THE FLOW PROPERTIES OF BITUMEN IN THE PRESENCE OF CO2 by EHSAN BEHZADFAR B.A.Sc. Amirkabir University of Technology, Tehran, Iran, 2006 M.A.Sc. Amirkabir University of Technology, Tehran, Iran, 2008 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Chemical and Biological Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) September 2014 © Ehsan Behzadfar, 2014 ii ABSTRACT The present dissertation discusses the flow behaviour of bitumens in the presence of CO2. Firstly, the viscoelastic behaviour of bitumen is studied and an appropriate constitutive equation is identified to describe its rheological behavior. The K-BKZ constitutive equation has been shown to represent accurately the rheological properties of bitumen. Analysis of experimental results revealed that either the Papanastasiou or the Marucci form of the damping function can be used in the K-BKZ constitutive equation. Moreover, the damping function was found to be independent of temperature (0°C-50°C). Secondly, the effects of temperature, pressure, dissolved carbon dioxide and shear rate on the rheological response of bitumen are investigated by using the reduced variable method at the temperature range of –10°C to 180°C and pressures up to 15 MPa. The double–log model is found to be the most accurate equation in describing the effect of temperature on the viscosity of bitumen over a wide range of temperature while the Barus model with the temperature–dependent parameter is found to be the most appropriate correlation to represent the effect of pressure. The Fujita–Kishimato equation, resulting from the free volume concept modelling, is employed to account for the effect of dissolved CO2 on the viscosity of the bitumen–CO2 mixture. The results show that the viscosity is influenced by the temperature and saturation pressure. Thirdly, the combined pressure-decay technique with rheometry is developed to measure the diffusivity of CO2 in bitumen at the temperatures of 30˚C, 50˚C, 70˚C, 90˚C and 110˚C and saturation pressures of 2, 4 and 10 MPa. The impact of temperature on the diffusivity of CO2-bitumen systems can be described by the Arrhenius equation. The diffusivity increases with pressure at gaseous CO2 state. The increase is more dominant at lower temperatures while the diffusivity increase is 53% at 30˚C compared to 25% at 70˚C. It is shown that changing the state of CO2 impacts the diffusivity values of in bitumen while the diffusivity is higher for the liquid CO2 compared to supercritical CO2. iii PREFACE This dissertation is based on four journal articles: Chapter 5 is mainly based on a publication which has been published in Fuel: - Behzadfar, E., Hatzikiriakos, S.G. “Viscoelastic Properties and Constitutive Modeling of Bitumen” Fuel, 108, 391-399, 2013. Chapter 6 contains material from two publications: - Behzadfar, E., Hatzikiriakos, S.G. “Rheology of Bitumen: Effects of Temperature, Pressure, CO2 Concentration and Shear Rate” Fuel, 116, 578-587, 2014. - Behzadfar, E., Hatzikiriakos, S.G. “Investigation of the Viscosity of CO2-Bitumen Mixture at Different States of CO2” (under preparation). Chapter 7 is mainly based on two articles, one published in Energy and Fuels and the other one is under preparation: - Behzadfar, E., Hatzikiriakos, S.G. “Diffusivity of CO2 in Bitumen: Pressure-Decay Measurements Coupled with Rheometry” Energy & Fuels, 28 (2), 1304-1311, 2014. - Behzadfar, E., Hatzikiriakos, S.G. “Investigation of the Viscosity of CO2-Bitumen Mixture at Different States of CO2” (under preparation). The entire experimental study and data analysis have been conducted by Ehsan Behzadfar. The published articles were a collaborative effort between Ehsan Behzadfar and Prof. Savvas G. Hatzikiriakos. This dissertation was prepared by Ehsan Behzadfar, while revised and approved by Prof. Savvas G. Hatzikiriakos. iv TABLE OF CONTENTS ABSTRACT ................................................................................................................................... ii PREFACE ..................................................................................................................................... iii TABLE OF CONTENTS ............................................................................................................ iv LIST OF TABLES ...................................................................................................................... vii LIST OF FIGURES ................................................................................................................... viii NOMENCLATURE .................................................................................................................... xv ACKNOWLEDGMENTS ......................................................................................................... xix DEDICATION............................................................................................................................. xx 1 INTRODUCTION...................................................................................................................... 1 2 LITERATURE REVIEW ......................................................................................................... 4 2.1 Heavy oil and bitumen ................................................................................................... 4 2.1.1 Chemistry and structure ........................................................................................ 5 2.1.2 Fractionation of heavy oil and bitumen ................................................................ 7 2.1.3 Overall physical and chemical properties ............................................................ 8 2.1.4 Asphaltenes ......................................................................................................... 11 2.1.5 Structural models ................................................................................................ 13 2.2 Rheology of bitumen ..................................................................................................... 14 2.2.1 Early rheological techniques .............................................................................. 15 2.2.2 New techniques in evaluation of bitumen and heavy oil rheology ...................... 16 2.2.2.1 Oscillatory (dynamic) measurements .............................................. 16 2.2.2.2 Steady shear measurements ............................................................. 17 2.2.3 Effective parameters on bitumen rheology ......................................................... 17 2.2.3.1 Effect of temperature ....................................................................... 18 2.2.3.2 Effect of pressure ............................................................................ 19 2.2.3.3 Effect of shear rate .......................................................................... 21 2.2.3.4 Effect of dissolved CO2 ................................................................... 22 2.2.3.5 Effect of asphaltenes ....................................................................... 24 2.2.3.6 Effect of time (thixotropy) .............................................................. 25 2.3 Constitutive modeling of bitumen ............................................................................... 26 v 2.3.1 Mechanical models.............................................................................................. 26 2.3.2 K-BKZ model ....................................................................................................... 27 2.4 Mutual diffusivity of CO2 in bitumen ......................................................................... 31 2.4.1 Diffusivity measurement techniques .................................................................... 31 2.4.2 Pressure-decay technique ................................................................................... 32 2.4.2.1 Theory of diffusion .......................................................................... 34 3 THESIS OBJECTIVES AND ORGANIZATION ................................................................ 38 3.1 Thesis objectives ........................................................................................................... 38 3.2 Thesis organization ....................................................................................................... 39 4 MATERIALS AND METHODOLOGY................................................................................ 40 4.1 Materials ........................................................................................................................ 40 4.2 Methodology .................................................................................................................. 41 4.2.1 Rheological measurements ................................................................................. 41 4.2.3 Pressure cell set-up ............................................................................................. 45 5 RHEOLOGY AND CONSTITUTIVE MODELLING OF BITUMEN .............................. 48 5.1 Linear viscoelasticity .................................................................................................... 48 5.2 Nonlinear viscoelasticity .............................................................................................. 57 5.3 Model assessment .......................................................................................................... 62 5.3.1 Start-up of steady shear experiments .................................................................. 63 5.3.2 Cessation of steady shear flow experiments ....................................................... 63 5.4 Summary ....................................................................................................................... 65 6 RHEOLOGY OF CO2-BITUMEN MIXTURES .................................................................. 67 6.1 Effect of temperature (Ta ) ........................................................................................... 67 6.2 Effect of pressure (Pa ) ................................................................................................. 71 6.3 Effect of dissolved CO2 (Ca ) ........................................................................................ 73 6.4 Effect of shear rate (Sa ) ............................................................................................... 79 6.5 Thixotropy ..................................................................................................................... 82 6.6 Summary ....................................................................................................................... 83 7 MUTUAL DIFFUSIVITY OF CO2 IN BITUMEN .............................................................. 85 7.1 Diffusivity measurements ............................................................................................ 85 vi 7.2 Diffusivity-viscosity-temperature relationship .......................................................... 99 7.3 Summary ..................................................................................................................... 100 8 CONCLUSIONS AND CONTRIBUTIONS TO KNOWLEDGE ..................................... 102 8.1 Conclusions ................................................................................................................. 102 8.2 Contributions to knowledge ....................................................................................... 104 8.3 Recommendations for future work ........................................................................... 105 BIBLIOGRAPHY ..................................................................................................................... 106 vii LIST OF TABLES Table 2.1: Elemental analysis for core SHRP bitumens (The coding (AAA-1…) refers to the one used in the SHRP materials library) (Mortazavi and Moulthrop, 1993)................................. 5 Table 2.2: Typical H/C ratio, number average molecular weight and density for SARA fractions (Corbett, 1969; Speight, 1999)................................................................................................ 7 Table 2.3: Comparative chemical analysis of world typical oils and natural bitumens (Speight, 1999) ..................................................................................................................................... 10 Table 2.4: Correlations for bitumen viscosity as a function of temperature and pressure ........... 20 Table 2.5: Equations used to describe the effect of shear rate on the viscosity of heavy oils and bitumens by various investigators ......................................................................................... 21 Table 2.6: Selected studies on viscosity measurement of heavy oils and bitumens in the presence of CO2 ................................................................................................................................... 23 Table 2.7: Selected studies using the pressure-decay method to measure the CO2-oil diffusivity................................................................................................................................................ 32 Table 4.1. Compositional and Elemental analysis of the bitumen ............................................... 41 Table 5.1: Parameters of the generalized Maxwell model ........................................................... 52 Table 5.2: Parameters of the BSW spectrum for the bitumen ..................................................... 56 Table 7.1: Calculated parameters from the analysis of the pressure-decay experiments ............ 93 Table 7.2: Arrhenius equations for the diffusivity and viscosity of the CO2-bitumen system. ... 98 viii LIST OF FIGURES Figure 2.1: Some of functional groups present in heavy oil and bitumen structure (Branthaver et al., 1993; Quann and Jaffe, 1992) ........................................................................................... 6 Figure 2.2: Structural models of typical saturates, aromatics, resins and asphaltenes (Scotti and Montanari, 1998)..................................................................................................................... 8 Figure 2.3: Temperature dependence of bitumen density (Mochinaga et al., 2006) ..................... 9 Figure 2.4: Planar model of asphaltenes molecules (Scotti and Montanari, 1998) ..................... 12 Figure 2.5: The modified Yen model. (Left) The predominant asphaltene molecular architecture has a single, moderately large PAH with peripheral alkanes. (Center) Asphaltene molecules form asphaltene nanoaggregates. (Right) Asphaltene nanoaggregates can form clusters with aggregation numbers estimated to be ~8. The modified Yen model provides a framework to treat large numbers of diverse asphaltene studies (Mullins, 2010). ...................................... 14 Figure 2.6: Temperature–concentration (asphaltene mass fraction) phase diagram: Sketch of the phase diagram (boundaries anticipated from theory plus experimental measurements). “S” and “L” stand for solid and liquid phases, subscripts “M” and “A” denote maltenes and asphaltenes (Fulem et al., 2008a). ......................................................................................... 19 Figure 2.7: Shear thinning behaviour of heavy oil at different temperatures (Hasan et al., 2010)............................................................................................................................................... 22 Figure 2.8: Different viscoelastic mechanical models used for bitumen (a) The generalized Burger model. (b) The Huet model. (c) The Huet-Sayegh model. (d) The DBN (Di Benedetto and Neifar) model. (e) The 2S2P1D model. ........................................................ 27 Figure 2.9: (a) The schematic of bitumen structure including solid and liquid phases. The shell around the asphaltenic cores shows the interphase layer. The red arrows depict the short range connections which form the weak network; (b) The generalized Maxwell model and (c) the Zener model. .............................................................................................................. 28 Figure 2.10: Typical cylindrical geometry for the pressure-decay experiment. .......................... 35 Figure 4.1: Phase diagram of carbon dioxide. ............................................................................. 42 ix Figure 4.2. Anton Paar MCR501 rheometer. ............................................................................... 43 Figure 4.3. A schematic and picture of geometries in the pressure cell. ..................................... 44 Figure 4.5. Pressure cell set-up mounted on the rheometer. ........................................................ 46 Figure 4.6. Pressure cell and the magnetic coupling. ................................................................... 46 Figure 5.1: Storage modulus, 'G , of the bitumen versus frequency, , at selected temperatures................................................................................................................................................ 49 Figure 5.2: Loss modulus, "G , of the bitumen versus frequency, , at selected temperatures................................................................................................................................................ 50 Figure 5.3: Master curves of dynamic moduli (storage and loss) and complex viscosity of the bitumen against reduced frequency at the reference temperature of 10°C. The lines show fits of the generalized Maxwell model. ....................................................................................... 51 Figure 5.4: The shift factor values, Ta , at different temperatures obtained from the master curves at 10°C. The full and dashed lines show the Arrhenius and WLF models , respectively. .......................................................................................................................... 53 Figure 5.5: The relaxation spectrum of the bitumen at 10°C obtained from the generalized Maxwell model along with the BSW spectrum. Decomposition of the BSW spectrum is also presented. .............................................................................................................................. 54 Figure 5.6: The linear shear relaxation modulus of the bitumen, ( )G t , at 10°C ( 1 ). The dashed line shows the prediction of the generalized Maxwell model. ................................. 56 Figure 5.7: (a) The shear relaxation modulus of the bitumen, ( , )G t , after the imposition of sudden strain values, , at 0°C; (b) Superposition of the stress relaxation modulus data of Figure 5.7a to determine the damping function. ................................................................... 58 Figure 5.8: (a) The shear relaxation modulus of the bitumen, ( , )G t , after the imposition of sudden strain values, , at 10°C; (b) Superposition of the stress relaxation modulus data of Figure 5.8a to determine the damping function. ................................................................... 59 x Figure 5.9: (a) The shear relaxation modulus of the bitumen, ( , )G t , after the imposition of sudden strain values, , at 30°C; (b) Superposition of the stress relaxation modulus data of Figure 5.9a to determine the damping function. ................................................................... 60 Figure 5.10: (a) The shear relaxation modulus of the bitumen, ( , )G t , after the imposition of sudden strain values, , at 50°C; (b) Superposition of the stress relaxation modulus data of Figure 5.10a to determine the damping function. ................................................................. 61 Figure 5.11: The damping function of the bitumen, ( )h , at temperatures from 0°C to 50°C. The dashed and full lines show the fit of the Papanastasiou model using 5.4 and the prediction of the Marucci FBN (Force Balance Network) model, respectively. .................. 62 Figure 5.12: The stress growth coefficient of the bitumen, ( , )t , at different levels of shear rate, , at 10°C. The continuous lines represent the predictions of the K-BKZ model using the Papanastasiou and Marucci damping functions. ............................................................ 64 Figure 5.13: Testing the applicability of Cox-Merz rule by comparing the flow curve determined from steady shear experiments with dynamic complex modulus values, *| |G , versus angular frequency, , (dashed line) at 10°C. ................................................................................... 64 Figure 5.14: The shear stress decay coefficient, ( , )t , of the bitumen at different shear rate values, , at 10°C. The continuous lines represent the predictions of the K-BKZ model using the Papanastasiou and Marucci damping functions. .................................................. 65 Figure 6.1: (a) The zero–shear viscosity of the bitumen at different temperatures. The oscillatory data were collected in the linear viscoelastic region of the bitumen. The steady shear viscosity data were collected at the shear rate range of 0.5 to 2 s-1.The lines show fits of different functions to the experimental data. (b) The temperature shift factor, Ta , as a function of temperature using as reference temperature the value of –10°C with 65.7 10R Pa.s. .................................................................................................................. 68 Figure 6.2: (a) Thermal gravimetry analysis (TGA) and differential scanning calorimetry (DSC) of the bitumen in consecutive heating–cooling–heating cycles. (b) differential scanning calorimetry (DSC) of the bitumen and separated C5 maltenes and asphaltenes at the heating xi cycle. The temperature ramp for all measurement was 5°C/min under N2 atmosphere. There was no delay between the heating and cooling cycles. ......................................................... 70 Figure 6.3: (a) The zero–shear viscosity of the bitumen as a function of pressure at different temperatures. The dashed lines show fits of the Barus equation to the experimental data. (b) Pressure shift factor as a function of pressure at different temperatures. ............................. 72 Figure 6.4: (a) The zero–shear viscosity of the bitumen as a function of CO2 saturation pressure at different temperatures. The dashed lines show fits of combined functions (Equations 6.2, 6.3, 6.5, 6.7) to the experimental data. (b) CO2 concentration shift factor, Ca (obtained by accounting for pressure corrections shown by pa) , versus CO2 saturation pressure at different temperatures. (c, d) CO2 concentration shift factor, Ca (obtained by accounting for pressure corrections shown by pa) , versus the dissolved CO2 amount (calculated from (Mehrotra and Svrcek, 1984)) at different temperatures. The dashed lines are fits of Equation 6.5 to the experimental data. The dash–double dot line determines the border between the gaseous and supercritical (or liquid) states of CO2. The solid lines represent the proposed equation of Mehrotra and Svrcek (Mehrotra and Svrcek, 1984) for the bitumen normalized by the viscosity values of compressed bitumen (Mehrotra and Svrcek, 1986). 76 Figure 6.5: The dependence of constants of f and in Equation 6.5 on temperature. (a) Exponential equation. (b) Arrhenius equation.The dashed lines show the appropriate functions fitted to describe them as a function of temperature. ............................................ 78 Figure 6.6: The viscosity of the bitumen at different temperatures. The dashed line show the prediction of the Carreau-Yasuda model. ............................................................................. 80 Figure 6.7: The flow curves of the bitumen using various setups and type of testing at different saturation pressures at 10°C. At the legend, PP stands for parallel-plate, PR for the pressure cell, REG for set–up open to the atmosphere, SHEAR for steady shear testing and FR for frequency sweep experiment (small amplitude oscillatory shear). The power law index lies between 0.85 and 0.95 for 10°C. .......................................................................................... 