Luận án tiến sĩ: Characterizing the Full In-Situ Stress Tensor and Its Applications for Petroleum Activities

The stress concentration around a circular borehole subject to only uniaxial compression.An arbitrarily deviated wellbore with the orientations ofthe cirumferential Goo, axial ø;;, radia

Characterizing the Full In-SituStress Tensor and Its Applications

for Petroleum ActivitiesDepartment of Energy and Resources Engineering

Graduate School, Chonnam National University

Do Quang KhanhSupervised by Professor YANG, Hyung-Sik

A dissertation submitted in partial fulfillment of the requirements for the Doctor ofPhilosophy in Energy and Resources Engineering

Committee in Charge :

Dr So-Keul Chung (KIGAM) “hf \

Prof Tam Tran (CNU) ( a aProf Jeong-Hwan Lee (CNU) Tes

Prof Piyush Rai (BHU, India) pot aProf Hyung-Sik Yang (CNU) 5

%

August 2013

CONTENTSCharacterizing the Full In-Situ Stress Tensor

and Its Applications for Petroleum Activities

ContentsList of figures and tablesNomenclature of symbolsAbstract

CHAPTER 1: INTRODUCTION1.1 Project rationale

1.2 Project philosophy and purposes1.3 Review

1.4 Outline of thesis

CHAPTER 2: IN-SITU STRESS TENSOR

AND ITS RELATING CONCEPTS2.1 Introduction

2.2 In-situ stress tensor2.3 State of in-situ stress2.4 Pore pressure and effective stress2.5 Frictional limits to stress

2.6 Stresses and rock failure

CHAPTER 3: STRESS AND FAILURE ANALYSIS FOR WELLBORES3.1 Introduction

3.2 Stress and failure analysis for a vertical cylindrical wellbore3.2.1 Stresses around a vertical cylindrical wellbore

3.2.2 Failure analysis for a vertical wellbore3.3 Stress and failure analysis for an arbitrarily deviated wellbore3.3.1 Stresses around an arbitrarily deviated wellbore

3.3.2 Failure analysis for an arbitrary deviated wellbore

IVVill

“SID WOW NO —| —13141517

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CHAPTER 4: METHODS FOR DETERMINING IN-SITU STRESS4.1 In-situ stress measurements in drilling boreholes

4.1.1 Hydraulic fracturing methods4.1.2 Overcoring methods

4.1.3 Breakout methods4.1.4 Drilling induced tensile fractures methods4.1.5 Earth focal mechanism (FMS)

4.2 New integrated method for determining ISSusing petroleum exploration data

4.2.1 Introduction4.2.2 Determining the orientations of horizontal stresses4.2.3 Determining the vertical stress

4.2.4 Determining the minimum horizontal stress magnitude4.2.5 Constraining the maximum horizontal stress magnitude4.2.6 Determining pore pressure

CHAPTER 5: MODEL DEVELOPMENT FOR

FAILURE ANALYSIS OF WELLBORE (FAOWB)5.1 Introduction

5.2 Structures of the FAoWB software packages5.3 Validation of the results of the packages FAOWB5.3.1 Case 1: Cross-checking Barton’s study (1998) on compressive failure

and breakout width analysis at the KTB wellbore, Germany.5.3.2 Case 2: Cross-checking Meyer’s study (2002) on the well stability

at the Swan Lake field, South Australia

CHAPTER 6: CASE STUDIES AND IMPLICATIONS6.1 Introduction

6.2 Geological framework of the main studied area6.3 The White Tiger (Bach Ho) field, Centre of the Cuu Long basin, Vietnam6.3.1 Statement of problem

6.3.2 In-situ stress determination techniques6.3.3 In-situ stress tensor at the White Tiger field6.3.4 Implications

6.3.5 Summary of results

35353537394345

47474951545762

65656571

71

78

898989939396105106120

6.4 The X field, Northern of the Cuu Long basin, Vietnam6.4.1 Statement of problem

6.4.2 In-situ stress determination techniques6.4.3 In-situ stress tensor at the X field6.4.4 Implications

137

140

148

150

Figure 2.1:Figure 2.2:Figure 2.3:Figure 2.4:

Figure 2.5:Figure 2.6:Figure 2.7:

LIST OF FIGURES AND TABLES

Components of stresses acting on a plane.Components of stresses acting on the faces of a cube.The three states of stress and associated types of faulting.Frictional limits to stress based on the frictional strength

of favourably oriented fault planes for u = 0.6 and 1.0.Two-dimensional Mohr circle

Three-dimensional Mohr circle.Mohr diagram with a failure envelope that fits closely to

laboratory rock testing data.Three-dimensional Mohr diagram and Coulomb failure criterions

for pre-existing planes of weakness and for intact rock

Vertical cylindrical wellbore with the orientations of thecircumferential stress Ooo, axial stress o,, and radial stress o,,Stress concentration around a vertical in a bi-axial stress fieldbased on the Kirsch equations

