Copyright by Jianguo Zhang 2005

Copyright

by

Jianguo Zhang

2005

The Dissertation Committee for Jianguo Zhang Certifies that this is the approved version of the following dissertation:

THE IMPACT OF SHALE PROPERTIES ON WELLBORE

STABILITY

Committee:

Martin E. Chenevert, Supervisor

Mukul M. Sharma, Co-Supervisor

Jon E. Olson

Sanjay Srinivasan

Lynn E. Katz


STABILITY

by

Jianguo Zhang, B.S.; M.Sc.

Dissertation

Presented to the Faculty of the Graduate School of

The University of Texas at Austin

in Partial Fulfillment

of the Requirements

for the Degree of

Doctor of Philosophy

The University of Texas at Austin

August, 2005

Dedication

To my wife Hongying Cui

To my son Yunfan Zhang

v

Acknowledgments

It is impossible to complete this dissertation without the inspiration,

encouragement, and technical and financial support from Dr. Martin E. Chenevert during

each phase of my graduate research. His friendship, experience, knowledge, patience, and

humor were essential for this work. I would also like to thank my co-supervisor, Dr.

Mukul M. Sharma, for his valuable assistance. I truly appreciate his sound advice and

careful attention to details. Thanks are also extended to other members of the supervising

committee, Dr. Jon E. Olson, Dr. Sanjay Srinivasan, and Dr. Lynn E. Katz for managing

time out of their busy schedules to read this dissertation and provide valuable comments

and suggestions.

I am indebted to my colleague Talal Al-Bazali for reviewing my manuscript. I

also would like to express my gratitude to my friends, Dr. Guizhong Chen, Dr. Mengjiao

Yu, and Mr. Xingru Wu for their friendship and help.

Appreciation is also extended to the following staff of the Department of

Petroleum and Geosystems Engineering, Dr. John Holder, Mr. Glen Baum and Mr. Bob

Savicki for laboratory support, Mr. Tony Bermudez for Machine Shop assistance. The

support and encouragement from other faculty and staff in the department are always in

my heart.

Finally, my special gratitude is to my wife Hongying and my son Yunfan.

Hongying gave me the encouragement and love to complete this journey to a Ph.D., and

Yunfan was able to understand the effort that his father had to go through to achieve this

degree.

vi


STABILITY

Publication No._____________

Jianguo Zhang, Ph.D.

The University of Texas at Austin, 2005

Supervisors: Martin E. Chenevert and Mukul M. Sharma

Most wellbore instability problems occur in shales due to their unique properties.

Shales are highly laminated, have a very low permeability, and a high cation exchange

capacity. This dissertation investigates how these properties impact wellbore stability in

shales.

The stress distribution around deviated wellbores in laminated shale/sand

sequences is analyzed to show that failure can occur either along or across bedding

planes, depending on the well trajectory. It is pointed out that both in-situ stresses and

rock strength anisotropies should be considered in order to improve wellbore stability.

A model to predict pore pressure distribution within the shale sample during a

typical compression test is developed. Due to their low permeability, pore pressures often

build up in shales during axial loading, and can greatly influence the measured shale

strength. The effect of strain rate and permeability on pore pressure build-up, and thereby

the compressive strength of shale is assessed. Experimental results show that the

vii

deviatoric strength for soft Pierre I shale decreases, while for highly compacted Arco

shale its strength increases with increasing strain rates. The reasons for these observed

phenomena are analyzed, and their impact on drilling operations is briefly discussed.

A new Gravimetric–Swelling Test (GST), for quantitatively determining water

and ion movement during shale/mud interaction is developed. Results show that water

movement is controlled not only by osmosis, but is also influenced by ionic diffusion and

capillarity.

Experimental results are also presented to show how the compressive strengths

and acoustic velocities of shales change when they are exposed to water-based fluids. By

combining these tests with the results from GST, it is clearly shown that these different

effects correlate well with the movement of water and ions into or out of the shales.

Finally, the changes in shale properties observed in this dissertation are used to

study wellbore stability in shales by taking into account 3-dimensional earth stresses

around the wellbore as well as chemical and thermal effects. Results from this study

indicate that for low permeability shales, chemical and thermal interactions between the

shale and water-based fluids play an important role.

viii

Table of Contents

List of Tables ........................................................................................................ xii

List of Figures ...................................................................................................... xiii

Chapter 1 : Problem Statement ................................................................................1 1.1 Introduction...............................................................................................1 1.2 Properties of Shales...................................................................................1 1.3 Wellbore Instability in Shales...................................................................3 1.4 Scope of the Work ..................................................................................11 Nomenclature*..............................................................................................13 References.....................................................................................................13

Chapter 2: Properties of Shale ...............................................................................20 2.1 Introduction.............................................................................................20 2.2 Pierre I Shale...........................................................................................22 2.3 Arco Shale...............................................................................................22 2.4 Moisture Content of Native Shale...........................................................23 2.5 Adsorption Isotherm Tests......................................................................24 2.6 Conclusions.............................................................................................25 Acknowledgements.......................................................................................25 References.....................................................................................................25

Chapter 3 : Wellbore Instability of Directional Wells in Laminated and Naturally Fractured Shales............................................................................................31 Abstract .........................................................................................................31 3.1 Introduction.............................................................................................32 3.2 Wellbore Instability Model in Laminated Formations............................34 3.3 Wellbore Instability Analysis and Discussion ........................................39 3.4 Naturally Fractured Systems in Shale Formations..................................45 3.5 Conclusions.............................................................................................47 Nomenclature*..............................................................................................47 Acknowledgements.......................................................................................50 References.....................................................................................................50

ix

Chapter 4 : Effect of Strain Rate on Failure Characteristics of Shales ................. 67

Abstract ...........................................................................................................................................................................................................................67

4.1 Introduction.............................................................................................68 4.2 Law of Effective Stress...........................................................................70 4.3 Pore Pressure Build-up Effects on Shale Strength..................................71 4.4 Effects of Strain Rate on Shale Strength.................................................74 4.5 Discussion and Application ....................................................................76 4.6 Conclusions.............................................................................................77 Nomenclature................................................................................................78 SI Metric Conversion Factors .......................................................................80 Acknowledgements.......................................................................................80 References.....................................................................................................81

Chapter 5 : A New Gravimetric – Swelling Test for Evaluating Water and Ion Uptake in Shales ........................................................................................................97 Abstract .........................................................................................................97 5.1 Introduction.............................................................................................99 5.2 Gravimetric-Swelling Test (GST).........................................................101 5.3 Results and Discussion .........................................................................103 5.4 Limitations of the GST .........................................................................110 5.5 Conclusions...........................................................................................110 Nomenclatures ............................................................................................110 Acknowledgements.....................................................................................111 References...................................................................................................111

Chapter 6 : The Effect of Ion Movement on Shale Swelling...............................128 Abstract .......................................................................................................128 6.1 Introduction...........................................................................................129 6.2 Mechanisms Controlling the Movement of Water and Ions.................131 6.3 Results and Discussions for Water and Ion Movement Tests...............135 6.4 Effects of Water and Ion Movement on Swelling Property of Shales..140

x

6.5 Conclusions.......................................................................................... 142 Nomenclatures ........................................................................................... 143

Acknowledgement ......................................................................................144 References...................................................................................................144

Chapter 7 : Changes in Shale Strength and Acoustic Properties with Exposure to Water-Based Fluids.....................................................................................159 Abstract .......................................................................................................159 7.1 Introduction...........................................................................................160 7.2 Experimental Testing ............................................................................162 7.3 Results and Discussion .........................................................................164 7. 4 Applications .........................................................................................171 7.5 Conclusions...........................................................................................173 Nomenclature..............................................................................................174 Acknowledgements.....................................................................................174 References...................................................................................................174

Chapter 8 : Stability of Deviated and Horizontal Wells: Mechanical, Chemical and Thermal Effects...........................................................................................199 Abstract .......................................................................................................199 8.1 Introduction...........................................................................................200 8.2 Stresses Model ......................................................................................201 8.3 Failure Criteria ......................................................................................205 8.4 Wellbore Stability Analysis ..................................................................205 8.5 Conclusions...........................................................................................212 Nomenclature..............................................................................................213 References...................................................................................................215

xi

Chapter 9: Summary and Conclusions................................................................ 229

Appendix 1: Strength of Non-laminated Rock ................................................... 232

Appendix 2: Strength of Laminated Formations .................................................234

Appendix 3: Stress State Around Wellbore .........................................................235

Appendix 4: An Example to Determine Water and Ion Movement ....................238

Appendix 5: A Model to Predict Pore Pressure Build-up during a Compressive Strength Test ...............................................................................................240 Appendix 5.1 Model Development.............................................................240 Appendix 5.2 Boundary and Initial Conditions ..........................................242

References............................................................................................................243

Vita .....................................................................................................................260

xii

List of Tables

Table 2-1– Mineralogical composition of Pierre I shale .................................................. 28 Table 2-2 – Composition of interstitial pore fluid for Pierre I shale (cations) ................. 28 Table 2-3 – Composition of interstitial pore fluid for Pierre I shale (anions) .................. 28 Table 2-4 – Exchangeable bases for Pierre I shale ........................................................... 29 Table 2-5 – Mineralogical composition of Arco shale ..................................................... 29 Table 3-1 - Input data for base case .................................................................................. 55 Table 3-2 - Information from Pedernales Field, Venezuela (after Willson et al., 1999) .. 56 Table 3-3 - Formation and fracture properties.................................................................. 56 Table 4-1 - Data used in simulation.................................................................................. 85 Table 5-1 - Pore fluid composition. ................................................................................ 115 Table 5-2 - Dehydrated and hydrated radii of cations (after Pruett, 1987)..................... 115 Table 6-1 – Comparison of ions hydrated radii .............................................................. 149 Table 7-1 - Inoic radii (after Pruett, 1987)...................................................................... 179 Table 7-2 - Strength and Young's moduli used in DRILLER......................................... 179 Table 8-1 - In-situ stress state ......................................................................................... 220 Table 8-2 - Input data (after Yu et al., 2001) .................................................................. 220

xiii

List of Figures

Figure 1-1 – Wellbore instability in shales ....................................................................... 19 Figure 2-1– Adsorption and desorption isotherms for Pierre I and Arco shales. ............. 30 Figure 3-1 – Up-, down-, and cross-dip wells. ................................................................. 57 Figure 3-2 – Failure modes for laminated rocks............................................................... 58 Figure 3-3 – Influence of operation angle on compressive strength of laminated rocks.. 59 Figure 3-4 – Well configuration. ...................................................................................... 59 Figure 3-5 – Stress state at wellbore surface. ................................................................... 60 Figure 3-6 – Calculation of principal stresses................................................................... 60 Figure 3-7 – Definition of strike and dip. ......................................................................... 61 Figure 3-8 – Wellbore stability conditions in (a) non-laminated and (b) laminated

formations for a wellbore circumference. ................................................................. 61 Figure 3-9 – Wellbore stability conditions in (a) non-laminated, and (b) laminated

formations for a wellbore circumference being along the minimum horizontal stress ( hσ ). ......................................................................................................................... 62

Figure 3-10 – Wellbore stability conditions in (a) non-laminated, and (b) laminated formations for a wellbore circumference being along the maximum horizontal stress ( Hσ ).......................................................................................................................... 62

Figure 3-11 – Effect of inclination on critical mud weights............................................. 63 Figure 3-12 – Effect of inclination on critical mud weight for wellbore perpendicular to

formation strike......................................................................................................... 63 Figure 3-13 – Effect of dip angle on critical mud weight................................................. 64 Figure 3-14 – Effects of attack angle on critical mud weight........................................... 64 Figure 3-15 – Critical mud weight in Pedernales Field. ................................................... 65 Figure 3-16 – A natural fracture around a wellbore ......................................................... 65 Figure 3-17 – Effects of crack half-length on fracture propagation pressure. .................. 66 Figure 4-1 – Effects of strain rate on deviatoric strengths for Kimmeridge Bay Shale

under undrained and drained conditions (after Swan & Cook et al., 1989)............ 86 Figure 4-2 – Effects of temperature and strain rate on strengths of Galena ore (after

Atkinson, 1976)......................................................................................................... 86 Figure 4-3 – Effects of temperature and strain rate on strengths of Anhydrite (after Muller

and Briegel, 1978)..................................................................................................... 87 Figure 4-4 – Effects of confining pressure on deviatoric strength.................................... 87 Figure 4-5 – Effects of pore pressure on deviatoric strength............................................ 88 Figure 4-6 – Time-dependent pore pressure build-up....................................................... 88 Figure 4-7 – Effect of strain rate on the pore pressure build-up....................................... 89 Figure 4-8 – Effect of permeability on pore pressure build-up. ....................................... 89 Figure 4-9 – Fracture propagation at high pore pressure.................................................. 90 Figure 4-10 – Strength test equipment.............................................................................. 91 Figure 4-11 – Pore pressure change after applying 5 000 psi confining pressure (Pierre I

shale). ........................................................................................................................ 92

xiv

Figure 4-12 – Pore pressure change after applying 5 000 psi confining pressure (Arco shale). ........................................................................................................................ 93

Figure 4-13 – Effect of strain rate on stress-strain curves for Pierre I shale. ................... 93 Figure 4-14 – Effect of strain rate on peak strengths of Pierre I shale. ............................ 94 Figure 4-15 – Effect of strain rate on pore pressure build-up of Pierre I shale. ............... 94 Figure 4-16 – Effect of strain rate on stress-strain cures for Arco shale. ......................... 95 Figure 4-17 – Effect of strain rate on peak strengths of Arco shale. ................................ 95 Figure 4-18 – Effect of strain rate on pore pressure build-up of Arco shale. ................... 96 Figure 5-1 – Schematic of equipment used to measure linear swelling of shale. ........... 116 Figure 5-2 – Photo of swelling transducer...................................................................... 117 Figure 5-3 – Swelling of Pierre I shale immersed in NaCl solutions. ............................ 118 Figure 5-4 – Time-dependent water and ion movement for Pierre I shale immersed into

0.85 aw NaCl solution............................................................................................. 118 Figure 5-5 – Swelling of Pierre I shale immersed in simulated pore fluid. .................... 119 Figure 5-6 – Corrected swelling of Pierre I shale immersed in NaCl solutions. ............ 119 Figure 5-7 – Corrected time-dependent water and ion movement Pierre I shale immersed

in 0.85 aw NaCl solution. ....................................................................................... 120 Figure 5-8 – Influence of NaCl concentration on water/ion movement for Pierre I shale.

................................................................................................................................. 120 Figure 5-9 – Swelling of Pierre I shale immersed in CaCl2 solutions. ........................... 121 Figure 5-10 – Corrected swelling of Pierre I shale immersed in CaCl2 solutions. ......... 121 Figure 5-11 – Swelling of Pierre I shale immersed in KCl solutions. ............................ 122 Figure 5-12 – Swelling of Pierre I shale immersed in KCOOH solutions...................... 122 Figure 5-13 – Corrected swelling of Pierre I shale immersed in KCl solutions. ............ 123 Figure 5-14 – Corrected swelling for Pierre I shale immersed in KCOOH solutions. ... 123 Figure 5-15 – Influence of CaCl2 and KCl concentration on water/ion movement for

Pierre I shale. .......................................................................................................... 124 Figure 5-16 – Water activities of CaCl2, NaCl, and KCl solutions at room temperature.

................................................................................................................................. 124 Figure 5-17 – Effects of water activity on water/ions movement for Pierre I shale. ...... 125 Figure 5-18 – Swelling of Arco shale immersed in NaCl solutions. .............................. 125 Figure 5-19 – Swelling of Arco shale immersed in CaCl2 solutions. ............................. 126 Figure 5-20 – Effect of NaCl concentration on water/ion movement for Arco shale..... 126 Figure 5-21 – Effects CaCl2 concentration on water/ion movement for Arco shale. ..... 127 Figure 6-1 – Osmosis and ion diffusion.......................................................................... 150 Figure 6-2 – Brine water capillary imbibitions............................................................... 150 Figure 6-3 – Weight changes of Pierre I shale during desiccator-immersion-desiccator

test (NaCl)............................................................................................................... 151 Figure 6-4 – Weight changes of Pierre I shale during desiccator-immersion-desiccator

test (KCl)................................................................................................................. 151 Figure 6-5 – Weight changes of Pierre I shale during desiccator-immersion-desiccator

test (CaCl2).............................................................................................................. 152 Figure 6-6 – Combined adsorption isotherms of Pierre I shale. ..................................... 152 Figure 6-7 – Weight changes of Arco shale during desiccator-immersion-desiccator test

(NaCl). .................................................................................................................... 153

xv

Figure 6-8 – Weight changes of Arco shale during desiccator-immersion-desiccator test (KCl). ...................................................................................................................... 153

Figure 6-9 – Weight changes of Arco shale during desiccator-immersion-desiccator test (CaCl2). ................................................................................................................... 154

Figure 6-10 – Water and ion movement for Pierre I directly immersed in 0.85 aw CaCl2, 0.85 aw NaCl and 0.85 aw KCl solutions............................................................... 154

Figure 6-11 – Water and ion movement for Arco shale directly immersed in 0.85 aw NaCl and 0.85 aw CaCl2 solutions.......................................................................... 155

Figure 6-12 – Effects of water activity on water movement of Pierre I shale. ............... 155 Figure 6-13 – Swelling of Pierre I shale placed in controlled 85% humidity desiccator.

................................................................................................................................. 156 Figure 6-14 – Swelling properties of Pierre I shale immersed in 0.85 aw KCl solution.156 Figure 6-15 – Comparison of shale swelling when sample is immersed in a 0.85 aw KCl

solution versus placed in a 0.85 aw atmosphere (Pierre I shale). ............................ 157 Figure 6-16 – Correlation of water/ion movement with the swelling of Pierre I shale

exposed to NaCl solutions. ..................................................................................... 157 Figure 6-17 – Correlation of water/ion movement with the swelling of Pierre I shale

exposed to CaCl2 solutions. .................................................................................... 158 Figure 6-18 – Correlation of water/ion movement with the swelling of Pierre I shale

exposed to KCl solutions. ....................................................................................... 158 Figure 7-1 – Influence of pore pressure increase and formation weakening on wellbore

instability................................................................................................................. 180 Figure 7-2 – Schematic of equipment setup used to measure acoustic velocity............. 180 Figure 7-3 – Equipment for measuring acoustic velocity of shale. ................................ 181 Figure 7-4 – Transducer calibration and face-to-face time determination. .................... 181 Figure 7-5 – Stress-strain curve for Pierre I shale exposure to 19 wt% NaCl solution. . 182 Figure 7-6 – Stress-strain curve for Arco shale exposure to 19 wt% NaCl solution. ..... 182 Figure 7-7 – Effect of NaCl concentration on acoustic velocity of Pierre I shale. ......... 183 Figure 7-8 – Effect of CaCl2 concentration on acoustic velocity of Pierre I shale. ........ 183 Figure 7-9 – Effect KCl concentration on acoustic velocity of Pierre I shale. ............... 184 Figure 7-10 – Effect of different solution on acoustic velocity of Pierre I shale............ 184 Figure 7-11 – Effect of salt concentration on acoustic velocity change for Pierre I shale.

................................................................................................................................. 185 Figure 7-12 – Effects of water movement on acoustic velocity change of Pierre I shale.

................................................................................................................................. 185 Figure 7-13 – Effect of ion movement on acoustic velocity for Pierre I shale............... 186 Figure 7-14 – Effect of NaCl solution on stress-strain curves for Pierre I shale. ........... 186 Figure 7-15 – Effect of CaCl2 solution on stress-strain curves for Pierre I shale. .......... 187 Figure 7-16 – Effect of KCl solution on stress-strain curves for Pierre I shale.............. 187 Figure 7-17 – Effects of different solution on Young’s moduli of Pierre I shale........... 188 Figure 7-18 – Effect of water activity on deviatoric strength for Pierre I shale. ............ 188 Figure 7-19 – Effects of water movement on deviatoric strength of Pierre I shale. ....... 189 Figure 7-20 – Effect of ion movement on deviatoric strength for Pierre I shale. ........... 189 Figure 7-21 – Relationship between acoustic velocity and compressive strength for Pierre

I shale immersed in various solutions of NaCl, KCl, and CaCl2. ........................... 190

xvi

Figure 7-22 – Effect of NaCl concentration on acoustic velocity for Arco shale........... 190 Figure 7-23 – Effect of CaCl2 concentration on acoustic velocity for Arco shale.......... 191

Figure 7-24 – Effects of KCl concentration on acoustic velocity for Arco shale........... 191 Figure 7-25 – Effect of different solutions (aw= 0.85) on acoustic velocity of Arco shale.

................................................................................................................................. 192 Figure 7-26 – Effect of salt concentration on acoustic velocity for Arco shale. ............ 192 Figure 7-27 – Effect of water movement on acoustic velocity for Arco shale. .............. 193 Figure 7-28 – Effect of ion movement on acoustic velocity for Arco shale................... 193 Figure 7-29 – Effect of NaCl solution on stress-strain curves for Arco shale................ 194 Figure 7-30 – Effect of CaCl2 solution on stress-strain curves for Arco shale............... 194 Figure 7-31 – Effect of KCl solution on stress-strain curves for Arco shale.................. 195 Figure 7-32 – Effect of different solutions on Young’s moduli (Arco shale). ............... 195 Figure 7-33 – Effect of salt solution on deviatoric strength of Arco shale..................... 196 Figure 7-34 – Effect of water movement on deviatoric strength of Arco shale. ............ 196 Figure 7-35 – Effect of ion movement on deviatoric strength of Arco shale. ................ 197 Figure 7-36 – Relationship between acoustic velocity and compressive strength for Arco

shale immersed in various solutions of NaCl, KCl, and CaCl2. ............................. 197 Figure 7-37 – Effects of salt solution on mud weight window for Pierre I shale. .......... 198 Figure 7-38 – Influence of salt solution on mud weight window for Arco shale. .......... 198 Figure 8-1 – A typical directional well trajectory........................................................... 221 Figure 8-2 – Effect of inclination and azimuth on MWW under normal faulting stress

regime. .................................................................................................................... 222 Figure 8-3 – Effect of inclination and azimuth on MWW under thrust faulting stress

regime. .................................................................................................................... 222 Figure 8-4 – Effect of well inclination and azimuth on MWW under strike-slip faulting

stress regime............................................................................................................ 223 Figure 8-5 – Effect of cohesion on MWW. .................................................................... 223 Figure 8-6 – Effect of frictional angle on MWW. .......................................................... 224 Figure 8-7 – Effect of Poissons ratio on MWW. ............................................................ 224 Figure 8-8 – Effect of shale permeability on MWW. ..................................................... 225 Figure 8-9 – Effect of pore pressure on MWW. ............................................................. 225 Figure 8-10 - Effect of shale membrane efficiency on MWW ( sdf CC < ).................... 226 Figure 8-11 - Effect of ion diffusion constant on MWW ( sdf CC < ). ........................... 226 Figure 8-12 - Effect of mud temperature on MWW....................................................... 227 Figure 8-13 - Effect of geothermal gradient on MWW. ................................................. 227 Figure 8-14 - Effect of matrix volumetric-thermal-expansion-constants on MWW. ..... 228

1

Chapter 1 : Problem Statement

1.1 INTRODUCTION

Wellbore instability is one of the most serious problems in the oil industry. It can

lead to delays in the drilling process, increases in drilling cost, and in some cases even to

abandonment of the well (Bradley, 1979 a, b; Zamora et al., 2000). It is estimated that

this problem costs the oil industry one billion U.S. dollars a year (Chen et al., 2002).

Shales make up about three fourths of drilled formation and over 90% of the

wellbore instability problems that occur in shales (Steiger and Leung, 1992). Even though

shale stability has been studied for several decades, it still a serious problem in not only

the petroleum industry but also in the mining and construction industries (Chenevert,

1970; Carminati et al., 1997; Chenevert and Pernot, 1998). Before any measures are

taken to address this problem, it is crucial that potentially problematic formations and the

mechanisms of wellbore instability be identified. Once the mechanisms are understood,

well planning, drilling fluid design, and drilling operation strategies can be implemented

to ensure wellbore stability.

Due to the unique mechanical and physicochemical properties of shales, it is well-

recognized that wellbore instability in shales is a complicated problem.

1.2 PROPERTIES OF SHALES

Shales are laminated, clay-bearing sedimentary rocks with low permeability. They

typically have a finely laminated structure and are normally inter-bedded with sandstone

or limestone. The thickness of bedding layers can range from a few millimeters to

hundreds of meters (Davidson, 1999). These bedding layers are classified as transversely

isotropic, i.e., the material properties along the bedding planes are different from the

plane perpendicular to the bedding.

2

It is the clay minerals that give shales their unique physiochemical properties

compared to other sedimentary rocks (Sharma, 2004). At the atomic level, clays are

composed of an octahedral aluminum layer with one to two tetrahedral silica layers. The

various combinations of octahedral and tetrahedral layers form different clay minerals.

The unique structures of the various clay minerals result from the substitution of

ions within the tetrahedral and octahedral sheets. For example, the aluminum atoms in the

simple clay structure may be replaced by lower valence cations, such as Mg2+ or K+. This

substitution leads to the presence of excess negative charges on the crystal surface. These

excess negative charges must be countered by cations from the fluid so as to remain

electrically neutral. The cation exchange capacity (CEC) is a measure of these excessive

negative charges. The presence of charged surfaces in clay minerals results in a complex

electrochemical behavior that is largely responsible for the wellbore stability problems

exhibited by shales. For example, the movement of water/ions during shale/mud

interaction is influenced by the CEC. However, very little information on this subject has

been available until now.

The presence of clay in rocks also affects the acoustic properties of shales. Minear

(1980) found that elastic moduli and acoustic velocity decrease with increasing clay

content. Using experimental results, Tosaya and Nur (1982) derived the following

empirical equation to account for the effects of clay content on compressive velocity,

C4.26.88.5Vp −φ−= (1-1)

Note that the definition of all symbols is given in the Nomenclature at the end of

each chapter.

Han et al. (1985) found that large amounts of clay in a rock can reduce its

compressive velocity by 31% and the shear wave velocity by 38% compared to similar

3

rocks without clay.

Finally, shales consist predominantly of mud-sized (less than 0.006 mm) particles

of silt and clay, therefore, their permeability is very low. For example, the permeability of

Wellington shale is 0.3×10-6 md when measured under 8000 psi effective stress

(Chenevert and Sharma, 1993). Due to the shale’s low permeability, pore pressure cannot

be dissipated easily during the interaction between the shale and the mud. This pore

pressure elevation, that is called an “undrained condition” by Detournay and Cheng

(1988), can lead to reduced effective stress and rock failure (Chenevert, and Sharma,

1993; Chen and Ewy, 2002). During our compressive strength and acoustic testing

(Chapter 7), this undrained phenomenon influences test procedures and strength results.

In summary, three notable characteristics of shales must be included in a wellbore

stability study: 1) lamination; 2) low permeability; and 3) CEC.

1.3 WELLBORE INSTABILITY IN SHALES

The mechanisms of wellbore instability in shales can be grouped into three

categories (Bradley, 1979 a, b):

1) Fractures caused by tensile failure due to excessive wellbore pressure.

This causes lost circulation and often results in well control problems

experienced as a kick or an underground blowout (Figure 1-1 - a);

2) Hole size reductions due to swelling of shales (Figure 1-1 - b), which

results in repeat reaming, or in extreme conditions, stuck drill pipe; and

3) Hole enlargements resulting from compressive failure due to excessively

low wellbore pressure, which causes fill on trips, poor directional control,

and poor cementing (Figure 1-1 - b).

Numerous factors cause the wellbore to become unstable after the borehole is

4

drilled, such as in-situ stress state conditions, well types (vertical or directional), well

trajectories (inclination and azimuth), rock properties (strength, Poisson ratio, modulus

of elasticity, permeability), shale/fluid interactions and thermal effects. Generally

speaking, however, these factors can be classified as mechanical, chemical, and thermal

effects.

1.3.1 Mechanical Effects

In mechanical terms, failure occurs when the local stress exceeds the rock

strength based on a specific failure criterion. Therefore, three aspects of wellbore

instability in shales must be considered: 1) local stress conditions, 2) formation strength,

and 3) a proper strength failure criterion.

Formations located at a given depth, are under in-situ stresses, that include overburden stress, vσ ; two horizontal stresses, Hσ and hσ ; and pore pressure, pP . Before

a well is drilled, an equilibrium stress state exists. During the drilling process, the

wellbore rock is replaced by drilling fluids. As a result, the stress concentration around

the wellbore is changed, and wellbore failure (both compressive and tensile) occurs if the

rock is not strong enough (Bradley, 1979a, b).

By modeling the formation as an isotropic linear elastic solid in a condition of

plane strain along the axis of borehole, Bradley (1970a, b) calculated the local stress

around the wellbore by using Fairhurst’s work (Fairhurst, 1968). He applied the concept

of stress cloud with the help of the Drucker-Prager failure criterion to evaluate rock shear

failure. Many studies, based on Bradley’s pioneering work, can be found in the literature

(Aadnoy and Chenevert, 1987; Fuh et al., 1988; McLean and Addis, 1990; Zhou et al.,

1996).

By introducing non-linear elastic relationships, Santarelli (1986) obtained a better

fit between the stress and the strain. He suggested that a maximum stress level could

5

occur within the near wellbore formation. This high stress level leads to wellbore failure

not always at the wellbore wall, as predicted by the linear elasticity (Bradley, 1979 a, b),

but at some distance inside the shale.

During the drilling process, due to the extremely low permeability of shales, the

pore fluid cannot flow freely, which causes the redistribution of stresses (Detournay and

Cheng, 1988). This pore pressure storage effect is called “undrained situation”, which can

cause wellbore instability (Chen and Ewy, 2002).

Yew and Liu (1992) introduced poroelasticity theory into the wellbore instability

model in order to study the effects of fluid flow on wellbore stability because this flow

induces additional normal stresses. These additional stresses can lead to borehole failure

in some cases. Recently, Chen et al. (2003) developed a model that included poroelastic,

chemical, and thermal effects.

Besides the local stresses, rock strength needs to be determined in order to

develop a wellbore instability model. As discussed previously, the lamination of shales

contributes to the material anisotropy of shales. This anisotropy modifies the constitutive

equation of rock formations.

Chenevert and Gatlin (1964) found that rock compressive strength was reduced

by as much as 40% when the test sample was oriented at 20o ~30 o to the bedding planes

and tensile strength was lowest when failure occurred along bedding planes.

In most wellbore stability models, the rock is modeled as an isotropic material

(Bradley, 1979a, b; Yew and Liu, 1992). Aadnoy and Chenevert’s (1987) simulator was a

major advance in modeling the wellbore stability in laminated formations. However, two

assumptions limit their simulator’s application, 1) horizontal bedding layers, and 2) zero

shear stress acting on the wellbore wall.

When drilling through laminated shales, bedding plane splitting causes more

6

wellbore instability problems (Okland and Cook, 1998). Numerous wellbore instability

problems have been reported when drilling through laminated and fractured formations

(Last et al., 1995; Okland et al., 1998; Beacom et al., 2001; Edwards et al., 2003).

Okland and Cook (1998) pointed out in their paper on page 6 that “It has not yet been

possible to make a good predictive model for this type of failure.”

In addition, many shales are naturally fractured. These fractures also involve a

different mechanism for shale instability and require different measures to tackle

wellbore instability problems in naturally fractured formations. It would seem, therefore,

that further investigations are needed in order to maintain wellbore stability in laminated

and naturally fractured shales, which is one of the main objectives of this dissertation.

Generally, there are two ways to obtain the compressive strength of shales:

laboratory measurement and well log interpretation (Chenevert, 1964; Tixier et al., 1975;

Horsrud, 2001). Although experimental measuring of shale strength is expensive and

time consuming, it is more accurate. A key factor in measuring the compressive strength

of shales is the strain rate used during testing because this strain rate influences the test

results greatly due to the low shale permeability. This low permeability makes it very

difficult to control the pore pressure during experiments which are designed to measure

the mechanical properties under simulated downhole conditions.

Chiu et al. (1983) discussed an appropriate technique for triaxial testing of

saturated soft shale. They defined a critical strain rate below which the pore fluid can

dissipate completely with no pore pressure build-up. If the strain rate is higher than the

critical strain rate, negative pore pressure (caused by dilatancy) is generated, which

causes the pore pressure to decrease and thus the compressive strength to increase. Cook

et al. (1990) discussed the influence of the strain rate on shale strength. They defined an

upper rate below which the strength value is independent of the strain rate because there

7

is no pore pressure build-up. They also claimed that shale deformation and failure were

governed by effective stress at low strain rates, whereas the law of effective stress did

not hold true at high strain rates.

All the above studies are beneficial for understanding the failure characteristics of

shale. However, the dispute on the validity of the law of effective stress remains ongoing.

