1.1. Hydraulic fracturing methods
35
4.1.2. Overcoring methods
37
4.1.3. Breakout methods
39
4.1.4. Drilling induced tensile fractures methods
43
4.1.5. Earth focal mechanism (FMS)
45
4.2. New integrated method for determining ISS
using petroleum exploration data
47
4.2.1. Introduction
47
4.2.2. Determining the orientations of horizontal stresses
49
4.2.3. Determining the vertical stress
51
4.2.4. Determining the minimum horizontal stress magnitude
54
4.2.5. Constraining the maximum horizontal stress magnitude
57
4.2.6. Determining pore pressure
62
CHAPTER 5: MODEL DEVELOPMENT FOR
FAILURE ANALYSIS OF WELLBORE (FAOWB)
65
5.1. Introduction
65
5.2. Structures of the FAoWB software packages
65
5.3. Validation of the results of the packages FAoWB
71
5.3.1. Case 1: Cross-checking Barton’s study (1998) on compressive failure
and breakout width analysis at the KTB wellbore, Germany.
71
5.3.2. Case 2: Cross-checking Meyer’s study (2002) on the well stability
at the Swan Lake field, South Australia.
78
CHAPTER 6: CASE STUDIES AND IMPLICATIONS
89
6.1. Introduction
89
6.2. Geological framework of the main studied area
89
6.3. The White Tiger (Bach Ho) field, Centre of the Cuu Long basin, Vietnam
93
6.3.1.
Statement of problem
93
6.3.2.
In-situ stress determination techniques
96
6.3.3.
In-situ stress tensor at the White Tiger field
105
6.3.4.
Implications
106
6.3.5.
Summary of results
120
ii
6.4. The X field, Northern of the Cuu Long basin, Vietnam
121
6.4.1.
Statement of problem
121
6.4.2.
In-situ stress determination techniques
123
6.4.3.
In-situ stress tensor at the X field
129
6.4.4.
Implications
130
6.4.5.
Summary of results
135
CHAPTER 7: CONCLUSIONS AND RECOMMENDATIONS
137
Reference
140
Abstract in Korean
148
Acknowledgements
150
iii
LIST OF FIGURES AND TABLES
Figure 2.1: Components of stresses acting on a plane.
10
Figure 2.2: Components of stresses acting on the faces of a cube.
11
Figure 2.3: The three states of stress and associated types of faulting.
13
Figure 2.4: Frictional limits to stress based on the frictional strength
of favourably oriented fault planes for μ = 0.6 and 1.0.
17
Figure 2.5: Two-dimensional Mohr circle.
18
Figure 2.6: Three-dimensional Mohr circle.
19
Figure 2.7: Mohr diagram with a failure envelope that fits closely to
laboratory rock testing data.
20
Figure 2.8: Three-dimensional Mohr diagram and Coulomb failure criterions
for pre-existing planes of weakness and for intact rock.
21
Figure 3.1: Vertical cylindrical wellbore with the orientations of the
circumferential stress σϴϴ, axial stress σzz and radial stress σrr.
23
Figure 3.2: Stress concentration around a vertical in a bi-axial stress field
based on the Kirsch equations.
24
Figure 3.3: The stress concentration around a circular borehole subject to
only uniaxial compression.
25
Figure 3.4: An arbitrarily deviated wellbore with the orientations of
the cirumferential (σϴϴ), axial (σzz), radial (σrr),
minimum (tmin) and maximum (tmax) stresses.
29
Figure 3.5: Three coordinate systems used to transform
for an arbitrarily deviated wellbore.
30
Figure 3.6: Lower hemisphere projection used to display relatively stability
of wellbores with different azimuths and deviations.
34
Figure 4.1: A schematic diagram with the equipment set-up and
the propagation direction of the induced fracture during
a hydraulic fracturing test.
Figure 4.2: Typical procedure used in the overcoring technique
36
38
Figure 4.3: Circumferential stress around a vertical wellbore
with respect to the orientation of the maximum horizontal stress
iv
for formation of BOs and DITFs.
40
Figure 4.4: Section of four-arm dipmeter log data showing consistent
breakouts in a north-south direction.