81 Figure 6.8: Rotational and dynamic flow curves of the bitumen at different saturation pressures at 30°C. At the legend, PP and Vane are indicative of the measuring geometries. PR, REG, xii SHEAR and FR are abreviations for the pressure cell, regular set–up, shear sweep and frequency sweep experiment. The power law index lies between 0.91 and 0.98 for 30°C. . 82 Figure 6.9: Flow curves of the bitumen at different structural levels at saturation pressures of 0.13 and 0.92 MPa at 30°C. The shear rates in the legend represent the base shear rate at which the flow curve is built. ................................................................................................ 83 Figure 7.1: Pressure-decay experiments at 30˚C; a) initial pressure0 2.423p MPa , b) initial pressure 0 4.034p MPa and c) initial pressure MPap 57.90 . The experiment starts with diffusion under no shear and is followed up by the application of shear (10 and 30s-1) that causes mixing and enhanced diffusion. The viscosity is normalized by the viscosity value of the gas-free bitumen at the same temperature. The dashed line shows the fitted Equation 2.20 using the measured value of the equilibrium pressure,eqp, while the solid line is the fitted Equation 2.20 with the equilibrium pressure, eqp, as an adjustable variable. ............ 87 Figure 7.2: Pressure-decay experiments at 50˚C; a) initial pressure0 2.311p MPa , b) initial pressure0 5.008p MPa and c) initial pressure MPap 11.110 . The experiment starts with diffusion under no shear and is followed up by the application of shear (30, 50 and 100s-1) that causes mixing and enhanced diffusion. The viscosity is normalized by the viscosity value of the gas-free bitumen at the same temperature. The dashed line shows the fitted Equation 2.20 using the measured value of the equilibrium pressure,eqp, while the solid line is the fitted Equation 2.20 with the equilibrium pressure, eqp, as an adjustable variable. ... 88 Figure 7.3: Pressure-decay experiments at 70˚C; a) initial pressure0 2.244p MPa , b) initial pressure0 4.794p MPa and c) initial pressure MPap 396.100 . The experiment starts with diffusion under no shear and is followed up by the application of shear (30, 50 and 100s-1) that causes mixing and enhanced diffusion. The viscosity is normalized by the viscosity value of the gas-free bitumen at the same temperature. The dashed line shows the fitted Equation 2.20 using the measured value of the equilibrium pressure,eqp, while the solid line is the fitted Equation 2.20 with the equilibrium pressure, eqp, as an adjustable variable. ... 90 xiii Figure 7.4: Pressure-decay experiments at 90˚C; initial pressure MPap 13.110 . The experiment starts with diffusion under no shear and is followed up by the application of shear (100s-1) that causes mixing and enhanced diffusion. The viscosity is normalized by the viscosity value of the gas-free bitumen at the same temperature. The dashed line shows the fitted Equation 2.20 using the measured value of the equilibrium pressure,eqp, while the solid line is the fitted Equation 2.20 with the equilibrium pressure, eqp, as an adjustable variable................................................................................................................................................ 91 Figure 7.5: Pressure-decay experiments at 110˚C; initial pressure MPap 13.110 . The experiment starts with diffusion under no shear and is followed up by the application of shear (100s-1) that causes mixing and enhanced diffusion. The viscosity is normalized by the viscosity value of the gas-free bitumen at the same temperature. The dashed line shows the fitted Equation 2.20 using the measured value of the equilibrium pressure,eqp, while the solid line is the fitted Equation 2.20 with the equilibrium pressure, eqp, as an adjustable variable. .. 92 Figure 7.6: Measured diffusivities against equilibrium pressures at different temperatures. The circles show the thermodynamic state of CO2. ..................................................................... 95 Figure 7.7: a) Measured and PHC (Perturbed Hard Chain) predicted (solid lines) solubility of CO2 in bitumen. Open symbols: Cold Lake bitumen (Yu et al., 1989), full symbols: Cold Lake bitumen (Mehrotra and Svrcek, 1988), and half-filled symbols: Peace River bitumen (Han et al., 1992). b) The density of carbon dioxide as a function of pressure at different temperatures, Measured and PHC (Perturbed Hard Chain) predicted (solid lines) solubility of CO2 in bitumen. Open symbols: Cold Lake bitumen (Yu et al., 1989), full symbols: Cold Lake bitumen (Mehrotra and Svrcek, 1988), and half-filled symbols: Peace River bitumen (Han et al., 1992). ................................................................................................................. 96 Figure 7.8: Measured diffusivities and viscosities against inverse of temperature at equilibrium pressures of about 2, 4 and 10 MPa. The dashed lines show the Arrhenius equations fitted to every data set......................................................................................................................... 97 xiv Figure 7.9: Various groups of parameters plotted as a function of temperature. The dashed lines are fitted lines to the experimental data. The viscosity symbols bit denotes the viscosity of the neat bitumen. ................................................................................................................... 99 xv NOMENCLATURE aC Concentration shift factor aP Pressure shift factor aS Shear rate shift factor aT Temperature shift factor A Interface area, [m2] b1 Model parameter b2 Model parameter c Concentration, [mol/m3] c* Instantaneous saturation concentration, [mol/m3] C1 Model parameter, [K-1] C-1 Finger strain tensor C2 Model parameter, [K] csat Saturation concentration, [mol/m3] D Diffusion coefficient, [m2/s] Ea Activation energy, [kJ/mole] g Gravitational acceleration, [m/s2] G Relaxation modulus, [Pa] G* Complex modulus, [Pa] G’ Elastic modulus (storage modulus), [Pa] G” Viscous modulus (loss modulus), [Pa] Gi Relaxation modulus, [Pa] 𝐺𝑁0 Plateau modulus, [Pa] h Damping function H Heat flow, [W/g] k Crowding factor, [Pa.s] L Length, [m] m Memory function, [Pa/s] m Model parameter mg Mass of diffusing gas, [kg] xvi N Brunt–Väisälä frequency, [s-1] N Number of modes ne Slope of spectrum at long-time region ng Slope of spectrum at short-time region P Penetration depth, [m] p Pressure, [MPa] p0 Initial pressure, [MPa] Peq Equilibrium pressure, [MPa] ∆p Gauge pressure, [Pa] PI Penetration index R Universal gas constant, [JK-1mol-1] RA Diffusing particle radius, [m] Re Reynolds number Ri Richardson number Ricr Critical Richardson number s Integral variable, [s] T Temperature, [°C] t time, [s] t’ Integral variable, [s] Tr Reference temperature, [°C] TR&B Ring and ball softening temperature, [°C] Vg Volume of diffusing gas, [m3] z Diffusion axis, [m] Zg Compressibility factor Greek Letters 𝛼 Model parameter 𝛽 Model parameter 𝛽 Piezoviscous coefficient, [Pa-1] 𝛽 Pressure effectivity constant, [Pa-1] xvii 𝛾 shear deformation γ̇ shear rate, shear deformation rate, [s-1] 𝜂 Viscosity, [Pa.s] η0,𝐶𝑅 Zero-shear rate viscosity at reference concentration, [Pa.s] η0,𝑇𝑅 Zero-shear rate viscosity at reference temperature, [Pa.s] η0,𝑝𝑅 Zero-shear rate viscosity at reference pressure, [Pa.s] η0,C Zero-shear rate viscosity, [Pa.s] η0,p Zero-shear rate viscosity, [Pa.s] η0,R Reference zero-shear rate viscosity, [Pa.s] η0,T Zero-shear rate viscosity, [Pa.s] η0 Atmospheric viscosity, [Pa.s] η0 Zero-shear rate viscosity, [Pa.s] η𝑖 i-th mode of parsimonious viscosity, [Pa.s] 𝜂− Shear stress decay coefficient, [Pa.s] 𝜂+ Shear stress growth coefficient, [Pa.s] [𝜂] Intrinsic viscosity, [Pa.s] |𝜂∗| Complex viscosity, [Pa.s] 𝜃 Gas contribution to free volume increase 𝜆 Model parameter λ0 Rouse relaxation time, [s] λi i-th mode of parsimonious relaxation modulus, [s] λi Relaxation time, [s] λl Shortest Relaxation time, [s] λmax Longest relaxation time, [s] 𝜇 Viscosity, [Pa.s] 𝜌 Density, [kg/m3] 𝜌0 Liquid density, [kg/m3] 𝜎 Particle interaction coefficient σij Stress tensor, [Pa] xviii 𝜎− Shear stress, [Pa.s] 𝜎+ Shear stress, [Pa.s] 𝜐 Velocity, [m/s] 𝜑 Volume fraction 𝜑 Fraction to free volume 𝜔 Angular frequency, [rad/s] Ι𝐶−1 First invariant of Finger strain tensor Π𝐶−1 Second invariant of Finger strain tensor Abbreviations C Carbon CO2 Carbon Dioxide EOR Enhanced Oil Recovery FBN Force Balance Network H2 Hydrogen MFT Fillers–Moonan–Tschoegl N2 Nitrogen Ni Nickel O2 Oxygen PAH Polycyclic Aromatic Hydrocarbon ppm Part Per Million S Sulphur TTS Time-Temperature Superposition V Vanadium Vapex Vapor Extraction WLF William-Landel-Ferry PM Parsimonious xix ACKNOWLEDGMENTS First I would like to express my gratitude to my supervisor, Prof. Savvas G. Hatzikiriakos who was supportive during my PhD study. I would like to thank my committee members, Prof. David Sinton, Prof. Peter Englezos and Prof. Steven Rogak, for their interest, insightful questions and helpful comments. I also thank Prof. John M. Shaw and Prof. Steve Larter for their constructive comments on this study. I would like to acknowledge Carbon Management Canada for its financial support of the project and UBC for the 4YF scholarship. Sincere gratitude to my colleagues at the Rheology lab. Besides the informative discussions, they remained supportive to my family in all moments. Last but not least I wish to express my thanks to my wife, parents, sister, brothers and friends who endlessly and unconditionally inspired and supported me. xx DEDICATION To my beloved wife and family 1 1 INTRODUCTION Fossil fuels are one of the most common sources of energy in the world. These carbon-enriched fuels are in different forms such as natural gas, petroleum and coal, differing by carbon to hydrogen ratios. Fossil fuels formed about 80% of the world’s energy consumption in 2013 where petroleum was the most common source consisting about 30%. Considering the annual growth of about 2.3% for energy consumption, despite new energy source development, fossil fuels will still provide 78% of total energy use in 2035 with the same share for petroleum in total energy consumption (IEA, 2013). Petroleum (or crude oil) varies greatly in density and viscosity because of differences in composition. It can be classified as conventional light oil, heavy oil, extra-heavy oil and bitumen whose shares are 30%, 15%, 25% and 30% of world’s oil resources, respectively (Alboudwarej et al., 2006). Because of conventional oil reserves, high cost of oil explorations, development of new effective methods for heavy oil and bitumen recovery and transformation into usable refinery feedstock, the importance of unconventional oil comes to consideration more than what was in the past (Didier Lesueur, 2009; Upreti et al., 2007). The term “bitumen” has been used in ancient literature referring to sticky materials (Tacitus, 1964). Although about two tons of oil sands (mixture of sand, clay, water, and bitumen) are required to produce one barrel (~1/8 of a ton) of oil, there is still a great opportunity to Canada, which has one of the largest deposits of heavy oil and bitumen in the world (Government of Canada, 2010). As a result of the development of Canadian oil sands reserves, 49% of Canadian oil production in 2009 was from bitumen, with an additional 16% from heavy crude oil (Government of Canada, 2010, 2009). Apart from surface mining for the reservoirs closest to the surface, there are several methods in extraction of crude oil from reservoirs, which can be categorized in three general groups, namely, primary, secondary, and tertiary (or enhanced) recovery (Meyer et al., 1998). In primary recovery, under the effect of natural pressure or gravity, oil penetrates into the wellbore, where it can be pumped out to the surface, although only about 10% of original oil in reservoir can be recovered. In secondary recovery, water or gas injection is used to drive more oil into the wellbore resulting in the production of about 20 to 40% of the reservoir’s original oil. However, enhanced (or tertiary) recovery methods are nowadays common in most oil wells which 2 include CSS (cyclic steam stimulation), SAGD (steam assisted gravity drainage), VAPEX (vapor extraction process), THAI (toe to heel air injection), and COGD (combustion overhead gravity drainage). By using enhanced (or tertiary) recovery methods, the oil recovery increases about 30 to 60% of the original oil in the deposit. Three main categories of enhanced oil recovery are thermal recovery, gas injection and chemical injection methods (Meyer et al., 1998). During thermal recovery, an effort is made to reduce the viscosity of oil by transferring heat into the reservoir. Methods including gas injection use different gases such as nitrogen, carbon dioxide and natural gas with the ability of expansion and in some cases dissolution aiming to push more oil into the wellbore by reducing oil viscosity. Chemicals are also used to lower the surface tension of oil droplets and sometimes to increase the effectiveness of waterfloods, which finally cause more efficiency in oil recovery (Meyer et al., 1998; Upreti et al., 2007). Among these methods, enhanced oil recovery by using CO2 has lately received a huge attention due to its economic and environmental advantages. From the economical point of view, CO2 is easy to access from natural resources or industrial plants. It features low viscosity, low surface tension and high miscibility with oils (Svrcek and Mehrotra, 1982). On the other hand, carbon dioxide discharges can be captured and compressed in an industrial plant, shipped via pipeline into oil fields, then injected to reservoirs which leads to storage of a huge amount of CO2 underground. CO2 can be recycled over the lifetime of the EOR projects to continue generating production from the fields. This aspect of CO2-EOR is highly valued from environmental perspective. In order to optimize the CO2-EOR in the recovery of heavy oil and bitumen, a better understanding of the rheological behaviour of heavy oils and bitumens in the presence of CO2 is needed where flow properties is investigated as a function of temperature, pressure, CO2 concentration, and shear rate. Moreover, the diffusion of CO2 in bitumens or heavy oils is a property that needs to be known in order to utilize it in reservoir simulations. In the present study, the flow properties of bitumen in the absence and presence of CO2 are studied in detail. The effects of temperature, pressure, shear rate and CO2 concentration on the rheological properties of CO2-bitumen mixtures are precisely investigated. Different types of deformation are applied to the samples to study the rheological response of bitumen in the presence of CO2. Based on the experimental results, a rheological model is formulated which is needed to 3 other transport models that are planned in the future, i.e. reservoir simulations of CO2-EOR. Furthermore, the diffusion coefficient of CO2 through bitumen is important in enhanced oil recovery and therefore it is part of the current study. Finally, the additional gain by using supercritical CO2 as opposed to CO2 in modifying the rheological properties of bitumen is also part of this work. 4 2 LITERATURE REVIEW This chapter presents the literature review of different characteristics of heavy oils and bitumen as well as their rheological properties. The chemistry and structure, fractions and components, physical and chemical properties, structural models and asphaltene fraction in typical bitumen samples are particularly discussed. Moreover, the rheological techniques used to study the flow properties of heavy oils and bitumens along with the effects of important physical and chemical parameters on their rheological behavior are reviewed. It is followed by a review of the constitutive modelling of bitumen and also the diffusivity of CO2 in bitumen. 2.1 Heavy oil and bitumen Heavy oil and bitumen are accessible in two ways either from direct oil recovery or as a residue of crude oil distillation. Although there are significant amounts of natural deposits, heavy oil and bitumen can be produced from distillation of crude oil called artificial oils, which are virtually non-volatile, viscoelastic, mostly-hydrocarbon components of crude oil. There are numerous definitions for different grades of crude oil and therefore various terminologies used are sometimes confusing. Some definitions originate in antique applications and some arise from their composition or physiochemical properties. Precisely and according to UNITAR (United Nations institute for training and research), heavy crude oil is one that its density is between 0.934 and 1 g/cm3 (between 20° and 10° in American petroleum institute API gravity scale) with a viscosity under 10 Pa.s at 15.6°C (60°F) . The crude oil with a density greater than 1 g/cm3 (smaller than 10° API) but with a viscosity less than 10 Pa.s at 15.6°C (60°F) is called extra heavy crude oil. However, a tar (synonym for bitumen) is the name of crude oil whose density is greater than 1 g/cm3 (smaller than 10° API) and its viscosity is greater than 10 Pa.s at 15.6°C (60°F) (Meyer et al., 1998). However, there are oils whose density lies in a category different from the corresponding viscosity category. These oils can be classified either based on their density or viscosity. 5 2.1.1 Chemistry and structure Heavy oil and bitumen are described as paraffinic, naphthenic or aromatic depending on the presence of a majority of saturates, cyclic or aromatic structures, respectively (Speight, 1999). Elemental analysis of these materials provides a better picture of their exact composition. They are hydrocarbon-rich oils which encompass considerable amount of nitrogen, sulphur, oxygen and metals. Table 2.1: Elemental analysis for core SHRP bitumens (The coding (AAA-1…) refers to the one used in the SHRP materials library) (Mortazavi and Moulthrop, 1993) Origin AAA-1 AAB-1 AAC-1 AAD-1 AAF-1 AAG-1 AAK-1 AAM-1 Canada USA Canada USA USA USA Venezuela USA C wt.% 83.9 82.3 86.5 81.6 84.5 85.6 83.7 86.8 H wt.% 10.0 10.6 11.3 10.8 10.4 10.5 10.2 11.2 H+C wt.% 93.9 92.9 97.8 92.4 94.9 96.1 93.9 98.0 H/C Molar 1.43 1.55 1.57 1.59 1.48 1.47 1.46 1.55 O wt.% 0.6 0.8 0.9 0.9 1.1 1.1 0.8 0.5 N wt.% 0.5 0.5 0.7 0.8 0.6 1.1 0.7 0.6 S wt.% 5.5 4.7 1.9 6.9 3.4 1.3 6.4 1.2 V ppm 174 220 146 310 87 37 1480 58 Ni ppm 86 56 63 145 35 95 142 36 Mn g/mol 790 840 870 700 840 710 860 1300 As it is presented in Table 2.1, typical bitumens and heavy oils contain carbon and hydrogen as their most abundant elements (around 90 wt.%) with the molar ratio of H/C about 1.5 which is between the ratio of an aromatic (~1) and a saturate alkane (~2). The most present polar 6 atom is sulphur (0-9 wt.%) followed by nitrogen and oxygen (each 0-2 wt.%). Traces of metals such as vanadium and nickel (less than 2000ppm) can be also detected in the structure of heavy oil and bitumen. The number average molecular weight of neat heavy oil and bitumen lies in the range of 600-1,500g/mol, however, molecules with high molecular weights of ~15,000g/mol can be found in the mixture. In spite of the high molecular weight of heavy oil and bitumen, they are not considered as polymeric molecules since they do not show properties similar to those of polymers (Barth, 1962; Domin et al., 1999; Traxler, 1961). Figure 2.1: Some of functional groups present in heavy oil and bitumen structure (Branthaver et al., 1993; Quann and Jaffe, 1992) In addition to all compounds mentioned, a few amounts of functional groups are present in the structures of heavy oil and bitumen (less than 0.1mol/l) (Branthaver et al., 1993). However, this amount can be increased through post processing and thermal treatment of heavy oil and bitumen. The functional groups in the heavy oil and bitumen structure are of various types, although they are less in amount in a way that the average number of polar atoms in heavy oil and bitumen molecule is as low as 1-3 (Jennings et al., 1992). Some of these functional groups are depicted in Figure 2.1 in which some are naturally occurring and some are formed by the oxidative aging. 7 2.1.2 Fractionation of heavy oil and bitumen Characterization of heavy oils and bitumen is an essential step for monitoring and modeling of various involved processes. In order to understand the structure of heavy oil and bitumen, different approaches have been examined. Boussingault (Boussingault, 1836, 1837) has separated components of native bitumen by distillation at 230°C into two parts. He named the liquid part as petrolenes and the solid fraction as asphaltenes. Solubility in different solvents was another criterion for separating components of heavy oil and bitumen which is still the popular method among researchers. Based on the solubility in n-heptane, heavy oil and bitumen are separated in two components. The soluble part is called maltenes (similar to petrolenes) while the insoluble part is named asphaltenes. The maltenes part, itself, is divided into three fractions of saturates, aromatics and resins. Corbett (Corbett, 1969) proposed the elution-adsorption method for separation of maltenes using solvents with various polarity and aromaticity. The full description of separation process can be found in ASTM D2007 and D3279. In spite of different experimental set-ups, different solvents and also origin of oils, each separated fraction has some common properties and general features, taking into account that their chemical structure sometimes vary widely. Table 2.2: Typical H/C ratio, number average molecular weight and density for SARA fractions (Corbett, 1969; Greaves et al., 2004; Speight, 1999) Fraction H/C Mn (g/mol) 𝜌 (g/cm3) at 20˚C Saturates 1.9 470-880 ~0.90 Aromatics 1.5 570-980 ~1.00 Resins 1.4 780-1400 ~1.07 Asphaltenes 1.1 800-3500 ~1.15 Some properties of different fractions of heavy oil and bitumen, namely number-average molecular weight, hydrogen to carbon ratio and density are presented in Table 2.2. These data are typical results for SARA (saturates, aromatics, resins, asphaltenes) fractions and can vary from oil to oil. 8 Figure 2.2: Structural models of typical saturates, aromatics, resins and asphaltenes (Scotti and Montanari, 1998) Figure 2.2 depicts some of the typical structural models developed for saturates, aromatics, resins and asphaltenes existed in heavy oils and bitumens. The size of different fractions can be widely varied from small saturate molecules to large asphaltene molecules. 