UNIVERSITY of CALGARY Interfacial Phenomena of Bitumen and Water

UNIVERSITY OF CALGARY

Interfacial Phenomena of Bitumen and Water at Elevated Temperatures and Pressures

Maryam Rajayi

A THESIS

SUBMITTED TO THE FACULTY OF GRADUATE STUDIES

IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE

DEGREE OF MASTER OF SCIENCE

DEPARTMENT OF CHEMICAL AND PETROLEUM ENGINEERING

CALGARY, ALBERTA

APRIL, 2010

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UNIVERSITY OF CALGARY

FACULTY OF GRADUATE STUDIES

The undersigned certify that they have read, and recommend to the Faculty of Graduate

Studies for acceptance, a thesis entitled " Interfacial Phenomena of Bitumen and Water at

Elevated Temperatures and Pressures " submitted by Maryam Rajayi in partial fulfilment of the requirements of the degree of Master of Science.

Supervisor, Dr. Apostolos Kantzas, Chemical and Petroleum Engineering

Dr. Mingzhe Dong, Chemical and Petroleum Engineering

Dr. Brij Maini, Chemical and Petroleum Engineering

Dr. Ron C.K. Wong Civil Engineering

April 2010

ii Abstract

The main objectives of this research project are to develop an X-ray transparent cell and investigate the interfacial properties of bitumen and water at elevated temperatures and

pressures using the computed tomography technology (CT). Interfacial properties under

investigation are the contact angle and the interfacial tension of the system of bitumen-

water-quartz.

A visual, a micro CT, and a CT cells have been designed and constructed. A series of

visual experiments have been executed using the visual cell and a digital camera. These

were the preliminary tests necessary for further experiments performed at ambient

conditions. In the next step, two series of micro CT experiments have been accomplished

at elevated temperatures and pressures. The CT model was tested, but no experiments

have been completed.

Knowledge about the interfacial phenomena between bitumen and water at high

temperatures and pressures facilitates and improves the recovery of bitumen from oil

sands using thermal methods.

iii Acknowledgements

I deeply appreciate the help, support and encouragement from my supervisor Dr.

Apostolos Kantzas. Thank you Dr. Kantzas for the opportunity you provided for me to pursue my education at master’s level. I have learnt not only technical knowledge from you, but also many life lessons that will definitely help me in the future. I am sure I can still learn more.

Financial support from the sponsoring companies of the Canada Research Chair (CRC) in

Energy and Imaging (PetroCanada, Suncor, Nexen, Shell, ConocoPhillips, Laricina, ET-

Energy, Schlumberger, Paramount, CMG Foundation, Canadian Natural and Devon

Canada), the CRC program and NSERC is gratefully appreciated.

I would like to thank TIPM staff and students specially Dr. Sergey Kryuchkov, Mr. Dave

Moon who helped me with the experiments and Ms. Kayla Lakusta. I am very thankful of the administrative staff at the Chemical and Petroleum Engineering Department. Also,

I greatly appreciate the help of the staff at the Engineering Machine Shop specially Mr.

Rob Scorey. Besides, the technical help of Dr. Dave Dechka is greatly appreciated.

I am very grateful to my dear Juan M. Montelongo. Juan you are the one always standing by me throughout the journey. Your love and support helped me accomplish my work and I cannot imagine this would happen without you. Thank you for being with me during tough times and encouraging me with your sweet present and support. I love you.

iv I am thankful to my friends particularly Ms. Parnian Haghighat and Ms. Shirin Rafigh

whom were always there for me. You are my true friends and I am very lucky to have

met you.

Last but certainly not least, I am eternally grateful to my mother Maliheh, to my brothers

Mohsen and Kambiz, to my sister Mitra, to my aunts Mansooreh, Manijeh and Monireh for all the love and support you have given me throughout my life especially during this stage. Thank you for never giving up on me and for encouraging me to continue the pursuit of my dream. I love you.

v Dedication

To My Mother Maliheh Kasgini.

vi Table of Contents

Approval Page ...... ii Abstract ...... iii Acknowledgements ...... iv Dedication ...... vi Table of Contents ...... vii List of Tables ...... x List of Figures and Illustrations ...... xii List of Symbols, Abbreviations and Nomenclature ...... xviii

CHAPTER ONE: INTRODUCTION ...... 1 1.1 Background ...... 1 1.2 Research Objective ...... 6 1.3 Research Methodology ...... 7 1.4 Thesis Layout ...... 8

CHAPTER TWO: REVIEW OF THE LITERATURE ...... 9 2.1 Surface and Interfacial Tension ...... 9 2.1.1 Introduction ...... 9 2.1.2 Definition of Surface Tension and Interfacial Tension ...... 10 2.1.3 Thermodynamics of Surface and Interface ...... 14 2.1.4 The Equation of Young and Laplace ...... 14 2.1.5 Methods of Surface Tension and Interfacial Tension Measurement ...... 16 2.1.5.1 The Capillary Rise Method ...... 17 2.1.5.2 The du Nouy Ring Method ...... 18 2.1.5.3 The Wilhelmy Plate Method ...... 19 2.1.5.4 The Height of a Meniscus on a Vertical Plane Method ...... 21 2.1.5.5 The Spinning Drop Method ...... 22 2.1.5.6 The Maximum Bubble Pressure Method ...... 24 2.1.5.7 The Drop Weight Method ...... 25 2.1.5.8 The Drop or Bubble Shape Method ...... 26 2.2 Wettability and Contact Angle ...... 33 2.2.1 Introduction ...... 33 2.2.2 Definition of Wettability ...... 33 2.2.3 Methods of Wettability Measurement ...... 35 2.2.4 Definition of Contact Angle ...... 36 2.2.5 Contact Angle Hysteresis ...... 38 2.2.6 Methods of Contact Angle Measurement ...... 38 2.2.6.1 The Direct Measurement of Contact Angle ...... 39 2.2.6.2 Drop or Bubble Shape Method ...... 41 2.2.6.3 The Capillary Rise Method ...... 44 2.2.6.4 The Wilhelmy Plate Method ...... 44 2.3 Bitumen Interfacial Properties ...... 45 2.3.1 Effect of Temperature and Pressure on Surface Tension and Interfacial Tension ...... 45 2.3.2 Effect of Temperature and Pressure on Contact Angle ...... 47

vii CHAPTER THREE: METHODOLOGY AND THEORY ...... 50 3.1 Drop Shape Method ...... 50 3.1.1 The Principles of ADSA-P ...... 50 3.2 Image Processing and Edge Detection ...... 60 3.2.1 Edge Detection ...... 60 3.2.2 Canny Edge Detector ...... 61 3.2.3 Threshold ...... 62 3.2.4 Edge Detection Routine ...... 63 3.3 Computed Tomography ...... 64 3.3.1 Introduction to Computed Tomography ...... 64 3.3.2 CT Theory and Image Reconstruction ...... 65 3.3.3 Micro CT Imaging ...... 68

CHAPTER FOUR: DESIGN AND DESCRIPTION OF MODELS ...... 72 4.1 Visual Model ...... 72 4.2 Micro CT-Scanner Model ...... 74 4.3 CT-Scanner Model ...... 83 4.3.1 Measurement Cell Design ...... 88 4.3.1.1 Stress Analysis Design of the Regular CT-Scanner Model ...... 90 4.3.2 System Design ...... 114 4.3.2.1 The Cell Support ...... 114 4.3.2.2 Tubing and Fittings ...... 117 4.3.2.3 Quartz Plate ...... 117 4.3.2.4 Valves ...... 118 4.3.2.5 Pump ...... 118 4.3.2.6 Heating system ...... 118 4.3.2.7 Insulation ...... 118 4.3.2.8 Piston-Cylinder ...... 119 4.3.2.9 Safety System ...... 119 4.3.2.10 O-rings ...... 119

CHAPTER FIVE: VISUAL CONTACT ANGLE MEASUREMENTS RESULTS AND DISCUSSION ...... 120 5.1 Procedure of the Experiments ...... 120 5.2 Image Processing ...... 123 5.3 ADSA-P procedure ...... 126 5.4 The Results of Visual Contact Angle Measurements ...... 128

CHAPTER SIX: MICRO CT-SCANNER CONTACT ANGLE AND INTERFACIAL TENSION MEASUREMENTS RESULTS AND DISCUSSION ...... 162 6.1 Procedure of the Experiments ...... 162 6.2 The Results of the First Part of Micro CT Experiments ...... 168 6.2.1 Case 1 ...... 169 6.2.2 Case 2: ...... 171 6.2.3 Case 3: ...... 175 6.2.4 Case 4: ...... 176

viii 6.3 The Results of the Second Part of Micro CT Experiments ...... 179 6.3.1 Image Processing ...... 180 6.3.2 ADSA-P procedure ...... 180 6.3.3 Results of the Contact Angle and IFT Calculations ...... 181

CHAPTER SEVEN: CONCLUSIONS AND RECOMMENDATION FOR FUTURE WORK ...... 191 7.1 Conclusions from the Visual Experiments: ...... 191 7.2 Conclusions from the Micro CT Experiments: ...... 194 7.3 Overall Conclusions ...... 197 7.4 Recommendation for Future Work ...... 199

REFERENCES ...... 202

APPENDIX A: THERMODYNAMICS OF SURFACES AND INTERFACES ...... 221

APPENDIX B: CURVATURES AND THE YOUNG-LAPLACE EQUATION ...... 227 B.1. Curved Fluid Interface ...... 227 B.2. Young-Laplace Equation ...... 235

APPENDIX C: METHODS OF MESURING INTERFACIAL TENSION AND CONTACT ANGLE ...... 237 C.1. The Capillary Rise Method ...... 237 C.2. The du Nouy Ring Method ...... 244 C.3. The Wilhelmy Plate Method ...... 249 C.4. The Height of a Meniscus on a Vertical Plane Method ...... 252 C.5. The Spinning Drop Method ...... 255 C.6. The Maximum Bubble Pressure Method ...... 259 C.7. The Drop Weight Method ...... 263 C.8. The drop or bubble shape method ...... 266

APPENDIX D: COMPUTER ROUTINES ...... 280 D.1. Image Processing ...... 280 D.2. ADSA-P Routine ...... 281 D.2.1. Main Module ...... 281 D.2.2. Interface Module ...... 285 D.2.3. Functions Module ...... 302 D.2.4. Integrator Module ...... 312

APPENDIX E: BITUMEN PHYSICAL PROPERTIES ...... 316 E.1. Athabasca Bitumen Viscosity ...... 316 E.2. Athabasca Bitumen Density ...... 318 E.3. Cold Lake Bitumen Viscosity ...... 320 Cold Lake Bitumen Density ...... 321 E.4. Brine Density ...... 323

ix List of Tables

Table 1-1: Total Canadian crude oil and oil sand production in 2008 2015, 2020, and 2025 (CAPP, 2009) ...... 2

Table 1-2: Alberta crude oil reserves (ERCB, 2009) ...... 3

Table 4-1: The physical and mechanical properties of aluminum wrought alloy 6061- T6 ...... 75

Table 4-2: Tensile properties of aluminum wrought alloy 6061-T6 at different temperatures ...... 76

Table 4-3: The physical and mechanical properties of titanium alloy Ti-6Al-4V ...... 88

Table 4-4: Fraction of remained tensile strengths of Ti-6Al-4V at different temperatures ...... 89

Table 4-5: The physical and mechanical properties of stainless steel 316 ...... 107

Table 5-1: Athabasca bitumen-distilled water contact angle (first run) ...... 129

Table 5-2: Athabasca bitumen-distilled water contact angle (second run) ...... 130

Table 5-3: Athabasca bitumen-05% CaCl2 contact angle (first run) ...... 131

Table 5-4: Athabasca bitumen-05% CaCl2 contact angle (second run) ...... 132

Table 5-5: Athabasca bitumen-10% CaCl2 contact angle (first run) ...... 133

Table 5-6: Athabasca bitumen-10% CaCl2 contact angle (second run) ...... 134

Table 5-7: Cold Lake bitumen-distilled water contact angle (first run) ...... 135

Table 5-8: Cold Lake bitumen-distilled water contact angle (second run) ...... 136

Table 5-9: Cold Lake bitumen-05% CaCl2 contact angle (first run) ...... 137

Table 5-10: Cold Lake bitumen-05% CaCl2 contact angle (second run) ...... 138

Table 5-11: Cold lake bitumen-10% CaCl2 contact angle (first run) ...... 139

Table 5-12: Cold lake bitumen-10% CaCl2 contact angle (second run) ...... 140

Table E-1: Athabasca bitumen viscosity...... 316

Table E-2: Athabasca bitumen density ...... 318

Table E-3: Cold Lake bitumen viscosity ...... 320

x Table E-4: Cold Lake bitumen density ...... 321

Table E-5: Brine density ...... 323

xi List of Figures and Illustrations

Figure 1.1: Canadian oil sand and conventional oil production (CAPP, 2009) ...... 2

Figure 1.2: Canadian oil sands regions (CAPP, 2009) ...... 4

Figure 1.3: Proven world crude oil reserves (Government-of-Alberta, 2009) ...... 4

Figure 2.1: Soap film used for IFT measurement ...... 16

Figure 2.2: du Nouy ring method ...... 19

Figure 2.3: Wilhelmy plate method ...... 20

Figure 2.4: The height of a meniscus on a vertical plane method (Erbil, 2006) ...... 21

Figure 2.5: The spinning drop tensiometer ...... 22

Figure 2.6: The maximum bubble pressure method ...... 25

Figure 2.7: The drop weight method (Butt et al., 2006) ...... 26

Figure 2.8: Sessile and pendant drops...... 27

Figure 2.9: The angle of contact at the liquid-solid interface ...... 37

Figure 2.10: The contact angle measurement for a small-spherical drop ...... 40

Figure 2.11: The contact dual-drop-dual-crystal method (Rao, 1999) ...... 43

Figure 3.1: Coordinate system for sessile and pendant drops (Rotenberg et al., 1982) ... 52

Figure 3.2: Experimental curve (u), calculated Laplacian curve (v) and normal distances between points un and curve v (d(un, v)) (Rotenberg et al., 1982) ...... 55

Figure 3.3: A digital image (left) and its edge detected by ImageProcessing program (right) ...... 63

Figure 3.4: A CT-scanner and its computer ...... 65

Figure 3.5: A micro CT-scanner ...... 69

Figure 3.6: Two-dimensional image generated from a series of linear parallel X-ray beams ...... 70

Figure 3.7: Three-dimensional image of a drop generated from a series of linear parallel X-ray projections ...... 71

Figure 4.1: The capped and uncapped visual cell ...... 73

xii Figure 4.2: The loaded visual system ...... 74

Figure 4.3: Tensile properties of aluminum wrought alloy 6061-T6 at different temperatures ...... 77

Figure 4.4: The design of micro CT pressure cell ...... 78

Figure 4.5: PFD of micro CT-scanner system ...... 80

Figure 4.6: Styrofoam insulation constructed for the micro cell ...... 81

Figure 4.7: The micro cell support and a micro CT image of the micro cell ...... 82

Figure 4.8: The CT-scanner cell and the dividing head on the aluminum support ...... 86

Figure 4.9: PFD of the CT-scanner model ...... 87

Figure 4.10: Tensile properties of Ti-6Al-4V at different temperatures ...... 90

Figure 4.11: a: Circumferential loading, b: Longitudinal loading ...... 94

Figure 4.12: AutoCAD drawing of the CT-scanner measurement cell...... 97

Figure 4.13: General purpose Acme threads (Green et al., 1996) ...... 102

Figure 4.14: Titanium plug stress analysis ...... 103

Figure 4.15: Titanium plug detailed drawing ...... 105

Figure 4.16: Stainless steel end cap stress analysis ...... 109

Figure 4.17: Stainless steel end cap detailed drawing ...... 111

Figure 4.18: Titanium quartz holder image ...... 112

Figure 4.19: Titanium quartz holder drawing ...... 113

Figure 4.20: Aluminum support ...... 114

Figure 4.21: Aluminum support detailed drawing ...... 116

Figure 5.1: The visual system ready for contact angle measurements ...... 122

Figure 5.2: A raw and pre-processed (first stage) digital image of a visual experiment 124

Figure 5.3: A divided pre-processed (second stage) digital image of a visual experiment (the same image from Figure 5.2) ...... 125

Figure 5.4: Detected edge of a digital image from visual experiments ...... 126

xiii Figure 5.5: A screenshot from a sample ADSA-P calculation in Microsoft Excel ...... 128

Figure 5.6: Athabasca bitumen-distilled water contact angle (first run) ...... 141

Figure 5.7: Athabasca bitumen-distilled water contact angle (second run) ...... 141

Figure 5.8: Athabasca bitumen-05% CaCl2 contact angle (first run) ...... 142

Figure 5.9: Athabasca bitumen-05% CaCl2 contact angle (second run) ...... 142

Figure 5.10: Athabasca bitumen-10% CaCl2 contact angle (first run) ...... 143

Figure 5.11: Athabasca bitumen-10% CaCl2 contact angle (second run) ...... 143

Figure 5.12: Cold lake bitumen- distilled water contact angle (first run) ...... 144

Figure 5.13: Cold lake bitumen- distilled water contact angle (second run) ...... 144

Figure 5.14: Cold lake bitumen-05% CaCl2 contact angle (first run)...... 145

Figure 5.15: Cold lake bitumen-05% CaCl2 contact angle (second run) ...... 145

Figure 5.16: Cold lake bitumen-10% CaCl2 contact angle (first run)...... 146

Figure 5.17: Cold lake bitumen-10% CaCl2 contact angle (second run) ...... 146

Figure 5.18: Athabasca bitumen-distilled water contact angle vs. time ...... 147

Figure 5.19: Athabasca bitumen-05% CaCl2 contact angle vs. time ...... 148

Figure 5.20: Athabasca bitumen-10% CaCl2 contact angle vs. time ...... 150

Figure 5.21: Cold Lake bitumen-distilled water contact angle vs. time ...... 151

Figure 5.22: Cold Lake bitumen-05% CaCl2 contact angle vs. time ...... 152

Figure 5.23: Cold Lake bitumen-05% CaCl2 contact angle vs. time ...... 153

Figure 5.24: Athabasca bitumen-brine contact angle vs. time ...... 154

Figure 5.25: Cold Lake bitumen-brine contact angle vs. time ...... 155

Figure 5.26: Bitumen-distilled water contact angle vs. time ...... 157

Figure 5.27: Bitumen-05% CaCl2 contact angle vs. time ...... 158

Figure 5.28: Bitumen-10% CaCl2 contact angle vs. time ...... 159

Figure 5.29: A visual and a micro CT image of an identical drop-bulk-quartz system .. 160

xiv Figure 6.1: The micro CT-scanner system ready for contact angle and IFT measurements ...... 165

Figure 6.2: Micro-CT scanner SKYSCAN 1072 ...... 166

Figure 6.3: Micro-CT scanner SKYSCAN 1072 ...... 167

Figure 6.4: Results of contact angle measurements for case 1 at different temperatures for ambient pressure, 200psi and 400psi ...... 169

Figure 6.5: Results of contact angle measurements for case 1 at different temperatures for 600psi, 800psi and 1000psi ...... 170

Figure 6.6: Results of contact angle measurements for case 2 at different temperatures for ambient pressure, 200psi and 400psi ...... 171

Figure 6.7: Results of contact angle measurements for case 2 at different temperatures for 600psi, 800psi and 1000psi ...... 172

Figure 6.8: Effect of drop size on contact angle values at 200 psi ...... 173

Figure 6.9: Effect of drop size on contact angle values at 400 psi ...... 173

Figure 6.10: Effect of drop size on contact angle values at 600 psi ...... 174

Figure 6.11: Effect of drop size on contact angle values at 1000 psi ...... 174

Figure 6.12: Effect of drop size on contact angle values at different pressures ...... 175

Figure 6.13: Results for case 3 at different temperatures and pressures ...... 176

Figure 6.14: Results for case 4 at different temperatures and pressures ...... 177

Figure 6.15: Contact Angle values of bitumen-brine-quartz system at different temperatures and ambient pressure ...... 183

Figure 6.16: Contact Angle values of bitumen-brine-quartz system at different temperatures and 250psi ...... 184

Figure 6.17: Contact Angle values of bitumen-brine-quartz system at different temperatures and 500psi ...... 184

Figure 6.18: Contact Angle values of bitumen-brine-quartz system at different temperatures and 750psi ...... 185

Figure 6.19: Contact Angle values of bitumen-brine-quartz system at different temperatures and 1000psi ...... 185

xv Figure 6.20: Contact Angle values of bitumen-brine-quartz system at different temperatures pressures ...... 186

Figure 6.21: IFT values of bitumen-brine-quartz system at different temperatures and ambient pressure ...... 187

Figure 6.22: IFT values of bitumen-brine-quartz system at different temperatures and 250psi ...... 187

Figure 6.23: IFT values of bitumen-brine-quartz system at different temperatures and 500psi ...... 188

Figure 6.24: IFT values of bitumen-brine-quartz system at different temperatures and 750psi ...... 188

Figure 6.25: IFT values of bitumen-brine-quartz system at different temperatures and 1000psi ...... 189

Figure 6.26: IFT values of bitumen-brine-quartz system at different temperatures pressures ...... 190

Figure B.1: Definition of the two-dimensional curvature based on the coordinates (Rotenberg et al., 1982) ...... 228

Figure B.2: Definition of the two-dimensional curvature based on osculating circle method ...... 230

Figure B.3: Definition of the two independent radii of the three-dimensional curvature (Erbil, 2006) ...... 232

Figure B.4: Description of Young-Laplace equation using plane geometry concept (Erbil, 2006) ...... 235

Figure C.5: Liquid meniscus in a capillary tube (Erbil, 2006) ...... 238

Figure C.6: du Nouy Apparatus for measuring ST (du Nouy, 1919) ...... 245

Figure C.7: The ring detachment method ...... 247

Figure C.8: The factor f in different R3/V and R/r ranges (Huh et al., 1975) ...... 248

Figure C.9: Wilhelmy plate method and the meniscus profile ...... 250

Figure C.10: The meniscus profile in the height of a meniscus on a vertical plain method (Erbil, 2006) ...... 252

Figure C.11: Spinning drop method. (a): The drop shape at different velocities, (b): The spinning drop profile ...... 257

xvi Figure C.12: The maximum bubble pressure technique (Erbil, 2006) ...... 261

Figure C.13: The gas bubble growth by pressure in the maximum bubble pressure technique; (a): The liquid is the wetting phase. (b): The liquid is the non-wetting phase (Erbil, 2006) ...... 262

Figure C.14: The maximum bubble pressure technique for capillary tubes with a large radius [(r/a)>0.05] ...... 262

Figure C.15: The drop weight technique (Butt et al., 2006) ...... 264

Figure C.16: a: Pendant drop, b: Pendant bubble, c: Sessile drop, d: Sessile bubble ..... 267

Figure C.17: Experimental setup for pendant and sessile drop measurements using digital image processor (Li et al., 1992) ...... 273

Figure C.18: Schematic of ADSA-CB (Zuo et al., 2004a) ...... 278

Figure E.19: Athabasca bitumen viscosity...... 317

Figure E.20: Athabasca bitumen density ...... 318

Figure E.21: Cold Lake bitumen viscosity ...... 320

Figure E.22: Cold Lake bitumen density ...... 321

Figure E.23: Brine density ...... 323

xvii List of Symbols, Abbreviations and Nomenclature

Abbreviation Definition ADSA Axisymmetric Drop Shape Analysis ADSA-CB Axisymmetric Drop Shape Analysis-Captive Bubble ADSA-CD Axisymmetric Drop Shape Analysis-Contact Diameter ADSA-D Axisymmetric Drop Shape Analysis-Diameter ADSA-EF Axisymmetric Drop Shape Analysis-Electric Field ADSA-HD Axisymmetric Drop Shape Analysis-Height and Diameter ADSA-IP Axisymmetric Drop Shape Analysis-Imperfect Profile ADSA-MD Axisymmetric Drop Shape Analysis-Maximum Diameter ADSA-P Axisymmetric Drop Shape Analysis-Profile ADSA-TD Axisymmetric Drop Shape Analysis-Two Diameters ADT Automatic Digitization Technique ALFI Axisymmetric Liquid Fluid Interface ALFI-S Axisymmetric Liquid Fluid Interface-Smoothing APF Automated Polynomial Fit ASME American Society of Mechanical Engineers ASP Alkaline Surfactant Polymer BPR Back Pressure Regulator CAT Computed Axial Tomography CHOPS Cold Heavy Oil Production with Sand CSS Cyclic Steam Stimulation CT Computed Tomography DAS Data Acquisition System DDDC Dual-Drop-Dual-Crystal DPDSA Dynamic Pendent Drop Shape Analysis ERCB Alberta Energy Resources and Conservation Board FUPF Fifth Order Polynomial Fitting HU Hounsfield ID Inside Diameter IFT Interfacial Tension ISCO L-G Liquid-Gas L-L Liquid-Liquid MDF Medium Density Fiberboard NMR Nuclear Magnetic Resonance OD Outside Diameter PCSD Pressure Cyclic Steam Drive PFD Process Flow Diagram SAGD Steam Assisted Gravity Drainage SF Safety Factor S-G Solid-Gas S-L-F Solid-Liquid-Fluid ST Surface Tension STD Standard

xviii THAI Toe to Heel Air Injection TIFA Theoretical Image Fitting Analysis USBM VAPEX Vapor Extraction

Greek Symbol Definition α Mean Linear Coefficient of Thermal Expansion β Bond Number γ Interfacial Tension Surface Tension Δ Difference δ Small Distance ε Small Value θ Contact Angle κ Curvature π Pi Number ≈ 3.14 ρ Density σ Compression Stress Tensile Stress τ Shear Stress φ Electrical Potential Inclination Angle ϕ& First Order Differential Equation of φ ω Angular Velocity µ Chemical Potential Linear Attenuation Coefficient Viscosity

Latin Symbol Definition A Area a Length Radius of Curvature at Origin Square Root of Capillary Constant a2 Capillary Constant b Length Radius of the Interface at the Apex B Magnetic Field c Length d Diameter, Distance Length E Objective Function X-ray Energy e error f Fraction

xix Factor Function Mechanical Force F Helmholtz Free Energy Flat (in Threads) Force g Gravitational Acceleration G Gibbs Free Energy h Height H Contact Angle Hysteresis Enthalpy Mean Curvature I X-ray Intensity I Current K Gaussian Curvature l Length N Total Number of Items n Number of Items Number of Moles Number of Threads per Inch Na Avogadro Number P Pitch, Pressure p Perimeter q Electric Charge, Parameter Q Heat R Coefficient of Determination Radius r Radius s Arc Length S Entropy s Dimensionless Arc Length T Temperature t Thickness, Time u Experimental Interface Function U Internal Energy v Calculated Interface Function V Volume w Width W Weight, Work W' Real Weight x Abscissa, Length Thickness of material x Dimensionless x x& First Oder Differential Equation of x X x Coordinate y Ordinate, Radius from Axis of Rotation

xx Z Atomic Number z Coordinate z Axis Perpendicular to xy Plane Vertical Height z Dimensionless z z& First Oder Differential Equation of z

Subscript Definition 0 Reference Level A Curve A adv Advancing allow Allowable axial Axial B Curve B c Circumferential C Compression cap Capillary cn Internal Thread Crest cs External Thread Crest ef Effective i Item Counter Inside k Item Counter l Longitudinal lf Liquid-Fluid m Minimum max Maximum Outside mean mean min Inside Minimum n Item Counter non-PV Non-Volume Change o Origin Outside O Point O plug Plug PV Volume Change rec Receding rev Reversible Ring Ring rn Internal Thread Root rs External Thread Root s Shear s-allow Allowable Shear

xxi sf Solid-Fluid shear Shear slice Slice T Tensile tot Total Total Total u Ultimate w Water wire Wire y Yield θ Non Zero Contact Angle

Superscript Definition o Degree S Excess α Phase β Phase

xxii 1

Chapter One: Introduction

1.1 Background

Canada has extensive oil and natural gas resources across the country and its future energy lies on the oil and specially oil sands. Oil sand is defined as a mixture of sand, water, clay and bitumen. Bitumen is a type of oil that is too heavy or thick to flow or be pumped without being diluted or heated. Bitumen can be as hard as a hockey puck in

15oC.

The total Canadian crude oil and oil sand production in 2008 and the anticipated

production in 2015, 2020, and 2025 are reported in Table 1-1. Also Canadian oil sand

and conventional oil production rate from 2005 to 2025 is shown in Figure 1.1. As

shown in Table 1-1 and Figure 1.1 oil sands production currently in Canada is over 1.2

million barrels per day in 2008. Based on announced projects production of bitumen is

going to grow to approximately 2.2 million barrels per day in 2015 and to about 3.3

million barrels per day in 2025. The Growth Case is based on the assumption that oil

sands projects will be developed and brought into service gradually, at a pace similar to

historical and current trends.

Table 1-1: Total Canadian crude oil and oil sand production in 2008 2015, 2020, and 2025 (CAPP, 2009) Total Canadian Crude Oil Production (million barrels/day) – including oil sands

Year 2008 2015 2020 2025

Growth Case 2.7 3.3 4.0 4.2

Operating and in 2.7 3.0 3.0 2.8 Construction

Canadian Oil Sands Production (million barrels/day)

Growth Case 1.2 2.2 2.9 3.3

Operating and in 1.2 1.9 2.0 2.0 Construction

Figure 1.1: Canadian oil sand and conventional oil production (CAPP, 2009)

Alberta contains most of the Canada’s oil reserves. The three main oil sands deposits are located in the Peace River, Athabasca and Cold Lake areas in the province of Alberta

(Figure 1.2), which in total cover a 140800 km2 area. The Alberta Energy Resources and

Conservation Board (ERCB) has estimated that these designated three geological zones

for the major oil sands areas contain an ultimate recoverable resource of 315 billion

barrels, with remaining established reserves of 170 billion barrels at the end of 2007.

There are also smaller deposits in northwest Saskatchewan, next to the Athabasca oil

sands deposit, but they are considered for future rather than present time. Moreover,

based on the statistics of government of Alberta (Government-of-Alberta, 2009) these oil

sands deposits hold approximately 1.7 trillion barrels of bitumen in-place. Alberta crude

oil reserves are reported in Table 1-2 (ERCB, 2009).

Table 1-2: Alberta crude oil reserves (ERCB, 2009) Conventional Oil Oil sands

(Billion Barrels) (Billion Barrels)

Initial Volume in Place 67.8 1731

Remaining Established 1.5 170

Remaining Ultimate Potential 19.7 315

Including the oil sands, Alberta has the second largest petroleum reserves in the world

(Figure 1.3), second only to Saudi Arabia (ERCB, 2009).

Figure 1.2: Canadian oil sands regions (CAPP, 2009)

Figure 1.3: Proven world crude oil reserves (Government-of-Alberta, 2009)

There are two different methods of producing oil from the oil sands: open-pit mining and in situ or in place recovery. Bitumen that is close to the surface is mined. Bitumen that occurs deep within the ground is produced in situ using specialized extraction techniques.

In areas where the oil is located near the surface, open-pit mining is the most efficient method. Open-pit mining is similar to many coal mining operations where large shovels scoop the oil sand into trucks that then take it to crushers where the large clumps of earth are crushed into pieces. This mixture is then diluted with water and transported to a plant, where the bitumen is separated from the other components and upgraded to create synthetic oil. Just 20 percent of the oil sands are recoverable through open-pit mining

(CAPP, 2009).

To recover the oil that is located further below the surface, in situ techniques are employed. Based on the ERCB estimation the in situ technology is used for recovery of

80 percent of oil sands reserves (ERCB, 2009) that underlie approximately 97 percent of the oil sands surface area (CAPP, 2009). In general, the heavy, viscous nature of the bitumen means that it will not flow under normal conditions. Numerous in-situ technologies have been developed that apply thermal energy to heat the bitumen and allow it to flow to the well bore. Common in situ thermal extraction techniques include

Steam Assisted Gravity Drainage (SAGD), Cyclic Steam Stimulation (CSS), and pressure cyclic steam drive (PCSD). The majority of in situ operations use SAGD. This method involves pumping the steam underground through a horizontal well to warm up the bitumen and then pump the warm bitumen with lower viscosity to the surface through a

6 second well. Other technologies are emerging such as pulse technology, vapour recovery extraction (VAPEX) and toe-to-heel air injection (THAI).

There are reservoirs in the oil sands where primary or cold oil production is possible.

The bitumen in these areas will flow to the well bore and be produced with accompanying sand by the use of progressive cavity pumps. This is the same technology that is used in conventional heavy oil production. This type of production technology is commonly called cold heavy oil production with sand (CHOPS). While this bitumen is lighter than the other types of bitumen, it is heavier than conventional heavy oil

(Government-of-Alberta, 2009).

Over two decades, considerable number of experimental and theoretical researches has been done on the in situ techniques of bitumen recovery from oil sands, which improved the understanding of these complex phenomena. This work aims to contribute to the fundamental concepts of bitumen thermal recovery by investigating the contact angle and interfacial tension of different brine-bitumen-quartz systems at ambient and elevated temperatures and pressures when the system is in equilibrium.

1.2 Research Objective

This research endeavours to enhance the understanding of the interfacial phenomena in different brine-bitumen-quartz systems. More specifically, experimental methods for measuring interfacial properties of oil sands, which is a complex system of bitumen, sand, and brine, have been developed. To obtain the desired results, a visual model, a

7 micro X-ray transparent pressure cell and a normal-scale X-ray transparent pressure cell have been designed and developed. These equipments have been used to meet the following objectives:

• The contact angle and interfacial tension measurements for the brine-bitumen-quartz system.

• Changes in the contact angle values of the brine-bitumen-quartz system during the aging process.

• Behaviour of the contact angle and interfacial tension of the brine-bitumen-quartz system at different temperatures and pressures.

1.3 Research Methodology

Different techniques have been employed in this work. The first part of the bitumen- brine interfacial properties experiments have been completed using the visual method. In these experiments the visual images taken from the interface initially were processed in an image processor. The interface data then was sent to an axisymmetric drop shape analysis-profile (ADSA-P) routine for contact angle and interfacial tension calculations and finally the values of the contact angle and interfacial tension for each case have been reported and analysed.

The second part of the experiments has been accomplished by means of a micro X-ray tomography. The experiments were performed in two series for comparison between the results. The first series of experimental images were analysed manually and the values of

8 the system contact angle were reported. The second series employed the ADSA-P technique for the contact angle and the interfacial tension determination.

1.4 Thesis Layout

The current thesis begins with a review of the literature pertaining to methods of the contact angle and interfacial tension measurements in Chapter two. In Chapter three, the methods used for the contact angle and interfacial tension measurements are explained in detail. This chapter discusses about the desired image processing method, ADSA-P technique, computed tomography and micro tomography. Chapter four contains the design of the equipments needed for the contact angle and interfacial tension experiments. The results of the contact angle and interfacial tension measurements for visual and micro tomography systems are presented in Chapter five and Chapter six, respectively. These chapters also discuss and analyse the obtained results for each experiment. Finally, Chapter seven concludes the work and provides some recommendations for future research on this topic.

Chapter Two: Review of the Literature

2.1 Surface and Interfacial Tension

2.1.1 Introduction

In the universe, there are four primary distinctive forces acting on all materials. Two of them are known as subatomic forces acting between particles in atoms with a very short range of action, less than 10-5nm. The other two forces are the long range forces called

electromagnetic and gravitational forces interacting between elementary particles, atoms

and molecules in a much larger range of distance than the two subatomic forces

(Israelachvili, 1985).

These four forces govern many phenomena. They define and explain the interactions

between similar and dissimilar particles. They are very important in surface and interface

sciences, as well. In the interface or surface the molecules of two different phases

interact with each other. The attractive or repulsive forces between the molecules of

different phases in contact with each other create the interface. Therefore, the short-

range forces have a great effect in interfacial behaviour and the long-range nature of the

interaction plays only a minor role.

On the other hand, electromagnetic forces largely affect the solution properties. They

also cause water-rise phenomenon in a capillary tube. Gravitational forces, on the other

hand, limit the escalation of water in a capillary tube (Israelachvili, 1985). The

gravitational forces are also the basis of steam assisted gravity drainage (SAGD) process.

2.1.2 Definition of Surface Tension and Interfacial Tension

An interface is defined as the boundary between two phases and it is treated as an ideal mathematical line or an interface with no thickness. This is called the Gibbs model, because Gibbs assumed that the contact region of two phases is infinitely thin and it does not have any volume (Butt et al., 2006). There are several types of interfaces: liquid-gas

(L-G), liquid-liquid (L-L), solid-gas (S-G) and solid-liquid (S-L). The S-G and L-G interfaces are also called surfaces. The L-L interface arises between two immiscible liquids.

[There are also] solid-solid interfaces [that] separate two solid phases. They are important for the mechanical behaviour of solid materials. There is no gas-gas interfaces because gases mix (Butt et al., 2006).

generally, it can be said that

Where two phases meet is commonly called an interface. The term surface is used when one of the phases is gas or vapour (Jaycock et al., 1981).

On the other hand, the term inter-phase is also used for the contact region because in reality the properties of two bulk phases change gradually in this area. Therefore, based on the definition, inter-phase has a physical thickness. One of the people who treated the contact area as an inter-phase that has a finite volume was Guggenheim (Butt et al.,

2006).

In this work it is assumed that there is no thickness in the contact region, and the mathematical concept of an interface based on the Gibbs model is used because it is more practical in most applications. Therefore, the terms surface and interface are used to properly refer to phases in contact with each other.

The existence of surfaces and interfaces has a significant effect on the materials properties, because all the interactions of materials are through their surfaces and interfaces (Dobrzynski, 1978). Surfaces and interfaces also have important roles in different industries. One of the earliest studies on surfaces was done in metallurgy including morphology and kinetics of phase changes such as crystal growth, recrystallization, grain growth, twining, and precipitation. The study of chemical reactions and chemical catalysis on surfaces and interfaces is also very broad. Also, numerous surface and interface studies are done on plastic properties, adhesion, friction, wetting, electrochemistry, heterogeneous catalysis, and electronics that include miniaturization of electronic circuits (Dobrzynski, 1978). Some examples of surface and interface sciences in chemical and petroleum engineering can be the mechanism of detergents and oil recovery surfactant flooding process.

For each different type of interfaces there is a free energy change associated with its formation, termed the excess interfacial free energy (or excess surface free energy).

It represents the excess free energy that the molecules possess by virtue of their being in the interface [or surface] (Jaycock et al., 1981).

The conceptual definition of the surface free energy of the material is the work that is done to bring the interior bulk molecules to the surface to create a new surface having a unit area of 1m2. Hence, the dimension of the surface free energy is energy per unit area.

Also, the interface free energy for two immiscible phases in contact with each other is

defined as the work that is done to bring the molecules from inside of each bulk phase to

the interface to create a new interface having a unit area of 1m2 (Erbil, 2006).

The surface tension the interfacial tension (γ) are the basic properties used to describe an interface and denote force per unit length or energy per unit area. The term surface tension (ST) is commonly used to describe the tension in the interface of a gas phase with

a liquid or a solid phase. In the case of L-L or S-L interfaces the term interfacial tension

(IFT) is used.

The surface tension of a material is the force that operates inward from the boundaries of its surface perpendicularly, tending to contract and minimize the area of the surface. Its dimension is force per unit length. For a plane surface, the surface tension can be defined as the force acting parallel to the surface and at right angles to a line of unit length anywhere in the surface. This attraction makes the liquid behave as though surrounded by an invisible membrane skin, although there is actually no such skin in real systems.

When we consider two immiscible phases and an interface between them, we should define the interfacial tension as the force that operates inward from the boundaries of its surface perpendicularly to each phase, tending to contract and minimize the area of the interface. This process decreases the number of molecules in the interface, and this diminishes the interface area. This interface contraction continues until the interior accommodates the maximum possible number of molecules (Erbil, 2006).

The significant importance of ST and IFT in physicochemical science is because they explain the behaviour of liquid-fluid contacts in many applications of science and engineering. The IFT of L-L contact shows the dispersion magnitude of a liquid on another liquid. The same concept applies for the IFT of L-S contact. The spreading extent of fluids is important in chemical processes and petroleum recovery science; for example, it affects the coating processes and the migration of oil in porous media.

[It] is also important in the emulsification of liquids or oils in an immiscible continuous phase, resistance to flow through orifices, and the atomization/ dispersion of droplets in a continuous fluid phase (Dingle, 2005).

The dimensions of ST and specified excess surface free energy are the same (MT-2).

Furthermore, these two concepts are identical for pure liquids in equilibrium with their

vapour. This relation is true for IFT and excess interfacial free energy as well and they

are identical (Jaycock et al., 1981).

2.1.3 Thermodynamics of Surface and Interface

Similar to dimensions, the nature of ST and IFT is very close to the surface and interface free energy, respectively. Therefore, it is essential to introduce ST and IFT as thermodynamic concepts.

According to the thermodynamic definition, surface tension is defined as the isothermal work of formation of a unit area of interface (Schembre, 2004).

Based on Gibbs free energy IFT or ST can be written as Eqn. (2.1):

⎛ ∂G S ⎞ ⎛ ∂G ⎞ (2.1) γ = ⎜ ⎟ = ⎜ S ⎟ ⎜ ⎟ ⎝ ∂A ⎠ SS S ⎝ ∂A ⎠ ,, nPT ,, nPT i i

Further information about the thermodynamic concept of ST and IFT, the thermodynamic

relations of internal energy, Gibbs free energy and Helmholtz free energy, and derivation

of the related correlations with ST and IFT are available in Appendix A.

2.1.4 The Equation of Young and Laplace

According to the thermodynamic aspects of ST (or IFT), it is defined as the surface free energy per unit area or, in other words, surface force per unit length. The units commonly used are (dynes cm-1) or (mN m-1), indicating force per unit length, or (ergs

cm-2) indicating energy per unit area. The physical meaning of these units is shown

below:

Length Force Work Force Length =×= γldx

15 or

Work γ == γldxdA

For a better understanding of the ST, consider a spherical soap bubble of radius r (Figure

2.1) where its total surface free energy is 4πr2γ (Butt et al., 2006). If the radius is

decreased by dr, then the change in surface energy is 8πrγdr. Since shrinking decreases

the surface energy, the tendency to do so must be balanced by a pressure difference

through the surface, ΔP, such that the work against this pressure difference is equal to the

decrease in surface free energy. In other words:

2 (2.2) 4π =Δ 8 γπ drrPdrr

2γ (2.3) P =Δ r

where, ΔP = (Inside pressure) - (Outside pressure). Therefore, the smaller the soap

bubble, the larger the air pressure inside compared to the outside. Eqn. (2.3) is the basic

equation of capillarity for sphere shape interfaces and was driven by Young and Laplace

around 1805 (Peacock et al., 1855). In general, a curved surface is introduced with two

independent radii that are explained in detail in Appendix B. The general equation of

Young-Laplace is in form of Eqn. (2.4) that is the fundamental equation of capillarity:

11 (2.4) P γ ( +=Δ ) rr 21

Eqn. (2.3) is a special case of Young-Laplace equation (Eqn. (2.4)) for the curvatures with identical radii. Details of Young-Laplace equation, its derivation, and explanation of two independent radii of curvature can be found in Appendix B.