41
Figure 4.5: An imaging log data with borehole breakouts.
42
Figure 4.6: Hollow cylinder laboratory test.
42
Figure 4.7: An imaging log data with drilling induced tensile fractures
44
Figure 4.8: The three main fault regimes and their corresponding
fault plane solutions.
Figure 4.9: Integration of density logs to estimate overburden stress at depths
46
52
Figure 4.10: Resistivity image, density log (RHOB),
density correction log (DRHO) and caliper log (CALI).
53
Figure 4.11: Pressure vs. time record showing LOP, breakdown, Pc and Pr.
55
Figure 4.12: Pressure versus root time plot showing Pc.
57
Figure 5.1: Start screen of the software packages FAoWB.
66
Figure 5.2: Main screen of the software packages FAoWB.
66
Figure 5.3: Menu File of the software packages FAoWB.
66
Figure 5.4: Menu Input Data of the software packages FAoWB.
67
Figure 5.5: Tab Description of the software packages FAoWB.
67
Figure 5.6: Tab Stress of the software packages FAoWB.
68
Figure 5.7: Tab Rock properties of the software packages FAoWB.
68
Figure 5.8: Tab Well of the software packages FAoWB.
69
Figure 5.9: Menu Failure Criteria of the software packages FAoWB.
69
Figure 5.10: Menu Process of the software packages FAoWB.
70
Figure 5.11: Menu Output of the software packages FAoWB.
70
Figure 5.12: Stress distribution of case 1 (from packages FAoWB).
72
Figure 5.13: Risk diagrams of case 1 (from packages FAoWB).
73
Figure 5.14: The breakout risk diagrams of the KTB wells
for Mohr-Coulomb, Drucker-Prager and Mogi-Coulomb criteria.
74
Figure 5.15: The mud weight required of the KTB wells.
76
Figure 5.16: Risk diagrams of case 2 (from packages FAoWB).
79
Figure 5.17: The breakout risk diagrams of wells at Swan Lake field
for Mohr-Coulomb, Drucker-Prager and Mogi-Coulomb criteria.
81
Figure 5.18: The mud weight required at the Swan Lake field.
82
Figure 5.19: Stress distribution of case 2 (from packages FAoWB).
84
v
Figure 5.20: Stress polygon and constraints for case 1 and 2.
86
Figure 6.1: Location map of the Cuu Long Basin.
90
Figure 6.2: Schematic cross-section of the Cuu Long Basin.
91
Figure 6.3:Generalized stratigraphy column of the Cuu Long Basin.
92
Figure 6.4. Location map of the White Tiger field at the Cuu long basin.
93
Figure 6.5: Basement distribution at White Tiger field, Cuu Long basin.
94
Figure 6.6: Main fault and fracture system at the White Tiger field.
95
Figure 6.7: Generalized stratigraphy column at the White Tiger.
95
Figure 6.8: Examples of the occurrence of BOs and DIFTs at
the basement intervals of the wellbores at the White Tiger field.
96
Figure 6.9: Histogram and rose diagrams of the orientation of SHmax
from BOs at the basement intervals of the Whiter Tiger field.
97
Figure 6.10: Histogram and rose diagrams of of the orientation of SHmax
from DITFs at the basement intervals of the Whiter Tiger field.
97
Figure 6.11: Histogram and rose diagrams of the orientation of SHmax from
both BOs and DITFs at the basement intervals of the Whiter Tiger field.
98
Figure 6.12: Vertical stress or overburden stress at the White Tiger field.
99
Figure 6.13: Plots of treatment pressure in the hydraulic fracturing tests.
99
Figure 6.14: Minimum horizontal stress at the White Tiger field.
100
Figure 6.15: Pore pressure at the White Tiger field.
101
Figure 6.16: Stress Polygon and constraints at depths of the White Tiger field.
104
Figure 6.17: Stress distribution at the depth 3900 m of the White Tiger field.
106
Figure 6.18: Stress distribution at the depth 4100 m of the White Tiger field.
107
Figure 6.19: Stress distribution at the depth 4300 m of the White Tiger field.
108
Figure 6.20: Stress distribution at the depth 4500 m of the White Tiger field.