2.1.3 Overall physical and chemical properties Heavy oil and bitumen are viscoelastic materials exhibiting properties of both liquids and solids (Bazyleva et al., 2010; De Kee et al., 1998; Mortazavi-Manesh and Shaw, 2014; Rojas and Castagna, 2008). Typically, the density of heavy oils and bitumens ranges from 0.934 to 1.04 g/cm3 at 15.6°C (60°F). Increasing the temperature from ambient temperature up to 120°C causes a reduction of about 7% in the density of heavy oils and bitumens as shown typically in Figure 2.3 (Mochinaga et al., 2006). The geographical location of oil deposit is one of the parameters which affects the properties of different oils (Bazyleva et al., 2010), as can be realized from Table 2.3. In addition, the colloidal structure of heavy oil and bitumen imports solid particles as an effective parameter on various properties. This means that particle features such as amount, size, size distribution, density, shape, surface chemistry, compactness of aggregates and particles behaviour in different flow fields should be taken into account. Due to their viscoelastic nature, heavy oils and bitumens exhibit shear thinning behavior at lower temperatures (below room temperature) and, hence, it does not suffice to report a single value for viscosity (Bazyleva et al., 2010; De Kee et al., 1998; Rojas and Castagna, 2008). Heavy oil and bitumen exhibit a typical glass transition at temperatures 9 around -40°C and -20°C, respectively, which may differ from oil to oil (Claudy et al., 1992; Jiménez-Mateos et al., 1996; Rojas and Castagna, 2008; Schmidt and Santucci, 1966). Temperature, T (°C)0 20 40 60 80 100 120 140Density, (gr/cm3)0.920.940.960.981.001.02 Figure 2.3: Temperature dependence of bitumen density (Mochinaga et al., 2006) Similarly it is impossible to assign a temperature for the melting point of heavy oil and bitumen since they are comprised from at least two immiscible phases and each phase has its own melting temperature. According to the data reported in the literature, for maltenes in Maya crude oil and Athabasca bitumen, the solid-liquid transitions occur over a broad range of temperature. Starting from -113°C and -63°C, respectively, whereas the temperature that whole maltenes become liquid, is around 50°C (Hasan et al., 2009). For instance, at 25°C about 10.2% and 16.8% of maltenes fraction of Maya heavy oil and Athabasca bitumen is still solid (Fulem et al., 2008a, 2008b; Hasan et al., 2009). The onset of melting for Maya and Athabasca asphaltenes is around 67°C according to calorimetric data while phase angle results do not reveal any changes from 0° until temperatures around 107°C, i.e. 65% of asphaltenes are still solid (Fulem et al., 2008a). More interestingly, at 200°C, asphaltenes can be separated from maltenes by filtering, i.e. melted asphaltenes stay together with solid part of asphaltenes (Zhao and Shaw, 2007). 10 Table 2.3: Comparative chemical analysis of world typical oils and natural bitumens (Speight, 1999) Conventional oil Medium oil Heavy oil Extra-heavy oil Natural bitumen Reservoirs (number) 8102 816 1375 57 324 Depth to top of reservoir (m) 1556 1000 975 1106 147 Coke in crude oil (wt%) 10.4 17.6 21.8 28.1 Asphalt in crude oil (wt%) 8.8 25.0 38.4 61.9 69.6 Gasoline yield (wt%) 9.2 2.8 2.0 1.3 1.4 Gas oil yield (vol%) 17.4 21.9 15.9 16.9 7.2 Residuum yield (vol%) 21.9 39.5 52.6 62.6 18.1 Pour point of crude oil (˚C) -9 -13 -7 19 32 Crude oil density (g/cm3) 0.836 0.920 0.958 1.018 1.041 Crude oil gravity (˚API) 38.1 22.3 16.3 7.5 5.0 Crude oil dynamic viscosity (mPa, 100˚F) 9 63 593 7936 292991 Resins (wt%) 6.1 19.3 24.2 21.2 25.2 Asphaltenes (wt%) 2.1 6.6 12.4 13.2 30.6 Nickel (ppm) 8.0 33.4 54.0 129.9 78.2 Vanadium (ppm) 18.2 88.2 170.9 777.7 183.0 Nitrogen (wt%) 0.1 0.2 0.5 0.6 0.7 Sulphur (wt%) 0.4 1.5 2.9 4.9 3.3 In order to use suspension theories for modelling of the viscosity of heavy oil and bitumen, the viscosity of pure maltenes should be determined. Viscosity values reported for this purpose differ significantly due to different approaches used in obtaining the data. For example, data reported based on the chemical separation of maltenes from asphaltenes are about one order of magnitude smaller than the data calculated from extrapolation to zero percent of asphaltenes in the mixture at ambient temperature (Hasan et al., 2009). Considering the fact that this difference fades at higher temperatures, it can be concluded that chemically separated maltenes may contain some 11 residual amount of solvents resulting the viscosity to be stepped down. Typical values for pure maltenes of bitumen resulted from extrapolation methods are greater than those of heavy oils, having values around 187 and 0.385 Pa.s at 25°C, for Athabasca bitumen and Maya heavy oil, respectively (Fulem et al., 2008a). On the other hand, chemically separated maltenes have viscosities around 6.14 and 0.0501 Pa.s at 25°C, respectively. Besides the viscosity of pure maltenes, the viscosities of bitumen and heavy oil greatly depend on the amount of asphaltenes particles and also temperature, e.g. temperature influence the viscosity of Athabasca bitumen and Maya heavy oil about three and two order of magnitude, respectively, levelling up from at 25°C to at 100°C (Fulem et al., 2008a). Another important flow property of bitumen is yield stress, which has been studied by some researchers (De Kee et al., 1998; Sifferman, 1979; Yan and Luo, 1987). It is proposed that formation of an interlocking three dimensional architecture of structural units in the mixture might be responsible for the observed yield stress in heavy oils and bitumens. Applying enough stress causes a break-down in these structural units and makes the material to flow. A drop in yield stress values have been reported by increasing temperature (De Kee et al., 1998). 2.1.4 Asphaltenes Boussingault (Boussingault, 1837) in 1837 proposed the name of “asphaltenes” for distillation residue of bitumen according to its similarities to asphalt. Since the chemical identity of asphaltenes is still under investigation, asphaltenes are particularly defined as a component of heavy oil or bitumen which is insoluble in n-heptane but soluble in toluene. Asphaltenes are black powder at room temperature, which comprise about 5-20 wt.% of heavy oils and bitumens. They comprise most of the solid phase present in heavy oils and bitumens considering the contribution of solid maltenes in consisting the solid phase. Their density is about 1.15 g/cm3 at 20°C (Corbett, 1969) and they have a broad and asymmetric range of number-average molecular weight from 800-3500 g/mol (Table 2.2). However, Pomerantz and co-workers (Pomerantz et al., 2009) have reported that asphaltenes have lower molecular weight of about 200-1500 g/mol and form nanoaggregates at very low concentrations. The typical H/C ratio of asphaltenes particles has a range between 0.98 and 1.56 depending on the natural resource (Koots and Speight, 1975). Asphaltenes also contain traces of some metals such as Ni, Va, Fe in the form of complexes. Pieri 12 (Pierre et al., 2004), Mullins (Mullins, 1998), and Scotti et al. (Scotti and Montanari, 1998) showed that asphaltene molecules are comprised of fused aromatic rings and pending aliphatic chains. Owing to the condensed aromatic rings, asphaltene molecules are planar which form graphite-like aggregates through π-π bonds (Scotti and Montanari, 1998). This structure is presented in Figure 2.4. Figure 2.4: Planar model of asphaltenes molecules (Scotti and Montanari, 1998) Different structures have been proposed in order to depict the molecular structure of asphaltenes. However, all particles in the mixture are aggregates or agglomerates of mono-molecules (Zhao et al., 2001). These particles have an overall negative charge which results in a better adhesion of heavy oil and bitumen onto mineral aggregates (Bauget et al., 2001; Pernyeszi et al., 1998; Petersen and Plancher, 1998). Most of the complexity in rheological behaviour of heavy oils and bitumens originates from the presence of solid asphaltenes particles in the system which lead to a colloidal view toward heavy oils and bitumens. Asphaltene aggregates can vary in size depending on a number of factors such as viscosity of matrix, temperature, pressure, applied stress, flow field type, interfacial tension and surface chemistry. Behzadfar et al. (Behzadfar et al., 2009) showed that the aggregate size has a great influence on the flow properties of a mixture filled with solid particles. They studied the effect of aggregate size of calcium carbonate on the viscosity of PDMS and found a higher 13 viscosity for larger aggregates. In conclusion, asphaltenes are one of the key components of heavy oil and bitumen which have a significant contribution to the flow properties of the system. 2.1.5 Structural models Despite significant research to unravel the structure of heavy oils and bitumens, there is no structural model which can account for all features and properties of heavy oils and bitumens. However, there have been some models which have received fair attention in the open literature. Dickie and Yen (Dickie and Yen, 1967) proposed a hierarchical colloidal model known as the Yen model, which expressed the colloidal nature of crude oils. By exploring more complicated aspects of heavy oil and bitumen structure, there have been strong debates in petroleum science about the validity of the Yen model. Recently, Mullins (Mullins, 2010) has proposed a model which contains some modifications to the Yen model. The modified Yen model is presented in Figure 2.5 considering an aromatic core and alkane chain for molecular structure of asphaltene particles. In the modified Yen model, Mullins considered several levels for the structure of asphaltene particles, namely molecules, nanaoaggregates, clusters and flocs. The molecules of asphaltenes comprised of a polycyclic aromatic hydrocarbon (PAH) ring system with peripheral alkane chains. PAHs are polarizable and thus the primary sites of intermolecular attraction mostly induced dipole-dipole interactions, although alkane chains act as a hindrance in aggregation of molecules and introduce their steric repulsion effects. Unlike the exterior repulsive forces, the central attractive forces cause a small aggregation number for asphaltenes. The approximate size of molecules is 1-2nm, while aggregation of molecules forms larger nanoaggregates with specific size of 3nm having the aggregation number (the number of molecules in an aggregate) of ~6. Nanoaggregates can aggregate to make up fractal clusters of nanoaggregates with the aggregation number of ~8 having specific size of 6-100nm depending on the condition of aggregation process (Mullins, 2010; Zhao and Shaw, 2007). Clusters’ aggregation can result in ~300nm and even larger flocs rendering more fractal structures in the mixture. In a high enough concentration, the aggregation process of asphaltenes would be reaction limited which leads to aggregates with fractal dimension ~2-2.5 (Gawrys and Kilpatrick, 2004; Meakin, 1988). One of the fractions in heavy oil and bitumen is resins that play some role on stabilizing asphaltenes particles. Although there are some uncertainties in the role of resins, Zhao and co-workers (Zhao and Becerra, 2009) showed 14 via ultra-filtration experiments that the extent of resin-asphaltenes interaction varies with conditions and is in the order of 15 wt.% of whole resin. Using calorimetry, Merino-Garcia and Anderson (Merino-Garcia and Andersen, 2004) also indicated that only a part and not whole of resins involve in the stabilization process of asphaltene particles. Figure 2.5: The modified Yen model. (Left) The predominant asphaltene molecular architecture has a single, moderately large PAH with peripheral alkanes. (Center) Asphaltene molecules form asphaltene nanoaggregates. (Right) Asphaltene nanoaggregates can form clusters with aggregation numbers estimated to be ~8. The modified Yen model provides a framework to treat large numbers of diverse asphaltene studies (Mullins, 2010). 2.2 Rheology of bitumen Rheology is the study of flow and deformation of matter. In general, the main objective of rheology is to identify a relationship between deformation and/or deformation rate and stress applied on matter. This relationship is called “constitutive equation”. To acquire such a relationship, either a deformation is applied to matter and the corresponding stress response is recorded, or a stress is imposed on matter and the deformation is measured. Since heavy oil and bitumen have complex structures, complex rheological behaviour is expected. Heavy oil and bitumen are colloidal asphaltenes-rich hydrocarbon mixtures, which experience different processes before coming handy (Bazyleva et al., 2010; Didier Lesueur, 2009; Rojas and Castagna, 2008). Asphaltenes along with other solid components play a key role in the 15 rheological behaviour of these mixtures. Solid particles generate aggregates and agglomerates in the system, sometimes large enough to precipitate which may cause additional problems such as well plugging, distillation tower plugging and catalyst deactivation. Pfeiffer and Saal (Pfeiffer and Saal, 1940) attributed the non-Newtonian behaviour of heavy oils and bitumens to viscoelasticity which arises from gel structure. Mullins (Mullins, 2010) proposed the modified Yen model to explain the viscoelastic behaviour of heavy oil and bitumen. Hasan et al. (Hasan et al., 2009) showed that solid maltenes should be considered in interpreting the non-Newtonian behaviour of heavy oils and bitumens. They presented that the transition from solid to liquid state takes place at the temperature interval of about 50-degree and the most viscoelastic behaviour should be expected in this region. Fulem et al. (Fulem et al., 2008a) studied the phase behaviour of heavy oils and bitumens and reported the existence of minimum three phases at 23°C, namely solid asphaltenes, liquid maltenes, and solid maltenes. Solid content varies with temperature which makes it more challenging for relating rheological properties of heavy oils and bitumens to the structure. Moreover, adding other substances such as solvents makes it more problematic that calls for further investigation. Heavy oils and bitumens exhibit two transition temperatures called α-transition and β-transition which are attributed to transition from Newtonian flow to viscoelastic flow and from viscoelastic behaviour to elastic glassy behaviour, respectively. The α-transition occurs at temperatures above room temperature and originates from the Brownian motion of the colloidal solid particles. The β-transition shows up at low temperatures and is attributed to the solidification of maltenes (Didier Lesueur et al., 1996; Lesueur et al., 1997). However, the origin of β-transition is not fully understood. Although heavy oils and bitumens exhibit a gamut of rheological behaviour including shear-thinning, there are a few studies discussing their rheology. 2.2.1 Early rheological techniques Early rheological studies on heavy oils and bitumens are based on “needle penetration test” and “ring and ball softening temperature test” which are still being used in some cases. In the “needle penetration test” a standard needle with a load of 100 g penetrates into the material and the depth 16 of penetration is measured after 5 s which is expressed in a tenth of mm. “Ring and ball softening temperature test” includes an 8-mm thick film inside a 9.5 mm diameter ring and a 3.5 g ball on the top which is placed in a 5°C water bath with temperature increasing rate of 5°C/min. The temperature at which the film drops 25 mm until it contacts the vessel bottom is reported as TR&B. According to the two above test methods, Pfeiffer and Van Doormaal (Pfeiffer and Saal, 1940) proposed the “Penetration Index” as an indicator of classifying heavy oils: &log(800) log( ) 1 2050 10R BP PIT T PI (2.1) where P , &R BT , T and PI are penetration depth, ring and ball softening temperature, temperature of needle penetration test and penetration index, respectively. 2PI indicates a gel structure whereas 0PI is indicative of a sol (Pfeiffer and Saal, 1940). These tests are typically used in paving industry for extra heavy oils and bitumens because of simplicity and ease of measurement. There have been many efforts to relate the abovementioned test results to other rheological properties including viscosity but the proposed relationships are too specific and not applicable to all heavy oils and bitumens. 2.2.2 New techniques in evaluation of bitumen and heavy oil rheology With the advent of modern rheometers, the rheological studies of heavy oil and bitumen became more scientific. Heavy oil and bitumen are highly viscous viscoelastic liquids that typically exhibit shear thinning behaviour (Didier Lesueur et al., 1996). Furthermore, by adding other substances such as gases, water and polymers to heavy oil and bitumen, more complication arises in the study of their rheological behavior which calls for advanced techniques. 2.2.2.1 Oscillatory (dynamic) measurements Oscillatory (dynamic) measurements are extensively employed to study the viscoelastic response of a matter. In the oscillatory measurements, the moveable geometry oscillates and impose 17 sinusoidal deformation/stress to the matter so that the resultant stress/deformation is measured. Analysis of the recorded data presents an idea about the rheological properties of matter. Measurements in the oscillatory mode can be performed either in linear or nonlinear viscoelastic region. In the linear viscoelastic region, applied deformations and stresses are sufficiently small so that the structure of matter remains intact. The rheological response is acquired by slightly departing matter from its equilibrium state at rest. In the nonlinear viscoelastic region, larger deformations/stresses are applied so that there is a likelihood of structural breakage in matter. Various parameters are determined through oscillatory measurements including storage/elastic modulus, 'G , loss/viscous modulus, "G , complex modulus, * 2 2' "G G G , and complex viscosity, ** G , where is angular frequency of applied deformation/stress. More discussion on these properties will be presented in subsequent chapters. 2.2.2.2 Steady shear measurements Steady shear measurements include rheological experiments where a steady shear rate or deformation rate or stress is applied to matter and the corresponding response is recorded. As a result of this experiment, the flow curve of the fluid under consideration is built. Viscosity is the main outcome of steady shear measurements which is calculated by dividing the stress by the constant deformation rate. If the viscosity is dependent on deformation rate, the fluid is referred to as non-Newtonian and the zero-shear viscosity is reported as a material function of the material. In the following sections the significant parameters that play a crucial role on the rheological behaviour of bitumen will be presented. 2.2.3 Effective parameters on bitumen rheology Various parameters can potentially influence the rheological behaviour of heavy oil and bitumen in the presence of CO2 including temperature, pressure, gas concentration, shear rate, asphaltene amount, and aging. However, geographical location, depth of formation, production and post-18 production processes are other parameters that change the rheological properties of oils. All these parameters change the chemical and phase composition, strength of different interactions, strength and size of particle structure which are mainly responsible for the rheological behaviour of heavy oils and bitumens. In the following, some of these parameters are discussed in detail. 2.2.3.1 Effect of temperature The influence of temperature on the viscosity of heavy oils and bitumens is generally well understood and different models have been used to describe this dependency based on thermal activation theory such as the Arrhenius equation, free volume theory such as the William-Landel-Ferry (WLF) equation or even based on empirical equations (Dealy and Wissbrun, 1999). Heavy oils and bitumens are thoroughly solid at low temperatures typically below -50°C and -20°C, respectively. By increasing temperature, the maltenes start to melt and the viscosity drops until the materials become almost liquid after which the viscosity decreases gently at a low rate. Pierre and coworkers (Pierre et al., 2004) and Evdokimov and Eliseev (Evdokimov and Eliseev, 2006) suggested that temperature affects the asphaltene aggregates in heavy oils and causes them to dissociate rendering the viscosity to drop. Martin-Alfonso et al. (Martín-Alfonso et al., 2006) and Bazyleva et al. (Bazyleva et al., 2010) reported the decrease in the viscosity of heavy fuel oil with temperature independent of the amount of pressure and shear rate. Fulem et al., (Fulem et al., 2008a) studied the thermodynamic behaviour of Maya crude oil and proposed a phase diagram depicted in Figure 2.6. This diagram can, as a rule of thumb, be generalized to all types of heavy oils and bitumens being careful about the temperature range and slope of lines. As it can be seen, three phases are present at room temperatures which points to the complexity of their rheological behaviour. Table 2.4 lists a number of studies which have studied the effect of temperature and pressure on the viscosity of heavy oils and bitumens. It also presents a number of models proposed to account for the effects of temperature and pressure on the viscosity of heavy oils and bitumens. 19 Asphaltene mass fraction, wA0.0 0.2 0.4 0.6 0.8 1.0Temperature, T (°C)-200-1000100200300SM + SASM + LM+ SALM + LA+ SALM + LASMSALMLALM + SMLA + SALM + SA Figure 2.6: Temperature–concentration (asphaltene mass fraction) phase diagram: Sketch of the phase diagram (boundaries anticipated from theory plus experimental measurements). “S” and “L” stand for solid and liquid phases, subscripts “M” and “A” denote maltenes and asphaltenes (Fulem et al., 2008a). 2.2.3.2 Effect of pressure The effect of pressure on the rheology of heavy oil and bitumen is still under study due to experimental difficulties in performing measurements particularly at high pressures. Mehrota and Svrcek (Mehrotra and Svrcek, 1986) reported a profound impact of pressure on the viscosity of Athabasca bitumen while they did not observe any significant increase in the density. Martin-Alfonso et al. (Martín-Alfonso et al., 2006) investigated the effect of temperature and pressure on the flow behaviour of heavy fuel oil and reported that the viscosity is less sensitive to pressure at higher temperatures. They also showed that applying pressure makes the material more shear thinning between two relaxation temperatures while it does not alter the behaviour of the oil above α-transition (upper pouring point). 20 Table 2.4: Correlations for bitumen viscosity as a function of temperature and pressure Author(s) Effective parameters Equation Barus (Barus, 1893) Pressure 0, 0, exp( )Rp p p VFT (Vogel–Fulcher–Tammann) (Fulcher, 1925; Tammann, 1926; Vogel, 1921) Temperature exp ba T c Walther (Walther, 1931) Temperature log(log( )) log( )a m T c Eyring (Eyring, 1935) Temperature ln( ) /A B T WLF (Williams et al., 1955) Temperature 0,10, 2logRT RT RT TC C T T Khan et al. (Khan and Mehrotra, 1984) Temperature 11 221 2 1ln(ln( )) ln( )ln(ln( )) [1.0 ( ) ] b TC T CbT b bT e Mehrotra & Svrcek (Mehrotra and Svrcek, 1986) Temperature 1log(log( 0.7)) 3.63029log( )b T Mehrotra & Svrcek (Mehrotra and Svrcek, 1987, 1986) Temperature, Pressure Athabasca bitumen: 1 2 3ln(ln( )) ln( ) ga a T a p Cold Lake bitumen: 1 2 3ln(ln( )) ln( ) ga a T a p Canadian bitumens and heavy oils: 0ln( ) 2.30259 exp( )301303.15b B p dTT MFT (Fillers–Moonan–Tschoegl) (Fillers and Tschoegl, 1977; Moonan and Tschoegl, 1985) Temperature, Pressure 001 2( )( , )log ( , ) ( ) ( ( ))RR RT T pT p cT p c p T T p Seeton (Seeton, 2006) Temperature 00 20ln(ln( ( ))) ln( )cos( )( )1te K A B TxtK x dtt 21 Traditionally, the Barus empirical equation has been used to describe the effect of pressure on viscosity at constant temperature (Barus, 1893): 0 exp( )p (2.2) where is the viscosity at high pressures, 0 is the viscosity at atmospheric pressure, is the piezoviscous coefficient (coefficient of pressure dependency) and p is the gauge pressure. 