In this dissertation, the effects of strain rates on the failure characteristics of shale are

presented and the validity of the effective stress law is discussed.

Indeed, experimentally measuring strength is more accurate than well log

interpretation, however, it is impossible to obtain a complete formation strength profile

without performing many tests, which is required for complete wellbore stability

evaluation. Fortunately, well log information, which is considered to be continuous, can

be used to predict the mechanical properties of shale, including its strength. For example,

the elastic constants and uniaxial compressive strength (UCS) can be estimated by using

the following relationships (Tixier et al., 1975; Fjaer et al., 1992; Goodman et al., 1997)

( )( )2ps

2ps

V/V1

V/V5.0

−

−=ν

(1-2)

2sbVG ρ= (1-3)

( )( )C78.012111V103.3UCS

24

p220 +ν−⎟

⎠⎞

⎜⎝⎛

ν−ν+

ρ×= −

(1-4)

Relatively little has been published on acoustic measurements of the mechanical

properties of shale (Davidson, 1999). A similar problem as in the strength test is the

difficulty in controlling the pore pressure during the acoustic test under simulated

downhole conditions due to the extremely low permeability of shale. Uncertainty in

determining the pore pressure has lead to uncertainty concerning the applicability of the

8

elastic properties determined from such measurements in predicting downhole behavior.

In order to study the effects of a single factor, such as salt type, salt concentration, and

water activity on the sonic velocity of different shales, we performed the acoustic test

under atmospheric pressure and room temperature.

After the local stress and rock strength have been determined, whether the

formation will fail or not depends on the strength criterion used. Several compressive

strength criteria are available for studying wellbore instability (Bradley, 1979a, b; Fuh et

al., 1988; Woodland, 1990; Mclean, 1990; Zhou et al., 1996).

In his pioneering work, Bradley (1979a,b) used the Drucker-Prager failure

criterion to evaluate shear failure. Fuh et al. (1988) suggested an extended von Mises

criterion, or a modified Drucker-Prager failure criterion. Zhou et al. (1996) employed a

truncated Desai’s yield function, another criterion that is similar to the Drucker-Prager

failure criterion. Ewy (1999) introduced the modified Lade failure criterion to evaluate

wellbore stability status. In this dissertation, we use the Mohr-Coulomb failure criterion.

It has simplicity and practicality (McLean, 1990).

Once the local stresses and rock strength have been determined, for a preserved

shale, wellbore stability can be evaluated by use of the selected failure criteria. However,

should the shale be contacted by a fluid, the stress and strength might be altered by the

chemical interaction between the drilling fluid and shale. Therefore, chemical effects

must be considered in addition to the above mentioned mechanical effects.

1.3.2 Chemical Effects

One of the main causes of shale instability is believed to be the unfavorable

interactions between the shale and drilling mud (Chenevert, 1970; Bol et al., 1992; van

Oort, 2003). Although such interactions which include chemical, physical, hydraulic,

mechanical, thermal, and electrical phenomena, are very complicated (Maury et al., 1987;

9

Mody et al., 1993; van Oort, 2003), their primary cause is related to the movement of

water/ions into or out of shale. This movement causes alterations in mechanical and

physiochemical properties of the shale, and can lead to wellbore instability problems.

The adsorption of water leads to an increase in pore pressure near the wellbore

formation. This excessive pore pressure is difficult to dissipate due to the low

permeability of shale, which causes a decrease in the effective stress because the effective

stress is equal to the total stress minus the pore pressure. The movement of water from

the drilling fluid into the shale also leads to an expansion (swelling) of clay layers and

consequently a decrease in the interlayer-bonding and shale strength. The decrease in

shale strength resulting from relatively minor increases in water content has been well

documented in the literature (Chenevert, 1970; Hale et al., 1992). Both an increase in

pore pressure and a decrease in strength cause shale to deteriorate.

Many mechanisms, including convection, diffusion, osmosis, and capillary

phenomena are involved in the movement of water/ions (Mody et al., 1993; Lomba et al.,

2000; Simpson and Dearing, 2002). The hydraulic pressure difference between drilling

fluids and shale causes a bulk flow of drilling fluid and is governed by the Darcy

equation. However, this flow is generally considered to be quite low as the result of both

the relatively low pressure differential that typically exists for most drilling operations,

and the extremely low permeability of shales which is in the range from 10-5 to 10-12

darcy (Bol et al., 1992).

Low and Anderson (1958) suggested osmosis as a mechanism for the movement

of water, based on the principle that shale itself acts as a semi-permeable membrane, that

allows the movement of water but restricts the movement of ions. Fritz et al. (1983,

1986) supported the theory of osmosis as the mechanism controlling the movement of

water/ions, but they believed that clays are not “ideal” membranes, and that the ideality

10

of a clay membrane is a function of the CEC, porosity, and concentration of pore fluids.

Mody and Hale (1993) suggested that the membrane efficiency is also a function of

confining pressures. However, Ballard et al. (1992) and Bol et al. (1992) concluded that

osmosis was not observed in their lab experiments.

From the above review, it is seen that the movement of water/ions is critical when

studying wellbore instability in shales. It is of great importance, therefore, to

quantitatively measure the movement of water/ions in the interaction of shale/mud.

Currently, however, there is no simple way to quantitatively measure this movement. In

this dissertation, a new Gravimetric-Swelling Test (GST) is presented for determining the

movement of water/ions into or out of shale.

In addition to chemical effects, thermal effects influence the stress distributions

around the wellbore and the shale’s mechanical properties.

1.3.3 Thermal Effects

Maury and Guenot (1993) found that thermal effects also affected borehole

stability. Later on, Maury (1994) pointed out that thermal effects must always be

considered in stress analysis. He believed that cooling the wellbore was equivalent to an

increase in the mud weight in terms of tangential stresses at the wellbore wall (Maury and

Idelovici, 1995). Tang and Luo (1998) also pointed out that the stress distribution near

the wellbore is altered by thermal stresses driven by a cooler drilling fluid.

Li et al. (1998) presented a thermoporoelastic analysis of the wellbore instability

for directional wells. They discussed the wellbore heating and cooling effects on the

potential of borehole shear and spalling failure. Chen et al. (2003) studied the thermal

effects on wellbore stability. They found that formation cooling allows for a lowering of

the mud weight required for preventing wellbore compressive failure. Besides

compressive failure, thermal effects on tensile failure should also be considered

11

(Gonzalez et al., 2004). Gonazalez et al. (2004) found that cooling the formation is

detrimental to preventing tensile wellbore failure and thus circulation control can be

lost. Therefore, thermal cooling of the wellbore should be used cautiously especially

when drilling through natural fractured formations.

Recently, Yu et al. (2003) developed a three-dimensional wellbore stability model

by coupling the chemical and thermal effects into the mechanical stress state distribution

around the wellbore.

1.4 SCOPE OF THE WORK

From theoretical to experimental aspects, a comprehensive study, including

mechanical, and chemical effects on wellbore stability in shale have been considered in

this dissertation.

As discussed previously, wellbore instability in shales is related to the unique

properties of shales, including low permeability, lamination, natural fractures, and CEC.

Therefore, these notable properties should be included in wellbore stability studies. To

keep this dissertation focused squarely on the wellbore instability of shale, the chapters

have been based on the unique properties of shale in the following way.

The properties of shale used in our test are discussed in Chapter 2. Outcrop

(surface) as well as subsurface shales is included in this study. Their mineralogical

compositions, moisture content, CEC, adsorption, and desorption properties are

presented.

Chapter 3, “Wellbore Instability of Directional Wells in Laminated and Naturally

Fractured Shale” presents a simulator used to model wellbore instability in laminated

shale. The stress distributions around deviated wellbores in laminated shale/sand

sequences is analyzed to show that failure can occur either along or across the bedding

planes depending on the well trajectory. The effects of well inclination and well azimuth

12

orientation relative to the strike and dip of the bedding plane on wellbore instability are

analyzed. Critical mud weight windows are calculated for different well orientations

relative to the bedding planes.

In addition to strength anisotropy due to laminations, the measurement of shale

strength in the laboratory is included. A proper technique to measure shale strength is

discussed in Chapter 4. The effects of strain rate on compressive strength are presented

and the failure characteristics for shale are briefly assessed.

A new Gravimetric-Swelling Test (GST) that allows the quantitative

determination of water/ion movement during shale/mud interaction is presented in

Chapter 5. Experimental protocols and equations are presented that describe how such

measurements can be conducted and interpreted.

Based on the GST, the mechanisms causing the movement of water/ions are

analyzed and presented in Chapter 6. The effects of chemical osmosis, diffusive osmosis,

and capillarity on the movement of water/ions when shales interact with water-based

muds are analyzed. In addition, the effects of such movement on the swelling properties

of shales are also discussed.

Chapter 7 presents the acoustic and strength properties of shale after exposure to

ionic solutions. Experimental results show how the compressive strengths and acoustic

velocities of different types of shale change when they are exposed to water-based fluids.

By combining these tests with the GST, it is clearly shown that strength alteration and

acoustic velocity of shale correlate well with the movement of water and ions into or out

of the shale. The influence of salt type and salt concentration on the strength and sonic

velocity of two shales are investigated.

A comprehensive study including mechanical, chemical, and thermal effects on

the wellbore stability of directional wells is presented in Chapter 8. The effects of

13

borehole configuration (e.g. inclination and azimuth), rock properties (e.g. cohesion,

friction angle, Poisson’s ratio, membrane efficiency and permeability), temperature and

drilling fluid properties (e.g. mud density and chemical concentrations) on wellbore

stability in shale formations have been investigated.

Chapter 9 concludes this dissertation with a brief summary of conclusions.

NOMENCLATURE* C Clay content in fraction

G Shear modulus [=] m/L-t2

pV Compressive sonic wave velocity [=] L/t

sV Shear sonic wave velocity [=] L/t

UCS Uniaxial compressive strength [=] m/L-t2

ν Poisson ratio, dimensionless

φ Porosity in fraction

* [=] means has units of, L is a length unit, m mass, t time, and T temperature

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15

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16

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19

Figure 1-1 – Wellbore instability in shales

20

Chapter 2: Properties of Shale

2.1 INTRODUCTION

It is believed that unfavorable interactions between shales and drilling fluids are

the primary cause for wellbore instability. This interaction causes physiochemical and

mechanical property alterations, and can lead to wellbore instability problems. An

analysis of the intrinsic physical and chemical properties of shales can help us understand

the problems and lead to better formulation of drilling fluids (Osisanya, 1991; Breeden

and Shipman, 2004). In many cases, the solutions to wellbore instability problems

developed on the basis of laboratory tests.

Many researchers recognized the importance of laboratory testing of shale and

have come to the conclusion that successful drilling of troublesome shale requires

descriptive and analytical testing of the shale (Darley 1969; Chenevert, 1970a; Chenevert

and Pernot 1998; Chiu et al., 1983; Ballard et al., 1992; Bol et al., 1992; Bostrom et al.,

1998; Breeden and Shipman, 2004; Carminati et al., 2001; Ewy and Stankovich 2002;

Osisanya and Chenevert 1987).

Shales studied by various authors for wellbore stability can be divided into two

categories: surface (outcrop) and subsurface shales. Although outcrop shale is readily

available, this shale does not represent downhole shale. Therefore, results obtained from

outcrop shale should not be directly used to solve problems of downhole shale (Davidson,

1999). On the other hand, many of the problems associated with the subsurface samples

originate from cutting, retrieval, and handling of the core. During the coring operation,

the core experiences significant levels of compression and torque, which can alter its

properties. The physicochemical and mechanical properties of the subsurface shale are

further altered when the core is taken to the surface because of the alterations in stress

21

state and temperature.

During the process of sample storage and preparation, both outcrop and

subsurface samples may encounter surface desaturation to some degree. This desaturation

could lead to irreversible changes in the physiochemical and mechanical properties of

shale (Schmitt et al., 1994; Chenevert and Amanullah, 1997). Although the subsurface

shale may have been fully saturated in-situ, the coring, sampling, and storage can cause

loss of moisture (Chiu et al., 1981).

During laboratory testing, the most important and difficult issue is how to

simulate in-situ stress and temperature conditions. For outcrop shale, its mechanical

properties may be altered when loads higher than its original state are applied. On the

other hand, it is very difficult, if it is not impossible, to reproduce the native stress and

temperature conditions for subsurface shales. Even if the in-situ stress and temperature

can be accurately simulated, the properties of shale cannot be returned to its native state

because of the irreversible alterations caused by coring and sampling. Therefore, when

testing shale, much attention should be given to such items.

In our tests, outcrop as well as subsurface shale was used to evaluate water/ion

movement, acoustic velocity, and strength alterations when exposed to ionic solutions.

Water/ions movement and acoustic velocity were measured under ambient conditions,

and their compressive strength was measured at 5000 psi confining pressure. In this way,

the influences of a single factor on the properties of the shale were studied while keeping

other factors constant.

Keeping the purpose of specific tests in consideration, different sizes of samples

were prepared; 0.5 inch by 0.75 inch by 1 inch for the gravimetric-swelling test (GST),

0.75 inch by 0.75 inch by 1.5 inch for the acoustic and strength tests, and 0.5 inch cubic

for the adsorption and desorption tests. All cut samples were carefully preserved using

22

established laboratory techniques developed in our laboratory that limit alteration by

atmospheric humidity (Chenevert and Amanullah, 1997).

2.2 PIERRE I SHALE

Pierre I shale is an outcrop shale. Its mineralogical and internal pore fluid

composition, and cation exchange capacity are presented below.

2.2.1 Mineralogical composition

X-Ray Diffraction (XRD) was used to determine the crystalline structure and

composition of the shale minerals by determining the angles at which the x-Ray beam is

diffracted (Breeden and Shipman, 2004). The wavelength for an x-Ray is of the range of

0.01 to 100 Ǻ (1 Ǻ = 10-10m). Because the spacing of atomic planes in crystalline

materials is in the order of about 1 Ǻ, this makes x-Rays a useful tool in analyzing

crystalline structure and mineralogical composition of shale (Osisanya, 1991). In this

study, the XRD was performed by OGS Laboratory Inc. (Houston, TX). The results for

mineralogical composition of Pierre I are shown in Table 2-1.

2.2.2 Composition of the interstitial pore fluid

The cation and anion compositions of interstitial pore fluid of Pierre I shale are

presented in Table 2-2 and Table 2-3 respectively.

2.2.3 Cation exchange capacity (CEC) of Pierre I shale As discussed in Chapter 1, the ability of clays to exchange cations with the fluids

in the pore space is an interesting clay characteristic (Lake, 1989). The values of CEC for

Pierre I shale are shown in Table 2-2~ 2-4.

2.3 ARCO SHALE

Arco shale was cored in a well located in Northern USA at about 15,000 feet (see

23

Table 2-5 for its mineralogical composition). The composition of the pore fluid, and

CEC of Arco shale are not available.

2.4 MOISTURE CONTENT OF NATIVE SHALE

Three cut shale samples were used to determine the preserved water content ( pwC ) of a particular set of samples that had been cut from the same core horizon. The

following steps were used to obtain the original water content. The samples having been

stored in a light oil, were removed from the storage can and washed using a non-toxic

commercial form of hexane to remove oil from its surface. These samples were then weighed to obtain their “preserved” weights ( pW ). Finally the samples were placed in an

oven and heated to 200oF for 24 hours to obtain their weights after drying ( pdW ). It is

believed that drying the shales at the modest temperature of 200oF liberates the “free”

water and not the water “bound” to the surface of the clays. From the above two

measurements, the preserved water content (wt %) of the sample was calculated using the

equation.

%100W

WWC

pd

pdppw ×

−= (2-1)

As an example, values for one Pierre I shale were, pW = 4.836 g and pdW = 4.388

g, and the wt % water was calculated to be:

% 21.10%100388.4

388.4836.4Cpw =×−

=

The same calculation was used to obtain the native moisture content of the other

two samples. The average value among these three samples was considered to be the

native moisture content of that shale. It should be mentioned that this average value is

used in all subsequent calculations of water/ions movement for the various shale-fluid

experiments performed on that zone of Pierre I shale. Similarly it was found that Arco

Shale had an original moisture content of 3.3 wt %.

24

2.5 ADSORPTION ISOTHERM TESTS

Water activity of shale is an important parameter when dealing with wellbore

instability problems because it is a key factor in controlling the movement of water and

ions into and/or out of shale (Fonseca et al., 1998). The water activities of Pierre I and

Arco shales were determined using adsorption isotherm tests.

Richard and Peter (1960) used saturated salt solutions to control the humidity of

biological specimens in their research. Chenevert (1970b) introduced this method to

determine the water activity of shale. Different saturated salt solutions are normally used

to control the relative humidity in the determination of isotherms of shale. The advantage

of saturated solutions is that a constant relative humidity can be easily maintained as long

as salt crystals coexist with its solution. Although the water activity of subsurface shale is

influenced by stress and temperature (Fonseca, 1998), adsorption isotherms can be used

to determine the reactive potential of shale (Osisanya, 1991).

In our studies, pieces of shale were placed on plates in desiccators above different

saturated solutions. Equilibrium was established between the shale sample and the

solutions through movement of water only. In the desiccator, ions do not diffuse into or

out of the shale.

The following chemical materials: KH2PO4 (0.96), KCl (0.85), NaCl (0.755),

MnCl2 (0.56), MgCl2 (0.32), KCOOH (0.215) and ZnCl2 (0.1) were selected to achieve

constant relative humidity (water activity). The values in parenthesis are the relative

vapor pressures for the saturated solution at room temperature.

The adsorption isotherms for Pierre I and Arco shale are shown in Figure 2-1.

From this figure, it was found that the native water activities of Pierre I and Arco shales

were 0.98 and 0.78. This corresponded to native water contents of 10.21 wt % and 3.3 wt

% respectively.

25

2.6 CONCLUSIONS

Two types of shale, Pierre I and Arco, were used in this experimental study. The

high moisture content Pierre I can be used to represent surface shale. The relatively dry

Arco shale was cored in a well at about 15,000 feet, which can be used to represent

subsurface samples.

ACKNOWLEDGEMENTS

We would like to thank OGS Laboratory for supplying the Pierre I shale core used

in this study. Help from Mr. Harry L. Dearing and Mr. Jay P. Simpson is highly

appreciated.

REFERENCES

Ballard, T.J. Beare, S.P. and Lawless, T.A.: “ Fundamentals of Shale Stabilisation: Water Transport Through Shales”, IADC/SPE24974, presented at the European Petroleum Conference held in Cannes, France, 16-18 November, 1992.


Bostrom, B., Svano, G., Horsrud, P. and Askevold, A.: “ The Shrinkage Rate of KCl-Exposed Smectitic North Sea Shale Simulated by a Diffusion Model”, SPE/ISRM 47254 presented at the SPE/ISRM Eurock, 98 held in Trondhaim, Norway, 8-10 July 1998.

Breeden, D. and Shipman, J.: “ Shale Analysis for Mud Engineers”, AADE-04-DF-HO-30 presented at the AADE 2004 Drilling Fluids Conference, at the Radisson Astrodome in Houston, Texas, April 6-7, 2004.

Carminati, S., Del Gaudio L., Del, Piero G. and Brignoli, M.: “ Water- Based Muds and Shale Interactions”, SPE 65001 presented at the 2001 SPE International Symposium on Oilfield Chemistry held in Houston, Texas, 13-16 February 2001.

Chenevert M. E: “Shale Alteration by Water Adsorption”, Journal of Petroleum Technology, Sept. 1970a, pp 1141-1147.

Chenevert, M. E: “Shale Control with Balanced-Activity Oil-Continuous Muds”, Journal of Petroleum Technology, Oct. 1970b.

26

Chenevert, M. E and Amanullah, Md.: “Shale Preservation and Testing Techniques for Borehole Stability Studies”, SPE 37672 presented at the 1997 SPE/IADC

Drilling Conference held in Amsterdam, The Netherlands, 4-6, March, 1997.

Chenevert M. E and Pernot Vincent: “ Control of Shale Swelling Pressure Using Inhibitive Water – Based”, SPE 49263 presented at the 1998 SPE Annual Technical Conference and Exhibition held in New Orleans, Louisiana, 27-30, September, 1998.


Darley, H.C.H: “ A Laboratory Investigation of Borehole Stability”, JPT, July, 1969.

Davidson, J.A.: “ Application of Acoustic Measurements in Shale Stability Research”, Ph.D Dissertation, University of Texas at Austin, May 1999.

Ewy, R.T. and Stankovich, R.J.: “ Shale-Fluid Interactions Measured Under Simulated Downhole Conditions”, SPE/ISRM 78160 presented at the SPE/ISRM Rock Mechanics Conference held in Irving, Texas, 20-23 October 2002.

Fonseca, C.F., and Chenevert, M.E.: “ The Effects of Stress and Temperature on Water Acitivity of Shales”, presented at the 3rd North American Rock Mechanic Symposium, “ Rock Mechanics in Mining, Petrleum and Civil Works,” Cancum, Quintana Roo, Mexico, June 3-5, 1998.

Forsans, T. M. and Schmitt L.: “ Capillary forces: The neglected factor in shale instability studies?” SPE 28029 presented at the SPE/ISRM Rock Mechanics in Petroleum Engineering Conference held in Delft, The Netherlands, 29-31 August 1994.


Lomba, R.F.T., Chenevert, M. E. and Sharma, M. M.: “ The ion-selective membrane behavior of native shales”, Journal of Petroleum Science and Engineering 25 (2000) 9-23.

Nesbitt, L.E., King, G.P., and Thurber N.E.: “ Shale Stabilization Principles”, SPE 14248 presented at the 60th Annual Technical Conference and Exhibition of the Society of Petroleum Engineering held in Las Vegas, NV September 22-25, 1985.

Osisanya, S. O. and Chenevert, M.E.: “ Rigsite Shale Evaluation Techniques for Control of Shale Related Wellbore Instability Problems”, SPE 16054 presented at the Fourth SPE/IADC Drilling Conference, New Orleans, Louisiana, March 15-18, 1987.

27

Osisanya, S. O.: “Experimental Studies Of Wellbore Stability in Shale Formations”, Ph.D dissertation, The University of Texas at Austin, August 1991.

Richard, V. B., and Peter, W. G.: “ Saturated Solutions for the Control of Humidity in Biological Research”, Ecology, January 1960, Vol.41 No.1, 232-236.

Schmitt, L., Forsans, T. and Santarelli, F.J.: “ Shale Testing and Capillary Phenomena”, Forces May Induce Biased Laboratory Testing”, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 1994, No.5, pp411-427.

Sharma, M.M.: “Chapter 4 Clay Mineralogy and Colloid Chemistry”, notes for PGE 383: Near Wellbore Problems, The University of Texas at Austin, 2004.

28

Table 2-1– Mineralogical composition of Pierre I shale

Constituent % by weight

Quartz 19 Feldspar 4.0 Calcite 3

Dolomite 7 Pyrite 2

Siderite 1 Chlorite 2.6 Kaolinite 7.0

Illite 12.2 Smectite 10.9

Mixed layer 31.3

Clay

Total 64

Table 2-2 – Composition of interstitial pore fluid for Pierre I shale (cations)

Cation Concentration (meq/100g)

Potassium 0.7 Magnesium 0.4

Sodium 1.6 Calcium 1.0

Table 2-3 – Composition of interstitial pore fluid for Pierre I shale (anions)

Anion Concentration (meq/100g)

Chloride 1.1 Carbonate 0

Bicarbonate 6.7 Sulfate 0.2

29

Table 2-4 – Exchangeable bases for Pierre I shale

Cation Exchangeable bases (meq/100g)

Potassium 0.7 Magnesium 4.4

Sodium 0.4 Calcium 13.9

Table 2-5 – Mineralogical composition of Arco shale

Constituent % by weight

Quartz 23.6 Feldspar 4.0 Calcite -----

Dolomite 1.2 Pyrite 2.4

Siderite 4.1 Chlorite 3.6 Kaolinite 5.7

Illite 15.0 Smectite 11.0

Mixed layer 29.4

Clay

Total 64.7

30

0

1

2

3

4

5

6

7

8

9

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Relative Vapor Pressure, P/Po

Moi

stur

e C

onte

nt, w

t%

Pierre IArco Shale

Figure 2-1– Adsorption and desorption isotherms for Pierre I and Arco shales.

31

Chapter 3 : Wellbore Instability of Directional Wells in Laminated and Naturally Fractured Shales

ABSTRACT

Wellbores drilled into laminated shales or shale/sand sequences are found to be

more unstable than wellbores drilled into similar homogenous isotropic formations. This

is primarily due to the fact that in laminated formations, failure can occur along the

weaker bedding planes.

In this chapter, the stress distribution around deviated wellbores in laminated

shale/sand sequences is analyzed and it is shown that failure can occur either along or

across bedding planes, depending on the well trajectory. It is shown that well inclination

and well azimuth orientation, relative to the bedding plane strike and dip, have a

significant impact on wellbore stability. Critical mud weight windows are calculated for

different well orientations relative to the bedding planes. It is pointed out that both in-situ

stresses and rock strength anisotropies should be factored into wellbore trajectory

optimization in order to improve wellbore stability. Taking these factors into account can

result in significantly improved wellbore stability conditions and improve the mud weight

window within which to drill deviated wells.

It has been reported that the presence of natural fractures is sometimes the

primary factor causing lost circulation. Thus, when drilling through naturally fractured

shales, it is important to avoid pressurizing the fractures. Consequently, the upper level of

mud weight should be kept sufficiently low to prevent a natural fracture from

propagating.

32

3.1 INTRODUCTION

Wellbore instability in laminated and fractured shales is a critical problem in the

drilling industry. Numerous wellbore instability problems have been reported when

drilling through laminated and fractured formations (Last et al., 1995; Okland et al.,

1998; Beacom et al., 2001; Edwards et al., 2003). In addition to the unfavorable chemical

interaction between drilling fluid and shales that is covered in other chapters, it is

believed that micro-fractures and weak bedding planes can cause wellbore instability

(Labenski et al., 2003; Zhang et al., 2004).

It is well known that shale is laminated and the bedding layers serve as weak

planes that result in strength anisotropy (Chenevert 1965;Yang et al., 1970; Fjaer et al.,

1992; Yamamoto et al., 2002). Chenevert (1965) studied the mechanical anisotropies of

laminated sedimentary rocks experimentally. Aadnoy (1988) developed a simulator to

study the wellbore instability of highly inclined boreholes in transversely anisotropic rock

formations by using Chenevert’s (1965) results. Aadnoy pointed out that an error was

introduced when material anisotropies are ignored. However, two assumptions in

Aadnoy’s simulator limit its application; 1) horizontal bedding layers, and 2) a zero

shear-stress component for the wellbore.

Ong and Roegiers (1993) studied the influence of anisotropies on borehole

stability by using anisotropic strength criterion for assessing compressive failure. They

indicated that wellbore stability was significantly influenced by rock mechanical

anisotropies. Gazaniol et al. (1994) also found that rock strength anisotropy has great

influence on wellbore instability and that a wellbore could fail along the bedding planes if

the trajectory of the well is not properly selected.

In laminated formations, wells can be drilled either up, down or cross-dip, as

shown in Figure 3-1 (Last et al., 1995). Many field cases demonstrate that an up-dip well

33

is more stable than a down- or cross-dip well (Last et al., 1995; Skelton et al., 1995;

Okland et al., 1998).

Last et al. (1995) found that drilling normal to bedding planes was beneficial and

improved wellbore stability in the Cusiana Field. They pointed out that wellbore stability

was affected by the relative angle between the wellbore and the bedding planes. Similar

conclusions were reached by Skelton et al. (1995) who showed that the tangent section

and azimuth of the wellbore should be perpendicular to the bedding dip and strike of the

formation respectively, in order to avoid formation layers from sliding along their

bedding planes. Okland et al. (1998) pointed out that for the Draupne formation the

“angle of attack”, which is defined as the angle between the wellbore and the bedding

planes should always exceed 20o so as to improve wellbore stability.

Willson et al. (1999) noted that bedding-plane slippage could result from an

unfavorable interaction between in-situ stresses, well trajectory, and bedding planes.

They pointed out that the reduced strength (friction and cohesion) acting on the bedding

planes could also result in enhanced and sometimes catastrophic instability. Russell et al.

(2003) found that it was important to determine the relative angle between the well

trajectory and the rock structure because this angle dictates the stability of the formations

when drilling close to the bedding dips or at unfavorable angles to fracture planes.

It has also been established that the existence of natural fractures was one of the

main causes of wellbore instability (Stjern et al., 2000; Chen et al., 2002). Santarelli et al.

(1992) found that an increase in mud weight could not solve wellbore instability

problems in naturally fractured formations.

In summary, two notable mechanisms are known to contribute to wellbore

instability in laminated and fractured formations; 1) slippage along weak bedding layers,

and 2) the existence of a natural fracture system that facilitates pressure transmission

34

from the wellbore into adjacent formations. The latter enhances wellbore sloughing

especially during tripping, because the swab pressure caused by upward pipe movement

decreases the bottom hole pressure.

From the above review, we see that many authors have recognized wellbore

instability problems when drilling through laminated naturally fractured formations.

3.2 WELLBORE INSTABILITY MODEL IN LAMINATED FORMATIONS

When the stress at a point in a wellbore exceeds the rock strength, wellbore

instability problems occur. Strength anisotropy is one of the unique properties of

laminated shales. Therefore, not only the stress state around a wellbore but also the

variable strength properties of laminated formations should be considered in wellbore

stability calculations.

3.2.1 Anisotropic Strength Model in Laminated Formations

In developing this model, it is assumed that under triaxial compressive- strength

drained-test conditions, the pore pressure within the shale sample is zero (therefore the

total stress is equal to the effective stress).

During a typical compressive strength test, a laminated shale sample is subjected

to the stress state as shown in Figure 3-2. The angle between the bedding plane and the

axial stress, β , is defined as the “operation angle”. Depending on the operation angle,

there are two possibilities for laminated rock failure, either across or along the bedding

plane. If the sample fails across the bedding planes, the strength is defined as “normal

strength”, 'n1σ . On the other hand, if it fails along the bedding plane, its strength is

defined as the “bedding plane strength”, 'b1σ at that operation angle.

According to the Mohr-Coulomb failure criterion, the normal strength can be

calculated using following equation (Jaeger and Cook, 1979),

35

( ) ( ) ]1['C2'' 2303n1 µ+µ+µσ++σ=σ (3-1)

Similarly, the bedding plane strength can be calculated using following equation

(Jaeger and Cook, 1979),

( )( ) βµ⋅β−

σµ++σ=σ

2sintan1'C2

''w

3ww03b1 (3-2)

Note that the meaning of β here is different from that in the reference.

Differentiating Equation (3-2) with respect to β shows that 'bsσ has a minimum value

when

ww

12tanµ

=β (3-3)

This minimal value of min,bsσ is

( ) ( ) ⎥⎦⎤

⎢⎣⎡ µ+µ+σµ++σ=σ w

2w3ww03min,b1 1'C2'' (3-4)

By equating Equations (3-1) and (3-2), two values of operation angle, denoted as

1β and 2β ( 21 β<β ), can be calculated as;

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

µ+µ−−

=ββ −

w

w22

121 a2b

ab2baatan,

∓

(3-5)

where,

( ) ⎟⎠⎞⎜

⎝⎛ µ+µ+µσ+= 2

30 1'Ca

'Cb 3ww0 σµ+=

The cohesion ( 0C ) can be determined by using the uniaxial compressive strength

(UCS) equation (Jaeger and Cook, 1979):

36

⎟⎠⎞⎜

⎝⎛ µ+µ+

=2

012

UCSC

(3-6)

Application of the above equations is given below by using information from the

Pedernales Field in Venezuela (Willson et al., 1999). This formation is located at a depth

of 5500 ft, has a native internal frictional angle of 31o, a UCS value of 4180 psi, bedding

a plane shear strength ( w0C ) value of 300 psi, and a bedding plane frictional angle of

26.6o. Based on the formation depth, it is assumed that the effective confining pressure

( '3σ ) is about 2800 psi. According to the relationship between internal frictional angle

and frictional coefficient, we have 6.031tan ==µ and 5.06.26tanw ==µ . Based on

the relationship between UCS and cohesion, defined by Equation (3-6), we have

psi 1183C0 = . After substituting all the above information into Equations (3-1), (3-2), (3-

3), (3-4), and (3-5), we get psi 913,12'n1 =σ , 32w =β , psi 8301'min,bs =σ , 101 =β and

532 =β . These points are plotted in Figure 3-3, along with many other points calculated

in a similar manner.

It is seen in Figure 3-3 that when the operation angle is in the range of (0o, 1β ) or

( 2β , 90o), the laminated formation has its intrinsic strength and the rock fails across the

bedding planes. However, if the operation angle is in the range of 21 β<β<β , the

bedding plane strength is less than the intrinsic strength and the rock fails along the

bedding planes.