The stress concentration around a circular borehole subject to

only uniaxial compression.An arbitrarily deviated wellbore with the orientations ofthe cirumferential (Goo), axial (ø;;), radial (6,,),

minimum (Timin) and MaximuM (Timax) Stresses.Three coordinate systems used to transform

for an arbitrarily deviated wellbore

Lower hemisphere projection used to display relatively stability

of wellbores with different azimuths and deviations

A schematic diagram with the equipment set-up andthe propagation direction of the induced fracture duringa hydraulic fracturing test

Typical procedure used in the overcoring techniqueCircumferential stress around a vertical wellbore

with respect to the orientation of the maximum horizontal stress

10II13

171819

for formation of BOs and DITFs.Figure 4.4: Section of four-arm dipmeter log data showing consistent

breakouts in a north-south direction.Figure 4.5: An imaging log data with borehole breakouts.Figure 4.6: Hollow cylinder laboratory test

Figure 4.7: An imaging log data with drilling induced tensile fracturesFigure 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 depthsFigure 4.10: Resistivity image, density log (RHOB),

density correction log (DRHO) and caliper log (CALI).Figure 4.11: Pressure vs time record showing LOP, breakdown, P, and P,.Figure 4.12: Pressure versus root time plot showing P

Figure 5.1: Start screen of the software packages FAOWB.Figure 5.2: Main screen of the software packages FAOWB.Figure 5.3: Menu File of the software packages FAOWB.Figure 5.4: Menu Input Data of the software packages FAoWB.Figure 5.5: Tab Description of the software packages FAOWB.Figure 5.6: Tab Stress of the software packages FAoWB.Figure 5.7: Tab Rock properties of the software packages FAOWB.Figure 5.8: Tab Well of the software packages FAoWB

Figure 5.9: Menu Failure Criteria of the software packages FAOWB.Figure 5.10: Menu Process of the software packages FAOWB.Figure 5.11: Menu Output of the software packages FAoWB.Figure 5.12: Stress distribution of case 1 (from packages FAoWB).Figure 5.13: Risk diagrams of case Ï (from packages FAOWB).Figure 5.14: The breakout risk diagrams of the KTB wells

for Mohr-Coulomb, Drucker-Prager and Mogi-Coulomb criteria.Figure 5.15: The mud weight required of the KTB wells

Figure 5.16: Risk diagrams of case 2 (from packages FAOWB).Figure 5.17: The breakout risk diagrams of wells at Swan Lake field

for Mohr-Coulomb, Drucker-Prager and Mogi-Coulomb criteria.Figure 5.18: The mud weight required at the Swan Lake field

40

41424244

4652

535557

66666667676868696970707273

747679

8182

Figure 5.20: Stress polygon and constraints for case 1 and 2.

Figure 6.1: Location map of the Cuu Long Basin.Figure 6.2: Schematic cross-section of the Cuu Long Basin.Figure 6.3:Generalized stratigraphy column of the Cuu Long Basin.Figure 6.4 Location map of the White Tiger field at the Cuu long basin.Figure 6.5: Basement distribution at White Tiger field, Cuu Long basin.Figure 6.6: Main fault and fracture system at the White Tiger field.Figure 6.7: Generalized stratigraphy column at the White Tiger.Figure 6.8: Examples of the occurrence of BOs and DIFTs at

the basement intervals of the wellbores at the White Tiger field.Figure 6.9: Histogram and rose diagrams of the orientation of Sumax

from BOs at the basement intervals of the Whiter Tiger field.Figure 6.10: Histogram and rose diagrams of of the orientation of Snmax

from DITFs at the basement intervals of the Whiter Tiger field.Figure 6.11: Histogram and rose diagrams of the orientation of Symax from

both BOs and DITFs at the basement intervals of the Whiter Tiger field.Figure 6.12: Vertical stress or overburden stress at the White Tiger field.Figure 6.13: Plots of treatment pressure in the hydraulic fracturing tests.Figure 6.14: Minimum horizontal stress at the White Tiger field.Figure 6.15: Pore pressure at the White Tiger field

Figure 6.16: Stress Polygon and constraints at depths of the White Tiger field.Figure 6.17: Stress distribution at the depth 3900 m of the White Tiger field.Figure 6.18: Stress distribution at the depth 4100 m of the White Tiger field.Figure 6.19: Stress distribution at the depth 4300 m of the White Tiger field.Figure 6.20: Stress distribution at the depth 4500 m of the White Tiger field.Figure 6.21: Risk diagrams at the depth 3900 m of the White Tiger field.Figure 6.22: Risk diagrams at the depth 4100 m of the White Tiger field.Figure 6.23: Risk diagrams at the depth 4300 m of the White Tiger field.Figure 6.24: Risk diagrams at the depth 4500 m of the White Tiger field.Figure 6.25: Location map of the X field