2.2.3.3 Effect of shear rate Heavy oils and bitumens exhibit Newtonian behaviour at temperatures higher than α-transition (upper pouring point), while they behave analogous to shear thinning materials between α-transition and β-transition temperatures typically between -50°C and 15°C for heavy oil and between -20°C and 50°C for bitumen. This behaviour has mostly been attributed to the dissociation of solid aggregates and agglomerates (Behzadfar et al., 2009). Table 2.5 presents a number of models which have been used by researchers to account for the effect of shear rate on the viscosity of heavy oils and bitumens. Table 2.5: Equations used to describe the effect of shear rate on the viscosity of heavy oils and bitumens by various investigators Author(s) Equation Remarks Power law (Ostwald–de. Waele) 1nK Used by Martin±Alfonso et al. (Martín-Alfonso et al., 2006) Liu et al. (Liu et al., 1983) 01m Used by De Kee et al. (De Kee et al., 1998) Bingham (Bingham, 1922) 0y for y Used by Mouazen et al. (Mouazen et al., 2011) Carreau–Yasuda (Carreau, 1972; Yasuda, 1979) 101 ( )naa Used by Mouazen et al. (Mouazen et al., 2011) 22 Martin-Alfonso et al. (Martín-Alfonso et al., 2006) showed that the power law index, n , in the power law rheological model ( 1nK where is the shear rate) reached ~1 after melting of the highest molecular weight component in heavy fuel oils. They also observed that the shear thinning behaviour becomes stronger as pressure increases. Hasan et al. (Hasan et al., 2010) observed shear thinning behaviour of heavy crude oil to becoming weaker while the temperature levelled up from room temperature. Figure 2.7 shows typical shear thinning behaviour of heavy oil at different temperatures. Shear rate, (s-1)100 1000Viscosity, (Pa.s)567891025°C35°C45°C55°C65°C75°C. Figure 2.7: Shear thinning behaviour of heavy oil at different temperatures (Hasan et al., 2010) 2.2.3.4 Effect of dissolved CO2 Gases act as solvents to heavy oils and bitumens and cause the viscosity to drop. However, the extent of drop of viscosity in the presence of different gases is of great significance which needs to be determined through rheological experiments. A plethora of studies has focused on the viscous behaviour of gas–heavy oil/bitumen systems, among which some are summarized in Table 2.6 for the case of CO2. 23 Table 2.6: Selected studies on viscosity measurement of heavy oils and bitumens in the presence of CO2 Author(s) System Temperature (°C) Pressure (MPa) Viscometer Simon and Graue (Simon and Graue, 1965) CO2–saturated crude oils 43.3–121.1 15.6 Zeitfuchs cross–arm for the atmospheric–pressure viscosity and a rolling–ball viscometer for the high pressure viscometry Jacobs et al. (Jacobs, 1978) CO2–saturated Athabasca bitumen 20–140 5.7 In–line Contraves Model DC 44 viscometer coupled with a magnetic cup Svrcek and Mehrotra (Svrcek and Mehrotra, 1982) CO2–saturated Athabasca bitumen 25–100 6 In–line Contraves Model DC 44 viscometer coupled with a magnetic cup Mehrotra and Svrcek (Mehrotra and Svrcek, 1984) CO2–saturated Marguerite Lake bitumen 12–103 7 In–line Contraves Model DC 44 viscometer coupled with a magnetic cup Miller and Jones (Miller and Jones, 1981) CO2–saturated Wilmington and Cat Canyon heavy oils 24, 60 and 93 34.5 Rolling–ball Jha (Jha, 1985) CO2–saturated reservoir fluids and wellhead heavy oil 28 8.3 Pressure drop (capillary) Mehrotra and Svrcek (Mehrotra and Svrcek, 1988) CO2–saturated Cold Lake bitumen 15–97.9 11 In–line Contraves Model DC 44 viscometer coupled with a magnetic cup Chung et al. (Chung et al., 1988) CO2–saturated Bartlett heavy oil 24, 60 and 94 34.5 Rolling–ball Sayegh et al. (Sayegh et al., 1990) CO2–Lindbergh saturated heavy oils 21 and 140 15 Pressure drop (capillary) Kokal and Sayegh (Kokal and Sayegh, 1993) CO2–Lone Rock saturated heavy oils 21 and 140 12.4 Pressure drop (capillary) Badamchi–zadeh et al. (Badamchi-Zadeh and Yarranton, 2009) CO2–C3H8–Athabasca bitumen 0–90 5 ViscoPro2000 Cambridge viscometer limited to 6.9 MPa and 190°C 24 It should be pointed out that the measurement conditions are imperative to be reported since heavy oils and bitumens exhibit non–Newtonian behaviour over a wide range of temperatures (Behzadfar and Hatzikiriakos, 2013; Didier Lesueur, 2009) and more significantly they exhibit fracture particularly at higher shear rates (Motamed and Bahia, 2011). In addition to the experimental studies, there have been many attempts to develop constitutive models for the physical properties of the mixtures of heavy oils and bitumens with different gases and more specifically with CO2. However, not all proposed models are easily applicable and useful due to complications in the used functions and methods that demand laborious calculations. Moreover, they suffer from lack of physical basis in interpreting the influence of one parameter on the desired variable. Yet, many of these models have not considered the effect of shear rate at different levels of CO2 concentration. 2.2.3.5 Effect of asphaltenes The effect of asphaltene particles on the viscosity has been well investigated (Hasan et al., 2009; Hinkle et al., 2008; Evdokimov and Eliseev, 2006). Analogous to other colloids and suspensions, the viscosity of heavy oil and bitumen increases as asphaltene particles increase in number. Hasan et al. (Hasan et al., 2009) used a number of nanofilters to produce heavy oils and bitumens with different asphaltene content. They showed that increase in the fraction of asphaltene increases the viscosity of reconstituted Athabasca bitumen and Maya crude oil. Hinkle et al. (Hinkle et al., 2008) also showed that by increasing the asphaltenes content, the complex viscosity of heavy oils increases. Evdokimov and Eliseev (Evdokimov and Eliseev, 2006) studied the rheology of asphaltene-containing petroleum fluids and stated that the higher the amount of asphaltenes, the higher the value of yield stress. Sudduth (Sudduth, 1993) proposed a model to consider the effect of solid particle on the relative viscosity of dispersion which is a generalized form for numerous rheological models: 101ln (1 ) 11 kk (2.3) 25 where is the viscosity of the dispersion, 0 the viscosity of matrix, the intrinsic viscosity (2.5 for hard spheres in Newtonian fluid), the volume fraction of dispersed phase, the particle interaction coefficient ( 3.5 for non-interacting particles) , k is the crowding factor 1 2k . Although the effect of asphaltenes amount on viscosity is clear, the effects of their size, size distribution, and fractal shape is an area that needs more investigation. To the best of our knowledge, there is no systematic work done in this area. 2.2.3.6 Effect of time (thixotropy) The effect of time on the rheological properties of heavy oil and bitumen is still an area under debate. Physically, highly structured materials are influenced by time, depending on the medium viscosity and structures’ diffusion coefficients. On the contrary, less structural materials or simple materials with no structure show no dependency on time. Chemical reactions, oxidation, evaporation of light components and polymerization can occur over time, which leads to a change in viscosity. Moschopedis (Moschopedis and Speight, 1977) noticed an increase in asphaltenes molecular weight of bitumen after a few hours at 260°C that led to an increase in the viscosity of bitumen. Siddiqui (Siddiqui and Ali, 1999) observed an increment in the viscosity of bitumen due to generating of 6-7% more asphaltenes after 340 min at 163°C. Mastrofini and Scarsella (Mastrofini and Scarsella, 2000) observed higher stiffness and elasticity for aging bitumens at temperatures above 40°C using “Rolling Thin Film Oven Test” (RTFOT) for aging of different bitumens. They also reported an increase in asphaltenes amount and showed that complex modulus levels up only at low frequencies. It is worth noting that the time effect depends strongly on temperature and it is noticeable at high temperatures and long times. Hence, it is negligible at the time scale of usual rheological tests and low temperatures though enough care must be taken at higher temperatures. 26 2.3 Constitutive modeling of bitumen Constitutive modeling of bitumen aims at providing a relationship between deformation and/or deformation rate and stress applied on bitumen. The first attempt to model the flow behavior of bitumen was performed by Van Poel (Van Poel, 1954) followed by that of Heukolem and Klomp (Heukelom and Klomp, 1964). They utilized a nonlinear multivariable models (nomographs) to predict the stiffness modulus of bitumen having temperature, softening point, loading time and penetration index as inputs to their models. Improvements to this model were accomplished by McLeod in a series of papers (McLeod, 1976). Jongepier and Kuilman (Jongepier and Kuilman, 1969a) developed an empirical algebraic equation to predict the rheological properties assuming that the relaxation spectrum of bitumen is log normal. Several other authors proposed empirical models to evaluate the linear viscoelastic properties of bitumen (Didier Lesueur et al., 1996; Olard and Di Benedetto, 2003; Yusoff et al., 2011). These models are basically algebraic equations, and their parameters have in general no physical meaning. This causes difficulties in gaining an understanding of the rheological response of these materials. 2.3.1 Mechanical models Mechanical models offer a basic understanding of flow behaviour, which are more attractive to use. Some of these mechanical models employed to model the flow properties of bitumen are depicted in Figure 2.8. These models include combinations of an ideal elastic spring (elastic modulus), a viscous dashpot (viscosity) and a parabolic element (creep compliance response) (Olard and Di Benedetto, 2003). A generalized Burger model (Figure 2.8a) is constructed by placing a Maxwell model in series with a number of Kelvin-Voigt models (Burgers, 1935). Huet (Huet, 1963) proposed a model in which a spring is in series with two parabolic elements (Figure 2.8b). Sayegh (Sayegh, 1967) modified the Huet model (the Huet-Sayegh model) by putting a spring in parallel to the Huet model (Figure 2.8c). Olard and Di Benedetto (Olard and Di Benedetto, 2005) constructed the DBN model by eliminating the Maxwell model’s dashpot from the generalized Burger model (Figure 2.8d). In other works, researchers have added a dashpot to the Huet-Sayegh model in series with the parabolic elements and in parallel with the separate spring to build the 2S2P1D model (Figure 2.8e) (Di Benedetto et al., 2007, 2005). These models 27 may successfully model one type of experimental response (stress relaxation or creep). However, it is impossible to represent the complete rheological behaviour of the material at the all conditions by means of a simple mechanical model. Figure 2.8: Different viscoelastic mechanical models used for bitumen (a) The generalized Burger model. (b) The Huet model. (c) The Huet-Sayegh model. (d) The DBN (Di Benedetto and Neifar) model. (e) The 2S2P1D model. 2.3.2 K-BKZ model The K-BKZ model is one of the most popular constitutive equations used in the rheology of viscoelastic materials and it was proposed by Kaye (Kaye, 1962) and Bernstein et al. (Bernstein et al., 1963). A decade later, Wagner (Wagner, 1976) proposed a simplified version of the K-BKZ model, discarding the second normal stress difference and this made the model more successful in accurately representing the rheological response of viscoelastic materials, more particularly polymer melts. This equation can be written as follows: 28 1 11( ') ( , ) ( ') 'tij ijm t t h I II C t t dt C C (2.4) where ij , t , 't , ( )m t , 1 1( , )h I II C C and 1( )ijC t are the stress tensor, time, integral variable, memory function, damping function and Finger strain tensor, respectively. The 1I Cand 1II Care the 1st and 2nd invariants of the Finger strain tensor which are essentially strain-dependent (Dealy and Wissbrun, 1999). The memory function describes the linear viscoelastic behavior of the material which can be expressed as follows: ( ')( ') dG t tm t t dt (2.5) where ( )G t is the time-dependent linear relaxation modulus of material. Figure 2.9: (a) The schematic of bitumen structure including solid and liquid phases. The shell around the asphaltenic cores shows the interphase layer. The red arrows depict the short range connections which form the weak network; (b) The generalized Maxwell model and (c) the Zener model. Bitumens show a viscoelastic behaviour which is mainly due to their colloidal structures. Figure 2.9a depicts a schematic of bitumen structure including solid and liquid phases. The constituents of the phases and the interphase layer vary depending on temperature (see Figure 2.6). Asphaltenes remain as a core part of the solid phase at most temperatures while maltenes contribute mostly to the liquid phase and the interphase layer. To model the rheological response of bitumens, 29 the linear relaxation modulus should be represented by using an appropriate mechanical model. The generalized Maxwell model is a popular model which can capture most behaviour of viscoelastic materials (Figure 2.9b). The use of the generalized Maxwell model in modeling of bitumen rheology results into an infinity viscosity for one of the dashpots, and the model practically reduces to the Zener model (Figure 2.9c). In other words, the generalized Maxwell model or the Zener model can interchangeably be used to model the linear viscoelastic behavior of bitumen. Simply one of the relaxation times of the spectrum is much greater than the rest. The relaxation modulus in the generalized Maxwell model or the Zener model can be expressed in the following form: 101 1( ) exp( ) exp( )N Ni ii ii it tG t G G G (2.6) where iG and ( / )i i iG are the relaxation moduli or strengths and relaxation times of the ith element of the total number N of the modes. 0G is the relaxation modulus or strength of the dashpot with the practically infinite relaxation time depicted in Figure 2.9c. For most viscoelastic materials, the assumption of separaibilty is valid (Osaki, 1993; Soskey and Winter, 1984). It is assumed that the general relaxation modulus can be written as the product of a time-dependent and a strain-dependent function. The time-dependent function is simply the linear relaxation modulus, ( )G t , and the strain-dependent function is the damping function, 1 1( , )h I II C C. The damping function accounts for the departure of the rheological response from linear viscoelasticity. As seen in Equation 2.4, the separability assumption of the relaxation modulus is utilized for the modeling of the rheological behaviour of bitumen. Rolon-Garrido and Wagner (Rolón-Garrido and Wagner, 2009) reviewed the various damping functions which are of interest in rheology. Among numerous damping functions proposed, Papanastasiou’s function (Papanastasiou et al., 1983) has been extensively used as damping function of viscoelastic materials. Papanastasiou’s universal damping function (Papanastasiou et al., 1983) is: 1 11 1( , ) ( 3) (1 )h I II I II C C C C (2.7) 30 where and are adjustable parameter to be determined from the regression process on the experimental data and are dependent on the chemical structure, molecular weight and molecular weight distribution of the material. For simple shear flows, Equation 2.7 reduces to: 2 1 21( ) 1h (2.8) where is the shear deformation. We also found that the Marucci damping function represents the stress relaxation data of bitumen well (Marrucci et al., 2000). For simple shear this can be written as (no adjustable parameters): 2 2 1/ 26( ) 4 (4 )h (2.9) In the current study, we will examine both models to verify their suitability in describing the rheological response of bitumen, particularly using shear stress relaxation and startup of steady shear experiments (Osaki et al., 1976). Simple shear experiments will also be used to test the proposed constitutive equation. For such a test (constant shear rate), Equation 2.4 reduces to the following form: 120. ( )( ( )) ss m s h ds (2.10) where is the shear deformation rate, 12 is the shear stress and s is the integral variable. The stress growth and decay coefficients in the simple shear flows can be computed through the shear relaxation modulus values whose comparison with the experimental data is a quantitative tool to test the model’s capabilities in predicting different material functions. First the stress growth coefficient Equation reduces to (Osaki et al., 1976): 10( , )( , ) exp( ) ( ( ))t Ni si it s dt G h dsd (2.11) 31 Similarly, the shear stress decay coefficient for the stress relaxation after cessation of steady shear can be calculated by (Osaki et al., 1976): 21 0( , )( , ) ( ) exp( ) exp( )Niii i i iGt s tt h s sds (2.12) where ( , )t and ( , )t are stress at the steady shear and stress relaxation experiments, respectively. 2.4 Mutual diffusivity of CO2 in bitumen Diffusion takes place as a result of the random and thermal motion of molecules and originates from a gradient in the chemical potential (usually concentration) of a component in a multicomponent system. Diffusivity (diffusion coefficient) is a physical parameter, which is used to describe the diffusion process quantitatively. Carbon dioxide (CO2)-heavy oil/bitumen systems have recently drawn a great deal of attention due to the growing tendency to use CO2 in the enhanced oil recovery, while attempting to store it in depleted reservoirs. Thus, a precise methodology is required to measure the diffusivity of CO2 in reservoir fluids such as bitumen. 2.4.1 Diffusivity measurement techniques In general, the mutual diffusivity measurement techniques are classified as direct and indirect techniques. Direct techniques include the compositional analysis of the mixture (Schmidt et al., 1982; Wen et al., 2004), while indirect techniques encompass measurement of a physical property, which is correlated to the diffusivity (Riazi, 1996; Zhang et al., 2000; Upreti and Mehrotra, 2000, 2002; Das and Butler, 1996; Fadaei et al., 2011; Jamialahmadi et al., 2006; Zhang and Shaw, 2007; Song et al., 2010; Zhang et al., 2007; Yu, 1984; Yang and Gu, 2006). The indirect measurements in gas-liquid systems may include measurement of the pressure of the diffusing gas (Riazi, 1996; Zhang et al., 2000; Upreti and Mehrotra, 2000, 2002), the gas-liquid interface level (Das and Butler, 1996; Fadaei et al., 2011; Jamialahmadi et al., 2006), the density of the liquid phase (Zhang 32 and Shaw, 2007; Song et al., 2010; Zhang et al., 2007), the refraction of electromagnetic radiation (Yu, 1984) or the swelling of a pendant droplet (Yang and Gu, 2006). 2.4.2 Pressure-decay technique One of the most popular techniques to measure the mutual diffusivity of the gas-liquid systems is the pressure-decay experiment, which was introduced by Riazi (Riazi, 1996) for reservoir fluids. Unlike other conventional techniques, the pressure-decay technique is convenient, simple, and accurate for engineering applications (Upreti and Mehrotra, 2002; Zhang et al., 2000). In the oil and gas industry, this technique is widely used to measure the diffusivity of gases into different oils. Table 2.7 lists a number of studies which have employed the pressure-decay technique to determine the mutual diffusivity of CO2 in heavy oils and bitumens. Table 2.7: Selected studies using the pressure-decay method to measure the mutual CO2-oil diffusivity. Author(s) Liquid phase ( )T C 0( )p MPa ( )eqp MPa 9 210 ( / )D m s Boundary condition at interface Zhang et al. (Zhang et al., 2000) Heavy oil 21 3.4 ~2.85 4.76 Equilibrium Upreti and Mehrotra (Upreti and Mehrotra, 2000) Athabasca bitumen 25-90 4 ~3.1 to 3.5 0.16 to 0.47 Quasi-equilibrium Upreti and Mehrotra (Upreti and Mehrotra, 2002) Athabasca bitumen 50-90 8 N/A 0.40 to 0.93 Quasi-equilibrium Sheikha et al. (Sheikha et al., 2005) Bitumen 75, 90 4 ~3.1-3.2 0.51to 0.79 Quasi-equilibrium Tharanivasan et al. (Tharanivasan et al., 2006) Heavy oil 23.9 4.2 ~3.5 0.46 to 0.57 Equilibrium, Quasi-equilibrium, Non-equilibrium Unatrakarn et al. (Unatrakarn et al., 2011) Heavy oil 30-55 3.1 ~2.6 0.34 to 0.36 Non-equilibrium 33 In the pressure-decay technique, the pressure of the gas phase is monitored over time, while the molecules diffuse into the liquid. Then the diffusion equations in the gas and liquid phases along with the mass conservation equations on the interface are solved to calculate the diffusivity. To solve the diffusion equations, a sufficient number of boundary conditions should be imposed. An assumption for the concentration of the gas at the interface is an influential factor for which three different assumptions are commonly used. The first assumption, termed as the equilibrium boundary condition, considers the gas concentration at the interface as the saturated concentration of the gas at the equilibrium pressure, which remains the same during the diffusion process (Riazi, 1996; Zhang et al., 2000). The second assumption is to consider the interface concentration as the saturated concentration that corresponds to the overhead pressure which continuously varies with time (Upreti and Mehrotra, 2002, 2000) termed as quasi-equilibrium boundary condition. Finally, the last assumption is to consider the non-equilibrium boundary condition, where the interface concentration is calculated from a linear equation between the diffusant (CO2) mass flux and the difference of the saturation concentration at the equilibrium pressure and the present concentration at the interface (Civan and Rasmussen, 2006, 2009). Numerous studies have investigated the effect of the three different boundary conditions on the diffusivity of the CO2-heavy oil/bitumen systems (Sheikha et al., 2005; Tharanivasan et al., 2004). Sheikha et al. (Sheikha et al., 2005) showed that these assumptions did not influence the calculated value of diffusivity more than 14.1%, while Tharanivasan et al. (Tharanivasan et al., 2004) reported a significant influence at small diffusion times. In order to solve the diffusion equations, either the initial pressure or the final (or equilibrium) pressure must be determined. Therefore, selecting appropriate values for the initial and equilibrium pressures is notably important for the diffusivity calculations in the pressure-decay technique (Sheikha et al., 2006). In the case of the initial pressure, the difficulties arise since the interface filling phenomenon takes place simultaneously along with the diffusion process upon introduction of the gas phase to the liquid phase. Sheikha et al. (Sheikha et al., 2006) discussed the uncertainties in selecting the initial pressure and demonstrated that the values of diffusivity are strongly influenced by the initial value of pressure. Yang and Gu (Yang and Gu, 2006) ignored the early interface filling and thermal instability phenomena in their measurements and selected the 34 pressure at the isothermal point as the initial pressure. On the other hand, for gas-liquid mixtures comprised of highly viscous liquids such as heavy oils and bitumens, the equilibrium state of the mixture is unreachable in the absence of any mixing. This is indicative of the difficulties in determining the equilibrium pressure with certainty. Zhang et al. (Zhang et al., 2000) reported that the diffusivity is highly sensitive to the estimated value of the equilibrium pressure, while it varies up to 6.38% by altering the equilibrium pressure value only by 0.2%. Several techniques have been employed to predict the equilibrium pressure in such systems (Civan and Rasmussen, 2006, 2009; Tharanivasan et al., 2004; Unatrakarn et al., 2011; Zhang et al., 2000). Most studies have used the extrapolation method (or asymptotic line) to predict the equilibrium pressure (Tharanivasan et al., 2004; Unatrakarn et al., 2011; Zhang et al., 2000) while a few have examined other methods such as model assisted analysis (Civan and Rasmussen, 2006), solubility data analysis (Tharanivasan et al., 2006), and optimization method (Civan and Rasmussen, 2009). However, the reported values are only predictions to the realistic equilibrium pressure. 