Figure 2.1: Soap film used for IFT measurement

2.1.5 Methods of Surface Tension and Interfacial Tension Measurement

There are several different ways of measuring IFT and ST. The most commonly used

methods are categorized into shape methods and force methods. The shape methods

include the sessile drop, the pendant drop, and the spinning drop methods. They are

based on the analysis of the deformation of a drop or bubble in another fluid. The force

methods measure the force exerted on an object by the meniscus of a liquid. The Du

Nouy ring method and the Wilhelmy plate method are examples of force methods. Some

other methods not placed in these two categories are also used to measure IFT and ST.

They are the capillary rise, the drop weight, and the maximum bubble pressure methods.

In the following section methods of measuring ST and IFT are explained and compared briefly. A detailed explanation of each method is available in Appendix C. Since IFT and

17 contact angle are very relevant interfacial properties most of the techniques explained in

Appendix C are used for measurements of both properties.

2.1.5.1 The Capillary Rise Method

The Capillary rise method is the most primitive, well known and one of the most widely used ways of measuring ST and IFT. A liquid in contact with a capillary tube will ascend or descend in the capillary tube making a curved interface. The pressure difference across the interface is defined using Eqn. (2.4) (Ramakrishnan et al., 1981).

If ΔP is substituted by Δρgh in Eqn. (2.4):

11 (2.5) gh γρ ( +=Δ ) rr 21

Liquids can also wet the capillary tubes in different angles. In this case some

modifications should be done on the Young- Laplace equation and it will appear as:

11 (2.6) gh =Δ θγρ (cos + ) rr 21

The early experimental works on the capillary rise method go back to early twentieth

century done by Harkins and Brown (Harkins et al., 1919) for water and benzene ST

measurements in 1919 as well as Richards and Carver (Richards et al., 1921) for water,

benzene, toluene, chloroform, carbon tetrachloride, ether, and dimethyl aniline in 1921.

In the following years Edward (Edwards, 1925) and Jones and Ray (Jones et al., 1937)

18 measured the ST of aqueous solutions of various organic compounds and electrolyte solutions, respectively. Although not recommended, capillary rise method has been used to measure IFT of micro emulsion-oil-brine interfaces by Clarkson (Clarkson, 1984).

Later, Mumley and Williams worked on the kinetics of L-L capillary rise phenomenon as well (Mumley et al., 1986a; Mumley et al., 1986b). Consequently some works have been done on the movement of fluids in the porous media using capillary rise method

(Marmur, 1989; Marmur et al., 1997; Lago et al., 2001; Lockington et al., 2004).

Capillary rise method has also been used to measure contact angle of the fluid-fluid interface (Kwok et al., 1995; Gu et al., 1997; Gu et al., 1998). Recently, capillary rise of a meniscus has been investigated with phase change (Ramon et al., 2008).

2.1.5.2 The du Nouy Ring Method

A common way of measuring ST is using the ring method as shown in Figure 2.2. This method is attributed to du Nouy. The device used to measure ST is called Du-Nouy tensiometer. In this tensiometer (Figure 2.2) the force necessary to detach a ring form the surface of a liquid is measured. What is measured as the total weight is equal to the ring weight plus the ST force and is shown in Eqn. (2.7):

Total Ring += 4πRWW γ (2.7)

where R is the ring radius as shown in Figure 2.2. The thickness of the wire is negligible.

The ST is directly calculated from Eqn. (2.7).

Figure 2.2: du Nouy ring method

2.1.5.3 The Wilhelmy Plate Method

The Wilhelmy plate method is used commonly in ST measurement. A thin plate of glass, filter paper, or platinum (a water-wet surface) is vertically immerged into the liquid as shown in Figure 2.3. Subsequently, the force needed to prevent the plate from being descended into the liquid is measured (Butt et al., 2006). The total weight for a complete wetting liquid (θ = 0) is calculated using Eqn. (2.8):

Total Plate =−=Δ pWWW γ (2.8) where p is the contact perimeter. The best way to perform this experiment is to raise the liquid level gradually until it touches the hanging plate suspended from a balance. An increase in weight (ΔW) will be noted. In general case (θ ≠ 0) (Adamson et al., 1997):

ΔW (2.9) cosθγ = p

Figure 2.3: Wilhelmy plate method

Drelich and Miller (Drelich et al., 1992) used the Wilhelmy plate method to measure bitumen ST and IFT up to 60oC. The apparatus used for experiments was a digital- tensiometer KIOT (KRUSS, GmbH, Germany). The reproducibility for the bitumen- aqueous phase IFT measurement was poor in low IFT range (0.8-1.4 mN/m). Use of the ring method for the ST measurements of pure liquids showed higher accuracy comparing to the Wilhelmy plate method (Drelich et al., 1992). They applied hot water to the bitumen system and measured the IFT of the bitumen (Drelich et al., 1994).

Wilhelmy plate method is applicable for L-L and G-L systems, but it is not useful for surfactant solutions. This method cannot be applied to high temperature, high pressure processes (Xu et al., 2005). Therefore, it is not useful in thermal recovery methods.

2.1.5.4 The Height of a Meniscus on a Vertical Plane Method

The height of a meniscus on a vertical plane method is very similar to the Wilhelmy plate method (Figure 2.4). In this method, the height of the meniscus is accurately measured.

Using the measured height of the liquid on the solid plane, ST of the liquid and contact angle can be calculated (Eqns. (2.10) and (2.11)) (Erbil, 2006).

2 2 Δρgh F cap (2.10) γ = + 4 4Δρ 2 ()+ dwgh 2

2Δρ 2 ()+ Fdwgh (2.11) cos cap θ = 2 42 2 2 4()Δρ ( )++ Fdwhg cap

Figure 2.4: The height of a meniscus on a vertical plane method (Erbil, 2006)

2.1.5.5 The Spinning Drop Method

The spinning drop method is based on the analysis of the deformation of drops or bubbles caused by centrifugal force fields (Figure 2.5). This method has being used to measure

IFT since 1942. It is a very practical method and has been mostly used to measure IFT of different fluids specially surfactants and low IFT fluids. Therefore, this method is very popular in chemical flooding enhanced oil recovery.

Figure 2.5: The spinning drop tensiometer

In the spinning drop method the capillary pressure that is equal to the pressure difference between the aqueous and oil phase (ΔP) is calculated by:

2 Δρωγ y 22 (2.12) P −=Δ a 2 where y is the radius from the axis of rotation, a is the radius of curvature of the drop surface at the origin, and Δρ is the density difference between the aqueous and oil phase.

Recalling from the Young-Laplace equation (Eqn. B-28 Appendix B), for spinning drop with two principal radii r1 and r2:

2 Δρωγ y 22 ⎛ 11 ⎞ (2.13) − γ ⎜ += ⎟ a 2 ⎝ rr 21 ⎠

For low IFTs (less than 30mN/m) and in cases that the drop length is more than four times the drop diameter (xo/yo > 4), based on Vonnegut’s approximation (Vonnegut,

1942), the drop can be approximated by a cylinder with hemispherical ends. By applying the cylinder-drop shape assumption, IFT can be calculated by:

Δρω 2 y 3 (2.14) γ = 0 4

-1 -3 -1 where [γ ] = (dyne cm ), [Δρ] = (g cm ), [ω] = (radians s ) and [yo] = (cm) (Mannhardt et al., Fall 2005).

Based on previous works on measuring IFT, the spinning drop method is not recommended for very heavy oil and bitumen, because of their high viscosity. Also, this method is not useful for high IFT systems, since the RPM of the apparatus is limited and drops with high IFT will not stretch along the tube. Because this system is visual, there is a chance of error in reading the data. Recently, an automatic measuring system has been developed to eliminate these defects (Yamazaki et al., 2000). In the new technology an automatic recording system is combined with a video-image analyzer and a computer for the IFT calculation. The system is also able of capturing the images continuously for a long time and therefore, reducing the run time significantly. Yamazaki and co-workers

24 used the spinning drop method to evaluate the IFT of oil and surfactant-polymer and alkaline-surfactant-polymer (ASP) solution. The spinning drop apparatus cannot be used in high temperature and high pressure processes.

Another disadvantage of a visual system is that the bulk fluid should always be transparent. It cannot be oil. Therefore, the study of gas or water in oil environment is not possible.

On the other hand, this method has several advantages. It is widely applicable in surfactant solutions and L-L systems. It is also available commercially (Xu et al., 2005).

The spinning drop method is suitable for measuring the IFT of molten polymers as well

(Erbil, 2006).

2.1.5.6 The Maximum Bubble Pressure Method

In the maximum bubble pressure method as indicated in Figure 2.6 bubbles of gas are slowly blown into the liquid below the surface from a very thin capillary tube. As the pressure inside the injecting tube increases, the gas bubble grows larger. It will detach the surface at a certain pressure that is called maximum bubble pressure. Above this pressure there will be a chain of gas bubbles coming out from the tube. At the maximum bubble pressure the force balance can be written as Eqn. (2.15) (Adamson et al., 1997):

2γ (2.15) ρghP +Δ= max r

The only required parameters for the calculations are the densities of the fluids. The calculations are independent of the contact angle of the system.

Figure 2.6: The maximum bubble pressure method

2.1.5.7 The Drop Weight Method

Comparing to the maximum bubble pressure method, in the drop weight method the liquid (instead of gas) is coming out from the bottom of a capillary tube. As long as the weight of the liquid is less than the interfacial forces, it will remain attached to the tube.

When the liquid grows larger and reaches the critical mass m, it will detach from the surface and fall down. The force balance for the detachment moment is:

== 2πrmgW γ (2.16) where the r is the capillary tube radius. If the liquid coming out from the capillary tube is the non-wetting fluid, r is the internal radius of the tube and vice versa.

As shown in Figure 2.7 the drop detaches partially from the capillary tube, which means some part of the drop mass is still attached to the tube. Therefore, the real weight of the drop (W’) obtained from the experiment is less than W obtained from Eqn. (2.16). In

26 order to modify this equation a factor (f) should be added. Actual values for f are around

0.4 (Adamson et al., 1997). Applying f into the system Eqn. (2.16) changes to:

== 2'' π γfrgmW (2.17)

Or:

'gm (2.18) γ = 2πrf

Figure 2.7: The drop weight method (Butt et al., 2006)

In general, the maximum bubble pressure and the drop weight methods are not very common methods for measuring the ST and IFT, however they are using the basic concept of the Young- Laplace equation (Butt et al., 2006).

2.1.5.8 The Drop or Bubble Shape Method

Analyzing and studying the shape of immersed drops or bubbles in a second fluid can lead to IFT and contact angle measurement. Drops and bubbles attached to a solid surface are described in two different categories; pendant drops (or bubbles) and sessile drops (or bubbles). Pendent drops or bubble are the tear shape drops or bubbles clinging from a tip or a solid surface. Sessile drops are seated on the top of the surface and sessile

27 bubbles are trapped by a solid ceiling. Like the pendent drop method, the sessile drop method is also based on the analysis of the deformation of a drop or bubble caused by gravity.

The ST or IFT at the liquid interface can be related to the drop shape through the following equation (Erbil, 2006):

Δρgb2 (2.19) γ = β where β is the shape factor (bond number) and b is the radius of the interface at the apex

(origin).

Figure 2.8: Sessile and pendant drops

In early works for improving the determining IFT and contact angle from the shape of the drops, the sessile and pendant drops were analyzed and discussed separately. In order to be able to calculate the IFT and contact angle, numerous series of tables containing the shape parameters were generated by Bashforth and Adams (Bashforth et al., 1892) for sessile drops and by Fordham (Fordham, 1948) for pendant drops. The tables were suitable for a certain range of size and shape of drops. Later, more tables were generated by Padday (Padday, 1969) and also by Hartland and Hartley (Hartland et al., 1976).

Malcolm and Paynter (Malcolm et al., 1981) used an analytical method to calculate the

IFT and contact angle of non-wetting sessile drops (θ > 90o). Maze and Burnet (Maze et al., 1969; Maze et al., 1971) started the development of a numerical method to calculate the IFT and contact angle for sessile drops. Their method needed reasonable initial estimates of the drop shape and size parameters. They used the tables of Bashforth and

Adams for the initial estimates.

Rotenberg, Boruvka, and Neumann (Rotenberg et al., 1982) proposed a new computational procedure for determining values of the IFT and contact angle from the shape of axisymmetric fluid interfaces, named Axisymmetric Drop Shape Analysis

(ADSA). The development of this method was a great achievement in surface sciences, because no particular values were required for any parameters including the surface tension, the radius of curvature at the apex and the coordinates of the origin, as they were calculated in the program. This numerical method combined and unified both the sessile drop and pendant drop techniques without using any of the previously generated tables.

In their later works, Neumann and his collaborators improved and modified the ADSA technique and produced different versions for various applications. The modified versions are ADSA-P (profile), ADSA-D (Río et al., 1997) (diameter), ADSA-CD

(Skinner et al., 1989) (contact diameter), ADT (automatic digitization technique) in

ADSA (Cheng et al., 1990), ADSA-MD (Moy et al., 1991) (maximum diameter), ADSA-

HD (Río et al., 1997) (height and diameter), ADSA-TD (Amirfazli et al., 2000) (two diameters), ADSA-CB (Prokop et al., 1998; Zuo et al., 2004a; Zuo et al., 2004b) (captive bubble), ADSA-EF (Bateni et al., 2005; Bateni et al., 2006) (electric field), ADSA-IP

(Kalantarian et al., 2009) (imperfect profile), TIFA (Cabezas et al., 2004; Cabezas et al.,

2005) (theoretical image fitting analysis), ADSA for nearly spherical shape drops

(Hoorfar et al., 2006), and a new numerical method for finding the local contact angle of a drop that is axially non-symmetric (Iliev et al., 2006).

Since the development of ADSA, many researchers in numerous different areas of science have used it to obtain the IFT and contact angle of sessile drops, pendant drops, and captive bubbles in a variety of S-L-F systems. Application of this method for the calculation of IFT and contact angle can be found in polymer sciences (del Río et al.,

1998; Kwok et al., 1998; Regismond et al., 1999; Wulf et al., 1999; Welzel et al., 2002;

Zschoche et al., 2007; Aguilar-Mendoza et al., 2008), monolayers (Li et al., 1996; Wege et al., 1999), surface and chemistry sciences (Li et al., 1990; Susnar et al., 1996; Lam et al., 2002; Rao et al., 2002; Serrano-Saldaña et al., 2004; Zuo et al., 2004a; Zuo et al.,

2004b; Liu et al., 2007; Vrânceanu et al., 2007), oil and gas industry (Gu, 2001; Lam et al., 2001a; Lam et al., 2001b; Rao et al., 2003; Vijapurapu et al., 2004; Askvik et al.,

2005; Nobakht et al., 2008), road construction (Rodríguez-Valverde et al., 2002), biological sciences (Duncan-Hewitt et al., 1989; Moy et al., 1991; Voigt et al., 1991; Lin et al., 1993; Alvarez et al., 1999; Grundke et al., 1999; Lu et al., 2002; Wege et al., 2002;

Zuo et al., 2004a; Zuo et al., 2004b; Acosta et al., 2007; Mikhaylova et al., 2007;

Kalantarian et al., 2009), air stripping and wastewater treatment processes (Mak et al.,

2004).

The shape method has been used more than half a century to measure the IFT and contact angle of different S-L-F systems. One of the earliest experimental works on pendent drop method of IFT measurement was in 1951 (Hough et al., 1951). Hough and collaborators built an apparatus to measure the fluid-fluid IFT. They measured the IFT for methane-water system up to 137oC and 100MPa. The apparatus was designed so that the pendent drop was placed in a windowed-pressure chamber and its image could be captured by a camera. The IFT of the system was measured based on the shape of the drop. They calculated the IFT based on the drop profile and the density of the phases.

In 1953 Hassan and collaborators also measured the IFT of a series of hydrocarbons using pendent drop method (Hassan et al., 1953). They also constructed an apparatus very similar to the one used by Hough. They measured the IFT of benzene, propane, n- pentane, n-hexane, n-octane, and iso-octane against water up to 82oC and 200MPa.

In 1962 Stegemeier and collaborators worked on IFT of methane-normal decane system and they used the pendent drop method (Stegemeier et al., 1962). Also Jennings and

Newman in 1971 worked on a similar topic using the same method (Jennings et al.,

1971). In a short time, Warren and Hough used the same method for measuring the IFT of the ethylene-normal heptanes system (Warren et al., 1972) and Warren and Bills accomplished their work on measuring the IFT of Normal Heptane (Warren et al., 1973).

Also Jennings studied on caustic solution crude oil IFT using the pendent drop method.

The drop was placed in a windowed chamber and the profile of the drop was magnified by projection and recorded on a photosensitive emulsion. The experiments were performed at ambient temperature (Jennings, 1975).

In the early works, the IFT was obtained using Bashforth and Adams tables, but by development of ADSA technique, the drop shape method evolved significantly. In 1996

Huijgen and Hagoort measured the IFT of nitrogen-volatile oil systems using ADSA technique. The working temperature and pressure for their experiments were 100oC and

40MPa, respectively (Huijgen et al., 1996). They results showed high accuracy.

Yang and Gu used the pendent drop method for series of their IFT researches. They chose two see-through high pressure cells with windows for their experiments. One of the cells was used for measuring the diffusion coefficient of a solvent in heavy oil under reservoir conditions by Dynamic Pendent Drop Shape Analysis (DPDSA). The maximum working pressure and temperature of the cell was 70MPa and 148oC, respectively. The pressure cell was placed between a light source and a digital- microscopic camera and camera was taking sequential images of the pendent drops.

These images were analyzed to measure the IFT. From the IFT results they calculated

32 the diffusion coefficient of the solvent into the heavy oil (Yang et al., 2003). The other

Pressure cell was used to measure the dynamic and equilibrium IFT of crude oil-CO2 system at 27oC and different pressures. The maximum operating pressure and temperature of this pressure cell were 69MPa and 177oC, respectively. The pressure cell was placed between a light source and a digital-microscopic camera and the total system was mounted on a vibration-free table. Using the digital camera sequential images of the pendent drops were produced. These images were analyzed by applying image acquisition and processing techniques to measure the IFT (Yang et al., 2006).

In general the pendant drop method is very useful for thermal recovery research, because it can handle elevated temperatures and pressures. The only limitation for this technique is its need to be visualized. Therefore, the system should be clear and it is not suitable for opaque systems.

The sessile drop method, similar to the pendant drop method, is useful in thermal recovery methods and the designated apparatus can tolerate the temperature and pressure load. The apparatus can be used up to 200oC. However, recently the sessile drop method has not been used to measure IFT very often. Although it is a very accurate technique and it is applicable to L-L, G-L and surfactant solutions, but the apparatus in not commercially available and affordable. Sessile drop technique is very popular in contact angle measurements.

There are more methods of ST and IFT measurements that are not commonly used. They are liquid jets, floating sheet, oscillating drops, ripples, rupture of the surface tensiometer, rate of capillary rise, spraying (drop size), bubble size (Bikerman, 1958).

2.2 Wettability and Contact Angle

2.2.1 Introduction

Wetting has an important role in human’s daily life. Rain drops on a window, mixing a cocoa powder in milk, washing cloths and using detergents are very common examples of this phenomenon. Other examples include spreading of ink on paper, painting, coating, distributing the herbicides on the surface of plants’ leaves, and coating the insects’ body- surface by insecticides. In these situations a complete wetting is desired. On the other hand, in fabricating rain coats and constructing pavements wetting should be avoided

(Jaycock et al., 1981; Butt et al., 2006).

Generally, wetting phenomenon is the direct consequent of the interactions between three phases in the contact area. Two of these three phases are fluids, either gas or liquid. In the following sections wetting is completely introduced and explained. The methods for measuring wettability are also listed and described in detail.

2.2.2 Definition of Wettability

Wettability and the methods used to measure wettability are completely reviewed by

Anderson (Anderson, 1986a; Anderson, 1986b). He defines wettability as

The tendency of one fluid to spread on or adhere to a solid surface in the presence of the other immiscible fluids (Anderson, 1986a).

Wettability has a major role in controlling the flow and distribution of reservoir fluids.

For a rock-brine-oil system wettability is defined as

A measure of the preference that the rock has for either the oil or water. When the rock is water-wet, there is a tendency for water to occupy the small pores and to contact the majority of the rock surface. Similarly, in an oil-wet system, the rock is preferentially in contact with the oil; the location of the two fluids is reversed from the water-wet case, and oil will occupy the small pores and contact the majority of the rock surface (Anderson, 1986a).

Depending on the specific interactions of rock, oil, and brine, the wettability of a system can range from strongly water-wet to strongly oil-wet. When the rock has not strong preference for either oil or water, the system is said to be of neutral (or intermediate) wettability. Besides strong and neutral wettability, a third type is fractional wettability, where different areas of the core [or reservoir] have different wetting preferences (Anderson, 1986a).

Also there is another type of wettability that is called mixed wettability.

In this wettability state, the smaller pores are occupied by water and are water-wet, whereas the oil preferentially wets the interconnected larger pores. It is believed that the mixed wettability conditions are associated with the original oil invasion preferentially into the larger pores, followed by the deposition of asphaltenic compounds rendering the surface oil-wet (Dandekar, 2006).

Almost all clean sedimentary rocks are strongly water-wet specially sandstone, which was deposited in an aqueous environment and stayed there for a long time before the oil migrated and drained the water. Therefore, it is believed that most petroleum reservoirs are water-wet. However, further researches showed that not only the most carbonate reservoirs are oil-wet, but also some quartz surfaces (sandstone) are strongly oil-wet

(Anderson, 1986a). The fact is that reservoir rock preference can alter from strongly water-wet by adsorption of polar compounds or even the deposition of organic materials present in the crude oil. Some of these materials are also soluble in water so they can migrate through water and place themselves on the rock surface. Therefore, the wettability of reservoir rock can change in time.

Fractional or heterogeneous wettability of reservoir rock can be the consequence of altered wettability in some parts of oil reservoirs. In general, the surface of rock inside a reservoir can attract some components inside the crude oil. In the spots coated with more oil components, more oil-wet tendency of rock is observed.

2.2.3 Methods of Wettability Measurement

Wettability measurement in the oil recovery industry is quite popular and several different methods have been used to characterize the wettability of different reservoirs.

These methods are reviewed in detail by Anderson (Anderson, 1986b). They are generally categorized in two major groups; qualitative and quantitative methods.

Common qualitative methods for wettability measurement are imbibition rates, microscope examination, floatation, glass slide method, relative permeability curves, permeability-saturation relationships, capillary pressure curves, capillarimetric method, displacement capillary pressure, reservoir logs, nuclear magnetic resonance (NMR) and dye adsorption. Quantitative methods include contact angle, spontaneous imbibition and forced displacement (Amott), and USBM wettability method (Anderson, 1986b;

Dandekar, 2006).

Among all these methods, the quantitative methods are commonly used to measure the wettability of different systems. Nevertheless, there is no single universally accepted method. According to Anderson (Anderson, 1986b) the contact angle method is used to measure the wettability of a certain surface, but the Amott and USBM methods are used for core wettability measurements.

2.2.4 Definition of Contact Angle

When a liquid is located on a solid, it sometimes wets the surface thoroughly and spreads over the solid. However in most of the situations, the liquid does not wet the surface completely and remains as a drop having a finite contact angle between the solid surface and the liquid phase (Figure 2.9). In general term, contact angle (θ) is the angle at which a fluid-fluid interface meets the solid surface. The contact angle method is a common and useful means of measuring wettability. Measuring the contact angle of a S-L-F system will give information about surface energy, roughness, heterogeneity, and contamination (Matijevic, 1969b). Contact angle is always measured relative to the

37 denser phase. In most cases the denser phase is the aqueous phase. The contact angle method is very useful for wettability measurement when working with clean surfaces and pure fluids.

Figure 2.9: The angle of contact at the liquid-solid interface

Contact angle is dependant to ST or IFT by Young’s equation:

γ lf cos. θ γ −= γ slsf (2.20)

For contact angle measurement two immiscible fluids are placed on a solid surface; fluid

1 is the denser fluid and fluid 2 is the lighter phase. The contact angle that two fluids make in the intersection area with the solid, can vary between 0o and 180o. If contact angle is less than 75o, fluid 1 is the wetting phase and if contact angle is more than 105o fluid 2 is the wetting phase. The contact angle between 75o and 105o defines what is known as neutral wettability and indicate that the surface does not have any preference to contact more with any of the fluids.

2.2.5 Contact Angle Hysteresis

In order to apply Young’s equation, the solid should be ideal that means it must be completely homogeneous, flat in microscopic scale, rigid, and not perturbed by fluid adsorption or chemical interactions. The contact angle measured on an ideal solid surface would be unique (Erbil, 2006), but on real surfaces there will be contact angle hysteresis.

If the denser fluid phase is displacing the other fluid, the contact angle measured is called advancing contact angle (θadv) and if the denser fluid is displaced by the lighter one, the measured contact angle is named receding contact angle (θrec) (Butt et al., 2006) while these two contact angles are identical for an ideal solid surface, they usually have a significant difference in real systems. The contact angle hysteresis is the difference between these two angles:

H θadv −= θrec (2.21)

H is typically between 5o to 20o but it can be even more (Butt et al., 2006).

The dominant phenomena that can cause hysteresis in contact angle are surface roughness, heterogeneity and contamination. Other factors can be: molecular orientation and deformation on the solid surface, drop size, liquid adsorption (Erbil, 2006), swelling, and effect of solvents on the solid surface (Adamson et al., 1997).

2.2.6 Methods of Contact Angle Measurement

Contact angle measurements are in two categories: static and dynamic contact angle measurements.

The contact angle measurement for a static drop sometimes does not lead to a unique result because of different parameters such as surface roughness, surface heterogeneity, adhesion, and many more that can cause contact angle hysteresis. Therefore, it is suitable to study both advancing and receding contact angles in dynamic conditions. Receding contact angle usually depends on the solid roughness and impurity, thus it can be affected by pollution in the contact area. On the other hand, advancing contact angle mostly represents the solid- fluid interfacial properties. Therefore, advancing contact angle is a better choice for dynamic contact angle determination.

Meanwhile, static contact angle measurement has several advantages. It can be used for almost all smooth solid surfaces. Very small amount of liquid and a small piece of solid are needed. Also, it is appropriate for elevated temperature and pressure experiments.

In the following section, the common methods for each category (static and dynamic) are listed and briefly described. For detail explanation of each method, one can refer to

Appendix C. The various techniques of measuring static and dynamic contact angle are also described in Jonson and Dettre work (Matijevic, 1969a) as well as Neumann and

Good work (Moriya et al., 1986). The methods they discussed are suitable for systems of

S-L-F without adhesion.

2.2.6.1 The Direct Measurement of Contact Angle

The most commonly used method for determining contact angle is the direct measurement of contact angle for a drop of liquid on a horizontal and smooth solid

40 surface (sessile drop) or a gas bubble captured by a solid (captive bubble). The contact angle is measured by aligning a tangent with the drop profile at the point of contact with the solid surface. In this method a goniometer-microscope equipped with an angle- measuring eyepiece is mounted on the experimental setup and contact angle is measured by directly looking at the contact area (Erbil, 2006).

A modification to this method is use of a video camera equipped with a suitable magnifying lens to record the image of the contact area. The video camera is connected to a computer containing image processing software.

The contact angle of small sessile drops can be calculated indirectly using the drop dimensions. If the drop is very small, gravity effects can be neglected on the shape of the drop. Thus, the drop can be assumed as a part of a sphere (Matijevic, 1969a; Butt et al.,

2006). Consequently, the contact angle for wetting spherical drops is equal to:

⎛θ ⎞ 2h (2.22) tan⎜ ⎟ = ⎝ 2 ⎠ d where h is the drop height and d is the base diameter as shown in Figure 2.10.

Figure 2.10: The contact angle measurement for a small-spherical drop

This method is just an estimate and it is applicable to drops smaller than 10-4mm3

(Matijevic, 1969a).

The direct measurement of contact angle has many advantages such as: small solid can be used, very little amount of liquid is required, and control of the system temperature and pressure is easy.

2.2.6.2 Drop or Bubble Shape Method

2.2.6.2.1 Axisymmetric Drop Shape Analysis

One of the very accurate and recent ways of measuring the contact angle is axisymmetric drop shape analysis (ADSA) or ADSA-P (profile). ADSA-P, initiated by Rotenberg and coworkers (Rotenberg et al., 1982), is a user oriented scheme to determine the contact angle of the S-L-F systems by fitting the Young-Laplace equation of capillarity to a series of coordinate points selected on the experimental interface. ADSA-P finds the theoretical profile that best matches the drop profile extracted from the experimental image of the liquid-fluid interface. From the best fitted curve, contact angle and IFT can be determined.

Also for drops with small contact angles (θ < 30o) a modified version of ADSA is used that is called ADSA-CD (contact diameter). It measures the contact diameter and determines the contact angle of the drops of known IFT and drop volume. Also, there are some other modifications such as ADSA-D (diameter), ADSA-MD (maximum diameter),

42 and ADSA-TD (two diameters). These methods’ performance is similar to ADSA-CD and they are appropriate for different types of drops with different range of contact angle.

2.2.6.2.2 The Single-Crystal Sessile Drop Method

The single crystal sessile drop technique is very similar to sessile drop method, but it is meant to be used for advancing and receding contact angle measurements. A thin syringe-equipped needle is attached to the solid surface from underneath. The syringe is motor driven and can produce drops with certain sizes. The dynamic contact angle of the drop can be measured by increasing and decreasing the drop volume through the needle.

The single crystal method is a conventional method of contact angle measurement that has been used widely for static contact angle studies as well as dynamic ones.

2.2.6.2.3 The Dual-Drop-Dual-Crystal method

The dual-drop-dual-crystal (DDDC) technique is a modified version of sessile drop method. In DDDC method instead of one solid (crystal) surface, there are two solid plates positioned parallel to each other. The upper plate can move vertically to adjust the distance of two plates. The lower plate is capable of moving horizontally. This allows the operator to measure dynamic contact angles. The plates and drops are shown in

Figure 2.11:

Figure 2.11: The contact dual-drop-dual-crystal method (Rao, 1999)

This method was first used in 1962 by Leach and colleagues (Rao et al., 1996). Rao and coworkers used this method frequently for advancing and receding contact angle measurements (Rao, 1996; Rao et al., 1996; Rao, 2002). They tested the contact angle of a series of live oils on quartz and calcite surfaces (Rao, 1996; Rao, 1999).

At the same time they tested temperature dependence of advancing and receding contact angles of two different sandstone heavy oils. The results for both cases showed that the water-wet or neutrally-wet system became completely oil-wet at elevated temperatures, which could be a consequence of oil adhesion on quartz surface. The wettability nature switched at different temperatures for different brine concentrations.

2.2.6.3 The Capillary Rise Method

When a capillary tube is inserted inside a pool of liquid, the liquid level rises inside the tube for most of the liquids. The liquid ascends until the gravitational and interfacial forces balance each other. When it reaches equilibrium, the liquid surface will form a meniscus inside the tube. The angle of which the meniscus contacts the capillary tube can be visually measured and recorded as contact angle of the system.

One of the disadvantages of the capillary rise method is that the precision of contact angles measured by this method is not very high because of error in visual measurements of the contact angle. Also, large volumes of liquid are required.

2.2.6.4 The Wilhelmy Plate Method

Previously, two Wilhelmy plates were used to measure the contact angle. One of the plates was thoroughly wetted by the liquid and used as a reference plate. The second plate was the solid surface under investigation. Both plates had the same dimensions.

The contact angle could be calculated from the difference in the adhesion force of the two plates.

Later just one plate was used for contact angle measurements. The mechanism is that a vertical Wilhelmy plate is partially immersed into the liquid and the height of the liquid meniscus due to the capillary rise of the liquid on the solid plate is precisely measured.

The ST of the liquid should be known. Thus, the contact angle can be calculated from

Eqn. (2.23), which is derived from the equation of Young-Laplace (Erbil, 2006).

2 Δρ 2 ⎛ hgh ⎞ (2.23) θ 1sin −= 1−= ⎜ ⎟ 2γ ⎝ a ⎠

The Wilhelmy plate method is also suitable for dynamic contact angle measurements and it is called tensiometric contact angle method.

There are other methods of measuring contact angle as well, which are not very popular.

They are sliding drop on an inclined plate method, drop dimension method, vertical rod method, horizontal liquid surface method (Matijevic, 1969a), interference microscopy, and specular reflection.

2.3 Bitumen Interfacial Properties

2.3.1 Effect of Temperature and Pressure on Surface Tension and Interfacial Tension

It is very important to study the changes in ST and IFT with temperature and pressure increase because the variation of IFT or ST strongly affects the fluid transportation in an oil reservoir and therefore the recovery of oil in thermal recovery processes.

Generally, ST decreases when the temperature or pressure increases. As temperature increases, the molecules of each fluid phase move faster and the tendency of the molecules to travel outward increases, which causes a decrease in ST values. As an example, the values of ST for White Rocks bitumen are reported approximately 24mN/m at 20oC and they decrease to about 20mN/m at 60oC (Drelich et al., 1994).

The effect of pressure on ST is similar to the temperature effects to some extent. As the pressure increases, each fluid becomes more contracted and the number of molecules of each fluid, specially the gas phase, in the contact region increases. The gaseous molecules attract the liquid particles, which are close to the surface. This attraction from gas side will reduce the inward attraction from the bulk fluid molecules resulting in lower

ST values. In other words, at elevated pressures the gaseous phase shows tendency to become miscible to the liquid phase that decreases the ST. Many experiments approved this theory as well (Dandekar, 2006).

The effect of temperature and pressure increase on IFT of L-L systems is not very well understood. The experimental studies showed inconsistent trends of crude oil-brine IFT results (Dandekar, 2006). However, in many experiments the IFT of different crude oils including bitumen decreases as the temperature increases. In some cases the IFT is inversely proportional with the temperature (Rao, 1996; Zuo et al., 1998). There are some irregularities as well that the trends are totally different from above (Hepler et al.,

1989). Therefore, it is not possible to precisely predict the IFT behaviour with temperature change. In some works it has been reported that the IFT decreases as pressure of the system increases (Zuo et al., 1998), but still there is not a valid trend for it.

Because of the shortage of data in the past studies, more investigation on the ST and the

IFT of different crude oils especially bitumen is necessary. In this work it has been attempted to measure the IFT and the contact angle of bitumen-brine-quartz system for

47 two different bitumen samples from Athabasca and Cold Lake areas, which are two dominant oil sand regions in Alberta. The technique used to measure the IFT and the contact angle of the system is drop shape method. The measurements have been rendered at different times and elevated temperatures and pressures. The results have been analyzed and reported in detail.

2.3.2 Effect of Temperature and Pressure on Contact Angle

Most of the contact angle measurements available in the literature have been performed at atmospheric temperature and pressure conditions and there are a few works reporting the results of contact angle measurements at elevated temperatures and pressures.

Therefore, the effect of temperature and pressure on contact angle of the oil-brine-rock systems has still remained as a mystery in interface sciences.

Wang and Gupta (Wang et al., 1995) measured contact angle of crude oil-brine-quartz and crude oil-brine-calcite systems in different temperatures and pressures. The ranges are from room temperature to 200oF (93oC) and from 200psig to 3000psig (1.38MPa to

20.68MPa). Their results showed that the contact angle value for both systems increased as the pressure increased. The contact angle of the crude oil-brine- quartz system increase as the temperature increased, but for the crude oil-brine-calcite system the results were opposite. However, in both systems the contact angle did not vary significantly by changing either the temperature or the pressure and remained water-wet.

The quartz system showed a stronger water-wet behaviour. The contact angle values in

48 the quartz system varied between 20o and 32o while in the calcite system they ranged between 50o and 60o.

Rao (Rao, 1996) investigated the effect of temperature on values of the dynamic contact angle of two different crude oil-brine-quartz systems using the DDDC technique. In both cases as the temperature increased the contact angle of the system increased and the system switched from water-wet to intermediate wettability and finally oil-wet. The experiments were done at 4.4MPa.

Although wettability of the oil-brine-rock systems is very important to determine the amount of oil recovered from the reservoir, there is not a great amount of contact angle data available in the literature. Therefore, it is crucial to investigate the effects of temperature and pressure change on the wettability of the oil and especially oil sand reservoirs. In this work it has been attempted to measure the static contact angle and the

IFT of bitumen-brine-quartz system for two different bitumen samples from Athabasca and Cold Lake areas. The measurements have been rendered at different times. Also measurement of IFT and contact angle values for Athabasca bitumen has been done at elevated temperatures and pressures and the results have been analyzed and reported in detail. The technique used to measure the contact angle and IFT of the system is drop shape method.

The experiments are performed under room temperature up to 100oC. The pressure of the system changes from ambient pressure up to 1000psig (6.89MPa). The measurements are

49 done in a micro CT-scanner. The device considered for this purpose is an aluminum pressure cell and it is X-ray transparent.

Also another advanced pressure cell is designed, constructed and tested for IFT and contact angle measurements up to 300oC and 1500psig (~10MPa). The technique used for contact angle and IFT measurements in the mentioned device is drop shape method as well. However, this new device is capable of combining different techniques of measuring IFT. They are the drop (bubble) shape method, the maximum bubble pressure and the drop weight method. It can also be used in dynamic contact angle measurements since the cell is attached to a dividing head and therefore the quartz can tilt. The cell is

X-ray transparent and can be used in a regular CT-scanner.

The advantage of using CT-scanner is that the cell can be constructed from metal. The X-

Ray transparent metals are Aluminum and Titanium. Using these materials for the pressure vessels allows reaching up to the required temperature and pressure. A detailed description about computerized tomography, micro CT- scanner, and CT-scanner is available in Chapter three.

Chapter Three: Methodology and Theory

3.1 Drop Shape Method

As explained in chapter two in detail, the drop shape method is one of the convenient ways of measuring IFT and contact angle. The pendent drop and sessile drop methods are both considered as shape methods. These methods are based on the analysis of the deformation of a drop or bubble caused by gravity.

Axisymmetric Drop Shape Analysis-Profile, known as ADSA-P, is a technique to obtain

IFT, ST and the contact angle of a S-L-F system from the shape of axisymmetric menisci.

This method works for both sessile and pendant drops and bubbles. ADSA-P is based on curve fitting on the experimental data. The data from each image is a series of coordinate points on the interface of the drop in the experimental image. The strategy employed is to construct an objective function to calculate the deviation of the experimentally observed interface curvature from a theoretical Laplacian curve. In order to calculate the best Laplacian curve the objective function should be minimized. In the following section the details of ADSA-P method is described mathematically. Also, the computer routine developed to satisfy the method’s calculations is presented.

3.1.1 The Principles of ADSA-P

The ADSA and ADSA-P techniques have been introduced by Rotenberg and his colleagues (Rotenberg et al., 1982) and developed significantly by Neumann. In the current section this technique is summarized based on Rotenberg’s work (Rotenberg et

51 al., 1982) and the changes that have been applied to make it more convenient and suitable for this research are also explained.

In case of sessile or pendant drop formation, if the radii of curvature are sufficiently larger than thickness of the inter-phase separating two fluid phases the pressure difference across a curved interface is described by the Young-Laplace equation of capillarity as shown in Eqn. (3.1):

⎛ 11 ⎞ (3.1) P γ ⎜ +=Δ ⎟ ⎝ RR 21 ⎠ where ΔP is the pressure difference across the interface. As illustrated in Figure 3.1 the x axis is tangent to the curved interface at the apex and normal to the axis of symmetry.

The origin of the coordinate system is placed at the apex (point o). R1 in Eqn. (3.1) turns in the plane of the paper and R2 rotates in a plane perpendicular to the plane of the paper and about the axis of symmetry. Consequently, R2 equals to:

x (3.2) R = 2 sin ϕ where φ is the inclination angle measured between the tangent to the interface at the point

(x, z) and the datum plane.

Figure 3.1: Coordinate system for sessile and pendant drops (Rotenberg et al., 1982)

In the presence of gravity as an only external force, the pressure change with elevation is a linear equation as shown in Eqn. (3.3):

PP 0 ()Δ+Δ=Δ ρ gz (3.3) where ΔP0 is the pressure difference at the reference level plane, and z is the vertical height measured from the reference plane. By combining Eqns. (3.1) to (3.3), Eqn. (3.4) is concluded:

⎛ ⎞ 2sin1 γϕ (3.4) γ ⎜ + ⎟ ()Δ+= ρ gz ⎝ 1 ⎠ RxR o where Ro is the radius of curvature at the apex. Both radii of the curvature (R1 and R2) are equal to Ro at this point.

Mathematically, the interface is described as u, which is a function of x, y, and z. Also, x, y, and z are single valued functions of s, which is the arc length measured from the origin.

Therefore:

= (),, zyxuu (3.5)

(3.6) = ()sxx (3.7) = ()syy (3.8) = ()szz

In the differential form: dx (3.9) = cos ϕ ds dz (3.10) = sin ϕ ds

Also by definition the rate of change of the turning angle with respect to the arc-length parameter is:

1 dϕ (3.11) = R1 ds

By combining Eqns. (3.4) and (3.11) and rearranging them Eqn. (3.12) is generated: dϕ 2 ()Δρ g sin ϕ (3.12) += z − Rds o γ x

For this case the boundary conditions are:

(3.13) ()zx ()ϕ ()=== 0000

Eqns. (3.9), (3.10), (3.12) and the boundary conditions as shown in Eqn. (3.13) form a set of first-order differential equations for x, z, and φ, as functions of the argument s. By integrating these three equations at the same time the complete shape of the curve can be obtained. The shape of the curve v can be calculated from the values of Ro and the slope of the curvature, which is equal to (Δρ)g/γ.

In order to obtain IFT and contact angle values, the calculated Laplacian curve, v, should suitably fit the experimental curve, u. For this purpose, an objective function is introduced as Eqn. (3.14):

N (3.14) E = ,21 vud 2 ∑ []()n n=1 where un, n=1,2,…,N, are a set of experimental points which describe the meridian section of an interface and d(un, v) is the normal distance between u, and the curve v; shown in Figure 3.2.

The value of the objective function depends on the shape of the calculated Laplacian curve v, and on its position relative to the measured curve u. The minimum value of the objective function will be reached when the calculated curve has the least deviation from the experimental curve. In other words, when the correct shape of the curve is calculated the objective function will reach its minimum value.