Figure 6.26: The depth structural map at the X field.Figure 6.27: The stratigraphy column of the X field.Figure 6.28: Example of DITFs of the wellbore X1 at the X field.Figure 6.29: Histogram and rose diagrams of DITFs at the wellbore X1

86

90919293949595

96

97

97

989999100101104106107108109110113116118121121122123124

Figure 6.30: Vertical stress or overburden stress at the X field.Figure 6.31: Plots of surface pressure in the LOTs/FITs at the X field.Figure 6.32: Minimum horizontal stress at the X field.

Figure 6.33: Pore pressure at the X field.Figure 6.34: Stress Polygon and constraints at depth 2300 m of the X field.Figure 6.35: Stress distribution at the basement depth 2300 m of the X field.Figure 6.36: Risk diagrams at the basement depth 2300 m of the X field.Figure 6.37: Risk diagrams on evaluation for the applicability of

under-balanced drilling techniques (P,=22 MPa).Figure 6.38: Stress distribution at two deviated wellbores of the X field

Table 6.1: The full in-situ stress tensor at the basement depths

of the White Tiger field.Table 6.2: The full in-situ stress tensor at the basement depth 2300 m

of the X field

125126126127128130131

134135

105

129

NOMENCLATURE OF SYMBOLS

C: compressive strength

Co: uniaxial compressive strength

Cy: biaxial compressive strength

g: acceleration due to gravity

P: stress tensor due to pore pressure

P,: fracture closure pressure

P;: fracture initiation pressure

P,: pore pressure

P,: fracture reopening pressure

Py: wellbore fluid pressure

R,: coordinate transform matrix

Rg: coordinate transform matrix

S: applied stress tensor

S’: effective stress tensor

5¡, S2, S3: three principal stresses

Sp: Stress tensor in the borehole coordinate system

Sp: 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

Sy: vertical stress magnitude

T: tensile strength

z: depth

a, B, y: Euler rotation angles

6: wellbore azimuth

Ơi: Stress component acting in the j direction in the plane normal to the i direction

Ơn: Normal stress

Oi effective radial stress

Otmax Maximum effective stress tangential to the wellbore wall

Otmin Minimum effective stress tangential to the wellbore wall

Ơ;;: effective axial stress

Ooo: effective circumferential stress

Ooomin: Minimum of the effective circumferential stress

@: wellbore deviation

w: angle between Otmax and the wellbore axis

T: shear stress

Characterizing the Full In-Situ Stress Tensorand Its Applications for Petroleum Activities

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

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-inducedtensile 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

Mohr-Coulomb, 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

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 toDITFs) 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

under-balanced drilling techniques at the petroleum fields of the Cuu Long basin

Keywords: In-situ stress, wellbore failures, breakouts, drilling-inducedtensile fractures, wellbore instability

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 akey parameter in some activities including (Amadei and Stephansson, 1997; Tingay et al,

2009):

e plate tectonics and neotectonics;

e earthquake prediction and seal breach by fault reactivation;

e stability of underground excavations (tunnels, mines, caverns, shafts, stopes);

e slope stability;

e drilling borehole stability;

e induced hydraulic fracturing stimulation;

e reservoir drainage and flooding patterns;

e subsurface fluid flow in naturally-fractured reservoirs, and

e 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

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

state-of-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

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 1n 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 (S,), the minimum horizontal stress magnitude (Snmin) and the

maximum horizontal stress magnitude (Spmax)

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

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 1s 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 Spmin, but not as

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 Spmin 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 Stimax 11 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 Sumax can be

determined (Moos and Zoback, 1990, etc.) Like breakout occurrence, DITF occurrence can

be used to constrain Symax, 1n 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),

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 Gjonnes ef 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 1s 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 Sy and Spmin are known and the frictional limit 1s

used to provide an upper limit to Stimax

1.4 Outline of thesis

The thesis consists of seven chapters The first chapter states the rationale, philosophy and

purposes of project It also reviews studies on the determination of in-situ stresses and its

applications, particularly in the petroleum industry

Chapter 2 presents an introduction to the full in-situ stress tensor and its relating concepts,

such as the state of in-situ stress, the pore pressure and effective stress, frictional limits to

stress and rock failures

Chapter 3 provides the theoretical descriptions on stresses around borehole and wellbore

failures Especially, the stress concentration and wellbore failures in arbitrary wellbores