2.4.2.1 Theory of diffusion The first step in the calculation of the diffusivity is to define the appropriate mass transfer equations. As illustrated in Figure 2.10, for a non-volatile liquid phase, the pressure-decay experiment can be considered an isothermal one-dimensional diffusion process occurring along the z axis, which leads to: 22c c cDt z z (2.13) where c is the concentration of the diffusant, t is time, D is the diffusivity of the diffusant in the liquid phase, z is the axis of diffusion and is the velocity in the liquid phase. Given the high viscosity of the liquid phase, the effect of the bulk flow is eliminated and thus the diffusion equation reduces to: 22c cDt z (2.14) 35 Figure 2.10: Typical cylindrical geometry for the pressure-decay experiment. Assuming the equilibrium boundary condition for the concentration at the interface, the initial and boundary conditions are as follows: 0I.C. 0; 0 for all B.C.1 ; for 0B.C.2 0; 0 for 0satzt c zz L c c tcz tz (2.15a) (2.15b) (2.15c) The diffusivity is a physical parameter that depends on the diffusant concentration. However, since the variation of the diffusivity during a diffusion experiment is relatively small (Upreti and Mehrotra, 2002, 2000), it can safely be considered constant (Sheikha et al., 2006; Tharanivasan et al., 2006; Unatrakarn et al., 2011; Zhang et al., 2000). The analytical solution of Equation 2.14 for the concentration profile subject to the initial and boundary conditions 2.15a-2.15c, is: 22214( , ) ( 1) exp (2 1) cos (2 1)(2 1) 4 2n satsatncc t z c n Dt n zn L L (2.16) From the mass transport perspective, the mass flow rate of the gas through the interface is described as following: 36 gz Ldm cDAdt z (2.17) where gm is the mass of the gas phase and A is the cross sectional area of the interface. Assuming a non-volatile liquid, negligible swelling of the liquid phase (here bitumen) (Sheikha et al., 2005; Svrcek and Mehrotra, 1982; Tharanivasan et al., 2004; Unatrakarn et al., 2011; Zhang et al., 2000) and constant compressibility for the gas phase (Ghaderi et al., 2011; Sheikha et al., 2005; Zhang et al., 2000), the consumption rate of the diffusant molecules is: g ggdm V dpdt Z RT dt (2.18) where gV is the volume of the gas phase, R is the universal gas constant, T is temperature, gZis the compressibility factor of the gas and p is the pressure of the gas phase. In an isolated system, the consumption rate of the gas molecules is equal to the mass flow rate of the gas through the interface, which yields the following differential equation: 22212 exp (2 1) 4g satngV DAcdp n DtZ RT dt L L (2.19) Integration of Equation 2.19 from an arbitrary t to infinity leads to: 222 2 218 1 exp (2 1)(2 1) 4sat g leqngc Z RTVp p n DtV n L (2.20) where lV is the volume of the liquid phase. In Equation 2.20, it is assumed that at infinity the system reaches equilibrium where eqp is the equilibrium pressure. The series in Equation 2.20 is estimated by the first few terms in the right hand side that yield the diffusivity if the function is fitted to the pressure profile in the pressure-decay experiment. Apart from the diffusion process occurring continuously in the pressure-decay experiment, the interface-filling (or incubation) phenomenon takes place by the gas molecules at the early stages of the experiment. During interface-filling phenomena, the pressure drops significantly and 37 the pressure profile tends to deviate from Equation 2.20. To describe this phenomenon, Danckwerts (Danckwerts, 1970) used the following model for the pressure decay of the gas: *02gc ART Dp p V t (2.21) where 0p is the initial pressure and *c is the instantaneous saturation concentration at the interface. Therefore, it is more accurate to obtain the diffusivity from the regression of Equation 2.20 on the pressure profile excluding the initial pressure and the early stage pressure drop due to interface-filling phenomenon. This method is used in the present work as explained in detail below. 38 3 THESIS OBJECTIVES AND ORGANIZATION 3.1 Thesis objectives CO2 enhanced oil recovery (CO2-EOR) features both economically and environmentally benefits that makes it appealing to oil companies. On one hand, more oil can be produced from depleted reservoirs and on the other hand, it is a viable option to sequester CO2 deep underground. However, a good understanding of the rheological behaviour of bitumen and heavy oil in the presence of CO2 at real operational conditions is needed. Limited data on the rheology of heavy oil and bitumen as a function of pressure are known. Moreover, even less is the knowledge on the rheological behaviour of mixtures of heavy oil and bitumen with CO2. Furthermore, no rheological model exists that describes the rheology of such mixtures at high temperatures and pressures. Hence, the objectives of this work are set as follows: 1) To model the rheological behavior of CO2-free bitumen by using a suitable constitutive rheological model. This model should be capable of describing both its viscous and elastic behavior over a wide range of temperatures where bitumen undergoes transition from a solid-like to a fluid-like behavior. 2) To investigate the effects of temperature, pressure, concentration of CO2, shear rate and time on the rheological properties of bitumen. 3) To correlate rheological behavior of bitumen and its mixtures with CO2 with structural changes of bitumen. 4) To measure the diffusivity of CO2 in bitumen at different states including gaseous, liquid and supercritical states. 39 3.2 Thesis organization The overall organization of the present dissertation is as follows. A brief introduction to the existing knowledge on the flow properties of bitumen is presented in chapter 1. Chapter 2 includes the literature review on heavy oils and bitumens from the analytical and the rheological points of view. The objectives and organization of the dissertation are presented in chapter 3. Then, the used materials, instruments, experiments and methodologies are discussed in chapter 4. In chapter 5, the rheological behaviour of bitumen is discussed and a suitable constitutive modeling is presented (Objective 1). This chapter is heavily based on a paper already published in the Journal of Fuel (Center for History and New Media, n.d.). Chapter 6 focuses on the effects of different parameters including temperature, pressure, dissolved CO2, shear rate and time on the rheological properties of bitumen (Objective 2). It also discusses the structural change and constitutive modeling of bitumen-CO2 mixtures at various compositions, temperatures and pressures (Objectives 3 and 4). This chapter is based on a recent published paper in the Journal of Fuel (Behzadfar and Hatzikiriakos, 2014a). In chapter 7, the diffusivity of CO2 in bitumen at different states including gaseous, liquid and supercritical states are measured by a new method developed in this work (Objective 4). This chapter is based on the paper published in the Journal of Energy and Fuels (Behzadfar and Hatzikiriakos, 2014b). Finally, chapter 8 includes a summary of conclusions drawn based on the experimental results and provides recommendations for future studies. 40 4 MATERIALS AND METHODOLOGY 4.1 Materials The investigated materials in this study include bitumen and carbon dioxide. The specific gravity of the bitumen sample was 0.97 at 22°C which was obtained from Syncrude Canada. The asphaltenes and maltenes (saturates, aromatics, resins) contents of the bitumen were determined based on their solubility in n–pentane (see Table 4.1). The bitumen was mixed with n–pentane on a weight ratio of 1:40 and stirred overnight. The mixture was filtered twice by using paper filters of different pore sizes, namely 1–5 µm and 0.2 µm, respectively. Filtration was accompanied with continuous vacuuming and extra solvent was used to make the filter paper colorless. The retentates were dried in an oven at 60°C for 30 min and left in a vacuum oven at room temperature for 48 hr. The permeates were placed in the rotary evaporator at 60°C to remove out the n–pentane completely. Both retentates and permeates were weighted to obtain the weight percentage of the asphaltenes and maltenes. Elemental analysis of the sample was performed using the 2400 Perkin–Elmer CHNS/O Analyzer by combustion at 1000°C. The oxygen content was calculated from subtraction based on the weight contents of the other elements. Metal analysis data were provided from the supplier based on ASTM–D5600. The bitumen was stored at ambient temperature before testing and neither phase dissociation nor evaporation occurred. Carbon dioxide was purchased from Praxair Co., Canada, with purity of 99.99%. The phase diagram of CO2 and our experiment domain have been presented in Figure 4.1. The triple point of carbon dioxide is 0.518 MPa at −56.6 °C (see phase diagram, Figure 4.1). The critical point is 7.38 MPa at 31.1 °C. Carbon dioxide in three states of gaseous, liquid and supercritical liquid was used. To study the effect of pressure on the rheological behaviour of the bitumen independently from the effect of CO2 concentration, nitrogen was used which has a low solubility in bitumen. 41 Table 4.1. Compositional and Elemental analysis of the bitumen Fraction Mass fraction C5 asphaltenes 18.32 Maltenes 81.68 Element Mass fraction C 83.42 H 10.10 N 0.52 S 4.77 Oǂ 0.79 Atomic H/C 1.45 Metal ppm Fe 1.99 V 126 Mn 0.15 Ni 34.4 ǂ calculated from the difference of mass fractions of other elements from 1. 4.2 Methodology 4.2.1 Rheological measurements Rheological measurements were conducted at ambient and elevated pressures. The experiments at ambient pressure were performed by the Anton Paar MCR 501 (Anton Paar, Austria), a stress/strain controlled rheometer using the regular parallel–plate geometry of 25 mm diameter with different gap sizes. At pressures greater than atmospheric pressure, the measurements were performed inside the pressure cell set–up mounted on the rheometer. The geometries used in the pressure cell included the concentric cylinder, parallel-plate and vane–cup geometries. In the concentric cylinder and vane–cup geometries, the inner diameter of the cup was 27 mm separated 42 from the spinning inner cylinder by 1 mm gap (inner cylinder diameter was 25 mm) and from the spinning 4-blade vane by about 1.2 mm gap (vane diameter was 24.6 mm). The thickness of the blades was 1 mm, which was negligible compared to the cup diameter. The diameter of the parallel–plate geometry was 20 mm having a gap of about 1 mm. Temperature, T (K)200 250 300 350 400Pressure, p (bar)110100100010000GasSupercritical FliudLiquidSolidTriple PointCritical Point Figure 4.1: Phase diagram of carbon dioxide. The temperature range of the experimental testing was varied from –30°C to 180°C (±0.01°C). At temperatures below 10°C, bitumen is highly viscous and difficult to shear. Small amplitude oscillatory shear measurements were performed in the linear viscoelastic region over a wide range of frequencies (0.001-500 rad/s) and the complex viscosity data were determined. After examining the validity of the Cox-Merz rule, the zero-shear viscosity was determined from the complex viscosity curve of bitumen under study (see chapter 5 for more details). A number of experiments were repeated to ensure the reproducibility of the experimental data. These data were within an experimental error of ±10%. The saturation processes of the bitumen with CO2 took place over a long period of time inside the pressure cell depending on the pressure and temperature. The pressure was monitored 43 over time and the saturation was complete when no further reduction in pressure was observed. The viscosity of the mixture was also continuously measured during the diffusion process in order to identify the completion of the saturation state, which took place when no further drop in the viscosity was observed. Before and after the saturation processes, steady shear experiments were performed at different temperatures with different shear rates, while enough time was allowed for the material to reach steady state. This was followed by cessation of steady shear stress to allow the material to relax completely. Figure 4.2. Anton Paar MCR501 rheometer. Step shear rate measurements were also performed to check for changes in the rheological behaviour of the samples resulting from structural changes. This experiment was introduced by Cheng (Cheng, 1986) to build flow curves at different structural levels for thixotropic materials where the sample is subject to shear at a “reference” shear rate until the stress reaches its steady state value which is taken as an indication of the structural level at that “reference” shear rate. Consecutively, the shear rate value is abruptly adjusted to a new value, which causes the stress level to change accordingly. The first shear stress value at the new shear rate is collected and 44 recorded as the material’s response at the new shear rate at the structural level of the “reference” shear rate. Subsequently, the shear rate is adjusted to the “reference” shear rate again to rebuild the base structure level. The same procedure is repeated for other shear rates to determine the various shear stress values that correspond to various structural levels of the material. Consequently, the “reference” shear rate can be adjusted to another value and the procedure is repeated in order to determine the flow curve at different structural levels. Measurements were repeated to check for evaporation, thermal degradation or phase separation effects during the experiments. Figure 4.3. A schematic and picture of geometries in the pressure cell. 45 4.2.3 Pressure cell set-up The pressure cell set–up was consisted of various parts including the gas cylinder, regulator, sample cylinder, pressure supply unit, pressure transducer, liquid cup, measuring geometry, thermocouples and tubing between the parts. A schematic of the set–up is depicted in Figure 4.4. The geometries in the pressure cell was driven by a magnetic coupling, which was attached directly to the torque measuring system of the rheometer. The special design of the cell makes the calibration and motor adjustment steps important. These were performed carefully using standard oils prior to each set of experiments. PValveGas cylinderPressure gaugePressure regulatorIsothermal spaceSample cylinderPressure transducerMeasuring geometryMagnetic couplingFigure 4.4. A schematic diagram of the pressure cell set–up. The advantage of using the vane–cup geometry is to minimize any potential of wall slip and increase the mixing efficiency, which is of great importance in reaching saturation. A certain amount of the liquid was placed in the cup (~18 mL) and the cup was sealed from the environment by means of tightening several screws and nuts. During this procedure, enough care was taken not to disturb the oil. Enough time was allowed for the oil temperature to reach equilibrium at the desired set temperature. Simultaneously, the carbon dioxide was allowed to enter the sample cylinder at a fixed pressure (Figure 4.4) and then the valve was closed. Preheat time of 60 min was 46 applied in order to ensure stability of the gas temperature. The temperatures of the other parts of the set-up were adjusted by means of rope heaters, thermocouples and a temperature controller. Figure 4.5. Pressure cell set-up mounted on the rheometer. Figure 4.6. Pressure cell and the magnetic coupling. In the saturation experiments, CO2 was allowed to enter the cup by opening the valve between the sample cylinder and the pressure supply unit for a few seconds. As discussed above, 47 CO2 started to saturate the interface (incubation stage), which caused the pressure to drop significantly. The experiment was conducted in several steps. While no shearing was applied in the first step to capture the static diffusion process thoroughly, the second step was commenced after allowing the measuring geometry (vane) to spin gently at moderate shear rates. In the third step, saturation takes place by diffusion, which is facilitated by shear. Higher shear rates were applied to ensure the equilibrium state of the system. During testing, the viscosity and pressure are monitored simultaneously in order to ensure that the mixture has reached its saturated and final equilibrium state. The shear rates were imposed to the sample in a manner to avoid any potential disturbance or bubbling in the system. To check the reproducibility of our results, a number of experiments were repeated which resulted in the same results within the experimental errors. The nominal maximum pressure and temperature allowed by the specifications of the system were 15 MPa and 200°C, respectively. The experimental conditions were selected considering the fact that the geo-thermal and geo-pressure gradients are typically about 25°C/km and 30 MPa/km. 48 5 RHEOLOGY AND CONSTITUTIVE MODELLING OF BITUMEN In this chapter, the viscoelastic behaviour of bitumen is examined over a wide range of temperatures in an attempt to understand its complete rheological behaviour from elastic, to viscoelastic and to viscoelasto-plastic in some cases. The generalized Maxwell model is used to model the linear viscoelastic properties of bitumen, which serves as a basis for our study of the nonlinear viscoelasticity. An appropriate constitutive equation is proposed to account for the rheological responses of bitumen at both linear and nonlinear viscoelastic regions over a wide range of temperatures. The proposed constitutive equation is examined and tested for a number of different deformation histories in order to determine its ability in predicting the viscoelastic flow properties of bitumen. 5.1 Linear viscoelasticity It is generally accepted that bitumen is a colloidal suspension composed of maltenes and asphaltenes where maltenes encompass saturates, aromatics and resins. The major difference of bitumen with commonly known colloids and suspensions is the strong temperature-dependence of both solid and liquid phases. As asphaltenes are large molecules and solid at most temperatures, they account for the particulate part of the colloid whilst maltenes are assumed to form the liquid matrix. Asphaltenes start to melt at ~67°C while melting temperature of maltenes spans from around -50°C to 30°C (Hasan et al., 2009; Masson and Polomark, 2001). Accordingly, maltenes are likely transferred from the liquid to solid phase as the temperature decreases, while asphaltenes remain in solid phase for the most practical temperatures. This complication makes the study of the bitumen flow properties more complex since different parameters must be considered simultaneously to analyze the rheology of bitumen. Bitumen, like other viscoelastic materials, shows linearity between applied stress and induced strain at sufficiently low deformations (linear viscoelastic region). The linear viscoelastic region of a material in dynamic experiments can be determined by an amplitude sweep test in desired frequencies, preferably high frequencies to ensure the linearity at lower frequencies as well. The linear viscoelastic behaviour of bitumen was studied by means of small amplitude 49 oscillatory shear experiments at small strain values over a wide range of temperatures from -30°C to 90°C. Angular Frequency, (rad/s)10-210-1100101102103104105G'() (Pa)10-210-1100101102103104105106107108G' -30°CG' 0°CG' 10°CG' 30°CG' 60°CG' 90°C Figure 5.1: Storage modulus, 'G , of the bitumen versus frequency, , at selected temperatures. The storage, 'G , and loss, "G , moduli of bitumen are depicted in Figures 5.1 and 5.2, respectively, at selected temperatures. As shown, the loss modulus, "G (viscous behaviour) is more dominant at higher temperatures, while the measured storage modulus, 'G , at lower temperatures exhibits greater values. In fact at -30°C, 'G is greater than "G indicating the elastic behaviour of the material. It can also be observed that by increasing the temperature, 'G drops more rapidly than "G , demonstrating the dominance of the viscous behaviour at higher temperatures. While the bitumen acts as a truly elastic material at -30°C, it behaves like an entire viscous liquid at 90°C and above. Increasing the temperature, more maltenes migrate from the solid phase to the interlayer region and advance to the liquid phase. This migration is also accompanied with the mobility increment of the bitumen molecules improving its tendency to mechanical energy dissipation rather than energy storage. A plateau can be noticed in the storage modulus values, which is more evident at higher temperatures where the stress values are quite 50 small. The plateau reveals of the presence of a weak network in the bitumen. While this delicate network is easy to deform and break at very small strain, it is also recoverable at very short times after deformation. The influence of this formed structure will also be seen in the relaxation spectrum. Although some researchers believe that bitumen shows no yield stress (D Lesueur, 2009), our finding is in agreement with authors who confirmed the existence of the three-dimensional network in bitumen (Mouazen et al., 2011; Mullins, 2010). Angular Frequency, (rad/s)10-210-1100101102103104105G''() (Pa)10-210-1100101102103104105106107108G'' -30°CG'' 0°CG'' 10°CG'' 30°CG'' 60°CG'' 90°C Figure 5.2: Loss modulus, "G , of the bitumen versus frequency, , at selected temperatures. Using the principle of time-temperature superposition the master curve of dynamic moduli and complex viscosity were constructed at the reference temperature of 10°C. These are depicted in Figure 5.3. It appears that the time-temperature superposition (TTS) principle is applicable for the bitumen over the wide range of temperatures from -30°C to 90°C which covers the temperature range for most practical applications. Although there is no consensus in the literature that the time-temperature superposition (TTS) principle holds true for bitumens (Abivin et al., 2012; D Lesueur, 2009), our finding confirmed the applicability TTS. It is noted that this superposition was 51 performed by using only horizontal shifting and application of vertical shift did not improve the quality of the superposition significantly. Reduced angular frequency, aT (rad/s)10-810-710-610-510-410-310-210-1100101102103104105106107108G'() & G"() (Pa)10-310-210-1100101102103104105106107108|*()|/aT(Pa.s)10-210-1100101102103104105106107G'G"|*| Figure 5.3: Master curves of dynamic moduli (storage and loss) and complex viscosity of the bitumen against reduced frequency at the reference temperature of 10°C. The lines show fits of the generalized Maxwell model. The values of the shift factors, Ta calculated to produce the master curves depicted in Figure 5.3, are plotted in Figure 5.4. The shift factor values follow both the Arrhenius, exp / 1/ 1/T a ra E R T T where aE is the activation energy and rT is the reference temperature and the WLF (Baurngaertel et al., 1992), 1 2log ( ) /( ( ))T r ra C T T C T T equations. Using the Arrhenius equation, we calculated activation energy for flow of 134.5 kJ/mol considering 10°C as the reference temperature. Our finding of the activation energy was consistent with reported values in the literature (Mouazen et al., 2011). 52 Table 5.1: Parameters of the generalized Maxwell model Relaxation times (s) Relaxation strength (Pa.s) 1.00×10-7 14843332.28 1.50×10-6 12362273.82 1.83×10-5 10973131.27 1.84×10-4 4876916.70 1.46×10-3 2312245.10 8.34×10-3 776419.25 0.05 194903.82 0.55 10978.29 3.93 906.21 27.14 58.41 1144.49 0.36 11294.91 0.10 120403.99 8.32×10-3 1097863.45 0.04 220300543.94 0.05 As seen from Figure 5.3, the complex viscosity exhibits a significant shear-thinning behaviour while the upturn of the viscosity curve at very low frequencies confirms the presence of a small network in the bitumen. This upturn in the complex viscosity is accompanied by the plateau in the storage modulus at diminishingly small frequencies, also manifesting the existence of some structured networks with very long relaxation times. 