In laminated formations, a decrease in strength causes wellbore instability

problems if the well is drilled along an unfavorable operation angle ( 21 β<β<β ). In

order to predict the strength in laminated formations, the operation angle should be

determined according to the stress state around the wellbore.

37

3.2.2 Stress Model

3.2.2.1 Stress state at wellbore

As shown in Figure 3-4, the stress state at the wellbore surface can be expressed

as (Fjaer et al., 1992):

( ) ( )( )[ ]

( )⎪⎪⎪

⎩

⎪⎪⎪

⎨

⎧

=τ=τ

θτ−θτ=τ

θτ+θσ−σν−σ=σ

−θ⋅τ−θσ−σ−σ+σ=σ=σ

θ

θ

θθ

0

sincos2

2sin42cos2

P2sin42cos2P

rzr

xzyzz

xyyxzzz

wxyyxyx

wrr

(3-7)

3.2.2.2 Principal stresses

It can be seen from Equation (3-7) that wrr P=σ is one of the principal stresses in

the (r, θ, z) coordinate system because 0rzr =τ=τ θ . The other two principal stresses can

be calculated by using the following equation (see Figure 3-5 for the notation).

( ) ( )2zz

2zzz2,1 4

121

σ−σ+τ±σ+σ=σ θθθθθ (3-8)

The direction of these principal stresses can be determined by calculating the

angle,ϕ (see Figure 3-6) as,

zz

z22tan

σ−στ

=ϕθθ

θ

(3-9)

After the angle, ϕ has been determined, the orientation of the maximum principal

stress ( 1σ ) can also be determined.

3.2.3 Operation Angle

As discussed previously (section 3.2.1), the strength of a laminated formation is

directly dependent on the operation angle. After the direction of the maximum principal

38

stress has been determined, the orientation of the bedding plane should be identified in

order to determine the operation angle.

Shale planes can be defined in space by their inclination (dip) and their strike,

which is the bearing of the line of intersection of the plane and a horizontal surface, as

shown in Figure 3-7. Notice that the bearing of the projection of the dip on a horizontal

surface is in a direction at right angle to the strike. This is called dip direction.

Based on the coordinate transformation, the normal direction of the bedding

planes can be expressed as,

( )( )[ ]

( )[ ]

( )[ ]⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪

⎨

⎧

++=

++−=

++

⋅=

p2

p2p

p2

p2

pp

p2

p2

ppp

Stan1)D(tan1

1n

Stan1)D(tan1

)Dtan(m

Stan1)D(tan1

Stan)Dtan(l

(3-10)

After the orientations of the maximum principal stress ( 1σ ) and the bedding

planes are determined, the following equation can be used to calculate the operation

angle,

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

++++

++=β −

2p

2p

2p

2m

2m

2m

pmpmpm1

nmlnml

nnmmllsin

(3-11)

3.2.4 Attack Angle

In oil field publications, the attack angle, which is the orientation of the wellbore

with respect to the bedding planes, is usually used to evaluate the wellbore stability of

laminated formations (Okland and Cook, 1998; Willson et al., 1999). According to

Okland and Cook’s (1998) definition, the attack angle is equal to 90o when the wellbore

39

is perpendicular to the bedding planes and 0o when the well is parallel to the bedding

planes. However, Willson et al. have a completely different definition of this angle.

They define the attack angle as zero when the well is drilled perpendicular to the bedding

planes, and 90 o when the well lies in the bedding planes. In our discussions, Okland and

Cook’s definition is used.

The orientation of the wellbore can be calculated as:

⎪⎩

⎪⎨

⎧

=⋅=

⋅=

)Icos(n)asin()Isin(m

)acos()Isin(l

ww

www

www

(3-12)

According to the orientations of the wellbore and bedding plane, the attack angle

can be calculated by using the following equation

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

++++

++=β −

2p

2p

2p

2w

2w

2w

pwpwpw1a

nmlnml

nnmmllsin

(3-13)

Based on the above strength and stress model, a simulator has been developed

which can be used to perform an investigation of wellbore instability of laminated shales.

Not only the stability condition around a wellbore circumference, but also the critical

mud weights can be determined by using this simulator.

3.3 WELLBORE INSTABILITY ANALYSIS AND DISCUSSION

3.3.1 Input Data

The parameters provided in Table 3-1 were used as a base case for performing

calculations using our simulator. A sensitivity analysis was conducted by varying one

parameter at a time from this base case.

3.3.2 Effects of Well Configuration on Wellbore Stability

Wellbore stability conditions for both non-laminated (strength isotropic) and

40

laminated (strength anisotropic) formations are shown in Figure 3-8.

In Figure 3-8, the irregular line section represents unstable conditions and the

solid line represents stable conditions. It is seen that wellbore failure occurs in both non-

laminated and laminated formations. Starting from the highest point at the wellbore (as

shown in Figure 3-4) and moving anticlockwise, in non-laminated formations failure

occurs from 78o to 127o and from 258o to 307o. For laminated formations, failure occurs

from 73o to 130o and from 253o to 310o. A wider failure window was experienced for

laminated formations due to the fact that strengths in laminated formations are always

lower than in homogeneous, isotropic formations (McLellan and Cormier 1996; Willson

et al., 1999).

In directional wells, drilling along the minimum horizontal stress ( hσ ) is

considered to be beneficial and improves wellbore stability in non-laminated formations

under normal faulting stress regime conditions ( hHv σ>σ>σ ) (Zheng 1998; Awal et

al., 2001). Figure 3-9 shows wellbore stability when the well azimuth is changed from

50o to 90o so as to drill along the direction of minimum horizontal stress.

As shown by Figure 3-9, the wellbore fails in laminated formations (b) while it

remains stable in non-laminated formations (a). The stress concentration around the

wellbore decreases when the well is drilled along the minimum horizontal stress direction

under a normal faulting stress regime. This improves wellbore stability in non-laminated

formations (Zheng 1998; Awal et al., 2001), whereas the wellbore experiences more

failure in laminated formations due to the unfavorable operation angles caused by the

alteration of well azimuth. Therefore, a significant difference exists between laminated

and non-laminated formations due to well azimuth alteration. In non-laminated

formations, it is beneficial, from a wellbore stability point of view, to drill along the

minimum horizontal stress direction under normal faulting stress regime conditions,

41

whereas drilling along the minimum horizontal stress direction can be detrimental to

wellbore stability in laminated formations. As a result, ignoring strength anisotropy can

be costly and detrimental to wellbore stability during drilling.

It is interesting to note from Figure 3-9 that failures should occur within four

ranges ( 40~0 , 147~86 , 220~180 , and 327~246 ) around the wellbore

circumference in the laminated formation. Such failures could result in developing a

“square hole” as was observed by Cook et al. (1994) in their lab tests.

Figure 3-10 shows the wellbore stability condition after changing the azimuth to

zero, which makes the wellbore oriented along the maximum horizontal stress direction

( Hσ ). It is seen that the wellbore is made unstable by changing the azimuth compared to

the base case in non-laminated formations. This is due to the stress concentration increase

caused by the unfavorable wellbore direction. Meanwhile, the failure window is also

expanded in laminated formations.

3.3.3 Effects of Wellbore Configuration on Critical Mud Weights

Generally, mud weight is adjusted to address wellbore instability problems. It is

agreed upon that there exits a lower bound of mud weight, below which compressive

failure of the wellbore occurs. This mud weight is defined as the “lower critical mud

weight”. On the other hand, mud weight should not be too high because there exists an

upper bound, defined as the “upper critical mud weight”, beyond which wellbore tensile

failure occurs. In naturally fractured shale formations, there is a different meaning for the

upper critical mud weight, which will be discussed later. The lower critical mud weight is

discussed below.

The effect of well inclination on lower critical mud weight for both non-laminated

and laminated formations is shown in Figure 3-11. It is seen that the critical mud weight

increases smoothly with increasing inclinations in non-laminated formations. This mud

42

weight increase means that more wellbore instability problems occur in directional and

horizontal wells than in vertical wells. This wellbore stability deterioration is due to the

higher stress concentration at the wellbore in directional and horizontal wells under the

simulated normal in-situ stress state.

Some interesting phenomena are observed in laminated formations. The critical

mud weight decreases with well inclinations up to 35o, and then it increases with

increasing inclinations. When well inclination reaches about 80o, it decreases again. This

changing pattern of the critical mud weight with well inclinations in laminated formations

is caused by variation in the rock strength with operation angle, as shown in Figure 3-3.

As discussed previously, the operation angle changes with inclination of the wellbore.

It is important to note that all critical mud weights in laminated formations are

higher than those for non-laminated formations at the same inclination due to the strength

decrease in laminated formations. This explains why more wellbore instability problems

occur in laminated formations (McLellan and Cormier, 1996).

Last et al. (1995) and Skelton et al. (1995) found that wellbore stability can be

improved in laminated formations by drilling wells perpendicular to the formation strike.

After changing the well azimuth to make the wellbore perpendicular to the formation

strike, we can see in Figure 3-12 that the effects of inclination on the critical mud weights

for both non-laminated and laminated formations.

Compared with the base case (Figure 3-11), changing the well azimuth does not

affect the critical mud weight greatly in non-laminated formations. As for laminated

formations, significant changes were observed. At low inclination angles (less than 30 o)

or higher inclination angles (greater than 65 o), the critical mud weights decreased due to

the alteration of well azimuth. This means that the alteration of well azimuth is beneficial

to wellbore stability in laminated formations under our simulation conditions. However,

43

when the inclination lies between 30o to 65o, the critical mud weight increases compared

with the base case. Therefore, it can be concluded that changing the well azimuth to be

perpendicular to the formation strike is detrimental to wellbore stability in laminated

formations when the well inclination lies in the range of 30o to 65o. Consequently,

drilling a well through laminated formations perpendicular to the formation strike is not

always a good strategy.

3.3.4 Effects of Dip Angles on Critical Mud Weight

It can be seen in Figure 3-13 that except for the horizontal layers (Dip = 0o) at low

inclinations (less than 20o), the required critical mud weight in laminated formations is

always higher than that in non-laminated formations. In the lower or higher inclinations,

the higher the dip angle, the higher the required mud weight. Under a certain range of

inclination angles, an opposite phenomenon is observed.

When the dip angle equals zero, the bedding plane is horizontal, as in the case

discussed by Aadnoy (1988). The critical mud weight is equal to that in non-laminated

formations when the inclination is less than 20o. This demonstrates that wellbore failure

occurs along the native failure plane when the well inclination is less than 20o. However,

when the inclination is greater than 20o, the mud weight increases significantly with

increasing inclination and the wellbore fails along the bedding planes.

3.3.5 Effect of Attack Angle on Critical Mud Weight

According to many field observations, the wellbore is more stable when the well

is drilled perpendicular to the bedding planes, which means that the attack angle is 90o

(Last et al., 1995; Okland et al., 1998; Beacom et al., 2001; Edwards et al., 2003).

Here, it is important to clarify the differences between two angles, operation angle

and attack angle. As discussed previously, we can see that the operation angle is defined

as the angle between the maximum principal stress ( 1σ ) and the bedding plane, while the

44

attack angle is defined as the angle between the wellbore and the bedding plane. For

example, if the bedding planes are horizontal, then the attack angle is equal to 90o less

the well inclination. This means the attack angle equals 90o for vertical wells while it is

0o for horizontal wells in horizontal laminated formations. However, the operation angle

varies with the well inclination, well azimuth, in-situ stress and the azimuth around the

wellbore. It cannot be easily observed without performing calculations.

From the previous analysis, we can see that it is the operation angle, not the attack

angle that directly affects the strength in laminated shales. In the oil field, it should be

relatively easy to figure out the attack angle based on the bedding planes and the wellbore

trajectory information. Unfortunately, the attack angle, not the operation angle is widely

used in the oil field. The effect of attack angle on the critical mud weight is shown in

Figure 3-14.

It is shown by Figure 3-14 that the critical mud weight is low at high attack angles

(greater than 63o for the base case), which fits field observations very well (Okland and

Cook, 1998). There exists an attack angle (15 o for the base case) under which the mud

weight should be very high to secure wellbore stability, just as Okland and Cook (1998)

stated “Both field experience and laboratory evidence from cylinder collapse tests,

indicate that hole instability in the Draupne Formation, a fissile Jurassic shale, is not a

problem when drilling normal to bedding, or even almost parallel to bedding, but

becomes very serious when the hole is parallel or very nearly parallel to bedding.” Their

hollow cylinder tests suggest this minimum “ attack angle” to be 10o, but field experience

from Oseberg suggests 20o. By using their data, our simulation result suggests this attack

angle to be 15o.

3.3.6 Field Case Study

Willson et al. (1999) studied wellbore instability problems under complex

45

geologic conditions, such as Pedernales Field, Venezuela and Cusiana Field, Colombia.

Table 3-2 shows the data from the Pedernales Field, Venezuela.

After running our simulator using the data shown in Table 3-2, we get the critical

mud weights for cross, up, and down-dip wells (see Figure 3-1 for their definition), as

shown in Figure 3-15.

It is clearly seen from Figure 3-15 that the critical mud weights in up-dip wells

are lower than these in down- or cross-dip wells, especially in high inclination wells.

These results fit well with the field observation by Skelton et al. (1995). Furthermore, it

was pointed out by Willson et al. (1999) that wellbores are predicted to be stable with

mud weights of around 11.5 ppg for up-dip wells, which is almost identical to that

predicted by our model.

From the above analysis, we see that higher mud weights are required to address

wellbore instability problems in laminated formations. However, in laminated naturally

fractured formation, significant mud loss occurs when excessive mud weight is used,

especially when the mud weight is high enough to cause the existing fractures to

propagate. Therefore, the upper critical mud weight should not exceed the existing

fracture propagation pressure.

3.4 NATURALLY FRACTURED SYSTEMS IN SHALE FORMATIONS

In naturally fractured shales, it is important to avoid pressurizing existing cracks

with drilling fluids. In this chapter, the wellbore pressure needed to pressurize natural

fractures is called the fracture propagation pressure.

The stress intensity factor for a uniformly loaded, isolated, plane strain crack (see

Figure 3-16) of length 2a is defined as (Lawn and Wilshaw, 1975; Olson et al., 2001)

a K II πσ∆= (3-14)

When the stress intensity factor is equal to or greater than the fracture toughness,

46

the crack begins to propagate

ICI KK ≥ (3-15)

Equation (3-15) can be defined in terms of fracture propagation pressure and

minimum horizontal stress ( hσ ) as

( ) ICIh Ka P ≥πσ− (3-16)

Generally, natural fractures have been formed as a result of Mode I (opening

mode) failure (Close 1993; Ong et. al., 1993). Mode I cracks propagate in the direction

perpendicular to the minimal principal horizontal stress. Based on assumptions of plane

strain, linear elastic formation with thermoelastic effects , that is given by (Blanton and

Olson 1999)

( )ν−∆α

+εν−

+α+α−σν−

ν=σ

1TE

1EPP

1T

tect2ppvh (3-17)

Combining Equations (3-16) and (3-17), the wellbore pressure required for

fracture propagation can be determined as (Engelder and Lacazette, 1990)

( )

( )ν−α−ν−π

ν−+⎟⎠

⎞⎜⎝

⎛ ∆α+ν+

ε+µσ

=211

aK

1T1

EP

p

ICT

tectv

(3-18)

Equation (3-18) can be used to analyze the influence of fracture length on fracture

propagation with the data listed in Table 3-3.

The effects of crack half-length on fracture propagation pressures are shown in

Figure 3-17. It can be seen that fracture propagation pressure decreases with the increase

of fracture half-length. It decreases significantly when the half-length increases from 2

mm to 20 mm. During drilling of naturally fractured formations, such as coal seams, it is

important to keep the mud hydrostatic pressure below the above calculated fracture

47

propagation pressure in order to avoid pressuring the existing fractures. Once fractures

begin to propagate, it is a self-advancing process, and lost circulation and wellbore

instability may occur immediately. This phenomenon can be used to explain why it is not

proper to indiscriminately increase the mud density to address wellbore instability

problems in naturally fractured formations, as pointed out by Santarelli et al. (1992).

3.5 CONCLUSIONS

1. Changes of hole inclination and azimuth may produce unfavorable wellbore

stress states in laminated formations around the borehole. Depending on

specific conditions, such effects may lead to compressive wellbore failure.

2. A model was developed for coupling the strength of laminated shales with the

stress state at the wellbore wall. This model allows the simulation of wellbore

instability for directional wells in laminated formations.

3. The interaction angle between the wellbore and bedding plane is critical for

the determination of whether drilling through laminated formations will

induce instability along bedding planes.

4. Model mud weight results compared to the Pedernales Field case show an

excellent agreement.

5. Critical mud weights are strongly wellbore orientation dependent.

6. Optimal well trajectory for wellbore stability control must be designed by

considering both the strength and in-situ stress anisotropies of laminated

shales.

7. Mud density should be kept low enough to prevent pressurizing up naturally

fractured formations.

NOMENCLATURE*

a Main crack half-length [=] L

48

wa Well azimuth [=] degrees

0C Intrinsic cohesion [=] m/L-t2

w0C Weak plane cohesion [=] m/L-t2

pD Dip angle [=] degrees

E Young’s modulus [=] m/L-t2

wi Well inclination [=] degrees

IK Mode I stress intensity factor [=] m/t2- L

ICK Fracture toughness or critical stress intensity factor [=] m/t2- L

ml , mm , mn The cosines of the angles between the maximum principal

stress ( 1σ ) and the x’-, y’-, z’- axes, dimensionless pl , pm , pn The cosines of the angles between the normal direction of

bedding plane and the x’-, y’-, z’- axes, dimensionless

wl , wm , wn The cosines of the angles between the wellbore axis and the

x’-, y’-, z’- axes, dimensionless

P Fracture propagation pressure [=] m/L-t2

pP Pore pressure [=] m/L-t2

wP Wellbore pressure [=] m/L-t2

P∆ Swab pressure [=] m/L-t2

r Radius of gas bubble [=] L

pS Strike azimuth (clockwise from the normal north to strike line) [=] degrees

T∆ Temperature at a particular depth minus the ambient surface temperature

[=] T

UCS Uniaxial compressive strength [=] m/L-t2

µ Intrinsic coefficient of friction [=] dimensionless

wµ Weak plane coefficient of friction [=] dimensionless

49

1σ Total maximum principal stress [=] m/L-t2

'1σ Effective axial stress for shale failure across bedding plane[=] m/L-t2

2σ Intermediate principal stress [=] m/L-t2

3σ Total minimum principal stress [=] m/L-t2

'3σ Effective minimum principal stress [=] m/L-t2

cσ Confining pressure [=] m/L-t2

Hσ Maximum in-situ horizontal stress [=] m/L-t2

hσ Minimum in-situ horizontal stress [=] m/L-t2

'n1σ Normal compressive strength [=] m/L-t2

'b1σ Bedding plane compressive strength [=] m/L-t2

'min,bsσ Minimum bedding plane compressive strength [=] m/L-t2

vσ Overburden stress [=] m/L-t2

xσ Normal stress in x-direction [=] m/L-t2

yσ Normal stress in y-direction [=] m/L-t2

zσ Axial stress [=] m/L-t2

xyτ In-situ shear stress in (x, y, z) coordinated system [=] m/L-t2

yzτ In-situ shear stress in (x, y, z) coordinated system [=] m/L-t2

zxτ In-situ shear stress in (x, y, z) coordinated system [=] m/L-t2

rrσ Radial normal stress at wellbore [=] m/L-t2

θθσ Hoop stress at wellbore [=] m/L-t2

zzσ Axial stress at wellbore [=] m/L-t2

zθτ Shear stress at wellbore [=] m/L-t2

rzτ Shear stress at wellbore [=] m/L-t2

θτr Shear stress at wellbore [=] m/L-t2

Iσ∆ Mode I crack driving stress [=] m/L-t2

50

Φ Naïve internal frictional angle [=] degrees

wΦ Bedding plane frictional angle [=] degrees

pα Biot’s constant, dimensionless

tα Thermal expansion coefficient of rock matrix [=] 1/T

β Operation angle between the bedding plane and maximum principal stress

[=] degrees

21 , ββ Special operation angles at which the bedding strength

transfers from native to bedding strength [=] degrees

wβ Special operation angle at which the bedding strength gets to minimum [=]

degrees

aβ Attack angle between the bedding plane and wellbore [=] degrees

tectε Tectonic strain, dimensionless


θ Angular polar coordinate, degrees

* [=] means has units of, L is a length unit, m mass, t time, and T temperature

ACKNOWLEDGEMENTS

I am grateful to Dr. Seehong Ong for his support, guidance, and encouragement

throughout this work. His friendship, experience, and knowledge were essential for this

work. Special thanks are given to Dr. Mohammed Azeemuddin, Dr. Xianjie Yi, and Mr.

Chris Wolfe for their valuable suggestions.

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55

Table 3-1 - Input data for base case

Well Depth (ft) 10,000

Well Azimuth (degrees) N50 oE

Inclination (degrees) 60

Mud Weight (ppg) 9.6

Pore Pressure (ppg) 9

Overburden Stress Gradient (psi/ft) 1

Maximum Horizontal Stress Gradient (psi/ft) 0.9

Minimum Horizontal Stress Gradient (psi/ft) 0.8

Maximum Horizontal Stress Direction N0o E

Young's Modulus (106 psi) 1

Native Cohesion (psi) 1000

Bedding Plane Cohesion (psi) 200

Native Frictional Angle (Degrees) 30

Bedding-plane Frictional Coefficient 0.5

Poisson’s Ratio 0.3

Biot’s Constant 0.8

Strike and Dip N40º E, 20 ºNW

56

Table 3-2 - Information from Pedernales Field, Venezuela (after Willson et al., 1999)


Pore Pressure (ppg) 9

Overburden Stress Gradient (psi/ft) 0.98 Maximum Horizontal Stress Gradient (psi/ft) 1.2Minimum Horizontal Stress Gradient (psi/ft) 0.92

Maximum Horizontal Stress Direction 315o Young's Modulus (106 psi) 1

Native Cohesion (psi) 1188 Bedding Plane Cohesion(psi) 300

Native Frictional Angle (Degrees) 31Bedding plane frictional coefficient 0.5

Poisson’s Ratio 0.3Biot’s Constant 0.8Strike and Dip N45ºW, 45ºSW

Table 3-3 - Formation and fracture properties

Thermal Expansion Coefficient (10-6/oF) 0.33

Young's Modulus (106 psi) 1

Geothermal Gradient (oF/100ft) 1.5


Biot's Constant 0.75

Overburden Stress Gradient (psi/ft) 1

Pore Pressure Gradient (psi/ft) 0.465

Poisson’s Ratio 0.25

Tectonic Strain 0.0013

Fracture Toughness (psi in⋅ ) 220.5

57

Figure 3-1 – Up-, down-, and cross-dip wells.

58

Figure 3-2 – Failure modes for laminated rocks.

59

7000

8000

9000

10000

11000

12000

13000

0 10 20 30 40 50 60 70 80 90

Operation Angle, Degrees

σ s ,

psi

β1 β2

Figure 3-3 – Influence of operation angle on compressive strength of laminated rocks.

σ

σ v

σ H

x1

y

x

r

θ

z

a w

iw

Highest Point of Wellbore

hx’y’

z’

Figure 3-4 – Well configuration.

60

Figure 3-5 – Stress state at wellbore surface.

Figure 3-6 – Calculation of principal stresses.

61

Figure 3-7 – Definition of strike and dip.

Figure 3-8 – Wellbore stability conditions in (a) non-laminated and (b) laminated formations for a wellbore circumference.

62

Figure 3-9 – Wellbore stability conditions in (a) non-laminated, and (b) laminated formations for a wellbore circumference being along the minimum horizontal stress

( hσ ).

Figure 3-10 – Wellbore stability conditions in (a) non-laminated, and (b) laminated formations for a wellbore circumference being along the maximum horizontal stress

( Hσ ).

63

9

9.5

10

10.5

11

11.5

12

0 10 20 30 40 50 60 70 80 90

Inclination, degrees

Crit

ical

Mud

Wei

ght,

ppg Non-laminated

Laminated

Figure 3-11 – Effect of inclination on critical mud weights.

8

8.5

9

9.5

10

10.5

11

11.5

12

0 10 20 30 40 50 60 70 80 90


Crit

ical

Mud

Wei

ght,

ppg Non-laminated

Laminated

Figure 3-12 – Effect of inclination on critical mud weight for wellbore perpendicular to formation strike.

64

9

9.5

10

10.5

11

11.5

12

12.5

0 10 20 30 40 50 60 70 80 90


Crit

ical

Mud

Wei

ght,

ppg Nonlaminated

Dip=0Dip=20Dip=40

Figure 3-13 – Effect of dip angle on critical mud weight.

9

9.5

10

10.5

11

11.5

12

0 10 20 30 40 50 60 70 80 90

Attack Angles, degrees

Crit

ical

Mud

Wei

gh, p

pg

Figure 3-14 – Effects of attack angle on critical mud weight.

65

10

10.5

11

11.5

12

12.5

0 10 20 30 40 50 60 70 80 90


Crit

ical

Mud

Wei

ght,

ppg

Down-dipUp-dipCross-dip

Figure 3-15 – Critical mud weight in Pedernales Field.

Figure 3-16 – A natural fracture around a wellbore

66

14

16

18

20

22

0 20 40 60 80 100

Half Length of Fracture, mm

Frac

turin

g Pr

opag

atio

n Pr

essu

re, p

pg

Figure 3-17 – Effects of crack half-length on fracture propagation pressure.

67

Chapter 4 : Effect of Strain Rate on Failure Characteristics of Shales

ABSTRACT

Accurate strength data are critical when determining safe mud weight windows

during drilling, and also for understanding shale deformation mechanisms. A key factor

in measuring the compressive strength of shale is the strain rate used during laboratory

testing. Two phenomena are attributed to strain rate related strength alteration: pore

pressure build-up and dilatancy hardening.

Due to low shale permeability, pore pressure of high water content shales usually

builds up during high axial loading. Pore pressure greatly influences shale strength. A

theoretical analysis on the influence of confining and pore pressures on the deviatoric

strength of shale is presented in this chapter. Additionally, a model to predict pore

pressure distribution within our shale sample during a typical triaxial compression test is

developed. The effects of strain rate and permeability on pore pressure build-up, and

thereby the compressive strength are assessed.

On the other hand, certain rocks (low water content shales included) experience a

strength increase at high shear rates. This may be due to a form of micro-cracking that

leads to dilatancy and thus pore pressure reduction.

Experimental results for two preserved shale samples obtained from the field are

presented. It is shown that strain rates have different effects on the compressive strength

for the two shale types. The deviatoric strength for the soft Pierre I shale decreases, while

the strength for the highly compacted Arco shale increases with increasing strain rates.

The reasons for these observed phenomena are analyzed, and their impacts on drilling

operations are briefly discussed.

68

4.1 INTRODUCTION

The determination of the compressive strength of shale is a key factor in drilling

operation, bit optimization, and wellbore stability management (Robinson, 1958; Spaar et

al., 1995; McLellan et al., 1996; Ong et al., 2000). A better understanding of the

mechanisms of shale failure is useful in each of these areas.

Generally, there are two ways to obtain the compressive strength of shales: direct

laboratory measurement and indirect well log interpretation (Horsrud, 2001). Although

laboratory experiments are expensive and time consuming, they are more accurate. Our

results are based on laboratory measurements.

A key factor that controls the compressive strength of high water content shale is

its pore pressure. For such shale, pore pressure depends on the strain rate used during

testing. The compressive strength of low water content shales is also affected by strain

rate, but not by pore pressure effects as shown by the work of Swan et al. (1989).

Although many studies have been performed on hard crystalline rocks, relatively

few studies have been performed on the mechanical behavior of soft shale rocks due to

the technical problems involved in sample preparation and shale testing (Cook et al.,

1990; Chenevert and Amanullah, 1997). Shales make up over 75% of drilled formation

and 90% of wellbore instability problems occur in shale formations (Steiger et al., 1992),

therefore there is a need for such studies. Several researchers have theoretically and

experimentally examined this topic for several decades (Chenevert et al., 1964, 1998;

Closmann and Bradley, 1977; Swan et al., 1989; Cook et al., 1990; Yu et al., 2001; Chen

and Ewy, 2002).

By performing triaxial compressive strength tests, Robinson (1958) studied the

effects of pore and confining pressures on the failure characteristics of sedimentary rocks.

He found that the rock strength decreases with increasing pore pressure and it increases

69

with the increase of confining pressure. Chiu et al. (1983) discussed an appropriate

technique for triaxial testing of saturated soft shale. They found that pore pressure

alteration had significant influence on the measured strength and the deformation

properties of the specimen tested. It was found that positive or negative pore pressure

could be generated depending on the strain rates used during testing. They defined a

critical strain rate below which the pore fluid can dissipate completely with no pore

pressure build-up. If the strain rate is higher than the critical strain rate, negative pore

pressure (dilatancy) is generated, and thus the compressive strength to increase. Swan et

al. (1989) investigated the strain rate effects on Kimmeridge Bay shale. Some of their

results are shown in Figure 4-1. It was observed that as the strain rate increases, the

strength first decreases (implying a pore pressure increase), goes through a minimum

strength at about 0.1×10-6/min, then increases (implying a pore pressure decrease).

Cook et al. (1990) discussed the effects of strain rate and confining pressure on

the deformation and failure of shale. They concluded that shale deformation and failure

are governed by effective stress at low strain rates. However, the strength depends on

total pressure at a high strain rate.

Chen et al. (2002) compared the drained and undrained loading effects on

wellbore stability. They concluded that undrained effects cause wellbore instability

problems. This may be the reason why shales are more problematic than sandstone due to

their low permeability.

Several researchers studied the effects of strain rate on the failure mechanism of

non-shale rocks. Brace and Martin (1968) tried to test the principal of effective stress for

crystalline rocks of low porosity by running triaxial compressive experiments at strain

rates from 10-3 to 10-8 S-1. It was found that compressive strength increased with

increasing strain rates due to “dilatancy hardening”. They also found that the law of

70

effective stress was valid only when the loading rate was below some critical value. At

high strain rates, the law of effective stress could not be used to interpret the strength

results. Because there exists discrepancy between the “true pore pressure” and the

“measured pore pressure” (due to the low permeability), their conclusions were doubted

by Ladanyi (1970). The effects of strain rate on the strength and ductility of Solenhofen

limestone at low temperature and confining pressure were studied by Rutter (1972). He

also found that the law of effective stress was applicable under low strain rates.

In 1976, Atkinson ran experiments to study the influence of temperature and

strain rate on the strength of Galena ore and Muller et al. (1978) ran similar experiments

on Anhydrite. Their results are shown in Figures 4-2 and 4-3 respectively. It is easy to

see that the strength increases with increasing strain rate. They postulated that such

increases can be attributed to a “work – hardening” effect.

All the above studies are beneficial for understanding the failure characteristics of

shale. It can be concluded that strain rate strength alteration is caused by the two

phenomena: pore pressure build-up effect and pore pressure reduction by dilatancy. The

strength of the rock increases with an increase in strain rate due to the dilatancy effects

and it decreases with an increasing strain rate due to the pore pressure build-up effects.

Before a theoretical analysis on the effects of confining and pore pressure on the

compressive strength of shales is discussed, let’s briefly review the law of effective

stress.

4.2 LAW OF EFFECTIVE STRESS

It is well accepted that a wide range of rock properties, i.e., shear strength,

acoustic velocity, electrical resistivity, elastic modulus, thermal conductivity etc., depend

on effective stress (Ladanyi 1970; Ward et al., 1995; Khaksar and Griffiths, 1999). From

a wellbore stability point of view, this implies that the effective stress, rather than the

71

total stress, determines whether or not a rock fails due to external loading. Therefore,

determination of effective stress is crucial when considering rock behavior mechanisms

under external loading.

Through a study on saturated soil deformation behavior, Terzaghi et al. (1923)

introduced the concept of effective stress for porous media (Terzaghi, 1960). In equation

form, the effective normal stress ( eσ ) is equal to the total normal stress minus the

hydraulic pore pressure ( pP )

ijpijije P δ−σ=σ (4-1)

Biot (1941) improved the Terzaghi equation by introducing a Biot’s constant ( pα ) that accounts for effective pore fluid and rock compressibility:

ijppijije P δα−σ=σ , (4-2)

where,

s

frp K

K1−=α. (4-3)

4.3 PORE PRESSURE BUILD-UP EFFECTS ON SHALE STRENGTH

4.3.1 Theoretical Analysis

The Mohr-Coulomb failure criterion is widely used in rock mechanics due to its

simplicity (Mclean et al., 1990; Horsrud, 2001). It can be expressed as

Φ⋅σ+=τ tanC0 (4-4)

Under triaxial compressive strength test condition, it becomes

0ppcppa Csin1

cos2)P(sin1sin1P ⋅

Φ−Φ

+α−σΦ−Φ+

=α−σ (4-5)

Therefore the deviatoric strength can be expressed as

72

)P(sin1

sin2Csin1

cos2ppc0D α−σ

Φ−Φ

+⋅Φ−Φ

=σ (4-6)

where

caD σ−σ=σ (4-7)

It is easily seen from Equation (4-6) that differential strength ( Dσ ) increases with

an increase in confining pressure ( cσ ) and decreases with pore pressure ( pP ). Figure 4-4

shows the relationship between deviatoric strength and confining pressure by assuming

MPa 10C0 = , and 21=Φ , which fits the experimental data obtained by Cook (1990)

very well.