They are necessary background for the discussion of the methods for determining the in-situ

stress tensor used in the petroleum industry

Chapter 4 presents and discusses the methods for determining in-situ stress It introduces to

in-situ stress indicators in drilling boreholes from hydraulic fracturing, overcoring, breakout,

drilling-induced tensile fractures and earth focal mechanism Especially, it presents and

discusses in detail the new integrated method for determining in-situ stress using petroleum

exploration data available, covering the techniques for the determination of the maximum

horizontal stress, the magnitudes of S,, Simin and pore pressure P, and constraints of the

maximum horizontal stress magnitude Stmin from the occurrence of wellbore failures and the

frictional limits to stress

Chapter 5 introduces and presents the software packages FAoWB on failure analysis of

wellbores They are designed and developed based on the applying of the theories in chapters

2, 3 and the new integrated method for determining the full in-situ stress tensor presented in

chapter 4 Two well-known investigations earlier are considered and compared by the

software packages FAoWB The results obtained from these software packages have

confirmed their accuracy and reliability and showed their other potentials, such as their

user-Chapter 6 reports the use of the software packages FAoWB to study the real cases at the

petroleum fields belonging to the Cuu Long basin, Vietnam General geological information

on the Cuu Long basin is introduced Two petroleum fields at the Cuu Long basins are the

White Tiger field, located in the centre and the X field, located in the northern of this basin

The full in-situ stress tensors at these petroleum fields are characterized by applying the new

integrated method using the available petroleum data from two petroleum fields and using

the packages FAOWB Next, under these full in-situ stress tensors the risk diagrams of the

occurrence of drilling-induce tensile fractures (DITFs) and/or breakouts (BOs) of the

packages FAoWB were established and analyzed With advanced knowledge of the full

in-situ stress tensors including both the orientations and magnitudes at these petroleum fields,

their implications should be derived on the choice of the optimum drilling trajectories, the

predictions and prevention the wellbore instability and the evaluation for the applicability of

the drilling under-balance techniques at these petroleum fields at the Cuu Long basin

Finally, conclusions and recommendations were drawn from applying this new integrated

method for determining the full in-situ stress tensor and the using of the packages FAOWB

with the available petroleum data at the petroleum fields

CHAPTER 2

IN-SITU STRESS TENSOR AND ITS RELATING CONCEPTS

2.1 Introduction

Until now the in-situ stresses within the Earth’s crust have been of the main interest of many

researchers at scales ranging from the formation of mountain belts (~1000 km) to wellbore

failure (~ cm) In-situ stress data are critical to a number of areas such as understanding the

driving forces of plate tectonics, seismic hazard assessment and mine stability (Hoek and

Brown, 1980), especially in to the petroleum-related applications as wellbore stability,

hydraulic fracturing stimulation, reservoir drainage and flooding patterns, etc (Amadei and

Stephansson, 1997; Tingay et al, 2009)

The in situ stress field is the present-day stress field and is responsible for contemporary

failures It is the result of a variety of forces acting at differing scales These forces result in

variations in the stress field at the scales of several hundred kilometres to less than a

kilometre They can be dividing into first and second order forces (Zoback, 1992) First

order forces are the result of plate boundary interactions and are responsible for the

continental-scale stress field Second order forces are the result of topography, lithospheric

flexure, lateral density and strength variations and geologic structure

Stresses within rocks at a depth in the subsurface in the Earth’s crust are referred as in-situ

stresses The quantitative investigation of the above phenomena requires a mathematical

representation of in situ stresses within the Earth’s crust The state of in-situ stresses can be

mathematically described by using the concepts of the full in-situ stress tensor

2.2 In-situ stress tensor

Stress at a point is defined as a force (F) acting over a unit area (A) It is usually divided into

acting normal to the plane The shear stress (7) is the stress component acting parallel to a

plane, inducing sliding along that plane Alternatively, the components of stresses acting on a

plane can be completely described by the normal stress (On) acting on the plane, the

maximum shear stress (T max) acting on the plane and the orientation of that shear stress

The maximum shear stress (T max) 1s also divided into two perpendicular directions (tT x and

Ty) on the plane (Figure 2.1)

To be more precise, stress is a tensor which describes the density of forces acting on all

surfaces passing through a given point The full stress tensor in a three-dimensional space at

depth can be described as a second-rank tensor by normal stress acting on each of three

orthogonal planes and the two orthogonal components of shear stress acting on those planes

(Figure 2.2)

k

—.X Y

Figure 2.2: Components of stresses acting on the faces of a cube

These nine components of the full three-dimensional stress tensor can be written as:

( ẢO > Ory orS =| 0,0, Ø„ (2.1)

xz Fr Ox: |

where S is the stress tensor, S; is the normal stress in the 1 direction, Š; 1s the shear stress

acting in the j direction in the plane containing the j and k directions and $;, =S-

The stress tensor can be simplified by choosing a coordinate system such that the planes have

no shear stress acting upon them The normals to these planes are principal stress directions

In this case the complete stress tensor can be completely defined by the magnitudes of the

three principal stresses and the orientations of two of the principal stresses The stress tensor

is fully constrained if the magnitudes and orientations of the three principal stresses S1, Š›

and Sa with the convention S;>S›>_ S3 are known:

(S0 0Ì

S=|0 S, 0 (2.2)(0 0 6,

whereS[ is the maximum principal stress, S2 1s the intermediate principal stress and

533 1s the minimum principal stress

The earth’s surface is in contact with a fluid which cannot support shear tractions.