53 Temperature, T (°C)-40 -20 0 20 40 60 80 100Horizontal shift factor, aT10-710-610-510-410-310-210-1100101102103104105Experimental dataArrhenius model (Ea=134.5kJ/mol)WLF model (Tr= 10°C,C1=17.57,C2=184.82) Figure 5.4: The shift factor values, Ta , at different temperatures obtained from the master curves at 10°C. The full and dashed lines show the Arrhenius and WLF models , respectively. In order to model the linear rheological behaviour of the bitumen by means of discrete relaxation time spectra, the parsimonious (PM) model (Baumgaertel and Winter, 1989) was used with the dynamic rheological data in which the relaxation time spectrum is shown in terms of Maxwell modes (the generalized Maxwell model). Equivalently, the Zener model can be used since one of the relaxation times in the generalized Maxwell model possess a very long relaxation time which can practically be considered as infinite leading to the Zener model. The dynamic moduli can be written as (Baumgaertel and Winter, 1989; Baurngaertel et al., 1992): 221( )' 1 ( )Ni ii iGG (5.1) 21( )" 1 ( )Ni ii iGG (5.2) where 'G , "G , , iG and i are the storage modulus, the loss modulus, the frequency, the ith relaxation strength and the ith relaxation time, respectively. Following the analysis proposed by 54 Winter (Winter, 1997), the optimum number of modes (mode density) was found to be 15. The agreement between the calculated parsimonious (PM) model with 15 modes (continuous lines) and the experimental data is excellent as can be seen in Figure 5.3. The computed relaxation moduli, iG , and times, i , of the model are depicted in Figure 5.5 and the values are listed in Table 5.1. The number of modes is in agreement with the usual analyses in rheology where approximately one mode corresponds for every decade of frequency. i (s)-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10Gi (Pa)-6-5-4-3-2-1012345678910Linear G(t)BSW spectrumngneneG0ngG0max0NN Figure 5.5: The relaxation spectrum of the bitumen at 10°C obtained from the generalized Maxwell model along with the BSW spectrum. Decomposition of the BSW spectrum is also presented. A few past studies on the rheology of bitumen have reported on the analysis of the relaxation spectrum in terms of complex viscosity or shear modulus in order to describe the linear viscoelastic properties of bitumen (Christensen and Anderson, 1992; Dickinson and Witt, 1974; Jongepier and Kuilman, 1969b; D Lesueur et al., 1996). However, the relaxation spectrum concept in terms of the generalized Maxwell (Zener) model is a well-developed concept in polymer rheology, which is also used here to analyze it. Baumgaertel et al. (Baumgaertel et al., 1990) used 55 the following continuous representation of the relaxation spectrum with an abrupt cut-off to define the maximum relaxation time (hereafter called BSW spectrum): 0 0max 0( ) ( )( )0ge nne N g Nn G n GH forfor maxmaxl (5.3) where en and gn are the slopes of the spectrum in the long-time and short-time regions, respectively, l , 0 and max are the shortest relaxation time, the Rouse time (the relaxation time for the onset of the glass transition) and the longest relaxation time, respectively, 0NG is the plateau modulus. The first term represents the entanglement and flow region, whereas the second term describes the high frequency region. The decomposition of the BSW spectrum is provided in Figure 5.5 for the case of bitumen which seems to fit its relaxation spectrum. The continuous BSW spectrum is plotted in Figure 5.5 along with the discrete data obtained from the generalized Maxwell model. The agreement between the discrete and continuous data confirms the interchangeability in the representation of the relaxation spectra, as proposed by Baumgaertel and Winter (Baurngaertel et al., 1992). This allows one to benefit from the accurate manifestation of the linear viscoelastic behaviour by using the minimum possible number of modes. The values for the parameters obtained from the BSW spectrum are presented in Table 5.2. The value of 0NG is much lower than that has been reported for typical polymers (>1MPa) which is because of the smaller size of bitumen molecules compared to those of polymers. gn was calculated to be 1.13, which is slightly above the values commonly reported for polymers showing the broad relaxation times with diverse relaxation strength in bitumen microstructure. However, the value of en , unlike other parameters, is in the range similar to that reported for polymeric substances (Ferry, 1980; Hatzikiriakos et al., 2000) while 0 was also far above the values reported for polymers (~10-7s) (Baumgaertel and Winter, 1992). In spite of dissimilarities in the parameters obtained for the bitumen with typical polymers, arising from the structural differences, the BSW spectrum is a useful tool to describe the linear viscoelastic behaviour of bitumen satisfactorily and possibly differences between various bitumen specimens can be reflected in terms of these spectrum. 56 Table 5.2: Parameters of the BSW spectrum for the bitumen Parameter Value )(0 PaGN 0.30 gn 1.13 en 0.20 0 ( )s 3272.33 max ( )s 2.20×108 Time, t (s)10-1100101102103104Relaxation mudulus, G(t,) (Pa)10-210-1100101102103104Linear G(t)Predicted G(t) Figure 5.6: The linear shear relaxation modulus of the bitumen, ( )G t , at 10°C ( 1 ). The dashed line shows the prediction of the generalized Maxwell model. Figure 5.6 compares the experimentally determined relaxation modulus with that predicted by the multimode Maxwell model using the relaxation spectrum depicted in Figure 5.5. As it can be deduced, the agreement between the experimental data and calculated function based on the dynamic rheometry is excellent. The existence of a delicate structure slows down the relaxation considerably at longer relaxation times (about 100 s) with a tendency of obtaining an equilibrium 57 modulus at even longer times. This is also shown by the maximum relaxation time of the last mode of the spectrum listed in Table 5.2. 5.2 Nonlinear viscoelasticity Once the magnitude of the strain or strain rate exceeds a critical value, the material structure is affected and the applied stress does not follow a linear relationship with the imposed strain (nonlinear viscoelasticity). In the context of the K-BKZ model, the damping function should be determined in order to capture the nonlinear viscoelasticity of bitumen. This can be done by means of stress relaxation experiments after the imposition of sudden strains. Figures 5.7 to 5.10 present the relaxation modulus of the bitumen at 0°C, 10°C, 30°C and 50°C, respectively. For instance, Figure 5.8a shows the relaxation modulus of the bitumen at 10°C and at different applied strains, , ranging from 0.2 to 10. As shown, the behaviour remains in the linear region for all strain magnitudes less than about 2 while at 2 the relaxation modulus starts showing strain dependence and deviates from the linear viscoelastic modulus also shown by the continuous line. In order to determine the damping function, the various curves were shifted upward to superpose to the relaxation modulus in the linear viscoelastic region. The resulted superposition is depicted in Figure 5.8b, and the shift factors are listed in the legend of Figure 5.8b. It can be inferred from Figure 5.8b that the superposition is perfect, confirming that the time-deformation separability assumption used to write Equation 2.4. The damping function was determined at various temperatures, namely 0°C, 10°C, 30°C, 40°C and 50°C to examine possible dependence on temperature. Similar to the data at 10°C, in all cases excellent superposition was obtained, confirming again the applicability of the separability assumption. 58 Time, t (s)0.1 1 10 100 1000Relaxation mudulus, G(t,) (Pa)10-210-1100101102103104105106=0.20=0.50=1.00=2.00=4.00=6.00=8.00=10.0a) Time, t (s)0.1 1 10 100 1000Relaxation mudulus, G(t,)/h() (Pa)10-210-1100101102103104105106=0.20=0.50=1.00=2.00=4.00=6.00=8.00=10.0b) Figure 5.7: (a) The shear relaxation modulus of the bitumen, ( , )G t , after the imposition of sudden strain values, , at 0°C; (b) Superposition of the stress relaxation modulus data of Figure 5.7a to determine the damping function. 59 Time, t (s)0.1 1 10 100Relaxation mudulus, G(t,) (Pa)0.010.1110100100010000=0.10=0.50=1.00=2.00=4.00=6.00=8.00=10.0a) Time, t (s)0.1 1 10 100Relaxation mudulus, G(t,/h() (Pa)10-1100101102103104105=0.10, h=1.00=0.50, h=1.00=1.00, h=1.00=2.00, h=0.62 =4.00, h=0.29=6.00, h=0.11=8.00, h=0.08=10.0, h=0.06b) Figure 5.8: (a) The shear relaxation modulus of the bitumen, ( , )G t , after the imposition of sudden strain values, , at 10°C; (b) Superposition of the stress relaxation modulus data of Figure 5.8a to determine the damping function. 60 Time, t (s)0.1 1 10Relaxation mudulus, G(t,) (Pa)0.0010.010.11101001000=0.50=1.00=2.00=4.00=6.00=8.00a) Time, t (s)0.1 1 10Relaxation mudulus, G(t,)/h() (Pa)0.010.11101001000=0.50, h=1.00=1.00, h=1.00=2.00, h=0.67=4.00, h=0.24=6.00, h=0.08=8.00, h=0.02b) Figure 5.9: (a) The shear relaxation modulus of the bitumen, ( , )G t , after the imposition of sudden strain values, , at 30°C; (b) Superposition of the stress relaxation modulus data of Figure 5.9a to determine the damping function. 61 Time, t (s)0.1 1 10Relaxation mudulus, G(t,) (Pa)10-310-210-1100101=1.00=2.00=4.00=6.00a) Time, t (s)0.1 1 10Relaxation mudulus, G(t,)/h() (Pa)0.010.101.00=1.00, h=1.00=2.00, h=0.53=4.00, h=0.38=6.00, h=0.09b) Figure 5.10: (a) The shear relaxation modulus of the bitumen, ( , )G t , after the imposition of sudden strain values, , at 50°C; (b) Superposition of the stress relaxation modulus data of Figure 5.10a to determine the damping function. 62 Time, t (s)0.01 0.1 1 10Damping factor, h()0.010.11 0°C10°C30°C40°C50°CPapanastasiou model (1983) = 5.40FBN model (2000) Figure 5.11: The damping function of the bitumen, ( )h , at temperatures from 0°C to 50°C. The dashed and full lines show the fit of the Papanastasiou model using 5.4 and the prediction of the Marucci FBN (Force Balance Network) model, respectively. The calculated values of the damping function at different temperatures are plotted in Figure 5.11. As it can be deduced, the data follow a unique pattern independent of temperature. The slight scattering along the line does not cause a noticeable change in the rheological response. The Papanastasiou and Marruci functions (Equations 2.8 and 2.9) have also been plotted along with the data points showing an excellent agreement. As shown, both forms of the damping function can be utilized to properly describe the damping function of the bitumen. However, it must be pointed out that the Marruci model does not contain any adjustable parameter (Marrucci et al., 2000). Once the damping function is known, the K-BKZ model is complete and ready to use in order to make predictions of the material rheological response in various deformation histories. 5.3 Model assessment The start-up of steady shear and cessation of steady shear flow experiments were conducted and the results were compared to the predictions of the K-BKZ model in order to test the capabilities of this model in capturing the rheological behaviour of bitumen. 63 5.3.1 Start-up of steady shear experiments In the start-up experiment, a desired shear rate is applied at 0t to the sample already at equilibrium for a certain period of time, while the shear stress rise is monitored. Figure 5.12 plots the shear stress growth coefficient, ( , )t , at 10°C along with the K-BKZ model prediction (Equation 2.11) using the Papanastasiou and Marucci models (Equations 2.8 and 2.9). At every shear rate the material behaviour initially follows linear behaviour. At some point, it deviates from linear behavior, exhibiting an overshoot (typical viscoelastic behaviour) before settling to its steady-state value. The linear viscoelastic region can be found at progressively shorter times depending on the level of the shear rate. The agreement is overall good, although the model underpredicts the strong experimentally observed overshoot. Having the steady shear values of the viscosity at different shear rates, the applicability of the Cox-Merz rule can be tested. Figure 5.13 depicts the flow curve of bitumen determined from steady shear experiments (Figure 5.12) in comparison with the linear viscoelastic data (LVE) plotted as a flow curve ( *| |G versus ) at 10°C, respectively. As it can be seen the agreement is excellent implying (i) the applicability of the Cox-Merz at least at 10°C and (ii) the absence of any possibly strong slip effects (Hatzikiriakos, 2012). 5.3.2 Cessation of steady shear flow experiments In this experiment, the material which undergoes a steady shear flow is subjected to cessation of the steady shear flow at 0t . As the motion is suddenly halted, the stress starts dropping with time until complete relaxation. This decrease is typically represented in terms of the shear stress decay coefficient, ( , )t , defined by dividing the instantaneous decaying shear stress by the shear rate preceding the relaxation part of the experiment. The results for several levels of shear rates are plotted in Figure 5.14. 64 Time, t (s)0.01 0.10 1.00 10.00 100.00Stress growth coefficient, +(t,) (Pa.s)2x1043x1044x104104Papanastasiou model (1983)FBN model (2000)0.010.050.100.501.00(s-1).. Figure 5.12: The stress growth coefficient of the bitumen, ( , )t , at different levels of shear rate, , at 10°C. The continuous lines represent the predictions of the K-BKZ model using the Papanastasiou and Marucci damping functions. (rad/s) or (s-1)10-310-210-1100101|G*()| (Pa) or (Pa)101102103104105106Steady shearLVE.. Figure 5.13: Testing the applicability of Cox-Merz rule by comparing the flow curve determined from steady shear experiments with dynamic complex modulus values, *| |G , versus angular frequency, , (dashed line) at 10°C. 65 Time, t (s)0 5 10 15 20 25 30Stress decay coefficient, -(t,) (Pa.s)10100100010000Papanastasiou model (1983)FBN model (2000)0.01s-10.05s-10.10s-10.50s-11.00s-1... Figure 5.14: The shear stress decay coefficient, ( , )t , of the bitumen at different shear rate values, , at 10°C. The continuous lines represent the predictions of the K-BKZ model using the Papanastasiou and Marucci damping functions. The continuous lines represent the predictions of the K-BKZ model (Equations 2.12) using the Papanastasiou and Marucci damping functions (Equations 2.8 and 2.9). Overall the representation is satisfactory. 5.4 Summary The rheological behaviour of bitumen as a viscoelastic material has been studied in this work, experimentally by performing several types of experiments and theoretically in terms of modeling its rheological response by means of a continuum constitutive equation, namely the K-BKZ. The generalized Maxwell model was found to be an excellent equation that fits the linear response of the bitumen in dynamic flow fields such as small amplitude oscillatory shear. The parameters obtained from the generalized Maxwell model (relaxation spectrum) were fed into the K-BKZ constitutive equation to predict the linear viscoelastic behaviour of the bitumen which was shown 66 to be excellent. The time-temperature superposition was found to apply in the case of bitumen over a wide range of temperatures, namely from -30°C to 90°C, essentially covering the range for most practical applications. The damping function data, ( )h , was also determined over a wide range of temperatures. It was found to be independent of temperature. The Papanastasiou and the Marruci models were utilized to represent the effect of shear strain on the damping function which was found to be adequate in most cases. The implementation of these two damping function models into the K-BKZ constitutive equation predicted the flow behaviour of the bitumen both in the linear and nonlinear viscoelastic regions adequately in most cases. 67 6 RHEOLOGY OF CO2-BITUMEN MIXTURES In this chapter, the effects of temperature, pressure, dissolved CO2 and shear rate on the flow properties of the CO2-bitumen mixtures are investigated. The reduced variable approach is taken into account to develop a convenient model capable of predicting the viscosity of the mixtures at various conditions. This approach simplifies the procedure by studying each parameter independently through a simple shift factor. The effects of temperature, pressure, dissolved CO2 and shear rate are summarized in four shift factors which are denoted by Ta , Pa , Ca , and Sa , respectively. 6.1 Effect of temperature (Ta ) Temperature has a significant effect on the flowability of heavy oils and bitumens. In the literature, a plethora of correlations has been proposed to account for the temperature effect on the viscosity of heavy oils and bitumens where some of them are listed in Table 2.4. Unlike most materials whose viscosity follows the Arrhenius (or Eyring (Eyring, 1935)) or WLF equations (Williams et al., 1955), the double–log function is the most suitable equation to represent the temperature dependency of the viscosity of heavy oils and bitumens. The double–log function was firstly proposed by Walther (Walther, 1931) for petroleum products and it was subsequently well developed by Mehrotra and Svrcek (Mehrotra and Svrcek, 1987, 1986; Mehrotra, 1990) for the special case of heavy oils and bitumens. The zero–shear viscosity values obtained from either rotational or dynamic viscometry of the bitumen are depicted in Figure 6.1. The measurements cover the temperature range of –10°C to 180°C. As mentioned earlier, it is difficult to shear the highly viscous bitumen and therefore dynamic data are used to determine the zero shear viscosity by assuming the validity of the Cox–Merz rule (see chapter 5). Although in chapter 5, the Arrhenius (or Eyring (Eyring, 1935)) or WLF models (Williams et al., 1955) were found to fit to the available data well, including measurements at higher temperatures (from 90°C to 180°C) demonstrates the superiority of the double–log function in describing the viscosity data. 68 Temperature, T (°C)0 50 100 150 200Zero-shear viscosity, 0 (Pa.s)10-310-210-1100101102103104105106107108DynamicZero-shearDouble-log modelWLF model, TR=10°CWLF model, TR=-41.7°C, R=1012Pa.sArrhenius modela) Temperature, T (°C)0 50 100 150 200Temperature shift factor, aT10-910-810-76-510-410-310-210-1100101Dynamic Zero-shearDouble-log modelWLF model, TR=-41.7°C,R=1012Pa.sArrhenius modelb) Figure 6.1: (a) The zero–shear viscosity of the bitumen at different temperatures. The oscillatory data were collected in the linear viscoelastic region of the bitumen. The steady shear viscosity data were collected at the shear rate range of 0.5 to 2 s-1.The lines show fits of different functions to the experimental data. (b) The temperature shift factor, Ta , as a function of temperature using as reference temperature the value of –10°C with 65.7 10R Pa.s. 69 The double–log model can be written as: 20 1ln( ) bbT or 0 1 2ln(ln( )) ln lnb b T (6.1) where 0 are the zero–shear viscosity in mPa.s, T the absolute temperature in K, and 1b and 2b are constants, respectively. In terms of temperature, the shift factor, Ta , Equation 6.1 reduces to: 2 20,10,exp( ( ))RT b bT RTa b T T (6.2) where 0,T and 0, RTare the zero–shear viscosities at temperature T and the reference temperature, TR, respectively. Regarding the constants, 1 exp(24.15)b and 2 3.781b were obtained which are in agreement with values reported for the bitumen (Khan and Mehrotra, 1984). The primary reason behind the complexity of the temperature effect lies in the existence of more than one phase in the bitumen. Heavy oils and bitumen are composed of two main constituents, namely maltenes and asphaltenes, where maltenes themselves are formed from different substances such as aromatics, saturates and resins. Each of these fractions contributes in making different phases and structures inside heavy oils and bitumens which makes rheological study more challenging. Figures 6.2a and 6.2b depict the results from thermal gravimetric analysis (TGA) and differential scanning calorimetry (DSC) of the bitumen and separated C5 maltenes and asphaltenes at the temperature range of –90°C to 180°C. In all these experiments, the temperature ramp was 5°C/min either in heating or cooling cycles. As it can be inferred, the DSC graph of the bitumen shows quiet complex behaviour having a glass transition (gT) at low temperatures around –30°C which is a characteristic of maltenes. The irregularities in the DSC graph at higher temperatures are attributed to the asphaltenes (Figure 6.2b). However, since the bitumen consists of different fractions, one must expect many overlaps in the calorimetric measurements. Modular differential scanning calorimetry (MDSC) has been of interest to some authors to differentiate the reversible and non–reversible phenomena occurring during heating or cooling processes of bitumen (Masson and Polomark, 2001). 70 Temperature, T (°C)-100 -50 0 50 100 150 200Heat flow, H (W/g)-0.20-0.15-0.10-0.050.00Mass loss (%)051015201st heating (DSC)Return cooling (DSC)2nd heating (DSC)Mass loss (TGA)Exoa)Temperature, T (°C)-100 -50 0 50 100 150 200Heat flow, H (W/g)-0.20-0.15-0.10-0.050.000.050.10BitumenMaltenesC5-AsphaltenesExob) Figure 6.2: (a) Thermal gravimetry analysis (TGA) and differential scanning calorimetry (DSC) of the bitumen in consecutive heating–cooling–heating cycles. (b) differential scanning calorimetry (DSC) of the bitumen and separated C5 maltenes and asphaltenes at the heating cycle. The temperature ramp for all measurement was 5°C/min under N2 atmosphere. There was no delay between the heating and cooling cycles. 71 Additionally, the heating and cooling cycles in Figure 6.2a are different from each other, which are an indication of time and temperature dependent processes in the bitumen. There are also differences between two heating cycles. In the first heating run, the bitumen has no thermal history compared to the second run. The discrepancies between the two runs show the existence of diffusion limited processes taking place in the bitumen structure and amplify the significance of removing any thermal history from the material prior to measurements. A more detailed study of the calorimetric behavior of heavy oils and bitumens can be found elsewhere (Bagheri et al., 2012; Bazyleva et al., 2011; Fulem et al., 2008a). To conclude the effect of temperature, it is worth mentioning that, hitherto, the efforts to obtain a comprehensive model to describe the viscosity of heavy oils and bitumens have been unsuccessful and all models have remained empirical in nature, needing experimental measurements to find the adjustable parameters for specific oils. Nevertheless, there have been some efforts to relate the correlation constants to physical properties like the boiling points of the fractions, the API gravity and the molecular weight (Amin and Maddox, 1980; Beg et al., 1988). 6.2 Effect of pressure (Pa ) Pressure is another parameter that plays a significant role in most processes of heavy oils and bitumens including EOR. However, the influence of pressure is not as profound as that of temperature. Nevertheless, as the pressure increases, one must consider its effect on the flow properties of heavy oils and bitumens. There have been many attempts to correlate the viscosity increase of heavy oils and bitumens to the pressure values through different functions. Nonetheless, the Barus equation has remained the most popular one due to its simplicity, acceptable accuracy and its physical significance. A number of proposed equations to model the pressure dependency of viscosity are listed in Table 2.4. Figure 6.3 depicts the zero–shear viscosity as a function of pressure in the temperature range from 30°C to 90°C. Nitrogen was used to pressurize the bitumen since it has very low solubility in heavy oils and bitumens. 72 Pressure, P (MPa)0 5 10 15 20Zero-shear viscosity, 0 (Pa.s)10-110010110210310430°C45°C60°C90°Ca)Pressure, p (MPa)0 5 10 15 20Pressure shift factor, ap0.9231.030°C45°C60°C90°Cb) Figure 6.3: (a) The zero–shear viscosity of the bitumen as a function of pressure at different temperatures. The dashed lines show fits of the Barus equation to the experimental data. (b) Pressure shift factor as a function of pressure at different temperatures. 