The relationship between deviatoric strength and pore pressure within ashale

sample is shown in Figure 4-5. It is seen that the deviatoric strength decreases with an

increase in pore pressure.

From the above analysis, we can argue that the pore pressure build-up during a

test causes shale strength decreases, and likewise, should the pore pressure decrease, the

strength would increase.

4.3.2 Numerical Simulation

A model to simulate the pore pressure build-up within a shale sample is shown as

follows (see Appendix 5 for derivation, boundary and initial conditions).

( ) 2p

2

p

zp

z

PCkt

21Ct

P

∂

∂

µα+

∂ε∂

ν−=∂

∂

(4-8)

4.3.2.1 Input data

The data used in simulation are listed in Table 4-1.

4.3.2.2 Time-dependent pore pressure build-up

Figure 4-6 shows pore pressure build-up profile in the core as a function of time

73

during the simulated test when the strain rate is equal to 10-6 S-1. It can be observed that

pore pressure builds up within the sample with time under such conditions.

The top and bottom of the sample (at positions of 0 and 40 mm) are exposed to

constant atmospheric pressure, thus their values are zero during compaction. Therefore,

in order to ensure that the pore pressure within the sample is zero, as required by drained

experiment condition, a lower strain rate may be required, so that pore fluid can bleed off

out of the ends of the sample.

4.3.2.3 Effects of strain rate on pore pressure build-up

Figure 4-7 shows pore pressure within the sample after 1 minute of axial loading

for different values of strain rate. From this figure, we see that the pore pressure is very

sensitive to strain rate. At high strain rates, the rate for pore pressure build-up is higher

than its dissipation rate, so the pore pressure increases with increasing strain rate.

Therefore, one way to test the strength of shales accurately is to load the sample at a low

strain rate, as suggested by Chiu et al. (1983) and Ewy et al. (2001).

4.3.2.4 Effects of permeability on pore pressure puild-up

The effect of permeability on pore pressure build-up for the drained test sample of

Figure 4-10 is shown in Figure 4-8. As expected, pore pressure increases with decreasing

permeability. It is hard for pore pressure contained within low permeability shales to

dissipate quickly.

From the above simulation results, we see that pore pressure builds up during the

compressive strength test under high strain rate. If however micro-fractures begin to

propagate, then pore pressure can leak off and it no longer increases.

74

4.4 EFFECTS OF STRAIN RATE ON SHALE STRENGTH

4.4.1 Strength Test Equipment

The laboratory equipment used to measure the shale compressive strength is

shown in Figure 4-10. In each strength test, a sample was jacked using heat shrink tubing

and surrounded on the vertical surfaces with three layers of 70×70 mesh screen wire. The

purpose of this screen wire is to let the pore fluid flow in radial and vertical directions

and thereby allow pore pressure to dissipate more rapidly. Porous disks were then placed

on the top and bottom of the sample, which were open to the upper and lower flow lines.

These lines were open to air, so pore fluid could exit toward atmosphere pressure during

compression.

Before applying an axial load, a confining pressure of 5000 psi was applied over a

10-minute period, and then kept at this value for one hour to make sure that the pore

pressure within the sample has completely dissipated. This period of time was determined

by running the pore pressure simulator as described in Equation (4-8).

In order to run the simulator, we must first determine the parameters for Equation

(4-8). Young’s moduli for Pierre I and Arco were determined to be 165,000 psi and

262, 000 psi respectively by running a compressive strength test under a low strain rate,

and Poisson’s ratio was assumed to be 0.25 for Pierre I and Arco shales. By using these

data, the axial strain rate applied during the application of confining pressure was

calculated in the following manner.

( )( )( )14cz

r s1002.2s/m 60 m. 1025.0psi 165000

psi 5000tE

Pt

S −−×=×

=∆⋅γ⋅

=∂ε∂

= .

Using the same method, the strain rate for the Arco shale was determined to be

1.27×10-4 S-1. Permeability values of 100 nD and 50 nD were used for the Pierre I and

Arco shale, respectively, as listed in the thesis of Nair (2005). The other information used

75

in the simulation is shown in Table 4-1. The simulation results of pore pressure change

for Pierre I and Arco during applying confining pressure are shown in Figures 4-11 and

4-12 respectively.

From these two figures, we see that pore pressure within the two shales is

approximately zero after maintaining 5000 psi for about 1 hour. For each test run, the

confining pressure was maintained at 5000 psi for about 1 hour before axial stress was

applied. In this way, the pressure had completely dissipated before testing began.

4.4.2 Effects of Strain Rate on Peak Strength of Pierre I Shale

The stress-strain curves at different strain rates for the high water content Pierre I

shale are shown Figure 4-13. From this figure, we see that the peak strength decreases as

the strain rate increases from 1.2×10-5 to 5.9×10-5 S-1 due to pore pressure increase. These

results plus other such tests were performed and plotted in Figure 4-14.

It is seen that the deviatoric strength for the soft, high water content, Pierre I shale

decreased with increasing strain rates. At a certain strain rate, it tended to level off. For

example, when the strain rate was increased to about to 5.0×10-5S-1 and beyond, the

deviatoric strength leveled off between 3600~3,800 psi. This strength decrease with

increasing strain rate is due to pore pressure build-up within Pierre I shale. When the

strain rate was less than 2.0×10-5 S-1, the deviatoric strength had increased to about 5100

psi.

The effects of strain rate on pore pressure build-up within Pierre I samples (Figure

4-15) were obtained by running our simulator. As shown in this graph, pore pressure

increases linearly with increasing strain rate. After regressing these simulation results, we

obtain a regression line. From the intercept of the regression line with the axis of strain

rate, we determine that the pore pressure is zero when the strain rate is 6.2×10-8 S-1,

which is exactly of the same order as suggested by Ewy et al. (2001).

76

4.4.3 Effects of Strain Rate on Peak Strength of Arco Shale

Typical stress-strain curves for the Arco shale are shown in Figure 4-16. It is

seen that as the strain rate increases, there is a definite increase in strength. Figure 4-17

shows the results of six such tests.

We also performed a simulation under the strain rates used in the compressive

strength test to study the effects these strain rates on pore pressure build-up within Arco

samples. The simulation result is shown in Figure 4-18. We see from this figure that pore

pressure increases with increasing strain rates. This pore pressure build-up should cause

the strength of Arco shale to decrease. However, from Figure 4-17, we see a rapid

increase in shale strength at strain rates above 3.7×10-5 S-1. This effect is the inverse of

what was seen for the Pierre I shale. It is assumed here that the increase is due to

dilatancy. Similar effects were seen by Swan et al. (1989) when testing the Kimmeridge

shale. They reported such an increase in strength was due to a “change in the deformation

mechanism from macroscopic fault plane formation at low rates, to distributed shear

micro-cracking at high rates”. Such cracks could provide the voids that promote

dilatancy. Such strength increases with strain rate increase are not uncommon for other

types of rocks as shown in Figure 4-2 by Atkinson (1976) and in Figure 4-3 by Muller

and Briegel (1978).

In addition, from the regression line between the pore pressure and strain rate, as

shown in Figure 4-18, it is determined that pore pressure build-up is zero when the strain

rate is below 3.5 ×10-8 S-1. This value of strain rate for Arco shale is lower than that for

Pierre I shale due to the fact that the permeability of Arco shale is less than the

permeability of Pierre I shale.

4.5 DISCUSSION AND APPLICATION

The strain rate used during a compressive strength test plays a crucial role for

77

proper strength determination. Previous work suggests that low strain rates should be

used in testing the mechanical properties of shale (Chiu et al., 1983; Cook et al., 1990).

However, performing strength tests under low strain rates may take days, even weeks.

We think that the selection of strain rate depends on the purpose of the test. If the result is

used for bit selection (Spaar et al., 1995), high strain rate should be used because the

strain rate during drilling is very high (Cook et al., 1990). However, if the test is used to

evaluate shale wellbore stability, the strain rate should be low enough to reflect shale

wellbore pore pressure behavior.

As to the validation of the law of effective stress, several researchers believe that

it holds true at low strain rates and does not hold true under high strain rates (Brace and

Martin, 1968; Rutter, 1972; Cook et al., 1990). Such a conclusion is doubt, because it is

very difficult, if not impossible, to measure the pore pressure within cracks during failure.

The results from this study can also be used to direct drilling operations. If a soft

shale with high water content and low permeability is encountered, like the Pierre I shale

used in our studies, high weight on bit and rotary speed should be used to increase the

pore pressure and thus the rate of penetration. On the other hand, if hard shale with low

moisture content is encountered, like the Arco shale, low weight on bit and low rotary

speed should be implemented during drilling operation in order to avoid dilatancy effects

on the formation strength.

4.6 CONCLUSIONS

1. Two phenomena: pore pressure build-up and dilatancy effects are

attributed to stain rate related compressive strength alteration. The

compressive strength can increase with the strain rate if dilatancy exists,

and decrease with pore pressure build-up.

2. A model is presented to predict pore pressure changes during a test. The

78

simulation results show that pore pressure increases with an increase in

strain rate and decreases with an increase in permeability.

3. Our experimental results show that the compressive strength for soft

Pierre I shale decreases, while the strength for hard Arco shale increases

with an increase in strain rate. In our tests, dilatancy effects are more

dominant in the hard Arco shale and pore pressure build-up effects are

more dominant in soft Pierre I shale.

4. When the strain rate for our drained biaxial compressive strength test is

6.2×10-8s-1 for Pierre I shale and 3.5×10-8s-1 for Arco shale, there is no

pore pressure build-up.

5. During shale compressive strength evaluation, different strain rates

should be selected in accordance with the purpose of the test.

NOMENCLATURE a Half -length of the crack [=] L

A Cross section area of the sample [=] L2

M,C Elastic moduli required to describe a two-phase medium [=] m/L-t2];

0C Cohesive strength [=] m/L-t2


G Shear Modulus [=] m/L-t2

fK Bulk moduli for pore fluid [=] m/L-t2

frK Bulk moduli of frame [=] m/L-t2

IK Fracture stress intensity factor [=] m/t2-L1/2

ICK Fracture toughness, [=] m/t2-L1/2

79

sK Bulk moduli of solid [=] m/L-t2

k Permeability [=] L2

L Length of rock sample [=] L


Q Flow rate [=] L3/t

t Time [=] t

u Pore fluid viscosity [=] m/L-t

fu Pore fluid displacement [=] L

su Solid grain displacement [=] L

z Distance from the bottom of sample[=]L

ν Poisson’s ratio, dimensionless

σ Normal stress [=] m/L-t2

aσ Axial stress at failure [=] m/L-t2

cσ Confining pressure [=] m/L-t2

Dσ Deviatoric strength [=] m/L-t2

ijσ Total normal stress [=] m/L-t2

eijσ Effective normal stress [=] m/L-t2

Iσ∆ Mode I crack driving stress [= m/L-t2

xε Normal strain in x-direction, dimensionless

yε Normal strain in y-direction, dimensionless

80

zε Normal strain in z-direction, dimensionless

vε Volumetric strain, dimensionless

ζ Strain parameter, dimensionless

φ Porosity, dimensionless

τ Shear stress [=] m/L-t2

Φ Internal friction angle, degrees


ijδ Kronecker delta, dimensionless

SI METRIC CONVERSION FACTORS ft × 3.048* E – 01 = m

gal × 3.785 E – 03 = m3

in × 2.54* E – 02 = m

in2 × 6.452 E – 04 = m2

lbm × 4.54 E – 01 = kg

psi × 6.8948 E – 03 = MPa

* Conversion factor is exact.

ACKNOWLEDGEMENTS We gratefully acknowledge Dr. Russ Ewy, Dr Guizhong Chen, Dr. Rosana

Lomba and Mr. Ben Bloys for their valuable suggestions. The help from Dr. John Holder

and Mr. Glem Baum is greatly appreciated. Especially, the authors would like to thank

Dr. Mengjiao Yu for his input.

81

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82

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83

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84

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85

Table 4-1 - Data used in simulation

Variables Values Bulk moduli of fluid , Kf 1.45×106psi Bulk moduli of solid , Ks 58×106psi

Bulk moduli of frame , Kfr 30.5×106psi

Porosity, φ 0.2

Biot constant, pα 1

Poisson’s ratio, ν 0.22

Permeability, k 2 nD Pore fluid viscosity, u 1 cp

Confining pressure, cσ 5000 psi

86

70

80

90

100

110

120

130

140

0.001 0.01 0.1 1 10

Strain Rate, 10-6/min.

Dev

iato

ric S

tren

gth,

MPa

Undrained Conditions

Drained Conditoins

Figure 4-1 – Effects of strain rate on deviatoric strengths for Kimmeridge Bay Shale under undrained and drained conditions (after Swan & Cook et al., 1989).

0

0.5

1

1.5

2

2.5

3

3.5

1 10 100 1000 10000 100000

Strain Rate, 10-8 S-1

Stre

ngth

, Kba

r

T=20 CT=200 CT=300 CT=400 C

Figure 4-2 – Effects of temperature and strain rate on strengths of Galena ore (after Atkinson, 1976).

87

0

1

2

3

4

5

10 100 1000 10000


Stre

ngth

, Kba

r

T=300 C

T=350 C

T=400 C

T=450 C

Figure 4-3 – Effects of temperature and strain rate on strengths of Anhydrite (after Muller and Briegel, 1978).

0

20

40

60

80

100

120

0 20 40 60 80 100

Effective Confining Pressure, MPa

Dev

iato

ric S

tren

gth,

MPa

Theoretical Results

Experimental Results( COOK, 1990)

Figure 4-4 – Effects of confining pressure on deviatoric strength.

88

40

45

50

55

60

65

70

-10 -6 -2 2 6 10

Pore Pressure, MPa

Dev

iato

ric S

tren

gth,

MPa

Figure 4-5 – Effects of pore pressure on deviatoric strength.

0

1

2

3

4

5

6

0 5 10 15 20 25 30 35 40Sample Length, mm

Pore

Pre

ssur

e, M

Pa

t=10 minutes t=20 minutest=30 minutes t=40 minutes

Figure 4-6 – Time-dependent pore pressure build-up.

89

0

0.4

0.8

1.2

1.6

2

0 5 10 15 20 25 30 35 40Sample Length, mm

Pore

Pre

ssur

e, M

Pa

Sr=2e-6 Sr=4e-6

Sr=6e-6 Sr=8e-6

Figure 4-7 – Effect of strain rate on the pore pressure build-up.

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20 25 30 35 40

Sample Length, mm

Pore

Pre

ssur

e, M

Pa

K=1 nDK=2 nDK=3 nDK=4 nD

Figure 4-8 – Effect of permeability on pore pressure build-up.

90

Figure 4-9 – Fracture propagation at high pore pressure.

91

Figure 4-10 – Strength test equipment.

Heat shrink Tube Sample 0.75”X0.75”X1.5”

Open to Air Open to Air

Porous Disk

Porous Disk

Porous Screen

92

0

1000

2000

3000

4000

5000

6000

0 10 20 30 40 50 60 70

Time, minute

Con

fing

Pres

sure

, psi

0

1000

2000

3000

4000

5000

6000

Pore

Pre

ssur

e, p

si

Figure 4-11 – Pore pressure change after applying 5 000 psi confining pressure (Pierre I shale).

93

0

1000

2000

3000

4000

5000

6000

0 10 20 30 40 50 60 70Time, minute

Con

fing

Pres

sure

, psi

0

1000

2000

3000

4000

5000

6000

Pore

Pre

ssur

e, p

si

Figure 4-12 – Pore pressure change after applying 5 000 psi confining pressure (Arco shale).

0

1000

2000

3000

4000

5000

6000

0 20000 40000 60000 80000

Micro-strain

Dev

iato

ric S

tres

s, p

si

Sr=1.2E-5Sr=3.4E-5Sr=5.9E-5

Figure 4-13 – Effect of strain rate on stress-strain curves for Pierre I shale.

94

3000

3500

4000

4500

5000

5500

6000

0 2 4 6 8 10


Dev

iato

ric S

tren

gth,

psi

Figure 4-14 – Effect of strain rate on peak strengths of Pierre I shale.

Pp = 458.35Sr - 2.841R2 = 1

0

1000

2000

3000

4000

0 2 4 6 8 10


Pore

Pre

ssur

e, p

si

Figure 4-15 – Effect of strain rate on pore pressure build-up of Pierre I shale.

95

0

2000

4000

6000

8000

10000

12000

14000

0 10000 20000 30000 40000 50000

Micro Strain

Dev

iato

ric S

tres

s, p

si

Sr=3.6E-5Sr=4.1E-5Sr=5.4E-5

Figure 4-16 – Effect of strain rate on stress-strain cures for Arco shale.

10000

11000

12000

13000

14000

0 1 2 3 4 5 6 7


Dev

iato

ric S

tren

gth,

psi

Figure 4-17 – Effect of strain rate on peak strengths of Arco shale.

96

Pp = 455.73Sr - 1.6143

R2 = 1

0

500

1000

1500

2000

2500

3000

0 2 4 6 8Strain Rate, 10-5 S-1

Pore

Pre

ssur

e, p

si

Figure 4-18 – Effect of strain rate on pore pressure build-up of Arco shale.

97

Chapter 5 : A New Gravimetric – Swelling Test for Evaluating Water and Ion Uptake in Shales

ABSTRACT

The primary cause of wellbore instability is the interaction of water-based muds

with shales. The movement of water and ions into or out of a shale can result in large

changes in pore pressure in the vicinity of the wellbore, potentially leading to wellbore

failure.

A new method, the Gravimetric–Swelling Test (GST), for determining the

expansion and movement of water and ion between shale and drilling fluids is presented

in this chapter. Experimental protocols and equations are presented that describe how

such measurements can be conducted and interpreted with relative ease. GST allows for

the determination of the mass of water and ions entering or leaving shale samples. With

additional and separate swelling measurements, the impact of the water and ions uptake

on swelling pressures generated can also be obtained.

In this chapter, results are presented for two preserved shale samples. The

influence of different types of ionic solutions on water and ion movement is presented for

each shale. It is shown that water uptake and swelling of shales is controlled not only by

differences between shale water activity and mud water activity (as assumed in the past),

but ion type and concentration also play an important role. In these tests it is shown that

with increasing salt concentrations water uptake decreases, while the ion adsorption

increases. Different types of cations are shown to have a large influence on water/ion

movement.

This chapter presents a data set showing the influence of ion type and

98

concentration on water uptake by shales. The role of capillary pressure, osmotic effects,

and ionic diffusion on swelling behavior of shales is also discussed. The technique

presented herein may possibly be used at the rig-floor to determine the compatibility of

shales with salt-water drilling fluids.

99

5.1 INTRODUCTION

It is believed that the main cause of shale instability stems from unfavorable

interactions between water - based muds and shale formations (Chenevert, 1970; Bol,

1992; Van Oort, 2003). Shale instability is generally caused by pore pressure changes and

mechanical property alterations around the wellbore, induced by chemical, hydraulic, and

electrical effects. Both pore pressure and mechanical property alterations are caused by

water and ion movement into or out of the shale formations. Chenevert (1970) showed

that differences in water activity could cause an osmotic flux of water into or out of shale.

Ballard et al. (1992) developed an experimental technique using radioactive tracers to

monitor water and ion movement in shale and found it to be a diffusion-dominated

process under zero applied pressure. They suggested that concentration gradients were

the driving force for the transfer of ions into or out of shale. Van Oort (1997) attributed

pore pressure changes to the flux of water and ions.

A considerable body of research concerning moisture adsorption in shales and

clays has shown that absorbed water leads to clay layers expanding (swelling) and

consequently a decrease in the interlayer-bonding and shale strength. The decrease in

shale strength associated with the water adsorption results in eventual material failure. In

the case of a wellbore being drilled through shale, this failure leads to the collapse of the

wellbore wall and often completes borehole failure.

It is also known that the amount of absorbed water, as well as the impact of the

absorbed water on material properties, is altered by the presence of ions in the solution

(Bol, 1986). Yu et al. (2001) developed a model to predict the flux of both water and ions

into or out of shale. They found that the difference in water activity between the drilling

fluid and the shale formation induced water movement, which changes the pore pressure

distribution. In addition to changes in pore pressure distribution, the movement of water

100

and ions also affects the mechanical properties of shales, such as strength, modulus of

elasticity etc. Hale et al. (1992) measured the mechanical properties of shale after

exposure to oil-based muds. They found that shale strength increased when the activity of

the mud was low enough to remove water from shale.

In studying wellbore instability in shale formations, one of the most important and

widely studied problems is shale swelling (Chenevert, 1970; Steiger, 1993). It is widely

believed that shales swell when interacting with drilling fluids due to osmotic effects.

Some researchers have postulated that capillary effects due to the dehydration of shales

cause swelling of shales during coring and sample preparation (Santarelli, 1995;

Carminati, 1997). Other researchers believe that shale swelling is caused by the physio-

chemical interactions of drilling fluids with reactive components present in shales such as

montmorillonite (Norrish, 1954). We believe that understanding the causes of shale

swelling is critical in drilling fluid optimization and wellbore stability control. If shale

swelling is only caused by the capillary effects which are probably not present downhole,

then mechanical effects should be the primary concern during drilling. On the other hand,

if osmotic effects also influence the shale swelling, then drilling fluid chemistry should

be optimized to inhibit such swelling.

It is shown in this chapter that, depending on the laboratory procedures used; both

capillary pressure and osmotic effects can be significant. In addition, it is shown that

ionic diffusion plays a very important role in shale swelling behavior.

From the above review, we can see that the movement of water and ions into or

out of shale when interacting with a water-based fluid is critical for maintaining wellbore

stability. Quantitatively measuring the movement of water and ions during interaction

with a drilling fluid is, therefore, of great importance in studying wellbore instability

mechanisms.

101

Although various authors have measured water movement into and out of shale,

there is currently no simple way to monitor the movement of water and ions. This

chapter presents a Gravimetric-Swelling Test (GST) for measuring the quantity of water

and ions entering/leaving the shale after coming in contact with aqueous solutions or

drilling muds. We believe that this test is important to the proper design of drilling fluids

and the maintenance of wellbore stability because it can potentially be used on the rig

floor.

In addition to presenting the GST method, data showing the influence of ionic

concentration and type on water and ion movement into and out of shales are provided.

5.2 GRAVIMETRIC-SWELLING TEST (GST)

GST consists of performing two independent tests: a gravimetric test and a

swelling test using a single test sample. In doing so, only one sample is needed, instead of

two, and a direct comparison can be made between the two sets of data because sample

variation has been eliminated.

5.2.1 Apparatus

When performing the gravimetric measurements, a top loading balance model GT

410 made by OHAUS Corporation was used. This electrical balance, that has a resolution

of 1 mg, was employed for weighing samples, and it met our accuracy requirements very

well.

For the displacement measurements, a digimatic indicator, Model ID-110 E was

used. Figure 5-1 shows a schematic of the equipment used and a photo of this transducer

is shown in Figure 5-2. The measuring range of the transducer is 10mm, with a resolution

of 0.001mm. This transducer shows good reproducibility and suits this study very well.

The threaded anvil can be adjusted according to the original length of the sample.

102

5.2.2 Experimental Procedures

When performing the GST, the following procedures were followed. A sample

with the dimension of 0.5 "×0.75 "×1.0 " was taken out of the storage can and quickly

washed using “ Skelly-B” to remove all surface oil. Its preserved weight in air (Wp) was

obtained. It was then placed in a small plastic bag. The sample was positioned between

the movable and stationary anvils of the transducer. In order for the sample to be at the

same original stress and to obtain an indication of sample shrinkage, the threaded anvil

was adjusted until it read 1.27 mm (0.05 inch), thereby placing the sample in slight

compression. In this way a minus reading would be recorded if the shale shrank. The unit

was then set on zero. A 50 ml volume of solution was then poured into the plastic bag

and the bag was sealed immediately. As the fluid was poured, a stopwatch was started to

begin recording the elapsed time. Normally there was a roughly linear relationship

between swelling and the logarithm of time. The early stage readings were taken quite

frequently and then the interval became longer. Normally a complete test lasted for 24

hours. By dividing the displacement readings by the original length of the sample and

multiplying by 100, we obtain the linear swelling percentage. The sample was then taken

out of the solution and blotted dry with a paper towel before its “altered” weight (Wa)

was measured. Finally, it was dried at 200 ºF for 24 hours in an oven and weighed again.

Its “altered-dried-weight” was represented as Wad. After such information was obtained,

the ion and water movement during the interaction of the shale and the solution was

determined using equations (5-1) to (5-4).

Water and ion transport can be calculated using the equation:

pdpadawt WWWWW +−−= (5-1)

pdadit WWW −= (5-2)

103

In summary, the following equations can be used to calculate the weight percent

of water and ions gained or lost using the GST technique (see Appendix 4 for more

detailed information).

%100W

WWWW%W

p

pdpadawt ×

+−−=

(5-3)

%100W

WW%W

p

pdadit ×

−=

(5-4)

The definitions of the various terms used in our calculations are:

pW = Weight of preserved sample in air

pdW = Weight of preserved sample after drying

pwC = Preserved water content, weight percent

aW = Altered weight of sample after immersion in solutions

adW = Dry weight of altered sample

wpW = Weight of water in preserved sample = pwp CW ×

waW = Weight of water in altered sample

wtW = Weight of water transferred into (+) or out of (-) shale

wt%W =Normalized water transferred into (+) or out of (-) shale, %

itW = Weight of ions transferred into (+) or out of (-) shale

it%W =Normalized ions transferred into (+) or out of (-) shale, %

5.3 RESULTS AND DISCUSSION

5.3.1 Swelling Test Results for Pierre Shale Immersed in NaCl Solutions

Typical swelling test data obtained from the GST method for Pierre I shale

immersed in NaCl solutions are shown in Figure 5-3. It can be seen from this figure that,

all tests showed swelling during the first 30 minutes followed by shrinkage at later time.

104

Such a response raised the question: “What caused Pierre I shale to swell at early times

despite the fact that the shale had a higher water activity than the salt solutions?”

To better understand this early time swelling phenomena, we employed our new

GST method.

5.3.2 Time-dependent Gravimetric Test

Using the GST technique, the time-dependent response for Pierre I shale was

measured. Different samples were placed into 0.85 activity NaCl solutions. At different

times, each of these samples was taken out of the solution and weighed and dried for 24

hours in an oven. Water and ion movement at various times were calculated. Results for

Pierre I are shown in Figure 5-4.

From Figure 5-4, we see that the Pierre I shale lost water and gained ions over

time. It can also be seen that at early time it gained water even though its water activity

(0.98) was higher than the water activity of the NaCl (0.85). This observation is

consistent with our swelling test results (Figure 5-3). The early time swelling and weight

gain must be caused by water uptake by the shale. Since there is no osmotic pressure

gradient driving the water into the shale (in fact, osmosis should be extracting water out

of the shale under those conditions), the water uptake observed gravimetrically and in the

swelling tests must be caused by surface capillary effects.

5.3.3 Experimental Confirmation of Early-Time Capillary Effects.

In order to check our hypothesis that capillary pressure effects were causing the

initial swelling, we ran a swelling test with a Pierre I shale immersed in a simulated pore

fluid that was formulated based on pore fluid compositional data as shown in Table 5-1.

The result is shown in Figure 5-5.

It can be seen from Figure 5-5 that Pierre I shale experienced significant swelling,

especially at early time, when immersed in simulated pore fluid. Since the simulated pore

105

fluid has nearly identical ionic composition and water activity, as does the shale, one can

assume that osmosis and ionic diffusion effects are negligible. Therefore, the early time

swelling behavior observed is probably due to capillary effects. The presence of capillary

effects is because the sample surfaces have been altered during the sample preparation

process. Such effects can distort the data and lead to false conclusions. Capillary effects

are probably not present in downhole shales since they are usually fully saturated.

Therefore, it is important to eliminate capillary pressure effects from our laboratory data

in order to better analyze the results. This was done as follows.

The simulated pore fluid was used as a base line to correct for capillary effects in

all our data for Pierre I shale. This base line swelling was subtracted from all of our

swelling measurements to obtain the “true” swelling due to osmotic effects.

Figure 5-6 shows results of correcting Figure 5-3 for capillary effects. It can be

seen from Figure 5-6 that, except for deioned water, Pierre I shale shrank when exposed

to NaCl solutions because of osmotic effects, as was expected based on osmotic concepts.

After correcting Figure 5-4 for capillary effects, the time dependent water and ion

movement for the 19 wt % NaCl test is shown in Figure 5-7. Water was removed while

the ions were adsorbed because of osmotic and ionic diffusion effects. More water is

removed and more ions are adsorbed with time. Such corrected results are consistent with

osmotic fluid transfer theory.

5.3.4 Influence of NaCl Solutions on Water/Ion Movement

After correcting for capillary surface effects, the influence of NaCl solutions on

water/ion movement into/out of Pierre I is shown in Figure 5-8. It can be seen that when

the salt concentration increases, free water is removed because of osmotic effects and

ions are added due to diffusion effects. It is interesting to note that, this may explain why

high salinity salt-water muds often act in an inhibitive manner.

106

5.3.5 Swelling Properties of Pierre I Shale Immersed in CaCl2, KCl and KCOOH Solutions

The swelling behavior including capillary and osmotic effects, for Pierre I shale

exposed to CaCl2 solutions is shown in Figure 5-9. It can be seen that, the Pierre I shale

experienced early time swelling when exposed to CaCl2 solutions. According to our

earlier analysis, we believe that capillary effects caused this early time swelling (about 30

minutes).

After correcting Figure 5-9 for capillary effects, Figure 5-10 was obtained, which

shows the swelling due only to osmotic and ion diffusion effects.

It can be seen that, as expected, Pierre I shale shrank at the beginning of the test

and then it swelled. Once the shale was exposed to the CaCl2 solution, water was

extracted because the water activity in the shale is higher than that in the solutions.

Meanwhile, ions are entering the shale due to diffusion effects. The water extraction

causes the shale to shrink, while ion adsorption causes shale expansion. This is because

of the large hydrated calcium ions, as shown in Table 5-2. However, the rate of water

extraction is much higher than the rate of ion adsorption, which makes the sample shrink.

Some time later, the water activity difference is reduced because of the water and ion

movement and the swelling behavior of the shale become dominated by ion diffusion.

Therefore, the shale exhibited expansion with the ions that were adsorbed. When Pierre I

shale was exposed to low concentration CaCl2 solutions, expansion occurred after about

two hours. This demonstrates the time-dependent wellbore instability phenomena. It is

plausible that when shale is exposed to salt water muds, it is stable at first because of

water extraction, then, some time later, ionic diffusion dominates the swelling behavior

of shale.

Many authors have published on the effect of potassium ions on wellbore stability

(Clark et al., 1976; Walker et al., 1984; Pruett, 1987; Bostrom et al., 1998; Van Oort

107

2003). It is shown herein that the exchange of the sodium and calcium ions on the clay

surfaces with potassium can minimize clay swelling and thereby strengthen the shale,

which is beneficial for wellbore stability (Pruette 1987; Bostrom et al., 1998). Two

potassium salts, KCl and KCOOH were used in our tests.

The swelling behavior, including capillary and osmotic effects for Pierre I shale

exposed to KCl and KCOOH solutions are shown in Figure 5-11 and Figure 5-12

respectively.

Once again, we believe that capillary effects cause the early time swelling. After

correcting Figure 5-11 and Figure 5-12 for capillary effects by using Figure 5-5, the

swelling behavior of Pierre I shale for KCl and KCOOH solutions is shown in Figure 5-

13 and Figure 5-14. The shale shrinks quickly at early time, and then its shrinkage rate

slows down. Compared to CaCl2 solutions, more shrinkage was observed when the shale

was exposed to KCl solutions under similar water activity conditions. This could be

attributed to the difference in the radius of the hydrated calcium and potassium ions.

Table 5-2 shows that the hydrated radius for potassium ions is smaller than that for

calcium ions. Therefore shale swelling when exposed to potassium salts is smaller than

that when exposed to calcium chloride.

Compared with the NaCl, CaCl2 and KCl solutions, the KCOOH solutions

provided different swelling behavior. Normally, less swelling is found when Pierre I

shale was exposed to more concentrated NaCl, CaCl2 and KCl solutions. However, this

phenomena is not be observed when Pierre I shale was exposed to KCOOH solutions. For

example, Pierre I shale shrank more when exposed to a 10 wt% solution than when

exposed to a 20 wt% KCOOH solution. This phenomenon was also observed by Van oort

(2003). There is no reasonable explanation for this phenomenon, so further study is

needed.