Consequently, one principal stress is generally normal to the earth’s surface with the other

two principal stresses acting in an approximately horizontal plane Alternately, the vertical

orientation can be assumed to be one of the principal stress orientations Consequently, the

in-situ stress tensor, completely constrained by the orientation of one of the horizontal

stresses and the magnitudes of the vertical and two horizontal principal stresses, can be

written:

Sr max 0 0

S =| 0 Simin Ö (2.3)0 0 S,

where Sy is the vertical principal stress, Shmin 1S the minimum horizontal principal stress

and SHmax is the maximum horizontal principal stress (note that the positions of SHmax

Shmin and Sy on the diagonal are interchangeable depending on which is larger)

Since no shear stress can exist in the plane of the earth’s surface, one of the principal

stresses in the upper crust must be oriented perpendicular to the surface In general, one

principal stress is usually within 20° of vertical except beneath very rough topography It

must be true close to the earth’s surface and it is also generally true to the depth to the

brittle-ductile transition in the upper crust at about 15 ~ 20 km depth (Zoback, 1992) Thus, the

other two principal stresses are oriented approximately horizontal, parallel to the ground

surface Throughout this thesis the assumption that the vertical stress (Sy) 1s a principal

stress and hence the maximum and minimum horizontal stresses (SHmax and Shmin) are

also principal stresses has been used Consequently, the state of the stress tensor at depth 1s

fully described by three principal stress magnitudes, including the vertical stress Sy

corresponding to the weight of overburden; SHmax, the maximum principal horizontal stress;

and Shmin, the minimum principal horizontal stress and one stress orientation, usually taken

to be the azimuth of the maximum horizontal stress (M.D Zoback, 2010).

2.3 States of in-situ stress

According to the relative magnitudes of the vertical stress and two mutually perpendicular

horizontal stresses, Anderson (1951) assumed vertical and horizontal stresses are principal

stresses and classified three possible states of stress and associated faulting styles (Figure

Figure 2.3: The three states of stress and associated types of faulting (after Engelder, 1993)

The different states of stress and associated fault styles are the normal faulting stress

regime (S, > Shmax > Shmin), the strike-slip faulting stress regime (Sumax > Sy >

Shmin) and the reverse or thrust faulting stress regime (SHmax > Shmin > Sv)

These three states of stress correspond to the three commonly seen modes of faulting in the

earth’s crust and are used throughout this thesis to describe relative stress magnitudes in the

earth’s crust

When studying stress it is often convenient to consider the reference state of stress that

may occur in the absence of tectonic forces and density heterogeneities The simplest

reference state is that of lithostatic stress found in magma:

Si =S2=S3 => Sunax 7 Shmin = Sy = Prag (2.4)

where P„a 1s the pressure within the magma The lithostatic state of stress implies that the

rocks have no long term shear strength and thus behave as a fluid (Engelder, 1993)

However, experiments suggest that most rocks support at least a small differential stress

for very long periods The lithostatic state of stress is likely to dominate in the deeper

mantle and core, but is likely to be rare in the lithosphere

The uniaxial strain reference state assumes the rocks in the sub-surface are constrained

laterally and deform elastically Hence, there is no strain in the horizontal direction and

horizontal compression is developed due to the inability of the rocks to expand laterally In

the uniaxial strain reference state, horizontal stress increases as a function of the depth of

burial, but at a slower rate than the vertical stress:

Stim ax= Samir = (=) Sy = (CC) 992 (2.5)

where v is Poisson’s ratio, varying between 0 and 0.5, g is the acceleration due to gravity

and z 1s the depth When v = 0.5 (e a fluid) the uniaxial strain reference state 1s the same

as the lithostatic reference state The uniaxial reference state is thought to approximate that

of newly deposited sediments in a sedimentary basin However, modification in the elastic

properties of the sedimentary rocks during diagenesis and creep relaxation may bring the

state of stress in sedimentary basins closer to lithostatic (Engelder, 1993)

2.4 Pore pressure and effective stress

Rocks under natural conditions generally contain pore fluid at some pressure Pore fluid

pressure has a critical influence on the physical properties of the porous solids (Terzaghi,

1943) Most physical properties of porous rocks obey a law of effective stress where the

effective stress (S’) is the difference between the total applied stress (S) and the pore fluid

pressure (P,):

S’=S—P, (2.6)

Most porous rocks obey Terzaghi’s effective stress law for rocks, which states that a

pressure of Pp in the pore fluid of a rock will cause the same reduction in peak normal

stress as caused by a reduction of the confining pressure by an amount equal to pore

pressure.