Figure 3.2: Experimental curve (u), calculated Laplacian curve (v) and normal distances between points un and curve v (d(un, v)) (Rotenberg et al., 1982)

In order to write the mathematical formulation of the objective function and determine the minimum of this function the coordinates, x, z, and s are transformed into dimensionless coordinates. The dimensionless parameters are:

s (3.15) s = Ro

x (3.16) x = Ro

z (3.17) z = Ro

Therefore, the system of first-order ordinary differential equations becomes as follows:

dx (3.18) x& == cos ϕ ds

dz (3.19) z& == sin ϕ ds

dϕ ()Δρ gR 2 sin ϕ (3.20) ϕ& 2 +== o z − ds γ x

Four parameters that are called as the variables of the objective function E are defined as:

= Xq (3.21) 1 o

= Zq (3.22) 2 o

= Rq (3.23) 3 o

()Δρ gR 2 (3.24) q = o = β 4 γ

By defining these four parameters, the objective function can be written as:

N (3.25) ,,, = ,,, qqqqeqqqqE ()()4321 ∑ n 4321 n=1 where

= ,21 vude 2 (3.26) n ()n

Since in ADSA-P method it is assumed that the drop is axisymmetric, the drop curves possess symmetry with respect to the z axis. Hence, it is only required to consider one- half of the meridian section. Any point on the other side of the curve can be simply

57 reflected from the negative side. As shown in Eqn. (3.27), this is accomplished by using the positive sign for Xn ≥ q1 and using the negative sign for Xn < q1.

The objective function as shown in Eqn. (3.25) is the summed squares of the normal distances between a calculated curve and the data points. The error in the objective function for one single experimental point (n) that is simplified by eliminating the subscript n is as following:

= ,21 2 +−± , −+ ZqqqXqqqe 2 (3.27) n [()3 ()()sx m 4 1 ( 3 (sz m 4 ) ( 2 )) ] where

, = xqq (3.28) 3 ()sx m 4

, = zqq (3.29) 3 ()sz m 4

Eqns. (3.28) and (3.29) are the coordinates of a point on the curve v that is closest to the experimental point (X, Z). sm is the arc length value from the origin to the point on the calculated curve that is closest to the experimental point. Therefore at constant q1, q2, q3, and q4:

∂e (3.30) ≡ 0 ∂s m

The value of sm varies if the values of ql, q2, and q4. Therefore, sm is also a function of these variables and Eqn. (3.27) can be expressed as:

(3.31) = ()s m () ,,,,,, qqqqqqqee 4321421

When the error function reaches its minimum value Eqn. (3.25) is rewritten as

∂E N ∂e (3.32) = ∑ n ,0 k == , , , 4321 ∂q k n=1 ∂q k

For a single nth datum point

(3.33) ∂e ⎛ ∂e ⎞ ∂s m ⎛ ∂e ⎞ = ⎜ ⎟ + ⎜ ⎟ ∂q k ⎝ ∂s m ⎠ ∂q k ⎝ ∂q k ⎠

The brackets in Eqn. (3.33) indicate partial differentiation, thus (∂e/∂sm) is interpreted as the derivative of e with respect to sm at constant values of qk. Similarly, (∂e/∂qk) are the derivatives of e with respect to qk at fixed sm.

As illustrated in Eqn. (3.30), the first term on the right-hand side in Eqn. (3.33) is equal to zero and thus eliminated. At the minimum values of the error function, the objective function can be expressed as:

N (3.34) ∂E ⎛ ∂en ⎞ = ∑ ⎜ ⎟ = 0 ∂q k n=1 ⎝ ∂q k ⎠

The system of equations shown in Eqn. (3.34) constitutes a set of non-linear algebraic equations in the parameters q1, q2, q3, and q4. In order to solve for these parameters, regularly an iterative procedure is employed. In Rotenberg’s work (Rotenberg et al.,

1982) the authors employed the Newton-Raphson technique combined with the

59 incremental loading method to calculate and minimize the objective function. The loading started with value of q4 equal to zero. In this condition IFT value reaches the infinity and the Laplacian curve will have a circular shape. Then, q1, q2, and q3 are calculated. The incremental loading continues until the optimization procedure terminates by reaching the minimum value of the objective function. At this point of calculations, the correct shape of the Laplacian curve and the correct positioning of the curve relative to the experimental curve are obtained. As a result, the interfacial properties of the S-L-F system can be derived.

In the present work, instead of Newton-Raphson method, Microsoft Excel solver has been applied. First, the data points on the curvature of the experimental image of the drop are entered into a Microsoft Excel sheet, which is macro enabled. After the data is entered, the initial guess for q1, q2, q3, and q4 are assigned. Then the Visual Basic macros are activated to calculate the objective function and integrate the differential equations.

Employing the Microsoft Excel’s solver the value of the objective function is minimized by changing the parameters q1, q2, q3, and q4 automatically during the optimization process.

The system of differential equations described above is integrated using the Runge-Kutta fourth order numerical method. A series of Visual Basic routines are developed to solve the differential equations, minimize the objective function and calculate the IFT and contact angle of the investigated drop. The details of these routines are available in

Appendix D.

3.2 Image Processing and Edge Detection

3.2.1 Edge Detection

Digital image processing is the use of computer algorithm to perform image processing on digital images. The digital image processing has many advantages over analog image processing; it allows a much wider range of algorithms to be applied to the input data, it is noise resistance and can avoid signal distortion during the process.

Edge detection is a terminology in image processing that refers to algorithms which aim at identifying points in a digital image at which the image brightness changes sharply or in other words, places in the digital image that have discontinuities.

There are many methods for edge detection, but most of them can be grouped into two categories, search-based and zero-crossing based. The search-based methods detect edges by first computing a measure of edge strength, usually a first-order derivative expression such as the gradient magnitude, and then searching for local directional maxima of the gradient magnitude using a computed estimate of the local orientation of the edge, usually the gradient direction. The zero-crossing based methods search for zero crossings in a second-order derivative expression computed from the image in order to find edges, usually the zero-crossings of the Laplacian or the zero-crossings of a non- linear differential expression. As a pre-processing step to edge detection, a smoothing stage, typically Gaussian smoothing, is almost always applied. Smoothing results in noise reduction.

There are many edge detection methods such as: Sobel, Prewitt, Roberts, Laplacian of

Gaussian, zero-crossing and Canny edge detector. Among all of them Canny edge detector is the strongest and the most popular one. Canny Edge detection method is the optimal edge detector. In this situation, an optimal edge detector means good detection: the algorithm should mark as many real edges in the image as possible; good localization: marked edges should be as close as possible to the edge in the real image; and minimal response: a given edge in the image should only be marked once, and where possible, image noise should not create false edges.

3.2.2 Canny Edge Detector

Canny in 1986 considered the mathematical problem of deriving an optimal smoothing filter given the criteria of detection, localization and minimization of the number of responses to a single edge. He showed that the optimal filter given for these assumptions is a sum of four exponential terms. He also showed that this filter can be well approximated by first-order derivatives of Gaussians.

Given estimates of the image gradients, a search is then carried out to determine if the gradient magnitude assumes a local maximum in the gradient direction. So, for example, if the rounded angle is zero degrees the point will be considered to be on the edge if its intensity is greater than the intensities in the north and south directions, if the rounded angle is 90 degrees the point will be considered to be on the edge if its intensity is greater than the intensities in the west and east directions, if the rounded angle is 135 degrees the

62 point will be considered to be on the edge if its intensity is greater than the intensities in the north east and south west directions, and finally if the rounded angle is 45 degrees the point will be considered to be on the edge if its intensity is greater than the intensities in the north west and south east directions. This is worked out by passing a 3x3 grid over the intensity map.

Although his work was done in the early days of computer vision, the Canny edge detector is still a state-of-the-art edge detector and it is hard to find an edge detector that performs better than the Canny edge detector.

3.2.3 Threshold

Upon measuring the edge strength (typically the gradient magnitude), a threshold will be applied to the image to decide whether edges are present or not at an image point. The lower the threshold, the more edges will be detected, and the result will be increasingly susceptible to noise, and also to selecting irrelevant features from the image. Conversely a high threshold may miss subtle edges, or result in fragmented edges.

A commonly used approach to handle the problem of appropriate thresholds is by using thresholding with hysteresis. This method uses multiple thresholds to find edges. It begins by using the upper threshold to find the start of an edge. Once the start point is obtained, then the path of the edge through the image is traceable, so the lower threshold can be chosen. In this work the best threshold to find edges of the visual experiment interfaces is 0.3.

3.2.4 Edge Detection Routine

In order to define the bitumen-water interfaces in the visual experiments a computer routine called ImageProcessing has been developed. The program uses the Canny edge detection method, which results in thinner and more precise edges. The lower threshold for the Canny edge detector has been set at 0.3. ImageProcessing program is applicable for any type of digital image with any size.

The image processing routine used in this work is written for Matlab as an m file function. This program is shown in detail in Appendix D.

As an example, one of the images and its detected edge by the ImageProcessing program are shown in Figure 3.3. This image is taken during the visual experiments.

Figure 3.3: A digital image (left) and its edge detected by ImageProcessing program (right)

3.3 Computed Tomography

3.3.1 Introduction to Computed Tomography

Computed Tomography (CT) Scanning or Computed Axial Tomography (CAT) Scanning is a radiological imaging technique initially developed and used by Hounsfield in 1972.

Its first application was in medicine, where it was used to generate anatomical images of the human body. Now CT-scanning has become a routine procedure with numerous applications in different industries, geosciences, physics, petro-physics, reservoir engineering (Wellington et al., 1987), and life sciences.

The advantages of CT-scanning technique to other imaging techniques are its rapidness, non-destructive visualization and accuracy in analysis of internal structure of materials.

CT technology is very versatile and it is not restricted by the shape or the composition of the object being inspected. By using CT technology, three dimensional images of the scanned object can be generated. Also, CT technique can be applied to objects with different sizes, weights, shapes and densities. These aspects cause the technique to be suitable for processes running at elevated temperatures and pressures.

The typical structure of an X-ray CT-scanner consists of an X-ray source, a detector, gantry, and a rotation system. Recently, industrial scanners have been developed specifically for material research. The advantages of industrial CT-scanners include the possibility of using higher X-ray intensities and attaining higher resolutions. An image of a CT-scanner is shown in Figure 3.4.

Figure 3.4: A CT-scanner and its computer

3.3.2 CT Theory and Image Reconstruction

CT-scanners can generate cross sectional images from slices of an object. For this purpose, an X-ray tube revolves around the object and projects different shots of X-ray attenuation at different angles. The X-ray passes through the object and partially is absorbed by the mass of the object. A part of the beam is also scattered when hitting the object. The attenuated X-ray is collected by a detector. Then by using an image reconstructing algorithm in the scanner’s computer, a cross sectional image of the object is reconstructed from a series of obtained X-ray projections. In fact, the cross sectional image shows the X-ray attenuation coefficient based on the X-ray intensity, material density and atomic number. Finally, a three-dimensional image is generated from sequential transverse cross-sectional images (Kantzas, 1990).

The basic quantity measured in each pixel of a CT image is called linear attenuation coefficient, µ, and is defined from Beer’s law (Vinegar et al., 1987; Wellington et al.,

1987; Mees et al., 2003) for a monochromatic source of X-ray:

II −= μx)exp(/ (3.35) o where Io is the incident X-ray intensity and I is the transmitted intensity of X-ray after traveling through the material with thickness x. The linear attenuation coefficient depends on density, atomic number and X-ray intensity as below:

0.2 8.3 (3.36) − 28 ⎪⎧ Z ef Z ef ⎪⎫ = ρμ N a ⎨ − E +− + 8.925.1))30(028.0exp(597.0105 ⎬ ⎪ E 9.1 E 2.3 ⎪ ⎩ ⎭

The first term in the right hand side of Eqn. (3.36) is called Compton scattering effect.

At high X-ray energies (above 100KeV) the linear attenuation coefficient will only depend on this term, which means that the attenuation of the X-ray beam depends only on the density of the material and not on chemical composition. However for radiation energies below 100KeV, photoelectric effect becomes important and the attenuation will depend on density and chemical composition of the absorbent. In Eqn. (3.36) Zef is called effective atomic number and is defined as:

8.31 = ZfZ 8.3 (3.37) ef ()∑ ii where fi is the fraction of electrons on the ith atomic number species.

The data stream representing the varying radiographic intensity sensed at the detectors on the opposite side of the circle during each sweep is then processed in a computer to

67 calculate cross-sectional estimations of the radiographic densities. These numerical values of the linear attenuation coefficient are expressed in Hounsfield units (HU).

Sweeps cover 360 or just over 180 degrees in conventional machines. Hounsfield units are expressed as:

μ yx ),( − μ (3.38) HU = w × 1000 μ w

Hounsfield Units are also known as CT numbers. Therefore, CT numbers show the X-ray attenuation for different materials based on the attenuation for water.

A pixel is a two dimensional unit based on the matrix size and the field of view. Pixels in an image obtained by CT scanning are displayed in terms of relative radio-density. The pixel itself is displayed according to the mean attenuation of the object that it corresponds to on a scale from +3071 (most attenuating) to -1024 (least attenuating) on the Hounsfield scale. When the CT slice thickness is also factored in, the unit is known as a voxel, which is a three dimensional unit. Water has an attenuation of about 0HU while air CT number is around -1000HU. Materials with higher densities such as metals have higher

HU or CT numbers and can cause artefacts. The attenuation of metals depends on atomic number of the element used; titanium usually has an amount of almost +1000HU, iron and steel can completely extinguish the X-ray and are therefore responsible for well- known line-artefacts in computed tomograms.

The final CT image is a digital picture of the object and can be post-processed in a number of ways. Smoothing, windowing, and contrast enhancing can be some of them.

Windowing is the process of using the calculated Hounsfield units to make an image.

Typically the spatial resolution of conventional medical CT scanners is in range of 1-

2.5mm that is 1-10mm3 voxel (volume element).

3.3.3 Micro CT Imaging

The technique of micro CT imaging is very similar to the regular CT technique. In a micro CT-scanner, as well as a regular CT-scanner, by passing an X-ray beam, cross- sections of a real three dimensional object are created that later can be used to recreate a virtual model without destroying the original model. Thus, the internal structure can be reconstructed and analyzed fully and nondestructively. One of the advantages of micro tomography is the high resolution one can achieve. In the micro CT system the best spatial resolution can be reached is 5μm corresponding to near 1x10-7mm3 voxel size.

The micro CT machine is much smaller in design compared to the regular CT scanner and is used to model smaller objects. In general, there are two types of scanner setups.

In one setup, the X-ray source and the detector are stationary during the scan while the object rotates. The second setup, much more like a regular CT scanner, is gantry based where the specimen is stationary in space while the X-ray tube and the detector rotate around. An image of a micro CT-scanner device is presented in Figure 3.5.

Figure 3.5: A micro CT-scanner

In a micro CT, two dimensional X-ray attenuated images are generated from two- dimensional projections of the three-dimensional object. In the simplest way, the X-ray beam can be assumed parallel. In a parallel geometry a two-dimensional X–ray image is reconstructed from a series of slices generated from a one-dimensional shadow line.

Each point on the two-dimensional shadow image contains the integration of absorption information inside the three-dimensional object generated by the attenuated X-ray beam as illustrated in Figure 3.6.

Figure 3.6: Two-dimensional image generated from a series of linear parallel X-ray beams

In order to obtain more precise shadow images from the micro CT projections, it is recommended to rotate the object and use a large number of projections. In each new rotation the lines of possible object positions will be added to the area of reconstruction.

This operation is named back-projection. After several rotations and projections the correct image of the object can be reconstructed.

CT-scanners and micro CT-scanners have the ability of constructing a three-dimensional image of the scanned object. They integrate several two dimensional images taken from the object to create the three dimensional image. The image illustrated in Figure 3.7 is a three-dimensional image of an oil drop on top of the quartz plate in aqueous environment.

Figure 3.7: Three-dimensional image of a drop generated from a series of linear parallel X-ray projections

Chapter Four: Design and Description of Models

4.1 Visual Model

The method of contact angle and IFT measurements for visual experiments is the drop shape method. In this technique a smooth quartz plate is placed horizontally in a visual cell and a drop of bitumen is placed on top of it. The bulk fluid surrounding the bitumen drop and the quartz plate is CaCl2 solution in different concentrations. The whole system is transparent and the interface curvature can be captured by a normal digital camera.

The images are processed by ImageProcessing and ADSA-P routines, as explained in

Chapter three to obtain the values of the contact angle and IFT for each drop. The main purpose of visual contact angle and IFT measurements is to find the equilibrium time and study the changes in interfacial properties of the system by changing the concentration of

CaCl2 for two different types of bitumen.

In order to investigate the effect of salinity on the contact angle and IFT of quartz- bitumen-brine system and also measure the optimal time needed for the system to reach equilibrium, a visual cell has been used. The visual cell is an appropriate model for contact angle and IFT measurements at ambient temperature and pressure. Therefore, there is no need for further studies on the material and thickness of the cell body and its joints.

The model should be see-through so that one can capture images of the interface area.

Therefore, a clear glass vial with a plastic threaded cap on top of it has been chosen. The

73 dimensions of the vial are 14.70mm OD and 40.05mm in length excluding the cap. The vial is shown in Figure 2.1.

Figure 4.1: The capped and uncapped visual cell

In the bottom, the glass vial is flat; therefore the quartz plate can be easily placed on the vial’s floor. Then, the vial is filled with enough CaCl2 brine and the bitumen drop placed on top of the quartz plate. The drop is injected from the tip of a very thin needle connected to a medical syringe with 3.5mm3 capacity. The fully loaded visual system is shown in Figure 4.2.

Figure 4.2: The loaded visual system

4.2 Micro CT-Scanner Model

Micro CT-scanner as explained in Chapter three is a device used for micro tomographic studies. Using this device is completely safe and the sample will not be undergone any damages during the imaging process. The micro CT-scanner used in this study is a

Skyscan 1072 model. The highest resolution obtainable from this scanner is 2µm.

In order to run contact angle and IFT measurement experiments in the micro CT-scanner a micro CT model has been designed and constructed. The model consists of the micro pressure cell, a piston-cylinder pump, tubing, high pressure valves and an injection system.

The micro pressure cell should be X-ray transparent and as small as possible so the highest possible resolution can be obtained. Also it should have a high resistance against the elevated temperatures and pressures.

In the first step, the material of the pressure cell should be selected. There are not many options for designing a micro CT pressure cell. Only plastics and aluminum are transparent in the micro CT-scanner machine. Among all plastics, peek is a very strong type. Unfortunately, peek is not applicable for high temperatures. Therefore, the only remaining material for the pressure cell is aluminum. Aluminum has higher strength against pressure comparing to peek. It also maintains its strength at higher temperatures up to 120oC while the cell is pressurized. If the ambient pressure is used, the aluminum cell can also tolerate higher temperatures. Aluminum has many more advantages to other materials. They are high strength-weight ratio, excellent corrosion resistance, high thermal conductivity, high fatigue strength, and superior workability.

The aluminum used for the micro pressure cell is Al-6061-T6 and the cell is machined from half an inch standard aluminum rod. The physical and mechanical properties of this alloy are listed in Table 4-1 (ASM, 1990; Gere, 2004; Hosford, 2005; Beer et al., 2006;

Kutz, 2006; ASTM, 2007b; Hibbeler, 2008).

Table 4-1: The physical and mechanical properties of aluminum wrought alloy 6061-T6 Melting Ultimate Tensile Yield Tensile Strength Shear Density at 20oC Temperature Strength (0.2% offset) Strength g/cm3 (lb/in3) oC (oF) MPa (ksi) MPa (ksi) MPa (ksi)

2.71 (0.098) 577 (1070) 310 (45) 276 (40) 207 (30)

The ultimate and yield strength of the alloy for tensile and compressive stress at standard conditions are at least 45ksi (310MPa) and 40ksi (276MPa), respectively. At 120oC the value of the ultimate tensile and yield strengths are about 39ksi (267MPa) and 35ksi

(242MPa), respectively (ASM, 1990); thus it still has an acceptable yield strength, but it decreases in higher temperatures with a faster rate. The effect of temperature on ultimate tensile and yield strengths of aluminum alloy 6061-T6 is listed in Table 4-2 and shown in

Figure 4.3 (ASM, 1990).

Table 4-2: Tensile properties of aluminum wrought alloy 6061-T6 at different temperatures Ultimate Tensile Yield Tensile Strength Temperature Strength (0.2% offset) oC (oF) MPa (ksi) MPa (ksi)

24 (75) 310 (45) 276 (40)

100 (212) 290 (42) 262 (38)

149 (300) 234 (34) 214 (31)

204 (400) 131 (19) 103 (15)

260 (500) 51 (7.5) 34 (5)

316 (600) 32 (4.6) 19 (2.7)

371 (700) 24 (3) 12 (1.8)

This phenomenon makes aluminum an inappropriate material for higher temperature applications especially when the system is pressurized. In order to use aluminum for

77 higher temperatures and pressures, a thicker wall should be considered for the cell. The problem with this statement is that the size of the cell would be significantly larger, which causes a lower resolution in the micro CT-scanner or in some situations it may not even fit in the X-ray chamber of the micro CT-scanner. Moreover, if the wall of the micro pressure cell is very thick, the X-ray emitting from the X-ray tube of the micro CT- scanner will be entirely absorbed by the metal and therefore, the micro CT image will be completely dark. In this situation, it is not possible to investigate the interfacial properties of the fluids inside the cell. Therefore, optimal thickness and total size for the micro cell should be considered.

Figure 4.3: Tensile properties of aluminum wrought alloy 6061-T6 at different temperatures

A rod shape stub should be added to the solid end of the cell. Actually, this end can be machined along with the whole cell. A schematic of it is shown in Figure 4.4.

Figure 4.4: The design of micro CT pressure cell

For contact angle and IFT measurements, a smooth piece of quartz in shape of a flat circular plate has been used. The purpose of using quartz is its compositional similarity to sandstone. Sandstone is mostly made of silica (SiO2) and the main component of quartz is silica. The quartz plate is placed horizontally, in the bottom of the cell and the two fluids under investigation are placed on top as bulk and drop phases. The diameter of the quartz plate should be small enough so that it can be inserted inside the cell.

The pressure of the system is generated using a piston-cylinder type micro pump. The pump is connected to a pressure gauge and can provide desired pressure for the experiments. When the micro cell is pressurized, the pump will be disconnected and the pressure cell can be placed in micro CT-scanner X-ray chamber for further image capturing.

The micro pump transfers the pressure to the cell through a series of 1/8 inch and 1/16 inch stainless steel tubing, which are connected to the pump and the cell, respectively.

Two micro valves are considered in the tubing system. One is 1/16 inch and is connected to the cell by the 1/16 inch tubing. This valve allows the cell to maintain the pressure when is disconnected from the pump. The second valve is mounted on the pump tubing and is used to disconnect the pump from the measurement cell. The schematic of the whole micro CT-scanner system is illustrated as a process flow diagram (PFD) in Figure

4.5. In order to inject the fluids, particularly the drop an injection system consisting of a needle and a 3.5mm3 medical syringe is considered. Also if necessary, the pump can be used for injection of the drop.

Figure 4.5: PFD of micro CT-scanner system

Temperature of the system can be measured by a thermocouple mounted on the outside wall of the pressure cell. The thermocouple is taped to the cell by a piece of high temperature resistant tape. In order to warm up the system of the pressure cell, tubing and the micro valve to the desired temperature, a conventional oven from Cheldon manufacturing Inc. is used. The insulation to maintain the system’s temperature is glass wool, which is considered to be wrapped around the tubing and the valve, and Styrofoam for the main body of the micro cell. The Styrofoam is cut in a shape to cover the whole cell except for the stub that goes inside the sample holder of the X-ray chamber. A photo of the Styrofoam insulation is shown in Figure 4.6.

Figure 4.6: Styrofoam insulation constructed for the micro cell

A medium density fiberboard (MDF) support is constructed to hold the cell upright. The support and the cell is shown in the left image in Figure 4.7. The image in the right side of the Figure 4.7 is a micro-CT image of the cell. The injection line and the quartz plate on the bottom of the cell are visible as well.

Figure 4.7: The micro cell support and a micro CT image of the micro cell

The specifications of the micro CT model are listed below:

Maximum working pressure: 1000psi (6.9MPa)

Maximum working temperature: 120oC (at 1000psi)

Total length: 40.0mm

Length of the vessel: 20.0mm

OD in the threaded area: 12.6mm

OD in the scanning area: 10mm

ID: 8.6mm

Minimum wall thickness: 0.26mm

Maximum wall thickness: 2.00mm

Wall thickness in the scanning area: 0.7 mm

The micro valve used for the micro cell system is a stainless steel 1/16 inch Swagelok valve with catalogue number SS-41G-S1. This valve can be used up to 300oF at 2500psi

(~150oC at 17.2MPa).

The tubing used for connecting the micro cell to the valve is 316 stainless steel seamless tubing from Swagelok. The outside diameter of the tubing is 1/16in and the wall thickness is 0.014in. The catalogue number for this item is SS-T1-S-014-6ME.

The fitting used to seal the cell and connect it to the valve through the tubing is a male connector body type fitting. The fitting material is 316 stainless steel. The size of the fitting in the cell side is 1/8in NPT male and in the tubing side is 1/16in tube OD

Swagelok male tube fitting.

The quartz plate used for the micro CT model is ¼in (~6.5mm) in diameter and 1.4mm in thickness.

4.3 CT-Scanner Model

The visual model as explained before has been developed and used for experiments in ambient conditions. The glass vial cannot tolerate higher temperatures or pressures.

There are some visual models that have thicker body and can be used for high pressures.

Normally the glass visual cells are not appropriate for high temperature operations, but there are some specially designed for this purpose and can bear up to 200oC.

The micro model can endure higher temperatures and pressures comparing to the glass canister. Using micro tomography technique made it possible to design the cell using a more resistant material, which was aluminum. Aluminum is X-ray transparent and stronger than glass when exposing to high pressures and temperatures.

The third model that is introduced in detail in the current section is the CT-scanner model that has been specifically designed and constructed to be used in regular CT-scanners.

The significant purpose of developing the model is the shortcomings of the visual and micro CT-scanner models. In this new system a cylindrical pressure cell has been designed that is suitable for experiments under elevated temperatures and pressures well beyond the other cells. Also, the cell is applicable to phase change experiments, which include the conditions where water turns to steam or steam condenses into water.

Therefore, the CT-scanner model is very useful in thermal recovery method experiments and steam injection technique of bitumen recovery.

In order to investigate the interfacial properties of bitumen-water-quartz or bitumen- steam-quartz systems, the most severe reservoir conditions should be reached. Elevated temperature of 300oC and pressure of 1500psi (10.34Mpa) are needed. Thus, design temperature and pressure of the cell should be considered as 350oC and 2000psi

(13.8Mpa), respectively.

Different methods of measuring contact angle and IFT can be employed using the CT scanner cell. The sessile drop shape method or the captive bubble shape method is the most common way of IFT and contact angle measurements in the cell. For this purpose, a quartz plate is provided to represent the reservoir sandstone as it does in the visual and micro model. An internal rod has been mounted to a plug and inserted into the cell. At the other end, the rod is connected to a flat plate that supports the quartz plate. The cell is filled with the bulk fluid and through a 1/16in injection line, the drop or the bubble of the second fluid is injected on or under the quartz plate, respectiely.

The supporting plate is made of titanium and holds the quartz surface completely in horizontal position or at any required angle. The titanium and the quartz plate are tied up together with a thick rubber O-ring designed for high temperatures. The entire cell is connected to a dividing head that can adjust the angle of the cell and therefore, the quartz plate. By tilting the cell and the plate, dynamic contact angle measurements can be performed in the cell as well.

Moreover, a quartz injection line has been designed for measurement of IFT from the shape of a pendant drop, the maximum bubble pressure and the drop weight methods.

The cell is sealed by a combination of a nut and a plug containing two high temperature

O-rings. The cell, the plug-nut combination, and also the dividing head are supported by an aluminum frame. An image of this system is shown in Figure 4.8.

Figure 4.8: The CT-scanner cell and the dividing head on the aluminum support

In order to inject the drop or steam a pump is attached to the system. Also for safety reasons and maintaining the pressure at the desired level a back pressure regulator (BPR) is connected to the cell. The PFD of the CT-scanner system is shown in

Figure 4.9.

Figure 4.9: PFD of the CT-scanner model

4.3.1 Measurement Cell Design

As explained above, the regular CT-scanner measurement cell is meant to work under elevated temperatures and pressures. Therefore, it should be build from a very strong material. Meanwhile, the body of the cell should be X-ray transparent to show the interfacial phenomena happening inside it. X-ray transparent materials are plastics, glass to some extent, aluminum and titanium. Metals are preferred for the cell body material since they have higher strength. Aluminum is a very useful metal for the design of X-ray transparent cells, but due to its high strength-loss at elevated temperatures it cannot be an appropriate choice for this work. As shown in Table 4-2 and Figure 4.3 the yield tensile strength of aluminum alloy 6061-T6 at 316oC is less than 10% of its yield strength in ambient temperature. Therefore, titanium is the only and best choice for the body material of the Cell. It has a very high strength and fairly low density.

The titanium alloy used for the design of the cell is Ti-6Al-4V. This alloy is a grade 5 titanium alloy. Its physical and mechanical properties are listed in Table 4-3 (Beer et al.,

2006; Kutz, 2006; ASTM, 2007a; Hibbeler, 2008).

Table 4-3: The physical and mechanical properties of titanium alloy Ti-6Al-4V Density at Melting Ultimate Tensile Yield Tensile Strength Shear

20oC g/cm3 Temperature Strength (min) (min) (0.2% offset) Strength

(lb/in3) oC (oF) MPa (ksi) MPa (ksi) MPa (ksi)

4.43 (0.160) 1649 (3000) 895 (130) 828 (120) 550 (80)

At higher temperatures, like any other metal, titanium’s ultimate and yield strength decrease. However, this declination is not very large comparing to aluminum and thus titanium remains strong enough for high temperature and high pressure applications. The effect of temperature on the ultimate and yield tensile strength of Ti-6Al-4V is shown in

Table 4-4 (Kutz, 2006).

Table 4-4: Fraction of remained tensile strengths of Ti-6Al-4V at different temperatures Fraction of Remained Temperature Fraction of Remained Yield Tensile Strength oC (oF) Ultimate Tensile Strength (0.2% offset)

93 (200) 0.90 0.87

204 (400) 0.78 0.70

316 (600) 0.71 0.62

427 (800) 0.66 0.58

482 (900) 0.60 0.53

538 (1000) 0.51 0.44

The effect of temperature on the ultimate and yield tensile strength of titanium alloy Ti-

6Al-4V is shown in Figure 4.10.

Figure 4.10: Tensile properties of Ti-6Al-4V at different temperatures

Since the design temperature of the titanium cell is 350oC the ultimate and yield tensile strengths should be determined for this temperature. They are marked as black points in

Figure 4.10. Therefore, the Ultimate tensile strength for the design is equal to 622MPa.

In order to design the pressure cell for the CT scanner use, a complete stress analysis design has been used. The method is explained in details in the following section.

4.3.1.1 Stress Analysis Design of the Regular CT-Scanner Model

When a cell is under pressure, the material of the cell that it is made of is subjected to loadings from all directions. The total stress caused by the pressure loading should not exceed the allowable stress of the material. In this design, titanium alloy Ti-6Al-4V has

91 been chosen for the material of the cell’s body. The thickness of the cell should be enough to overcome a stress as large as the yield stress of the alloy.

By definition, the force per unit area or intensity of the forces distributed over a section is called the stress (Smith, 1990; Budinski, 1996; William D. Callister, 2000; Gere, 2004;

Hosford, 2005; Askeland et al., 2006; Beer et al., 2006; Hibbeler, 2008) on the section.

The stress in a member of cross-sectional area A subjected to an axial load F is equal to:

F (4.1) σ = axial A where σ is a tensile stress. If the force has a tension nature, a positive sign will be used in

Eqn. (4.1). On the other hand if the force is toward the member, the stress on that member is called compression stress and a negative sign is applied in Eqn. (4.1).

Because the force is perpendicular to section A (axial loading), the stress is described as a normal stress. The units of stress are the same as the units used for pressure.

Another type of stress that is very common is bolts, pins and rivets is shear stress. Shear stress is the elementary internal force causing shear in the section divided by the cross sectional area of that section. It is mathematically described as:

F (4.2) τ = shear A

Each material can carry a limited amount of load. The largest tension that may be applied to a member is called ultimate tensile strength. If the load reaches this maximum value, the specimen begins to carry fewer loads or even breaks. The same concept

92 applies to shear stress and the maximum transverse load tolerated by the specimen that is called ultimate shear strength.

For normal condition utilizations, the maximum allowable load on a structure should be significantly smaller than the ultimate load. This load that is a fraction of the ultimate load is called allowable load (Beer et al., 2006). Sometimes, it is called working load or even design load. The remaining part of the ultimate load, which is not applied to the member, is for safe performance. Therefore, a safety factor (SF) is considered for each design that is:

load ultimate load (4.3) SF = load allowable load or equally:

stress ultimate stress σ (4.4) SF = = u stress allowable stress σ allow

The safety factor should be carefully chosen. An appropriate safety factor requires engineering judgement based on different factors such as: variations that may happen to the members physical and mechanical properties, the type of loading being applied on the structure, uncertainty due to methods of analysis, the expected number of loading on the structure, the type of possible failure, future deterioration of the structure material due to poor maintenance or unpreventable natural causes, and the importance of the structure in the whole system. The SF of 4 is chosen for the design of the regular CT scanner model.

This SF is relatively a high SF and is chosen because the operator will need to be

93 working close to the cell most of the times. Also based on ASME code section VIII division 1, the allowable stress is the lower value of the stress obtained from Eqns. (4.5) and (4.6). In case of titanium alloy Ti-6Al-4V the smaller value is ¼ of the ultimate strength, which is identical with choosing a safety factor of 4.

σ (4.5) σ = u allow 4

2 (4.6) σ = σ allow 3 y

If a pressure vessel’s radius is more than 10 times of its thickness, r / t ≥ 10, the vessel is referred as a thin wall vessel (Hibbeler, 2008). When a vessel is a thin wall type of vessel, the stress distribution throughout its wall thickness is uniform.

In a thin wall pressure vessel that has a cylindrical shape, there are two types of stress caused by the pressure inside the vessel. They are circumferential stress (σc) and longitudinal or axial stress (σl) (Hibbeler, 2008). Both of these stress components exert tension on the wall of the cell. Therefore, a minimum wall thickness based on the radius of the cell should be determined to overcome these tensions. The schematic of the circumferential loading and the longitudinal loading for a cylindrical pressure vessel are illustrated in Figure 4.11.

Figure 4.11: a: Circumferential loading, b: Longitudinal loading

The two types of stress on the cell wall can be formulated with respect to the cell dimensions considering the force equilibrium. For equilibrium in the direction of the cell radius (circumferential):

(4.7) ∑ Fc = 0

By writing the balance between the inside pressure and the tension on the wall:

2[]σ c () ()rdlptdl =− 02 (4.8) where r is the mean radius of the cell. Since the vessel is a thin wall type, the mean radius is very close to internal radius and the assumption of internal radius of the vessel for r is acceptable. Therefore:

pr (4.9) σ = c t

For axial equilibrium in the direction of the cell length:

(4.10) ∑ Fl = 0

By writing the balance between the inside pressure and the tension on the wall:

2 (4.11) l ()2 (ππσ rprt )=− 0

Therefore:

pr (4.12) σ = l 2t

Since these two stress components are perpendicular to each other, the value of the total tension on the pressure vessel wall is:

2 2 (4.13) tot += σσσ lc

Substituting the equivalent of the circumferential stress and the axial stress from Eqns.

(4.9) and (4.12), Eqn. (4.13) will change to:

pr (4.14) σ = 5 tot 2t

The maximum value of σtot in Eqn. (4.14) can be equal to the allowable stress. Titanium alloy Ti-6Al-4V ultimate strength equals to 622MPa at 350oC, which is the design

96 temperature of the cell. This value is 69.5% of the ultimate tensile strength of the alloy at ambient temperature. Therefore, the allowable stress for this particular alloy calculated from Eqn. (4.4) is:

σ (4.15) σ = u allow SF

×1022.6 8 Pa σ =⇒ allow 4 8 σ allow 10555.1 Pa =×=⇒ 5.155 MPa

As mentioned before, the design pressure for the vessel is 2000 psi (13.8MPa). The ID needed for experimental needs has a minimum of 2.5in (63.5mm), so the internal radius of the vessel is equal to 1.25in (31.75mm). Therefore by substituting the value of the allowable stress, design pressure and the internal radius in Eqn. (4.14) the thickness of the pressure vessel can be calculated.

MPa × 75.318.13 mm 5.155 MPa = 5 mmt )(2 =⇒ mmt = 124.015.3 in

Therefore, the needed thickness of the pressure cell is 0.124in, which also agrees with assumption of thin-walled pressure cell. However, the cell has been machined from a titanium alloy Ti-6Al-4V bar that was initially 3.5in (88.9mm) in diameter. Therefore, a greater value can be assigned to the wall thickness of the pressure cell. In reality, a

0.325in (8.255mm) wall thickness has been allotted to the pressure cell. The AutoCAD drawing of the pressure cell is shown in Figure 4.12.

Figure 4.12: AutoCAD drawing of the CT-scanner measurement cell.

As shown in Figure 4.12 the cell is open just from one side. In the other end, it is machined as a flat end from the rod. The thickness of the flat end also should be determined. Thus an equilibrium equation should be obtained for the forces exerted on this element. The internal pressure causes a stress outward and it should not be more than the allowable shear stress that the material can bear. Therefore in the longitudinal direction (Figure 4.11-d):

(4.16) ∑ Fl = 0

rp 2 − πσπ rt = 02 (4.17) ( ) −allows ()

The thickness from Eqn. (4.17) would be:

pr (4.18) t = 2σ −allows

The allowable shear strength is also calculated similar to the allowable tensile strength.

The value of the ultimate shear strength for Ti-6Al-4V referring to Table 4-3 is equal to

550MPa or 80ksi at ambient temperature. First, the value of the ultimate shear strength at the design temperature 350oC is estimated. Since no data found for the fraction of shear strength at elevated temperature, the estimation is done based on the fraction of the remained ultimate tensile strength of the material at higher temperatures. As mentioned before this fraction is equal to 0.695 or 69.5% of the initial strength. Therefore, the ultimate shear strength of Ti-6Al-4V at 350oC is:

σ o = 550)C350( MPa × 695.0 s o ⇒ σ s = 25.382)C350( MPa

Then, the SF of 4 is also used for calculating the allowable shear stress:

σ 25.382 MPa σ s == −allows 4 4

⇒ σ −allows = 6.95 MPa

Finally, the value of the allowable shear stress can be entered into Eqn. (4.17):

MPa × 75.318.13 mm t = × 6.952 MPa =⇒ mmt = ≈ 1.009.03.2 inin

The thickness required for the flat end of the vessel is equal to 0.1in as shown in the stress analysis calculations. However, practically a thickness of 1inch has been considered for the flat end of the vessel.

As shown in Figure 4.12 the cell is threaded at one end and can be sealed by mating a screw and nut thread system. The threads are on both vessel side and nut side. The vessel has external Acme threads and the nut has internal Acme threads.

The formulas for finding the basic dimensions of general purpose Acme threads are listed in Eqns. (4.20) to (4.25) (Green et al., 1996). Also the detail of Acme thread form for general purpose type is shown in Figure 4.13. The angle between the sides of the thread, measured in an axial plane is 29o. The line bisecting the angle should be perpendicular to the axis of the screw threads.

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The pitch is equal to:

1 (4.19) P = n where n is the number of threads per inch.

The basic thread height and thickness are:

= 5.0 Ph (4.20) = 5.0 Pt (4.21)

The basic internal flats at crest (Fcn) and at root (Frn) are:

F = 3707.0 P (4.22) cn

Frn = P 259.03707.0 ×− (major diameter allowance internalon thread) (4.23)

The basic external flats at crest (Fcs) and at root (Frs) are:

F = P 259.03707.0 ×− (pitch diameter allowance externalon thread) (4.24) cs

Frs = P 259.03707.0 ×− (minor diameter allowance externalon thread (4.25) pitch - pitch diameter allowance externalon thread)

Major and minor diameter allowances for both external and internal threads are equal to

0.02 inch for pitches of 10 threads per inch and coarser, and are equal to 0.01 inch for finer threads (Green et al., 1996). Pitch diameter allowances for nominal size range of

3¼ inch to 3¾ inch- the maximum diameter on the cell is 3.27 inch- are equal to 0.0150

101 inch (Green et al., 1996). The number of threads chosen for the pressure cell is n = 10.

Therefore, the thread basic calculations are as follow:

1 P == 1.0 in 10 h =×= 05.01.05.0 in t =×= 05.01.05.0 in

Fcn =×= 03707.01.03707.0 in

Frn =×−×= 03189.002.0259.01.03707.0 in

Fcs =×−×= 03319.00150.0259.01.03707.0 in

Frs −×−×= = 03578.0)0150.002.0(259.01.03707.0 in

In order to calculate the length of the thread needed to handle the pressure, the shear stress applied to each thread should be analysed. The ratio of the allowable shear stress at the design temperature to the shear stress exerted on each thread will show the number of threads needed and consequently the total length of the thread. The force balance for the thread element stress analysis is as follow:

(4.26) ∑ Fl = 0

rp 2 − 2πσπ nFPr =×− 0 (4.27) ( o ) − allows []o ()rs where here n is the number of threads needed and ro is the outside radius of the pressure vessel that is equal to 1.575in (40.0mm). Thus, the number of threads needed will be:

pro (4.28) n = 2σ −allows ()− FP rs

MPa × 408.13 mm n = 4.25 mm MPa ()−×× 03578.01.026.95 in × 1in n ≈= 277.1

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Based on stress analysis of the thread section of the vessel, just 2 threads are needed.

Practically 15 threads are machined on the cell and the mating nut.

The details of the designed Acme thread on the pressure vessel are shown in the drawing of the cell (Figure 4.12).

Figure 4.13: General purpose Acme threads (Green et al., 1996)

All the internal components in the pressure vessel have been designed out of titanium or quartz so that they would be X-ray transparent and would not reflect the X-rays, which causes artefacts. The internal components are: the quartz plate, the titanium quartz holder, titanium tubing or quartz tubing, titanium plug and high temperature O-rings.

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In the titanium plug the value of a and b as shown in Figure 4.14 should be calculated to assure that the plug will not fail under pressure.