73 As shown in Figure 6.3, pressure causes significant increase to the viscosity values (log scale is used in Figure 6.3a), more substantially at lower temperatures. By increasing the temperature, the effect of the pressure on the viscosity is relatively reduced, which is seen from the Pa values. The Barus equation can be written as (Barus, 1893): 0,0,exp( )Rpppa p (6.3) where 0, p, and 0, Rp are the zero–shear viscosities at the desired and reference, p is the pressure in MPa and is the pressure effectivity constant in MPa–1. In terms of the bitumen sample under study, the value of shows an almost Arrhenius relationship with temperature, which can be written as follows: 0.001569exp(9062.26/ )RT (6.4) where R is the universal gas constant in J/(mol.K) and T is the temperature in K. Therefore, it can be concluded that although the Barus equation seems to be adequate to express the effect of pressure on the flow behaviour of bitumen, a temperature dependent constant needs to be introduced to the equation to improve the accuracy of the predictions. 6.3 Effect of dissolved CO2 (Ca ) Various gases are used to reduce the viscosity of heavy oils and bitumen and raise the production rate in enhanced oil recovery (EOR). Carbon dioxide is one of the most effective gases because of its high solubility in heavy oils and bitumens (Mehrotra and Svrcek, 1988). There have been numerous efforts to measure the viscosity of the oil – CO2 mixture. Some of these studies are listed in Table 2.6. Most of the reports have made no mention to details of experimental conditions, e.g. the applied shear stress and shear rate or any possible flow instabilities such as bubbling, tertiary flow, flow field heterogeneity or evaporation that might occur during testing. Such instabilities may occur because of the complicated fluid path in apparatuses, which definitely influence the rheological results. 74 Figure 6.4a depicts the viscosity reduction of the the bitumen–CO2 mixture with different amounts of dissolved gas in the temperature range from 30°C to 110°C and up to saturation pressures of 10 MPa. In the calculation of Ca , the effect of the pressure was taken into account and corrections were performed to identify the influence of CO2 as a viscosity modifier independently. In Figure 6.4b, the lines split the graph area to three zones where CO2 is either gaseous, liquid or supercritical. In Figures 6.4c and 6.4d, the Mehrotra–Svrcek equation (Mehrotra and Svrcek, 1986) for the bitumen was used to calculate the amount of dissolved CO2 in the oil. Then, Ca is plotted against the amount of diffused CO2 at the saturated state. All measurements were performed in the laminar flow regime by knowing that the Reynolds number is well below the critical Reynolds number for the stirred tanks (~ 10000crUDRe Re ) (Sinnott and Gavin, 2009) where is the liquid density (0.969 gr/cm3), U is the representative velocity of the rotating geometry (maximum 0.12 m/s), D is the geometry diameter (25 mm) and is the liquid viscosity (Figure 6.1). In addition, enough care was taken to ensure that no bubbling occurred by preventing the Kelvin–Helmholtz instability satisfying the Richardson number criterion (25.0)/()/( 2022 crRidzddzdUgdzdUNRi ) (Miles, 1986), where N is the Brunt–Väisälä frequency, dzdU / is the velocity gradient along the interface, g is the gravitational acceleration, 0 is the liquid density and dzd / is the density difference between liquid and gas in the interface. Cavitation is another phenomenon that generates bubbles in the system and occurs at very high shear rates. We also prevented its occurrence by setting relatively low shear rates. On the other, the chosen shear rates were selected high enough to generate enough torque for accuracy of the measurements i.e. to exceed the lower torque limit of the magnetic coupling of the rheometer. As shown in Figures 6.4a to 6.4d, at a given amount of dissolved carbon dioxide, the viscosity drop at lower temperatures is higher. Analogous to the greater effects of temperature and pressure on the bitumen viscosity at lower temperature, it can be inferred that the flow properties of bitumen are more sensitive to the experimental conditions at lower temperatures. This can be attributed to the high level of heterogeneity in the structure of bitumens at lower temperatures (Mullins et al., 2012), while the temperature increase improves the homogeneity of the structure and morphology, which consequently results into less sensitivity to the experimental conditions. 75 Saturation pressure, psat (MPa)0 2 4 6 8 10Zero-shear viscosity, 0 (Pa.s)0.010.1110100100030°C50°C70°C90°C110°CFitted Function a)30°C50°C70°C90°C110°C Saturation pressure, psat (MPa)0 2 4 6 8 10aC0.0010.010.11110°C90°C70°C50°C30°CFitted Functionb) 76 Gas amount (cm3 at NPT CO2/cm3 bitumen)0 10 20 30 40 50 60aC0.0010.010.1170°C50°C30°CFitted FunctionMehrotra and Svreck (1982)70°C-Jacobs et al. (1980)50°C-Jacobs et al. (1980)c) Gas amount (cm3 at NPT CO2/cm3 bitumen)0 10 20 30aC0.11110°C90°CFitted FunctionMehrotra and Svreck (1982)100°C-Jacobs et al. (1980)d) Figure 6.4: (a) The zero–shear viscosity of the bitumen as a function of CO2 saturation pressure at different temperatures. The dashed lines show fits of combined functions (Equations 6.2, 6.3, 6.5, 6.7) to the experimental data. (b) CO2 concentration shift factor, Ca (obtained by accounting for pressure corrections shown by pa) , versus CO2 saturation pressure at different temperatures. (c, d) CO2 concentration shift factor, Ca (obtained by accounting for pressure corrections shown by pa ) , versus the dissolved CO2 amount (calculated from (Mehrotra and Svrcek, 1984)) at different temperatures. The dashed lines are fits of Equation 6.5 to the experimental data. The dash–double dot line determines the border between the gaseous and supercritical (or liquid) states of CO2. The solid lines represent the proposed equation of Mehrotra and Svrcek (Mehrotra and Svrcek, 1984) for the bitumen normalized by the viscosity values of compressed bitumen (Mehrotra and Svrcek, 1986). 77 The reported results in Figures 6.4c and 6.4d are in good agreement with data points reported by Jacob et al. (Jacobs, 1978) at lower temperatures (50°C and 70°C), while some disagreement appears at higher temperatures. It shows that the viscosity is affected by the temperature and saturation pressure which determines the amount of diffused substance into the oil. In addition to the experimental measurements, researchers have attempted to propose a comprehensive model to account for the effect of CO2 on the viscosity of oils (Beggs and Robinson, 1975; Chung et al., 1988; Mehrotra and Svrcek, 1982; Pedersen and Fredenslund, 1987; Yarranton and Satyro, 2009). A number of proposed correlations are listed in Table 2.6. Most of proposed correlations contain too many adjustable parameters or they require other physical properties of the mixture and pure components, which are difficult to measure. The Lobe mixing rule (Lobe, 1973) and the equation proposed by Mehrotra and Svrcek (Mehrotra and Svrcek, 1982) are amongst the most popular ones for bitumen and CO2 systems mainly due to their simplicity. From the two, the equation of Mehrotra and Svrcek (Mehrotra and Svrcek, 1982) has shown a good agreement with experimental data at lower CO2 concentrations (Figure 6.4). In addition, most of the proposed equations lack physical significance. Fujita and Kishimato (Fujita and Kishimoto, 1958) developed an equation to consider the effect of the dissolved gas on the flow properties of a polymer by using the free volume concept. After examining most of the Equations proposed in the literature and comparing them with experimental data obtained in this study, the Fujita–Kishimato equation was found the most appropriate from all. This is as follows: 0,0,1 1expRCCCa f f (6.5) where Ca is the shift factor accounting for the effect of the dissolved CO2, 0,C is the zero–shear viscosity at the reference CO2 concentration (in this case zero concentration), 0, RCis the zero–shear viscosity at the desired CO2 concentration, is the amount of the solvent and f and are the fractions of free volume and the contribution of the dissolved gas in increasing the free volume respectively. 78 Temperature, T (K)300 320 340 360 380 400 and f0.00.20.40.60.81.0fFitted Function= 4×10-6exp(0.0189T(K))R2=0.8763f= 0.0013exp(0.0133T(K))R2=0.967a) Temperature inverse, 1/T (K-1)0.0020 0.0025 0.0030 0.0035 0.0040 and f0.00010. 10.010.11fFitted Function= exp(0.3332)exp(-2163.9/T(K))R2=0.851f= exp(2.42)exp(-1536.6/T(K))R2=0.9605b) Figure 6.5: The dependence of constants of f and in Equation 6.5 on temperature. (a) Exponential equation. (b) Arrhenius equation.The dashed lines show the appropriate functions fitted to describe them as a function of temperature. Following the trend of the variation in f and , the best functions found to describe their dependence on the temperature should possess an exponential form (Figure 6.5). To find the appropriate values for f and , the inverse weight function was utilized to place more emphasis 79 on the small numbers of Ca which are more important due to the applied high pressures at the practical situations. 6.4 Effect of shear rate (Sa ) Apart from the effects that temperature, pressure and amount of dissolved solvent on the flow properties of heavy oils and bitumen, shear rate has also a significant effect on the rheological response of heavy oils and bitumens (see chapter 5). Different levels of shear rate and shear stress change the microstructural morphology in heavy oils and bitumens and accordingly alter the rheological response of the oils. The effect can be more pronounced at lower temperatures where most part of maltenes starts to solidify and form structured networks in the oil. In spite of many studies on the effect of shear rate on the flow properties of different heavy oils and bitumen (D Lesueur, 2009), there are limited reports on the shear rate effect on the oil–CO2 mixtures (Seifried and Temelli, 2011). A summary of studies on the effect of shear stress on the rheology of heavy oils and bitumens are listed in Table 2.5. According to the study on the neat bitumen in chapter 5, a non–Newtonian behaviour of the bitumen is detected at temperatures lower than 30°C, while slight shear thinning behaviour is observed at 30°C. Furthermore, at lower temperatures significant amounts of solid fractions cause the existence of a small yield stress for the oils. At values higher than the yield stress, a plateau viscosity is seen which is followed by a shear thinning behaviour at higher shear rates. For temperatures higher than 30°C, the Newtonian behaviour appears indicating the absence of yield stress effects at practical levels of shear rate. Figure 6.6 shows the viscosity data of the bitumen obtained from the experiments at ambient pressure and at different temperatures. It is evident that the bitumen behaves as a shear thinning material at temperatures below 30°C while it is almost Newtonian at temperatures above 30°C. The Carreau-Yasuda model is capable of describing this non-Newtonian behavior with an excellent agreement. Figure 6.7 depicts the flow curves of neat bitumen and bitumen–CO2 mixture obtained at different saturation pressures at 10°C. The agreement between the dynamic and steady viscosity values collected from both oscillatory and steady shear measurements using the parallel plate geometries of the rheometer at ambient pressure and that used in pressure cell set–ups is excellent. 80 As it is also evident from Figure 6.7, the rheological response of the bitumen and bitumen–CO2 mixture are Newtonian except at shear rates beyond 1 s–1 which indicated the onset of shear thinning. This behaviour can be described by using the Carreau–Yasuda model (Carreau, 1972; Yasuda, 1979) with 0 or the equation proposed by Liu et al. (Liu et al., 1983). Then with reference to the zero–shear viscosity, one may write: Shear rate, (s-1)10-210-1100101102103104Viscosity, () (Pa.s)100101102103104105106107108109-10°C 10°C 30°C 50°CCarreau-Yasuda (1979).. Figure 6.6: The viscosity of the bitumen at different temperatures. The dashed line show the prediction of the Carreau-Yasuda model. 101 ( )naaSa or 011S ma (6.6) where Sa is the shear rate shift factor, is the shear rate, n is the power law index,, is the viscosity at the desired shear rate and 0 is the zero–shear viscosity. , a , and m are the adjustable parameters which need to be determined for each system. Another significant point in Figure 6.7 is that the addition of CO2 to the bitumen does not cause any change in the rheological response of the bitumen other than simply shifting the data to lower stress levels. The dissolved carbon dioxide neither changes the colloidal structures nor alters 81 the interactions between the dispersed phase and matrix inside the bitumen, which are responsible for the non–Newtonian behaviour of heavy oils and bitumens. However, the addition of CO2 causes the fracture of the bitumen to be postponed to higher shear rates as no fracture was observed for saturation pressure of 4.50 MPa at 10°C. It is noted that for the neat bitumen (no CO2) fracture occurred at shear rates around 2 s–1. Shear rate or angular frequency, (s-1) or (rad/s)10-310-210-1100101102Stress or complex mudulus, or |G*| (Pa)1011021031041051060.13MPa-PP/REG/FR0.13MPa-PP/REG/SHEAR0.13MPa-PP/PR/SHEAR0.26MPa-PP/PR/SHEAR4.50MPa-PP/PR/SHEARNewtonian Curve (n=1).T=10°C Figure 6.7: The flow curves of the bitumen using various setups and type of testing at different saturation pressures at 10°C. At the legend, PP stands for parallel-plate, PR for the pressure cell, REG for set–up open to the atmosphere, SHEAR for steady shear testing and FR for frequency sweep experiment (small amplitude oscillatory shear). The power law index lies between 0.85 and 0.95 for 10°C. Similar observations can be made at 30°C by dissolution of various amounts of CO2 into the bitumen as can be seen in Figure 6.8. The vane–cup and parallel plate geometries were utilized to examine possible effects of geometry on the flow curves, which might come from slip and secondary flows. 82 Shear rate or angular frequency, (s-1) or (rad/s)10-210-1100101102Stress or complex mudulus, or |G*| (Pa)1001011021031041051060.13MPa-PP/REG/FR0.13MPa-PP/REG/SHEAR0.13MPa-PP/PR/SHEAR0.13MPa-VANE/PR/SHEAR0.63MPa-PP/PR/SHEAR0.92MPa-PP/PR/SHEAR1.30MPa-VANE/PR/SHEAR2.06MPa-VANE/PR/SHEARNewtonian Curve (n=1)T=30°C. Figure 6.8: Rotational and dynamic flow curves of the bitumen at different saturation pressures at 30°C. At the legend, PP and Vane are indicative of the measuring geometries. PR, REG, SHEAR and FR are abreviations for the pressure cell, regular set–up, shear sweep and frequency sweep experiment. The power law index lies between 0.91 and 0.98 for 30°C. 6.5 Thixotropy To investigate the effect of CO2 on the colloidal structure of the bitumen, step shear rate testing was performed to obtain the flow curves of the neat bitumen and the bitumen–CO2 samples at different structural levels. As discussed in the experimental section, the step shear rate test is very useful in determining the effect of the structure levels on the rheological behaviour in thixotropic materials whose structure is time and shear rate dependent. This experiment is a typical method of obtaining flow curves for thixotropic materials and it has been employed for different complex materials with time dependent structures (Ardakani et al., 2011). Materials with time and shear rate dependent structure are prone to structural change at different shear rates. Therefore, given enough time at a “reference” shear rate, the material’s structure reaches to a steady state and the stress response of the material is unchanged. Establishing the structural level at the “reference” shear rate, an abrupt change in the shear rate causes the stress to alter suddenly, which follows the intention to reach a new steady state at the new shear rate. However, after the first stress response 83 is recorded, the shear rate is adjusted to the “reference” shear rate to acquire the primary structural level. This sequence is repeated for different shear rates to build a flow curve at the structural level of that “reference” shear rate. Accordingly, the “reference” shear rate is changed and the same procedure is followed to draw more flow curves at various structural levels. The rheological responses of the bitumen and bitumen–CO2 mixtures in terms of flow curve are shown in Figure 6.9 at 30°C. As depicted, the rheological response of the samples exhibits no thixotropic effects at 30°C since the stress values collected at similar shear rates but different structural levels are within the rheometer accuracy. Therefore, none of the systems shows thixotropic behaviour at 30°C. Shear rate, (s-1)0.1 1 10 100Stress, (Pa)0100002000030000400000.13MPa-0s-10.13MPa-5s-10.13MPa-10s-10.92MPa-0s-10.92MPa-30s-10.92MPa-50s-1.T=30°C Figure 6.9: Flow curves of the bitumen at different structural levels at saturation pressures of 0.13 and 0.92 MPa at 30°C. The shear rates in the legend represent the base shear rate at which the flow curve is built. 6.6 Summary The rheological response of the bitumen–CO2 mixture has been investigated by using the method of the reduced variables in order to study independently the effects of temperature, pressure, 84 dissolved CO2 and shear rate. First, the double–log model was found to be the most accurate equation in describing the effect of temperature on the viscosity of bitumen. Secondly, the Barus model (Barus, 1893) with the temperature–dependent parameter was found to be the most appropriate correlation to represent the effect of pressure. Excluding the effect of overhead pressure, Equation 6.5 was introduced to account for the effect of the dissolved CO2 on the viscosity of the bitumen–CO2 mixture more accurately. It was found that the addition of CO2 to bitumen does not alter the rheological response of the bitumen, which implies that carbon dioxide does not change the colloidal structure of bitumen. However, the addition of CO2 postpones the bitumen fracture at higher shear rates. Having all the shift factors determined, the following equation can be written in order to calculate the viscosity of the bitumen–CO2 system: , , ,|T p C ST p C SRa a a a (6.7) where is the viscosities at the desired conditions of temperature, pressure, CO2 concentration and shear rate. , , ,|T p C SRis the viscosity the reference temperature, pressure, CO2 concentration and shear rate. The shift factors at the right hand side are to account for the effects of temperature (Equation 6.2), pressure (Equation 6.3), CO2 concentration (Equation 6.5) and shear rate (Equation 6.6). 85 7 MUTUAL DIFFUSIVITY OF CO2 IN BITUMEN In the present chapter, the pressure-decay technique is combined with rheological experiments to measure the equilibrium pressure precisely, and hence, to determine the mutual diffusivity based on the final equilibrium state. Mixing due to shear imposed by rheometry allows rapid direct measurement of the equilibrium pressure with a high degree of accuracy. This is achieved by monitoring both the viscosity and pressure of the system at the shearing step to ensure that the system reaches equilibrium. The advantage of the proposed technique is that the diffusivity is calculated directly from the measured equilibrium pressure with no assumptions for the equilibrium pressure. In addition, it is easy to apply while it eliminates the errors arising from the uncertainty of estimating the equilibrium pressure. 7.1 Diffusivity measurements The pressure profiles obtained from the pressure-decay experiments at 30°C, 50°C, 70°C, 90°C and 110°C are presented in Figures 7.1-7.5, respectively. The different steps of the experiment with different shear levels are separated by vertical dashed lines. As it is inferred from Figures 7.1-7.5, the pressure starts decaying once the carbon dioxide is allowed to come into contact with the bitumen. This is the case for a period of about 28hrs (first step). This allows performing the pressure-decay analysis in order to calculate the diffusivity as described in chapter 2. Once shear is applied, the pressure drops dramatically due to the shear induced diffusion (second step). The second step continues for about 35 hrs. To ensure the saturation of the system, a higher level of shear is applied in order to enhance the mixing until saturation occurs and therefore no further decrease in pressure and viscosity are observed (third step). Nevertheless, the second and third steps can be combined if adequately high shear rate is applied to the mixture (some experiments are in two steps). As shown in Figures 7.1-7.5, the high shear rate did not change the pressure level significantly, indicating that the equilibrium pressure was essentially reached during the moderate shear level. 86 Time, t (hr)0 20 40 60 80 100Pressure, p (MPa)1.82.02.22.42.62.8Reduced viscosity, /00.00.10.20.30.40.50.6Pressure-decay with no shearPressure-decay with shear Fitted function with measured peqFitted function with adjusted peqReduced viscosityT=30°Ca)0s-110s-130s-1 Time, t (hr)0 20 40 60 80 100Pressure, p (MPa)3.23.43.63.84.04.24.4Reduced viscosity, /00.00.10.20.30.4.5Pressure-decay with no shearPressure-decay with shearFitted function with measured peqFitted function with adjusted peqReduced viscosityT=30°Cb)0s-110s-130s-1 87 Time, t (hr)0 20 40 60 80 100 120 140Pressure, p (MPa)9.09.29.49.69.8Reduced viscosity, /00.000.020.040.060.080.10Pressure-decay with no shearPressure-decay with shear 30s-1Fitted function with measured peqFitted function with adjusted peqReduced viscosityT=30°Cc)0s-130s-1 Figure 7.1: Pressure-decay experiments at 30˚C; a) initial pressure0 2.423p MPa , b) initial pressure 0 4.034p MPa and c) initial pressure MPap 57.90 . The experiment starts with diffusion under no shear and is followed up by the application of shear (10 and 30s-1) that causes mixing and enhanced diffusion. The viscosity is normalized by the viscosity value of the gas-free bitumen at the same temperature. The dashed line shows the fitted Equation 2.20 using the measured value of the equilibrium pressure,eqp, while the solid line is the fitted Equation 2.20 with the equilibrium pressure, eqp, as an adjustable variable. Time, t (hr)0 20 40 60 80 100Pressure, p (MPa)1.82.02 22 42 6Reduced viscosity, /00.10.20.30.40.50.60.7Pressure-decay with no shearPressure-decay with shearFitted function with measured peqFitted function with adjusted peqReduced viscosityT=50°Ca)0s-130s-150s-1 88 Time, t (hr)0 20 40 60 80 100Pressure, p/Zg (MPa)4.04.24.44.64.85.05.25.4Reduced viscosity, /00.10.20.30.40.50.60.7Pressure-decay with no shearPressure-decay with shear Fitted function with measured peqFitted function with adjusted peqReduced viscosityT=50°Cb)0s-130s-150s-1 Time, t (hr)0 20 40 60 80Pressure, p (MPa)10.610.811.011.211.4Reduced viscosity, /00.00.10.20.30.40.5Pressure-decay with no shearPressure-decay with shear 100s-1Fitted function with measured peqFitted function with adjusted peqReduced viscosityT=50°Cc)0s-1100s-1 Figure 7.2: Pressure-decay experiments at 50˚C; a) initial pressure0 2.311p MPa , b) initial pressure0 5.008p MPa and c) initial pressure MPap 11.110 . The experiment starts with diffusion under no shear and is followed up by the application of shear (30, 50 and 100s-1) that causes mixing and enhanced diffusion. The viscosity is normalized by the viscosity value of the gas-free bitumen at the same temperature. The dashed line shows the fitted Equation 2.20 using the measured value of the equilibrium pressure,eqp, while the solid line is the fitted Equation 2.20 with the equilibrium pressure, eqp, as an adjustable variable. 