It has been demonstrated both by laboratory testing and in oil fields by the compaction of

sediments from which oil has been drained and pore pressure reduced (Teufel et al., 1991)

that rock deformation and failure occurs 1n response to the effective, not total stress

Pore fluid pressure is isotropic and the stress tensor associated with pore fluid pressure is

given by:

P 0 0P=|0 P, 0 (2.7)

Since rock failure obeys an effective stress law, the abscissa of the Mohr diagram is given by

the effective, not total stress

2.5 Frictional Limits to Stress

The stresses at which rocks in the subsurface fail provide useful theoritical limits to the

magnitudes of in-situ stresses Shear failure occurs if the ratio of shear stress to normal

stress becomes too large (Byerlee, 1978) Shear failure acts to reduce the ratio of principal

stresses to below critical levels Shear failure in the normal fault regime acts to increase Shmin,

which moves the Mohr circle below the failure envelope and away from failure (Zoback and

Healy, 1992) Shear failure in the reverse fault regime acts to decrease Spmax, which again

moves the Mohr circle below the failure envelope and away from failure

The ratio of the maximum to minimum effective stress that causes slip on pre-existing

faults that are optimally oriented with respect to the stress field was determined by Jaeger

and Cook (1979):

Sy-P 2

S—P, = f(y) = |u + (w2 + 12)? ] (2.9)

This relation provides frictional limits to the ratio of maximum to minimum effective

principal stresses provided there exists optimally oriented faults of no cohesion If the ratio

exceeds the above function of h (usually from 0.6 to 1.0), then slip occurs in order to reduce

that ratio to within frictional limits For the case of u = 0.6 the ratio of the effective

maximum principal stress to the effective minimum principal stress equals 3.12 For the case

of u = 1.0 the ratio of the effective maximum principal stress to the effective minimum

principal stress equals 5.83 This requires the value of u to either be known or assumed A

large number of in situ stress measurements 1n seismically active regions have shown stresses

to be at frictional limit (Zoback and Healy, 1984) Consequently, this ratio can be used to

constrain the ratio of the magnitudes of the maximum and minimum stress in seismically

active regions Furthermore, this ratio can be used to place upper or lower bounds on the

maximum and minimum stress magnitude respectively in seismically inactive regions Š va

and S,, are commonly known and the relationship can be used to place a limit on the more

poorly constrained value of SHmax'

Depending on the stress regime of in-situ stress, the above equation becomes:

- — =fq)= [u + (u2 + 1)1⁄2|Ý, for the normal faulting (2.10)Hmin''p

— az - 2 =f(u)= [u + (2 +1)” 2l, for the strike-slip faulting (2.11)

Hm Tp

amare P= f(y) = [w+ (2 + 1)1 2|, for the reserve faulting (2.12)The allowable values for the horizontal principal stresses in the earth’s crust are calculated

by the above equations The plot has been depth normalized by dividing the horizontal

stresses by the vertical stress, which allows data at all depths to be plotted on the one

diagram, called the stress polygon Normal, reverse and strike-slip faulting environments

have been marked out according to Anderson's (1951) theory of faulting The in-situ

stresses are expected to plot within the area bound by the frictional limits (Figure 2.4)

Figure 2.4: Frictional limits to stress based on the frictional strength of favourably oriented

fault planes for u = 0.6 and 1.0 RF : reverse fault regime; SS: strike-slip fault regime; NF:

normal fault regime (After Moos and Zoback, 1990)

2.6 Stresses and rock failure

The rock properties and the in-situ stress tensor will control rock failure Failure occurs on

planes as a function of the shear and normal stress acting on a plane, its frictional properties

The normal and shear stress acting on a plane in a two-dimensional stress field can be

calculated using:

6, = + (S, + $2) +5(S, — Sz) cos 2Ø (2.13)T= =(S, — Sz) sin 2Ø (2.14)

where on 1s the normal stress, t is the shear stress, S] 1s the maximum principal stress, S2

is the minimum principal stress and 9 is the angle between Sj] and the normal to the plane

(Jaeger and Cook, 1979) The shear and normal stress calculated from equations 2.13 and

2.14 can be simply displayed on a Mohr diagram Plotting the shear and normal stresses on a

Mohr diagram for @ varying between 0°and 90° and a given $1 and S2, forms a circle the

centre of which is at a normal stress of (S{ + S2)/2 and shear stress of zero, and the radius

of which is (Sj - S2)/2 All two-dimensional states-of-stress lie on the perimeter of this

circle (Figure 2.5)