Figure 4.14: Titanium plug stress analysis

The shear analysis in order to determine a is as follow:

(4.29) ∑ Fl = 0

rp 2 − πσπ 2 arr 2 =−− 0 (4.30) ( i ) − allows [ ( ()ii )] where ri is the inside radius of the cell and is equal to 1.25in (31.75mm). By rearranging

Eqn. (4.30) to calculate a a second order equation with respect to a is generated:

⎛ pr 2 ⎞ (4.31) 2 2 ara +− ⎜ i ⎟ = 0 ()i ⎜ ⎟ ⎝ σ −allows ⎠

By solving this second order equation, the required thickness for a is calculated:

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22 2 ⎛ MPa × 75.318.13 mm ⎞ a ()×− 75.312 amm + ⎜ ⎟ = 0 ⎝ 6.95 MPa ⎠ a 2 ()a =+−⇒ 05.1455.63 a =⇒ amm = 12.61,38.2 mm

These two values of a show the position of the plug extension in the circumferential axis of the plug. Therefore, section a should be at least 2.38mm. However, the plug maximum diameter has been designed and constructed equal to 2.438in (61.93mm) instead of 2.5in to allow the plug slide smoothly into the cell. The plug has to have 3 and

4 holes on the outside and inside part, respectively. The holes are for the bulk fluid injection line, drop injection line, safety line and the internal rod, which is connected to the titanium quartz holder. All these are shown in detail in Figure 4.15. The length assigned to the thinner part of the plug for 4 holes is equal to 1.955in (49.7mm).

Therefore the remaining length can be considered for a, which is 0.2415in (6.13mm).

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Figure 4.15: Titanium plug detailed drawing

106

In order to calculated the length of plug inside the cell (b), tensile-compression stresses related to the moment caused by inside pressure should be analysed. The stress on the plug from the nut to keep the plug in place under high pressure causes a moment in the plug as shown in Figure 4.14. Figure 4.14 is a slice of the plug that has 1mm thickness.

The portion of the force exerting on this part is:

(πrp 2 ) prw (4.32) F = w = slice 2πr 2 where r is the maximum radius of the plug an is equal to 1.219in (30.96mm). Thus, the force exerted on the slice of the plug is:

MPa × ×196.308.13 mmmm F = slice 2

Fslice =⇒ 64.213 N

By performing force balance over point O in Figure 4.14-b for the tensile and compression forces:

F = 0 (4.33) ∑

FF =− 0 (4.34) CT (4.35) ⎡ 1 ⎛ b ⎞ ⎤ FF CT == σ allow ⎢ ⎜ ⎟w⎥ ⎣ 2 ⎝ 2 ⎠ ⎦

Therefore:

⎛ 1 mmb )( ⎞ FF CT == 5.155 MPa ⎜ ××× 1mm ⎟ ⎝ 2 2 ⎠

FF CT == ()875.38 Nb

Momentum balance over point O is in form of Eqn. (4.36):

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⎛ b ⎞ ⎛ a ⎞ (4.36) O ()FFM TC ×+= ⎜ ⎟ Fslice ×= ⎜ ⎟ ⎝ 3 ⎠ ⎝ 2 ⎠

⎛ b ⎞ ⎛ 13.6 mm ⎞ M O ×= ()875.382 Nb × ⎜ ⎟mm = 64.213 N × ⎜ ⎟ ⎝ 3 ⎠ ⎝ 2 ⎠ 92.25 b 2 =×⇒ 24.655 =⇒ 03.5 mmb

The amount calculated for b is the required thickness so the torque exerted on the part cannot deform it. However, the size chosen for b is 1inch (25.4mm) so that there will be enough space to mount the high temperature O-rings on it.

The only remaining part of the pressure vessel that should be sized is the end cap. The cap does not need to be made of titanium because it is not in the scanning area. The best choice of material for the cap is stainless steel 316, because it is commercially available, it is much cheaper than titanium, it is very strong, and it can stand the high temperatures and pressures very well. The physical and mechanical properties of stainless steel 316 are shown in Table 4-5 (ASTM, 2009).

Table 4-5: The physical and mechanical properties of stainless steel 316 Density at Ultimate Tensile Yield Tensile Strength Melting Temperature oC 20oC g/cm3 Strength (min) (min) (0.2% offset) (oF) (lb/in3) MPa (ksi) MPa (ksi)

8 (0.29) 1371-1399 (2500-2550) 515 (75) 205 (30)

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According to Eqn. (4.5) allowable tensile strength of this type of steel is 128.75MPa

(18.7ksi) have been chosen. The stress analysis of the cap is very similar to the plug. As shown in Figure 4.16 the necessary thickness of cap to prevent it from failing (c or d) can be obtained by calculating the torque exerted on the cap. Figure 4.16 is a slice of the plug that has 1mm thickness. The portion of the internal pressure force on this part is:

MPa × ×196.308.13 mmmm F = slice 2

Fslice =⇒ 64.213 N

This is the same as the plug slice calculations. By performing force balance over point O in Figure 4.16 for the tensile and compression forces:

F = 0 (4.37) ∑

FF =− 0 (4.38) CT (4.39) ⎡ 1 ⎛ c ⎞ ⎤ FF CT == σ allow ⎢ ⎜ ⎟w⎥ ⎣ 2 ⎝ 2 ⎠ ⎦

Therefore:

⎛ 1 mmc )( ⎞ FF CT == 75.128 MPa ⎜ ××× 1mm ⎟ ⎝ 2 2 ⎠

FF CT == ()2.32 Nc

Momentum balance over point O is in form of Eqn.(4.40):

⎛ c ⎞ ⎛ a ⎞ (4.40) O ()FFM TC ×+= ⎜ ⎟ Fslice ⎜ +×= t ⎟ ⎝ 3 ⎠ ⎝ 2 ⎠

109 where t is thickness of the pressure cell including the thread thickness that is equal to

0.385inch (9.78mm).

⎛ c ⎞ ⎛ 13.6 mm ⎞ M O ×= ()2.322 Nc × ⎜ ⎟mm = 64.213 N × ⎜ + 78.9 mm ⎟ ⎝ 3 ⎠ ⎝ 2 ⎠ 46.21 c 2 =×⇒ 21.2744 =⇒ 3.11 mmc

Thickness of part d is also the same as part c. The thickness considered for both parts c and d is 0.8inch (20.32mm), which is a lot more than the required thickness.

Figure 4.16: Stainless steel end cap stress analysis

The mean linear coefficient of thermal expansion for stainless steel 316 is 16.2*10-6 / oC in the range of 0-315oC. The mean linear coefficient of thermal expansion for Ti-6Al-4V is 9.2*10-6 / oC in the range of 0-300oC as well. The plug thinner diameter is almost

2inch (50.8mm). The changes in the plug diameter and the opening of the cap at design temperature comparing to the ambient temperature will be less than 0.2mm and 0.3mm, respectively. Therefore, the difference between the steel and titanium linear thermal

110 expansion will be almost 0.1mm. This value will not cause problems in high temperature experiments. The same rule applies for the cap and the cell body. Therefore, the opening space between the inside and outside thread at design temperature can be neglected. This makes steel a suitable substitute material for titanium. The detailed drawing of the end cap is shown in Figure 4.17.

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Figure 4.17: Stainless steel end cap detailed drawing

112

The quartz plate holder is one of the internal structures in the pressure cell and is designed to hold the quartz plate in place for experiments. Thus, this part will be directly in the scanning area and it should be made of titanium. The image and the drawing of this part are illustrated in Figure 4.18 and Figure 4.19.

Figure 4.18: Titanium quartz holder image

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Figure 4.19: Titanium quartz holder drawing

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4.3.2 System Design

The regular CT-scanner system, as mentioned previously, consists of a high pressure cell, a dividing head, an aluminum support, a quartz plate and a titanium plate holder, injection lines, a safety line, connections and fittings, tees, a cross, valves, a BPR, a pump, piston cylinders, heating tapes, insulation, thermocouples, pressure transducers, temperature and pressure indicators, data acquisition system (DAS), and a computer. In the following sections these components are briefly described.

4.3.2.1 The Cell Support

In order to hold the pressure cell still during the experiments a saddle type aluminum support has been designed and constructed. An image of the constructed aluminum support and detailed drawing of the support are shown in Figure 4.20 and Figure 4.21, respectively.

Figure 4.20: Aluminum support

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Figure 4.21: Aluminum support detailed drawing

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4.3.2.2 Tubing and Fittings

The stainless steel tubing, fittings, tees and the cross are as following. Their Swagelok catalogue number and quantity of each item are also mentioned in parenthesis in front of them:

1/8” OD X 0.028” Wall, 316SS, Seamless Tubing (SS-T2-S-028-20) x 20ft

Reducing Union ¼” X 1/8” T (SS-400-6-2) x 1

1/8” Tube X ¼” FNPT Branch Tee (SS-200-3-4TTF) x 6

Cross 1/8” Swagelok (SS-200-4) x 1

Also pieces of titanium tubing and quartz tubing are used for the drop injection system inside the pressure cell. They are:

1/8” OD X 0.028” Wall, Ti-6Al-4V, Seamless Tubing x 2ft

1/16” OD Quartz Tubing 2” Length x 2

1/8” OD Quartz Tubing 2” Length x 2

1/16” OD Quartz Tubing 3” Length x 2

1/8” OD Quartz Tubing 3” Length x 2

4.3.2.3 Quartz Plate

The quartz plate has been ordered from chemglass company. The specifications and catalogue number of it are:

Quartz Disc, 2"O.D. x 1/16" Thick (CGQ-0600-07)

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4.3.2.4 Valves

There are two different types of valves in the regular CT system. The valves that are directly connected to the pressure cell and the second row valves. The first category should be suitable for elevated temperature and pressure experiments, but the second category will bear the lower temperatures. The valves are Swagelok valves and their specifications and catalogue numbers are as followings:

Valve W/Grafoil Packing 3700psi @ 343oC (SS-6NBF4-G) x3

1/8” Tube Ball Valve (SS-41GS2) x 3

4.3.2.5 Pump

Any kind of ISCO D-Series Syringe pump is suitable for this system. These pumps can inject the accurate amount of a fluid to the system. Also, the rate of injection can be set very low so a growing drop can be studied during the experiment.

4.3.2.6 Heating system

Ultra high temperature heating tape from Omega supplier has been chosen for the cell body, tubing, fittings, and the piston-cylinders. Each heating tape is connected to a controller so that its temperature can be fixed and controlled. Also two thermocouples are assigned to each heat tape to transfer the temperature of the tape ends to the indictor.

4.3.2.7 Insulation

The insulation expected for the experiments is Aerogel insulation with 5mm thickness.

Aerogel is a manufactured material with the lowest bulk density of any known porous

119 solid. It is derived from a gel in which the liquid component of the gel has been replaced with a gas. The result is an extremely low-density solid with several remarkable properties, most notably its effectiveness as a thermal insulator.

4.3.2.8 Piston-Cylinder

Two piston-cylinders are needed to pump both fluids to the system. The size of piston- cylinders is recommended to be at least 500mm3 and 1000mm3 for the drop and the bulk fluid, respectively.

4.3.2.9 Safety System

For the safety of the system a back pressure regulator (BPR) is considered that is connected to the safety line. This device can be set at a desired pressure and will not allow the system pressure exceed the set pressure.

4.3.2.10 O-rings

For sealing the system at design conditions, high temperature O-rings should be considered. These O-rings are built by hitechseals:

228-4079 Kalrez O-ring (316oC) x 2

In order to hold the quartz plate on top of the titanium quartz holder a thick high temperature O-ring is needed. The specifications of this O-ring are:

1.985” ID x 2.250” OD x 0.250” Wide, Machined Kalrez Ring Cmpd # 7075, (327oC)

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Chapter Five: Visual Contact Angle Measurements Results and Discussion

5.1 Procedure of the Experiments

Several experiments have been completed using the visual model to study the contact angle of bitumen-brine-quartz system. All of the visual experiments have been done at ambient temperature and pressure (22oC and 1atm) for a period of approximately 120 hours. The main purpose of the visual experiments is to find the time needed for the system of drop-bulk fluid-quartz to reach equilibrium. Other expectations of the visual experiments are to compare the contact angle of different bitumen types in different brine systems. Also the values of the contact angle are achievable through the process of visual measurements.

Two types of bitumen are chosen for the study of the contact angle in this work. One of them is from Athabasca region and the second bitumen is from Cold Lake oil sand area.

The physical properties of these oils are available in Appendix E. The bitumen has been always used as a drop in the visual experiments, because the interface and the contact area is detected using a regular digital camera. No doping was added to bitumen in any of the visual experiments.

The bulk fluid used in the experiments could be distilled water, 5%wt CaCl2 aqueous solution, and 10%wt CaCl2 aqueous solution. One solution of each concentration was prepared for the whole experiments. In fact, visual experiments are a series of necessary preliminary tests for the micro CT-scanner experiments. Therefore, the purpose of

121 measuring the contact angle in different CaCl2 concentrations is because the micro CT- scanner experiments had to be run using 10%wt CaCl2 aqueous solution.

The solid surface in the visual contact angle measurements is a piece of smooth and circular quartz that has been inserted in to the model. The quartz plate is ¼ inch

(~6.5mm) in diameter and 1.4mm in thickness.

The experiments executed in a transparent glass container. The dimensions of the vial are 14.70mm OD and 40.05mm in length. The vial is sealed with a plastic threaded cap.

First, the quartz plate was placed in the vial. Then, the vial is partially filled with the brine under study. The system of quartz-brine was left for 24 hours so that the surface of the quartz comes to equilibrium with the brine and the ions in the brine. This stage is very important because based on the theory of the oil formation, brine filled the reservoir pores first and after a long time the oil was formed and replaced the brine in the reservoir.

Therefore, in this work 24 hours are given to the system to reach equilibrium before introducing the bitumen into the system.

After the brine-quartz system reached equilibrium, a drop of bitumen was placed on the quartz plate in presence of the brine. The drop was placed on the quartz by a free fall from the tip of a needle placed about 1cm above the quartz plate. The system was sealed by tightening the plastic cap to the top of the glass vial. At this stage the system was ready for the contact angle measurements. It was placed on a horizontal surface with less

122 than 0.1 degree inclination error. A sample picture of the bitumen-brine-quartz system inside the glass vial is shown in Figure 5.1.

Figure 5.1: The visual system ready for contact angle measurements

In order to obtain the contact angle of the bitumen-brine-quartz system at different times and concentrations of CaCl2 solutions, visual images from the interface region are taken using a regular digital camera. The camera is a Canon PowerShot SD900 digital ELPH and it was adjusted to the digital macro setting and placed on automatic diaphragm opening. The camera was precisely placed in front of the drop. A tungsten source of light was placed behind the vial, which provided enough light for the experiments. The light was approximately 20cm away from the vial to avoid heat transfer from the light to the system.

For each type of bitumen as a drop, experiments were performed using distilled water,

5%wt, and 10%wt CaCl2 aqueous solutions as bulk fluid. For each concentration, the

123 experiment was repeated for comparison and reproducibility purposes. The images were taken at different times starting from 0 hour up to 120 hours, which is considered as the equilibrium time. At each time, generally four images of the system were taken. The contact angle values were obtained based on ADSA-P procedure. They were reported at each time to determine the equilibrium time and at equilibrium stage. The details of the results are explained later in the same chapter.

5.2 Image Processing

Digital image processing allows the use of much more complex algorithms for image processing, and hence can offer both more sophisticated performance at simple tasks, and the implementation of methods which would be impossible by analog means. Digital cameras generally include dedicated digital image processing chips to convert the raw data from the image sensor into a color-corrected image in a standard image file format.

Images from digital cameras then receive further processing to improve their quality.

This is a distinct advantage that digital cameras have over film cameras. The digital image processing is done by special software programs that can manipulate the images in many ways.

In this work the digital images after being transferred to a computer, were pre-processed through two stages. In the first stage Microsoft Office Picture Manager was employed to enhance the colors and optimize the brightness and color contrast of the drop images. In the second stage, Microsoft Office Picture Manager and Paint software were utilized to adjust the size and colors. In addition to color enhancement, in this stage the solid

124 surface was eliminated from the image and image was divided into two parts, which each part was a bit more than half of the image. Therefore, each part of an image contained the apex information and the contact angle of one side of the drop in itself. The main purpose of dividing each image is to process and obtain two values of contact angle.

These preliminary processes made the images more clear and readable in the image processor. A sample of pre-processed image after the first stage as well as unprocessed version of it is illustrated in Figure 5.2.

Figure 5.2: A raw and pre-processed (first stage) digital image of a visual experiment

Also the divided images of the same drop are shown in Figure 5.3. By dividing the images into two sections, the contact angle and the interface for the left and right sides of one drop could be determined. Therefore in general, in each desired time there would be

8 interface profiles available for the study of the interfacial properties of the system.

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Figure 5.3: A divided pre-processed (second stage) digital image of a visual experiment (the same image from Figure 5.2)

After preliminary image processing and image enhancing, each divided image was used as an input file in the ImageProcessing routine generated in Matlab. The routine is available in Appendix D. The output of each image from the ImageProcessing routine was an array containing the coordinates of the interface detected as an edge in the processor. The array was the feed for ADSA-P routine, which calculates the contact angle values. Also a figure showing the experimental and calculated interface profiles was generated when the ImageProcessing routine finished calculating. The produced edge image from the routine is shown in Figure 5.4. In this figure, the image is the same drop as shown in Figure 5.2 and Figure 5.3.

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Figure 5.4: Detected edge of a digital image from visual experiments

5.3 ADSA-P procedure

The output array from the ImageProcessing routine for each image was imported in to a macro enabled Microsoft Excel worksheet. Each pair of digits in the array represented x and y coordinates of a point on the bitumen-brine interface. These pairs of numbers were the feed for ADSA-P calculations.

The first step performed in the ADSA-P calculations was importing the Visual Basic modules in to the related Microsoft Excel worksheet. The modules include the main

127 body, the interface, all the functions and integrals needed for the calculations of the

ADSA-P procedure. The functions developed in the modules were assigned to some of the cells in the worksheet. Therefore, the name of the functions were entered in the formula bar for the relevant cells and copied to all the worksheets. These cells were the error function, the contact point in the experimental image, contact angle value, initial guess for coordinates of the apex, radius of the apex and parameter q4, which initially is considered equal to zero. The initial guess for the coordinates of the apex was also obtained using a function that finds the point with the largest vlaue of y among the experimental coordinates. The initial guess for the radius of the apex was given by the user.

The routine has been developed in a way that the first cell of the experimental data points should be selected when reaching for the macros in the Microsoft Excel worksheet. The first macro selected was ShowExcelSolver. This macro has been designed to run the

Microsoft Excel solver to minimize the error function by changing the parameters q1 to q4. These parameters were initially guessed as explained above. By minimizing the error function all the parameters were recalculated and the contact angle values of the system were also determined.

In the next step a macro named PlotOriginalData was chosen. The role of this macro is to generate a plot showing the information about the position of the experimental interface. Then, by calling another macro named GenerateOptimizedCurves the calculated curve coordinates were listed and a plot comparing both the experimental and

128 the calculated interface would appear on the worksheet. At this point, the ADSA-P calculations were completed for one image. In Figure 5.5 a screenshot of a worksheet for a random image is presented. In this case all the calculations are completed.

Figure 5.5: A screenshot from a sample ADSA-P calculation in Microsoft Excel

5.4 The Results of Visual Contact Angle Measurements

The results of visual experiments for contact angle measurement are listed in Table 5-1 to

Table 5-12 for Athabasca and Cold Lake bitumen samples. The tables are based on the type of the bitumen and concentration of CaCl2 solution at ambient temperature and pressure. In these tables all 8 experimental data for each time are presented as well as their average. The last two rows in each table represent the standard deviation in the distribution and the standard error in the mean of 8 observations.

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The contact angle reported in this work is the angle that the aqueous phase forms with the surface of the solid. Generally, the contact angle is measured toward the denser phase.

Here, the denser phase in most of the cases is the aqueous phase. Therefore, for consistency all the contact angles are reported toward the aqueous phase.

Table 5-1: Athabasca bitumen-distilled water contact angle (first run) Time (hr) 0 24 48 72 96 120

Image 1L 27 37 24 23 25 29

Image 2L 28 27 32 22 34 29

Image 3L 26 36 35 38 23 29

Image 4L 29 22 23 22 30 24

Image 1R 34 28 28 28 36 36

Image 2R 29 28 28 25 24 28

Image 3R 21 22 21 32 28 26

Image 4R 36 22 35 35 29 29

Average 29 28 28 28 29 29

STD 5 6 5 6 4 3 Deviation

STD Mean 2 2 2 2 2 1 Error

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Table 5-2: Athabasca bitumen-distilled water contact angle (second run) Time (hr) 0 24 48 72 96 120

Image 1L 59 71 55 83 74 70

Image 2L 79 74 76 75 70 65

Image 3L 73 74 78 75 83 68

Image 4L 70 59 70 53 61 74

Image 1R 68 80 69 78 53 70

Image 2R 58 78 55 75 70 70

Image 3R 78 58 79 55 72 72

Image 4R 76 71 79 68 71 71

Average 70 71 70 70 69 70

STD 8 8 10 11 9 3 Deviation

STD mean 3 3 4 4 3 1 Error

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Table 5-3: Athabasca bitumen-05% CaCl2 contact angle (first run) Time (hr) 0 24 48 72 96 120

Image 1L 13 15 25 22 16 20

Image 2L 17 18 19 14 22 16

Image 3L 15 22 13 19 19 22

Image 4L 14 18 19 19 20 16

Image 1R 14 23 19 20 16 25

Image 2R 15 18 19 12 20 18

Image 3R 16 14 19 29 20 25

Image 4R 15 18 21 19 28 20

Average 15 18 19 19 20 20

STD 1 3 3 5 4 4 Deviation

STD mean 0 1 1 2 1 1 Error

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Table 5-4: Athabasca bitumen-05% CaCl2 contact angle (second run) Time (hr) 0 24 48 72 96 120

Image 1L 22 22 28 33 25 31

Image 2L 30 30 26 30 41 36

Image 3L 34 27 30 30 26 31

Image 4L 20 26 35 23 37 26

Image 1R 34 31 21 30 30 30

Image 2R 36 32 28 21 30 29

Image 3R 30 22 21 39 20 29

Image 4R 33 27 38 30 30 29

Average 30 27 28 29 30 30

STD 6 4 6 6 7 3 Deviation

STD mean 2 1 2 2 2 1 Error

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Table 5-5: Athabasca bitumen-10% CaCl2 contact angle (first run) Time (hr) 0 24 49 73 97 116

Image 1L 8 12 22 33 27 31

Image 2L 17 24 29 32 24 33

Image 3L 9 13 21 33 24 33

Image 4L 11 16 34 22 33

Image 1R 11 16 20 33 29 22

Image 2R 9 16 29 33 12 29

Image 3R 12 16 27 33 23 27

Image 4R 11 24 31 29 32

Average 11 16 23 33 24 30

STD 3 4 5 1 5 4 Deviation

STD mean 1 2 2 0 2 1 Error

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Table 5-6: Athabasca bitumen-10% CaCl2 contact angle (second run) Time (hr) 0 10 24 34 48 72 97 120

Image 1L 29 36 39 39 43 39 43 41

Image 2L 33 39 39 44 44 34 46 43

Image 3L 37 37 43 40 40 46 38 36

Image 4L 41 36 38 39 31 44 47 45

Image 1R 32 40 40 36 45 38 39 36

Image 2R 32 34 38 39 36 35 39 42

Image 3R 37 33 39 39 43 43 36 40

Image 4R 38 32 35 43 39 35 37 43

Average 35 36 39 40 40 39 41 41

STD 4 3 2 3 5 5 4 3 deviation

STD mean 1 1 1 1 2 2 1 1 error

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Table 5-7: Cold Lake bitumen-distilled water contact angle (first run) Time (hr) 0 24 49 72 96 120

Image 1L 19 25 25 20 17 25

Image 2L 28 23 25 19 28 23

Image 3L 25 17 24 28 24 18

Image 4L 31 26 22 16 26 21

Image 1R 31 20 24 33 23 20

Image 2R 24 25 20 20 23 30

Image 3R 11 23 24 19 23 22

Image 4R 23 23 25 30 19 23

Average 24 23 24 23 23 23

STD 7 3 2 6 3 4 Deviation

STD mean 2 1 1 2 1 1 Error

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Table 5-8: Cold Lake bitumen-distilled water contact angle (second run) Time (hr) 0 24 49 73 96 122

Image 1L 44 47 44 56 35 58

Image 2L 44 39 45 56 54 38

Image 3L 45 59 40 46 54 57

Image 4L 44 47 55 33 54 46

Image 1R 35 55 42 46 33 47

Image 2R 44 41 55 42 46 42

Image 3R 39 47 33 55 37 46

Image 4R 56 41 45 34 52 37

Average 44 47 45 46 46 46

STD 6 7 7 9 9 8 Deviation

STD mean 2 2 3 3 3 3 Error

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Table 5-9: Cold Lake bitumen-05% CaCl2 contact angle (first run) Time (hr) 0 12 24 49 72 98 120

Image 1L 55 48 48 47 51 51 49

Image 2L 50 48 50 43 48 52 59

Image 3L 58 48 44 53 50 50 51

Image 4L 46 47 50 56 50 53

Image 1R 56 43 54 47 48 55 50

Image 2R 54 48 48 48 63 54 51

Image 3R 62 51 47 50 51 58 52

Image 4R 54 47 54 53 53 58

Average 56 48 48 49 52 53 53

STD 4 7 7 7 8 8 8 deviation

STD mean 2 3 3 3 3 3 3 error

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Table 5-10: Cold Lake bitumen-05% CaCl2 contact angle (second run) Time (hr) 0 24 48 72 96 120

Image 1L 60 73 69 70 76 76

Image 2L 62 72 72 68 72 77

Image 3L 58 66 78 74 77 71

Image 4L 51 70 70 72 73 77

Image 1R 54 75 78 74 78 75

Image 2R 59 74 62 77 74 81

Image 3R 61 77 74 78 74 74

Image 4R 64 76 74 77 74 75

Average 59 73 72 74 75 76

STD 4 4 5 3 2 3 Deviation

STD mean 1 1 2 1 1 1 Error

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Table 5-11: Cold lake bitumen-10% CaCl2 contact angle (first run) Time (hr) 0 10 24 48 76 96 120

Image 1L 42 42 37 46 46 38 51

Image 2L 48 36 52 42 49 56 43

Image 3L 36 49 39 48 52 42 46

Image 4L 46 39 50 46 36 52 46

Image 1R 37 44 34 53 43 43 56

Image 2R 45 44 43 48 44 53 35

Image 3R 30 49 38 44 53 35 53

Image 4R 49 35 49 38 42 52 42

Average 42 42 43 46 46 46 46

STD 7 6 7 4 6 8 7 deviation

STD mean 2 2 2 2 2 3 2 error

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Table 5-12: Cold lake bitumen-10% CaCl2 contact angle (second run) Time (hr) 0 24 48 72 99 124

Image 1L 13 16 22 35 18 23

Image 2L 14 23 21 25 18 28

Image 3L 15 21 22 21 35 26

Image 4L 15 22 22 18 28 23

Image 1R 15 21 21 31 21 29

Image 2R 18 20 25 15 24 34

Image 3R 14 24 15 23 25 28

Image 4R 15 19 28 18 25 29

Average 15 21 22 23 24 28

STD 1 3 4 7 5 3 Deviation

STD mean 1 1 1 2 2 1 Error

The charts showing the relation between the contact angle of bitumen-brine-quartz system and the age of the system are shown in Figure 5.6 to Figure 5.17. These charts are showing the data presented in Table 5-1 to Table 5-12. Illustration of the distribution of contact angle values at each time is the main purpose of these charts.

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Figure 5.6: Athabasca bitumen-distilled water contact angle (first run)

Figure 5.7: Athabasca bitumen-distilled water contact angle (second run)

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Figure 5.8: Athabasca bitumen-05% CaCl2 contact angle (first run)

Figure 5.9: Athabasca bitumen-05% CaCl2 contact angle (second run)

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Figure 5.10: Athabasca bitumen-10% CaCl2 contact angle (first run)

Figure 5.11: Athabasca bitumen-10% CaCl2 contact angle (second run)

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Figure 5.12: Cold lake bitumen- distilled water contact angle (first run)

Figure 5.13: Cold lake bitumen- distilled water contact angle (second run)

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Figure 5.14: Cold lake bitumen-05% CaCl2 contact angle (first run)

Figure 5.15: Cold lake bitumen-05% CaCl2 contact angle (second run)

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Figure 5.16: Cold lake bitumen-10% CaCl2 contact angle (first run)

Figure 5.17: Cold lake bitumen-10% CaCl2 contact angle (second run)

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The following charts (Figure 5.18 to Figure 5.23) illustrate the contact angle of each type of bitumen at different times. Also every chart is assigned to a different concentration of

CaCl2 solution. The value of the contact angle for each point on the diagrams is the average contact angle value for that time. In order to show the distribution of all 8 contact angle measurements error bars have been inserted into the sets. These error bars show the difference of the minimum and maximum measured contact angle at each time with the mean value of it. Also a linear trend line has been passed through every set of measurements showing the relative slope and the trend of the results over time.

Figure 5.18: Athabasca bitumen-distilled water contact angle vs. time

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As it is shown in Figure 5.18 in the system of Athabasca bitumen-distilled water-quartz, the changes in the contact angle values by time for both series of experiments are quite minor. Also the drop is very stable on top of the quartz surface. In this system the values of the contact angle at equilibrium stage are 29 degrees and 70 degrees for the first and second runs, respectively. The difference between these two contact angles can be because of some errors in the experiments including the accuracy in injecting the drop, deviation of the surface from being completely flat and contamination of the surface.

Results of the contact angle changes in each time for the system of Athabasca bitumen-

05% CaCl2-quartz are shown in Figure 5.19.

Figure 5.19: Athabasca bitumen-05% CaCl2 contact angle vs. time

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In this diagram, the contact angle value of the system at each time is different for both of the experiments. The contact angle values decrease or increase over time until they reach equilibrium at the end of the experiments (120 hours).

For the first run, the average of the initial contact angle (at 0 hour) is very low (15 degrees). Therefore, during 24-hour period it increases to 18 degrees. The final contact angle at equilibrium is reported 20 degrees.

For the second run, also some changes occur in the value of the contact angle until it reaches equilibrium at 120 hours. The final contact angle at equilibrium is reported 30 degrees. The difference between these two final contact angles can be because of the initial contact angle values specially the first run’s very low initial contact angle.

In both cases it is apparent that the contact angle values at 96 hours and 120 hours are very similar, which means the system has reached equilibrium.

In Figure 5.20 results of the contact angle in different times for system of Athabasca bitumen-10% CaCl2-quartz are displayed.

The first run in this system is very similar to the first run from the system of Athabasca bitumen-05% CaCl2-quartz. The initial contact angle is very low and consequently, there are lots of fluctuations for the value of the contact angle during the experiment. The contact angle reported at 72 hours is barely acceptable. Finally, the contact angle value

150 approaches the equilibrated value of it at 120 hours. The final contact angle at equilibrium is reported 30 degrees.

In the second run, the initial contact angle is relatively high and at the equilibrium the value of the contact angle is equal to 41 degrees. The fluctuations in the second case are less than the first case and it is obvious that the contact angle values at 96 hours and 120 hours are very similar, which means the system has reached equilibrium.

Figure 5.20: Athabasca bitumen-10% CaCl2 contact angle vs. time

Figure 5.21 demonstrates the results of the contact angle in different times for system of

Cold Lake bitumen-distilled water-quartz.

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The average contact angle values shown in each time are quite similar to each other and therefore, both series are very smooth over the period of the experiments. The changes in contact angle values by time for both series of experiments are quite minor. Also the drop is very stable on top of the quartz surface for both sets. In this system the values of the contact angle at equilibrium stage are 23 degrees and 46 degrees for the first and second runs, respectively.

Figure 5.21: Cold Lake bitumen-distilled water contact angle vs. time

Figure 5.22 exhibits the results of the contact angle in each experimental time for Cold

Lake bitumen-05% CaCl2-quartz system.

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Figure 5.22: Cold Lake bitumen-05% CaCl2 contact angle vs. time

In this diagram, the contact angle values for the system at each time are displayed for both of the experiments. The contact angle values decrease or increase over time until they reach equilibrium at the end of the experiments (120 hours). In case of fluctuation there are some similarities between this system and Athabasca bitumen-05% CaCl2- quartz system.

For the first run, some changes occur in the value of contact angle until it reaches equilibrium at 120 hours. The final contact angle at equilibrium is reported 53 degrees.

The same value is also seen at 96 hour. Therefore, it is the equilibrium contact angle.

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For the second run, changes in the system contact angle are larger at the beginning of the experiment. As the system ages the values of contact angles show a smoother trend. The final contact angle at equilibrium is reported 76 degrees. Similar to the first run, the contact angle value is the same at 96 hour that is the equilibrium contact angle.

The diagram illustrated in Figure 5.23 reveals the results of the contact angle in each experimental time for Cold Lake bitumen-10% CaCl2-quartz system.

Figure 5.23: Cold Lake bitumen-05% CaCl2 contact angle vs. time

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There are some minor oscillations in the value of the contact angle at the beginning of both experiments. The graphs show smoother trends at the end of the experiments and approach their equilibrium value. The final contact angle values for the first and second run are 46 degrees and 28 degrees, respectively.

For a better comparison between the contact angle values at different times and CaCl2 solution concentration, all the experiments for each type of bitumen are demonstrated in one graph (Figure 5.24 and Figure 5.25).

Figure 5.24: Athabasca bitumen-brine contact angle vs. time

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The values of contact angle in the second run for Athabasca bitumen-distilled water- quartz system are higher than any other series of experiments for Athabasca bitumen.

That can be interpreted as an error than a reasonable phenomenon. It is possible that when the drop was injecting on the solid surface, the aqueous phase was not completely in contact with the quartz, letting bitumen spread over the solid surface and wetting the quartz more than what it was supposed to. It is recommended to ignore this set of data.

Figure 5.25: Cold Lake bitumen-brine contact angle vs. time

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In general, the contact angle values and changes depend on the angle that the drop makes with the surface at the moment of contact. If in the first moment contact angle is very close to the equilibrium contact angle, variation of the contact angle over time is less than when the drop touches the surface with a very uncommon angle.

In most of the cases, the value of the contact angle increases as the drop ages. This phenomenon shows that the system advances to oil-wet characteristics. But it is obvious that the system tendency to be oil-wet is not very significant, because in all experiments the aqueous phase remains the wetting phase. Therefore, the shift to oil-wet quality is very slight and insignificant.

There is not a very obvious relation between the concentration of CaCl2 solution and the equilibrium contact angle. The only observation is that in lower concentrations of CaCl2 solution the trend of contact angle value in time is smoother. The equilibrium contact angle is generally in range of 20-40 degrees for Athabasca bitumen and 20-55 degrees for

Cold Lake bitumen independent of CaCl2 solution concentration.

In most of the experiments the value of contact angle after 72 hours becomes stable and constant. In the tests with large fluctuation, system may not reach stability after the experimental time. Also in the tests with major fluctuations, no trend can be assigned to the graph, while in the rest of them the value of contact angle slightly increases with time turning the system into a less water-wet system.

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In the following graphs (Figure 5.26 to Figure 5.28) the contact angle values at all times are illustrated for different concentration of CaCl2 solution. In each diagram the contact angle values of both Athabasca bitumen and Cold Lake bitumen are displayed. In these graphs, the blue series represent Athabasca bitumen contact angle values and the red series represent Cold Lake bitumen contact angle values.

Figure 5.26: Bitumen-distilled water contact angle vs. time

In Figure 5.26 the contact angles for bitumen-distilled water experiments are exhibited.

All the series show very smooth behaviour through time. It can be seen that the contact

158 angle values do not change significantly from the beginning to the end of each experiment. If the second run of Athabasca bitumen-distilled water is excluded, the equilibrium contact angles are in range of 23-46 degrees.

Figure 5.27: Bitumen-05% CaCl2 contact angle vs. time

In Figure 5.27 the contact angles for bitumen-05% CaCl2 experiments are shown. There are some fluctuations in the early contact angle values but after 72 hours the series show very smooth behaviour. The equilibrium contact angles are in range of 20-76 degrees.

This range is considerably wider than the bitumen-distilled water contact angles.

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Finally, the contact angles for bitumen-10% CaCl2 experiments revealed in Figure 5.28 show the largest fluctuations through time among all other experiments with different concentration of CaCl2. The equilibrium contact angles are in range of 28-46 degrees.

The equilibrium contact angle is presented in a range because it is a static contact angle that does not show unique value. Its value depends on the initial contact angle.

Figure 5.28: Bitumen-10% CaCl2 contact angle vs. time

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Because the visual cell is cylindrical, it can cause some horizontal image distortion.

Also, the presence of brine intensifies the distortion. Therefore, the visual images show the drop wider than its real size. In order to realize the effect of the distortion on the contact angle, some visual and micro CT images have been taken and compared to each other. A visual and a micro CT image of an identical system are shown in Figure 5.29.

The horizontal distortion is obvious in these two images.

Figure 5.29: A visual and a micro CT image of an identical drop-bulk-quartz system

The coordinate points of the interface for both visual and micro CT cases were obtained and fed into the ADSA-P routine. The contact angle values were calculated. For both cases the contact angle values were very similar and the results showed approximately 1 degree difference. This is within the range of the contact angle error measurement in the visual experiments; therefore this visual distortion does not affect the value of the contact angle reported in the visual experiments.

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On the other hand, horizontal distortion in the visual images affects the profile of the bitumen-brine interface and can have a significant effect on the value of the system’s

IFT. Therefore, it is recommended to use a square visual cell for visual IFT measurements to avoid horizontal distortion. A cylindrical cell with relatively large diameter comparing to the size of the drop should also decrease the visual distortion.

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Chapter Six: Micro CT-Scanner Contact angle and Interfacial Tension Measurements Results and Discussion

6.1 Procedure of the Experiments

Several experiments have been completed using the micro CT- scanner model to study the contact angle and IFT of bitumen-brine-quartz system. All of these experiments have been done in the micro CT-scanner pressure cell that is an X-ray transparent canister.

The maximum temperature and pressure could be reached in the experiments are 120oC and 1000psi (6.9Mpa). The experimental setup was left still for a period of approximately 120 hours before the experiment started so that the bitumen-brine-quartz system could reach equilibrium. The main purpose of the micro CT- scanner experiments is to find the value of the contact angle and IFT of the bitumen-brine-quartz system at different temperatures and pressures when the system is at the equilibrium. Other expectations of the micro CT- scanner experiments are to compare and investigate the relation between the contact angle and IFT of the system at different temperatures and pressures.

For this purpose a sample of Athabasca bitumen has been chosen and studied. The physical properties of this oil are available in Appendix E. The bitumen in some experiments was the drop phase and in other experiments was the bulk phase. In some experiments 1-Idododecane added to bitumen as a doping for generating clear images.

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The second fluid used in the experiments was either 10%wt or 20%wt CaCl2 aqueous solution. One solution of each concentration was prepared for all experiments. The reason why CaCl2 solution was used in the micro CT-scanner experiments is to make more contrast between the two fluid phases in the micro CT images. Since the density of distilled water and bitumen is very similar, by adding the CaCl2 to the distilled water the density difference between the two fluids increases and therefore more contrast in the images taken by the micro CT-scanner device appears.

In the micro CT-scanner contact angle and IFT measurements, the solid surface is a piece of smooth and circular quartz inserted in to the micro CT model. The quartz plate is ¼in

(~6.5mm) in diameter and 1.4mm in thickness.

The experiments were executed in an X-ray transparent pressure cell. The container is made of aluminum. A detailed design of the micro CT-scanner model is presented in

Chapter four. The total length of the micro CT model is 40.0mm, the vessel length is

20.0mm, the maximum OD is 12.6mm, the OD in the scanning area is 10mm, and the ID of the cell is 8.6mm.

In the experimental procedure first, the quartz plate was placed in the vial. Then, the vial is partially filled with the brine under study. The system of quartz-brine was left for 24 hours so that the surface of the quartz comes to equilibrium with the brine and the free ions in the brine. This stage is very important because based on the theory of the oil formation, brine filled the reservoir pores first and after a long time the oil was formed

164 and replaced the brine in the reservoir. Therefore, in this work 24 hours are given to the system to reach equilibrium before introducing the bitumen into system.

when the brine-quartz system reached equilibrium, the system was ready for the experiments so the system of bitumen-brine-quartz could be made. In different experiments either bitumen or brine could have the role of the drop. The drop was placed on the quartz by a free fall from the tip of a needle about 1cm above the quartz plate. The system was sealed by screwing a stainless steel fitting to the aluminum cell. The cell was connected to a micro valve through 1.59mm (1/16 inch) tubing for pressure control and the valve was connected to the micro pump by 3.2mm (1/8 inch) tubing. The pump could be set at any pressure from ambient to 1000psi.

The entire system was left for 120 hours to let the bitumen-brine-quartz interface reach equilibrium as well. Previously in Chapter five, the contact angle of bitumen-brine- quartz system had been measured at several time intervals and it had been observed that the changes in the contact angle are minor after 72 hours. Therefore 120 hours for the system equilibrium is sufficient.

The system at this stage was ready for the contact angle and IFT measurements. The system was placed on a horizontal surface with less than 0.1 degree error. A micro- tomographic image of the bitumen-brine-quartz system inside the aluminum vial is shown in Figure 5.1.

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Figure 6.1: The micro CT-scanner system ready for contact angle and IFT measurements

Two series of micro CT-scanner experiments have been completed. In the first part a piece of glass wool insulation was wrapped around the aluminum cell to avoid fast heat loss. Glass wool made the images very vague. Thus, a 4%vol 1-Iodododecane added to the Athabasca bitumen and 20%wt CaCl2 solution was used as the brine to have distinguishable bitumen-brine interface. In the second part of experiments, the pressure cell insulation was substituted with Styrofoam, which has a very low density and does not affect the micro CT images. Therefore, no doping added to the bitumen and 10% wt

CaCl2 solution could be used for the aqueous phase. The results from these two series of experiments are separately studied and discussed later in the current chapter.

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The micro-CT scanner used for imaging the contact angle was a SKYSCAN 1072 that is shown in Figure 6.2. The system is composed of a sealed micro-focus X-ray tube, air cooler and a CCD camera. Images were obtained at 100KV and 98µA with no filter. For each specimen, a series of projection images were produced with a rotation of 45 degrees between each image. The magnification used was 24.8 (pixel size = 10.8µm). Given a series of projection images, a stack of 2D sections was reconstructed for each specimen and stored in .bmp format with indexed grey levels ranging from 0 (black) to 255 (white).

Also, Figure 6.3 shows the cell inside the micro-CT scanner X-ray chamber.

Figure 6.2: Micro-CT scanner SKYSCAN 1072

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Figure 6.3: Micro-CT scanner SKYSCAN 1072

Micro CT experiments were performed at different pressures and temperature. The maximum temperature that can be reached in the cell is 393K (120oC) under the experimental pressure. In order to heat the system, a Sheldon Manufacturing Inc. conventional oven was used. The oven model number is 1350FM. A micro pump was also used to pressurize the system.

After the cell was placed in a conventional oven to reach the experimental temperature and adjusted at the desired pressure, it was inserted in a glass wool or Styrofoam insulation to avoid a very rapid heat loss during the scanning process. The micro valve and the connected tubing were wrapped in glass wool insulation. The whole system was inserted in the X-ray chamber of micro CT-scanner to obtain the images of the fluid-fluid interface.