109
Figure 6.21: Risk diagrams at the depth 3900 m of the White Tiger field.
110
Figure 6.22: Risk diagrams at the depth 4100 m of the White Tiger field.
113
Figure 6.23: Risk diagrams at the depth 4300 m of the White Tiger field.
116
Figure 6.24: Risk diagrams at the depth 4500 m of the White Tiger field.
118
Figure 6.25: Location map of the X field.
121
Figure 6.26: The depth structural map at the X field.
121
Figure 6.27: The stratigraphy column of the X field.
122
Figure 6.28: Example of DITFs of the wellbore X1 at the X field.
123
Figure 6.29: Histogram and rose diagrams of DITFs at the wellbore X1.
124
vi
Figure 6.30: Vertical stress or overburden stress at the X field.
125
Figure 6.31: Plots of surface pressure in the LOTs/FITs at the X field.
126
Figure 6.32: Minimum horizontal stress at the X field.
126
Figure 6.33: Pore pressure at the X field.
127
Figure 6.34: Stress Polygon and constraints at depth 2300 m of the X field.
128
Figure 6.35: Stress distribution at the basement depth 2300 m of the X field.
130
Figure 6.36: Risk diagrams at the basement depth 2300 m of the X field.
131
Figure 6.37: Risk diagrams on evaluation for the applicability of
under-balanced drilling techniques (Pw=22 MPa).
Figure 6.38: Stress distribution at two deviated wellbores of the X field.
134
135
Table 6.1: The full in-situ stress tensor at the basement depths
of the White Tiger field.
105
Table 6.2: The full in-situ stress tensor at the basement depth 2300 m
of the X field.
129
vii
NOMENCLATURE OF SYMBOLS
C: compressive strength
C0: uniaxial compressive strength
Cb: biaxial compressive strength
g: acceleration due to gravity
P: stress tensor due to pore pressure
Pc: fracture closure pressure
Pi: fracture initiation pressure
Pp: pore pressure
Pr: fracture reopening pressure
Pw: wellbore fluid pressure
Rb: coordinate transform matrix
RS: coordinate transform matrix
S: applied stress tensor
S’: effective stress tensor
S1, S2, S3: three principal stresses
Sb: stress tensor in the borehole coordinate system
Sg: stress tensor in the geographic coordinate system
SHmax: maximum horizontal stress magnitude
Shmin minimum horizontal stress magnitude
Ss: stress tensor in principal stress coordinate system
Sv: vertical stress magnitude
T: tensile strength
z: depth
α, β, γ: Euler rotation angles
δ: wellbore azimuth
viii
δij: Kronecker delta
ΔP: difference between wellbore and pore pressure
μ: coefficient of friction
ʋ: Poisson’s ratio
ƍ: density
σij: stress component acting in the j direction in the plane normal to the i direction
σn: normal stress
σrr: effective radial stress
σtmax: maximum effective stress tangential to the wellbore wall
σtmin: minimum effective stress tangential to the wellbore wall
σzz: effective axial stress
σϴϴ: effective circumferential stress
σϴϴmin: minimum of the effective circumferential stress
φ: wellbore deviation
ω: angle between σtmax and the wellbore axis
: shear stress
ix
Characterizing the Full In-Situ Stress Tensor
and Its Applications for Petroleum Activities
Do Quang Khanh
Department of Energy and Resources Engineering
Graduate School, Chonnam National University
(Supervised by Professor YANG, Hyung-Sik)
(Abstract)
Knowledge of the full in-situ stress tensor has an importance for
petroleum activities. A demand in the determination of in-situ stress using
petroleum exploration data available has increased during the last decades
over the world. The new integrated method for determining the full in-situ
stress tensor using the available petroleum data has been accepted as more
reliable and widely applicable in many petroleum basins.