108

5.3.6 Effect of Salt Concentration on Water/Ion Movement

Figure 5-15 shows the influence of CaCl2 and KCl concentration on water/ion

movement into/out of the Pierre I shale after 24 hours of exposure and after correcting for

capillary effects. It can be seen that when the salt concentration increases, free water was

removed because of the osmotic effects and ions were added due to diffusion effects.

Compared with KCl, more water was removed and more ions were adsorbed when Pierre

I shale was exposed to CaCl2 solutions at the same concentration. This occurred because

the water activity of the CaCl2 solution is lower than the water activity of KCl at the same

concentration, as shown in Figure 5-16. Therefore, more osmotic effects took place when

Pierre I shale was exposed to CaCl2 solution, which caused more water to be removed

from Pierre I shale.

5.3.7 Effects of Water Activity on Water/Ion Movement

After correcting for capillary effects, the influence of water activity on water/ion

movement is shown in Figure 5-17.

Just as expected, with decreasing water activity (increasing salt concentration),

more water was removed due to osmotic effects and more ions were absorbed because of

the ionic diffusion effect. Compared to NaCl solution exposure, more water was removed

and more ions were added when Pierre I shale was exposed to CaCl2 solutions at the

same water activity. It is believed that the osmotic effect is the same for both NaCl and

CaCl2 solutions at the same water activity. Ion movement is dominated by the

concentration gradient, which can be expressed by Fick’s law (Bird et al. 2002)

xC D- J

∆∆

×= (5-6)

As shown in Table 5-1, the sodium concentration in the shale pore fluid was

higher than the calcium concentration; therefore the concentration gradient for the CaCl2

109

solution was higher than that for NaCl. This difference in concentration resulted in more

calcium ions being added to Pierre I shale.

5.3.8 Experimental Results for Arco shale

Figures 5-18 and 5-19 show the swelling behavior, including capillary effects,

when Arco shale was exposed to NaCl and CaCl2 solutions of different concentrations.

We were not able to correct for the capillary effects since the pore fluid composition was

unknown. However, it can be argued that some early swelling might have occurred due to

surface capillary effects.

Figures 5-20 and 5-21 show the influence of salt concentration on water and ion

movement during interaction with Arco shale. It is important to mention that capillary

effects have not been corrected for in these figures.

5.3.9 Comparison Between Pierre I and Arco Shales

Compared with Pierre I shale, Arco shale experienced much more swelling when

it was exposed to similar solutions. It can be observed from Figures 5-3 and 5-18, and

Figures 5-9 and 5-19, that Arco shale experienced more early-time swelling. From the

previous analysis, this early-time swelling was attributed to capillary effects. Arco shale

was cored at great depth (15,000 ft), therefore more capillary effects were possibly

introduced during coring and sample processing. Pierre I was an outcrop shale, therefore

less capillary effects were possibly introduced. The increased swelling of Arco shale was

first caused by capillary effects. Secondly, we can see from the adsorption isotherm for

Arco shale that the water activity for Arco shale is 0.78, which is much lower than that

for Pierre I shale (0.98). It has a higher potential to absorb water from ionic solutions, and

therefore swells more.

110

5.4 LIMITATIONS OF THE GST From the above discussion, it can be concluded that the GST is a very simple

and effective method to directly measure water and ion uptake by shales immersed in

aqueous solutions. However, it cannot be used for very reactive shales that have high

dispersion tendencies. We tried to use this method to study Gumbo and Speeton shales

but they disintegrated too rapidly to obtain data.

5.5 CONCLUSIONS

1. A new simple method, GST has been developed that allows for the direct

measurement of water and ion movement into or out of a shale sample.

2. During sample preparation, should the shale experience any water loss,

air may enter the shale and thereby introduce capillary suction pressures.

Therefore, it is important to eliminate capillary effects when analyzing

data.

3. Time-dependent data from the GST technique show significant changes

in water and ion movement during the interaction between shales and

drilling fluids.

4. Different types of cations are shown to have different and large influences

on water/ion movement.

5. Combined with other tests, GST can be used to evaluate mud systems.

These tests are simple to conduct and, therefore, can be conducted at the

rig floor.

NOMENCLATURES C Concentration [=] amount / volume

111

pwC Preserved water content, weight fraction, %

D Diffusivity [=] L2/s

J The mass flux [=] amount / L2-t

pW Weight of preserved sample [=] m

itW Weight of ion transferred into (+) or out of (-) shale [=] m

pdW Weight of preserved sample after drying [=] m

aW Altered weight of sample by immersion in drilling fluid [=] m

wpW Weight of water in preserved sample [=] m, pwp CW ×

wtW Weight of water transferred into (+) or out of (-) shale [=] m

adW Dried weight of altered sample [=] m

waW Weight of water in altered sample [=] m

ACKNOWLEDGEMENTS

Special thanks are given to Dr. Russ Ewy, Dr Guizhong Chen, Dr. Rosana

Lomba, and Mr. Ben Bloys for their valuable suggestions. The assistance of Dr. John

Holder and Mr. Glem Baum is greatly appreciated. The authors would like to thank Dr.

Mengjiao Yu for his input.

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112

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Fonseca, C.F., and Chenevert, M.E.: “ The Effects of Stress and Temperature on Water Acitivity of Shales”, presented at the 3rd North American Rock Mechanic

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Richard V. Bovbjerc, and Peter W. Glynn: “ Saturated Solutions for the Control of Humidity in Biological Research”, Ecology, January 1960, Vol.41 No.1, 232-236.



Steiger, R. and Leung , P. K. (1991), “ Consolidated undrained triaxial test procedure for shales”, in Rock Mechanics as a Multidisciplinary Science, Balkema, Rotterdam.

Steiger, R.P. “ Advanced Triaxial Swelling Tests on Preserved Shale Cores”, presented at the 34th U. S. Symposium on Rock Mechanics (June 27-30, 1993) and to be published in the Int.J. Rock Mech. Min. & Geomech. Abstr. (1993).

Van Oort, E.: “ Physico-chemical Stabilization of Shales”, SPE paper 37263 presented at 1997 International Symposium on Colloid Chemistry, Houston, Texas, USA, Feb.

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18-21.


Walker, Thad O., Dearing, H.L. and Simpson, J.P.: “ The Role of Potassium in Lime Muds”, SPE 13161 presented at the 59th Annual Technical Conference and Exhibition held in Houston, Texas, September 16-19, 1984.

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Yu, M., Chen G., Chenevert, M. E., and Sharma, M. M.: “Chemical and Thermal Effects on Wellbore Stability of Shale Formations”, SPE71366, New Orleans, USA, Sept. 30-Oct. 3, 2001.

115

Table 5-1 - Pore fluid composition.

Cations/Ions Amount (meq/100 g) Potassium (K+) 0.7

Magnesium (Mg2+) 0.4 Sodium (Na+) 1.6

Calcium (Ca2+) 1.0 Chloride (Cl-) 1.1

Carbonate (CO32-) 0

Bicarbonate (HCO3-) 6.7

Sulfide (S2-) 0.2

Table 5-2 - Dehydrated and hydrated radii of cations (after Pruett, 1987)

Ions

Dehydrated (Angstrom)

Hydrated (Angstrom)

Li 0.78 10.03 Na 0.98 7.9 K 1.33 5.32

NH4 1.43 5.37 Mg 0.78 10.8 Ca 1.06 9.6

116

Figure 5-1 – Schematic of equipment used to measure linear swelling of shale.

117

Figure 5-2 – Photo of swelling transducer.

118

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0 300 600 900 1200 1500

Time, Minutes

Swel

ling

Perc

enta

ge, %

aw=1 Deioned wateraw=0.95 NaClaw=0.85 NaClaw=0.75 NaCl

Figure 5-3 – Swelling of Pierre I shale immersed in NaCl solutions.

-1

-0.5

0

0.5

1

1.5

2

0 200 400 600 800 1000 1200

Time, Minutes

Wat

er/Io

ns G

ain/

Loss

(%) WaterIonsNet

Figure 5-4 – Time-dependent water and ion movement for Pierre I shale immersed into 0.85 aw NaCl solution.

119

0

0.1

0.2

0.3

0.4

0.5

0 300 600 900 1200 1500

Time, Minutes

Swel

ling

Perc

enta

ge, %

Figure 5-5 – Swelling of Pierre I shale immersed in simulated pore fluid.

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0 300 600 900 1200 1500

Time, Minutes

Swel

ling

Perc

enta

ge, %

aw=1 Deioned wateraw=0.95 NaClaw=0.85 NaClaw=0.75 NaCl

Figure 5-6 – Corrected swelling of Pierre I shale immersed in NaCl solutions.

120

-0.5

0

0.5

1

1.5

0 200 400 600 800 1000 1200

Time, Minutes

Wat

er/Io

ns G

ain/

Loss

, %WaterIonsNet

Figure 5-7 – Corrected time-dependent water and ion movement Pierre I shale immersed

in 0.85 aw NaCl solution.

-1

-0.5

0

0.5

1

1.5

2

0 5 10 15 20 25 30

Salt Concentration, %

Wat

er &

Ions

Mov

emen

t, % Water

Ions

Figure 5-8 – Influence of NaCl concentration on water/ion movement for Pierre I shale.

121

0

0.1

0.2

0.3

0.4

0.5

0 300 600 900 1200 1500Time, Minutes

Swel

ling

Perc

enta

ge, %

aw=0.95 CaCl2aw=0.85 CaCl2aw=0.75 CaCl2

Figure 5-9 – Swelling of Pierre I shale immersed in CaCl2 solutions.

-0.4

-0.3

-0.2

-0.1

0

0.1

0 300 600 900 1200 1500

Time, Minutes

Swel

ling

Perc

enta

ge, %

aw=0.95 CaCl2aw=0.85 CaCl2aw=0.75 CaCl2

Figure 5-10 – Corrected swelling of Pierre I shale immersed in CaCl2 solutions.

122

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 300 600 900 1200 1500Time, Minutes

Swel

ling

Perc

enta

ge, %

10 % KCl20% KCl25.5 % KCl

Figure 5-11 – Swelling of Pierre I shale immersed in KCl solutions.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 300 600 900 1200 1500

Time, Minutes

Shal

e Ex

pans

ion,

%

10% KCOOH20% KCOOH30% KCOOH40% KCOOH

Figure 5-12 – Swelling of Pierre I shale immersed in KCOOH solutions.

123

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0 300 600 900 1200 1500

Time, Minutes

Swel

ling

Perc

enta

ge, %

10 % KCl

20% KCl

Figure 5-13 – Corrected swelling of Pierre I shale immersed in KCl solutions.

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0 300 600 900 1200 1500

Time, Minutes

Swel

ling

Perc

enta

ge, %

10% KCOOH20% KCOOH30% KCOOH40% KCOOH

Figure 5-14 – Corrected swelling for Pierre I shale immersed in KCOOH solutions.

124

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20 25 30


Wat

er/ I

ons

Gai

ned/

Loss

KCl, WaterKCl, IonsCaCl2, WaterCaCl2, Ions

Figure 5-15 – Influence of CaCl2 and KCl concentration on water/ion movement for Pierre I shale.

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50

Salt Concentration, w%

Wat

er A

ctiv

ity

CaCl2NaClKCl

Figure 5-16 – Water activities of CaCl2, NaCl, and KCl solutions at room temperature.

125

-1.5

-0.5

0.5

1.5

2.5

0.7 0.75 0.8 0.85 0.9 0.95 1

Water Activity

Wat

er/ I

ons

Gai

ned/

Loss

, %CaCl2, WaterCaCl2, IonNaCl, WaterNaCl, Ion

Figure 5-17 – Effects of water activity on water/ions movement for Pierre I shale.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 300 600 900 1200 1500

Time, Minutes

Swel

ling

Perc

enta

ge, %

aw=1 Deioned Wateraw=0.95 NaClaw=0.85 NaClaw=0.75, NaCl

Figure 5-18 – Swelling of Arco shale immersed in NaCl solutions.

126

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 300 600 900 1200 1500

Time, Minutes

Swel

ling

Perc

enta

ge, %

aw=0.95 CaCl2aw=0.85 CaCl2aw=0.75, CaCl2

Figure 5-19 – Swelling of Arco shale immersed in CaCl2 solutions.

-1

-0.5

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20 25 30


Wat

er/Io

ns M

ovem

ent,

% NaCl, WaterNaCl, Ions

Figure 5-20 – Effect of NaCl concentration on water/ion movement for Arco shale.

127

-1

-0.5

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20 25 30Salt Concentration, %

Wat

er/Io

ns M

ovem

ent,

% CaCl2, Water

CaCl2, Ions

Figure 5-21 – Effects CaCl2 concentration on water/ion movement for Arco shale.

128

Chapter 6 : The Effect of Ion Movement on Shale Swelling

ABSTRACT

The movement of water and ions into or out of shales causes physiochemical and

mechanical property alterations, and can lead to wellbore instability problems.

This chapter presents three series of experiments which analyze the effects of

chemical osmosis, diffusive osmosis, and capillary suction on water and ion movement

when shales interact with salt solutions. Results show that water movement is not only

controlled by chemical osmosis (water activity), but is also influenced by diffusive

osmosis and capillary suction. It was found that the immersion of shale into salt solutions

changes the chemical composition of the shale due to ion movement, and thus its

physicochemical and mechanical properties are altered. By applying the gravimetric-

swelling test (GST) to the various tests presented here, a deeper insight into the

relationship between water flow, ion flow, and swelling is obtained.

129

6.1 INTRODUCTION

Wellbore instability in shale formations has been a significant problem for many

years. As discussed in Chapter 5, the primary cause of this problem is the unfavorable

interactions between shales and water-based muds (WBMs) (Chenevert, 1969; Bol, 1992;

Carminati, 2001; Ewy et al., 2002; van Oort, 2003). Although such interactions,

including chemical, physical, hydraulic, mechanical, thermal, and electrical phenomena,

are very complicated (Maury et al., 1987; Mody et al., 1993; van Oort, 1997; Chen et al.,

2003), the primary cause is related to the movement of water and ions into or out of a

shale. The physiochemical and mechanical properties of shale around the wellbore, such

as permeability, pore pressure, swelling, strength, and elastic modulus are altered due to

such movement (Chenevert, 1969; Hale et al., 1992; Carminati, 2001).

The mechanisms for water and ion movement are convection and chemical

activity driven. The hydrostatic pressure difference between a drilling fluid and the

formation pore fluid causes convective flow. Chemical activity effects include osmosis,

diffusion, and capillary effects (Mody et al., 1993; Lomba et al., 2000; Ewy et al., 2000;

Simpson et al., 2002).

By considering shale as a semi-permeable membrane that allows the movement of

water and restricts the movement of ions, Low and Anderson (1958) presented an

osmotic pressure equation for determining the swelling of soils. Their theory suggested

osmosis as a mechanism for explaining the movement of water and ions during

interactions between a shale and a drilling fluid. Chenevert (1970) successfully used this

osmotic pressure theory to explain shale stability control with oil-based muds (OBMs),

using the concept of “balanced water activity”. Simpson (1971) also suggested that a

shale body in contact with a WBM could act as a semi-permeable membrane. However,

there are no experimental data to justify Simpson’s statements. Hale et al. (1992)

130

conducted an experimental study on the effects of chemical potential on wellbore

stability. They concluded that the difference in chemical potential between shales and

OBMs is one of the fundamental driving forces for the movement of water into or out of

shale.

Although it is well accepted that an OBM has excellent semi-permeable

membrane components, it has always been a point in dispute whether or not the shale can

act as an effective membrane that can control water and ion movement when contacted

by a WBM. Using radioactive tracers, Ballard et al. (1992) investigated water and ion

transport through shales and concluded that the shales and fluids they studied did not act

as semi-permeable membranes and that ions can freely diffuse through them. Bol et al.

(1992) came to the same conclusion after performing other experiments. However, the

shales used in both studies had a high permeability and therefore did not represent typical

highly compacted shales found in highly stressed environments.

Fritz et al. (1983, 1986) supported osmosis as a possible mechanism for

controlling water and ion movement, and they recognized that clays are not “ideal”

membranes. They felt that the ideality of a clay membrane is a function of cation

exchange capacity (CEC), porosity, and the concentration of ions in the pore fluid. Mody

and Hale (1993) found in their study that the shale’s membrane efficiency was also a

function of confining pressures. Recent work concluded that membrane efficiencies of

shales were in the range from 0.18 % to 4.23% when contacted by WBMs (AL-Bazali,

2005).

The movement of water and ions into or out of shale is critical to wellbore

instability. In this study, we investigated such movement by performing various

gravimetric and swelling experiments using several different shales and ionic solutions. It

was found that all movement was driven by an imbalance in the chemical activity of

131

water and ions. This includes mechanisms often referred to as chemical osmosis,

diffusive osmosis, and capillary suction. No convection experiments were performed in

this study.

6.2 MECHANISMS CONTROLLING THE MOVEMENT OF WATER AND IONS

In a general sense, all movement of water and ions is governed by the imbalance

of water and ion chemical potentials as reflected in their chemical activities. Although the

literature often refers to various mechanisms for such movement, the basic chemical

property involved is activity.

6.2.1 Chemical Osmosis

By definition, the chemical potential of an aqueous system is the partial molar

free energy of the water with respect to a given component at constant pressure and

temperature. It is this coefficient that describes the way the Gibbs free energy of a system

changes per mole of component if the temperature, pressure, and number of moles of all

components are held constant. For a system in equilibrium, the chemical potential of each

component must be the same in all phases.

It is difficult to directly measure the chemical potential of a system, however, the

chemical potential of the water phase can be closely estimated through its water activity.

It is most difficult to independently measure the chemical potential of the ions, however,

their effect on water activity is well known.

By definition, the water activity ( ia ) of a shale is related to the free energy by the

equation:

( )i0

ii alnRT+µ=µ (6-1)

The water activity of the shale is an excellent indicator of the shale’s state of

hydration and its potential to absorb water. Unfortunately, this parameter cannot be

132

measured directly. In the laboratory, it is determined by measuring the relative aqueous

vapor pressure of the atmosphere above the shale using the following relationship

(Chenevert, 1970)

0shale,w P

Pa ≅ (6-2)

Using thermodynamic principles and the classical concept of an osmotic cell, Low

and Anderson (1958, 1987) derived the following equation to determine the osmotic

pressure that could develop between a shale and a mud.

⎟⎟⎠

⎞⎜⎜⎝

⎛−=π

mud,w

shale,w

w aa

lnVRTP

. (6-3)

It should be pointed out that for an osmotic pressure to develop that is equal to the

theoretical osmotic potential defined by the above equation, a perfect membrane

restricting ion movement must exist. As discussed previously, studies have shown that a

shale does not act as a perfect semi-permeable membrane when contacted by a WBM, so

a membrane efficiency term ( mI ) is introduced to correct for the “non-ideality” (Fritz et

al. 1983, 1986). The non-ideal osmotic pressure equation becomes;

⎟⎟⎠

⎞⎜⎜⎝

⎛−=π

mud,w

shale,w

wm a

aln

VRTIP

(6-4)

The membrane efficiency term ( mI ) has been discussed in detail in the

dissertation of AL-Bazali (2005).

As shown in Figure 6-1, the following cases can be highlighted from Equation (6-

4): 1) mud,wshale,w aa < , chemical osmosis flow of water into the shale

increases the water content and the pore pressure near the wellbore wall, and

thus destabilizes the wellbore;

133

2) mud,wshale,w aa = , no aqueous chemical osmosis flow; and

3) mud,wshale,w aa > , chemical osmosis flow out of the shale is beneficial

in terms of wellbore stability because this back flow reduces the near

wellbore pore pressure and thereby “strengthens” the shale.

6.2.2 Diffusive Flow

Although the movement of ions is restricted due to cation exchange and

negatively charged clay surfaces, a shale cannot completely prevent such movement

because it does not act as a perfect semi-permeable membrane. The diffusion of ions with

their associated water is dominated by a concentration gradient that can be expressed by

using Fick’s law (Bird et al., 2002)

⎟⎟⎠

⎞⎜⎜⎝

⎛∆

−=

xCC

D- J mud,ishale,isi

(6-5)

Here siD is the diffusion coefficient of the ith ion in the shale. In general thi will

be smaller than the bulk diffusion coefficient.

Similarly, the following cases can be highlighted from Equation (6-5): 1) mud,ishale,i CC < , diffusive flow of hydrated ions into shale;

2) mud,ishale,i CC = , no diffusive flow; and

3) mud,ishale,i CC > , diffusive flow of hydrated ions out of shale.

6.2.3 Capillary Suction

When a wetting phase, such as pore water, comes into contact with a non-wetting

phase, such as air, surface tension forces, aw−σ , develop at their interfaces (Schmitt et

al., 1994). These surface tension forces give rise to capillary pressures, which can be

expressed as:

134

r

cos2PPPP a-w

wacθσ

=−==∆ (6-6)

In classical capillary pressure diagrams, such as shown in Figure 6-2, the rise of

liquid level from the dish into the capillary tube is governed by Equation (6-6). These

surface tension forces result in the reduction of the vapor pressure of the water just above

the meniscus ( mP ) relative to the vapor pressure of the water in the solution ( sP ). Thus

we have an aqueous activity imbalance that governs this capillary rise, i.e., wswm aa <

where 0

mwm P

Pa ≅ and

0

sws P

Pa ≅ (Chenevert, 1970).

There has been much discussion regarding the mechanisms whereby water is

driven into a shale. One camp has postulated that it is driven by the presence of clays and

ions that results in a reduced water activity environment (Norrish 1954; Chenevert,

1970). The other camp insists that such surface forces could not exist, and the water flow

is driven by capillary suction only (Santarelli et al., 1995). It is very difficult, if not

currently impossible, to settle this conflict from direct experimental observations because

of the complexity of shale composition, and the submicroscopic site of such clay surfaces

and capillarities. It should be pointed out that such arguments are not important and that

the key is water activity. The intensity of water moved by either mechanism is reflected

in its activity. Thus, the measurement of the net water activity of shale reflects the

intensity of the driving forces regardless of being caused by clay surfaces, ions, or

capillaries.

6.2.4 Convective Flow

Convective flow is governed by the Darcy equation (Bird et al., 2002):

( )gpkv0 ρ−∇µ

−= (6-7)

135

where p∇ is pressure gradient between hydraulic mud pressure and pore pressure. This

flow is quite slow as the result of a relatively low-pressure gradient ( p∇ ) that typically

exists for most drilling operations and the extremely low permeability (k) of shale. This

well-known mechanism for water and ion movement will not be discussed in this chapter.

6.3 RESULTS AND DISCUSSIONS FOR WATER AND ION MOVEMENT TESTS

The first series of experiments was performed in order to study the mechanisms

controlling the movement of water and ions when shales interact with various ionic

solutions.

6.3.1 Desiccator-Immersion-Desiccator Test

The following experimental steps are designed to study the effects of chemical

osmosis, capillary suction, and diffusive flow on the movement of water and ions into or

out of shales:

Step 1: Three Pierre I and three Arco shale samples were placed in a

controlled relative humidity environment of 85% (aw = 0.85)

desiccator, weighed and recorded as 185.0W − after equilibrium was

achieved.

Step 2: The above “conditioned” samples were then immersed into 0.85 aw

KCl, 0.85 aw NaCl, and 0.85 aw CaCl2 solutions separately for 24

hours, and then removed, weighed, and their altered weights recorded

as aW .

Step 3: These samples were then placed back into a 85% controlled relative

humidity desiccator until equilibrium was reached. Their weight was

recorded as 285.0W − .

Step 4: The final step consisted of drying them out, by placing them in a

200ºF oven for 24 hours. Their “dried” weight was recorded as adW .

136

We will first discuss the result of one Pierre I shale sample, then later discuss the

results for all tests as a group.

6.3.1.1 Result for Pierre I shale/NaCl solution test

In order to determine the water and ion weight change during each step of the

process, it was necessary to know the initial water content of the Pierre I and Arco shales.

This was done by drying one separate native sample of Pierre I and one Arco shale in a

200ºF oven overnight, as discussed in Chapter 2. We will refer to these as native weight

(Na) and dried weight (Nd).

Using such measurements, it was possible to obtain the change of weight (relative

to dry weight) of the Pierre I when it interacted with 0.85 aw NaCl solution during the

above four steps (shown in Figure 6-3).

In Figure 6-3, “Na” represents the native state of a Pierre I sample. After this

native sample was dried, it lost 10.2 wt% of water and turned into a dried state. This dried

weight was selected as the base weight, so its weight change is zero, shown as “Nd” in

Figure 6-3. For the native Pierre I shale equilibrated in the 0.85 aw atmosphere, it lost 4.1

wt% water, so its weight change is 6.1 wt% compared to the dried weight, as shown in

“Step 1”. In this state, equilibrium was reached by means of “gaseous osmosis”. Under

such conditions, the Pierre I sample was not brought into contact with liquid water, so

water molecules moved by means of the third phase - gaseous phase. Equilibrium was

established between the shale and the solution through their vapor pressure. Since there

was no ion movement, the atmosphere can be taken as a perfect semi-permeable

membrane, and water movement is caused by chemical osmosis. This amount of water

loss (4.1 wt%) was driven by the water activity difference between the 0.98 aw Pierre

shale and the conditioned 0.85 aw atmosphere.

After Step 1, the Pierre I sample was immersed into a 0.85 aw NaCl solution. Its

137

weight increased by 11.8 wt% as shown in “Step 2” of Figure 6-3. This weight increase

(including water and ion movement) was primarily caused by ion and water diffusion.

After Step 2, water was removed from the sample in two steps, first it was placed

in a 0.85 aw atmosphere (Step 3), and then it was dried out in an oven (Step 4). In Step 3

we see that it has a larger weight change as compared to Step 1, even though the sample

was exposed in Step 1 to a 0.85 atmosphere and in Step 2 to a 0.85 aw NaCl solution.

From this comparison, we concluded that hydrated ions must have been diffusing into the

shale.

By drying the shale in Step 4, we observe that ions have definitely entered the

shale, its weight has increased by 0.64 wt% as compared to the dried native weight, “Nd”

in Figure 6-3.

6.3.1.2 Results for Pierre I shale/ KCl and CaCl2 tests

The results for Pierre I shale interacted with 0.85 aw solutions of KCl and CaCl2

are shown in Figures 6-4 and 6-5 respectively.

Comparing the amount of water loss in “Step 1” among the three Pierre I shale

samples, we see that they lost nearly the same amount of water (4 wt%) after they were

equilibrated in the 0.85 aw atmosphere. This demonstrates that the native water contents

of these three samples are nearly identical.

Comparing the amount of water loss in “Step 3” among the three Pierre samples,

we see that the amount of water loss for the CaCl2 solution is more than that for the NaCl

and KCl solutions. This can be explained by the diameter difference between the

dehydrated and hydrated ions, as shown in Table 6-1. The diameter of the hydrated

calcium ion is ten times larger than the dehydrated ion, therefore the associated water

carried by these ions is easily lost.

Comparing “Nd” with “Step 4” in Figures 6-3 ~ 6-5, we see that the Pierre I shale

138

gained ions when immersed in ionic solutions. This ionic gain raised the question: “ is

such ionic transfer sufficient to significantly alter the chemical properties of the shale?”

To answer this question, adsorption isotherms were developed for the immersed shale

sample (step 4) and compared to the adsorption isotherm for native Pierre I shale. The

results are shown in Figure 6-6.

It is seen from Figure 6-6 that the amount of moisture adsorbed was highest for

the samples immersed in 0.85 aw CaCl2 solution and least for the samples immersed in

0.85 aw KCl solution. This result can be used to demonstrate that the adsorption of ions

has changed the chemical properties of the shale. The difference in behavior between the

samples immersed in CaCl2 and KCl solutions was probably due to the fact that the

adsorption of K+ ions led to the collapse of the spacing between the clay platelets, thus

reducing the amount of water adsorbed (Osisanya, 1991).

6.3.1.3 Results for Arco shale/ NaCl, KCl and CaCl2 tests

Tests similar to the above Pierre I tests were carried out for the Arco. Results are

shown in Figures 6-7 ~ 6-9. We see that the three Arco shale samples gained water after

they were equilibrated in the 0.85 aw atmosphere. This amount of water gain is caused by

the chemical potential difference between the 0.78 aw Arco shale and the 0.85 aw

atmosphere.

Comparing the amount of water loss in “Step 3” among the three Arco shale

samples, we again observe that the water loss for the CaCl2 solution test is greater than

that for NaCl and KCl solutions. Once again, this can be explained by the difference in

diameter between the dehydrated and hydrated ions.

Comparing “Nd” with “Step 4” in Figures 6-7 ~ 6-9, we see that the Arco shale

samples also gained ions when they were immersed into ionic solutions. This amount of

ion adsorption has altered the chemical properties of the shale. Due to a lack of samples,

139

it was not possible to develop adsorption isotherms for the Arco shale, as was done for

the Pierre I shale.

6.3.2 Test of Direct Exposure to 0.85 aw Solutions

A second series of experiments were performed in order to study the movement of

water and ions for native Pierre I shale interacting with different ionic solutions with the

same water activity.

The native 0.98 aw Pierre I shale samples were directly immersed into 0.85 aw

solutions of CaCl2, NaCl and KCl without removing water in a 85% relative humidity

desiccator, as was done in the first series of experiments. The movement of water and

ions during the exposure of native Pierre I shale to such salt solutions were determined by

using the gravimetric method as discussed in Chapter 5. The results of such movement

are shown in Figure 6-10.

In these tests, capillary, osmotic, and diffusive processes are acting

simultaneously. If the movement of water and ions was only caused by capillary effects,

the shale should absorb the whole solution fluid (water and ions) simultaneously.

However, it is seen from Figure 6-10 that these native Pierre I shale samples lost water

after immersion into 0.85 aw solutions of CaCl2, NaCl and KCl. This demonstrates that

osmosis also caused the water and ion movement.

For the native Arco shale directly exposed to 0.85 aw NaCl and CaCl2 solutions,

the results of water and ion movement are shown in Figure 6-11. It is seen that Arco shale

absorbed 1.16 wt % water and 0.7 wt% ions for the CaCl2 solution, and 0.9 wt% water

and 0.3 wt% ions for the NaCl solution. Such movements are reasonable because of the

large imbalance of water activity and ion concentration between the 0.78 aw Arco shale

and the 0.85 aw salt solutions. As discussed previously, this amount of water and ions

movement is probably driven by capillarity, diffusion, and chemical osmosis.

140

6.3.3 Test of Direct Immersion to Solutions with Different Water Activities

The above tests were repeated using CaCl2, NaCl, and KCl solutions of other

water activities, namely 0.75, 0.85, and 0.95. The results are presented in Figure 6-12. It

is easily seen that as expected the amount of water loss increased at the lower water

activities. It is also shown in Figure 6-12 that there exist differences among these three

types of ionic solutions. These differences in water movement demonstrated that in

addition to osmosis (driven by water activity), the movement of water and ions is

influenced by ionic diffusion.

6.4 EFFECTS OF WATER AND ION MOVEMENT ON SWELLING PROPERTY OF SHALES

From the above discussion, it is easily seen that water and ions moved into or out

of the shale when it interacted with ionic solutions. This movement alters the

physiochemical and mechanical properties of the formation. The effects of such

movement on mechanical and acoustic properties of shales will be discussed in detail in

Chapter 7. The focus of this chapter is to study the effects of water and ion movement on

swelling properties of shales.

In order to investigate the effects of water and ions movement on swelling

properties of Pierre I shale, a third series of experiments were performed. The results for

these experiments are discussed below.

6.4.1 Effects of Water Movement on Swelling Properties of Pierre I Shale

This test was developed to investigate the effects of water movement on swelling

property of Pierre I shale. A preserved Pierre I shale sample with dimensions

0.157.05.0 ′′×′′×′′ , was taken out of the storage can and quickly washed using “Skelly B”

to remove all surface oil. It was then positioned between the movable and stationary

anvils in a swelling transducer and then placed in a controlled 85% humidity environment

and its swelling behavior measured. As shown in Figure 6-13, the shale shrank

141

continuously due to the loss of water only.

6.4.2 Effects of Water and Ions Movement on Swelling Properties of Pierre I Shale

The following swelling test was performed differently from the above test in that

the sample was immersed directly into 0.85 aw KCl solution. The procedure for this

experiment consisted of: 1) washing the sample with “Skelly B”; 2) placing it in a small

plastic bag and positioning it in the swelling transducer; and 3) pouring 50 ml 0.85 aw

KCl solution into the bag and measuring the swelling properties. The result is shown in

Figure 6-14.

It is shown in Figure 6-14 that the sample swelled at early time and sometime

later it began to shrink. It is postulated that the early swelling is caused by a surface

capillary effect (Zhang et al., 2004). After correcting Figure 6-14 for capillary effects

(see Chapter 5 for this correction technique), the comparison of the swelling properties of

Pierre I shale placed in a 0. 85 aw atmosphere and immersed into a 0.85 aw KCl solution

is shown in Figure 6-15.