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6.2 The Results of the First Part of Micro CT Experiments

Images taken for the first part of micro CT experiments had 7500ms X-ray exposure time. Images were obtained at 100KV, 98µA and 24.8 times magnification.

In the first part of micro CT experiments the contact angle for the system of quartz-brine- bitumen is measured at different temperatures and pressures for four different cases. In these cases the bitumen or brine could be either drop of the continuous phase. The bitumen used for the experiments was Athabasca bitumen. 1-Iodododecane doping added to bitumen to make a 4%vol 1-Iodododecane- bitumen solution. The brine used for the experiments was 20%wt CaCl2 solution. Also the order of contact in these four cases is different.

In the first case 20%wt CaCl2 solution (brine) was the drop, bitumen was the bulk phase.

The quartz surface was exposed to bitumen before the drop of brine was placed on it. In the second case brine was the drop and bitumen was the bulk phase, which is very similar to the first case. The only difference is that in the second case the drop was placed on the quartz surface first followed by the bitumen filling the cell. In the third case, the drop and the bulk fluid changed. Bitumen was the drop, the brine was the bulk phase and the drop of bitumen was placed on the quartz surface before the brine filling the cell. Finally, in fourth case bitumen was the drop, brine was the bulk phase, the quartz surface was in contact with brine first and then a drop of bitumen was placed on the surface. The contact angle values from the images taken were measured directly by a goniometer.

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6.2.1 Case 1

In the first case brine was the drop and bitumen was the bulk phase. The quartz surface was exposed to bitumen before the drop of brine was placed on it. The system went under different pressures and temperatures. In each pressure and temperature a micro-CT image of the interface was taken. The direct results of contact angle measurements at different temperatures for ambient pressure, 200psi and 400psi are shown in Figure 6.4.

These results for 600psi, 800psi and 1000psi are shown in Figure 6.5.

Figure 6.4: Results of contact angle measurements for case 1 at different temperatures for ambient pressure, 200psi and 400psi

As shown in Figure 6.4 and Figure 6.6 as pressure increases the contact angle values become smaller and therefore, the system turns from weak oil-wet to intermediate

170 wettability. As it can be seen in the figure, at ambient pressure the range of contact angles is 130 degree to 140 degree and at 1000psi the contact angles are mostly in the range of 100 degree to 110 degree that is less oil-wet. When the pressure changes from

200psi to 800psi the contact angle does not change as dramatically. In each pressure, the contact angle decreases as the temperature increases, this means the system becomes more water-wet at elevated temperatures. In general the system shows oil-wet tendency because it contacted the bitumen prior to the brine. Therefore, these results show higher contact angle values than the real contact angle values.

Figure 6.5: Results of contact angle measurements for case 1 at different temperatures for 600psi, 800psi and 1000psi

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6.2.2 Case 2:

In the second case brine was the drop and bitumen was the bulk phase. The drop was placed on the quartz surface first followed by the bitumen filling the cell. Here, the contact angles are totally different to those from case 1. Figure 6.6 and Figure 6.7 present these results. In this case, the quartz shows clearly water-wet tendency. In reality, the reservoirs were exposed to the connate water first and subsequently the oil was produced and entered the reservoirs. Therefore, the results from case 2 introduce a more similar situation to what is encountered in the oil reservoirs.

Figure 6.6: Results of contact angle measurements for case 2 at different temperatures for ambient pressure, 200psi and 400psi

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Figure 6.7: Results of contact angle measurements for case 2 at different temperatures for 600psi, 800psi and 1000psi

Comparable to case 1, as the pressure and temperature increase the contact angle becomes smaller and the quartz shows more water-wet affinity.

In the second case, two drops of water with different diameters (1mm and 2.5mm) were studied. The results of contact angle measurements at different temperatures for 200psi,

400psi, 600psi, and 1000psi are illustrated in Figure 6.8 to Figure 6.11. The contact angles measured for the smaller drop (1mm diameter) are generally smaller than the bigger drop (2.5mm diameter) at all studied pressures.

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Figure 6.8: Effect of drop size on contact angle values at 200 psi

Figure 6.9: Effect of drop size on contact angle values at 400 psi

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Figure 6.10: Effect of drop size on contact angle values at 600 psi

Figure 6.11: Effect of drop size on contact angle values at 1000 psi

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At all pressures the contact angle values are slightly decreasing as the temperature increases, but this trend is very insignificant. Therefore, it can be interpreted that the value of contact angle is not very sensitive to temperature of the system. For each drop size and pressure an average has been calculated and assigned. They are presented in

Figure 6.12. As shown, the contact angle values for the smaller drop (1mm diameter) are smaller at all different pressures. Also at the highest pressure (1000psi) the contact angle values of the both drops show stronger water-wet tendency of the system.

Figure 6.12: Effect of drop size on contact angle values at different pressures

6.2.3 Case 3:

In the third case, bitumen was the drop, brine was the bulk phase and the drop of bitumen was placed on the quartz surface before brine filling the cell. The contact angle measurement results in Figure 6.13 show that increasing pressure from 500psi to 1000psi

176 decreases the contact angle and therefore the system turns toward water-wetness. The results for ambient pressure do not follow this trend. Also, in both 500psi and 1000psi the contact angle decreases as the temperature goes up and therefore, the system tends to move toward intermediate wettability from its initial oil-wet characteristics.

Figure 6.13: Results for case 3 at different temperatures and pressures

6.2.4 Case 4:

In the fourth case bitumen was the drop, brine was the bulk phase, the quartz surface was in contact with the brine first and then a drop of bitumen was placed on the surface. The result trends of the contact angle measurement for different pressures and temperatures in this case are not comparable to the other three cases. The results are illustrated in Figure

6.14.

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Figure 6.14: Results for case 4 at different temperatures and pressures

All the contact angle measurements results presented in Figure 6.4 to Figure 6.14 are based on the average of two measurements from both sides of the drop. The contact angle error in these results is about ±3 degrees. The error happens because of the direct measurements of contact angle by drawing a tangent line to the interface passing from the contact area and then measuring the angle that the line makes with the solid surface. This error is shown in the relevant curves using the error bars.

Another source of error could be the accuracy in measuring the temperature. The thermocouple and the temperature indicator were tested and they were exact. The precision of the temperature measurements in the indicator is 1oC. Therefore the

178 systematic error caused by the device is less than ±0.5oC. The thermocouple in the micro

CT experiments was mounted on the outside wall of the aluminum cell and they both were wrapped in the insulation. There was a small error in reading the temperature of the cell’s wall and the fluid itself. This error was assessed less than 1oC. Also, the thermocouple had to be detached from the indicator when the cell was placed in the X- ray chamber to allow the door of the X-ray chamber of the micro CT scanner to close thoroughly. Therefore, the temperature of the system was an estimate at the time image was taken. Many temperature against time tests were done to predict the temperature of the system at the time the image was going to be taken. The error in this estimation can be up to 2oC. Therefore, by adding all these temperature errors, the total error in the temperature assigned to each contact angle is ±3.5oC.

A shown in Figure 6.4, Figure 6.5, Figure 6.6, Figure 6.7, Figure 6.13, and Figure 6.14 the contact angle results are not consistent and in most of the cases no trend could be assigned to them. The main reason could be the doping in the oil and very high concentration of CaCl2 in the brine. In the next part of the micro CT experiments it was attempted to correct the shortcomings of the first part to achieve better and more reliable results. Therefore, a better insulation (Styrofoam) was found and substituted for glass wool. Using Styrofoam lowered the concentration of CaCl2 and no doping in the oil was needed. Also the micro CT-scanner was tested in different voltages, currents and exposure times to find the optimum settings.

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Also, possible contamination and deviation of the surface from being thoroughly smooth can cause some errors in the contact angle measurements.

6.3 The Results of the Second Part of Micro CT Experiments

In the second part of the micro CT experiments Athabasca bitumen has been chosen and tested. The physical properties of it have been measured and are presented in Appendix

E as well as brine physical properties. No doping was added to the oil. The brine used for this series of tests was 10%wt CaCl2 solution. There was no need for higher concentrations of CaCl2 solution because of using Styrofoam insulation instead of glass wool. Use of Styrofoam insulation caused clearer images that did not need any doping.

The system was completely X-ray transparent and the fluid-fluid interface was comprehensible.

Images taken for the second part of micro CT experiments had 8100ms X-ray exposure time. Images were obtained at 100KV, 98µA and 24.8 times magnification.

In the second part of experiments bitumen was always the drop because of more clarity.

In order to be able to substitute the brine as a drop some doping and higher concentration of CaCl2 solution was needed.

The images taken from the drops at different pressures and temperatures were assumed axisymmetric; therefore ADSA-P technique could be used for calculating the contact angle and IFT value for each system from the shape of the axisymmetric drop.

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6.3.1 Image Processing

In these experiments the ADSA-P procedure has been employed to measure both the contact angle and IFT of the brine-bitumen interface on top of the quartz plate. After generating the micro CT images at each temperature and pressure, the interface coordinates were determined and inserted into ADSA-P routine written in Visual Basics as Microsoft Excel macros. In the micro CT experiments the ImageProcessing routine could not be employed because the noise level in the micro CT images is too high.

Therefore the interface coordinates fed into the ADSA-P procedure were produced manually. The coordinate points of the drop interface were chosen randomly from the drop profile. In general, 10 points were selected for each drop profile.

In this work the micro CT images after being transferred to a computer, were pre- processed using Microsoft Office Picture Manager and Paint software to enhance the colors, optimize the brightness, adjust the color contrast and the size of the image. These preliminary processes made the images more clear and readable.

6.3.2 ADSA-P procedure

The interface coordinate points for each image were imported in to a macro enabled

Microsoft Excel worksheet. Each pair of digits represented the x and y coordinates of a point on the bitumen-brine interface. These pairs of numbers were the feed for ADSA-P calculations.

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The steps performed in the ADSA-P calculations are the same as the visual experiments.

First, the Visual Basic modules including the main body, the interface, all the functions, and integrals were imported to the related Microsoft Excel worksheet. Then the initial guesses for coordinates of the apex, radius of the apex and parameter q4 were entered.

Parameter q4 at first is considered equal to zero. The preliminary guess for the coordinates of the apex was also obtained using a function that finds the point with the largest amount of y among the experimental coordinates. The initial guess for the radius of the apex was given by the user.

The first macro selected was ShowExcelSolver. This macro has been designed to run the

Microsoft Excel solver to minimize the error function by changing the parameters q1 to q4. By minimizing the error function all the parameters were recalculated and the contact angle and IFT of the drop were also determined.

In the next step a macro named PlotOriginalData was chosen to generate a plot showing the information about the position of the experimental interface. Then, by calling another macro named GenerateOptimizedCurves the calculated curve coordinates were listed and a plot comparing both the experimental and the calculated interface would appear on the worksheet. At this point, the ADSA-P calculations were completed for one image.

6.3.3 Results of the Contact Angle and IFT Calculations

The contact angle and IFT values for the system of quartz-brine-bitumen were determined at different temperatures at ambient pressure, 1.724MPa (250psi), 3.447MPa

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(500psi), 5.171MPa (750psi), and 6.895MPa (1000 psi) using ADSA-P numerical method to assess the images taken by a SKYSCAN 1072 micro-CT scanner.

The results for the calculated contact angles are shown in Figure 6.15 to Figure 6.19. In these charts the values of the drop contact angle at different temperatures for each pressure are shown as a point. The general behaviour of the contact angle value at different temperatures is also shown by a linear trend line. The trend line is not accurate enough to represent a mathematic model of the contact angle behaviour with temperature, but it can show how generally the contact angle is changing with temperature.

The trends in Figure 6.15 to Figure 6.19 show that generally, the contact angle of the bitumen-water interface increases as the temperature increases. At lower temperatures the system is more water wet and the wettability of the system is changing toward neutral wettability as the temperature increases.

Also, comparing the same charts, it is found that the contact angle of the bitumen-brine interface normally increases as the pressure increases. At higher pressures (3.447MPa

(500psi) and higher), larger contact angle values are reported compared to ambient pressure and 1.724MPa (250psi) experiments. This increase in the contact angle values is to the extent that the wettability of the system changes totally from water-wet to neutral wettability.

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The contact angle curves show a smoother trend at higher temperatures at each level of experimental pressure. Also, the contact angle curves are smoother in higher pressures.

As it is apparent in Figure 6.15, at ambient pressure the contact angle range is over 40 degrees, but as the pressure increases the range of contact angle changes narrows down to

20 degrees at 6.895MPa (1000 psi) as shown in Figure 6.19.

Figure 6.15: Contact Angle values of bitumen-brine-quartz system at different temperatures and ambient pressure

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Figure 6.16: Contact Angle values of bitumen-brine-quartz system at different temperatures and 250psi

Figure 6.17: Contact Angle values of bitumen-brine-quartz system at different temperatures and 500psi

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Figure 6.18: Contact Angle values of bitumen-brine-quartz system at different temperatures and 750psi

Figure 6.19: Contact Angle values of bitumen-brine-quartz system at different temperatures and 1000psi

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The contact angle calculations were done for 10 random profile points of the drop. In order to assure the accuracy of the calculations for ten points, a series of 40 random points were selected on one of the drop profiles. The ADSA-P routine was run for this set of data and the contact angle and IFT values obtained were compared to the 10 point calculated contact angle and IFT values. The difference was minor and negligible. In order to assure the accuracy of the results, some coordinate points close to the contact area were altered by small amounts to see how the contact angle and IFT values would change. These two tests would show a total error of ±3 degrees in the contact angle values. The error is shown in Figure 6.15 to Figure 6.19 as error bars. Also all of these graphs are shown in 1 graph for better comparison illustrated in Figure 6.20.

Figure 6.20: Contact Angle values of bitumen-brine-quartz system at different temperatures pressures

The results of the IFT calculations are shown in Figure 6.21 to Figure 6.25.

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Figure 6.21: IFT values of bitumen-brine-quartz system at different temperatures and ambient pressure

Figure 6.22: IFT values of bitumen-brine-quartz system at different temperatures and 250psi

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Figure 6.23: IFT values of bitumen-brine-quartz system at different temperatures and 500psi

Figure 6.24: IFT values of bitumen-brine-quartz system at different temperatures and 750psi

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Figure 6.25: IFT values of bitumen-brine-quartz system at different temperatures and 1000psi

From the results of IFT calculations(Figure 6.21 to Figure 6.25) it is apparent that a general trend exists when the pressure increases. The interfacial tension for the system tends to increase with the pressure for these experiments.

By considering each individual test another apparent trend appears. At a given pressure the IFT values tends to decrease with an increase in temperature. This can be found in each graph’s trend line.

The IFT trends are smoother at lower pressures. As shown in Figure 6.21 (ambient pressure), the interfacial tension ranges is less than 2mN/m, but as the pressure increases

190 the range of interfacial tension changes are larger so that in Figure 6.25 (6.895MPa or

1000psi) the range is as large as almost 7mN/m.

The accuracy of the results can be attributed to the interpretation of the image taken by the micro-CT scanner. Any small deviation from the actual drop shape can cause the

ADSA-P algorithm to converge to a sub-optimal curve. Experimental error in preparing the samples also influences the calculations. As mentioned earlier, the contact angle and

IFT calculations were done for 10 random profile points of the drop. A series of 40 random points were generated on one of the drop profiles for comparison. The IFT values obtained were compared to the 10 point calculated IFT values. The error achieved was less than ±0.5mN/m. This error is shown in all charts as error bars. Also all of these graphs are shown in 1 graph for better comparison illustrated in Figure 6.20.

Figure 6.26: IFT values of bitumen-brine-quartz system at different temperatures pressures

191

Chapter Seven: Conclusions and Recommendation for Future Work

7.1 Conclusions from the Visual Experiments:

• The value of contact angle strongly depends on the way the drop is placed on top of the quartz surface. Some of the factors that can significantly change the initial contact angle are the distance of the injection needle from the surface, the size of the falling drop, the pressure applied to inject the drop. Therefore, some preliminary tests have been executed to investigate these changes and avoid them. Yet, some of the unusual changes in the contact angle of the systems can be a consequence of the method of drop injection.

• Some of the curves in the visual experiments show higher contact angle values comparing to the rest of them. This phenomenon can be interpreted as an error cause by many factors mainly possible surface contamination and also surface roughness. In microscopic scales the quartz surface is not very smooth and that affects the contact angle value.

• The values of contact angle in the second run for Athabasca bitumen-distilled water- quartz system are higher than any other series of experiments for Athabasca bitumen.

That can be interpreted as an error than a reasonable phenomenon. It is possible that when the drop was injected on the solid surface, the aqueous phase was not completely in contact with the surface, letting bitumen spread over the surface and wetting the surface more than what it was supposed to.

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• In general, depending on the angle that the drop initially contacts the surface the contact angle values can vary and oscillate. If the first moment contact angle is very close to the equilibrium contact angle, variation of the contact angle over time is less than when the drop touches the surface with a very uncommon angle. In the first run of

Athabasca-05% CaCl2, first run of Athabasca-10% CaCl2, and second run of Cold Lake-

10% CaCl2 systems the initial contact angle is very low comparing to the equilibrium contact angle values. Therefore, in these cases more contact angle fluctuation during the experiment is observed.

• In most of the cases, the value of the contact angle increases as the drop ages. This phenomenon shows that the system characteristics change toward an oil-wet system. But it is obvious that the system tendency to be oil-wet is not very strong, because in all experiments the aqueous phase eventually remains the wetting phase. Therefore, the shift to an oil-wet system is not significant. The important thing is that change of the system to a less water-wet system happens in almost all of the cases and for both Athabasca and

Cold Lake bitumens. As mentioned in the results section, the quartz system was placed in the aqueous phase for 24 hours prior to the start of the experiments. This is because of the theory involves the oil formation in the reservoirs specially the sandstone reservoirs.

In this theory brine first contacted the sand and came into equilibrium with the surface.

That is why sand stone reservoirs mainly are water-wet. In visual experiments during this pre-experimental time the quartz-brine system came to equilibrium in sense of ion exchange and some surface properties. Then the bitumen drop was placed on the water- wet quartz surface and contacted the surface. Upon the initial contact, the surface and the

193 bitumen started to come in to equilibrium and adsorb each others’ ions. As the time passed, the surface showed a little less water-wet tendency that is directly related to the surface contact with bitumen.

• The correspondence between the concentration of CaCl2 solution and the equilibrium contact angle is not obvious. The equilibrium contact angle is generally in range of 20-40 degrees for Athabasca bitumen and 20-55 degrees for Cold Lake bitumen regardless of the concentration of CaCl2 solution.

• In most of the visual experiments the contact angle value stabilizes after 72 hours and becomes constant. If the initial contact angle is very different from the equilibrium value of it, the system fluctuates more and may not reach stability after the experimental time (120hr).

• In the tests with major fluctuations (such as first run of Athabasca bitumen-10%wt

CaCl2, no trend can be assigned to the graph at early times ( before 72 hours), while in the rest of them the value of contact angle slightly increases with time turning the system into a less water-wet system.

• In the contact angle graphs for bitumen-distilled water very smooth behaviour through time is observed. The contact angle values do not change significantly from the beginning to the end of each experiment for both bitumens. If the second run of

194

Athabasca bitumen-distilled water is excluded, the equilibrium contact angles are in range of 23-46 degrees.

• There are some fluctuations in the early contact angle values in bitumen-05% CaCl2 experiments. However, after 72 hours the series show very smooth behaviour. The equilibrium contact angles are in range of 20-76 degrees. This range is considerably wider than the bitumen-distilled water contact angle measurements.

7.2 Conclusions from the Micro CT Experiments:

• In the first part of the micro CT Experiments, investigations on temperature changes show that in general the system becomes more water-wet as the temperature increases.

Although these changes are neither very significant nor very smooth, but the trend of the curves shows this fact in all the cases. The quality of ion exchange between the two fluids and the solid surface changes as the temperature increases and can cause some changes in the wettability of the system. The water molecules and the calcium ions present in the brine can move easier at higher temperatures and therefore make more bonds with the surface. Since the brine used in these experiments is a very concentrated solution of CaCl2 (20%wt) they overcome the bitumen on the surface and displace the bitumen to some extent.

• In most of the cases in the first part of micro CT experiments, when the pressure goes up, the quartz surface shows more water-wet characteristics comparing to the lower

195 pressures. The results at 1000psi show the wettability changes to more water-wet more clearly.

• From the results of all four cases of the first part of the micro CT experiments, it is evident that the order of substance exposure affects the wettability characteristics of the system. When the surface is exposed to the brine first, it shows a water-wet property and on the other side, when the surface is exposed to the bitumen first, it shows more oil-wet tendency. That is because the surface of the solid can absorb the minerals in water and the polar molecules in oil and change the wettability of the surface.

• In the first part of the micro CT experiments, as the brine drop becomes smaller, it spreads more easily over the quartz surface and therefore, there is a smaller contact angle for the quartz-brine drop-bitumen system. Therefore, the system appears more water-wet when the brine drop size decreases.

• Comparison between the results of interfacial tension in the second part of micro CT experiments shows that the interfacial tension of the bitumen-brine system under study decreases as the temperature increases at each experimental pressure. Since the mobility of the fluid molecules increases at higher temperatures, they can mix better and therefore the IFT between them becomes smaller.

196

• In the second part of the micro CT experiments the results show that generally the interfacial tension is increasing as the pressure of the system increases. The fluids are mixing more at lower pressures and it is harder to mix them at higher pressures.

• The interfacial tension curves for the second part of the micro CT experiments show a smoother trend at lower pressures. At ambient pressure, the IFT range is less than

2mN/m, but as the pressure increases the range of IFT changes are larger so that at

6.895MPa (1000psi) the range is almost as large as 7mN/m.

• In the second part of micro CT experiments the contact angle of the bitumen-brine interface with the solid surface increases as the temperature increases. At lower temperatures the system is more water-wet and the wettability of the system is changing toward neutral wettability as the temperature increases. In these experiments comparing to the first part of micro CT experiments, the CaCl2 has lower concentration (10%wt) and the bonds between the ions cannot be as strong as the first part of micro CT experiments.

The bitumen in these experiments does not have any doping (1-Iodododecane). The doping was a very large paraffinic molecule. Therefore, now it is easier for bitumen to establish more bonds with the surface at higher temperatures than before.

• In the second part of the micro CT experiments, it is found that the contact angle of the bitumen-brine interface with the quartz surface normally increases as the pressure increases. At higher pressures (3.447MPa (500psi) and higher), higher contact angle values are reported compared to ambient pressure and 1.724MPa (250psi) experiments.

197

This increase in the contact angle values is to the extent that the wettability of the system changes totally from water-wet to neutral wettability. As the pressure increases the contact between the particles of each phase increases, as well. Therefore, bitumen has more chance to contact the solid and change it to oil-wet.

• The contact angle curves show a smoother trend at higher temperatures at each level of experimental pressure for the second part of the micro CT experiments. Also, the contact angle curves are smoother at higher pressures.

• Comparison between the first and second parts of the micro CT experiments shows great dissimilarities in the behaviour of the contact angle and IFT against temperature and pressure. These differences can be the consequent of changes in CaCl2 concentration and doping in the bitumen.

7.3 Overall Conclusions

• The ADSA technique is suitable for visual experiments because of the excellent contrast between the fluids, but in micro-CT can have large errors due to medium to low contrast between the two fluids and the fuzziness of the image.

• Density of distilled water and the brine has a linear relation with temperature following the equation of state rules. In case of bitumen because there are many components in a large range of molecular weights and volatilities, it is not precise to predict the density change with temperature similar to pure components and solutions.

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There are some empirical equations that are appropriate for measuring and predicting the density of different types of oil at various temperatures. However, they do not fit well in to the measured density data for both Athabasca and Cold Lake bitumen and result in a large coefficient of determination value.

• Contact angle values in all experiments are very different from case to case. The reason behind this observation is that the contact angles measured in all of the experiments are static contact angles and therefore they can vary significantly in each case depending on the initial contact angle. This phenomenon is called contact angle hysteresis. Moreover, bitumen is an extremely adhesive type of oil because of the presence of asphaltene in it. The asphaltene glues to the surface and can alter the contact angle value from its real value.

• Comparing the first and the second series of micro CT measurements, the differences in the trend of contact angle against temperature and pressure can be the consequence of doping in the first part and also difference in concentration of CaCl2 in the brine.

• Use of X-ray tomography makes it possible to measure the interfacial properties of opaque systems using the drop shape methods. Therefore, the drop shape techniques can be used widely for different systems and for study of steam or brine drops inside the oil phase.

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7.4 Recommendation for Future Work

• The Canny edge algorithm is adaptable to various environments. Its parameters allow it to be tailored to recognition of edges of different characteristics depending on the particular requirements of a given implementation. Canny edge detector is suitable for any kind of edge in any direction (horizontal, vertical and diagonal) due to its three optimal criteria for performance evaluation of good detection, strong localization, and single response to an edge. If the image is very noisy the Canny edge may encounter some problems in detecting the only and the right edge. This happens in the micro CT experimental images. Therefore, further work is needed on the image processing of these images.

• Clearer images should be produced from the micro CT-scanner so the Canny edge detector can be easily applied for the images. Therefore, further investigation on the micro CT-scanner settings, doping, use of brine, the cell material, and the type of insulation can be done.

• More micro CT experiments for Athabasca bitumen-10%wt CalCl2 solution should be run at least two more times for comparison of the contact angle and IFT of the system at different temperatures and pressures.

• It is recommended to attempt in reducing the concentration of the CalCl2 in the brine to achieve more realistic answers. The application of the regular CT-scanner can detect the interfaces with less density difference comparing to the micro CT-scanner.

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• The Cold Lake bitumen was used only in the visual experiments. At least three sets of micro CT experiments at elevated temperatures and pressures can be run for this oil and the results can be analyzed and compared.

• In this work, a regular scale CT-scanner pressure cell have been designed and constructed. No contact angle and interfacial tension experiments were fulfilled using this equipment. Therefore, at least three sets of CT experiments can be run for each available type of oil.

• In order to find the reservoir characteristics in thermal recovery techniques, it is recommended that the micro model and the regular CT model be employed for obtaining the contact angle and IFT values of the bitumen-steam-quartz systems. Because of significant difference in bitumen and steam densities, clear images can be generated without adding any doping.

• The contact angle measurement for a static drop sometimes does not lead to a unique result because of different parameters such as surface roughness, surface heterogeneity, adhesion, and many more that can cause contact angle hysteresis. Therefore, it is suitable to study both advancing and receding contact angles in dynamic conditions. The CT scanner model is designed so that it can fulfill the dynamic contact angle measurements.

The dividing head can rotate the whole system ad tilt the quartz plate till the drop slides

201 down the surface. At this moment the front and hind angles of contact will be considered at advancing and receding contact angles of the system, respectively.

202

References

Acosta, E. J., R. Gitiafroz, Y. Y. Zuo, Z. Policova, P. N. Cox, M. L. Hair and A. W.

Neumann (2007). "Effect of humidity on lung surfactant films subjected to

dynamic compression/expansion cycles." Respiratory Physiology & Neurobiology

155(3): 255-267.

Adamson, A. W. and A. P. Gast (1997). Physical Chemistry of Surfaces Sixth, John

Wiley & Sons, Inc.

Aguilar-Mendoza, J. A., J. I. Rosales-Leal, M. A. Rodríguez-Valverde, S. González-

López and M. A. Cabrerizo-Vílchez (2008). "Wettability and bonding of self-

etching dental adhesives: Influence of the smear layer." Dental Materials 24(7):

994-1000.

Alvarez, J. M., A. Amirfazli and A. W. Neumann (1999). "Automation of the

axisymmetric drop shape analysis-diameter for contact angle measurements."

Colloids and Surfaces A: Physicochemical and Engineering Aspects 156(1-3):

163-176.

Amirfazli, A., J. Graham-Eagle, S. Pennell and A. W. Neumann (2000). "Implementation

and examination of a new drop shape analysis algorithm to measure contact angle

and surface tension from the diameters of two sessile drops." Colloids and

Surfaces A: Physicochemical and Engineering Aspects 161(1): 63-74.

Anderson, W. G. (1986a). "Wettability Literature Survey- Part 1: Rock/ Oil/ Brine

Interactions and the Effects of Core Handling on Wettability." Journal of

Petroleum Technology 38(11): 1125-1144.

203

Anderson, W. G. (1986b). "Wettability Literature Survey- Part 2: Wettability

Measurement." Journal of Petroleum Technology 38(12): 1246-1262.

Askeland, D. R. and P. P. Phule (2006). The Science and Engineering of Materials, Fifth,

Thomson.

Askvik, K. M., S. Høiland, P. Fotland, T. Barth, T. Grønn and F. H. Fadnes (2005).

"Calculation of wetting angles in crude oil/water/quartz systems." Journal of

Colloid and Interface Science 287(2): 657-663.

ASM, Ed. (1990). Metals Handbook. Vol. 2, Tenth. Cleveland, ASM International.

ASTM, Ed. (2007a). Annual Book of ASTM Standard. Vol. 02.04, ASTM International.

ASTM, Ed. (2007b). Annual Book of ASTM Standard. Vol. 02.02 Aluminum and

Magnesium Alloys, ASTM International.

ASTM, Ed. (2009). Annual Book of ASTM Standard. Vol. 01.01 Steel-Piping, Tubing,

Fittings, ASTM International.

Bashforth, F. and J. C. Adams (1892). An Attempt to Test the teory of Capillary Action,

Cambridge, Cambridge University Press and Deighton Bell.

Bateni, A., A. Ababneh, J. A. W. Elliott, A. W. Neumann and A. Amirfazli (2005).

"Effect of gravity and electric field on shape and surface tension of drops."

Advances in Space Research 36(1): 64-69.

Bateni, A., A. Amirfazli and A. W. Neumann (2006). "Effects of an electric field on the

surface tension of conducting drops." Colloids and Surfaces A: Physicochemical

and Engineering Aspects 289(1-3): 25-38.

204

Bateni, A., S. S. Susnar, A. Amirfazli and A. W. Neumann (2003). "A high-accuracy

polynomial fitting approach to determine contact angles." Colloids and Surfaces

A: Physicochemical and Engineering Aspects 219(1-3): 215-231.

Beer, F. P., J. E. Russell Johnson and J. T. DeWolf (2006). Mechanics of Materials,

Fourth, New York, McGraw-Hill.

Bikerman, J. J. (1958). Surface Chemistry, Theory and Applications, Second, Academic

Press Inc.

Budinski, K. G. (1996). Engineering Materials: properties and Selection, Fifth, Prentice

Hall.

Butt, H.-J., K. Graf and M. Kappl (2006). Physics and Chemistry of Interfaces Second,

Wiley –VCH.

Cabezas, M. G., A. Bateni, J. M. Montanero and A. W. Neumann (2004). "A new drop-

shape methodology for surface tension measurement." Applied Surface Science

238(1-4): 480-484.

Cabezas, M. G., A. Bateni, J. M. Montanero and A. W. Neumann (2005). "A new method

of image processing in the analysis of axisymmetric drop shapes." Colloids and

Surfaces A: Physicochemical and Engineering Aspects 255(1-3): 193-200.

CAPP. (2009). from

http://www.capp.ca/energySupply/Pages/default.aspx#VimtTumpw8iG.

Cash, L., J. L. Cayias, G. Fournier, D. Macallister, T. Schares, R. S. Schechter and W. H.

Wade (1977). "The application of low interfacial tension scaling rules to binary

hydrocarbon mixtures." Journal of Colloid And Interface Science 59(1): 39-44.

205

Cayias, J. L., R. S. Schechter and W. H. Wade (1975). The Measurement of Low

Interfacial Tension via the Spinning Drop Technique in Adsorption at Interfaces.

ACS Symposium Series 8, Washington, D.C. , American Chemical Society.

Cheng, P., D. Li, L. Boruvka, Y. Rotenberg and A. W. Neumann (1990). "Automation of

axisymmetric drop shape analysis for measurements of interfacial tensions and

contact angles." Colloids and Surfaces 43(2): 151-167.

Clarkson, M. T. (1984). "Measurements on the liquid rise in glass capillaries at

microemulsion/oil/brine interfaces." Journal of Colloid and Interface Science

102(2): 563-566.

Currie, P. K. and J. Van Nieuwkoop (1982). "Buoyancy effects in the spinning-drop

interfacial tensiometer." Journal of Colloid And Interface Science 87(2): 301-316.

Dandekar, A. Y. (2006). Petroleum Reservoir Rock and Fluid Properties, CRC Press. del Río, O. I., D. Y. Kwok, R. Wu, J. M. Alvarez and A. W. Neumann (1998). "Contact

angle measurements by axisymmetric drop shape analysis and an automated

polynomial fit program." Colloids and Surfaces A: Physicochemical and

Engineering Aspects 143(2-3): 197-210.

Dingle, N. M. (2005). A finite element based algorithm for determining interfacial

tension and contact angle from pendant and sessile drop profiles. United States --

Indiana, Purdue University.

Dobrzynski, L. (1978). Handbook of Surfaces and Interfaces. 1, Garland STPM Press.

Drelich, J. and J. D. Miller (1992). Surface/Interfacial Tension of the Whiterocks

Bitumen and Its Relationship to Tar Sand Processing. Eastern Oil Shale

Symposium.

206

Drelich, J. and J. D. Miller (1994). "Surface and Interfacial Tension of the Whiterocks

Bitumen and Its Relationship to Bitumen Release from Tar Sand During Hot

Water Processing." Fuel 73(9): 1504-1510. du Nouy, P. L. (1919). "A new apparatus for measuring surface tension." Journal of

General Physiology 1(5): 521-524.

Duncan-Hewitt, W. C., Z. Policova, P. Cheng, E. I. Vargha-Butler and A. W. Neumann

(1989). "Semiautomatic measurement of contact angles on cell layers by a

modified axisymmetric drop shape analysis." Colloids and Surfaces 42(2): 391-

403.

Edwards, P. R. (1925). "The surface tensions of aqueous solutions of various organic

compounds." Journal of the Chemical Society 127: 744-747.

Erbil, H. Y. (2006). Surface Chemistry of Solid and Liquid Interfaces, Wiley-Blackwell.

ERCB. (2009). from http://www.ercb.ca/portal/server.pt?

Fordham, S. (1948). "On the Calculation of Surface Tension from Measurements of

Pendant Drops." Proceesings of Royal Society London A 194.

Gaines, G. L. (1977). "On the use of filter paper wilhelmy plates with insoluble

monolayers." Journal of Colloid And Interface Science 62(1): 191-192.

Gere, J. M. (2004). Mechanics of Materials, Sixth Thomson Brooks/Cole.

Government-of-Alberta. (2009). from http://www.oilsands.alberta.ca/.

Green, R. E. and C. J. McCauley, Eds. (1996). Machinery's Handbook. Twenty Fifth.

New York, Industrial Press.

Grundke, K., C. Werner, K. Pöschel and H. J. Jacobasch (1999). "Characterization of

adsorbed protein layers by low-rate dynamic liquid-fluid contact angle

207

measurements using axisymmetric drop shape analysis (part II)." Colloids and

Surfaces A: Physicochemical and Engineering Aspects 156(1-3): 19-31.

Gu, Y. (2001). "Drop size dependence of contact angles of oil drops on a solid surface in

water." Colloids and Surfaces A: Physicochemical and Engineering Aspects

181(1-3): 215-224.

Gu, Y. and D. Li (1998). "Measurements of Contact Angles between an Oil-Water

Interface and a Fiber by the ACDPAC Technique." Journal of Colloid and

Interface Science 206(1): 288-296.

Gu, Y., D. Li and P. Cheng (1997). "A novel contact angle measurement technique by

analysis of capillary rise profile around a cylinder (ACRPAC)." Colloids and

Surfaces A: Physicochemical and Engineering Aspects 122(1-3): 135-149.

Harkins, W. D. and F. E. Brown (1919). "The determination of surface tension (free

surface energy), and the weight of falling drops - The surface tension of water and

benzene by the capillary height method." Journal of the American Chemical

Society 41: 499-524.

Harkins, W. D. and H. F. Jordan (1930). "A method for the determination of surface and

interfacial tension from the maximum pull on a ring." Journal of the American

Chemical Society 52: 1751-1772.

Hartland, S. and R. W. Hartley (1976). Axisymmetric Fluid-Liquid Interfaces,

Amesterdam, Elsevier.

Hassan, M. E., R. F. Nielsen and J. C. Calhoun (1953). "Effect of Pressure and

Temperature on Oil-Water Interfacial Tensions for a Series of Hysdrocarbon."

Society of Petroleum Engineers 198: 299-306.

208

Hayes, R. A., A. C. Robinson and J. Ralston (1994). "A WILHELMY TECHNIQUE

FOR THE RAPID ASSESSMENT OF SOLID WETTING DYNAMICS."

Langmuir 10(8): 2850-2852.

Hepler, L. G. and C. Hsi, Eds. (1989). AOSTRA. Edmonton, AOSTRA.

Hibbeler, R. C. (2008). Mechanics of Materials, Seventh, Upper Saddle River, Pearson

Prentice Hall.

Holgado-Terriza, J. A., J. F. Gómez-Lopera, P. L. Luque-Escamilla, C. Atae-Allah and

M. A. Cabrerizo-Vílchez (1999). "Measurement of ultralow interfacial tension

with ADSA using an entropic edge-detector." Colloids and Surfaces A:

Physicochemical and Engineering Aspects 156(1-3): 579-586.

Hoorfar, M. and A. W. Neumann (2006). "Recent progress in Axisymmetric Drop Shape

Analysis (ADSA)." Advances in Colloid and Interface Science 121(1-3): 25-49.

Hosford, W. F. (2005). Mechanical behavior of Materials, Cambridge University Press.

Hough, E. W., M. J. Rzasa and B. B. Wood (1951). "Interfacial Tensions at Reservoir

Pressure and Temperatures; Apparatus and the Water-Methane System." Society

of Petroleum Engineers 192: 57-60.

Huh, C. and S. G. Mason (1975). "RIGOROUS THEORY OF RING TENSIOMETRY."

Colloid and Polymer Science 253(7): 566-580.

Huijgen, R. J. M. and J. Hagoort (1996). "Interfacial Tension of Nitrogen/Volatile Oil

Systems." Society of Petroleum Engineers Journal: 125-132.

Iliev, S. and N. Pesheva (2006). "Nonaxisymmetric drop shape analysis and its

application for determination of the local contact angles." Journal of Colloid and

Interface Science 301(2): 677-684.

209

Israelachvili, J. N. (1985). Intermolecular and Surface Forces: with Applications to

Colloidal and Biological Systems, Academic Press.

Jaycock, M. J. and G. D. Parfitt (1981). Chemistry of Interfaces, Prentice Hall Europe.

Jennings, H. Y. (1975). "A Study of Caustic Solution-Crude Oil Interfacial Tension."

Society of Petroleum Engineers Journal: 197-202.

Jennings, H. Y. and G. H. Newman (1971). "The Effect of Temperature and Pressure on

the Interfacial Tension of Water Against Methane-Normal Decane Mixtures."

Society of Petroleum Engineers Journal 251: 171-175.

Jones, G. and W. A. Ray (1937). "The surface tension of solutions of electrolytes as a

function of the concentration I A differential method for measuring relative

surface tension." Journal of the American Chemical Society 59: 187-198.

Kalantarian, A., H. Ninomiya, S. M. I. Saad, R. David, R. Winklbauer and A. W.

Neumann (2009). "Axisymmetric Drop Shape Analysis for Estimating the Surface

Tension of Cell Aggregates by Centrifugation." Biophysical Journal 96(4): 1606-

1616.

Kantzas, A. (1990). "Investigation of Physical Properties of Porous Rocks and Fluid Flow

Phenomena in Porous Media Using Computer Assisted Tomography " In Situ

14(1): 56.

Kutz, M., Ed. (2006). Mechanical Engineers' Handbook: Materials and Mechanical

Design. Hoboken, John Wiley & Sons.

Kwok, D. Y., C. J. Budziak and A. W. Neumann (1995). "Measurements of Static and

Low Rate Dynamic Contact Angles by Means of an Automated Capillary Rise

Technique." Journal of Colloid and Interface Science 173(1): 143-150.

210

Kwok, D. Y., A. Leung, C. N. C. Lam, A. Li, R. Wu and A. W. Neumann (1998). "Low-

Rate Dynamic Contact Angles on Poly(methyl methacrylate) and the

Determination of Solid Surface Tensions." Journal of Colloid and Interface

Science 206(1): 44-51.

Lago, M. and M. Araujo (2001). "Capillary Rise in Porous Media." Journal of Colloid

and Interface Science 234(1): 35-43.

Lam, C. N. C., N. Kim, D. Hui, D. Y. Kwok, M. L. Hair and A. W. Neumann (2001a).

"The effect of liquid properties to contact angle hysteresis." Colloids and Surfaces

A: Physicochemical and Engineering Aspects 189(1-3): 265-278.

Lam, C. N. C., R. H. Y. Ko, L. M. Y. Yu, A. Ng, D. Li, M. L. Hair and A. W. Neumann

(2001b). "Dynamic Cycling Contact Angle Measurements: Study of Advancing

and Receding Contact Angles." Journal of Colloid and Interface Science 243(1):

208-218.

Lam, C. N. C., R. Wu, D. Li, M. L. Hair and A. W. Neumann (2002). "Study of the

advancing and receding contact angles: liquid sorption as a cause of contact angle

hysteresis." Advances in Colloid and Interface Science 96(1-3): 169-191.

Lane, J. E. (1973). "CORRECTION TERMS FOR CALCULATING SURFACE-

TENSION FROM CAPILLARY RISE." Journal of Colloid And Interface Science

42(1): 145-149.

Laplace, P. S. d. (1806). Mechanique Celeste.

Li, D., P. Cheng and A. W. Neumann (1992). "Contact angle measurement by

axisymmetric drop shape analysis (ADSA)." Advances in Colloid and Interface

Science 39: 347-382.

211

Li, D. and A. W. Neumann (1990). "Determination of line tension from the drop size

dependence of contact angles." Colloids and Surfaces 43(2): 195-206.

Li, J., R. Miller and H. Möhwald (1996). "Phospholipid monolayers and their dynamic

interfacial behaviour studied by axisymmetric drop shape analysis." Thin Solid

Films 284-285: 357-360.

Lin, F. Y. H., Z. Policova, H. K. Yueh, E. Moy and A. W. Neumann (1993). "Application

of freezing front technique and axisymmetric drop shape analysis-profile for the

determination of surface tensions of adsorbed protein layers." Colloids and

Surfaces B: Biointerfaces 1(1): 23-32.

Liu, D. and D. L. Tomasko (2007). "Carbon dioxide sorption and dilation of poly(lactide-

co-glycolide)." The Journal of Supercritical Fluids 39(3): 416-425.