This thesis developed and applied the new integrated method for determining
the full tensor of in-situ stress using the available petroleum data. This
method involves many aspects in which the constraining related to the
magnitude of the maximum horizontal stress is the most challenge. It also
requires the integration and modification many techniques for studying
specific problems using available datasets.
x
The software packages on failure analysis of wellbores (FAoWB) written in
the programming language MATLAB were designed and developed from this
new integrated method for determining the full stress tensor and the
extended theories on stresses and failures around the wellbore. They
facilitate the determination of the full in-situ stress tensor using the
observations of wellbore failures (breakouts BOs and/or drilling-induced
tensile fractures DIFTs) in petroleum wellbores. The forward calculating of
stresses around the wellbores will be constrained with the observations of
borehole failures and rock strength, pore pressure or mud pressure
depending on available data at a particular petroleum field. Moreover, under
the full in-situ stress tensor determined they also help to derive easily the
implications related to the state of in-situ stress. Their accuracy and
reliability were confirmed through the cross-checking of two well-known
investigations earlier. Three different strength criteria including the MohrCoulomb, Drucker-Prager and Mogi-Coulomb criteria also were applied to
recommend the selection of an appropriate criterion for relatively strong
rocks. Furthermore, they have been demonstrated to be user-friendly,
attractive and easy to develop the codes for other real cases.
The software packages FAoWB were used to characterize well the state of
the full in-situ stress tensors from the new integrated method with available
data of basement reservoirs of the petroleum fields belonging to the Cuu
Long basin, Vietnam. Those are the White Tiger field located at the centre of
xi
the Cuu Long basin and the X field located at the northern of the Cuu Long
basin. Results showed that the stress regimes at basement reservoirs of the
Cuu Long basin should be the normal faulting (NF) or the strike-slip (SS)
with the orientation of the maximum horizontal stress oriented in the
direction NW-SE being consistent with the previous studies. The change of
the stress regimes from NF to SS together with the strength rock measured
should affect the risk of the occurrence of BOs and/or DITFs. These
predictions are suitable to the practical problems at the petroleum fields of
this basin as the wellbore collapse (due to BOs) or the lost circulation (due to
DITFs). Moreover, with advanced knowledge of the full in-situ stress tensors
including both the orientations and magnitudes, we could choose the optimum
drilling trajectories oriented in the direction NE-SW, change the suitable mud
weight to prevent wellbore instability or evaluate the applicability of underbalanced drilling techniques at the petroleum fields of the Cuu Long basin.
Keywords: In-situ stress, wellbore failures, breakouts, drilling-induced
tensile fractures, wellbore instability.
xii
CHAPTER 1
INTRODUCTION
1.1. Project rationale
Knowledge of in-situ stress plays a great role in solving both science and engineering
problems, encountered in geology, geophysics, civil, mining, and petroleum development. It
is a key parameter in some activities including (Amadei and Stephansson, 1997; Tingay et al,
2009):
·
plate tectonics and neotectonics;
·
earthquake prediction and seal breach by fault reactivation;
·
stability of underground excavations (tunnels, mines, caverns, shafts, stopes);
·
slope stability;
·
drilling borehole stability;
·
induced hydraulic fracturing stimulation;
·
reservoir drainage and flooding patterns;
·
subsurface fluid flow in naturally-fractured reservoirs, and
·
storage and extraction of oil and gas from the subsurface.
A dramatic increase in the determination of in-situ stress using petroleum exploration data
and its applications to problems in petroleum exploration and production has been seen
during the last decades over the world. One key driver for the increased awareness has been
the increasing quality and use of borehole imaging tools, and the geomechanical information
yielded by these tools. Nowadays, drilling induced failures including breakouts and/or
drilling induced tensile fractures from borehole imaging tools are recognized and used to
determine in-situ stress (Zoback et al., 1985; Peska and Zoback, 1995). Furthermore, the
1
increased incidence of deviated drilling has provided both new techniques for constraining
the in situ stress tensor and increased demand for solutions to problems related to the stateof-stress such as wellbore stability and fracture stimulation.
1.2. Project philosophy and purposes
There have been a number of different methods available to determine the in-situ stress in
the Earth’s crust. These methods include earthquake focal mechanisms, hydraulic fracturing,
overcoring, borehole breakouts, drilling induced tensile fractures and geological indicators.
Each stress measurement technique has advantages and limitations. The relationship between
in situ stress and induced failures in drilling boreholes can have significant implications for
in-situ stress determination methods. Therefore, the philosophy of this project was to
integrate and/or modify techniques as required for studying specific problems using available
datasets in the case studies.