Shear Stress30.0 -

20.0 10.0-

-0.0 r r L r i r L r L T L r r ' T ' r ' r T r L r '

0.0 10.0 20.0 30.0 40.0 50.0

Normal Stress

Figure 2.5: Two-dimensional Mohr circle

A three-dimensional Mohr diagram can also be used to represent three-dimensional stress

fields In this case the diagram contains three Mohr circles with centres at {S1 + S2)/2,0},

{(S1 + 53)2,0} and {S2 + S3)/2,0}, and radii of(S1 523⁄2,(S1 S3)/2 and (S2

-S3)/2 respectively All three-dimensional states of stress lie within the shaded area defined by

the three Mohr circles (Figure 2.6)

Shear Stress30.04

20.01

10.0¬

0.0 Ỹ u Ỹ v T T T T T T T T T T T T T T T T T T0.0 10.0 20.0 30.0 40.0 50.0

Normal Stress

Figure 2.6: Three-dimensional Mohr circle

The rock properties can also be displayed on a Mohr diagram in the form of a failure

envelope A failure envelope separates two shear/normal stress regions Normal stress/shear

stress combinations within the region below the failure envelope do not result in failure while

those above the failure envelope do result in failure

Failure envelopes can either be theoretically or empirically determined An empirical failure

envelope is based on laboratory rock tests, in which the maximum stress applied to a rock is

increased until failure occurs This results in a shear and normal stress value for failure,

which can be plotted as a point on a Mohr diagram (Figure 2.7) A series of points, which

form a failure envelope, can be determined by failing the rock under many different stress

States

Figure 2.7: Mohr diagram with a failure envelope that fits closely to laboratory rock testing

data (after Meyer, 2002)

A commonly used failure envelope 1s the Mohr-Coulomb failure criterion For pre-existing

planes of weakness with no cohesive strength, the Coulomb failure envelope is

represented by a straight line passing through zero shear stress (Figure 2.8):

T=U(On - Pp) (2.15)

Where ơn and + are, respectively, the components of normal and shear stressacting on the failure plane, P, is pore pressure, and II 1s the coefficient of internal friction.

Laboratory experiments on a wide variety of rock types have suggested that the

coefficient of internal friction, u, lies between 0.6 and 1.0 (Byerlee, 1978) This range

suggested by laboratory measurements seems to be applicable to crustal faults (Zoback

and Healy, 1984) This failure envelope represents frictional sliding on a pre-existing failure

plain with no cohesive strength 1.e for a normal stress of zero, any shear stress greater than

zero causes sliding

For intact rocks where the cohesive strength is non-zero, the Coulomb failure

criterion for frictional sliding is defined by:

t=C+u(On - Po), (2.16)

where C is the cohesive or shear strength of the rock In this case, the Coulomb failure

envelope is represented by a straight line passing through the value of non-zero shear stress

Figure 2.8: Three-dimensional Mohr diagram and Coulomb failure criterions for pre-existing

planes of weakness and for intact rock (after Reynolds, 2001)

CHAPTER 3

STRESS AND FAILURE ANALYSIS FOR WELLBORES

3.1 Introduction

When petroleum wells are drilled into a formation, the stressed solid material is removed

The rock surrounding the borehole must support the stresses previously carried by the

removed material This causes an alteration of the stress state surrounding the borehole

because the fluid pressure in the hole generally does not match the in-situ formation stresses

There will be a stress concentration in the vicinity of the wellbore The stress concentration

in an elastic material depends on the far field in-situ stresses as well as the wellbore

trajectories This can also result in wellbore failures if induced stresses around wellbores are

over the rock strength These wellbore failures may be compressive failures known as

borehole breakouts BOs and/or tensile failures as drilling-induced tensile fractures DITFs at

the wellbore wall Therefore, observations of wellbore failures have also been proposed to

determine both stress orientations and magnitudes of the in-situ stress tensor (Bell and

Gough, 1979; Zoback et al., 1985, etc.)

3.2 Stress and failure analysis for a vertical cylindrical wellbore

3.2.1 Stresses around a vertical cylindrical wellbore

Assuming the vertical stress is a principal stress and the rock behaves elastically, stresses

around a vertical cylindrical wellbore are considered 1n cylindrical coordinates Kirsch (1898)

developed a set of equations describing the stress components around a circular borehole

subjected to far in-situ stresses in a thick, homogenous, isotropic elastic medium The three

principal wellbore stresses of a vertical cylindrical wellbore of radius R are the effective

radial stress (6,,), the effective axial stress (o,,) and the effective circumferential stress (Geo)

as shown in figure 3.1 The radial stress Ø„ acts normal to the wellbore wall The axial stress

6,, acts parallel to the wellbore axis The circumferential stress ogo acts orthogonal to ø„ and