Lockington, D. A. and J. Y. Parlange (2004). "A new equation for macroscopic

description of capillary rise in porous media." Journal of Colloid and Interface

Science 278(2): 404-409.

Lu, J. J., W. W. Y. Cheung, L. M. Y. Yu, Z. Policova, D. Li, M. L. Hair and A. W.

Neumann (2002). "The effect of dextran to restore the activity of pulmonary

surfactant inhibited by albumin." Respiratory Physiology & Neurobiology 130(2):

169-179.

Mak, C., E. Cornu, C. Moresoli and P. Chen (2004). "Surface tension, diffusion and

kinetics studies of an air-stripping process." Separation and Purification

Technology 36(2): 95-106.

212

Malcolm, J. D. and H. M. Paynter (1981). "Simultaneous determination of contact angle

and interfacial tension from sessile drop measurements." Journal of Colloid And

Interface Science 82(2).

Mannhardt, K., A. Kantzas and F. Hum (Fall 2005). Laboratory Exercises ENPE 513:

Flow in Porous Media. Calgary, University of Calgary.

Marmur, A. (1989). "Capillary rise and hysteresis in periodic porous media." Journal of

Colloid and Interface Science 129(1): 278-285.

Marmur, A. and R. D. Cohen (1997). "Characterization of Porous Media by the Kinetics

of Liquid Penetration: The Vertical Capillaries Model." Journal of Colloid and

Interface Science 189(2): 299-304.

Matijevic, E., Ed. (1969a). Surface and Colloid Science. Vol. 2, Wiley-Interscience.

Matijevic, E., Ed. (1969b). Surface and Colloid Science. Vol. 1, Wiley-Interscience.

Maze, C. and G. Burnet (1969). "A non-linear regression method for calculating surface

tension and contact angle from the shape of a sessile drop." Surface Science

13(2).

Maze, C. and G. Burnet (1971). "Modifications of a non-linear regression technique used

to calculate surface tension from sessile drops " Surface Science 24(1).

Mees, F., R. Swennen, M. V. Geet and P. Jacobs (2003). "Application of X-Ray

Computed Tomography in the Geoscience." Geological Society 215: 6.

Mikhaylova, Y., V. Dutschk, M. Müller, K. Grundke, K. J. Eichhorn and B. Voit (2007).

"Study of the solid-liquid interface of hydroxyl-terminated hyperbranched

aromatic polyesters (HBP-OH) in aqueous media: II. Adsorption of model

213

proteins." Colloids and Surfaces A: Physicochemical and Engineering Aspects

297(1-3): 19-29.

Moriya, S., K. Adachi and T. Kotaka (1986). "DEFORMATION OF DROPLETS

SUSPENDED IN VISCOUS MEDIA IN AN ELECTRIC-FIELD .1. RATE OF

DEFORMATION." Langmuir 2(2): 155-160.

Moy, E., P. Cheng, Z. Policova, S. Treppo, D. Kwok, D. P. Mack, P. M. Sherman and A.

W. Neuman (1991). "Measurement of contact angles from the maximum diameter

of non-wetting drops by means of a modified axisymmetric drop shape analysis."

Colloids and Surfaces 58(3): 215-227.

Mumley, T. E., C. J. Radke and M. C. Williams (1986a). "Kinetics of liquid/liquid

capillary rise : I. Experimental observations." Journal of Colloid and Interface

Science 109(2): 398-412.

Mumley, T. E., C. J. Radke and M. C. Williams (1986b). "Kinetics of liquid/liquid

capillary rise : II. Development and test of theory." Journal of Colloid and

Interface Science 109(2): 413-425.

Nobakht, M., S. Moghadam and Y. Gu (2008). "Mutual interactions between crude oil

and CO2 under different pressures." Fluid Phase Equilibria 265(1-2): 94-103.

Padday, J. F., Ed. (1969). Surface and Colloid Science. Vol. 1. New York, John Wiley

and Sons.

Padday, J. F. and A. Pitt (1972). "AXISYMMETRIC MENISCUS PROFILES." Journal

of Colloid And Interface Science 38(2): 323-&.

Peacock, G. and J. Murray, Eds. (1855). Miscellaneous Works of Thomas Young. Vol. 1.

London.

214

Princen, H. M. (1970). "Advantages and limitations of the grooved Wilhelmy plate."

Australian Journal of Chemistry 23(9): 1789-1799.

Princen, H. M., I. Y. Z. Zia and S. G. Mason (1967a). "MEASUREMENT OF

INTERFACIAL TENSION FROM SHAPE-OF A ROTATING DROP." Journal

of Colloid And Interface Science 23(1): 99-&.

Princen, H. M., I. Y. Z. Zia and S. G. Mason (1967b). "Measurement of Interfacial

Tension from the Shape of a Rotating Drop " Journal of Colloid and Interface

Science 23: 99-107.

Prokhorov, V. A. (1996). "Refinement of Rayleigh's equation for calculation of surface

tension of a liquid from its capillary rise height." Colloids and Surfaces A:

Physicochemical and Engineering Aspects 116(3): 309-316.

Prokop, R. M., A. Jyoti, M. Eslamian, A. Garg, M. Mihaila, O. I. del Río, S. S. Susnar, Z.

Policova and A. W. Neumann (1998). "A study of captive bubbles with

axisymmetric drop shape analysis." Colloids and Surfaces A: Physicochemical

and Engineering Aspects 131(1-3): 231-247.

Ramakrishnan, S. and S. Hartland (1981). "Effect of contact angle on capillary rise

annular meniscus." Journal of Colloid and Interface Science 80: 497.

Ramon, G. and A. Oron (2008). "Capillary rise of a meniscus with phase change."

Journal of Colloid and Interface Science 327(1): 145-151.

Rao, D. N. (1996). "Wettability Effects in Thermal Recovery Operations." Society of

Petroleum Engineers: 623-639.

Rao, D. N. (1999). "Wettability Effects in Thermal Recovery Operations." SPE Reservoir

Evaluation and Engineering 2(5): 420-430.

215

Rao, D. N. (2002). "Measurement of Dynamic Contact angles in Solid-Liquid-Liquid

Systems at Elevated Pressures and Temperatures." Colloids and Surfaces A 206:

203-216.

Rao, D. N. and M. G. Girard (1996). "A new Technique for Reservoir Wettability

Characterization." Journal of Canadian Petroleum Technology 35(1): 31-39.

Rao, D. N. and J. I. Lee (2002). "Application of the new vanishing interfacial tension

technique to evaluate miscibility conditions for the Terra Nova Offshore Project."

Journal of Petroleum Science and Engineering 35(3-4): 247-262.

Rao, D. N. and J. I. Lee (2003). "Determination of gas-oil miscibility conditions by

interfacial tension measurements." Journal of Colloid and Interface Science

262(2): 474-482.

Rayleigh, L. (1916). "On theory of the capillary tube." Proceedings of the Royal Society

of London Series a-Containing Papers of a Mathematical and Physical Character

92(637): 184-195.

Regismond, S. T. A., Z. Policova, A. W. Neumann, E. D. Goddard and F. M. Winnik

(1999). "Static and dynamic surface tension of dilute polyelectrolyte solutions."

Colloids and Surfaces A: Physicochemical and Engineering Aspects 156(1-3):

157-162.

Richards, T. W. and E. K. Carver (1921). "A critical study of the capillary rise method of

determining surface tension, with data for water, benzene, toluene, chloroform,

carbon tetrachloride, ether and dimethyl aniline. [Second paper.]." Journal of the

American Chemical Society 43: 827-847.

216

Río, O. I. d. and A. W. Neumann (1997). "Axisymmetric Drop Shape Analysis:

Computational Methods for the Measurement of Interfacial Properties from the

Shape and Dimensions of Pendant and Sessile Drops." Journal of Colloid and

Interface Science 196(2): 136-147.

Rodríguez-Valverde, M. A., M. A. Cabrerizo-Vílchez, P. Rosales-López, A. Páez-Dueñas

and R. Hidalgo-Álvarez (2002). "Contact angle measurements on two (wood and

stone) non-ideal surfaces." Colloids and Surfaces A: Physicochemical and

Engineering Aspects 206(1-3): 485-495.

Rotenberg, Y., L. Boruvka and A. W. Neumann (1982). "Determination of Surface

Tension and Contact Angle from the Shapes of Axisymmetric Fluid Interfaces."

Journal of Colloid And Interface Science 93(1): 15.

Schembre, J. M. (2004). Temperature, surface forces, wettability and their relationship to

relative permeability of porous media. United States -- California, Stanford

University.

Serrano-Saldaña, E., A. Domínguez-Ortiz, H. Pérez-Aguilar, I. Kornhauser-Strauss and

F. Rojas-González (2004). "Wettability of solid/brine/n-dodecane systems:

experimental study of the effects of ionic strength and surfactant concentration."

Colloids and Surfaces A: Physicochemical and Engineering Aspects 241(1-3):

343-349.

Shinoda, K. and Y. Shibata (1986). "Principles for the attainment of minimum oil--water

interfacial tension by surfactants: The characteristics of organized surfactant

phase." Colloids and Surfaces 19(2-3): 185-196.

217

Skinner, F. K., Y. Rotenberg and A. W. Neumann (1989). "Contact angle measurements

from the contact diameter of sessile drops by means of a modified axisymmetric

drop shape analysis." Journal of Colloid and Interface Science 130(1): 25-34.

Smith, W. F. (1990). Principles of Materials Science and Engineering, Second, McGraw-

Hill.

Spelt, J. K., Y. Rotenberg, D. R. Absolom and A. W. Neumann (1987). "Sessile-drop

contact angle measurements using axisymmetric drop shape analysis." Colloids

and Surfaces 24(2-3): 127-137.

Stegemeier, G. L., B. F. Pennington, E. B. Brauer and E. W. Hough (1962). "Interfacial

Tension of the Methane-Normal Decane System." Society of Petroleum Engineers

Journal: 257-260.

Sugden, S. (1921). "The determination of surface tension from the rise in capillary

tubes." Journal of the Chemical Society 119: 1483-1492.

Sugden, S. (1922). "The determination of surface tension from the maximum pressure in

bubbles." Journal of the Chemical Society 121: 858-866.

Sugden, S. (1924). "The determination of surface tension from the maximum pressure in

bubbles Part II." Journal of the Chemical Society 125: 27-31.

Susnar, S. S., P. Chen, O. I. del Rio and A. W. Neumann (1996). "Surface tension

response to area changes using axisymmetric drop shape analysis." Colloids and

Surfaces A: Physicochemical and Engineering Aspects 116(1-2): 181-194.

Vijapurapu, C. S. and D. N. Rao (2004). "Compositional effects of fluids on spreading,

adhesion and wettability in porous media." Colloids and Surfaces A:

Physicochemical and Engineering Aspects 241(1-3): 335-342.

218

Vinegar, H. J. and S. L. Wellington (1987). "Tomographic Imaging of Three-Phase Flow

Experiments." Rev. Sci. Instrum. 58(1): 12.

Voigt, A., O. Thiel, D. Williams, Z. Policova, W. Zingg and A. W. Neumann (1991).

"Axisymmetric drop shape analysis (ADSA) applied to protein solutions."

Colloids and Surfaces 58(3): 315-326.

Vonnegut, B. (1942). "Rotating Bubble Method for the Determination of Surface and

Interfacial Tensions." Review of Scientific Instruments 13(6-9).

Vrânceanu, M., K. Winkler, H. Nirschl and G. Leneweit (2007). "Surface rheology of

monolayers of phospholipids and cholesterol measured with axisymmetric drop

shape analysis." Colloids and Surfaces A: Physicochemical and Engineering

Aspects 311(1-3): 140-153.

Wang, W. and A. Gupta (1995). "Investigation of the Effect of Temperature and Pressure

on Wettability Using Modified Pendant Drop Method " SPE Journal: 10.

Warren, H. G. and R. V. Bills (1973). "Interfacial Tension of Normal Heptane." Journal

of Petroleum Technology: 543-544.

Warren, H. G. and E. W. Hough (1972). "Interfacial Tension of the Ethylene-Normal

Heptane System." Society of Petroleum Engineers.

Wege, H. A., J. A. Holgado-Terriza, A. W. Neumann and M. A. Cabrerizo-Vílchez

(1999). "Axisymmetric drop shape analysis as penetration film balance applied at

liquid-liquid interfaces." Colloids and Surfaces A: Physicochemical and

Engineering Aspects 156(1-3): 509-517.

Wege, H. A., J. A. Holgado-Terriza, J. I. Rosales-Leal, R. Osorio, M. Toledano and M.

Á. Cabrerizo-Vílchez (2002). "Contact angle hysteresis on dentin surfaces

219

measured with ADSA on drops and bubbles." Colloids and Surfaces A:

Physicochemical and Engineering Aspects 206(1-3): 469-483.

Wellington, S. L. and H. J. Vinegar (1987). "X-Ray Computerized Tomography." Journal

of Petroleum Technology: 14.

Welzel, P. B., C. Rauwolf, O. Yudin and K. Grundke (2002). "Influence of Aqueous

Electrolytes on the Wetting Behavior of Hydrophobic Solid Polymers--Low-Rate

Dynamic Liquid/Fluid Contact Angle Measurements Using Axisymmetric Drop

Shape Analysis." Journal of Colloid and Interface Science 251(1): 101-108.

Wilhelmy, L. (1863). "Ueber die Abhängigkeit der Capillaritäts-Constanten des Alkohols

von Substanz und Gestalt des benetzten festen Körpers." Annalen der Physik und

Chemie 195(6): 177-217.

William D. Callister, J. (2000). Materials Science and Engineering: An Introduction,

Fifth, John Wiley & Sons.

Wulf, M., S. Michel, K. Grundke, O. I. del Rio, D. Y. Kwok and A. W. Neumann (1999).

"Simultaneous Determination of Surface Tension and Density of Polymer Melts

Using Axisymmetric Drop Shape Analysis." Journal of Colloid and Interface

Science 210(1): 172-181.

Xu, W., S. C. Ayirala and D. N. Rao (2005). "Measurement of Surfactant-Induced

Interfacial Interactions at Reservoir conditions." Society of Petroleum Engineers.

Yamazaki, T., H. Okabe, Y. Akita and K. Aso (2000). "Automatic Continuous-Measuring

System of Interfacial Tension by Spinning Drop Technique." Society of

Petroleum Engineers.

220

Yang, C. and Y. Gu (2003). "A New Method for Measuring Solvent Diffusivity in Heavy

Oil by Dynamic Pendent Drop Shape Analysis (DPDSA)." Society of Petroleum

Engineers.

Yang, D. and Y. Gu (2006). "A New Experimental Technique for Studying Gas Mass

Transfer in the Crude Oil by Analysis of the Measured Dynamic and Equilibrium

Interfacial Tensions." Society of Petroleum Engineers.

Zschoche, S., R. David, H. Tavana, K. Pöschel, N. Petong, V. Dutschk, K. Grundke and

A. W. Neumann (2007). "Robustness of wetting and morphology of maleimide

copolymer films to choice of solvent and annealing." Colloids and Surfaces A:

Physicochemical and Engineering Aspects 307(1-3): 53-61.

Zuo, Y.-X. and E. H. Stenby (1998). "Prediction of Interfacial Tensions of Reservoir

Crude Oil and Gas Condensate Systems." SPE Journal: 12.

Zuo, Y. Y., M. Ding, A. Bateni, M. Hoorfar and A. W. Neumann (2004a). "Improvement

of interfacial tension measurement using a captive bubble in conjunction with

axisymmetric drop shape analysis (ADSA)." Colloids and Surfaces A:

Physicochemical and Engineering Aspects 250(1-3): 233-246.

Zuo, Y. Y., M. Ding, D. Li and A. W. Neumann (2004b). "Further development of

Axisymmetric Drop Shape Analysis-Captive Bubble for pulmonary surfactant

related studies." Biochimica et Biophysica Acta (BBA) - General Subjects

1675(1-3): 12-20.

221

APPENDIX A: THERMODYNAMICS OF SURFACES AND INTERFACES

As mentioned in the literature review section, the Gibbs model introduces an imaginary mathematical interface without any physical volume. This model is acceptable and applies because in reality the interface volume is insignificant in comparison to the bulk phases on each side.

In order to apply thermodynamics, it is necessary to compare the Gibbs interface with the real surface. In the Gibbs model it is assumed that all the extensive properties of two bulk phases are unchanged up to the dividing surface (Erbil, 2006). But in the real system there are an excess number of moles of each component, energy, and entropy that are not considered in the Gibbs model. These excess quantities are known as surface excesses. In this work they are shown with superscript S. The definition of surface excess properties of each component is the difference in amount of the total quantity of that specific component property in the actual system and the ideal system.

In the Gibbs model because the interface ideally has no thickness (V S = 0 ) the total volume (V ) is:

α β += VVV (A.1) where α and β represent the two phases in contact with each other. All other extensive quantities can be written as a sum of the two bulk phases’ properties and the surface excess properties. Some examples of these extensive properties are the number of moles

222 of component i (ni), the internal energy (U), and the entropy (S) of the system. Eqns.

(A.2) to (A.4) show these properties respectively:

βα ++= nnnn S (A.2) iiii

α β ++= UUUU S (A.3)

βα S ++= SSSS (A.4)

ST or IFT can be expressed thermodynamically based on internal energy change. The change in the internal energy of the system is shown as:

α β S ++= dUdUdUdU (A.5)

Based on thermodynamic definition for open systems, the internal energy change is:

(A.6) PdVTdSdU +−= ∑ μ dnii i

Eqn. (A.6) can be rewritten as:

αααα α a ββββ ββ S (A.7) −= dVPdSTdU + ∑ μ ii −+ dVPdSTdn + ∑ μ ii + dUdn i i

The last term, dUS, in Eqn. (A.7) should be thermodynamically defined. Thus, we can use the work of the system to define it. We can divide the work into two different categories; the work based on the volume change (dWPV = -PdV), and the work not based on the volume change (dWnon-PV). The total work will be:

dWdW += dW −= + dWPdV (A.8) PV − PVnon − PVnon

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Following the first Law of Thermodynamics we have:

+= dWdQdU (A.9) where Q is the heat in the system. By combining Eqns. (A.8) and (A.9):

+−= dWPdVdQdU (A.10) − PVnon

If it is assumed that the system is reversible and that it has reached equilibrium:

= TdSdQ (A.11) rev

The internal energy change for a reversible and open system will be:

(A.12) rev +−= dWPdVTdSdU − PVnon + ∑ μ dnii i

The term (dWnon-PV) in Eqn. (A.12) is the work that the system supplies to reduce the interfacial area. Therefore, dW = γdA (A.13) − PVnon

If Eqn. (A.13) is substituted to Eqn. (A.12), the result will be:

(A.14) rev +−= dWPdVTdSdU − PVnon + ∑ μ dnii i

Eqn. (A.14) for excess internal energy will be in form of Eqn. (A.15):

SSSSS S S S (A.15) γdAdVPdSTdU ++−= ∑ μi dni i

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Therefore, the thermodynamic definition of ST or IFT at constant entropy, volume and number of moles is:

⎛ ∂U S ⎞ (A.16) γ = ⎜ ⎟ ⎜ S ⎟ ⎝ ∂A ⎠ SS S ,, nVS i

ST or IFT can be also expressed thermodynamically based on changes in the Gibbs free energy. The Gibbs free energy function is defined thermodynamically as:

−+=−≡ TSPVUTSHG (A.17) where H is the enthalpy of the system. The change in the Gibbs free energy is expressed as:

−++= − SdTTdSVdPPdVdUdG (A.18)

For a plane interface in a reversible process, the change in the excess Gibbs free energy

(dGS) is defined as:

S SSSSS S S (A.19) γ dTSdPVdAdG +−+= ∑ μi dni i

The typical derivation for Gibbs free energy relation to IFT, as what is done above for the internal energy and its relation to IFT, will lead to:

⎛ ∂G S ⎞ ⎛ ∂G ⎞ (A.20) γ = ⎜ ⎟ = ⎜ S ⎟ ⎜ ⎟ ∂A SS S ⎝ ∂A ⎠ ,, nPT ⎝ ⎠ ,, nPT i i

On the other hand, the Helmholtz free energy function is expressed as:

−≡ TSUF (A.21)

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Therefore:

−−= SdTTdSdUdF (A.22)

By substituting Eqn. (A.22) in Eqn. (A.15) and applying to the excess Helmholtz free energy of the interface we will obtain:

S SSSSS S S (A.23) γ dTSdVPdAdF +−−= ∑ μi dni i

Therefore, the relation of IFT and Helmholtz free energy is as below:

⎛ ∂F S ⎞ ⎛ ∂F ⎞ (A.24) γ = ⎜ ⎟ = ⎜ S ⎟ ⎜ ⎟ ⎝ ∂A ⎠ SS S ⎝ ∂A ⎠ ,, nVT ,, nVT i i

What showed above is the thermodynamic expression of ST or IFT (Jaycock et al., 1981;

Butt et al., 2006; Erbil, 2006). Another approach to express ST or IFT in mathematical and thermodynamic terms is to use the general definition of Gibbs free energy, which includes all the different kinds of energies applied to a system. The detail is:

(A.25) VdPSdTdG ++−= ∑ ii γμ ϕ BdIdqfdldAdn +++++ ... i

In Eqn. (A.25) f, l,ϕ, q, B, I represent mechanical force, length, electric potential, electric charge, magnetic field ,and current, respectively. Therefore:

(A.26) = ∑ dXPdG jj j r −= VSP ϕγμμ Bf ,...],,,,,...,,,[ (A.27) 1 nc r = IqlAnnPTX ,...],,,,,...,,,[ (A.28) 1 nc

226

If there are no external forces such as f, φ and B, the differential form of G and therefore γ will be:

(A.29) VdPSdTdG ++−= ∑ ii + γμ dAdn i

⎡ ∂G ⎤ (A.30) ⎛ ⎞ VdPSdTdG ++−= ∑ μ dn ii + ⎢⎜ ⎟ ⎥dA i ⎝ ∂A ⎠ r ⎣⎢ X j ⎦⎥

⎛ ∂G ⎞ (A.31) γ = ⎜ ⎟ ⎝ ∂A ⎠ r X j

Eqns. (A.31) and (A.20) are identical. The same derivation can be applied to the

Helmholtz free energy and the internal energy and the same result will be obtained.

The physical interpretation of the above equations is that ST or IFT is the change of the amount of energy per unit of area. This amount, compared to other energies, is very small and negligible. That is why most of the time this term is eliminated from the Gibbs energy equation (Adamson et al., 1997; Butt et al., 2006). On the other hand, the effect of ST and IFT on the processes and the behaviour of fluids are very important; this justifies the need to research and study the nature and effects of the surface and interfacial properties.

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APPENDIX B: CURVATURES AND THE YOUNG-LAPLACE EQUATION

B.1. Curved Fluid Interface

Determination of the ST and IFT of fluids is closely related with the properties of curved fluid surfaces.

Curvature is defined as the amount by which a geometric object deviates from being flat (Erbil, 2006).

The formation of curved fluid interfaces such as air bubbles in liquid, liquid drops in a gas phase or another immiscible liquid phase, or curved liquid meniscus in a capillary tube is the consequence of surface area minimization due to the existence of fluid surface

(interface) free energy.

In a two-phase system containing a curved interface, the pressure is always greater on the concave side than the convex side of the curvature by an amount ΔP. This pressure difference depends on the ST (IFT) and the radii or the magnitude of the curvature. The

Young-Laplace equation is the expression that relates the pressure difference in both fluids to the ST (IFT) and the curvature of the surface (interface). This equation was derived by T. Young (Peacock et al., 1855) and P.S. Laplace (Laplace, 1806) independently around the same time (1805). To explain the method they used to derive the equation, first the mathematical definition of a two-dimensional and a three- dimensional curvature should be explained;

In two-dimensional term, curvature is the rate of change of the slope of a curve with arc length (Erbil, 2006).

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If the curve slope does not change with the arc length, the curvature is called flat.

Otherwise, a curvature can be either convex or concave. The rate of change of slope with the arc length is called inclination angle and is shown by φ. The absolute magnitude of the curvature is defined as:

dϕ (B.32) κ = ds where s is the arc length (Figure B.1)

Figure B.1: Definition of the two-dimensional curvature based on the coordinates (Rotenberg et al., 1982)

The unit of curvature, κ, is (m-1) and is called dioptre. The reciprocal of the curvature is the radius of the curvature r:

1 ds (B.33) r == dϕκ

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If change of slope with arc length is small, which results in smaller amount of κ, the curvature is less curved and therefore it has a greater radius. In the extreme case, where κ is equal to zero, the curvature is flat and not bending at all. In this situation r is infinite.

On the other hand, if the slope changes very fast with the arc length, there will be a greater magnitude and a smaller radius of curvature.

The tangent of the inclination angle, ϕ , is the slope of the change in y coordinate due to the x coordinate as shown in Figure B.1. Therefore, for any position with arbitrary x and y:

dy (B.34) tan ϕ = dx

The arc length, s, between two points of A and B in Figure B.1 can be determined from analytical geometry as follow:

= Bx 2 (B.35) ⎛ dy ⎞ s 1 += dx AB ∫ ⎜ ⎟ = Ax ⎝ dx ⎠

The curvature in two dimensions can be calculated from Eqn. (2.1) for any curvature written in form of y=f(x), where f is a function in Cartesian coordinate with continuous first and second derivatives. Therefore, from Eqn. (2.1), (B.34) and (B.35):

2 yd (B.36) 2 dx κ = 3 2 2 ⎡ ⎛ dy ⎞ ⎤ ⎢1 + ⎜ ⎟ ⎥ ⎣⎢ ⎝ dx ⎠ ⎦⎥

Therefore:

230

3 2 2 (B.37) ⎡ ⎛ dy ⎞ ⎤ ⎢1 + ⎜ ⎟ ⎥ ⎢ ⎝ dx ⎠ ⎥ r = ⎣ ⎦ 2 yd dx 2

In order to determine the magnitude of curvature for a two-dimensional curve, there is another approach that is called osculating circle approach. The osculating circle is a circle that is tangent to the curve at a given point as shown in Figure 3.6:

Figure B.2: Definition of the two-dimensional curvature based on osculating circle method

The value of the circle radius (rA and rB in Figure 3.6), which is a vector pointing in the direction of the centre of each of A and B circles, characterizes and quantifies the curvature at points A and B, respectively.

If the mathematical function of the curve, f, is known, the coordinates of the centre of the curvature can be calculated for any curve in form of y=f(x). Again f should have

231 continuous first and second derivatives. The coordinates of the centre of the curvature are:

2 (B.38) ⎡ ⎛ dy ⎞ ⎤ ⎢1 + ⎜ ⎟ ⎥ ⎛ dy ⎞⎢ ⎝ dx ⎠ ⎥ c xx −= ⎜ ⎟ ⎝ dx ⎠⎢ ⎛ 2 yd ⎞ ⎥ ⎜ ⎟ ⎢ ⎜ 2 ⎟ ⎥ ⎣⎢ ⎝ dx ⎠ ⎦⎥

2 (B.39) ⎡ ⎛ dy ⎞ ⎤ ⎢1 + ⎜ ⎟ ⎥ dx yy += ⎢ ⎝ ⎠ ⎥ c ⎢ ⎛ 2 yd ⎞ ⎥ ⎜ ⎟ ⎢ ⎜ 2 ⎟ ⎥ ⎣⎢ ⎝ dx ⎠ ⎦⎥

Consequently, the radius of the curvature will be:

2 2 (B.40) A ()()cA −+−= yyxxr cA

The radius obtained from Eqn. (B.40) is identical with the one from Eqn. (B.37).

In a three-dimensional arbitrary curved object (ABCD in Figure B.3), two independent radii are needed to define the curvature thoroughly. If a normal to the surface is defined at the point in question, point z in Figure B.3, and a plane containing this normal is passed through the surface (klmn plane in Figure B.3), the line at the curvature intersection with the plane will also be a curve. The radius of this curvature is the radius of a circle that is tangent to the curvature at point z. The second radius of the three- dimensional curvature will be the radius of a two-dimensional curve that is generated at the intersection of the curved object and the second plane (pqrs plane in Figure B.3).

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This plane contains the curvature normal passing from point z and it is perpendicular to the first plane.

Figure B.3: Definition of the two independent radii of the three-dimensional curvature (Erbil, 2006)

The two radii of curvature (r1=1/κ1, r2=1/κ2) obtained above are not necessarily the principal radii of the curvature. In order to find the principal radii of a three-dimensional curvature, the first plane (klmn) should rotate through a full circle so that the first radius of the curvature will reach a minimum. The value of r1 at the minimum is the value of the first principal radius of the curvature. Consequently the radius of the two- dimensional curve on the second plane (pqrs), which is perpendicular to the principal first plane, will be the second principal radius of the curvature.

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Anyways the pressure difference through the surface, ΔP, is independent of the way r1 and r2 are chosen and they do not need to be the principal radii of the curvature. In other words, sum of the two-dimensional curvatures (κ1 + κ2 = 1/ r1 + 1/ r2) is independent of how the first plane is oriented when the second plane is always perpendicular to it.

The mathematical expression of an arbitrary three-dimensional curvature is as following:

2 yd (B.41) 2 1 dx κ 1 == 3 r 2 2 1 ⎡ ⎛ dy ⎞ ⎤ ⎢1 + ⎜ ⎟ ⎥ ⎣⎢ ⎝ dx ⎠ ⎦⎥

dy (B.42) 1 dx κ 2 == 1 r 2 2 2 ⎡ ⎛ dy ⎞ ⎤ x⎢1 + ⎜ ⎟ ⎥ ⎝ dx ⎠ ⎣⎢ ⎦⎥ where r2 is the second radius of curvature and it is perpendicular to r1 and:

sin1 ϕ (B.43) = 2 xr

In order to describe a three-dimensional curvature, two methods are defined; mean curvature and Gaussian curvature. The mean curvature is defined as H and is the arithmetic mean of curvature:

1 + rr 21 (B.44) H κκ 21 )( =+= 2 2 rr 21

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Dimension of H is (m-1). In a three-dimensional Cartesian coordinate system H is written as (Erbil, 2006):

2 2 2 2 2 (B.45) ⎡ ⎛ ∂z ⎞ ⎤⎛ ∂ z ⎞ ⎛ ∂z ⎞⎛ ∂z ⎞⎛ ∂ z ⎞ ⎡ ⎛ ∂z ⎞ ⎤⎛ ∂ z ⎞ ⎢1 + ⎜ ⎟ ⎥⎜ ⎟ − 2 ⎜ ⎟⎜ ⎟ 1 ++ ⎜ ⎟ ⎜ ⎟ ⎜ 2 ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎢ ⎜ ⎟ ⎥⎜ 2 ⎟ ⎢ ⎝ ∂y ⎠ ⎥ ∂x ⎝ ∂x ⎠⎝ ∂y ⎠ ∂∂ yx ⎝ ∂x ⎠ ∂y ⎣ ⎦⎝ ⎠ ⎝ ⎠ ⎣⎢ ⎦⎥⎝ ⎠ H = 3 2 2 2 ⎡ ⎛ ∂z ⎞ ⎛ ∂z ⎞ ⎤ ⎢12 + ⎜ ⎟ + ⎜ ⎟ ⎥ ∂x ⎜ ∂y ⎟ ⎣⎢ ⎝ ⎠ ⎝ ⎠ ⎦⎥

The other curvature term, Gaussian curvature, K, is defined as:

1 (B.46) K κκ 21 == rr 21

Dimension of K is (m-2). K and H are related to each other and based on curvature or the radius of the curvature they can be written as Eqns. (B.47) and (B.50), respectively:

2 2 κκ KH =+− 0 (B.47)

2 (B.48) κ 1 −+= KHH

2 (B.49) κ 2 −−= KHH

1 (B.50) += 21 )( KrrH 2

In a three-dimensional Cartesian coordinate analytical geometry model of K can be written in form of Eqn. (B.51):

2 ⎛ ∂ 2 z ⎞⎛ ∂ 2 z ⎞ ⎛ ∂ 2 z ⎞ (B.51) ⎜ ⎟⎜ ⎟ − 2⎜ ⎟ ⎜ ∂x 2 ⎟⎜ ∂y 2 ⎟ ⎜ ∂∂ yx ⎟ ⎝ ⎠⎝ ⎠ ⎝ ⎠ K = 2 2 2 ⎡ ⎛ ∂z ⎞ ⎛ ∂z ⎞ ⎤ ⎢1 + ⎜ ⎟ + ⎜ ⎟ ⎥ ∂x ⎜ ∂y ⎟ ⎣⎢ ⎝ ⎠ ⎝ ⎠ ⎦⎥

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B.2. Young-Laplace Equation

As described in the previous section the two radii of the curvature are determined by cutting the curved surface (ABCD in Figure B.3) with two perpendicular planes intersecting each other on the curved surface. Each plane’s intersection with the curved surface generates a two-dimensional curvature containing one of the two independent radii of the curved surface (r1 and r2). If the curved surface becomes a little larger and moves outward by an amount of dz (Figure B.4), the new position of the surface will become (A’B’C’D’).

Figure B.4: Description of Young-Laplace equation using plane geometry concept (Erbil, 2006)

Therefore, there will be changes in surface dimensions x (abscissa), y (ordinate) and z

(normal coordinate to paper plain) to x+dx, y+dy and z+dz amounts. Consequently, the changes in area, Gibbs free energy, and work will be:

236

))(( =−++=Δ + + ≈ + ydxxdydxdyydxxdyxydyydxxA (B.52)

γ += ydxxdydG )( (B.53)

PdVW Pxydz =Δ=Δ= γ + ydxxdy )( (B.54)

Referring to Figure B.4, r1 and r2 are changing when x,y and z change. Applying the triangle rule of geometry:

+ dxx x (B.55) = 1 + dzr r1 which simplifies to:

dx 1 (B.56) = rxdz 1

And:

+ dyy y (B.57) = 2 + dzr r2 which simplifies to:

dy 1 (B.58) = rydz 2

Substituting Eqns. (B.56) and (B.58) into Eqn. (B.54) generates Eqn. (B.59) that is the

Young-Laplace equation of capillarity.

11 (B.59) P γ ( +=Δ ) rr 21

237

APPENDIX C: METHODS OF MESURING INTERFACIAL TENSION AND

CONTACT ANGLE

C.1. The Capillary Rise Method

When a capillary tube is inserted into a liquid, the liquid will ascend or descend in the tube and will reach a certain height. An inverse proportionality between the height of the liquid and the radius of the capillary tube has been observed.

Capillary rise happens when the adhesion interactions between the liquid and the capillary tube wall are stronger than the cohesion interactions within the liquid. In the contrary, capillary depression happens when the cohesion interactions are dominant. The latter phenomenon is very rare.

A strong suggestion for the capillary rise mechanism is as following (Erbil, 2006); when the capillary tube and the liquid come into contact with each other, first a thin film of liquid on the inside wall of capillary tube is formed as a consequence of adhesion interactions. This phenomenon will result in a large surface area. Then, very quickly, the liquid ascend in the capillary tube decreasing the surface area. The rise of liquid in the tube cannot be infinite, because of the existence of gravity (hydrostatic) forces.

Therefore, the liquid will rise to a certain height, h, until the weight of the liquid column in capillary tube is in equilibrium with the capillary forces. The attractive forces that pulled the liquid upward in the capillary tube are exerted only on the upper edge of the liquid in contact with the tube, which is the tube perimeter, 2πr.

238

On the other hand, the rise of the liquid in the capillary tube is relevant to the pressure difference, ΔP. In Figure 3.6 the pressure at the liquid level and point a just above the meniscus is atmospheric. The height of the liquid in the capillary tube is such that at point c pressure is also atmospheric. Therefore, at point b pressure is lower than atmospheric pressure by an amount 2γ/r. At equilibrium:

2γ (C.60) ρghP =Δ=Δ r where Δρ is the difference in liquid and air densities.

Figure C.5: Liquid meniscus in a capillary tube (Erbil, 2006)

The curvature of the liquid surface meniscus is determined by the radius of the tube and the angle of contact, θ, between the liquid and the capillary wall. If the cross section of capillary tube is circular and has a very small radius, the meniscus will be completely

239 hemispherical that results to θ = 0 and r = r1 = r2 in the Young-Laplace equation (Eqn.

(B.28)). By rearranging Eqn. (C.60) for a completely hemispherical meniscus:

2γ (C.61) rh = = a 2 Δρg o

2 2 2 where ao is defined as the capillary constant at θ = 0. The dimension of ao is m .

Eqn. (C.61) is correct for the ideal-simplest form of capillary rise, but in reality the liquid surface may become in contact with the capillary wall in an angle rather than zero, θ ≠ 0.

In this case cos θ = r/r1. If the radius of the capillary tube is sufficiently small and the gravitational distortion of the curvature is neglected, the two radii of the curvature will be identical and therefore r/cos θ = r1 = r2. Consequently, Eqn. (C.61) will be modified as:

γ cos2 θ (C.62) rh = = a 2 Δρg θ

2 where aθ is the capillary constant for θ ≠ 0. The angle of contact and the curvature of the surface are dependent to the magnitudes of the adhesive and cohesive forces. If the adhesive forces are greater than the cohesive force, the contact angle will be smaller than the straight angle (0o ≤ θ ≤ 90o) and a concave meniscus toward the gas phase will form, otherwise the contact angle will be greater than the straight angle (90o ≤ θ ≤ 180o) and a convex meniscus toward the gas phase will form. In the rare-latter case the liquid level in the capillary tube is lower than the liquid level in the container. A very good example of capillary depression phenomenon is the liquid mercury in a glass capillary tube, which is useful for mercury injection porosimetry technique in measuring the porosity of different solids.

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Practically in capillary rise method, the angle of contact between the capillary tube wall and the liquid surface will be smaller than 40o (0o ≤ θ ≤ 40o). Measuring ST by capillary rise method in cases with θ ≠ 0 is not recommended, because inaccuracy in observing the contact angle will cause a significant error.

In Eqns. (C.61) and (C.62) the weight of the liquid in the crown of the concave meniscus is neglected (Figure 3.6). Thus, these equations are just approximates and need some correction factors. If the meniscus is assumed hemispherical, an addition of (r/3) to the height of the liquid column would be a reasonable correction. This correction factor considers the weight of the extra liquid in shaping the hemispherical curvature.

r (C.63) 2 (hra += ) 3

In case the meniscus has some deviations from the hemisphere shape, the capillary constant can be modified as Eqn. (C.64) given by Lord Rayleigh (Rayleigh, 1916).

r r 2 r 3 (C.64) 2 (hra −+= 1288.0 + 1312.0 + ...) 3 h h 2

Later in 1996, Prokhorov (Prokhorov, 1996) refined Eqn. (C.64) for more accurate ST determination.

For the exact solution to capillary rise method, the curvature must correspond to

ΔP=Δρgy at each point on the meniscus, where y is the elevation of that point above the liquid surface in the container. Also, two independent radii of curvature should be

241 considered therefore, the general form of Eqn. (C.60) for each arbitrary point ([x, y]) on the meniscus using the Young-Laplace equation (Eqn. (B.28)) will be:

11 (C.65) gyP γρ ( +=Δ=Δ ) rr 21

If r1 and r2 are replaced by the expressions from the analytical geometry (Eqns. (B.10) and (B.11)) Eqn. (C.65) will change to:

⎡ ⎤ (C.66) ⎢ ∂ 2 y ∂y ⎥ ⎢ 2 ⎥ ∂x ∂x gyP =Δ=Δ γρ ⎢ 3 + 1 ⎥ 2 2 2 2 ⎢ ⎡ ⎛ ∂y ⎞ ⎤ ⎡ ⎛ ∂y ⎞ ⎤ ⎥ ⎢ ⎢1 + ⎜ ⎟ ⎥ x⎢1 + ⎜ ⎟ ⎥ ⎥ x ⎣⎢ ⎣⎢ ⎝ ∂x ⎠ ⎦⎥ ⎣⎢ ⎝ ∂ ⎠ ⎦⎥ ⎦⎥

Eqn. (C.66) is the general equation of capillary rise in Cartesian coordinate system.

The exact total weight of the column of liquid in the capillary tube is in form of Eqn.

(C.67):

= πrW γ cos2 θ (C.67)

The general equation of capillary rise has been solved for different conditions by

Bashforth and Adams (Bashforth et al., 1892). They used a numerical integration procedure. The two radii of the meniscus curvature are equal at the apex (r1 = r2 = b), where b is the radius of the curvature at the apex. If the elevation of a general point on the surface is called z, where z = y – h, then the Young-Laplace equation (Eqn. (B.28)) can be written as:

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11 2γ (C.68) γ ( ) ρgz +Δ=+ rr 21 b

In dimensionless form Eqn. (C.68) will change to:

sin1 ϕ βz (C.69) +=+ 2 1 bxbr b

In Eqn. (C.69) β is called the Bond number and is equal to:

Δρ 2 2bgb 2 (C.70) β = = γ a 2

β is positive for a meniscus in a capillary tube, a sessile drop, and a captive bubble. It is negative for a pendant drop, and a clinging bubble. As it is shown in Eqn. (C.70), β and γ are inversely proportional. Therefore, smaller Bond numbers result to larger surface tension values. The results of Bashforth and Adams numerical calculations are reported in variety of tables (Bashforth et al., 1892). These tables have values of x/b and z/b for each amount of β and φ. Their work was extended by Sugden (Sugden, 1921), Lane

(Lane, 1973) and Padday (Padday et al., 1972). Lane generated two accurate polynomial curves that fit to Bashforth and Adams numerical solutions. For r/a ≤ 2 he proposed: b r r r r (C.71) += 2 + 3 − 4 + )(569.663)(926.473)(263.65)(9.3327[1 5 − r a a a a r r r 6 + 7 − 8 × 10])(3163.7)(1929.75)(032.300 −4 a a a and for r/a ≥ 2 (Lane, 1973): r r ⎡ r a a ⎤ (C.72) = 23 − + + + )(37136.0)(14681.066161.0)(41222.1exp)( 2 b a ⎣⎢ a r r ⎦⎥

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These polynomials can be used in iterations to find b1 from an initial amount of (r/a)1

2 2 where (a1 =rh). Then b2 is calculated using the same equations, but this time a2 in (r/a)2

2 is found from the exact equation a2 = b1h. This iteration process is repeated until bn – bn-1 < ε (ε →0). Then the exact value of the ST can be found from the following equation

(Eqn. (C.73)):

2 )( Δρga (C.73) γ = nb 2

Capillary rise method is one of the most accurate methods for measuring ST to a few hundredths of a percent, but it is necessary to have a large amount of liquid in the container and the liquid wets the inside wall of the capillary tube thoroughly. In this case the contact angle, θ, in the surface area is equal to zero; therefore no uncertainty will affect the measurements. For contact angles greater than zero there is an error in determining the contact angle and it will reduce the accuracy of the method. On the other hand, capillary rise method is not recommended for L-L IFT measurements because it is usually hard to see the exact location of the L-L interface.