In-situ stress determination in any oil field or sedimentary basin involves some aspects, such
as determination of the maximum horizontal stress orientations, the magnitude of the vertical
stress, the magnitude of the minimum horizontal stress and the constraining related to the
magnitude of the maximum horizontal stress. The approach to aspects of stress determination
is dependent upon the dataset available. The main purpose of this project is to formulate and
apply the new integrated method for determining the full tensor of in-situ stress based on
new and existing techniques from available petroleum data. Next, the use of these techniques
within several case studies at the petroleum fields will be analyzed to examine the wide
range of implications of in situ stress data to petroleum exploration and production activities.
A significant part of this project has involved designing and developing the software
packages on failure analysis of wellbores (FAoWB) written by programming language
MATLAB. They facilitate the determination of the full in-situ stress tensor using the
observations of wellbore failures in petroleum wellbores. Moreover, under the full in-situ
2
stress tensor determined the FAoWB software packages also help to derive easily the
implications related to the state of in-situ stress, such as the choice of the optimum drilling
trajectories for wellbore planning and the suitable mud weights for well stability.
1.3. Review
During the last decades there has been extensive research on the determination of in situ
stresses and its applications, particularly in the petroleum industry. To provide a contextual
framework for the more detailed discussion of the new integrated method for the in-situ
stress determination based new and existing techniques, a brief review of existing techniques
is presented here.
Generally, in sedimentary basins occurred the petroleum activities, the vertical stress is a
principal stress. Consequently the full in-situ stress tensor can be reduced to four
components. These components are the orientation of the maximum horizontal stress, the
vertical stress magnitude (Sv), the minimum horizontal stress magnitude (Shmin) and the
maximum horizontal stress magnitude (SHmax).
The orientation of the maximum horizontal stress can be determined from observations of
breakouts and drilling-induced tensile fractures commonly seen on borehole image logs.
Borehole breakouts (BOs) were first described by Bell and Gough (1979) as stress-induced
compressive failure of the wellbore, and have subsequently been used to determine
maximum horizontal stress orientations throughout the world (Zoback and Zoback, 1980;
Plumb and Cox, 1987, etc.). The advent of borehole imaging tools has confirmed the nature
of breakouts and has led to the recognition of stress-induced tensile wellbore failure known
as drilling induced tensile fractures (DITFs). DITFs are oriented orthogonal to breakouts and
can also be used to determine the orientation of the maximum horizontal stress (Aadnoy,
1990b; Brudy and Zoback, 1993, etc.).
The vertical stress magnitude can be determined from the weight of the overburden (McGarr
3
and Gay, 1978), which can be calculated using density logs and checkshot velocity surveys.
Density logs are routinely run during petroleum exploration and conventionally provide a
density measurement every 15 cm. However, density logs are rarely run to the surface
resulting in a lack of shallow data. Density in the shallow section can be estimated by
transforming sonic velocity from a checkshot velocity survey (Ludwig et al., 1970).
Hydraulic fracture test is an early and reliable method for determining in situ horizontal
stress magnitudes and orientations (Haimson and Fairhurst, 1967). Hydraulic fracture tests
involve isolating a section of the wellbore and increasing the pressure in the isolated interval
by pumping fluid into it, and thereby creating a fracture in the wellbore wall. This fracture
forms parallel to the wellbore axis (for a vertical wellbore) and orthogonal to the minimum
horizontal stress. In general the fracture propagates away from the wellbore in this
orientation as fluid continues to be pumped into the interval. In a thrust faulting stress regime
the fracture may rotate to horizontal, as it propagates away from the wellbore, complicating
the analysis. However, in general it is the minimum horizontal stress that acts to close the
fracture (Hubbert and Willis, 1957), and consequently the pressure at which the fracture
closes is a measure of the minimum horizontal stress and can be determined from the
pressure versus time record (Haimson and Fairhurst, 1967, etc.).