It is seen that the sample shrank after it was exposed to the 0.85 aw KCl solution.

The sample experienced more shrinkage when it was placed in a 0.85 aw atmosphere than

when immersed into the 0.85 aw KCl solution. It is postulated that, for the immersion test

the movement of ions into the shale lowers the water activity of the shale, thus reducing

the osmotic driving force, and swelling percentage.

6.4.3 Swelling of Pierre I Immersed in Different Ionic Solutions

The swelling percentages of Pierre I shales were measured after they were

immersed into salt solutions that had different water activities. After the swelling test was

completed, the movement of water and ions was determined by the GST technique

discussed in Chapter 5. In this way, the effects of water and ion movement on swelling

percentages of Pierre I shale were studied.

142

The effects of water and ion movement on swelling percentage of Pierre I shale

after they were exposed to NaCl solution of different concentrations are shown in Figure

6-16.

It is seen from Figure 6-16 that as water enters the shale and ions are leaving, the

shale swells. By using this figure, we are able to demonstrate the net effect of ion

movement on the swelling properties of Pierre I shale. For example, after the Pierre I was

immersed into the 0.95 aw NaCl solution, it lost 0.1 wt% of water and gained 0.1 wt % of

ions. With this amount of water loss and ions gain, the Pierre I shale had a resulting

expansion of about 0.3%. The sample had expanded even with water loss, which clearly

demonstrated that ion absorption can cause the shale to swell.

The results for Pierre I shale immersed in CaCl2 and KCl solutions with various

concentrations are shown in Figures 6-17 and 6-18 respectively. Effects very similar to

those seen with NaCl solution can be observed from these figures.

6.5 CONCLUSIONS

1. The new simple method, called the Gravimetric – Swelling Test, that

measures water and ion entering or leaving a shale sample provides a good

way to study water and ions movement and the effects of such movement on

the swelling properties of shales.

2. After the native Pierre I shale samples immersed in 0.85 aw solutions, they lost

water and gained ions. However, they gained both water and ions if the Pierre

I shale samples were equilibrated in a controlled relative humidity

environment of 85% before immersed in 0.85 aw solutions.

3. Both the native and the conditioned Arco shale gained water and ion after they

were exposed to 0.85 aw solutions.

4. The transport of water is not only controlled chemical osmosis, but also

143

affected by ionic diffusion and capillary effects under zero hydraulic pressure

difference.

5. The immersion of shale samples into salt solutions alters the chemical

composition of the shale due to ions movement.

6. The swelling of the shale is influenced by both water and ion movement.

7. Combined with other tests, the Gravimetric–Swelling Test can be used to

evaluate mud systems.

NOMENCLATURES

d,wa Water activity for desiccator, dimensionless

mud,wa Water activity of a mud, dimensionless

shale,wa Water activity of a shale, dimensionless

mud,iC Concentration of species i in mud [=] amount/volume

shale,iC Concentration of species i in pore fluid in shale [=]

amount/volume

D Diffusivity [=] L2/t

g Gravitation acceleration [=] L/t2

J Mass flux [=]

k Permeability [=] L2

mI Membrane efficiency, dimensionless

P Vapor pressure of shale at temperature T [=] m/L-t2

0P Vapor pressure of pure water at temperature T [=] m/L-t2

aP Pressure air phases [=] m/L-t2

cP Capillary pressure between water and gas phases [=] m/L-t2

mP Vapor pressure of water above the meniscus [=] m/L-t2

sP Vapor pressure of water above in the solution [=] m/L-t2

144

p∇ Pressure difference gradient between the mud hydraulic pressure

and pore pressure [=] m/L2-t2

P∆ Pressure difference between air and water phases [=] m/L-t2

r Tube radius [=] L

R Gas law constant, KmoleKgS/mkg1031451.8 223 ⋅−⋅⋅× ;

T Absolute temperature [=] T

iu Chemical potential of ith component

µ Viscosity of drilling fluid [=] m/L-t

0v Bulk flow velocity [=] L/t

wV Molar volume of water, 0.018 m3/mol

nW Native weight [=] m

ndW Native dried weight [=] m

ρ Density of drilling fluid [=] m/L3

aw−σ Interfacial tension [=] m/t2

θ Contact angle between the fluids interface and the solid

surface [=] degree

ACKNOWLEDGEMENT

Special thanks are given to Dr. Russ Ewy, Dr Guizhong Chen, Dr. Rosana Lomba

and Mr. Ben Bloys for their valuable suggestions. The assistance of Dr. John Holder and

Mr. Glen Baum is greatly appreciated.

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Ballard, T.J., Beare, S.P. and Lawless, T.A.: “ Fundamentals of Shale Stabilisation: Water Transport Through Shales”, IADC/SPE24974, presented at the European

145

Petroleum Conference held in Cannes, France, 16-18 November, 1992.

Bird, R.B., Stewart, W.E. and Lightfoot, E.N.: “ Transport Phenomena”, Second Edition, John Wiley & Sons, Inc., 2002.

Bol, G.M., “ The Effects of Various Polymers and Salts on Borehole and Cutting Stability in Water-Base Shale Drilling Fluids”, SPE 14802 presented at the 1986 IADC/SPE Drilling Conference help in Dallas, TX, February 10-12, 1986.


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Carminati, S., Del Gaudio L., Del, Piero G. and Brignoli, M.: “ Water- Based Muds and Shale Interactions”, SPE 65001 presented at the 2001 SPE International Symposium on Oilfield Chemistry held in Houston, Texas, 13-16 February 2001.



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Chenevert, M. E: “Shale Control with Balanced-Activity Oil-Continuous Muds”, Journal of Petroleum technology, Oct. 1970.


Ewy, R.T. and Stankovich R. J. “ Pore pressure change due to shale-fluid interaction: measurements under simulated wellbore conditions”, presented at the Proceedings

146

Pacific Rocks 2000, Fourth North American Rock Mechanics Symposium, Seattle, July 31-Auguest 3, 2000, pp147-154, Balkema, Rotterdam.

Ewy, R.T. and Stankovich R.J.: “ Shale-Fluid Interactions Measured Under Simulated Downhole Conditions”, SPE/ISRM 78160 presented at the SPE/ISRM Rock Mechanics Conference held in Irving, Texas, 20-23 October 2002.

Forsans, T. M. and Schmitt, L.: “ Capillary forces: The neglected factor in shale instability studies?” SPE 28029 presented at the SPE/ISRM Rock Mechanics in Petroleum Engineering Conference held in Delft, The Netherlands, 29-31 August 1994.


Fritz, S.J.: “ Ideality of Clay Membranes in Osmotic Process: A Review”, Clay and Clay Minerals, Vol.34, No.2, 214-223, 1986.

Hale, A. H., Mody F. K. and Salisbury, D. P.: “ Experimental Investigation of the Influence of Chemical Potential on Wellbore Stability”, IADC/SPE Paper 23885, presented at the 1992 IADC/SPE Drilling Conference in New Orleans, Louisiana, Feb. 18-21, 1992.


Low, P.F., Anderson, D.M.: “ Osmotic Pressure Equation for Determining Thermodynamic Properties of Soil Water”, Soil Science, V.86, 251-258, 1958.



Newsham, K. E., Rushing, J. A. and Lasswell, P.M.: “ Use of Vapor Desorption Data to Characterize High Capillary Pressure in a Basin-Centered Gas Accumulation with Ultra-Low Connate Water Saturations”, SPE 84596, presented at the SPE Annual Technical Conference and Exhibition held in Denver, Colorado, U. S. A., 5-8 October.

Norrish, K.: “ The Swelling of Montmorillonite”, Disc. Of Faraday Soc., V.18, P.120, 1954.

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Olsen, H.W., Yearsley, E.N. and Nelson, K.R.: “ Chemico-Osmosis Versus Diffusion-Osmosis”, Transportation Research Record 1288.

Osisanya, S. O.: “Experimental Studies Of Wellbore Stability in Shale Formations”, Ph.D dissertation, The University of Texas at Austin, August, 1991.

Pernot, Vincent: “ Troublesome Shale Control Using Inhibitive Water-Base Muds”, master’s thesis, the University of Texas at Austin, May 1999.

Santarelli, F.J. and Carminati S.: “Do Shale Swell? A Critical Review of available Evidence”, IADC/SPE Paper 29421, presented at the 1995 IADC/SPE Drilling Conference in Amsterdam, 26 Feb. 26-2 March, 1995.

Santos, H., Diek, A., Roegiers, C. and Fontoura, S.: “ Can shale swelling be (easily) controlled?” Eurock’96, Barla(ed) 1996 Balkema, Rotterdam. ISBN 90 5410 8436.

Santos, H., Diek ,A., Fontoura, S. and Roegiers, C.: “ Shale Reactivity Test : A Novel Approach to Evaluate Shale-Fluid Interaction”, Int., J. Rock Mech. & Min. Sci. 34: 3-4, paper No. 268.

Santos, H.: “ What Have We Been Doing Wrong in Wellbore Stability?”, SPE 69493 presented at the SPE Latin American and Caribbean Petroleum Engineering Conference held in Buenos Aires, Argentina, 25-28 March 2001.

Schlemmer, R., Friedheim, J.E., Growcock, F.B., Bloys, J.B., Headley, J.A., and Polnaszek, S.C.: “ Membrane Efficiency in Shale – An Empirical Evaluation of Drilling Fluid Chemistries and Implication for Fluid Design”, IADC/SPE 74557 presented at the IADC/SPE Drilling Conference held in Dallas, Texas, 26-28 February, 2002.

Schmitt, L., Forsans, T. and Santarelli, F.J.: “ Shale Testing and Capillary Phenomena”, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 1994, No.5, pp411-427.

Simpson, J.P.: “ Drilling Fluids – Today and Tomorrow”, Journal of Petroleum Technology, November 1971.



Steiger, R.P. “ Advanced Triaxial Swelling Tests on Preserved Shale Cores”, presented at the 34th U. S. Symposium on Rock Mechanics (June 27-30, 1993) and to be

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published in the Int.J. Rock Mech. Min. & Geomech. Abstr. (1993).

Tan, C.P., Amanullah M., Mody, F.K. and Tare, U.A.: “ Novel High Membrane Efficiency Water-Based Drilling Fluids for Alleviating Problems in Troublesome Shale Formations”, IADC/SPE 77192 presented at the IADC/SPE Asia Pacific Drilling Technology held in Jakarta, Indonesia, 9-11 September 2002.

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Van Oort, E., Hale, A.H. and Mody, F.K.: “ Manipulation of Coupled Osmotic Flows for Stabilisation of Shales Exposed to Water-Based Drilling Fluids”, SPE 30499 presented at the SPE Annual Technical Conference & Exhibition held in Dallas, U.S.A., 22-25 October, 1995.

Van Oort, E.: “Physico-chemical Stabilization of Shales”, SPE paper 37263 presented at 1997 International Symposium on Colloid Chemistry, Houston, Texas, USA, Feb. 18-21.

Van Oort, E.: “On the physical and chemical stability of shales”, Journal of Petroleum Science & Engineering, 38 (2003) 213-235.

Wong, S.W., Kenter, C.J., Schokkenbroek, H., Bordes, P.D and Regteren, J.V.: “ Optimizing Shale Drilling in the Northern North Sea: Borehole Stability Considerations”, SPE 26736 presented at the Offshore Europe Conference held in Aberdeen, 7-10 September 1993.

Yousif K.K. and Willard C.S.: “ Flow of Water and Solutes through Compacted Clays”, The American Association of Petroleum Geologists Bulletin, V. 60, No. 6 (June 1976), P.973-980.



149

Table 6-1 – Comparison of ions hydrated radii

Dehydrated Diameter (Angstrom)

Hydrated Diameter (Angstrom)

Sodium 1.9 5.5-11.2Potassium 2.66 4.64-7.6Cesium 3.34 4.6-7.2Magnesium 1.3 21.6Calcium 1.9 19

150

Figure 6-1 – Osmosis and ion diffusion.

Figure 6-2 – Brine water capillary imbibitions.

151

0

2

4

6

8

10

12

Wei

ght C

hang

e, w

t%

1 2 3 4Na Nd

Figure 6-3 – Weight changes of Pierre I shale during desiccator-immersion-desiccator test (NaCl).

0

2

4

6

8

10

12

Wei

ght C

hang

e, w

t%

1 2 3 4Na Nd

Figure 6-4 – Weight changes of Pierre I shale during desiccator-immersion-desiccator test (KCl).

152

0

2

4

6

8

10

12

14

16

Wei

ght C

hang

e, w

t%

1 2 3 4Na Nd

Figure 6-5 – Weight changes of Pierre I shale during desiccator-immersion-desiccator test (CaCl2).

0

2

4

6

8

10

12

14

0 0.2 0.4 0.6 0.8 1Relative Vapor Pressure, P/Po

Moi

stur

e C

onte

nt (w

t%) Native

NaClKClCaCl2

Figure 6-6 – Combined adsorption isotherms of Pierre I shale.

153

0

1

2

3

4

5

6

Wei

ght C

hang

e, w

t%

1 2 3 4Na Nd

Figure 6-7 – Weight changes of Arco shale during desiccator-immersion-desiccator test (NaCl).

0

1

2

3

4

5

6

Wei

ght C

hang

e, w

t%

1 2 3 4Na Nd

Figure 6-8 – Weight changes of Arco shale during desiccator-immersion-desiccator test (KCl).

154

0

1

2

3

4

5

6

Wei

ght C

hang

e, w

t%

1 2 3 4Na Nd

Figure 6-9 – Weight changes of Arco shale during desiccator-immersion-desiccator test (CaCl2).

-0.8

-0.4

0

0.4

0.8

1.2

1.6

2

2.4

Wat

er/Io

n M

ovem

ent,

wt%

WaterIons

NaCl KClCaCl2

Figure 6-10 – Water and ion movement for Pierre I directly immersed in 0.85 aw CaCl2, 0.85 aw NaCl and 0.85 aw KCl solutions.

155

0

0.2

0.4

0.6

0.8

1

1.2

Wat

er/Io

n M

ovem

ent,

wt% Water

Ions

NaClCaCl2

Figure 6-11 – Water and ion movement for Arco shale directly immersed in 0.85 aw NaCl and 0.85 aw CaCl2 solutions.

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.75 0.8 0.85 0.9 0.95 1

Water Activity

Wat

er M

ovem

ent,

wt%

CaCl2NaClKCl

Native Shale

Figure 6-12 – Effects of water activity on water movement of Pierre I shale.

156

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0 300 600 900 1200 1500Time, Minutes

Swel

ling

Stra

in (%

)

Figure 6-13 – Swelling of Pierre I shale placed in controlled 85% humidity desiccator.

-0.1

0

0.1

0.2

0.3

0 300 600 900 1200 1500Time, Minutes

Swel

ling

Stra

in (%

)

Figure 6-14 – Swelling properties of Pierre I shale immersed in 0.85 aw KCl solution.

157

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0 300 600 900 1200 1500Time, minutes

Swel

ling

perc

enta

ge, %

Above KCl Desiccator, aw=0.85 Dipped into aw=0.85 KCl Solution

No Ion Flux

With Ions and Water Flux

Figure 6-15 – Comparison of shale swelling when sample is immersed in a 0.85 aw KCl solution versus placed in a 0.85 aw atmosphere (Pierre I shale).

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

-0.8 -0.4 0 0.4 0.8 1.2 1.6 2 2.4

Water/Ions Movement, %

Swel

ling

Perc

enta

ge, %

WaterIons

Figure 6-16 – Correlation of water/ion movement with the swelling of Pierre I shale exposed to NaCl solutions.

158

0

0.1

0.2

0.3

0.4

0.5

0.6

-1 -0.5 0 0.5 1 1.5 2 2.5


Swel

ling

Perc

enta

ge, %

WaterIons

Figure 6-17 – Correlation of water/ion movement with the swelling of Pierre I shale exposed to CaCl2 solutions.

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

-0.6 0 0.6 1.2 1.8 2.4


Swel

ling

Perc

enta

ge, %

WaterIons

Figure 6-18 – Correlation of water/ion movement with the swelling of Pierre I shale exposed to KCl solutions.

159

Chapter 7 : Changes in Shale Strength and Acoustic Properties with Exposure to Water-Based Fluids

ABSTRACT

Experimental results are presented in this chapter to show how the compressive

strengths and acoustic velocities of different types of shale change when they are exposed

to water-based fluids. The acoustic velocity and compressive strength of a soft, high

water activity, Pierre I shale increased after exposure to different ionic solutions, while

for the lower water activity Arco shale, acoustic velocity and strength decreased. By

combining these tests with a new gravimetric test that quantitatively determined the flux

of water and ions into or out of the shale, it was clearly shown that these different effects

correlated well with the movement of water and ions. In every case, water adsorption

weakened, while ion adsorption strengthened the shale.

The influence of salt type and salt concentration on the strengths and acoustic

velocities of two shales was also investigated. It was seen that the ionic content of water-

based fluid had a significant effect on the changes in shale properties. It was also shown

that the changes in acoustic velocity and compressive strength were highly correlated.

This suggests that it may be feasible to use acoustic logging data to determine changes in

the mechanical properties of shale.

Finally, the impact of the reported changes in the mechanical properties of the

shale and wellbore stability was demonstrated through the use of Driller, a 3-d wellbore

stability analysis program.

160

7.1 INTRODUCTION

Wellbore instability problems in shale formation have plagued the petroleum

industry since it began over one hundred years ago. These problems often occur when

water or saline fluids come into contact with shales. The primary cause of such problems

is the interaction between the drilling fluid and shale formations. This interaction may

cause pore pressure and mechanical property alterations around the wellbore formations,

thereby leading to wellbore collapse.

One method for visualizing the effects of such alterations on wellbore stability is

through the use of Mohr-Coulomb failure diagrams. Referring to Figure 7-1, we see that

if the pore pressure increases, the Mohr circle shifts to the left approaching the

safe/failure boundary. Simultaneously, if the strength of the formation decreased due to

interaction between shale and mud, this safe/failure boundary shifts downwards. Once the

Mohr circle contacts the safe/failure envelope due to these shifts, wellbore instability

occurs. Therefore, wellbore stability can be achieved by preventing pore pressure

propagation and by reducing formation weakening. Many studies have been done on

preventing pore pressure build-up around wellbores caused by the interaction between

shales and drilling fluids (Bol et al., 1992; Van Oort et al., 1994, 1995; Caminati 1999;

Ewy et al., 2000; Tare et. al., 2000; Schlemmer et al., 2002). In our work, we focus on

the selection of drilling fluids that maintain shale strength.

Chenevert (1969, 1970) studied shale alteration by water adsorption and measured

the linear swelling of shale in various muds which had different water activities (salt

concentrations). He found that the higher the water activity, the higher the swelling. Hale

et al. (1992) measured the mechanical properties of shale after being contacted with oil-

based muds. They found that the shale strength increased when the water activity of the

mud was lower than that of the shale. Although oil-based muds provide a solution to the

161

shale/mud problem, cost and environmental concerns often restrict their use (Clark et

al., 1976).

In their studies, Mody et al. (1993) and Yu et al. (2002) developed models that

coupled mechanical and chemical interactions between the shale and the drilling fluid. In

addition to chemical and mechanical effects, Chen et al. (2001) considered thermal

effects on wellbore stability.

Generally speaking, wellbore instability occurs when the local stress exceeds the

rock strength. Therefore, the rock strength plays an important role in determining

wellbore stability. Two methods: direct laboratory measurement, and indirect well

logging interpretation are used to determine rock strength. The direct method is more

accurate, but expensive and time consuming. Furthermore, it is difficult to obtain a

complete formation strength profile without running many tests. The indirect method

predicts rock strength by using acoustic log data and log/strength correlations. One

limitation of this method is that it requires accurate experimental data to establish

correlations between strength and acoustic velocity (Horsrud, 2001).

The most valuable information is obtained by testing native shale at its in-situ

stress and temperature conditions. However, it is nearly impossible to know its original

state accurately. Even if outcrop shale samples are used, their properties would be altered

as they are processed during sample preparation, no matter what measures are taken

(Chenevert, 1969). With this in mind, we performed experiments under ambient

controlled stress conditions and studied the influence of a single factor on the properties

of the shale while keeping other factors constant.

The purpose of this study is to find a relationship between water activity, acoustic

velocity, and compressive strength of shale. If there is a close relationship among these

properties, it is hoped that we can determine shale strength using logging methods.

162

Another aim is to study the role of water and ion transport on shale strength and acoustic

velocity.

7.2 EXPERIMENTAL TESTING

The basic test procedure consisted of first measuring the acoustic velocity of a

shale sample as it absorbed water and/or ions from a solution, then secondly placing this

altered sample into a biaxial test chamber and measuring its compressive strength under

elevated stress conditions.

7.2.1 Acoustic Velocity Test

7.2.1.1 Ultrasonic propagation system

The schematic of the equipment setup used to measure the acoustic velocity of

shale is shown in Figure 7-2. It consists of a pulser-receiver and an oscilloscope. The

pulser-receiver creates an electrical pulse, which is transformed into acoustic energy by a

transmiter transducer. The acoustic energy travels through the rock sample and is then

converted back into electrical energy by a receiver transducer. If necessary, the electrical

signal may be amplified after it reaches the input of the pulser-receiver. The signal is then

displayed on a digital oscilloscope and is recorded.

The pulse generator used in studying the acoustic properties of shale is a

Panametrics High Voltage Pulser-Receiver, Model 5058. This model is very flexible. We

can adjust the repetition rate, damping, and pulse height of the initial signal in order to

enhance the display on an oscilloscope. The oscilloscope used in this study is a Tektronix

TDS3000 Digital Phosphor Oscilloscope (Figure 7-3). This digital oscilloscope uses an

analog-to-digital converter (ADC) to convert the measured voltage into digital

information. The oscilloscope receives a series of wave samples, and stores these samples

until it accumulates enough wave samples to create a waveform (Popp, 2004). When

163

using this equipment, extra care was taken to pick the first arrival time in the waveform

in order to avoid introducing errors.

7.2.1.2 Transducer calibration and face-to-face time determination

During the operation, transducer calibration and face-to-face time determination

were accomplished by using Lucite plates that had different thickness. The calibration

results are shown in Figure 7-4. As shown in this graph, there exits a linear relationship

between the thickness of the Lucite plate and the transmitted time. After regressing these

experimental results, we obtain a regression line. From the slope of this regression line,

the acoustic velocity of Lucite was determined to be 2720 m/s. The published acoustic

velocity for Lucite is 2680 m/s (Reference 41). Therefore, we have concluded that our

equipment and experimental set up is accurate enough to be used for measuring the

acoustic velocity of shale. The face-to-face transmited time between the two transducers

was determined to be 0.1043 microseconds by using the intercept of the regression line

with the axis of transmitted time.

7.2.1.3 Acoustic velocity test

After a 0.75 "×0.75 "×1.5 " shale sample was taken out of the storage can, its

original velocity was measured and designated “original sample velocity”. This sample

was then washed with “Skelly B” to remove the oil from its surface, and then placed into

a plastic bag fixed between the transmitter and receiver transducers (Figure 7-3). A test

solution was then poured into the bag. As the solution interacted with the sample, the

transit time was recorded over time until equilibrium was reached. Normally, equilibrium

took about 24 hours. From such measurements, the alteration of acoustic velocity with

time was obtained for shale sample exposed to different salt solutions. After determining

the acoustic velocity, the sample was placed into a test cell and a compressive strength

test performed.

164

7.2.2 Compressive Strength Test

For details on the compressive strength test equipment and the determination of

the strain rate applied during the test, please refer to Chapter 4: “The Effects of Strain

Rates on Failure Characteristics of Shales.”

During the compressive strength test, two failure mechanisms were observed:

brittle failure and plastic failure. An obvious failure stage was observed when the shale

failed in a brittle manner, as shown in Figure 7-5. After this failure stage, the stresses

decreased with increasing strains. If the shale failed in this brittle manner, the peak value

was chosen as the compressive strength. On the other hand, if the shale failed in a plastic

manner, there is no obvious failure stage and the stresses increased continuously with

increasing strains, as shown in Figure 7-6. For plastic failure, the shale strength value is

chosen at a strain offset of 2 % (Robinson, 1958; Chenevert et al., 1998).

7.3 RESULTS AND DISCUSSION

7.3.1 Acoustic Properties of Pierre I Shale

The effects of salt concentrations of NaCl, CaCl2 and KCl on the acoustic

velocities of Pierre I shale are shown in Figures 7-7, 7-8, and 7-9 respectively.

It can be seen from these figures that except for deioned water, the acoustic

velocity of Pierre I shale increased with time after it was exposed to various salt

solutions. Such results suggest that Pierre I shale is giving up pore fluid and taking water

when exposed to a “more fresh” solution. When it reacts with salt solutions, the more

concentrated the solution, the higher the increase of acoustic velocity.

Figure 7-10 shows the effects of different salt solutions with the same water

activity on acoustic velocities of Pierre I shale. It can be observed that the acoustic

velocity for 0.98 aw Pierre I shale increased after it was exposed to 0.85 aw NaCl, CaCl2

and KCl solutions. The acoustic velocity for Pierre I shale increased by 7.0 % after

165

exposure to the KCl solution, 5.8 % to the NaCl, and 4.9 % to the CaCl2.

We define the relative acoustic velocity change as,

%100V

VVVi

ifcr ×

−=

(7-1)

Note: A positive value of crV represents an acoustic velocity increase and a negative

value represents an acoustic velocity decrease.

It is reasonable to assume that there is no flux of water due to the same osmotic

effects after exposure to salt solutions with the same water activity. Therefore, we believe

that the difference in the alteration of acoustic velocity is caused by ion diffusion between

salt solution and pore fluid and by cation exchange at the clay surfaces.

The effects of different salt solutions on acoustic velocity change for Pierre I

shale are shown in Figure 7-11. From this figure, we see that the higher the concentration

of the salt solution, the higher the increase in the acoustic velocity. After Pierre I shale

was exposed to concentrated salt solutions, water was extracted which caused the

porosity of the shale to decrease. The decrease in porosity caused the acoustic velocity to

increase.

According to the time average equation presented by Wyllie et al. (1958),

RFM V1

VV1 φ−

+φ

= (7-2)

After rearranging the above equation, we have:

( ) FFR

RFM VVV

VVV+−φ

⋅=

(7-3)

Normally, the velocity in a rock matrix ( RV ) is greater than the velocity of the

pore fluid ( FV ). Therefore, it is easily seen from Equation (7-3) that the velocity of the

shale increases with decreasing porosity.

166

Using our “Gravimetric-Swelling Test” (GST), described in Chapter 5, water

and ion movement during shale/salt interactions were determined. The effect of water

movement on acoustic velocity alteration for Pierre I is shown in Figure 7-12. It can be

seen that the loss of water increased the acoustic velocity for Pierre I shale. For the same

amount of water movement, different ionic solutions had various influences on acoustic

velocity. For example, under zero water movement, the acoustic velocity increased by 1.8

% for KCl, 6% for NaCl, and 0% for CaCl2 solutions. This difference in acoustic velocity

change demonstrates that in addition to water transport, the type of ion and ion movement

have an influence on the acoustic velocity of the shale. The effect of ion movement on

acoustic velocity of Pierre I shale is shown in Figure 7-13.

It is seen from Figure 7-13 that the acoustic velocity increased with increasing ion

adsorption. From Figures 7-12 and 7-13, we conclude that the acoustic velocity is altered

by both water and ion movement.

7.3.2 Strength Properties of Pierre I Shale

Figures 7-14, 7-15, and 7-16 show the stress-strain curves for Pierre I shale

exposed to NaCl, CaCl2 and KCl solutions with different salt concentrations. From these

figures, we see that the strength of Pierre I increased after exposure to ionic solutions,

while it decreased after exposure to deioned water due to water and ion movement.

We also see that the failure mechanism of Pierre I shale changed from brittle to

plastic after it was exposed to ionic solutions. Pierre I shale failed in a brittle manner at

low salt concentration or in its native condition, whereas it failed in a plastic manner

when it was exposed to concentrated salt solutions. This was possibly caused by the

alteration of the shale fabric structure by the adsorption of ions (Amanullah et al., 1994;

Simpson et al., 2000). The bonding force between particles can be strengthened with the

adsorption of ions, which can change the failure mode of the shale. Compared with NaCl

167

and CaCl2 solutions, Pierre I shale exhibited much higher plastic deformations after it

was exposed to KCl solutions. This may be because the ionic solutions (particularly K+

ions) provide a reduction in intergranular friction. This allows grains to slip over each

other as the stress is increased leading to plastic failure.

In summary, failure mechanisms for Pierre I shale were influenced by exposure to

the brine, which induced plastic deformation and enhanced its ductility. Amanullah et al.

(1994) reached similar conclusion.

After the stress-strain curves were obtained during the strength tests, the Young’s

moduli were determined. The influence of different solutions on the Young’s moduli of

Pierre I shale is shown in Figure 7-17. It is seen that for NaCl and CaCl2 tests, the

Young’s moduli decreased with an increase in the water activity. Once again, we see that

exposure to KCl solutions greatly increased the Young’s modulus of elasticity of Pierre I

shale.

We obtained the strength values by using the method discussed in Section 7.2.2.

The overall effect of various salt solutions on the deviatoric strength of Pierre I is shown

in Figure 7-18.

Using the GST discussed in Chapter 5, it was possible to determine the movement

of water and ion that produced such strength alteration. Figures 7-19 and 7-20 show these

effects.

Note that for the KCl test, the final strength of 9500 psi was the result of the shale

losing 0.5 wt% water, and gaining 1.8 wt% ions. In general, it is seen that for all tests,

when water is removed and ions are added, the strength increases, and the inverse is true,

when ions are removed and water is added, (the strength decreases).

Zhang et al. (2004) found that water was extracted out of the Pierre I shale, and

ions were added after it was immersed into concentrated salt solutions. The higher the

168

concentration (lower water activity), the more water is extracted and the more ions are

added into the shale. Water extraction under high salt concentration causes the strength

to increase (Chenevert, 1969; Hale et al., 1992). We see from Figure 7-19 that at the

same amount of water movement, different types of salt have various influences on

strength of Pierre I shale. For example, under zero water movement, the strength

increased to 6500 psi for NaCl, 5900 psi for CaCl2, and 8900 psi for KCl. This difference

in strength increase suggests that in addition to water movement, ion movement has an

impact on shale strength.

Figure 7-20 shows the effects of ion movement on deviatoric strength of Pierre I

shale. In this figure, we see that ion adsorption (coupled with water removal) can increase

the shale strength to a large degree. It is worth noting that ion adsorption is coupled to

water extraction from the shale (as shown here and Chapter 5). An interesting question

arises; is the strength enhancement caused by ion adsorption or by water extraction?

There is no doubt that water extraction strengthens shale (Chenevert, 1969; Hale

et al., 1992). We believe that the effects of ions adsorption on mechanical properties

alteration depend on their physical and mechanical characteristics. Table 7-1 shows the

hydrated radius for different ions. We can see that there is a difference in the hydrated

radius for different ions. When the larger ions are displaced by smaller ions, the shale

shrinks. On the contrary, smaller ions are exchanged with larger ions, and the shale

swells. On the other hand, there are differences among bonding forces between ions and

clay surfaces. It was reported that the bonding force for potassium is much larger than

that of other ions (Walker et al., 1984; Pruett 1987). Our data show that the adsorption of

potassium coupled with water removal can strengthen the Pierre I shale to a great degree.

169

7.3.3 Relationship between Acoustic Velocity and Compressive Strength of Pierre I Shale

The relationship between the acoustic velocity and strength for Pierre I is shown

in Figure 7-21. It is seen from this graph that there is a close relationship between the

strength and acoustic velocity and that compressive strength increases with the acoustic

velocity. Therefore, it is possible to use acoustic well log data to deduce formation

strength and detect mechanical property alteration due to shale/mud interaction in wells.

7.3.4 Acoustic Properties of Arco Shale

The effects of salt concentrations of NaCl, CaCl2 and KCl on the acoustic velocity

of Arco shale are shown in Figures 7-22, 7-23, and 7-24 respectively. From these figures,

we see that the acoustic velocity of Arco shale decreased after exposure to NaCl and

CaCl2 solutions. The acoustic velocity decreased when Arco shale was exposed to low

concentrations of KCl, and it increased after exposure to KCl solution that had high

concentration.

The effects of different salt solutions with the same water activity (aw=0.85) on

the acoustic velocity of Arco shale are shown in Figure 7-25. It is seen that the acoustic

velocity of Arco shale decreased after exposure to NaCl and CaCl2 solutions, but it

increased when exposed to KCl solutions. In that all salt solutions had the same water

activity, it is reasonable to assume that the aqueous osmotic effects are the same.