Also the capillary tube should be completely cleaned, positioned precisely vertical and it should not deviate from circularity in its cross section by more than a few percents. The radius of the capillary tube should be accurately known and uniform throughout the tube length.

The capillary rise method is commonly used to measure the static ST of pure, completely-wetting liquids. It is not recommended for measuring the IFT of two liquids

244 because it is very hard to see the exact interface. The contact angle between the liquid and the capillary tube should be zero for an accurate measurement. Thin-walled glass tubes are preferred because their interior diameter is more uniform along the length of the tube.

Although the capillary rise method has been widely used to measure ST of liquids, but it is applicable to contact angle, θ, measurements as well (Kwok et al., 1995; Gu et al.,

1997; Gu et al., 1998). Accuracy of the method for contact angle measurements is not very high.

C.2. The du Nouy Ring Method du Nouy ring method is one of the oldest methods of measuring ST. The first time this technique was used goes back to 1878. In this method, a small circular loop of metal wire called ring, which is often made of pure platinum or an alloy of platinum-iridium, is suspended from a balance. The radius of the ring is not usually larger than 2-3 cm and the radius of the wire ranges from 1/60 to 1/30 of the ring radius. In addition, the contact angle between the ring and the liquid should be zero or very close to zero. During ST measurement experiments, the ring is immersed into the liquid completely horizontally.

Then, the ring is raised slowly toward the liquid surface. Because metals are high-surface energy materials, the adhesion force between the liquid and the metal ring is stronger than the cohesion force between the liquid particles. The maximum weight sensed by the balance is recorded. The maximum weight happens at the moment when the ring detaches from the liquid surface. The recorded weight of the system at this moment is

245 the weight of the ring itself plus the ST of the liquid (the adhesion force between the liquid and the metal).

In 1919, a French scientist called du Nouy (du Nouy, 1919) designed and constructed a new apparatus (Figure C.6) for this technique. He measured ST of water, sodium oleate, and heptilic acid using his new apparatus and verified the results by comparing them with the same ST measurement results using the capillary rise method. Because of his great contribution to this method, it became very popular and was named after him.

Figure C.6: du Nouy Apparatus for measuring ST (du Nouy, 1919)

From the force balance at the detachment moment:

246

tot WF ring += 2π min γ + 2πrr max γ (C.74) where rmin and rmax are the inside and outside diameter of the wire, respectively.

Therefore:

+ rr (C.75) WF += πγ (4 min max ) tot ring 2

The general equation of ring detachment can be written as:

tot WF ring += 4πrmean γ (C.76) where rmean = (rmin +rmax)/2.

Eqn. (C.76) is a preliminary equation of the ring detachment. This equation has a significant error. The error is because of the part of liquid that rises along with the ring.

Therefore, Harkins and Jordan (Harkins et al., 1930) and later Huh and Mason (Huh et al., 1975) suggested an empirical correction factor, f. The f factor is a function of mean radius of the ring, thickness of the ring, and also the meniscus volume. Thus, f depends on two dimensionless ratios as shown in Eqn. (C.77):

γ R 3 R (C.77) f == F ),( γ ideal V r

In Eqn. (C.77) V denotes of the meniscus volume (Figure 3.6). Usually f values vary between 0.75 and 1.05 according to the size and shape of the ring and difference between the fluid densities.

247

Figure C.7: The ring detachment method

This modification has shown that the simple equation of ring detachment (Eqn. (C.76)) has almost 25% error (Figure C.8).

The f values can also be calculated by using the following approximate equation (Erbil,

2006):

1 (C.78) ⎛ × 10075.9 − 4 F 679.1 r ⎞ 2 f 725.0 += ⎜ − wire + 04534.0 ⎟ ⎜ 3 3 ⎟ ⎝ Δρπ grmean rmean ⎠

3 where F is the interfacial (surface) force. Eqn. (C.78) is valid for 0.045 ≤ Δρgr mean/F ≤

7.5. In the modern computerized systems, the ST readings do not require an extra calculation for the f factor, because it is done inside the software.

248

Figure C.8: The factor f in different R3/V and R/r ranges (Huh et al., 1975)

Ring method is applicable to IFT measurements between two liquids. One should just ensure that the bulk of the ring probe is submerged in the light phase before the experiment starts. The ring is then carefully immersed in to the heavy phase underneath and slowly raised to the interface. Therefore, the ring carries a small amount of the heavy liquid in shape of a meniscus up to the light phase. By measuring the maximum weight of the probe before detachment, the IFT can be calculated. In this case the density difference between two liquid phases should be considered in IFT calculations. In IFT measurement using the ring method, the heavy phase should be completely the wetting phase. Otherwise, θ is above zero and an additional correction factor is necessary.

249

C.3. The Wilhelmy Plate Method

Another most widely used and simplest method of measuring ST and IFT is the

Wilhelmy plate method. In contrast to other methods such as capillary rise, ring, sessile and pendant drop, drop weight, and maximum bubble pressure methods, this method does not need any correction factor for measuring ST and IFT. For more accurate ST and IFT measurement the plate should be perfectly smooth and homogeneous.

Wilhelmy plate method is attributed to Wilhelmy (Wilhelmy, 1863) in 1863, because he was the first person who applied this method by using a thin plate and a lever balance. In this method as illustrated in Figure C.9 a vertical thin plate (or wire or fibre), which can be platinum, iridium-platinum alloy, glass, mica, steel, or plastic, will be in contact with the liquid surface. This plate that is called Wilhelmy plate will support a meniscus of the liquid generated by the adhesion forces between the liquid and the plate. The plate is attached to a balance and the total weight can be sensed by the balance. The total weight can be formulated as:

plate += pWF γ (C.79) where p is the perimeter of the plate. Eqn. (C.79) is valid when the θ between the liquid and the plate is zero; therefore the liquid surface is vertically upward in the contact area.

The ST of the liquid exerts a downward force that is transferred to the plate through the meniscus contact area and is equal to the weight of the arisen meniscus. Value of ST can be formulated as Eqn. (C.79) above.

250

An alternate and popular procedure for Wilhelmy plate method is to raise the liquid level very slowly and smoothly until the liquid surface and the vertical plate slightly come into contact with each other. If the weight of the plate probe is zeroed in the balance before the liquid surface touches the plate, then the extra force exerted on the balance is because of the weight of the formed meniscus or interfacial force. Therefore, Eqn. (C.79) can be rewritten as:

cap max plate =−==Δ γ = + dwpWFFW )(2 γ (C.80)

If the angle that the liquid makes with the plate is not zero then Eqn. (C.80) changes to:

=Δ pW γ cos θ (C.81)

Figure C.9: Wilhelmy plate method and the meniscus profile

In 1970 Princen (Princen, 1970) compared a grooved Wilhelmy plate with smooth one in measuring ST and modified Eqn. (C.81) by adding a correction factor for rough solid surfaces.

251

Wilhelmy plate technique can be also applied to monolayer studies, where the plate will be partially placed in the liquid. Therefore, the force necessary to keep the plate at constant depth of immersion is determined as the ST is changed due to the presence of solutes forming the monolayer film. In this case, the forces acting on the plate consist of the gravity and ST effects downward, the buoyancy effect due to the displaced water upward, and correction due to the buoyancy of sub phase is required.

If the plate dimensions are d, l, w and h is the depth that the plate immersed in the liquid

(Figure C.9), the total forces can be written as Eqn. (C.82):

F = ρ s glwd γ ++ dw cos)(2 θ − ρ l ghwd (C.82) where ρs and ρl are densities of the plate and the liquid, respectively. The density of air is neglected in all Eqns. (C.79) to (C.82).

One of the people who worked on this topic was Gaines (Gaines, 1977) who used filter paper Wilhelmy plates for measuring ST of insoluble monolayers during the surface adsorption in 1977.

Wilhelmy slide method can be also operated for measuring the IFT of two immiscible liquids. The plate should be completely wetted by one liquid, preferably the heavy phase.

The plate should not submerge into the heavy liquid. Existence of contact angles greater than zero causes problems in IFT measurements.

252

More than ST and IFT measurements, Wilhelmy plate method is a useful means of measuring dynamic (advancing and receding) contact angle (Adamson et al., 1997).

Hayes and his colleagues (Hayes et al., 1994) in 1994 used this method to measure the receding and advancing contact angle of glycerol-water on PMMA (poly methyl methacrylate) solid at different plate velocities.

C.4. The Height of a Meniscus on a Vertical Plane Method

The height of a meniscus on a vertical plain method is very similar to Whilhelmy plate method. When a solid plane is vertically in contact with a liquid phase the liquid climbs on the surface of the solid as shown in Figure C.10.

Figure C.10: The meniscus profile in the height of a meniscus on a vertical plain method (Erbil, 2006)

253

In this method the height of the meniscus is accurately measured. Using the measured height of the liquid on the solid plane, ST of the liquid and contact angle can be calculated. In order to calculate these interfacial properties of the liquid, the general equation of Young-Laplace for interfaces (Eqn. (B.28)) is recalled. Therefore, two radii of the curvature are needed. As shown in Figure C.10, one of the radii of the curvature made against the vertical plane is infinite because the plane is planar and therefore, just one radius is needed for calculating ST and contact angle. Consequently the Young-

Laplace equation will be modified to:

γ (C.83) ρgyP =Δ=Δ r1 where y is the vertical axis coordinate (Figure C.10). In Figure C.10 φ that is called inclination angle shows the rate of change in direction of the surface curvature:

dy (C.84) tan ϕ =− dx

The inclination angle makes a straight angle with the angle of contact, θ, at the interface

(φ = 90o – θ). By combining the analytical geometry of the independent curvature radii

(Eqn. (B.10)) and Eqn. (C.84), Eqn. (C.85) can be derived:

⎡ d ⎛ sin ϕ ⎞⎤ (C.85) ⎢ ⎜ − ⎟⎥ 1 ⎣ dx ⎝ cos ϕ ⎠⎦ = 3 r 2 2 1 ⎡ ⎛ sin ϕ ⎞ ⎤ ⎢1 + ⎜ ⎟ ⎥ ⎣⎢ ⎝ cos ϕ ⎠ ⎦⎥

By differentiation and rearrangement Eqn. (C.85) changes to:

254

1 dϕ d sin ϕ (C.86) −= cos ϕ −= r1 dx dx

That is equal to:

1 d cos ϕ (C.87) −= r1 dy

Combining Eqns. (C.83) and (C.87) will result to:

Δ ρ dg cos ϕ (C.88) −= γ ydy

By integrating Eqn. (C.88) in correspondence to φ and y:

ϕ Δρg y (C.89) − ∫ d cos ϕ = ∫ ydy 0 γ 0 and therefore:

Δ ρg (C.90) ϕ 1cos −= y 2 2γ

Since at the interface where y=h (φ = 90o – θ):

ϕ = sincos θ (C.91)

Therefore by substituting θ for φ in Eqn. (C.90):

2 Δρg ⎛ h ⎞ (C.92) θ 1sin −= h 2 1 −= ⎜ ⎟ 2γ ⎝ a ⎠

Based on Eqn. (C.92) contact angle can be calculated if the density and ST of the liquid are known. On the other hand, in order to determine the ST, there should be an equation independent of contact angle. If the plane is connected to a balance when it contacts the

255 liquid surface, the difference in force because of addition of the capillary force, (Fcap) can be measured. The general force balance equation will be:

cap 2()+= dwF γ cos θ (C.93)

Therefore:

2 (C.94) 2 ⎡ Fcap ⎤ cos θ = ⎢ ⎥ ⎣ 2()+ dw γ ⎦

Since (sin2θ+cos2θ=1) in trigonometry, from Eqns. (C.92) and (C.94):

2 2 (C.95) ⎡ Δρg 2 ⎤ ⎡ Fcap ⎤ ⎢1 − h ⎥ + ⎢ ⎥ = 1 ⎣ 2γ ⎦ ⎣ 2()+ dw γ ⎦

By rearranging Eqn. (C.95):

2 2 Δρgh F cap (C.96) γ = + 4 4Δρ 2 ()+ dwgh 2

As shown above ST can be calculated from Eqn. (C.96) that is independent of contact angle. By replacing Eqn. (C.96) in Eqn. (C.94):

2Δρ 2 ()+ Fdwgh (C.97) cos cap θ = 2 42 2 2 4()Δρ ( )++ Fdwhg cap

In Eqn. (C.97) contact angle can be calculated independently, as well.

C.5. The Spinning Drop Method

The spinning drop method is based on the analysis of the deformation of drops or bubbles caused by centrifugal force fields. This method has been used to measure IFT since

1942. It is mostly used to measure IFT and it is applicable in chemical flooding

256 enhanced oil recovery. Spinning drop method works better for lower IFTs than higher ones (Mannhardt et al., Fall 2005).

In this method a small drop of the less dense phase is placed in a glass capillary tube filled with the denser phase. The glass tube is rotated horizontally around its axis, and the drop stretches in the centrifugal force field as the angular velocity increases. Figure

C.11-a shows a drop of less dense fluid immersed in the high dense fluid at different velocities. The IFT can be measured using the results of the shape of the drop at different velocities.

The pressure at radius r in a rotating fluid is given by

ρω r 22 (C.98) PP += 0 2 where P is the pressure, P0 is pressure at the axis of rotation; r is radius, ρ is density of the fluid and ω is angular velocity. Aqueous (denser) phase pressure is built up from centrifugal force. Inside the drop, there is a capillary pressure across the interface in addition to the centrifugal force. Using the coordinate system in Figure C.11-b for a rotating drop of oil in water, aqueous phase pressure (Pw), drop pressure at radius y inside the drop (Po), and pressure difference (ΔP) are given by:

ωρ y 22 (C.99) PP += w w 0 2

2 ωργ y 22 (C.100) PP ++= o o 0 a 2

257

2 Δ ρωγ y 22 (C.101) P −=Δ a 2 where ρw is the density of the aqueous phase, y is the radius from the axis of rotation, a is the radius of curvature of the drop surface at the origin, ρo is density of the drop (oil), and

Δρ is equal to (ρw - ρo).

Figure C.11: Spinning drop method. (a): The drop shape at different velocities, (b): The spinning drop profile

Recalling from the Young-Laplace equation for pressure difference between two phases across the interface (Eqn B.28), for spinning drop with two principal radii r1 and r2:

2 Δρωγ y 22 ⎛ 11 ⎞ (C.102) − γ ⎜ += ⎟ a 2 ⎝ rr 21 ⎠

Calling radii of curvatures from Appendix B and substituting them into Eqn. (C.102) will result in a differential equation that expresses IFT in terms of density difference, rotational velocity, and drop shape, all of which are measurable quantities as below:

⎛ ⎞ (C.103) ⎜ 2 xd dx ⎟ ⎜ ⎟ 2 Δρωγ y 22 dy 2 dy − = γ ⎜ + ⎟ a 2 ⎜ 2 2/3 2 2/1 ⎟ ⎡ ⎛ dx ⎞ ⎤ ⎡ ⎛ dx ⎞ ⎤ ⎜ ⎢1 + ⎜ ⎟ ⎥ y ⎢1 + ⎜ ⎟ ⎥ ⎟ ⎜ ⎜ dy ⎟ ⎜ dy ⎟ ⎟ ⎝ ⎣⎢ ⎝ ⎠ ⎦⎥ ⎣⎢ ⎝ ⎠ ⎦⎥ ⎠

258 or

2 Δρωγ y 22 ⎛ x ′′ x′ ⎞ (C.104) − = γ ⎜ + ⎟ ⎜ 2 2/3 2 2/1 ⎟ a 2 ⎝ []1 + x′ []1 + xy ′ ⎠

The spinning drop equation has been solved, and the solution tabulated as a function of xo/yo, the ratio of drop length to drop diameter. This table can be used to calculate IFT from measurements of the drop dimensions (Vonnegut, 1942; Princen et al., 1967b;

Cayias et al., 1975).

Simplification can be done on Eqn. (C.104) to get a simple model for IFT of drops in the apparatus. The lower the IFT, the more stretched the drop becomes. For low IFTs (less than 30mN/m) and in cases that the drop length is more than four times the drop diameter

(xo/yo > 4), based on Vonnegut’s approximation (Vonnegut, 1942) the drop can be approximated by a cylinder with hemispherical ends. The error in IFT will be less than

0.05%. This will narrow down the differential equations solution for long drops from the more general solution of the spinning drop equation (Eqn. (C.104)) and only the drop diameter needs to be measured (Princen et al., 1967b; Cayias et al., 1975). By applying the cylinder-drop shape assumption, IFT can be calculated from:

Δρω 2 y 3 (C.105) γ = 0 4

-1 -3 -1 where [γ ] = (dyne cm ), [Δρ] = (g cm ), [ω] = (radians s ) and [yo] = (cm). Eqn. (C.105) is called Vonnegut’s equation.

259

Princen and co-workers (Princen et al., 1967a) extended Vonnegut's approximate solution for the shape of a fluid drop in a horizontal rotating tube filled with a liquid of higher density. They suggested numerical solutions based on exact equations from which it is possible to calculate the IFT from the length of an elongated drop along the axis of rotation when the drop volume, speed of rotation, and density difference between the two phases are known. Their results show good agreement with other methods. The technique is considered to be especially useful for systems in which either phase is highly viscous (the rotational velocity is very low) or IFT is too large.

In cases with high values of IFT and low rotational velocity, a correction factor may be applied for Buoyancy and Coriolis effects. Currie and Van Nieuwkoop (Currie et al.,

1982) investigated the effect of Buoyancy in the spinning drop tensiometer in 1981.

Although many people worked on the correction factors, still the best IFT results are obtained when the work is under conditions such that Eqn. (C.105) applies. The spinning drop method is very successful for IFT values below 0.001dyn/cm (Cash et al., 1977;

Shinoda et al., 1986).

C.6. The Maximum Bubble Pressure Method

In the maximum bubble pressure method the ST of a liquid is determined by measuring the maximum pressure needed to push a gas bubble out of a capillary tube into the liquid.

This pressure should overcome the capillary and hydrostatic forces to push the gas out of the capillary tube. In order to determine the maximum bubble pressure, a capillary tube of internal radius r is vertically placed into a liquid of known density (Figure C.12). A

260 flow of gas (usually air) is blown into the capillary tube. At a certain pressure the gas starts to come out of the capillary tube in shape of a sphere segment (images number 1 in

Figure C.13-a, b). By increasing the gas pressure gradually, the bubble grows and consequently the radius of the curvature becomes smaller. At a certain pressure, the bubble becomes completely hemispherical (images number 2 in Figure C.13-a, b). At this moment the radius of the curvature is at its minimum value and it is equal to the radius of the capillary tube. If the liquid is the wetting phase, it covers the lower edge of the tube completely and the radius of the L-G interface curvature is equal to the internal radius of the tube and if the gas is the wetting phase, the radius of the curvature is equal to the external radius of the capillary tube. Based on Young-Laplace equation, the pressure applied on the gas to shape a hemispherical bubble is the maximum pressure inside the bubble because the radius of the curvature is minimum. After this moment the bubble grows further and obtains a larger radius. Since the radius is larger now, less pressure than the maximum pressure is needed to push the bubble out of the capillary tube. Therefore, the bubble becomes unstable and detaches from the capillary tube.

Consequently, a chain of bubbles comes out of the capillary tube. So by measuring the maximum pressure needed to detach the bubble from the tip of the capillary tube, IFT can be determined. In formulating the maximum pressure and IFT, the hydrostatic pressure corresponding to the liquid above the tip of the capillary tube should be considered as well. The pressure balance for the hemispherical bubble is given as (Erbil, 2006):

2γ (C.106) ρghPPP +Δ=+= max hyd cap r

261

It is important to realize that Eqn. (C.106) is only valid for the capillary tubes with a very small radius. If the radius of capillary tube is large, (r/a) > 0.05, the maximum pressure may not be reached until the drop is bigger than a hemisphere as shown in Figure C.14.

In this situation a correction factor should be applied to obtain a more accurate ST.

Sugden (Sugden, 1922; Sugden, 1924) used Bashforth’s and Adams’ tables to determine the correction factor. Therefore, Eqns. (C.69), (C.71), and (C.72) can be used and ST is determined by iteration.

Figure C.12: The maximum bubble pressure technique (Erbil, 2006)

262

Figure C.13: The gas bubble growth by pressure in the maximum bubble pressure technique; (a): The liquid is the wetting phase. (b): The liquid is the non-wetting phase (Erbil, 2006)

Figure C.14: The maximum bubble pressure technique for capillary tubes with a large radius [(r/a)>0.05]

263

The maximum bubble pressure method can be used for calculating the ST of molten metals and is amenable to remote operations. It does not depend on contact angle, requires only the densities of the fluids, and it is a very fast method. This method was very popular in the past, but now is not frequently used because of its poor precision.

C.7. The Drop Weight Method

The drop weight method, formerly called stalagmometer method (Erbil, 2006), is one of the fairly accurate, convenient and oldest detachment methods for measuring ST and IFT of L-G and L-L systems. This method was first used by Tate in 1864. The drop weight method mechanism is very similar to the maximum bubble pressure method. The only difference is that in the drop weight method a liquid (instead of gas) is coming out from the bottom of a capillary tube. During the experiments, a stream of drops of liquid falls slowly from the tip of a capillary tube having a radius of approximately 2-3 mm (Figure

C.15). For the liquid to be able to detach from the surface of the tube, it should be massive enough to defeat the interfacial force. As long as the weight of the liquid is less than the ST force, the drop remains attached to the tube, but when it reaches the critical mass m, it will detach and fall down. Therefore, the drops falling from the tip of the tube have critical sizes. In theory, a single drop enlarges to the size that the gravity and capillary forces are in equilibrium and if it grows more than this critical size, it will detach from the tube. By measuring the weight of the fallen drop ST or IFT can be calculated. The simplest force balance expression for the detachment moment, which is called Tate’s law, is written as follows:

264

== 2πrmgW γ (C.107) where the r is the capillary tube radius and m is the mass of the drop. If the capillary tube is not wetted by the liquid, the internal radius appears in Eqn. (C.107); otherwise the external radius appears in the equation (Butt et al., 2006). The tip of the capillary tube should be very smooth. Mostly glass capillary tubes are used for ST and IFT measurements using the drop weight method, but sometimes metal tubes are applied if needed.

Figure C.15: The drop weight technique (Butt et al., 2006)

In reality and as shown in Figure C.15 it is impossible to apply Eqn. (C.107) without any correction because the drop detaches partially from the capillary tube, which means some part of the drop mass is still attached to the tube. Therefore, the real weight of the drop

(W’) obtained from the experiment is less than W obtained from Eqn. (C.107). In order to modify this equation a correction parameter (f) should be added. Applying f into the system, Eqn. (C.107) changes to:

== 2'' π γfrgmW (C.108)

Or:

265

'gm (C.109) γ = 2πrf where f is related to two dimensionless ratios similar to the one in the ring method:

r r (C.110) = Ff ),( 1 a V 3

Although the drop weight technique is very simple and easy to use, it is very sensitive to vibration. Vibration in the system can cause premature separation of the drop from the tip of the capillary tube and therefore there will be a significant error in the measured drop weight.

To obtain higher degrees of precision, in practice the mass of a defined number of drops is calculated and divided by the number of drops (Butt et al., 2006). The drop weight method eliminates prolonged aging of the liquid surface because a fresh drop forms during the measurement; however, a very rapid formation of drops should be avoided, otherwise the weight of each drop will be too large. This method is also suitable for ST measurement of solutions as well as viscous liquids.

In order to simplify the experiments and calculations, a reference liquid with known ST can be used. Consequently, there will be no need to calculate r and f for every capillary.

So, the ST of the unknown liquid will be:

W γ (C.111) 1 = 1 W 2 γ 2

266 where subscripts 1 and 2 denote the liquid with the known ST and the liquid under experiment, respectively. Since each liquid has different ST and interaction with the solid, this approach is just an approximate.

The drop weight method is also applicable for IFT measurements between two immiscible liquids. In this application, the effect of buoyancy forces should be considered. The liquid coming out of the capillary tube is usually the liquid with a higher density and the other liquid forms the bulk fluid. The liquid with the lower density can also be the drop phase, but the capillary tube should be inverted. When a certain number of drops detached from the tube, their volume will be measured. The IFT can be calculated from:

ΔρgV (C.112) γ = drops 2πrf where Δρ represents the density difference between two liquids.

C.8. The drop or bubble shape method

The shape of drops or bubbles attached to a solid surface and immersed in a second fluid is very important in obtaining the interfacial properties of the S-L-F system. The interfacial forces tend to make a bubble or a drop spherical so it can have the minimum surface interfacial area. On the other hand, the effect of other external forces such as gravitational forces can deform the drop or bubble. Analyzing and studying the shape of immersed drops or bubbles can lead to IFT and contact angle measurement. Drops and

267 bubbles attached to a solid surface are described in two different categories; pendant drops and sessile drops (Figure C.16).

Figure C.16: a: Pendant drop, b: Pendant bubble, c: Sessile drop, d: Sessile bubble

Pendent drops are the tear shape drops or bubbles clinging from a tip or a solid surface.

They elongate as they grow larger because of the hydrostatic pressure. The pendent drop method is a very popular method for measuring IFT and it is used for different projects and purposes for a long time.

Sessile drops are seated on the top of a solid surface and sessile bubbles are trapped by a solid ceiling. Like the pendent drop method, the sessile drop method is also based on the analysis of drop or bubble deformation caused by gravity.

268

The Young-Laplace fundamental equation for capillary under gravitational and interfacial forces is in form of Eqn. (C.68) and in dimensionless form Eqn. (C.68) will change to

Eqn. (C.69). In Eqn. (C.69) β is called the Bond number and is given in Eqn. (C.70).

Therefore, the ST or IFT at the liquid interface can be related to the drop shape through the following equation (Erbil, 2006):

Δρgb2 (C.113) γ = β where b is the radius of the interface at the apex (origin). IFT can be determined by iterative calculations of Eqn. (C.113).

The sessile drop and pendant drop methods are the most general experimental methods which are applicable for measurements of both IFT and contact angle simultaneously in many research areas. In early works for determining IFT and contact angle from the shape of the drops, accuracy and consistency were the main problems in this method.

The sessile and pendant drops were analyzed and discussed separately. In order to be able to calculate the IFT and contact angle, numerous series of tables containing the shape parameters were generated by Bashforth and Adams (Bashforth et al., 1892) for sessile drops and by Fordham (Fordham, 1948) for pendant drops. They generated drop profiles with known values of IFT and contact angle and tabulated the data for further research on the IFT and contact angle of different fluids. The tables were suitable for a certain range of size and shape of drops. In order to obtain the interfacial properties, the experimental information had to be interpreted with the relevant tables of data, if

269 available. More tables were generated by Padday (Padday, 1969) and also by Hartland and Hartley (Hartland et al., 1976). In their book, they collected and described various approaches and solutions for obtaining IFT of axisymmetric liquid-fluid interfaces of different shapes and sizes. The result of their work is tabulated in the book. They also modified the tables for determining IFT and contact angle for sessile and pendant drops.

Finally, they extended these tables for different shapes and sizes of interfaces. Obtaining

IFT from the tabulated data caused a significant error, mainly because of the data acquisition. The input data to use the tables consisted of limited critical points on the interface instead of considering the whole profile. The selected points corresponded to special features and they had to be determined with high precision. Also if determination of contact angle was needed, the location of the S-L-F contact should have been accurately verified. Such measurements were not easily gained.

Malcolm and Paynter (Malcolm et al., 1981) used another analytical approach to calculate the IFT and contact angle of non-wetting sessile drops (θ > 90o). This approach was very limited because it was not applicable to pendant drops or the wetting sessile drops (θ < 90o).

Maze and Burnet (Maze et al., 1969; Maze et al., 1971) started the development of a numerical method to calculate the IFT and contact angle for sessile drops. In the new technique, a nonlinear regression procedure was used to calculate the drop shape so that it could fit a number of arbitrarily selected and measured coordinate points on the interface profile. The best numerical fit was determined by varying two parameters in the system

270 of the equations. Their method needed reasonable initial estimates of the drop shape and size parameters. They used the tables of Bashforth and Adams for the initial estimates.

The error function they used was summing just the square of horizontal distances, which caused large errors in the final answer because of the downward gravity effects.

(ADSA). The development of this method was a great achievement in surface sciences, because no particular values are required for any parameters, i.e. the surface tension, the radius of curvature at the apex and the coordinates of the origin, as they are calculated in the program. This numerical method combines and unifies both the sessile and pendant drop techniques without using any of the previously generated tables.

Their new technique relied on numerical integration of the Young-Laplace equation of capillarity in presence of gravity forces (Eqn. (C.68)). The objective function defined in

ADSA optimization scheme was equal to the sum of the squares of the normal distances between the calculated Laplacian curve and the measured curved points obtained from the image of the interface. During the calculation procedure IFT was considered as an adjustable parameter that the final value of it would be determined at the end of the optimization. The objective function was minimized by numerically solving a system of non linear algebraic equations. The minimum value of the objective function showed that the best calculated curve with respect to the experimental one was found. The IFT and

271 contact angle were obtained from the shape of the calculated drop. This method is also called ADSA-P (profile) (del Río et al., 1998) that calculates the IFT, contact angle, the drop volume, radius of curvature and the interface area.

ADSA has many advantages comparing to the other techniques that are accuracy, simplicity, versatility and many more. It is suitable for determining the IFT and contact angle of L-L and L-G systems of all range of fluids. It iss applicable to low and high temperatures and covers a wide range of pressures from vacuum to very high pressures.

It is also suitable for aging systems where IFT and contact angle of the drop are needed with time and also for dynamic measurements of IFT and contact angle. Just small amount of liquid is needed to produce the drop and a very small piece of solid substrate is required to place the drop on it (Skinner et al., 1989; Cheng et al., 1990; Li et al., 1992;

Río et al., 1997; Holgado-Terriza et al., 1999).

On the other hand, the first generation of ADSA did not have a high accuracy. The profile points extracted from the image of the experimental drops were generated by using either manual digitizing tablets or a telescope equipped with a goniometer eye piece. The precision of these methods is approximately ±2o (Li et al., 1992); hence the coordinate points were significantly inaccurate (Spelt et al., 1987). Manual digitization was a time consuming procedure, as well. The results of measuring IFT and contact angle from manually processed images showed that reproducibility of IFT is less than contact angle. The other source of error was optical distortion that negatively affects the

272 sharpness of the taken image (Cheng et al., 1990). Therefore, the first generation of image processing procedure was modified with substituting a digital image processor.

The schematic of the experimental setup using digital image processing for both pendant and sessile drops is shown in Figure C.17 (Li et al., 1992). In this procedure a video source such as a camera or a video cassette captured an analog image of the drop. The analog image was converted to a digital format and stored in a computer. Then the digital image processor automatically found the drop profile coordinates and sent the points to ADSA-P program to optimize the shape of the calculated drop and calculate the

IFT and contact angle. Also, the optical distortion due to the camera and lenses deficiency was corrected.

The coordinate points first were generated by using global thresholding. This technique converted the gray level intensity of the image to numbers 0 to 255 where 0 was the darkest color (black) and 255 was the lightest point (white). Then the program defined a global threshold number. The pixels containing numbers lower than the threshold were considered as the drop (object) and the rest were the background (Cheng et al., 1990).

The problem was that the global threshold was very sensitive to the lighting condition of the system. In addition, since global thresholding assumed just one object in the image, it was not applicable for sessile drop experiments where the solid surface was the second object. Therefore, an adaptive threshold was introduced that varied for each image based on the intensity of the color throughout the image. The adaptive thresholding method

273 was not sensitive to lighting, but still had problems with the presence of the solid substrate.

Figure C.17: Experimental setup for pendant and sessile drop measurements using digital image processor (Li et al., 1992)

The third method called gradient magnitude solved all problems of thresholding (Cheng et al., 1990; Li et al., 1992). It was applicable to both pendant and sessile drops, it needed minimal computation time and memory, and it was insensitive to lighting condition. The gradient magnitude method relied on the analysis of small square portion of the digital image preferably 3x3 pixel points. The X and Y coordinates of each pixel point were considered as two dimensions and the gray level intensity associated with

274 each pixel represented the third dimension of the image definer matrix. This scheme was called edge operator. The edge operator started by fitting a best least-squares plane through nine gray level pixels of the 3x3 array. Then, it calculated the slope of this plane in both X and Y directions to obtain the overall gradient of the plane. This gradient represents the gradient of the gray level at the centre point of the 3x3 array of pixels. The procedure was repeated for the whole image so that each pixel of the image would be the central point of a 3x3 array, and therefore a gray level gradient for each pixel was created.

This leads to a gradient image in which the drop profile points were the pixels with maximum gradient. In other words, the drop profile was approximated by the pixels having the maximum gray level gradient.

There were two types of operators to process the 3x3 operators. They were named Sobel and Prewitt operators (Li et al., 1992). The Sobel operator is based on a least-squares plane with weighted average while Prewitt gives an equal weight to a 3x3 array. The

Sobel operator was superior for diagonal edges; therefore it was selected for the edge operator.

In their later works, Neumann and his collaborators modified the ADSA technique and produced different versions for various applications. They are: ADSA-CD (Skinner et al., 1989) (contact diameter) for drops with very small contact angles (θ < 30o) where the drop is almost flat and acquiring profile points is impossible. Input parameters for

ADSA-CD are the IFT, contact diameter and drop volume. It calculated the value of the contact angle.

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Another modification of ADSA was ADSA-MD (Moy et al., 1991) (maximum diameter) developed specially for non wetiing drops (θ > 90o). It was very similar to ADSA-CD and calculated the value of the contact angle.

ADSA-D (Río et al., 1997) (diameter) was very similar to ADSA-MD but more general.

This modification was based on contact or maximum diameter of the drop.

ADSA-HD (Río et al., 1997) (height and diameter) was also in this category, but it was applicable to any type of drop. Any measured height and diameter could be used for the calculations of the contact angle value.

ADSA-TD (Amirfazli et al., 2000) (two diameters) was very similar to ADSA-D but IFT as an input was eliminated by analyzing the shape of two sessile drop profiles from the same liquid on the same solid but with different sizes.

ADSA-CB (Prokop et al., 1998; Zuo et al., 2004a; Zuo et al., 2004b) (captive bubble) was developed for very low ST values when the pendant drops cannot hang from the capillary tube.

ADSA-EF (Bateni et al., 2005; Bateni et al., 2006) (electric field) was a modification for the situations with electric field presence.

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Finally, ADSA-IP (Kalantarian et al., 2009) (imperfect profile) was a branch of ADSA for imperfect shapes of the interface profile. Also another branch that was suitable for nearly spherical shape drops (Hoorfar et al., 2006) was also developed.

On top of all these, a new numerical method for finding the local contact angle of a drop that is axially non-symmetric was created for cases with partial wetting for given values of drop volume and capillary length (Iliev et al., 2006). In this new technique there are no special restrictions: the solid substrate can be heterogeneous or rough or both, horizontal or tilted. The method was intended to be used in conjunction with experimental results similar to ADSA-D and ADSA-P methods.

Since ADSA-CB configuration is generally used for film balance applications (low ST) and for investigating the dynamic behaviour of both adsorbed and spreading films (Zuo et al., 2004a), the images are not very clear. Therefore, different edge detection techniques were created to minimize the curve fitting error. Peokop and collaborators (Prokop et al.,

1998) developed the first generation of captive bubble method. The edge detection method used in the beginning was the global thresholding. In order to identify the bubble’s surface profile, a fifth order polynomial fitting (FOPF) was generated that converted the profile to a smoother one. The method worked by establishing a centre for the bubble profile and calculating the distance of each edge pixel from the centre. These distances were fitted to a fifth order polynomial. Then any point that was more than 3δ away from the fitted polynomial was rejected as an outlier (Zuo et al., 2004a).

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The significant disadvantage of the edge detectors in the first generation of captive bubble method was a poor noise resistancy. Therefore, a new technique was developed by Zuo and coworkers (Zuo et al., 2004a) that substituted a Canny edge detector (Zuo et al., 2004b) for the thresholding technique. Canny edge detector became popular due to its three optimal criteria for performance evaluation: 1) good detection, 2) strong localization, and 3) single response to an edge (Zuo et al., 2004a). Also, instead of FOPF a novel edge smoothing technique named axisymmetric liquid fluid interface-smoothing

(ALFI-S) (Zuo et al., 2004b) was used. The replacing method was worked very well in noisy conditions with low image contrast. ALFI-S is a novel edge smoothing technique that compares the experimental shape of a drop or a bubble with the best fitted Laplacian curve. The curve generated using the Young-Laplace equation of capillarity (Zuo et al.,

2004a). The experiments were performed on the aging processes of lung surfactant systems (Zuo et al., 2004b). These systems were very noisy and the image contrast was very low. The combination of the Canny edge detector and ALFI-S used in the new version of the captive bubble method satisfied the limitations. The Canny edge detector is very robust against noise and ALFI-S is very powerful in smoothing the Laplacian curve (Zuo et al., 2004b). The most recent schematic of ADSA-CB technique is shown in

Figure C.18.

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Figure C.18: Schematic of ADSA-CB (Zuo et al., 2004a)

Along with the improvement of ADSA different modifications, similar techniques and more precise edge detectors were developed. They are automated polynomial fit (APF), axisymmetric liquid fluid interface (ALFI), and theoretical image fitting analysis (TIFA).

In the following paragraphs these techniques are briefly explained.

Preliminary tests showed that in contact angle calculations the use of straight lines or low-order polynomials for fitting the profile points in the contact area produced large contact angle calculation error. Also, the methods were very sensitive to the number of points used. Therefore, a high-order polynomial should have been considered. In APF method variable number of points was used to implement a high-order polynomial for the contact area (del Río et al., 1998). The basics of APF method was fitting a polynomial curve to the drop or meniscus meridian profile and calculating the slope of the curve at the contact point, which would lead to the value of the contact angle. The APF scheme

279 consisted of two main modules; the first one was to generate a high resolution image of the S-L-F system and extracted the interface profile. The second module fitted a polynomial curve to the contact part of the drop profile and calculated the contact angle using the slope of the theoretical curve at the contact point. The results of contact angle measurements by ADSA and APF indicated good agreements (Bateni et al., 2003).

In ALFI method unique shape of the axisymmetric liquid-fluid interface was calculated by simultaneous numerical integration. It generated a Laplacian profile of the liquid- fluid interface for both sessile and pendant drops (Río et al., 1997). ALFI is a very useful tool to produce the Laplacian data tables and plots similar to the ones done by Hartland and Hartley (Hartland et al., 1976) and by Bashforth and Adams (Bashforth et al., 1892).

This technique is usually used to test and evaluate different drop shape analysis methods

(Río et al., 1997).

TIFA (Cabezas et al., 2004; Cabezas et al., 2005) methodology is the most recent technology in image processing and has been developed to eliminate the edge detection module of ADSA. In this approach IFT and contact angle were calculated by fitting the experimental image to the theoretical one that was a black and white (binary) image. The theoretical image was generated by solving the Young-Laplace equation of capillarity.

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APPENDIX D: COMPUTER ROUTINES

D.1. Image Processing

%************************************************************************** %Author: Maryam Rajayi, [email protected] %Last Modification: 2009 10 29

%Routine leads the calculations for finding the edge in a digital image. %**************************************************************************

function xy = ImageProcessing(filename) filename = input('Enter the file name:'); thresh = 0.3; I = imread(filename); %Reads the image of the drop I = I(:,:,1); %The initial image is 3D therefore this line makes it a 2D image bw = edge(I,'canny',thresh); %bw is a logical matrix as same order as I. ...It contains the edge detected by Canny method and threshod of 0.3 fig1 = imshow(bw); %It shows the image of the edge bw1 = +bw; % bw1 changes the logical bw matrix to double (0 and 1 numbers) dim = size(I); %Returns the order of the image n = 0; for j = 1 : dim(1,2) for i = 1 : dim(1,1) if bw1(i,j) > 0 %If bw1(j,j) >0 it means that the point we are at is an edge point n = n + 1; xy(n,1) = j; %Returns the X of edge points xy(n,2) = dim(1,1) ‐ i + 1; %Returns the Y of edge points, flipped vs. x coordinate end; end; end; %**************************************************************************

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D.2. ADSA-P Routine

ADSA-P routine is consisted of four modules: main, interface, functions, and integrator.