In petroleum drilling, hydraulic fracture tests are not generally undertaken but the leak-off
test (LOT) is somewhat similar in procedure to the initial stages of a hydraulic fracture test
and is routinely conducted during petroleum drilling. Leak-off tests are conducted to
determine the maximum fluid density that can be used in the next drilling section (i.e.
fracture gradient) and not for stress determination per se. During a LOT the pressure is
increased until a decrease in the rate of pressurization is observed. Consequently the induced
fracture is comparatively small compared to that induced during a hydraulic fracture test,
resulting in fracture closure not generally being observed. However, Breckels and van
Eeklen (1982) showed that leak-off test pressures provide an estimate of the Shmin, but not as
4
accurate an estimate as that yielded by hydraulic fracture tests.
Recognizing the similarity between LOTs and hydraulic fracture tests, Kunze and Steiger
(1991) proposed the Extended Leak-Off Test (XLOT). This test uses the same equipment as
a LOT, but a procedure more similar to the hydraulic fracture test, with multiple cycles of
pressurization and de-pressurization, results in a pressure versus time record that can be used
to determine the Shmin with increased confidence. The orientation of the maximum horizontal
stress may be determined by observing the orientation of the induced fracture using an
impression packer or a borehole imaging tool (Engelder, 1993; Haimson, 1993). The
magnitude of the maximum horizontal stress can be determined from XLOTs and hydraulic
fracture tests in some circumstances where a re-opening pressure can be interpreted
(Haimson and Fairhurst, 1967; Enever et al., 1996, etc.).
With the improvements of wellbore imaging tools, borehole breakouts BOs and/or DITFs
can be more accurately interpreted and their geometry observed. Zoback et al. (1985)
proposed a method for determining the magnitude of the maximum horizontal stress using
the angular width of breakouts around the wellbore is proposed. This technique was used to
obtain SHmax in New Mexico (Barton et al., 1988). However, this technique is controversial
because attempts to relate size and shape of breakouts to stress magnitudes requiring
consideration of the geometrical effects of breakout development and the failure mechanisms
of the material (Detournay and Roegiers, 1986, etc.). Nonetheless if breakouts are observed
and compressive rock strength measurements available, a lower bound for SHmax can be
determined (Moos and Zoback, 1990, etc.). Like breakout occurrence, DITF occurrence can
be used to constrain SHmax, in this instance given knowledge of tensile rock strength (Moos
and Zoback, 1990, etc.). Tensile rock strength is typically low compared to compressive rock
strength and rocks typically contain planes of weakness on which the tensile rock strength is
negligible. Consequently the tensile rock strength can be assumed to be negligible (Brudy
and Zoback, 1999).
5
Widespread application of deviated drilling led to new techniques being utilized for stress
determination. Aadnoy (1990) proposed a method for inverting three or more LOTs from
wellbores of different trajectories to determine the complete stress tensor. Gjønnes et al.
(1998) suggested the original method was inaccurate, because it ignored shear stresses, and
proposed an improved method. However, the improved inversion also contained large
uncertainties, in part due to the inaccuracy of LOTs and suggested the use of multiple
techniques to determine the in situ stresses. Image logging in deviated wells led to the
observation that breakout orientations rotate as deviation increases, depending on the stress
regime and borehole azimuth (Mastin, 1988). A technique for inverting the variation in
breakout orientations with borehole deviation and azimuth to determine the complete stress
tensor is proposed (Qian and Pedersen, 1991). Peska and Zoback (1995) developed a similar
technique for using rotation of breakout azimuths with deviation to constrain the stress tensor.
However, the rotation of DITF azimuths and variations in the occurrence of both breakouts
and DITFs are considered to constrain the full in-situ stress tensor. Using observations of
both DITFs and BOs occurrence and change in orientation, the full in-situ stress tensor can
be determined from a single deviated borehole.
Besides the frictional failure provides a theoretical limit to the ratio of the maximum to
minimum effective stress beyond which failure of optimally-oriented pre-existing faults
occurs (Sibson, 1974). A large number of in situ stress measurements in seismically active
regions have shown stresses to be at frictional limit (McGarr, 1980; Zoback and Healy, 1984).
Where one or more of the stress magnitudes are known, frictional limits can be used to
constrain stress magnitudes in seismically inactive regions and estimate stress magnitudes in
seismically active regions. Most commonly SV and Shmin are known and the frictional limit is
used to provide an upper limit to SHmax.
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