Therefore, we believe that the difference in acoustic velocity is caused by ion diffusion

between the pore fluids and salt solutions, and cation exchange between the pore fluid

and clay surfaces.

The effects of different salt solutions on acoustic velocities of Arco shale at

equilibrium are shown in Figure 7-26. It is seen that the higher the ionic concentration is,

the less decrease in acoustic velocity of Arco shale. Once again, the effects of ionic

170

solutions on acoustic velocity can be explained by water and ion movement during the

interaction between the shales and solutions. Figures 7-27 and 7-28 show such effects.

Because of the limited amount of Arco shale, we could not run GST with KCl

solutions. It is seen from Figure 7-27 that the acoustic velocity decreased with water

adsorption. For the same amount of water movement, this decrease for NaCl is higher

than for CaCl2. This difference in acoustic velocity decrease between NaCl and CaCl2

solutions demonstrates that in addition to water transport, ion movement has an influence

on acoustic velocity of the shale, as shown in Figure 7-28.

7.3.5 Strength Properties of Arco Shale

The effects of NaCl, CaCl2 and KCl concentrations on the stress-strain curves for

Arco shale are shown in Figures 7-29, 7-30 and 7-31 respectively. It can be seen from

these figures that the strengths of Arco shale decreased after exposure to NaCl and CaCl2

solutions. The lower the concentration, the larger the strength reduction. Comparing with

NaCl and CaCl2 solutions, we see that there is a completely different reaction for Arco

shale exposure to KCl solutions. The strength for Arco shale is enhanced after exposed to

KCl solutions, although there is no clear trend with respect to concentration. Similar

phenomena were observed by Horsrud et al. (1998). Maybe this is the reason why many

people are interesting in potassium fluids (Clark et al., 1976; Bostrom et al., 1998;

Horsrud et al. 1998; Kjosnes et al., 2003).

Young’s moduli of Arco shale are obtained from the stress-strain curves. The

effects of water activity of salt solutions on Young’s moduli of Arco shale are shown in

Figure 7-32. It is seen from this figure that the Young’s moduli of Arco shale decreased

after it was exposed to NaCl and CaCl2 solutions and the higher the water activity, the

larger the decrease. However, the Young’s moduli of Arco shale increased after it was

exposed to KCl solutions.

171

The overall effects of various salt solutions on the strengths of Arco shale are

shown in Figure 7-33. The movement of water and ions that produced such alteration is

shown in Figures 7-34 and 7-35.

As shown, the largest weakening of the shale was produced when the sample

gained 2.4 wt% water and lost 0.6 wt% ions. The strength of Arco shale decreased from

6000 psi to 1500 psi after it was exposed to deioned water. This pattern is exactly what

was observed for the Pierre I shale.

The movement of water and ion as measured in our tests exactly follows the

principle of osmotic flow. When a sample of shale is placed in a salt solution of lower

water activty, water is removed, and vice versa. What is interesting to note is that there is

another part of the reaction and that is ion flow. This ion flow is always going in the

opposite direction of water flow.

7.3.6 Relationship between Acoustic Velocity and Compressive Strength for Arco Shale

The relationships between the acoustic velocity and compressive strength for

Arco shale are shown in Figure 7-36. Once again, it is seen that that there is a good

relationship between the strength and acoustic velocity and that compressive strength

increases with the acoustic velocity for both shales.

7. 4 APPLICATIONS

The wellbore stability software, DRILLER that was developed by the University

of Texas (Yu, 2001, 2002) was used to study the influence of salt concentration on

wellbore stability. We assumed a vertical well was drilled. The strengths and Young’s

moduli used are listed in Table 7-2. Other data such as the thermal and mechanical

information are obtained from Yu’s (2001) paper.

172

7.4.1 Effects of Salt Solutions on Mud-Weight-Window (MWW) of Pierre I Shale

The influence of the sodium and calcium chloride solutions on MWW of Pierre I

is shown in Figure 7-37. Three points can be observed from this figure. First, the more

concentrated the solutions, the wider the MWW. Secondly, calcium chloride is more

effective than sodium chloride at the same water activity for the Pierre I formation.

Finally, the formations were strengthened after exposure to different solutions except for

deioned water. During our calculations, the tensile strength was assumed to be

unchanged.

7.4.2 Effects of Salt Solutions on MWW of Arco Shale

The influence of the sodium and calcium chloride solutions on MWW of Arco

shale is shown in Figure 7-38. There are also three points that can be seen from this

figure. First, the MWW narrowed significantly after exposure to different solutions

because of the strength decrease. When exposed to deioned water, width of the MWW

was essentially zero, which means that it is impossible to avoid wellbore instability

problems when deioned water is used as a drilling fluid. Secondly, the MWW would be

wider with an increase in salt concentration. Finally, sodium chloride is more effective

than calcium chloride when exposed to Arco shale at the same water activity.

Comparing Figure 7-37 and Figure 7-38 we can draw several interesting

conclusions. First, the MWW of Pierre I shale would be wider after exposure to ionic salt

solutions because of strength enhancement due to water loss. This is also the reason why

the acoustic velocity increased after exposure to salt solutions. Shales react differently to

various salt solutions. Because of its low native water activity, the Arco shale has a

different response and it is weakened. Meanwhile, its acoustic velocity decreased after

exposure to salt solutions. Also the influence of different solutions on the MWW is

different. From the wellbore stability point of view, calcium chloride is more effective for

173

Pierre I shale, while sodium chloride is more effective for Arco shale at the same water

activity. Therefore, we need to optimize the mud formulation according to different

types of shale. In our study, we did not find any single drilling fluid that would maintain

wellbore stability for all types of shale.

7.5 CONCLUSIONS

The main conclusions reached from this chapter are as follows:

1. Acoustic velocity, shale strength, and Young’s moduli for Pierre I shale

(aw=0.98) increased after interaction with ionic solutions. The more

concentrated the solution, the higher the acoustic velocity increase.

2. Acoustic velocity, shale strength, and Young’s moduli for Arco shale

(aw=0.78) deceased after exposure to both sodium and calcium chloride

solutions. The higher the water activity, the larger the reduction in shale

strength.

3. Adsorption of potassium ions greatly increased the strength of Pierre I shale.

4. The results from the “Gravimetric-Swelling Test” can be used to explain the

alteration of the mechanical properties of shale during interaction with fluids.

5. The loss of water increases the acoustic velocity and strength for Pierre I shale

and the uptake of water decreases the acoustic velocity and strength for Arco

shale.

6. We believe that shale fabric structure is altered after it is exposed to salt

solutions. Intergranular friction is reduced so that grains can slide past each

other to accommodate increasing stress. This lead to ductile failure.

7. There is a good relationship between the acoustic velocity and the mechanical

properties of shales. Therefore, it is feasible to use acoustic well logging data

to predict the mechanical properties of shale.

174

NOMENCLATURE

crV Relative acoustic velocity change, %;

fV Final acoustic velocity after exposure to ionic solution [=] L/t

FV Velocity of the pore fluid [=] L/t

iV Initial acoustic velocity [=] L/t;

MV Measured velocity [=] L/t

RV Velocity in rock solid φ Porosity, %

ACKNOWLEDGEMENTS

We greatly acknowledge the financial support provided by the companies

supporting Drilling Research Consortium.

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178

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http://hyperphysics.phy-astr.gsu.edu/hbase/tables/soundv.html

179

Table 7-1 - Inoic radii (after Pruett, 1987)

Ions

Dehydrated (Angstrom)

Hydrated (Angstrom)

Li 0.78 10.03 Na 0.98 7.9 K 1.33 5.32

NH4 1.43 5.37 Mg 0.78 10.8 Ca 1.06 9.6

Table 7-2 - Strength and Young's moduli used in DRILLER.

Shale Type

Strength

(Psi)

Young’s Modulus

(105 Psi) Native 5500 1.65 Water 4934 1.38

0.95 aw NaCl 5789 1.44 0.85 aw NaCl 6556 1.83 0.75 aw NaCl 8948 2.13 0.95 aw CaCl2 6258 1.56 0.85 aw CaCl2 8061 1.98

Pierre I

0.75 aw CaCl2 9600 2.12 Native 6000 2.62 Water 1600 1.28

0.95 aw NaCl 2600 1.40 0.85 aw NaCl 4600 2.31 0.75 aw NaCl 4700 2.47 0.95 aw CaCl2 2650 1.12 0.85 aw CaCl2 3300 1.92

Arco

0.75 aw CaCl2 3590 2.02

180

Figure 7-1 – Influence of pore pressure increase and formation weakening on wellbore instability.

Figure 7-2 – Schematic of equipment setup used to measure acoustic velocity.

181

Figure 7-3 – Equipment for measuring acoustic velocity of shale.

t = 0.3667Th+ 0.1043R2 = 0.9996

0

2

4

6

8

10

0 5 10 15 20 25

Thickness, mm

Tran

smit

Tim

e, u

s

Figure 7-4 – Transducer calibration and face-to-face time determination.

182

0

1000

2000

3000

4000

5000

6000

7000

0 20000 40000 60000 80000

Micro-Strain

Dev

iato

ric S

tres

s, p

si

Brittle Failure

Figure 7-5 – Stress-strain curve for Pierre I shale exposure to 19 wt% NaCl solution.

0

1000

2000

3000

4000

5000

6000

7000

0 20000 40000 60000

Micro-Strain

Dev

iato

ric S

tres

s, p

si

Plastic Failure

Figure 7-6 – Stress-strain curve for Arco shale exposure to 19 wt% NaCl solution.

183

2350

2400

2450

2500

2550

2600

2650

2700

0 300 600 900 1200 1500Time, minutes

Soni

c Ve

loct

iy, m

/s

DeionedWater8.0 wt % NaCl

19.0 wt% NaCl

Figure 7-7 – Effect of NaCl concentration on acoustic velocity of Pierre I shale.

2350

2400

2450

2500

2550

2600

2650

0 300 600 900 1200 1500Time, minutes

Soni

c Ve

loct

iy, m

/s

Deioned Water10.1 wt% CaCl218.8 wt% CaCl224.8 wt% CaCl2

Figure 7-8 – Effect of CaCl2 concentration on acoustic velocity of Pierre I shale.

184

2350

2400

2450

2500

2550

2600

0 300 600 900 1200 1500

Time, minutes

Soni

c Ve

loct

iy, m

/s Deioned Water10 wt% KCl20 wt% KCl25.6 wt% KCl

Figure 7-9 – Effect KCl concentration on acoustic velocity of Pierre I shale.

2400

2450

2500

2550

2600

2650

0 300 600 900 1200 1500

Time, minutes

Soni

c Ve

loct

iy, m

/s

aw=0.85 KClaw=0.85 NaClaw=0.85 CaCl2

Figure 7-10 – Effect of different solution on acoustic velocity of Pierre I shale.

185

-4

-2

0

2

4

6

8

10

0 5 10 15 20 25 30Salt Concentration, w%

Soni

c Ve

loci

ty C

hang

e, %

NaClCaCl2KCl

Figure 7-11 – Effect of salt concentration on acoustic velocity change for Pierre I shale.

-4

-2

0

2

4

6

8

10

-1 -0.5 0 0.5 1

Water Movement, %

Soni

c Ve

loci

ty C

hang

e, % NaCl

CaCl2KCl

Native Shale

Figure 7-12 – Effects of water movement on acoustic velocity change of Pierre I shale.

186

-4

-2

0

2

4

6

8

10

-0.2 0.2 0.6 1 1.4 1.8 2.2

Ions Movement, %

Soni

c Ve

loci

ty C

hang

e, % NaCl

CaCl2KCl

Native Shale

Figure 7-13 – Effect of ion movement on acoustic velocity for Pierre I shale.

0

2000

4000

6000

8000

10000

0 20000 40000 60000 80000

Micro Strain

Dev

iato

ric S

tres

s, p

si

Deioned Water19 wt% NaCl26 wt% NaClNative

Figure 7-14 – Effect of NaCl solution on stress-strain curves for Pierre I shale.

187

0

2000

4000

6000

8000

10000

0 20000 40000 60000 80000 100000Micro Strain

Dev

iato

ric S

tres

s, p

si

10.1 % CaCl218.8 % CaCl224.8 % CaCl2Native

Figure 7-15 – Effect of CaCl2 solution on stress-strain curves for Pierre I shale.

0

2000

4000

6000

8000

10000

12000

0 20000 40000 60000 80000 100000

Micro Strain

Dev

iato

ric S

tres

s, p

si

10 % KCl20 % KCl25.6 % KClNative

Figure 7-16 – Effect of KCl solution on stress-strain curves for Pierre I shale.

188

0

0.5

1

1.5

2

2.5

3

0.75 0.8 0.85 0.9 0.95 1

Water Activity

Youn

g's

Mod

ulus

, 105 p

si NaClCaCl2KCl

Native Shale

Figure 7-17 – Effects of different solution on Young’s moduli of Pierre I shale.

4000

5000

6000

7000

8000

9000

10000

0.75 0.8 0.85 0.9 0.95 1

Water Activity

Dev

iato

ric S

tren

gth,

psi

NaClCaCl2KCl Native Shale

Figure 7-18 – Effect of water activity on deviatoric strength for Pierre I shale.

189

4000

5000

6000

7000

8000

9000

10000

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6

Water Movement, %

Dev

iato

ric S

tren

gth,

psi NaCl

CaCl2KCl

Native Shale

Figure 7-19 – Effects of water movement on deviatoric strength of Pierre I shale.

4000

5000

6000

7000

8000

9000

10000

-0.2 0.2 0.6 1 1.4 1.8 2.2

Ion Movement, %

Dev

iato

ric S

tren

gth,

psi NaCl

CaCl2KCl

Native Shale

Figure 7-20 – Effect of ion movement on deviatoric strength for Pierre I shale.

190

Strength = 3*10-15Vp5.4121

R2 = 0.7366

4000

5000

6000

7000

8000

9000

10000

2300 2350 2400 2450 2500 2550 2600 2650 2700

Sonic Velocity, m/s

Dev

iatr

ic S

tren

gth,

psi

Figure 7-21 – Relationship between acoustic velocity and compressive strength for Pierre I shale immersed in various solutions of NaCl, KCl, and CaCl2.

3000

3100

3200

3300

3400

3500

3600

0 300 600 900 1200 1500

Time, minutes

Soni

c Ve

loct

iy, m

/s

Deioned Water8.0 wt % NaCl19.0 wt% NaCl26.0 wt% NaCl

Figure 7-22 – Effect of NaCl concentration on acoustic velocity for Arco shale.

191

3000

3100

3200

3300

3400

3500

3600

0 300 600 900 1200 1500

Time, minutes

Soni

c Ve

loct

iy, m

/s

Deioned Water10.1 wt% CaCl218.8 wt% CaCl224.8 wt% CaCl2

Figure 7-23 – Effect of CaCl2 concentration on acoustic velocity for Arco shale.

3000

3100

3200

3300

3400

3500

3600

0 300 600 900 1200 1500

Time, minutes

Soni

c Ve

loct

iy, m

/s

Deioned Water10 wt% KCl20 wt% KCl25.6 wt% KCl

Figure 7-24 – Effects of KCl concentration on acoustic velocity for Arco shale.

192

3200

3250

3300

3350

3400

3450

3500

3550

3600

0 300 600 900 1200 1500

Time, minutes

Soni

c Ve

loct

iy, m

/saw=0.85 KCl

aw=0.85 NaCl

aw=0.85 CaCl2

Figure 7-25 – Effect of different solutions (aw= 0.85) on acoustic velocity of Arco shale.

-14

-12

-10

-8

-6

-4

-2

0

2

4

0 5 10 15 20 25 30

Salt Concentration, wt%

Soni

c Ve

loci

ty C

hang

e, %

NaClCaCl2KCl

Figure 7-26 – Effect of salt concentration on acoustic velocity for Arco shale.

193

-14

-12

-10

-8

-6

-4

-2

0

0 0.5 1 1.5 2 2.5

Water Movement, %

Soni

c Ve

loci

ty C

hang

e, % NaCl

CaCl2

Figure 7-27 – Effect of water movement on acoustic velocity for Arco shale.

-14

-12

-10

-8

-6

-4

-2

0

-0.8 -0.5 -0.2 0.1 0.4 0.7 1

Ion Movement, %

Soni

c Ve

loci

ty C

hang

e, %

NaClCaCl2

Figure 7-28 – Effect of ion movement on acoustic velocity for Arco shale.

194

0

1000

2000

3000

4000

5000

6000

7000

0 20000 40000 60000 80000 100000Micro Strain

Dev

iato

ric S

tres

s, p

si

Deioned Water8 wt% NaCl19 wt% NaCl26 wt% NaClNative Shale

Figure 7-29 – Effect of NaCl solution on stress-strain curves for Arco shale.

0

1000

2000

3000

4000

5000

6000

7000

0 10000 20000 30000 40000 50000 60000

Micro Strain

Dev

iato

ric S

tres

, psi

10.1 wt% CaCl218.8 wt% CaCl224.8 wt% CaCl2Native Shale

Figure 7-30 – Effect of CaCl2 solution on stress-strain curves for Arco shale.

195

0

2000

4000

6000

8000

10000

12000

0 10000 20000 30000 40000 50000 60000Micro Strain

Dev

iato

ric S

tres

s, p

si

10 wt% KCl20 wt% KCl25.6 wt% KClNative Shale

Figure 7-31 – Effect of KCl solution on stress-strain curves for Arco shale.

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

0.75 0.8 0.85 0.9 0.95 1

Water Activity

Youn

g's

mod

ulus

, 105 p

si NaClCaCl2KCl

Native Shale

Figure 7-32 – Effect of different solutions on Young’s moduli (Arco shale).

196

0

2000

4000

6000

8000

10000

12000

0.75 0.8 0.85 0.9 0.95 1

Water Activity

Dev

iato

ric S

tren

gth,

psi

NaClCaCl2KCl

Native Shale

Figure 7-33 – Effect of salt solution on deviatoric strength of Arco shale.

1000

2000

3000

4000

5000

6000

0 0.4 0.8 1.2 1.6 2 2.4

Water Movement, wt%

Dev

iato

ric S

tren

gth,

psi NaCl

CaCl2Native Shale

Figure 7-34 – Effect of water movement on deviatoric strength of Arco shale.

197

1000

2000

3000

4000

5000

6000

-0.6 -0.2 0.2 0.6 1.0

Ions Movement, wt%

Dev

iato

ric S

tren

gth,

psi

NaClCaCl2

Native Shale

Figure 7-35 – Effect of ion movement on deviatoric strength of Arco shale.

Strength = 2*10-19Vp6.3082

R2 = 0.9217

0

1000

2000

3000

4000

5000

2900 3000 3100 3200 3300 3400 3500

Sonic Velocity, m/s

Dev

iato

ric S

tren

gth,

psi

Figure 7-36 – Relationship between acoustic velocity and compressive strength for Arco shale immersed in various solutions of NaCl, KCl, and CaCl2.

198

6

8

10

12

14

16

18

20

0.7 0.75 0.8 0.85 0.9 0.95 1Water Activity

Mud

Wei

ght,

ppg

NaCl

Break Down

Collapse

Safe RegionNative Shale

CaCl2

Figure 7-37 – Effects of salt solution on mud weight window for Pierre I shale.

5

7

9

11

13

15

17

19

0.7 0.75 0.8 0.85 0.9 0.95 1Water Activity

Mud

Wei

ght,

ppg

NaCl

CaCl2

Break Down

Safe Region

Native Shale

Collapse

Figure 7-38 – Influence of salt solution on mud weight window for Arco shale.

199

Chapter 8 : Stability of Deviated and Horizontal Wells: Mechanical, Chemical and Thermal Effects

ABSTRACT

Wellbore instability (particularly in shale) is regarded as a major problem in oil

and gas drilling operations. Many factors, such as rock properties, in-situ stresses,

chemical shale/fluid interactions and thermal effects, should be considered in well

trajectory designs and drilling fluid formulations in order to reduce wellbore instability

problems.

A comprehensive study of wellbore stability in shale formations that takes into

account the 3-dimensional earth stresses around the wellbore as well as chemical and

thermal effects is presented in this work. The effects of borehole configuration (e.g.

inclination and azimuth), rock properties (e.g. cohesion, friction angle, Poisson’s ratio,

membrane efficiency and permeability), temperature and drilling fluid properties (e.g.

mud density and chemical concentrations) on wellbore stability in shale formations have

been investigated.

Results from this study indicate that for low permeability shales, chemical

interactions between the shale and water-based fluids play an important role. Not only is

the activity of the water important but the diffusion of ions is also a significant factor for

saline fluids. Cooling drilling fluids is found to be beneficial in preventing compressive

failure. However, decreasing the mud temperature can be detrimental since it reduces the

fracture pressure of the formation, which can result in lost circulation problems. The

magnitude of these thermal effects, depend very much on shale properties, earth stresses

and wellbore orientation and deviation.

Conditions are identified when chemical and thermal effects play a significant

role in determining the mud-weight-window when designing drilling programs for

200

horizontal and deviated wells. The results presented in this chapter will help in lowering

the risks associated with wellbore stability and thereby lower the overall well drilling

costs.

8.1 INTRODUCTION

With the development of drilling technologies, directional, horizontal, and

extended-reach wells are becoming routine operations (Ottesen and Kwakwa, 1991; Ong

et al., 2000). However, one of the critical problems that has hampered the lowering of

drilling costs is wellbore instability. When combating this problem, a comprehensive

study must be undertaken due to the unique properties of shales, as discussed in previous

chapters.

Formation mechanical properties that affect wellbore stability include in-situ

stress state, compressive strength, internal frictional angle, elastic modulus, and Poisson

ratio. After analyzing 450 drilling records in the western Canadian Over-thrust Belt,

Woodland (1990) pointed out that borehole instability is a rock mechanics problem.

Ottesen et al. (1991) studied the mechanical effects on the wellbore stability of the first

horizontal well in the U. K. sector of the North Sea. They found that determining in-situ

stress is of great importance in studying wellbore stability in horizontal wells. Chen et al.

(1996) concluded that rock strength was much more important in wellbore stability than

rock elastic properties, drainage conditions and bedding planes.

Based on analyzing the in-situ stresses and rock properties, Moos et al. (1998) put

forward a method to optimize well trajectories. Awal et al. (2001) found that the

optimized trajectory can be vertical, directional, or horizontal, depending on whether the

region is tectonically relaxed or active and also whether or not, the prevailing in-situ

stress is normal, thrust, or of a strike-slip faulting type. When a vertical well is drilled

into a normal faulting stress regime ( hHv σ>σ>σ ), such as was done in the Ula Field a

201

stable wellbore resulted (Last et al., 1996). However, under a strike-slip faulting stress

regime ( hvH σ>σ>σ ), such as is found in the Cusiana Field, directional and

horizontal wells are more stable than vertical wells. Russell et al. (2003) recommended

that the wellbore should not be drilled parallel to the maximum horizontal stress ( Hσ ) in

the Tullich Field, North Sea.

From the above review, we see that an optimal well trajectory is one of the key

factors for successfully drilling through shales. In wellbore stability terms, optimal well

trajectory can be obtained by considering both strength and in-situ stress anisotropies

(Ong et al., 1993).

Several types of well trajectories, such as build-and-hold, S-shape etc. are

available (Ma et al., 1998). Normally, the build-and-hold trajectory, as shown in Figure

8-1, is chosen (Ma, et al 1998; Ong et al. 2000). This trajectory is also referred to as a

“three-section” trajectory as it includes a vertical section, a build section, and a hold

section. As with any wellbore profile, two key parameters in the tangent section: azimuth

( aΦ ) and inclination ( tα ) define the wellbore trajectory. Therefore, the well trajectory

optimization is based on the selection of these two parameters.

Wellbore stability should not be studied without considering chemical and

thermal effects because they affect both local stress distributions and rock mechanical

properties. From Chapter 7, we see that strength and acoustic properties of shales are

altered by the chemical shale/mud interaction. In addition, Fam et al. (2003) found that

the compressive strength can be reduced by 10% for an increase in temperature from 20

to 60oC.

8.2 STRESSES MODEL

The local stress distribution around a wellbore are controlled by in-situ stresses,

chemical, thermal, and hydraulic effects.

202

8.2.1 Local Stresses Induced by In-situ Stresses and Hydraulic Effects

The total stress states around a wellbore as governed by in-situ stresses and

hydraulic effects are expressed as follows (Fjaer et al., 1992):

( )

( )

( )⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪

⎨

⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛−θτ+θτ−=τ

⎟⎟⎠

⎞⎜⎜⎝

⎛+θτ+θτ−=τ

θ⎟⎟⎠

⎞⎜⎜⎝

⎛+−τ+θ⎟

⎟⎠

⎞⎜⎜⎝

⎛+−⎟⎟

⎠

⎞⎜⎜⎝

⎛ σ−σ=τ

⎥⎥⎦

⎤

⎢⎢⎣

⎡θτ+θσ−σν−σ=σ

−θ⎟⎟⎠

⎞⎜⎜⎝

⎛+τ−

θ⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛ σ−σ−⎟

⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛ σ+σ=σ

+θ⎟⎟⎠

⎞⎜⎜⎝

⎛−+τ+

θ⎟⎟⎠

⎞⎜⎜⎝

⎛−+⎟⎟

⎠

⎞⎜⎜⎝

⎛ σ−σ+⎟

⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛ σ+σ=σ

θ

θ

θθ

2

2w

yzxzrz

2

2w

yzxzz

2

2w

4

4w

xy2

2w

4

4wyx

r

2

2w

xy2

2w

yxzzz

ww

4

4w

xy

4

4wyx

2

2wyx

ww

2

2w

4

4w

xy

2

2w

4

4wyx

2

2wyx

rr

rr

1sincos

rr

1cossin

2sinr

r2

rr

312sinr

r2

rr

312

2sinr

r42cos

rr

2

Pr

r2sin

rr

31

2cosr

r31

2rr

12

Pr

r2sin

rr

4r

r31

2cosr

r4

rr

312r

r1

2

(8-1)

At the wellbore wall ( wrr = ), the above equations can be expressed as (see

Appendix 3 for derivation):

203

( ) ( )

( )[ ]( )

⎪⎪⎪

⎩

⎪⎪⎪

⎨

⎧

=τ=τ

θτ−θτ=τ



θ

θ

θθ

0

sincos2

2sin42cos2

P2sin42cos2P

rzr

xzyzz

xyyxzzz

wxyyxyx

wrr

(8-2)

8.2.2 Local Stresses Induced by Chemical and Thermal Effects

Local stresses induced by chemical and thermal effects can be expressed as (Yu et

al., 2001)

( )( ) ( ) ( )

( )( ) ( )

( ) ( ) ( )

( )( ) ( ) ( )⎪

⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪⎪

⎨

⎧

ν−α

+ν−

ν−α=σ

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡−

ν−α

−

⎥⎦

⎤⎢⎣

⎡ −ν−

ν−α−=σ

ν−α

+ν−

ν−α=σ

∫

∫ ∫

θθ

t,rT13

Et,rP

121

t,rTrdrt,rTr1

13E

t,rPrdrt,rPr1

121

rdrt,rTr1

13E

rdrt,rPr1

121

fmfp

pzz

r

r

ff2

m

fp

fp2

p

r

r

r

r

f2

mfp2

prr

w

w w

(8-3)

( ) ( ) ipf

p Pt,rPt,rP −= (8-4)

( ) ( ) if Tt,rTt,rT −= (8-5)

In Equation (8-3), the first term accounts for the chemical and the second term for

thermal effects.

At the wellbore wall ( wrr = ), Equation (8-3) can be expressed as

204

( )

( ) ( ) ( )

( )( ) ( ) ( )

⎪⎪⎪⎪

⎩

⎪⎪⎪⎪

⎨

⎧

−ν−

α+−

ν−

ν−α=σ

−ν−

α+−

ν−

ν−α−=σ

=σ

θθ

iwm

iwp

zz

iwm

iwp

rr

TT13

EPP

121

TT13

EPP

121

0

(8-6)

8.2.3 Pore Pressure and Temperature Profiles

It can be observed from Equation (8-6) that the pore pressure and temperature

profiles need to be determined in order to calculate the stress distribution around a

wellbore. The pore pressure profile is altered by water and ion movement into or out of

the shale due to hydraulic, chemical, and electrical potentials. The electrical effects are

beyond this discussion. Pore pressure caused by hydraulic and chemical potentials can be

calculated as (Lomba et al., 2000):

0t

CcD

nRTKPcK

tP s

feff

II2

f

I =∂

∂−∇−

∂∂

(8-7)

The solute concentration profile ( sC ) in the above equation can be calculated by

the following diffusivity equation (Yu et al., 2001):

0CDt

Cs

2eff

s =∇−∂

∂

(8-8)

Boundary and initial conditions for solute concentration and pore pressure can be

expressed as

( ) ( )( ) ( )( ) ( )⎪

⎪⎩

⎪⎪⎨

⎧

=∞=∞

==

==

ipis

wwpdfws

ipis

P0,P;Ct,C

Pt,rP;Ct,rC

P0,rP;C0,rC

(8-9)

For a radial system, the formation temperature equation can be described as (see

205

reference by Chen et al., 2003 for derivation and more detailed discussion)

⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+∂

∂=

∂∂

rT

r1

rTc

tT

2

2

0 (8-10)

The initial and boundary conditions are as follows

( )( )( )⎪

⎩

⎪⎨

⎧

=∞=

=

i

ww

i

Tt,TTt,rT

T0,rT

(8-11)

Pore pressure and temperature profiles can be obtained by solving Equations (8-

7), (8-8) and (8-10) with their corresponding initial and boundary conditions.

8.3 FAILURE CRITERIA

8.3.1 Compressive Failure

In this chapter, the Mohr-Coulomb failure criterion is used to evaluate

compressive failure (Fjaer et al., 1992):

( ) ( ) Φα−σ+≤α−σ 2pp30pp1 tanPCP (8-12)

8.3.2 Tensile Failure

When the minimum effective principle stress at the wellbore is less than the

tensile strength of the formation (assuming compression is positive), tensile failure

occurs. Therefore, the tensile criterion can be expressed as:

( ) tpp3 P σ−≤α−σ (8-13)

where, tσ is the tensile strength of the rock.

8.4 WELLBORE STABILITY ANALYSIS

8.4.1 Input Data

Three types of in-situ stress regimes are considered in this chapter: normal

206

faulting, thrust faulting, and strike-slip faulting. The data for in-situ stresses used in our

simulation are shown in Table 8-1.

Other information, including mechanical, chemical, and thermal properties is

listed in Table 8-2.

8.4.2 Mechanical Effects on Wellbore Stability

8.4.2.1 In-situ stresses

Under a normal faulting stress regime, the effects of well azimuth and inclination

(0o for a vertical well and 90o for a horizontal well) on the mud-weight-window (MWW)

are shown in Figure 8-2. The figure contains three pairs of lines, which represents three

well directions ( 0A = for a well along the Hσ , 90A = along hσ , and 45A = between

Hσ and hσ ). In this figure, the lower set of lines stands for the lower critical mud weight

below which compressive failure occur, and the upper set of lines indicates upper critical

mud weight beyond which tensile failure occurs.

It is seen from Figure 8-2 that when 0A = , the lower critical mud weight

increases (from 10.1 ppg for a vertical well to 12 ppg for a horizontal well), while the

upper bound decreases (from 19.1 ppg for a vertical well to about 18 ppg for a horizontal

well) with an increase of inclination. This is due to the fact that under a normal faulting

stress regime, the stress concentration increased with well inclination. This requires

higher mud weights to prevent compressive failure.

Comparing the three cases: 0A = , 45A = , and 90A = , we see that the lower

critical mud weight is the lowest, while the upper critical mud weight is the highest at the

same inclination when 90A = . Therefore, under the simulated normal faulting stress

regime, the optimized directional well trajectory is along hσ with low inclinations.

The effects of well inclination and azimuth on the MWW under a thrust faulting

stress regime ( vhH σ>σ>σ ) are shown in Figure 8-3. It is seen from this figure that

207

when 45A = , both lower and upper critical mud weight decreases with increasing

inclinations. This means that directional wells are less apt to have compressive failure,

and easier to have tensile failure than vertical wells.

Comparing the three cases: 0A = , 45A = , and 90A = , we see that the lower

critical mud weight is the lowest, while the upper critical mud weight is the highest at the

same inclination when 0A = . Therefore, under our simulated thrust faulting stress

regime, the optimized directional well trajectory is along Hσ with high well inclinations.

Figure 8-4 shows the effects of well inclination and azimuth on the MWW under

strike-slip faulting stress regime. It is seen that the lower critical mud weight decreases

while the upper critical mud weight increases with the increase of well inclination in all

three cases. This means that under strike-slip faulting conditions, directional and

horizontal wells are more stable than vertical wells. The effects of well azimuth should be

considered in two ways. If the wellbore instability problem is dominated by compressive

failure, then drilling along Hσ ( 0A = ) results in more stable boreholes. On the other

hand, if the wellbore instability problem is dominated by tensile failure, then drilling

along the direction between the maximum and minimum horizontal stresses ( 45A = )

will result in more stable boreholes. The specific direction will be determined by the

magnitude of the in-situ stresses.