They are as follow:

D.2.1. Main Module

'************************************************************************** 'Author: Maryam Rajayi, [email protected] 'Last Modification: 2009 11 12 ' 'Module to set the code related to the Routines that lead the calculation 'order using the functions and interfaces. 'Declaration of Public constants and variables is contained in this module 'too. '**************************************************************************

'************************************************************************** Option Explicit '... Force the declaration of all variables Option Base 1 '... All arrays and vectors start at index = 1 '**************************************************************************

'************************************************************************** 'Declaration of Global variables that can be used in any part of the code Public q1 As Double '... X0 ‐ x coordinate of the origin Public q2 As Double '... Z0 ‐ z coordinate of the origin Public q3 As Double '... R0 ‐ Radius of curvature at the origin Public q4 As Double '... (Drho*g*R0^2)/gamma) ‐ Shape parameter

'Miscellaneous Constants Global Const PI As Double = 3.141592654 '... A value for Pi Global Const NoEQ As Integer = 3 '... Number of ODEs in the system Global Const NoSteps As Integer = 50 '... Number of intervals for the ODE '... Integration

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'... Defines a structure for the settings and parameters needed to use the '... integrator functions Type ODESettings SolveMethod As String '... Numerical method to solve the ODE system Init As Double '... Initial value for the ODE Final As Double '... End value for the ODE StepSize As Double '... Size of the integration step for the ODE End Type '**************************************************************************

'************************************************************************** Sub Solve_ODESystem(ByRef x_dimless() As Double, ByRef z_dimless() As _ Double, ByRef AllResults() As Double, ByRef FirstCell _ As Range) 'Routine to drive the program to solve the ODE System that represents the 'drop in the ADSAP methodology

'... Declaration of variables Dim ODE_Settings As ODESettings '... Integration settings Dim y(1 To NoEQ) As Double '... y() at each step Dim dy(1 To NoEQ) As Double '... Change in y() for each step Dim y0(1 To NoEQ) As Double '... Initial y()

Dim X As Double '... Arc length

Dim NoPoints As Long '... Number of Point Coordinates Dim X_Coord() As Double '... X coordinates Dim Z_Coord() As Double '... Z coordinates Dim x_shifted() As Double '... x coordinates shifted to X0 = 0 Dim z_shifted() As Double '... z coordinates shifted to Z0 = 0 Dim col As Long, row As Long '... Address for the First Data Point

Dim check As Boolean '... Boolean Dim i As Integer, j As Integer '... Counters

'... Initialization of all parameters

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'... Initialize the ODE Settings for the Integration ODE_Settings.StepSize = 0.01 ODE_Settings.Init = 0# ODE_Settings.Final = PI

'... Load the Coordinate Vectors Call Load_DropCoordinates(X_Coord, Z_Coord, FirstCell)

'... Shift the coordinates NoPoints = UBound(X_Coord) ReDim x_shifted(NoPoints) ReDim z_shifted(NoPoints) ReDim x_dimless(NoPoints) ReDim z_dimless(NoPoints) For i = 1 To NoPoints x_shifted(i) = Abs(X_Coord(i) ‐ q1) z_shifted(i) = Abs(Z_Coord(i) ‐ q2) '... Now make them dimensionless x_dimless(i) = x_shifted(i) / q3 z_dimless(i) = z_shifted(i) / q3 Next

'... Actual Calculations begin

'... Initialize the ODEs y(1) = 0.00001 '... x coordinate y(2) = 0# '... z coordinate y(3) = 0# '... phi turning angle

j = 1 '... row

'... Record the Initial conditions ReDim AllResults(NoEQ + 1, j) AllResults(1, j) = X '... curvature length AllResults(2, j) = y(1) '... x coordinate

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AllResults(3, j) = y(2) '... z coordinate AllResults(4, j) = y(3) '... phi turning angle

'... Calculations for the rest of the integration steps are made in a '... loop Do While X < ODE_Settings.Final '... Increase the counter for the output j = j + 1

'... Calculate the next step check = RK4order(X, y(), ODE_Settings)

'... Record the results from the current step ReDim Preserve AllResults(NoEQ + 1, j) AllResults(1, j) = X '... curvature length AllResults(2, j) = y(1) '... x coordinate AllResults(3, j) = y(2) '... z coordinate AllResults(4, j) = y(3) '... phi turning angle

Loop

End Sub '**************************************************************************

'************************************************************************** Public Sub ShowExcelSolver() 'Loads default problem settings and runs the Excel Solver 'The Routine must be called when the First X point cell is selected

Dim FirstCell As Range '... Top Left Data Point Dim strObjective As String '... String defining the Objective '....Function cell Dim strParams As String '... String defining the Parameters the '... Solver can Change Dim lngRow As Long '... Cell's Row Dim lngCol As Long '... Cell's Column

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'... Get the Cell's Information Set FirstCell = ActiveCell

'... Determine the Cells address using the pre‐defined layout With FirstCell lngRow = .row lngCol = .Column End With

With ActiveSheet strObjective = .Cells(lngRow + 5, lngCol + 7).Address strParams = .Cells(lngRow ‐ 1, lngCol + 7).Address & ":" & _ .Cells(lngRow + 2, lngCol + 7).Address End With

SolverReset '... Clear all Solver settings

'... Set the Target function, the Manipulated variables and show the '... Solver SolverOkDialog SetCell:=strObjective, MaxMinVal:=2, ValueOf:=0, _ ByChange:=strParams

End Sub '**************************************************************************

D.2.2. Interface Module

'************************************************************************** 'Author: Maryam Rajayi, [email protected] 'Last Modification: 2009 11 12 ' 'Module to set the code related to the interface between the Spreasheets 'and the data needed to perform the calculations. Mainly to load/output 'data.

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'**************************************************************************

'************************************************************************** Sub Load_DropCoordinates(ByRef X() As Double, ByRef Z() As Double, _ ByRef FirstCell As Range) 'This Subroutine loads the Coordinates for the Current Drop.

Dim lngCol As Long, lngRow As Long '... Address for the First Data Point Dim count As Integer

'... Get the Address for the First Data Point lngCol = FirstCell.Column lngRow = FirstCell.row

count = 1 '... Load the data from the spreadsheet With Worksheets(FirstCell.Worksheet.Name) Doe Whil .Cells(lngRow + count ‐ 1, lngCol) <> "" And _ IsNumeric(.Cells(lngRow + count ‐ 1, lngCol)) '... Redefine the Vector/Arrays ReDim Preserve X(count) ReDim Preserve Z(count) '... Append the values to the Vector/Arrays X(count) = .Cells(lngRow + count ‐ 1, lngCol).Value Z(count) = .Cells(lngRow + count ‐ 1, lngCol + 1).Value '... Update the counter count = count + 1 Loop End With

End Sub

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'**************************************************************************

'************************************************************************** Public Sub GenerateCurves() 'Generates Curves on a specific worksheet

On Error GoTo local_Err

Dim TheResults() As Double '... Matrix that holds the calculated curve Dim x_dimless() As Double '... x coordinates dimensionless (X/R0) Dim z_dimless() As Double '... z coordinates dimensionless (Z/R0) '... Hold the values of q1, q2, q3 Dim q1 As Double, q2 As Double, q3 As Double '... Hold the values for the current Experimental Point Dim X As Double, Z As Double

Dim wsData As Worksheet '... Worksheet where the Experimental Data are Dim FirstCell As Range '... Top aLeft Dat Point Dim NoPoints As Long '... Number of Experimental Data Points Dim strSheetName As String '... Name of the Worksheet where the '... curve will be printed Dim intRowStart As Integer '... First Row where to Start printing Values Dim intColStart As Integer '... First Column where to Start printing '... Values Dim intColOffset As Integer '... Column offset between the First data '... cell and the Q parameters

Dim i As Long, j As Long, k As Long

'... Define the Column Offset based on the pre‐defined layout intColOffset = 7

'... Reference the Experimental Data Worksheet Set wsData = Application.ActiveSheet Set FirstCell = Application.ActiveCell q1 = wsData.Cells(FirstCell.row ‐ 1, FirstCell.Column + _

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intColOffset).Value q2 = wsData.Cells(FirstCell.row, FirstCell.Column + _ intColOffset).Value q3 = wsData.Cells(FirstCell.row + 1, FirstCell.Column + _ intColOffset).Value q4 = wsData.Cells(FirstCell.row + 2, FirstCell.Column + _ intColOffset).Value

'... Initialize Worksheet strSheetName = wsData.Name & "_AllCurves" Call PrepareWorksheet(strSheetName) intRowStart = 8 '... Has to be greater than 6 (i.e. 7 or more) intColStart = 2

'... Count the Rows of Data NoPoints = CountNumericRowsDown(FirstCell)

'... Solve the ODE System to obtain a Curve Call Solve_ODESystem(x_dimless, z_dimless, TheResults, FirstCell)

'... Print the results to a Spreadsheet With Worksheets(strSheetName) '... Bring the parameters from the Experimental Data Worksheet .Cells(intRowStart ‐ 5, intColStart + 2).Value = "q1 =" .Cells(intRowStart ‐ 5, intColStart + 3).Value = q1 .Cells(intRowStart ‐ 4, intColStart + 2).Value = "q2 =" .Cells(intRowStart ‐ 4, intColStart + 3).Value = q2 .Cells(intRowStart ‐ 3, intColStart + 2).Value = "q3 =" .Cells(intRowStart ‐ 3, intColStart + 3).Value = q3 .Cells(intRowStart ‐ 2, intColStart + 2).Value = "q4 =" .Cells(intRowStart ‐ 2, intColStart + 3).Value = q4

'... Print headings for the results .Cells(intRowStart ‐ 6, intColStart).Value = _ wsData.Cells(FirstCell.row ‐ 4, FirstCell.Column).Text .Cells(intRowStart ‐ 1, intColStart).Value = "s"

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.Cells(intRowStart ‐ 1, intColStart + 1).Value = "x" .Cells(intRowStart ‐ 1, intColStart + 2).Value = "z" .Cells(intRowStart ‐ 1, intColStart + 3).Value = "phi"

'... Now the Actual Results For i = 1 To 4 '... Number of Columns in the TheResults Matrix For j = 1 To UBound(TheResults, 2) '... Number of rows .Cells((intRowStart ‐ 1) + j, (intColStart ‐ 1) + i) = _ TheResults(i, j) Next Next

'... Bring the Experimental Data Points '... Headings .Cells(intRowStart ‐ 1, intColStart + 5).Value = "X" .Cells(intRowStart ‐ 1, intColStart + 6).Value = "Z" .Cells(intRowStart ‐ 1, intColStart + 7).Value = "~x" .Cells(intRowStart ‐ 1, intColStart + 8).Value = "~z" For i = 1 To NoPoints '... Experimental Data X = wsData.Cells((FirstCell.row ‐ 1) + i, _ FirstCell.Column).Value .Cells((intRowStart ‐ 1) + i, intColStart + 5).Value = X Z = wsData.Cells((FirstCell.row ‐ 1) + i, _ FirstCell.Next.Column).Value .Cells((intRowStart ‐ 1) + i, intColStart + 6).Value = Z '... Scaled Data .Cells((intRowStart ‐ 1) + i, intColStart + 7).Value = _ Abs((X ‐ q1) / q3) '... Always plot on the positive side .Cells((intRowStart ‐ 1) + i, intColStart + 8).Value = _ Abs((Z ‐ q2) / q3) '... Always plot on the positive side Next End With

'... Generate the Plots. Send the First cell with numbers Call PlotCurves(intRowStart, intColStart, strSheetName)

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Exit Sub

local_Err: Call gErrorMessage("Interface.GenerateCurves", Err.Number, _ Err.Description)

End Sub '**************************************************************************

'************************************************************************** Public Sub GenerateOptimizedCurves() 'Generates the Optimized Curves on the current worksheet

On Error GoTo local_Err

Dim TheResults() As Double '... Matrix that holds the calculated curve Dim x_dimless() As Double '... x coordinates dimensionless (X/R0) Dim z_dimless() As Double '... z coordinates dimensionless (Z/R0) '... Hold the values for the current Experimental Point Dim X As Double, Z As Double

Dim wsData As Worksheet '... Worksheet where the Experimental Data are Dim FirstCell As Range '... Top Left Data Point Dim NoPoints As Long '... Number of Experimental Data Points Dim strSheetName As String '... Name of the Worksheet where the curve '... will be printed Dim intRowStart As Integer '... First Row where to Start printing '... Calculated Values Dim intColStart As Integer '... First Column where to Start printing '... Calculated Values Dim intColOffset As Integer '... Column offset between the First data '... cell and the Q parameters

Dim i As Long, j As Long, k As Long

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'... Define the Column Offset based on the pre‐defined layout intColOffset = 7

'... Reference the Experimental Data Worksheet Set wsData = Application.ActiveSheet Set FirstCell = Application.ActiveCell q1 = wsData.Cells(FirstCell.row ‐ 1, FirstCell.Column + _ intColOffset).Value q2 = wsData.Cells(FirstCell.row, FirstCell.Column + _ intColOffset).Value q3 = wsData.Cells(FirstCell.row + 1, FirstCell.Column + _ intColOffset).Value q4 = wsData.Cells(FirstCell.row + 2, FirstCell.Column + _ intColOffset).Value

'... Initialize Worksheet strSheetName = wsData.Name intRowStart = FirstCell.row '... Same as the Measured Data intColStart = FirstCell.Column + 3 '... Pre‐defined layout

'... Count the Rows of Data NoPoints = CountNumericRowsDown(FirstCell)

'... Solve the ODE System to obtain a Curve Call Solve_ODESystem(x_dimless, z_dimless, TheResults, FirstCell)

'... Print the results to a Spreadsheet With Worksheets(strSheetName)

'... Actual Results For i = 2 To 3 '... Number of Columns in the TheResults Matrix '... (only x and z) For j = 1 To UBound(TheResults, 2) '... Number of rows .Cells((intRowStart ‐ 1) + j, (intColStart ‐ 2) + i) = _ TheResults(i, j) Next

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'... Bring the Scaled Experimental Data Points '... Headings .Cells(intRowStart + NoPoints + 5, intColStart ‐ 3).Value = "~x" .Cells(intRowStart + NoPoints + 5, intColStart ‐ 2).Value = "~z"

For i = 1 To NoPoints '... Experimental Data X = wsData.Cells((FirstCell.row ‐ 1) + i, _ FirstCell.Column).Value Z = wsData.Cells((FirstCell.row ‐ 1) + i, _ FirstCell.Next.Column).Value '... Scaled Data .Cells((intRowStart + NoPoints + 5) + i, intColStart ‐ 3).Value _ = Abs((X ‐ q1) / q3) '... Always plot on the positive side .Cells((intRowStart + NoPoints + 5) + i, intColStart ‐ 2).Value _ = Abs((Z ‐ q2) / q3) '... Always plot on the positive side Next End With

'... Generate the Plots. Send the First cell with numbers Call PlotOptimizedData(intRowStart, intColStart, strSheetName)

Exit Sub

local_Err: Call gErrorMessage("Interface.GenerateOptimizedCurves", Err.Number, _ Err.Description)

End Sub '**************************************************************************

'************************************************************************** Public Sub PlotOriginalData() 'This Routine Plots the original measured data in the same SpreadSheet

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'The Routine must be called when the First X point cell is selected

On Error GoTo local_Err

Dim CurrentChart As Chart '... The Current Plot Dim FirstCell As Range '... Top Left Data Point Dim xApex As Range '... x coordinate of the Apex (Q1) Dim lngRow As Long '... Cell's Row Dim lngCol As Long '... Cell's Column Dim NoPoints As Long '... Number of Points in the Data Series Dim ExpPoints As Long '... Number of Experimental Points Dim dblTop As Double, dblLeft As Double '... Chart's Location Dim intRow As Long, intCol Asg Lon '... Rown and Column positions Dim strSheet As String '... Current Worksheet's Name Dim strChartName As String '... Current Plot's Name Dim strDataSet As String '... Current Data Set's Name Dim cht As Object '... A chart object

'... Get the Cell's Information Set FirstCell = ActiveCell With FirstCell dblTop = .Top + 5 * .Height '... Want it to be 5 Rows below dblLeft = .Left '... Want it to be in the same Column lngRow = .row intRow = .row lngCol = .Column intCol = .Column End With strSheet = ActiveSheet.Name Set xApex = Worksheets(strSheet).Cells(intRow ‐ 1, intCol + 7)

'... Count the Rows of Data NoPoints = CountNumericRowsDown(FirstCell)

'... Add and Configure the Chart With Worksheets(strSheet)

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'... This is where the Title was printed strDataSet = .Cells(intRow ‐ 4, intCol).Text '... Get a "unique" name for the plot strChartName = strSheet & "_" & strDataSet & "_Measured"

'... Let's find if the Chart already exists For Each cht In ActiveSheet.ChartObjects If cht.Name = strChartName Then '... Chart already exists so delete it cht.Delete Exit For End If Next

'... Now add the Chart Set CurrentChart = .ChartObjects.Add(dblLeft, dblTop, 216, 216).Chart CurrentChart.HasTitle = True CurrentChart.ChartTitle.Caption = strDataSet '... The Name should be accessed through the chart's parent CurrentChart.Parent.Name = strChartName

'... Add the Measured Data Curve CurrentChart.SeriesCollection.NewSeries CurrentChart.SeriesCollection(1).Name = "Measured" '... "$A$2:$A$12" format CurrentChart.SeriesCollection(1).XValues = "=" & strSheet & "!" & _ FirstCell.Address & ":" & .Cells(lngRow + NoPoints ‐ _ 1, lngCol).Address '... "$B$2:$B$12" format CurrentChart.SeriesCollection(1).Values = "=" & strSheet & "!" & _ FirstCell.Next.Address & ":" & .Cells(lngRow + _ NoPoints ‐ 1, lngCol + 1).Address

'... Add the Apex Point CurrentChart.SeriesCollection.NewSeries CurrentChart.SeriesCollection(2).Name = "Apex"

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CurrentChart.SeriesCollection(2).XValues = "=" & strSheet & "!" & _ xApex.Address CurrentChart.SeriesCollection(2).Values = "=" & strSheet & "!" & _ .Cells(xApex.row + 1, xApex.Column).Address

'... Configure the chart CurrentChart.ChartType = xlXYScatter CurrentChart.SetElement (msoElementLegendRightOverlay) CurrentChart.Legend.Top = 130 CurrentChart.Legend.Left = 140

CurrentChart.SeriesCollection(1).MarkerSize = 3 CurrentChart.SeriesCollection(2).MarkerSize = 3

End With

Exit Sub

local_Err: Call gErrorMessage("Interface.PlotOriginalData", Err.Number, _ Err.Description)

End Sub '**************************************************************************

'************************************************************************** Private Sub PlotOptimizedData(ByVal intRow As Integer, ByVal intCol As _ Integer, ByVal strSheet As String) 'This Routine Plots the Scaled measured data along with the Optimized curve 'in the same SpreadSheet 'The Routine must be called when the First "X calc" point cell is selected

On Error GoTo local_Err

Dim CurrentChart As Chart '... The Current Plot Dim FirstCell As Range '... Top Left Data Point

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Dim FirstExp As Range '... x coordinate of the Apex (Q1) Dim lngRow As Long '... Cell's Row Dim lngCol As Long '... Cell's Column Dim NoPoints As Long '... Number of Points in the Data Series Dim ExpPoints As Long '... Number of Experimental Points Dim dblTop As Double, dblLeft As Double '... Chart's Location Dim strChartName As String '... Current Plot's Name Dim strDataSet As String '... Current Data Set's Name Dim cht As Object '... A chart object

'... Get the Cell's Information Set FirstCell = ActiveCell With FirstCell dblTop = .Top + 20 * .Height '... Want it to be 20 Rows below dblLeft = .Left '... Want it to be in the same Column lngRow = .row lngCol = .Column End With

'... Count the Rows of Data NoPoints = CountNumericRowsDown(FirstCell) Set FirstExp = Worksheets(strSheet).Cells(intRow + NoPoints + 6, lngCol)

'... Add and Configure the Chart With Worksheets(strSheet) '... This is where the Title was printed strDataSet = .Cells(intRow ‐ 4, lngCol).Text '... Get a "unique" name for the plot strChartName = strSheet & "_" & strDataSet & "_Scaled"

'... Let's find if the Chart already exists For Each cht In ActiveSheet.ChartObjects If cht.Name = strChartName Then '... Chart already exists so delete it cht.Delete Exit For

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End If Next

'... Add the Measured Data Curve CurrentChart.SeriesCollection.NewSeries CurrentChart.SeriesCollection(1).Name = "Calculated" '... "$A$2:$A$12" format CurrentChart.SeriesCollection(1).XValues = "=" & strSheet & "!" & _ .Cells(intRow, lngCol + 3).Address & ":" & _ .Cells(intRow + 316, lngCol + 3).Address '... "$B$2:$B$12" format CurrentChart.SeriesCollection(1).Values = "=" & strSheet & "!" & _ .Cells(intRow, lngCol + 4).Address & ":" & _ .Cells(intRow + 316, lngCol + 4).Address

'... Add the Apex Point CurrentChart.SeriesCollection.NewSeries CurrentChart.SeriesCollection(2).Name = "Experimental" CurrentChart.SeriesCollection(2).XValues = "=" & strSheet & "!" & _ FirstExp.Address & ":" & .Cells(intRow + 2 * NoPoints _ + 5, lngCol).Address CurrentChart.SeriesCollection(2).Values = "=" & strSheet & "!" & _ FirstExp.Next.Address & ":" & .Cells(intRow + 2 * _ NoPoints + 5, lngCol + 1).Address

'... Configure the chart CurrentChart.ChartType = xlXYScatter CurrentChart.SetElement (msoElementLegendRightOverlay) CurrentChart.Legend.Top = 130

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CurrentChart.Legend.Left = 140

CurrentChart.SeriesCollection(1).MarkerSize = 3 CurrentChart.SeriesCollection(2).MarkerSize = 3

End With

Exit Sub

local_Err: Call gErrorMessage("Interface.PlotOptimizedData", Err.Number, _ Err.Description)

End Sub '**************************************************************************

'************************************************************************** Private Sub PlotCurves(ByVal intRow As Integer, ByVal intCol As Integer, _ ByVal strSheet As String) 'This Routine Plots the Points generated withe th GenerateCurves routine

On Error GoTo local_Err

Dim CurrentChart As Chart '... The Current Plot Dim FirstCell As Range '... Top Left Data Point Dim FirstExp As Range '... Top Left Experimental Scaled point Dim lngRow As Long '... Cell's Row Dim lngCol As Long '... Cell's Column Dim NoPoints As Long '... Number of Points in the Data Series Dim ExpPoints As Long '... Number of Experimental Points Dim dblTop As Double, dblLeft As Double '... Chart's Location

'... Get the Cell's Information Set FirstCell = Worksheets(strSheet).Cells(intRow, intCol) Set FirstExp = Worksheets(strSheet).Cells(intRow, intCol + 7) With FirstCell

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dblTop = .Top + 5 * .Height '... Want it to be 5 Rows below dblLeft = .Left '... Want it to be in the same Column lngRow = .row lngCol = .Column End With

'... Count the Rows of Data NoPoints = CountNumericRowsDown(FirstCell) ExpPoints = CountNumericRowsDown(FirstExp)

'... Add and Configure the Chart With Worksheets(strSheet)

Set CurrentChart = .ChartObjects.Add(dblLeft, dblTop, 216, 216).Chart CurrentChart.HasTitle = True '... This is where the Title was printed CurrentChart.ChartTitle.Caption = .Cells(intRow ‐ 6, intCol).Text

'... Add the Generated Curve CurrentChart.SeriesCollection.NewSeries CurrentChart.SeriesCollection(1).Name = "Calc" '... "$A$2:$A$12" CurrentChart.SeriesCollection(1).XValues" = "= & strSheet & "!" & _ FirstCell.Next.Address & ":" & .Cells(lngRow + _ NoPoints ‐ 1, lngCol + 1).Address '... "$B$2:$B$12" CurrentChart.SeriesCollection(1).Values = "=" & strSheet & "!" & _ FirstCell.Next.Next.Address & ":" & .Cells(lngRow + _ NoPoints ‐ 1, lngCol + 2).Address

'... Add the Experimental Points CurrentChart.SeriesCollection.NewSeries CurrentChart.SeriesCollection(2).Name = "Exp" CurrentChart.SeriesCollection(2).XValues = "=" & strSheet & "!" & _ FirstExp.Address & ":" & .Cells(lngRow + ExpPoints ‐ _ 1, lngCol + 7).Address

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CurrentChart.SeriesCollection(2).Values = "=" & strSheet & "!" & _ FirstExp.Next.Address & ":" & .Cells(lngRow + _ ExpPoints ‐ 1, lngCol + 8).Address

'... Configure the chart CurrentChart.ChartType = xlXYScatter CurrentChart.SetElement (msoElementLegendRightOverlay) CurrentChart.Legend.Top = 130 CurrentChart.Legend.Left = 140

CurrentChart.SeriesCollection(1).MarkerSize = 3 CurrentChart.SeriesCollection(2).MarkerSize = 3

End With

Exit Sub local_Err: If False Then Resume Next End If Call gErrorMessage("Interface.PlotCurves", Err.Number, Err.Description) End Sub '**************************************************************************

'************************************************************************** Public Sub PrepareWorksheet(ByVal wsName As String, _ Optional ByVal wsAfter As String = "") 'Prepares a worksheet by deleting all its contents. If it doesn't exists 'it creates wa ne worksheet

'... wsName ‐ The name of the worksheet to prepare/create '... wsAfter ‐ The name of the worksheet after which the new one will be '... created. If empty the new worksheet will be placed after the last '... worksheet

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On Error GoTo local_Err

Dim ws As Worksheet Dim exists As Boolean

exists = False

'... Look for the Worksheet and clear it For Each ws In Worksheets If ws.Name = wsName Then ws.Cells.Clear If ws.ChartObjects.count > 0 Then ws.ChartObjects.Delete End If exists = True End If Next

'... Create a new worksheet and place it in the proper location If Not exists Then If wsAfter = "" Then Application.Sheets.Add After:=Sheets(Sheets.count) Else Application.Sheets.Add After:=Sheets(wsAfter) End If Application.ActiveSheet.Name = wsName End If

Exit Sub

local_Err: Call gErrorMessage("Interface.PrepareWorksheet", Err.Number, _ Err.Description)

End Sub '**************************************************************************

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D.2.3. Functions Module

'************************************************************************** 'Author: Maryam Rajayi, [email protected] 'Last Modification: 2009 11 12 ' 'Module to define the various functions that will be exposed as Excel Custom 'Functions 'All other functions necessary to do calculations are included here '**************************************************************************

'************************************************************************** Public Function GetContactAngle(ByVal par1 As Double, ByVal par2 As Double, _ ByVal par3 As Double, ByVal par4 As Double, _ ByVal FirstCell As Range, ByVal ContactPoint _ As Range) As Double 'This function calculates the Contact Angle by solving the ODE System with 'the optimized parameters q1, q2, q3 and q4.

'... par1 : q1 '... par2 : q2 '... par3 : q3 '... par4 : q4 '... FirstCell : Top left Cell of the Measured Coordinates '... ContactPoint : Cell of the X Coordinate for the Measured Contact Point

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Dim NoPoints As Long '... Number of Point Coordinates Dim lngCol As Long, lngRow As Long '... Address for the First Data Point Dim idxMinDist As Long Dim MinDist As Double Dim j As Integer, k As Integer

'... Load the function arguments to the global variables q1 = par1 q2 = par2 q3 = par3 q4 = par4

'... Solve the ODE System to obtain a Curve Call Solve_ODESystem(x_dimless, z_dimless, TheResults, FirstCell)

'... Get the Address for the Contact Data Point lngCol = ContactPoint.Column lngRow = ContactPoint.row

'... Find the Curvature Distance to each of the Points If Not (lngRow = FirstCell.row) Then NoPoints = lngRow ‐ FirstCell.row + 1 '... Only the Contact Point Else NoPoints = 1 '... The Contact Point is the First Cell End If

'... Initialize counters j = UBound(TheResults, 2) ReDim Distance(1, j) As Double idxMinDist = 0 '... Initialize values MinDist = 1E+30 '... Initialize values

For k = 1 To j '... Probably don't need this anymore as we are using Absolute values '... in the coordinates If x_dimless(NoPoints) < 0 Then

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Distance(1, k) = 0.5 * ((TheResults(2, k) + (x_dimless(NoPoints) _ )) ^ 2 + (TheResults(3, k) ‐ (z_dimless(NoPoints))) ^ 2) Else Distance(1, k) = 0.5 * ((TheResults(2, k) ‐ (x_dimless(NoPoints) _ )) ^ 2 + (TheResults(3, k) ‐ (z_dimless(NoPoints))) ^ 2) End If Next

'... Find the minimum distances andt ge the summation for all points Dim DistError As Double DistError = 0# For k = 1 To j '... Take into account only the first twirl If (MinDist > Distance(1, k)) And (TheResults(4, k) <= PI) Then MinDist = Distance(1, k) idxMinDist = k End If Next DistError = DistError + MinDist

'... Return the value GetContactAngle = TheResults(4, idxMinDist) '... Radians '... Correct phase taken into account GetContactAngle = 180# ‐ GetContactAngle * (180 / PI) '... Degrees

End Function '**************************************************************************

'************************************************************************** Public Function GetSumOfErrors(ByVal par1 As Double, ByVal par2 As Double, _ ByVal par3 As Double, ByVal par4 As Double, _ ByVal FirstCell As Range) As Double 'This function calculates the Sum of Errors between each measured point and 'the closest point in a curve calculated with q1, q2, q3 and q4.

'... par1 : q1

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'... par2 : q2 '... par3 : q3 '... par4 : q4 '... FirstCell : Top left Cell of the Measured Coordinates

Dim TheResults() As Double '... Matrix that holds the calculated curve Dim x_dimless() As Double '... x coordinates dimensionless (X/R0) Dim z_dimless() As Double '... z coordinates dimensionless (Z/R0) Dim NoPoints As Long '... Number of Point Coordinates Dim i As Integer, j As Integer, k As Integer

'... Load the function arguments to the global variables q1 = par1 q2 = par2 q3 = par3 q4 = par4

'... Solve the ODE System to obtain a Curve Call Solve_ODESystem(x_dimless, z_dimless, TheResults, FirstCell)

'... Find the Curvature Distance to each of the Points NoPoints = UBound(x_dimless) j = UBound(TheResults, 2) '... Number of rows

ReDim Distance(NoPoints, j) As Double, MinDist(NoPoints) As Double ReDim idxMinDist(NoPoints) As Integer

For i = 1 To NoPoints idxMinDist(i) = 0 '... Initialize values MinDist(i) = 1E+30 '... Initialize values For k = 1 To j If x_dimless(i) < 0 Then Distance(i, k) = 0.5 * ((TheResults(2, k) + (x_dimless(i) _ )) ^ 2 + (TheResults(3, k) ‐ (z_dimless(i))) ^ 2) Else Distance(i, k) = 0.5 * ((TheResults(2, k) ‐ (x_dimless(i) _

306

)) ^ 2 + (TheResults(3, k) ‐ (z_dimless(i))) ^ 2) End If Next Next

'... Find the minimum distances and get the summation for all points Dim DistError As Double DistError = 0# For i = 1 To NoPoints For k = 1 To j '... Take into account only the first twirl If (MinDist(i) > Distance(i, k)) And (TheResults(4, k) <= PI) Then MinDist(i) = Distance(i, k) idxMinDist(i) = k End If Next DistError = DistError + MinDist(i) Next

'... Return the value GetSumOfErrors = DistError

End Function '**************************************************************************

'************************************************************************** Public Function GetGamma(ByVal pQ3 As Double, ByVal pQ4 As Double, _ ByVal DeltaRho As Double, ByVal aG As Double, _ ByVal Pixels As Double, ByVal Length As Double) _ As Double 'Function to calculate the Interfacial Tension (Gamma)

'... pQ3: Optimized Q3 parameter (Radius of curvature at the origin) '... pQ4: Optimized Q4 parameter (Shape factor) '... DeltaRho: Density difference between the fluids in [kg/m^3] '... aG: Acceletation o gravity in [m/s^2]

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'... Pixels: Number of pixels in the selected length '... Length: Length equivalent to the number of pixels in [mm]

Dim num As Double, scaledR0 As Double

'... Scale the Radius of curvature scaledR0 = pQ3 * Length / Pixels '... in [mm] scaledR0 = scaledR0 / 1000# '... in [m]

'... Calculate the numerator num = DeltaRho * aG * (scaledR0 ^ 2)

'... Return the function value GetGamma = num / pQ4

End Function '**************************************************************************

'************************************************************************** Public Function GetXApexGuess(ByVal FirstCell As Range) As Double 'Function to Guess the X coordinate for the Apex frome th Measured values

'... FirstCell : Top left Cell of the Measured Coordinates

Dim X_Coord() As Double '... X coordinates Dim Z_Coord() As Double '... Z coordinates Dim i As Long '... Vector index

Call Load_DropCoordinates(X_Coord, Z_Coord, FirstCell)

'... Do a rudimentary search i = GetMinMaxIndex(Z_Coord, "Max") '... Look for the highest Y

GetXApexGuess = X_Coord(i) '... Return the X coordinate

End Function

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'**************************************************************************

'************************************************************************** Public Function GetYApexGuess(ByVal FirstCell As Range) As Double 'Function to Guess the X coordinate for the Apex from the Measured values

'... FirstCell : Top left Cell of the Measured Coordinates

Dim X_Coord() As Double '... X coordinates Dim Z_Coord() As Double '... Z coordinates Dim gi As Lon '... Vector index

Call Load_DropCoordinates(X_Coord, Z_Coord, FirstCell)

'... Do a rudimentary search i = GetMinMaxIndex(Z_Coord, "Max") '... Look for the highest Y

GetYApexGuess = Z_Coord(i) '... Return the Y coordinate

End Function '**************************************************************************

'************************************************************************** Public Function GetContactCellGuess(ByVal FirstCell As Range) As Range 'Function to Guesse th Cell where the X coordinate for the contact point is

'... FirstCell : Top left Cell of the Measured Coordinates

Dim X_Coord() As Double '... X coordinates Dim Z_Coord() As Double '... Z coordinates Dim i As Long '... Vector index

Call Load_DropCoordinates(X_Coord, Z_Coord, FirstCell)

'... Do a rudimentary search i = GetMinMaxIndex(Z_Coord, "Min") '... Look for the smallest Y

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'... Return the cell Set GetContactCellGuess = ActiveSheet.Cells(FirstCell.row + i ‐ 1, _ FirstCell.Column)

End Function '**************************************************************************

'************************************************************************** Public Function GetContactCellGuessAddress(ByVal FirstCell As Range) _ As String 'Function to Guess the Cell where the X coordinate for the contact point is

'... FirstCell : Top left Cell of the Measured Coordinates

Dim X_Coord() As Double '... X coordinates Dim Z_Coord() As Double '... Z coordinates Dim i As Long '... Vector index

Call Load_DropCoordinates(X_Coord, Z_Coord, FirstCell)

'... Do a rudimentary search i = GetMinMaxIndex(Z_Coord, "Min") '... Look for the smallest Y

'... Return the cell address GetContactCellGuessAddress = ActiveSheet.Cells(FirstCell.row + i ‐ 1, _ FirstCell.Column).Address

End Function '**************************************************************************

'************************************************************************** Public Function CalcDerivatives(X As Double, y() As Double, dy() As Double) _ As Boolean 'Function that contains the Dimensionless ODE System

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'... The Equations are defined in the paper: '... Determination of Surface Tension and Contact Angle from the Shapes of '... Axisymmetric Fluid Interfaces; Rotenberg, T., L. Boruvka, & A.W. Neumann '... Journal of Colloid and Interface Science, v. 93, n. 1, pp. 169‐183, 1983

'... dy(1) : dx/ds = cos(phi) Eq. 12a '... dy(2) : dz/ds = sin(phi) Eq. 12b '... dy(3) : dphi/ds = 2 + ((Drho*g*R0^2)/gamma)*z ‐ sin(phi)/x Eq. 12c

'... Calculate the ODE System dy(1) = Cos(y(3)) dy(2) = Sin(y(3)) dy(3) = 2# + q4 * y(2) ‐ Sin(y(3)) / y(1)

CalcDerivatives = True

End Function '**************************************************************************

'************************************************************************** Public Function CountNumericRowsDown(ByRef TopLeftCell As Range) As Long 'This function counts the number of Consecutive Rows that contain Numeric 'Values Starting on the Cell provided and going Down.

Dim lngCol As Long, lngRow As Long '... Address for the First Cell Dim count As Integer

'... Get the Address to start lngCol = TopLeftCell.Column lngRow = TopLeftCell.row

count = 0 '... Count the Rows With Worksheets(TopLeftCell.Worksheet.Name) Do While .Cells(lngRow + count, lngCol) <> "" And _ IsNumeric(.Cells(lngRow + count, lngCol))

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'... Update the counter count = count + 1 Loop End With

CountNumericRowsDown = count End Function '**************************************************************************

'************************************************************************** Private Function GetMinMaxIndex(ByRef vector() As Double, ByVal strMinMax _ As String) As Long 'Generic function to return the Vector Index of a Minimum or Maximum

'... vector(): The vector in which the search will happen '... strMinMax: Type of search

Dim i As Long, idx As Long Dim dTiny As Double Dim dHuge As Double

dTiny = 1E+300 '... Initial value dHuge = ‐1E+300 '... Initial value

Select Case strMinMax Case "Min" For i = 1 To UBound(vector) If vector(i) < dTiny Then idx = i dTiny = vector(i) End If Next Case "Max" For i = 1 To UBound(vector) If vector(i) > dHuge Then idx = i

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dHuge = vector(i) End If Next End Select

GetMinMaxIndex = idx

End Function '**************************************************************************

'************************************************************************** Public Sub gErrorMessage(Location As String, errNumb As Long, errDesc _ As String) 'Renders an Error Message and presents it to the user in a Message Box

'... Location ‐ Function or Routine calling this routine '... errNumb ‐ Error number '... errDesc ‐ Error description

MsgBox ("An error occurred in " & Location & vbCrLf & "ErrNum: " & _ CStr(errNumb) & vbCrLf & "ErrDesc: " & errDesc)

End Sub '**************************************************************************

D.2.4. Integrator Module

'************************************************************************** 'Author: Maryam Rajayi, [email protected] 'Last Modification: 2009 11 12 ' 'Module to define the various numerical methods that will be used 'throughout the code to complete calculations. '**************************************************************************

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'************************************************************************** Public Function RK4order(X As Double, y() As Double, Settings As _ ODESettings) As Boolean 'This function implements the Fourth Order Runge‐Kutta Method to solve 'Ordinary Diferential Equations. References are Chapter 16 of the Numerical 'Recipes in C; Cambridge University Press; Electronic version and Chapter '25 of the Numerical Methods for Engineers; Chapra, Steven; 3rd ed. McGraw‐ 'Hill

Dim h As Double Dim k1(1 To NoEQ) As Double, k2(1 To NoEQ) As Double Dim k3(1 To NoEQ) As Double, k4(1 To NoEQ) As Double Dim i As Integer Dim yk1(1 To NoEQ) As Double, yk2(1 To NoEQ) As Double Dim yk3(1 To NoEQ) As Double, yk4(1 To NoEQ) As Double Dim dy(1 To NoEQ) As Double Dim check As Boolean

'... eLoad th Step Size for the ODE system solving h = Settings.StepSize

'... Implement the Fourth Order Runge‐Kutta Numerical method '... CalcDerivatives is the function containing the ODE System check = yk(y(), k1(), 0, yk1()) check = CalcDerivatives(X, yk1(), dy()) For i = 1 To NoEQ k1(i) = h * dy(i) Next i

check = yk(y(), k1(), 0.5, yk2()) check = CalcDerivatives(X + h * 0.5, yk2(), dy())

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For i = 1 To NoEQ k2(i) = h * dy(i) Next i

check = yk(y(), k2(), 0.5, yk3()) check = CalcDerivatives(X + h * 0.5, yk3(), dy()) For i = 1 To NoEQ k3(i) = h * dy(i) Next i

check = yk(y(), k3(), 1, yk4()) check = CalcDerivatives(X + h, yk4(), dy()) For i = 1 To NoEQ k4(i) = h * dy(i) Next i

'... Update the values of y For i = 1 To NoEQ y(i) = y(i) + k1(i) / 6# + (k2(i) + k3(i)) / 3# + k4(i) / 6# Next i '... Update the value of x X = X + h

RK4order = True

End Function '**************************************************************************

'************************************************************************** Public Function yk(y() As Double, k() As Double, weight As Double, newy() _ As Double) As Boolean 'This function updates the value of the vector y() to be used in the RK 'routine

Dim j As Integer

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For j = 1 To NoEQ newy(j) = y(j) + k(j) * weight Next j

yk = True

End Function '**************************************************************************

316

APPENDIX E: BITUMEN PHYSICAL PROPERTIES

In order to calculate the IFT of bitumen-brine, the densities of both liquids in different temperatures are needed. In the following sections the measured densities of both

Athabasca and Cold Lake bitumen are reported in forms of tables and charts. The measurements are done for the bitumen in initial conditions as well as bitumen after adding 1%, 2%, and 4% of Idododecane as a doping. Also the density values of distilled water, 5%, 10%, and 20% CaCl2 brines are measured and reported for different temperatures. All the density values are reported in kg/m3. In addition to the densities, the viscosity values of both Athabasca and Cold Lake bitumen are measured and reported for different temperatures.

E.1. Athabasca Bitumen Viscosity

Table E-1: Athabasca bitumen viscosity Temperature oC Viscosity cp Viscosity Pa.S

15 646000.0 646.00

25 135500.0 135.50

50 2187.5 2.19

75 283.3 0.28

100 52.9 0.05

125 32.3 0.03

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Figure E.19: Athabasca bitumen viscosity

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E.2. Athabasca Bitumen Density

Table E-2: Athabasca bitumen density Athabasca Athabasca Athabasca

Temperature Athabasca Bitumen+1% Bitumen+2% Bitumen+4%

oC Bitumen (Vol) (Vol) (Vol)

Idododecane Idododecane Idododecane

15 1.0062 1.0081 1.0101 1.0140

25 1.0004 1.0023 1.0042 1.0080

30 0.9964 0.9983 1.0002 1.0040

40 0.9941 0.9960 0.9978 1.0015

50 0.9918 0.9936 0.9955 0.9991

Figure E.20: Athabasca bitumen density

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For each set of density measurements the best fit and coefficient of determination (R) has been calculated and showed as follow. They can be used for calculating the density of the bitumen at higher temperatures.

Athabasca bitumen:

ρ = 0.0095T2 - 1.0242 T + 1019.5

R² = 0.9895

Athabasca bitumen + 1% Idododecane:

ρ = 0.0095 T 2 - 1.0296 T + 1021.5

R² = 0.9899

Athabasca bitumen + 2% Idododecane:

ρ = 0.0095 T 2 - 1.0351 T + 1023.5

R² = 0.9902

Athabasca bitumen + 4% Idododecane:

ρ = 0.0096 T 2 - 1.046 T + 1027.5

R² = 0.9908

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E.3. Cold Lake Bitumen Viscosity

Table E-3: Cold Lake bitumen viscosity Temperature oC Viscosity cp Viscosity Pa.S

15 632000.0 632

25 134000.0 134

50 1847.5 1.84747

75 302.1 0.30208

100 335.4 0.33536

Figure E.21: Cold Lake bitumen viscosity

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Cold Lake Bitumen Density

Table E-4: Cold Lake bitumen density Cold Lake Cold Lake Cold Lake

Temperature Cold Lake Bitumen+1% Bitumen+2% Bitumen+4%

oC Bitumen (Vol) (Vol) (Vol)

Idododecane Idododecane Idododecane

15 1.0017 1.0037 1.0057 1.0096

25 0.9939 0.9959 0.9978 1.0017

30 0.9918 0.9937 0.9957 0.9995

40 0.9878 0.9897 0.9916 0.9955

50 0.9859 0.9878 0.9897 0.9935

Figure E.22: Cold Lake bitumen density

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Cold Lake bitumen:

ρ = 0.0111T2 - 1.1677T + 1016.6

R² = 0.9981

Cold Lake bitumen + 1% Idododecane:

ρ = 0.0111T2 - 1.1717T + 1018.6

R² = 0.9981

Cold Lake bitumen + 2% Idododecane:

ρ = 0.0112T2 - 1.1757T + 1020.7

R² = 0.9982

Cold Lake bitumen + 4% Idododecane:

ρ = 0.0112T2 - 1.1838T + 1024.7

R² = 0.9983

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E.4. Brine Density

Table E-5: Brine density Temperature Distilled 5% (wt) CaCl2 10% (wt) CaCl3 20% (wt) CaCl4 oC Water

15 0.9990 1.0393 1.0805 1.1688

25 0.9961 1.0357 1.0766 1.1633

30 0.9961 1.0358 1.0763 1.1629

40 0.9909 1.0333 1.0738 1.1608

50 0.9870 1.0263 1.0720 1.1588

Figure E.23: Brine density

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For each set of density measurements the best linear fit and coefficient of determination

(R) has been calculated and showed as follow. They can be used for calculating the density of the distilled water or CaCl2 solution with different concentrations at higher temperatures.

Distilled water: y = -0.3489x + 1005

R² = 0.9631

5% CaCl2 solution: y = -0.3422x + 1045

R² = 0.9097

10% CaCl2 solution: y = -0.2341x + 1083.3

R² = 0.9661

20% CaCl2 solution: y = -0.2653x + 1171.4

R² = 0.9147