Øz; (in the horizontal direction in the plane tangential to the wellbore wall)

~ —=— 1= —

_—T^” ”“T—

Figure 3.1: Vertical cylindrical wellbore with the orientations of the circumferential stress

Øoo, the axial stress o-, and radial stress 6,,

Mathematically, the effective stresses around a vertical cylindrical wellbore of radius R are

described in terms of a cylindrical coordinate system by the following equations:

+5 (Sum ax— Suma) (1-455 + 34) cos 26 + APS (3.2)

1 R? R*\

;o= 5 (Sum ax— Suma) (1 + 25 — 3) sin 26 (3.3)

where 7;o 1s the tangential shear stress, R is the radius of the hole, r is the radial distance

difference between the mud pressure Pm in the wellbore and the pore pressure Pp in the

surrounding formation

The stress concentration around the vertical cylindrical wellbore predicted by these equation

is illustrated in figure 3.2 The bunching up of stress trajectories at the azimuth of Shin

indicates strongly amplified compressive stress In contrast, the spreading out of stress

Figure 3.2: Stress concentration around a vertical in a bi-axial stress field based on the

Kirsch equations The principal stress trajectories are parallel and perpendicular to the

wellbore wall (after Zoback, 2002)

At the wellbore wall where R = r, these stress components reduce to:

O00 = (Sum ax? Sum in — 2P,) ~~ 2(SHm ax— SHm a) cos 26 — AP (3.4)

ø„- AP (3.5)

The axial stress at the wellbore wall can be calculated using:

where U is Poisson’s ratio and Sy is the vertical stress

The above equations are rewritten in terms of the far-field principal stresses as follows:

Goo= (Sym axT Suma) — 2(SHm ax— Sumi ) COS 20 — Py — P, (3.8)

Gr= Ry — Py (3.9)

Ox = Sy — 20(SHm ax— Sum n)@S 28 — P, (3.10)

where P,, is the wellbore fluid (mud) pressure

The variation of effective principle stresses around a vertical wellbore wall is a function of

relative bearing (©) around the wellbore from the orientation of Snmax

In the case of a uniaxial stress field (Srrmax) the stress concentration should be clearer as

shown in figure 3.3 The stress at the wellbore wall subjected to only a uniaxial stress field is

reduced to the following equation:

Goo — ŠHmax 7 2 Sumax cos20 (3 1 1)

where Gee is the circumferential or hoop stress and @ is the angle around borehole wall

measured from the direction of Srmax

compression

This figure 3.3 shows the stress concentration around a circular borehole in a plate of elastic

rock subject to uniaxial compression The maximum circumferential compression around the

borehole occurs at points M and N (6 = 90°) In this uniaxial case, equation (3.11) reduces to

3Stmax at those points The minimum amount of compression occurs at points A and B (9 =

0°) where equation 3.11 reduces to -Sumax Therefore, a total circumferential stress difference

field compression, however due to the stress perturbation around the borehole points A and B

are subjected to tension

3.2.2 Failure analysis for a vertical wellbore

3.2.2.1 Breakouts (BOs) or Compressive failure analysis for a vertical wellbore

Borehole breakouts are stress-induced ovalizations of the cross-sectional shape of the

wellbore (Bell and Gough, 1979) Ovalization 1s caused by compressive shear failure on

intersecting conjugate shear planes resulting in pieces of rock spalling off the wellbore wall

This occurs when the wellbore stress concentration exceeds that required to cause

compressive failure of intact rock

Assuming that the rock surrounding the wellbore is subjected to three principal stresses If

these stresses exceed the rock strength, the rock will fail The stress state at the wellbore wall

at the azimuth of Shmin (Where the stress concentration is most compressive) is compared to

the compressive failure law defining the strength of the rock The common used compressive

failure law 1s the Mohr-Coulomb failure criterion expressed in the space of principal stresses

In general ø; 1s the circumferential stress and 6; 1s the radial stress (Moos and Zoback, 1990)

From equation (3.8) the maximum of the circumferential stress occurs at @ = + 90° and can

be rewritten in the form:

Ooomax = 3S Hmax - Shmin — Pw — Đụ, (3 12)

For the simple case where 6; iS zero (1.e 63 1S 6, and the wellbore is in balance, Pw = Pp)

and ơi is the circumferential stress, Equation 3.12 can be substituted into the Mohr-Coulomb

criterion in the space of principal stresses resulting in a simple failure criterion:

Ooomax = 3ŠHmax - Shmin - 2Pp = C, (3.13)

where C is the appropriated compressive rock strength

Compressive failure occurs when the circumferential stress exceeds the rock strength, for an

in balance wellbore (P,, = P,) The significance of Equation 3.11 to the situation where the

wellbore is not in balance (Pw +# Pp) is discussed later