From the above analysis, we see that the in-situ stress state plays a critical role in

the determination of a suitable well trajectory for maintaining wellbore stability.

Different optimal well trajectories should be determined according to the various in-situ

stress conditions.

In addition to the in-situ stresses, other mechanical properties of rocks that affect

wellbore stability will be discussed below. In the following discussion, we only consider

the normal faulting stress regime.

208

8.4.2.2 Cohesive strength

As discussed in Chapter 7, we see that the compressive strength is altered due to

the interaction between shales and water based muds. Generally, in such cases, the

cohesive strength of the formation decreased (Chen et al., 2003). In order to study the

effects of cohesion on wellbore stability, we assumed the wellbore inclination to be 60˚,

well azimuth 30˚, and tensile strength to be constant. Other information used is shown in

Table 2. The effect of cohesion on the MWW is shown in Figure 8-5.

As shown in Figure 8-5, the lower critical mud weight increases with decreasing

cohesion. For example, we noted in Chapter 7 that the deviatoric compressive strength of

Arco shale decreases from 5950 psi to 2600 psi after it was exposed to a 0.95 aw NaCl

solution. By using the Griffith crack propagation theory, we have

( )cD

2D

0 2C

σ⋅+σσ

= (8-14)

After substituting the deviatoric strength and confining stress into the above

equation, we are able to obtain cohesion values to be between 2220 psi and 540 psi for

5950 psi and 2600 psi deviatoric strengths. Therefore, the cohesion decreased from 2220

psi to 540 psi after the Arco shale was exposed to the 0.95 aw NaCl solution. From Figure

8-5, we see that the mud weight must be increased from 11.1 ppg to 14.5 ppg in order to

maintain wellbore stability in the Arco shale when a 0.95 aw NaCl solution is used.

8.4.2.3 Frictional angle

In addition to cohesion, the frictional angle is altered by mud/shale interactions

(Chen et al., 2002a). It is seen in Figure 8-6 that the lower critical mud weight increases

significantly with a decreasing internal frictional angle. For example, lower critical mud

weights increased from 10 ppg to 13.5 ppg when the internal friction angle decreased

from 40˚ to 20˚.

209

8.4.2.4 Poissons ratio The effects of the Poisson ratio on the MWW are shown in Figure 8-7. It is seen

that the upper critical mud weight decreases with an increase in the Poissons ratio, while

the influence of Poissons ratio on the lower critical mud weight is small. Generally, the

mud density is determined based on the lower critical mud weight, so the effects of

Poissons ratio on wellbore stability is negligible. This result matches the observation by

Ottesen and Kwakwa (1991).

8.4.3 Chemical Effects in Wellbore Stability

8.4.3.1 Shale permeability

The effect of permeability on critical mud weight is shown in Figure 8-8. It can be

seen from this figure that the lower critical weight increases, while the upper critical mud

weight decreases with decreasing permeability (assuming all other parameters remain the

same). This is because the effective stress in a lower permeability formation is lower at

any given time compared to that of a high permeability formation, which causes wellbore

instability problems (Yu et al., 2001). For example, when the permeability is equal to 2

nd, the upper critical mud weight reaches the lower critical mud weight. This means that

wellbore instability problems cannot be avoided when drilling through such low

permeability formations.

8.4.3.2 Pore pressure

Pore pressure plays a crucial role in wellbore stability. The chemical effects,

involving water and ion movement into or out of shale formations, and thermal effects

can change the pore pressure distribution around the wellbore, which may cause wellbore

instability problems. The effects of pore pressure on MWW are shown in Figure 8-9.

We see from Figure 8-9 that the lower critical mud weight increases, while the

upper critical mud weight decreases with an increase in pore pressure. This means that

210

both compressive and tensile failures easily occur due to an effective stress decrease

with increasing pore pressure. Therefore, it is of great importance to prevent pore

pressure increases around a wellbore so as to improve wellbore stability.

8.4.3.3 Membrane efficiency

The effects of membrane efficiency (KII) on MWW are shown in Figure 8-10.

Here, it is important to note that KII is a negative value; therefore, a higher absolute value

represents a larger membrane efficiency.

It can be seen from Figure 8-10 that the lower critical mud weight increases,

while the upper critical mud weight decreases with increasing KII. This demonstrates that

when the concentration of the drilling fluid is less than that of the pore fluid, the semi-

membrane properties of shale is detrimental to wellbore stability. From this result, we are

able to predict that wellbore stability can be improved when high ionic concentration

drilling fluid is used to drill shale formation with high membrane efficiency.

8.4.3.4 Diffusion coefficient

The effects of the ionic diffusion constants on the MWW are shown in Figure 8-

11. It is seen that the lower critical mud weight decreases while the upper critical mud

weight increases with increased diffusion coefficient when the concentration of the

drilling fluid is lower than that of the pore fluid. From our discussion on water and ion

movement in Chapter 5 and Chapter 6, we know that the movement of water and ion

occurs simultaneously and that the movement of water is hampered by the movement of

ions. When the ion concentration in the drilling fluid is lower than that in the pore fluid,

ions diffuse from the pore fluid into the drilling fluid and water moves in the opposite

direction. For a high diffusion coefficient, diffusion of ions from the pore fluid into the

drilling fluid helps prevent more water movement into the formation. This, in turn,

prevents a high pore pressure increase, which improves wellbore stability.

211

8.4.4 Thermal Effects on Wellbore Stability

8.4.4.1 Mud in-let temperature

The effects of the mud inlet temperature on the MWW are shown in Figure 8-12.

It should be noted that the effects of temperature on strength (tension and compressive)

are not considered in this analysis.

It is seen that both lower and upper critical mud weights decrease with decreasing

mud inlet temperature due to the fact that a lower compressive stress is generated when

the mud temperature is lowered. This demonstrates that although mud cooling is

beneficial to prevent compressive failure, it is detrimental to tensile failure. Therefore in

formations with low fracture pressures, we should avoid mud cooling.

8.4.4.2 Geothermal gradient

Figure 8-13 shows the effects of the geothermal gradient on MWW. As shown in

this figure, both lower and upper critical mud weights decrease with an increase in the

geothermal gradient. This means that in high geothermal gradient formations, care should

be taken to avoid tensile failure, while in low geothermal gradient formations,

compressive failure is more likely and should be avoided.

8.4.4.3 Volumetric-thermal-expansion-constant

The volumetric-thermal-expansion-coefficient (sometimes simply called thermal

expansion coefficient) is a thermodynamic property of a substance given by

,constT

1

=ρ⎟⎠⎞

⎜⎝⎛

∂ρ∂

⎟⎟⎠

⎞⎜⎜⎝

⎛ρ

−=β (8-15)

Volumetric-thermal-expansion-coefficients for different rocks vary from 2.4×10-5 oF –1 for basalts to 5.5×10-5 oF-1 for sandstones (Yu et al., 2002). The effects of

volumetric- thermal-expansion-coefficients of the rock matrix on the MWW are shown in

212

Figure 8-14.

It can be seen from Figure 8-14 that both lower and upper critical mud weights

decrease with increasing matrix volumetric-thermal-expansion-constants. Since the

bottom hole mud temperature is less than the formation temperature, a lower thermal

compressive stress is generated when the matrix volumetric thermal expansion constant is

high, which causes both lower and upper critical mud weights to decrease.

8.5 CONCLUSIONS

1. Well trajectory optimization for wellbore stability purposes should be based

on the in-situ stress state. Under normal faulting stress regime conditions, a

vertical well is more stable than a directional or a horizontal well. However,

directional and horizontal wells are more stable than vertical wells in thrust

faulting stress regions. Under strike-slip faulting stress regime conditions, the

determination of the well inclination and azimuth should be based on the

magnitude and direction of the stress state.

2. Formation permeability has a significant effect on wellbore stability in shales.

More wellbore instability problems are expected in low permeable shales than

in high permeability shales (all else being the same).

3. Cooling drilling fluids is found to be beneficial for preventing compressive

failure. However, decreasing the mud temperature can be detrimental since it

reduces the fracture pressure of the formation, which can result in lost

circulation problems.

4. The thermal expansion coefficient of the rock matrix is a crucial controlling

parameter when studying thermal effects on wellbore instability. In formations

with a low thermal expansion coefficient, the thermal effect is not significant.

5. In weak and low permeability shale formations, besides the mechanical

213

properties, chemical and thermal effects should be considered when

addressing wellbore instability problems.

NOMENCLATURE

za Well azimuth [=] degree

0c Thermal diffusivity [=] L2/t

fC Fluid compressibility [=] t/m

0C Cohesive strength [=] F/L2

dfC Drilling fluid solute concentration [=] mol/L3

iC Initial pore fluid solute concentration [=] mol/L3

sC Pore fluid solute concentration [=] mol/L3

effD Effective solute diffusion coefficient [=] L2/t


wi Well inclination [=] degrees

IK A parameter related to permeability [=] L3-t/m

IIK A parameter related to membrane efficiency [=] L3-t/m

frK Bulk modulus of the skeleton material [=] m/L-t2

sK Bulk modulus of the dry rock [=] m/L-t2

n Number of molars of constituent of dissociating solute [=] amount


iP Initial pore pressure [=] m/L-t2

214

wP Wellbore pressure [=] m/L-t2

)t,r(Pf Pore pressure fluctuation [=] m/L-t2

r Near wellbore position [=] L

wr Wellbore radius [=] L

R Ideal gas constant [=] m-L2/t2-amount-T

t Time [=] t

T Formation temperature [=] T

0T Initial formation temperature [=] T

wT Wellbore wall temperature [=] T

∞ Far field position [=] L

θ Point location angle [=] degrees

Φ Internal frictional angle [=] degrees

1σ Maximum principle stress [=] m/L-t2

2σ Medium principle stress [=] m/L-t2

3σ Minimum principle stress [=] m/L-t2

hσ Minimum in-situ horizontal stress [=] m/L-t2

Hσ Maximum in-situ horizontal stress [=] m/L-t2

tσ Tensile strength [=] m/L-t2

vσ Overburden stress [=] m/L-t2

215

rrσ Radial normal stress at wellbore [=] m/L-t2

θθσ Hoop stress at wellbore [=] m/L-t2

zzσ Axial stress at wellbore [=] m/L-t2

xσ Normal stress in x-direction [=] m/L-t2

yσ Normal stress in y-direction [=] m/L-t2

zσ Axial stress [=] m/L-t2

zθτ Shear stress at wellbore [=] m/L-t2

rzτ Shear stress at wellbore [=] m/L-t2

θτr Shear stress at wellbore [=] m/L-t2

xyτ In-situ shear stress in (x, y, z) coordinated system [=] m/L-t2

yzτ In-situ shear stress in (x, y, z) coordinated system [=] m/L-t2

zxτ In-situ shear stress in (x, y, z) coordinated system [=] m/L-t2



zΦ Well azimuth in target section [=] degrees

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220

Table 8-1 - In-situ stress state

Stress State σv (psi/ft)

σH (psi/ft) σh (psi/ft)

Normal faulting 1.0 0.9 0.85 Thrust faulting 1.0 1.1 1.05

Strike-slip faulting 1.0 1.05 0.95

Table 8-2 - Input data (after Yu et al., 2001)

Variables Values Model Type Poroelasticity

Failure Criteria Mohr-Coulomb Well Depth 10,000 ft

Equivalent Pore Pressure 9 lbm/gal Poisson’s Ratio 0.22 Biot’s Constant 0.9

Young’s Modulus 106 psi Cohesion 2000 psi

Frictional Angle 30o

Mechanical

Tensile Strength 100 psi KI 2×10-19 KII -5 ×10-18 m3s/Kg

Drilling fluid concentration 0.1M Pore fluid concentration 1M

Fluid compressibility 10-6

Chemical

Diffusion constant 4.9×10-11 m2/s Geothermal gradient 1.1ºF/100ft

Thermal diffusivity constant 1.5×10-3in2/s Volumetric thermal expansion of

matrix 5×10-51/oF

Volumetric thermal expansion of fluid 5×10-41/oF Inlet mud temperature 100 oF

Earth surface temperature 60 oF Drilling fluid heat conductivity 1 Btu/hr-ft-ºF

Drilling fluid specific heat 0.4 Btu/lb-ºF Earth conductivity 1.3 Btu/hr-ft-ºF Earth specific heat 0.2 Btu/lb-ºF

Overall heat transfer coefficient in drill pipe

30 Btu/hr-ft2-ºF

Thermal

Overall heat transfer coefficient in annulus

1 Btu/hr-ft2-ºF

221

Figure 8-1 – A typical directional well trajectory.

222

10

12

14

16

18

20

22

0 10 20 30 40 50 60 70 80 90

Inclination, degree

Mud

Wei

ght,

ppg

A=0, CollapseA=0, BreakdownA=45, CollapseA=45,BreakdownA=90, CollapseA=90, Breakdown

Figure 8-2 – Effect of inclination and azimuth on MWW under normal faulting stress regime.

10

12

14

16

18

20

22

24

26

0 10 20 30 40 50 60 70 80 90

Inclination, degree

Mud

Wei

ght,

ppg

A=0, CollapseA=0, BreakdownA=45, CollapseA=45,BreakdownA=90, CollapseA=90, Breakdown

Figure 8-3 – Effect of inclination and azimuth on MWW under thrust faulting stress regime.

223

10

12

14

16

18

20

22

24

0 10 20 30 40 50 60 70 80 90

Inclination, degree

Mud

Wei

ght,

ppg

A=0, LowA=0, HighA=45, LowA=45,HighA=90, LowA=90, High

Figure 8-4 – Effect of well inclination and azimuth on MWW under strike-slip faulting stress regime.

10

11

12

13

14

15

16

17

18

19

400 600 800 1000 1200 1400 1600 1800 2000 2200 2400Cohesion, psi

Mud

Wei

ght,

ppg Collapse

Breakdown

Figure 8-5 – Effect of cohesion on MWW.

224

10

11

12

13

14

15

16

17

18

19

20 22 24 26 28 30 32 34 36 38 40Internal Friction Angle, degree

Mud

Wei

ght,

ppg Collapse

Breakdown

Figure 8-6 – Effect of frictional angle on MWW.

11

12

13

14

15

16

17

18

19

0.2 0.24 0.28 0.32 0.36 0.4Poissons Ratio

Mud

Wei

ght,

ppg

Collapse Breakdown

Figure 8-7 – Effect of Poissons ratio on MWW.

225

11

12

13

14

15

16

17

18

19

0 4 8 12 16 20 24 28 32 36

Permeability, nanodarcy

Mud

Wei

ght,

ppg

CollapseBreakdown

Figure 8-8 – Effect of shale permeability on MWW.

11

12

13

14

15

16

17

18

19

8 8.5 9 9.5 10 10.5 11

Equivalent Pore Pressure, ppg

Mud

Wei

ght,

ppg

Collapse

Breakdown

Figure 8-9 – Effect of pore pressure on MWW.

226

11

12

13

14

15

16

17

18

19

0 2 4 6 8 10 12 14 16

KII, m3s/Kg

Mud

Wei

ght,

ppg

CollapseBreakdown

Figure 8-10 - Effect of shale membrane efficiency on MWW ( sdf CC < ).

12

13

14

15

16

17

18

0 10 20 30 40 50 60 70 80

Diffusion Constant, 10-11m2/s

Crit

ical

Mud

Wei

ght,

ppg Collapse

Breakdown

Figure 8-11 - Effect of ion diffusion constant on MWW ( sdf CC < ).

227

11

12

13

14

15

16

17

18

19

100 120 140 160 180 200

Mud Inlet Temperature, OF

Mud

Wei

ght,

ppg

Collapse

Breakdown

Figure 8-12 - Effect of mud temperature on MWW.

10

11

12

13

14

15

16

17

18

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

Geothermal Gradient, OF/100 ft

Mud

Wei

ght,

ppg

Collapse

Breakdown

Figure 8-13 - Effect of geothermal gradient on MWW.

228

11

12

13

14

15

16

17

18

19

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6Volumetric Thermal Expansion

Constant of Rock, 10-5 OF -1

Crit

ical

Mud

Wei

ght,

ppg

Collapse

Breakdown

Figure 8-14 - Effect of matrix volumetric-thermal-expansion-constants on MWW.

229

Chapter 9: Summary and Conclusions

Based on analyzing the unique properties of shales, the problems related to

wellbore instability in shales are formulated and some solutions are presented. From

theoretical analysis to laboratory testing, a comprehensive study of mechanical effects,

chemical effects, and thermal effects is covered in this dissertation.

A model is developed for coupling the strength of laminated shales with the stress

state at the wellbore wall. This model allows the simulation of wellbore instability for

directional wells in laminated formations. In laminated shales, the interaction angle

between the wellbore and bedding plane is critical for the determination of whether

drilling through laminated formations will induce instability along bedding planes.

Critical mud weights are calculated for different well orientations relative to the bedding

planes. Results show that critical mud weights are strongly wellbore orientation

dependent. Therefore, optimal well trajectory for wellbore stability control can be

planned by considering both the strength and in-situ stress anisotropies in laminated

shales. Model results when compared to the Pedernales Field mud weight case show

excellent agreement.

A model was presented to predict pore pressure changes during a shale

compressive strength test. The simulation results show that pore pressure increases with

an increase in strain rate and decrease with an increase in permeability. Two phenomena,

pore pressure build-up and dilatancy effects are attributed to strain rate related

compressive strength alteration. The compressive strength can increase with the strain

rate if dilatancy exists, and decrease if pore pressure builds up. Our experimental results

show that the compressive strength for soft Pierre I shale decreases, while the strength for

hard Arco shale increases with increase of the strain rate. In our tests, dilatancy effects

230

are more dominant in hard Arco shale and pore pressure build-up effects are more

dominant in soft Pierre I shale. It was pointed out that during shale compressive strength

testing, different strain rates should be selected in accordance with the intended

application of the test.

A new simple method, called the Gravimetric–Swelling Test (GST), has been

developed that allows for the direct measurement of water and ion movement into or out

of a shale sample. Time-dependent data from this GST technique show significant

changes in water and ion movement during the interaction between shales and drilling

fluids. It was also shown that different types of cations have different influences on

water/ion movement. Combined with other tests, the GST can be used to evaluate the

effectiveness of mud systems. These tests are simple to conduct and, therefore, can be

conducted at the rig floor provided that shale samples (cm size drill cuttings) are

available.

Based on the GST results, this dissertation presents a set of experiments which

analyze the effects of osmosis, ion diffusion, and capillarity on water and ion movement

when shales interact with water-based muds. Results show that water movement is not

only controlled by osmosis (water activity), but is also influenced by ion diffusion and

capillary phenomenon. A method is presented for correcting for capillary effects, which

are not present downhole.

Experimental results are presented to show how the compressive strength and

acoustic velocities of different types of shale change when they are exposed to water-

based fluids. The acoustic velocity and compressive strength of a soft, high water

activity, Pierre I shale increased after exposure to different ionic solutions, while for the

lower water activity Arco shale, sonic velocity and strength decreased. By combining

these tests with GST results, it is clearly shown that these different effects correlate well

231

with the movement of water and ion into or out of the shale. In every case studied, water

adsorption weakens the shale, while ion adsorption strengthens the shale.

The influence of salt type and salt concentration on the strength and sonic velocity

of the two shales was also investigated. It was found that adsorption of potassium ions

greatly increased the strength of Pierre I shale. It was seen that the ionic content of a

water-based fluid has a significant effect on changes of shale properties. It is shown that

the changes in sonic velocity and compressive strength are highly correlated. This

suggests that it may be feasible to use sonic logging data to determine changes in the

mechanical properties of shale.

Finally, a modeling study of wellbore stability of shale formations is presented. It

takes into account earth stresses around the wellbore as well as chemical and thermal

effects. It is pointed out that well trajectory optimization for wellbore stability purposes

should be based on formation lamination as well as the in-situ stress state. For a normal

faulting stress regime, a vertical well was found to be more stable than directional and

horizontal wells. However, directional and horizontal wells are more stable than vertical

wells in thrust faulting stress regions. In the strike-slip faulting stress regime, the

determination of well inclination and azimuth should be based on the magnitude and

direction of the stress state. Results from this study indicate that for low permeability

shales, chemical interactions between the shale and water-based fluids play an important

role. Not only is the activity of the water important but the diffusion of ions is also a

significant factor. Cooling drilling fluids is found to be beneficial in preventing

compressive failure. However, decreasing the mud temperature can be detrimental since

it reduces the fracture pressure for the formation, which can result in lost circulation. The

magnitude of these thermal effects, depend very much on shale properties, earth stresses,

and wellbore orientation and deviation.

232

Appendix 1: Strength of Non-laminated Rock

Based on the Mohr-Coulomb failure criterion, for nonlaminated (strength

isotropic) formations, rock failure occurs when the combination of the normal and shear

stresses at the failure plane meets

Φσ+≥τ tanC0 (A1-1)

Normal and shear stresses at the failure plane can be calculated as

( )

( ) ( )⎪⎪⎩

⎪⎪⎨

⎧

Φσ−σ−σ+σ=σ

Φσ−σ=τ

sin21

21

cos21

3ns3ns

3ns

(A1-2)

Substituting Equation (A1-2) into (A1-1) yields

( )Φ−Φ

σ⋅Φ++σ=σtancos/1

1tanC2 303ns (A1-3)

There exists the following relationship between the cosine and tangent functions

of the internal frictional angle

Φ+=Φ

2tan1cos

1 (A1-4)

Substituting Equation (A1-4) into (A1-3) and arranging, we have:

( ) ( ) ]tantan1[tanC2 2303ns Φ+Φ+σ⋅Φ++σ=σ (A1-5)

In the above equation, the angle of internal friction, Φ is related to the coefficient

of internal friction, µ by

Φ=µ tan (A1-6)

Substituting (A1-6) into (A1-5) yields

233

( ) ( ) ]1[C2 2303ns µ+µ+µσ++σ=σ (A1-7)

234

Appendix 2: Strength of Laminated Formations

Referring to Figure 3-2, the rock fails along the bedding plane if the combination

of normal and shear stress at the bedding plane meets the following condition,

ww0 tanC Φσ+=τ (A2-1)

Normal and shear stress at the bedding plane can be calculated as

( )

( ) ( )⎪⎪⎩

⎪⎪⎨

⎧

βσ−σ−σ+σ=σ

βσ−σ=τ

2cos21

21

2sin21

3bs3bs

3bs

(A2-2)

The internal friction angle of a bedding plane, wΦ is related to the internal

frictional coefficient of the bedding plane, wµ by

wwtan µ=Φ (A2-3)

Substituting the Equation (A2-2) and (A2-3) into (A2-1) yields

( )( ) βµ⋅β−

σ⋅µ++σ=σ

2sintan1C2

w

3ww03bs

(A2-4)

235

Appendix 3: Stress State Around Wellbore

Referring to the well configuration in Figure 3-4, we assume that the principle

stresses in the virgin formation are: the vertical stress, vσ ; the maximum horizontal

stress Hσ ; and the minimum horizontal stress, hσ . A coordinate system (x’, y’, z’) is

oriented so that x’ is parallel to Hσ , y’ is parallel to hσ , and z’ is parallel to vσ . This in-

situ stress can be expressed in coordinated system (x’, y’, z’) as

[ ]( )

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

σσ

σ=σ

v

h

H'z,'y,'x

0

0

(A3-1)

The stresses in the vicinity of the wellbore are most conveniently described in a

co-ordinate system (x, y, z) where the z-axis is parallel to the wellbore (Fjaer et al.,

1992).

A transformation from (x’, y’, z’) to (x, y, z) can be obtained in two operations: 1)

a rotation of za around the z’-axis, and 2) a rotation of wi around the y’–axis. The angle

wi represents the wellbore inclination (deviation). The angle za can be used to represent

the well azimuth based on the direction of the maximum horizontal principle stress, Hσ .

This transform matrix can be expressed as

[ ]

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−

−=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡ −=

wzwzw

zz

wzwzw

zz

zz

ww

ww

icosasinisinacosisin0acosasin

isinasinicosacosicos

1000acosasin0asinacos

icos0isin010

isin0icosT

(A3-2)

Expressed in the (x, y, z) co-ordinate system, the formation in-situ stresses,

236

Hσ , hσ , and vσ become

[ ]( ) [ ][ ]( )[ ]T'z,'y,'x

zzyzx

yzyyx

xzxyxz,y,x TT σ=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

στττστττσ

=σ

(A3-3)

After submitting Equations (A3-1) and (A3-2) into (A3-3), we obtain the

following equation

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

σσσ

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

−−−

=

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

τττσσσ

v

h

H

wwwwz2

wwz2

wzzwwz

wzzwwz

w2

w2

z2

w2

z2

z2

z2

w2

w2

z2

w2

z2

zx

yz

xy

z

y

x

icosisinicosisinasinicosisinacos0isinacosasinisinacosasin0icosacosasinicosacosasin

icosisinasinisinacos0acosasin

isinicosasinicosacos

(A3-4)

Bradley (1979) derived stress induced by the in-situ stress as

237

( )

( )

( )⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪

⎨

⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛−θτ+θτ−=τ

⎟⎟⎠

⎞⎜⎜⎝

⎛+θτ+θτ−=τ

θ⎟⎟⎠

⎞⎜⎜⎝

⎛+−τ+θ⎟

⎟⎠

⎞⎜⎜⎝

⎛+−⎟⎟

⎠

⎞⎜⎜⎝

⎛ σ−σ=τ

⎥⎥⎦

⎤

⎢⎢⎣

⎡θτ+θσ−σν−σ=σ

θ⎟⎟⎠

⎞⎜⎜⎝

⎛+τ−θ⎟

⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛ σ−σ−⎟

⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛ σ+σ=σ

θ⎟⎟⎠

⎞⎜⎜⎝

⎛−+τ+

θ⎟⎟⎠

⎞⎜⎜⎝

⎛−+⎟⎟

⎠

⎞⎜⎜⎝

⎛ σ−σ+⎟

⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛ σ+σ=σ

θ

θ

θθ

2

2w

yzxzrz

2

2w

yzxzz

2

2w

4

4w

xy2

2w

4

4wyx

r

2

2w

xy2

2w

yxzzz

4

4w

xy4

4wyx

2

2wyx

2

2w

4

4w

xy

2

2w

4

4wyx

2

2wyx

rr

rr

1sincos

rr

1cossin

2sinr

r2

rr

312sinr

r2

rr

312

2sinr

r42cos

rr

2

2sinr

r312cos

rr

312r

r1

2

2sinr

r4

rr

31

2cosr

r4

rr

312r

r1

2

(A3-5)

Substituting wrr = into the above equation, we obtain the following equations for

calculating the stress state at the wellbore surface:

( ) ( )( )[ ]

( )⎪⎪⎪

⎩

⎪⎪⎪

⎨

⎧

=τ=τ

θτ−θτ=τ



θ

θ

θθ

0

sincos2

2sin42cos2

P2sin42cos2P

rzr

xzyzz

xyyxzzz

wxyyxyx

wrr

(A3-6)

238

Appendix 4: An Example to Determine Water and Ion Movement

As an example, a sample of Pierre I shale exposed to a 26 weight % solution of

sodium chloride had the following values:

pW =13.350 g, aW =13.503 g and adW =12.305 g.

The first step is to determine the weight of water in the shale after alteration

( waW ). This was done by subtracting the “altered –dried-weight ( adW ) from the shale’s

altered weight ( aW ) after immersion.

Water content of altered shale: adawa WWW −= .

For example, for the Pierre I sample, adawa WWW −= =13.503 g-12.305 g

=1.198 g.

The next step is to determine the amount of water transferred into (or out of) the

shale ( wtW ) during immersion. This was done by subtracting the water content of the

original preserved shale pwp CW × from the altered shale ( waW )

Water transferred during immersion = wtW = waW - pwp CW ×

i.e., wtW =1.198 g-13.350 g×9.263/100 = -0.038 g

Note: A positive value of wtW represents water uptake and a negative value

represents water removal.

The last step consists of determining the weight of ions transferred ( itW ) during

immersion. This is done by simply subtracting the water intake of the immersed sample

( wtW ) from the total weight gain of the immersed sample, Ionic transfer =

wtpait WWWW −−=

i.e., itW = (13.503 g-13.350 g) –(- 0.038 g) = 0.191 g

It is convenient to report final results on a percentage basis, by dividing the

weight of water and ion gained (or lost) by the original weight of the shale times 100 %

239

water gained or lost %285.0%100350.13038.0%100

WW

%Wp

wtwt −=×

−=×= , % ion gained or lost:

%431.1%100350.13191.0%100

WW

%Wp

itit =×=×=

We thus conclude that the sample immersed in the 26 weight % NaCl solution for

24 hours lost 0.038 g of water and gained 0.191 g of ions.

240

Appendix 5: A Model to Predict Pore Pressure Build-up during a Compressive Strength Test

APPENDIX 5.1 MODEL DEVELOPMENT

Biot (1962) showed that the pore pressure inside the rock sample during

compaction could be expressed as:

ζ−ε= MCP Vp (A5-1)

In the above equation, ζ is the volumetric deformation of the fluid relative to that

of the solid. It can be expressed as:

⎟⎠⎞

⎜⎝⎛

∂∂

−∂

∂φ=ζ

zu

zu fs

(A5-2)

According to biaxial experiment condition, we have:

zyx νε−=ε=ε (A5-3)

Therefore

( ) zzyxv 21 εν−=ε+ε+ε=ε (A5-4)

Substituting Equation (A5-4) into (A5-1), we obtain:

( ) ζ−εν−= M21CP zp (A5-5)

Viscous flow within the rock sample can be expressed by Darcy’s law as:

zPkAQ p

∂

∂

µ−=

(A5-6)

The flow rate can also be described as the difference between the solid and fluid

displacement rates:

241

⎟⎠

⎞⎜⎝

⎛∂

∂−

∂∂

φ=t

ut

uAQ fs

(A5-7)

Differentiating the Equation (A5-2) with respect to time t yields

⎟⎠

⎞⎜⎝

⎛∂

∂−

∂∂

∂∂

φ=∂ζ∂

tu

tu

ztfs

(A5-8)

Differentiating the Equation (A5-5) with respect to time t, we have:

( )t

Mt

21Ct

P zp

∂ζ∂

−∂ε∂

ν−=∂

∂

(A5-9)

Substituting Equations (A5-6), (A5-7) and (A5-8) into Equation (A5-9), we have:

( ) 2p

2zp

z

PkMt

21Ct

P

∂

∂

µ+

∂ε∂

ν−=∂

∂

(A5-10)

According to Biot’s theory,

s

frp K

K1

MC

−==α (A5-11)

Therefore Equation (A5-10) can be converted into:

( ) 2p

2

p

zp

z

PCkt

21Ct

P

∂

∂

µα+

∂ε∂

ν−=∂

∂

(A5-12)

Where

⎟⎟⎠

⎞⎜⎜⎝

⎛−φ−

φ+

−⋅

φ=

s

fr

s

f

s

fr

f

KK1

KK1

KK1

KC

(A5-13)

Under drained conditions, the following relationship for the porosity, bulk

modulus of the frame, solid, and fluid holds true:

242

fsfr KK

1K1 φ

+φ−

= (A5-14)

Substituting Equation (A5-14) into (A5-13), we have:

frs

frsKK

KKC

+=

(A5-15)

Equation (A5-12) is the model used to simulate time-dependent pore pressure

build-up during biaxial compressive strength tests.

APPENDIX 5.2 BOUNDARY AND INITIAL CONDITIONS

Under our experimental situation, the upper and bottom of the shale sample are

open to air (Figure 4-10). So the boundary conditions can be written as

( )( )⎪⎩

⎪⎨⎧

=

=

0t,LP

0t,0P

p

p

(A5-16)

And the initial condition is

( ) 00,zPp = (A5-17)

243

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250

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251

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252

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Vita

Jianguo Zhang was born in Tongzhou, Jiangsu province of China, on April 9th,

1969, the son of Cheng Zhang and Qiyun Zhou. Jianguo received a Bachelor of Science

degree in Drilling Engineering from the University of Petroleum, China (UPC) in July

1992 and a Master of Science degree in Petroleum Engineering from the same university

in January 1998. From 1992 to 2001, He taught and performed research work in the

Department of Petroleum Engineering at UPC. He taught Drilling Engineering and Basic

Petrophysics for six years. Meanwhile, he participated in several research projects

including Wellbore Stability and Horizontal Well Drilling. In August 2001, he entered

the Graduate School of the University of Texas at Austin. Jianguo is the author of several

papers and annual reports in petroleum engineering related topics.

Permanent address: #19 Yumin Village

Tongzhou City

Jiangsu Province, 226343

China

This dissertation was typed by the author.

Copyright by Jianguo Zhang 2005

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