89 Time, t (hr)0 20 40 60 80 100Pressure, p (MPa)1.82.02.22.42.6Reduced viscosity, /00.20.30.40.50.60.7Pressure-decay with no shearPressure-decay with shearFitted function with measured peqFitted function with adjusted peqReduced viscosityT=70°Ca)0s-130s-150s-1 Time, t (hr)0 20 40 60 80 100Pressure, p (MPa)4.04.24.44.64.85.05.2Reduced viscosity, /00.20.30.40.50.60.7Pressure-decay with no shearPressure-decay with shearFitted function with measured peqFitted function with adjusted peqReduced viscosityT=70°Cb)0s-130s-150s-1 90 Time, t (hr)0 20 40 60 80 100Pressure, p (MPa)9.810.010.210.410.6Reduced viscosity, /00.00.10.20.30.4Pressure-decay with no shearPressure-decay with shear 100s-1Fitted function with measured peqFitted function with adjusted peqReduced viscosityc)T=70°C 0s-1100s-1 Figure 7.3: Pressure-decay experiments at 70˚C; a) initial pressure0 2.244p MPa , b) initial pressure0 4.794p MPa and c) initial pressure MPap 396.100 . The experiment starts with diffusion under no shear and is followed up by the application of shear (30, 50 and 100s-1) that causes mixing and enhanced diffusion. The viscosity is normalized by the viscosity value of the gas-free bitumen at the same temperature. The dashed line shows the fitted Equation 2.20 using the measured value of the equilibrium pressure,eqp, while the solid line is the fitted Equation 2.20 with the equilibrium pressure, eqp, as an adjustable variable. The level of shear has been selected carefully in order to avoid fluid instabilities which cause bubbling or perturbation in the system leading to wrong viscosity measurements. The Kelvin–Helmholtz instability is one of the common instabilities in the gas-liquid systems which is prevented by satisfying the Richardson number Ri criterion, 2 20142crN gRi RiU U (Miles, 1986), where N is the Brunt–Väisälä frequency, U is the representative velocity of the geometry, g is the gravitational acceleration, 0 is the liquid density and is the density difference between liquid and gas in the interface. Bubbling might also happen due to cavitation if the shear rate exceeds a certain value. This phenomenon does not occur by choosing relatively low shear rates, which are 10 to 30s-1 at 30˚C, and 30 to 100s-1 at 50°C, 70°C, 90°C and 110°C. Another concern is with respect to the accuracy of the measurements where a high shear rate should be selected to generate enough torque and at the same time to be low enough to avoid the above 91 instabilities. This concern is also eliminated by choosing the abovementioned shear rates, which produce sufficient torques for accurate measurements. Time, t (hr)0 20 40 60 80Pressure, p (MPa)10.410.610.811.011.211.4Reduced viscosity, /00.00.10.20.30.40.5Pressure-decay with no shearPressure-decay with shear 100s-1Fitted function with measured peqFitted function with adjusted peqReduced viscosityT=90°C 0s-1100s-1 Figure 7.4: Pressure-decay experiments at 90˚C; initial pressure MPap 13.110 . The experiment starts with diffusion under no shear and is followed up by the application of shear (100s-1) that causes mixing and enhanced diffusion. The viscosity is normalized by the viscosity value of the gas-free bitumen at the same temperature. The dashed line shows the fitted Equation 2.20 using the measured value of the equilibrium pressure,eqp, while the solid line is the fitted Equation 2.20 with the equilibrium pressure, eqp, as an adjustable variable. To determine the diffusivity values from the pressure-decay experiments, Equation 2.20 was fitted to the first part of the pressure profile, shown in Figures 7.1-7.5. In order to examine the impact of the measured equilibrium pressure on the calculation, two scenarios are considered. In the first scenario, the parameters in Equation 2.20 are calculated by pre-setting eqp from the measured equilibrium pressures. In the other scenario, Equation 2.20 is fitted to the experimental data by allowing the equilibrium pressure to be an adjustable parameter. Table 7.1 lists the calculated diffusivities from both scenarios. It also presents the measured eqp along with the values obtained for eqp as an adjustable parameter. 92 Time, t (hr)0 20 40 60 80 100Pressure, p (MPa)10.210.410.610.811.011.211.411.6Reduced viscosity, /00.00.20.40.60.8Pressure-decay with no shearPressure-decay with shear 100s-1Fitted function with measured peqFitted function with adjusted peqReduced viscosityT=110°C0s-1100s-1 Figure 7.5: Pressure-decay experiments at 110˚C; initial pressure MPap 13.110 . The experiment starts with diffusion under no shear and is followed up by the application of shear (100s-1) that causes mixing and enhanced diffusion. The viscosity is normalized by the viscosity value of the gas-free bitumen at the same temperature. The dashed line shows the fitted Equation 2.20 using the measured value of the equilibrium pressure,eqp, while the solid line is the fitted Equation 2.20 with the equilibrium pressure, eqp, as an adjustable variable. The values of eqp determined from the data regression underestimate or overestimate the experimental values of the equilibrium pressure by 8% in the best case to 41% in the worst case. This can also be observed in Figures 7.1-7.5, where the two fitted lines diverge with time. This discrepancy influence the diffusivities determined from the pressure-decay experiments. The calculated diffusivities show that the adjusted eqp causes significant overprediction or underprediction of the diffusivity values in most cases. 93 Table 7.1: Calculated parameters from the analysis of the pressure-decay experiments ( )T C 0( )p MPa ( )eqp MPa 2R 9 210 ( / )D m s 30 2.423 Adjustable 2.251 0.990 2.632 Measured 1.997 0.985 0.493 4.034 Adjustable 3.566 0.992 1.871 Measured 3.311 0.990 0.755 9.57 Adjustable 7.206 0.991 0.044 Measured 9.24 0.98 1.395 50 2.311 Adjustable 2.122 0.997 2.660 Measured 1.932 0.994 0.731 5.008 Adjustable 3.796 0.998 5.586 Measured 4.280 0.998 1.080 11.112 Adjustable 10.97 0.993 6.157 Measured 10.766 0.99 1.019 70 2.244 Adjustable 1.115 0.996 0.110 Measured 1.896 0.992 0.928 4.794 Adjustable 4.506 0.994 4.419 Measured 4.173 0.993 1.162 10.396 Adjustable 7.955 0.993 0.039 Measured 9.914 0.9762 1.041 90 11.13 Adjustable 10.82 0.997 5.032 Measured 10.519 0.997 1.309 110 11.13 Adjustable 9.639 0.998 0.345 Measured 9.179 0.996 1.325 94 The diffusivities found by using the measured eqp are in the range of the diffusivity values reported in the literature (Fadaei et al., 2011; Upreti and Mehrotra, 2002, 2000). The values are well below the self-diffusivity values of carbon dioxide (Groß et al., 1998; Higashi et al., 2000; Winn, 1950) and lower than the diffusivities for CO2-heavy oil systems (Zhang et al., 2000), yet slightly above the reported values for CO2-Athabasca bitumen system (Upreti and Mehrotra, 2002, 2000). This is due to the difference in the oil composition which directly influences the physical properties including the diffusivity. This finding also emphasizes the usefulness of using the measured eqp in the accurate determination of the diffusivity values using the pressure-decay experiments. Thus, an accurate measurement of eqp is essential in the pressure-decay experiments which is achieved practically by employing the combined pressure-decay technique with rheometry. Figures 7.1-7.5 also plot the reduced viscosity of bitumen with shear as a function of time. The viscosity values are normalized to the viscosity of the pure bitumen which is 490, 30.55, 4.1, 0.915 and 0.2885 Pa.s at 30˚C, 50°C, 70°C, 90°C and 110°C, respectively. The viscosity of the CO2-bitumen mixture decreases significantly with time during the pressure decay experiments and this is due to the continuous CO2 diffusion into the oil. This decrease is neither due to thixotrophy nor due to shear thinning since bitumen does not show any significant thixotropic or shear thinning behavior at temperatures above 30˚C (Behzadfar and Hatzikiriakos, 2014a). The viscosity drop is more dominant at lower temperatures and higher pressures, which lead to dissolution of higher amounts of CO2 into the oil. This is in agreement with the findings reported previously in the literature (Behzadfar and Hatzikiriakos, 2014a; Mehrotra and Svrcek, 1982). It can also be observed from Figures 7.1-7.5 that the viscosity values reach their steady-state values before pressure. This is because the height of the rotating geometry (here 4-blade vane) is 19 mm which is shorter than the total height of the liquid sample in the cup (28-31 mm). Thus, once the height of liquid phase in contact with the geometry is saturated with CO2, the viscosity measurements do not show any further reduction. However, the diffusion process continues to saturate the remaining liquid below the four-blade vane. 95 Pressure, p (MPa)0 2 4 6 8 10 12Diffusivity, D×109 (m2/s)0.00.20.40.60.81.01.21.41.630°C50°C70°C90°C110°CGaseous CO2Supercritical CO2Liquid CO2 Figure 7.6: Measured diffusivities against equilibrium pressures at different temperatures. The circles show the thermodynamic state of CO2. Figure 7.6 depicts the calculated diffusivities from the above analysis based on using the measured values of eqp. As shown, the state of CO2 influences the trend of the diffusivity values. For the liquid state, the calculated value is higher while for supercritical CO2, the diffusivities are not far from the diffusivities measured for the gaseous state. This is due to the density and solubility of CO2 which changes with pressures in a non-linear trend. Figure 7.7a illustrates the weight fraction of CO2 in bitumens measured and predicted at different temperatures. As shown, while the solubility of CO2 keeps increasing with pressure at temperatures above 100˚C, it levels off with pressure at 50˚C. In Figure 7.7b, the density of carbon dioxide is depicted at different temperatures and pressures. The density increases dramatically once the state of carbon dioxide changes to liquid. This is the main reason of high diffusivity for the liquid carbon dioxide in Figure 7.6. Knowing that the diffusivities of CO2 into bitumen depend on the mass fraction of CO2 (Upreti and Mehrotra, 2000), the change in the solubility can be the main reason to have quite similar diffusivities at 50˚C and 70˚C once going to the supercritical region at elevated pressures. The CO2 density change is 333% and 211% at 50˚C and 70˚C, going from 5MPa to ~10MPa. However, it seems that the solubility constancy is more dominant in diffusion process compared to the density 96 increase which increases the diffusivity. For liquid CO2 at 30˚C, the density change is 736% moving from 4MPa to 10MPa which seemingly compensates the solubility constancy at 30˚C and leads to higher diffusivity values. Pressure, p (MPa)0 2 4 6 8 10 12Density, (gr/cm3)020040060080030°C50°C70°C90°C110°Cb) Figure 7.7: a) Measured and PHC (Perturbed Hard Chain) predicted (solid lines) solubility of CO2 in bitumen. Open symbols: Cold Lake bitumen (Yu et al., 1989), full symbols: Cold Lake bitumen (Mehrotra and Svrcek, 1988), and half-filled symbols: Peace River bitumen (Han et al., 1992). b) The density of carbon dioxide as a function of pressure at different temperatures, Measured and PHC (Perturbed Hard Chain) predicted (solid lines) solubility of CO2 in bitumen. Open symbols: Cold Lake bitumen (Yu et al., 1989), full symbols: Cold Lake bitumen (Mehrotra and Svrcek, 1988), and half-filled symbols: Peace River bitumen (Han et al., 1992). In Figure 7.8, the diffusivities are presented as a function of temperature at different levels of equilibrium pressures of about 2, 4 and 10 MPa. The diffusivity increases significantly with temperature due to the increase of the molecular mobility with temperature increase, e.g. altering the temperature from 30˚C to 50˚C and 70˚C leads to 88% and 54% increase in the diffusivity, respectively. This increase can be described by the Arrhenius equation effectively (dashed lines in Figure 7.8). These equations are listed in Table 7.2 for different equilibrium pressures. The calculated activation energies, as presented in Table 7.2, suggest that the diffusivities are slightly more sensitive to temperature at lower pressures. 97 103×T-1(K-1)2.6 2.8 3.0 3.2 3.4Diffusivity, D×109 (m2/s)0.1110100Viscosity, (Pa.s)0.010.11101001000D at p~2MPaD at p~4MPaD at p~10MPa at ambient pressuremix at p=2MPamix at p=4MPamix at p=10MPa Figure 7.8: Measured diffusivities and viscosities against inverse of temperature at equilibrium pressures of about 2, 4 and 10 MPa. The dashed lines show the Arrhenius equations fitted to every data set. Moreover, the diffusivity values show a slight increase with pressure, which indicates the effect of the dissolved gas in facilitating the diffusion process. At higher pressures the solubility of CO2 in the bitumen increases as more gas is dissolved. This finding is in agreement with the trend reported for the CO2-heavy oil systems in the literature (Upreti and Mehrotra, 2002). The diffusivity increase with pressure is more significant at 30˚C (increase by 53%) compared to an increase of 25% at 70˚C. This is due to the higher solubility of the bitumen at lower temperatures (Mehrotra and Svrcek, 1982). 98 Table 7.2: Arrhenius equations for the diffusivity and viscosity of the CO2-bitumen system. ( )p MPa Parameter Fitted equation Activation Energy (kJ) Ambient Diffusivity N/A N/A Viscosity 16 1036346.32 10 exp RT 103.6 2 Diffusivity 7 137431.17 10 expD RT 13.7 Viscosity 11 702763.54 10 exp RT 70.3 4 Diffusivity 8 94363.33 10 expD RT 9.4 Viscosity 10 614014.59 10 exp RT 61.4 10 Diffusivity 9 52326 97 10D . exp RT 5.2 Viscosity 8 46329 61 10 .exp RT 46.3 The measured viscosities are also plotted in Figure 7.7. The viscosity-temperature relationship is adequately described by the Arrhenius equations, as listed in Table 7.2 along with the fitted energy of activation values. The temperature causes the viscosity to decrease, while this decrease is more evident for the gas-free bitumen. This can be also inferred from the activation energies where a drop of 32% in the activation energy occurs by addition of CO2 increasing the pressure from ambient to 2 MPa. The viscosity also decreases by temperature at three different levels of pressure. 99 7.2 Diffusivity-viscosity-temperature relationship Numerous studies have proposed models to account for the relationship of the diffusivity with temperature and viscosity (Einstein, 2011; Umesi and Danner, 1981). The most well-known model is the Einstein’s model which is, 6 AkTD R (7.1) where k is the Boltzmann constant, AR is the radius of the diffusing particle and is the viscosity of the liquid mixture. Other models have also been proposed based on the Einstein’s model attempting to relate the diffusivity to temperature, viscosity and molecular characteristics. Temperature, T (K)300 320 340 360 380 40010-1310-1210-1110-1010-910-8D (m2/s) D/T (m2/(s.K)) Dbit/T (m2.Pa/K) Figure 7.9: Various groups of parameters plotted as a function of temperature. The dashed lines are fitted lines to the experimental data. The viscosity symbols bit denotes the viscosity of the neat bitumen. 100 These models suggest that the quantity of DT is constant for a given system and does not vary with temperature. In order to examine the accuracy of these models for the CO2-bitumen system, a number of groups of the parameters including diffusivity, temperature and viscosity are plotted as a function of temperature in Figure 7.9. As it is seen from Figure 7.9, the quantity of DT strongly depends on T for the CO2-bitumen system from 30˚C to 110˚C. The significant deviation from Equation 7.1 shows that the CO2-bitumen should not be considered as a simple liquid phase, since elements of maltenes yet undergo the melting process as the temperature changes from 30˚C to 110˚C (Bazyleva et al., 2011). The diffusivity itself, D , is also shown to strongly depend on temperature (doubles over a span of 40oC). 7.3 Summary The diffusivities of CO2 at three different states into bitumen are measured by employing a new technique that is the combined pressure-decay technique coupled with rheometry. This technique enhances mixing due to imposed shear and thus enables rapid direct measurement of the equilibrium pressure which is essential in the calculation of diffusivity in two phase systems as shown in this work. This technique benefits from the enhanced diffusion, induced by shear, after the initial diffusion process, which takes place in the absence of any shear. Thus, ensuring that no instability occurs in the system, the equilibrium state is reached efficiently even for highly-viscous liquids. The comparison of the measured equilibrium pressure with the predicted equilibrium pressure, obtained from assuming it as an adjustable parameter, demonstrate the significant deviation of the true value, which leads to a great discrepancy in the calculated diffusivity, e.g. about twenty-fold for the CO2-bitumen system. The combined pressure-decay technique with rheometry eliminates the errors associated with the prediction of the equilibrium pressure in various regression methods. The impact of temperature on the diffusivity of CO2-bitumen systems can be described by the Arrhenius equation. The diffusivity increases with temperature by 88% at the equilibrium pressure of 2 MPa and 54% at the equilibrium pressure of 4 MPa, respectively, increasing the temperature from 30˚C to 70˚C. The calculated diffusivity for gaseous CO2 increases with pressure 101 suggesting the ease of diffusion in the presence of more CO2 molecules in the oil phase. This increase is more dominant at lower temperatures while the diffusivity increase is 53% at 30˚C compared to 25% at 70˚C. It was shown that changing the state of CO2 impacts the diffusivity values of CO2 in bitumen and the diffusivity is higher for the liquid CO2 compared to supercritical CO2. 102 8 CONCLUSIONS AND CONTRIBUTIONS TO KNOWLEDGE 8.1 Conclusions The rheological behaviour of bitumen as a viscoelastic material has been investigated. Several types of experiments were performed to fully study the rheological response of bitumen at different temperatures and pressures. It was shown that the K-BKZ model is a continuum constitutive equation which can be appropriately used to model the rheological response of bitumens. It was found that the generalized Maxwell model is an excellent structural model in describing the linear response of bitumen in dynamic flow fields such as small amplitude oscillatory shear. Feeding the parameters acquired from the generalized Maxwell model (relaxation spectrum) into the K-BKZ constitutive equation, one is able to predict the linear viscoelastic behaviour of the bitumen. The agreement between the model predictions and the experimental data were excellent. The time-temperature superposition was found to apply in the case of bitumen over a wide range of temperatures, namely from -30°C to 90°C, essentially covering the range for most practical applications. To model the non-linear viscoelastic response of bitumen, the damping function data, ( ),h were determined over a wide range of temperatures. ( )h was found to be independent of temperature. The Papanastasiou and the Marruci models were utilized to represent the effect of shear strain on the damping function which was found to be adequate in most cases. The implementation of these two damping function models into the K-BKZ constitutive equation predicted the flow behaviour of the bitumen both in the linear and nonlinear viscoelastic regions adequately in most cases. Having identified an appropriate constitutive equation for bitumen, the presence of CO2 was taken into account to study its effect on the rheological behaviour of CO2-bitumen systems. The investigation was conducted by using the method of the reduced variables in order to independently study the effects of temperature, pressure, dissolved CO2 and shear rate. First, the double–log model was found to be the most accurate equation in describing the effect of temperature on the viscosity of bitumen. Secondly, the Barus model (Barus, 1893) with the temperature–dependent parameter was found to be the most appropriate correlation to represent the effect of pressure. Excluding the effect of overhead pressure, Equation 6.5 was introduced to 103 account for the effect of the dissolved CO2 on the viscosity of the bitumen–CO2 mixture more accurately. It was found that the addition of CO2 to bitumen does not alter the rheological response of the bitumen, which implies that carbon dioxide does not change the colloidal structure of bitumen. However, the addition of CO2 postpones the bitumen fracture to higher shear rates. Having all the shift factors determined, Equation 6.7 can be used in order to calculate the viscosity of the bitumen–CO2 system. The diffusivities of CO2 at three different states into bitumen are measured by employing a new technique that is the combined pressure-decay technique coupled with rheometry. This technique enhances mixing due to imposed shear and thus enables rapid direct measurement of the equilibrium pressure which is essential in the calculation of diffusivity in gas-liquid systems. This technique benefits from the enhanced diffusion induced by shear, after the initial diffusion process, which takes place in the absence of any shear. Thus, ensuring that no instability occurs in the system, the equilibrium state is reached efficiently even for highly-viscous liquids. The comparison of the measured equilibrium pressure with the predicted equilibrium pressure, obtained from assuming it as an adjustable parameter, demonstrate the significant deviation of the true value, which leads to a great discrepancy in the calculated diffusivity, e.g. about twenty-fold for the CO2-bitumen system. The combined pressure-decay technique with rheometry eliminates the errors associated with the prediction of the equilibrium pressure in various regression methods. The impact of temperature on the diffusivity of CO2-bitumen systems can be described by the Arrhenius equation. The diffusivity increases with temperature (30˚C to 70˚C) by 88% at the equilibrium pressure of 2 MPa and 54% at the equilibrium pressure of 4 MPa respectively. The calculated diffusivity increases with pressure suggesting the ease of diffusion in the presence of more CO2 molecules in the oil phase. This increase is more dominant at lower temperatures while the diffusivity increase is 53% at 30˚C compared to 25% at 70˚C. It is shown that the viscosity is influenced by the temperature and saturation pressure which determines the amount of diffused substance into the oil. 104 8.2 Contributions to knowledge The present work has yielded the following contributions to knowledge: 1- A suitable structural model has developed to account for the colloidal structure of bitumens and heavy oils. Using the generalized Maxwell model, all rheological properties of bitumens and heavy oils such as the yield stress can be described. 2- Although there is a controversy on the applicability of the Cox-Merz rule for bitumens and heavy oils, our finding shows that the Cox-Merz rule holds true for our studied bitumen. 3- Depending on the structure of bitumens and heavy oils, they might show small yield stresses where it can impact their rheological behavior at low shear rates. 4- An appropriate continuum constitutive model (K-BKZ model) has developed to model the rheological behaviour of bitumens and heavy oils over a wide range of temperatures. A universal damping function (Marruci) has been introduced to account for the non-linear viscoelastic behaviour of bitumens over a wide range of temperatures. 5- According to the results of this study, the reduced parameter model can be used to study the effects of temperature, pressure, CO2 concentration and shear rate on the flow properties of bitumens and heavy oils. Using this model, one can easily determine the effect of different parameters on the rheology of bitumen. This model benefits from highest degree of simplicity and accuracy in predicting the experimental results. The applicability of the model is also extended to higher temperatures and pressures to account for the effects of supercritical and liquid CO2. 6- A novel and reliable method has been developed to measure the diffusivity in gas-liquid and liquid-liquid systems. Combining the pressure decay experiment coupled with rheometry, the diffusivity values can be measured in shorter times and with higher accuracy. This method eliminates the errors arising from the prediction of the equilibrium pressure in diffusivity measurements. 7- The diffusivities of CO2 in bitumen are determined over a wide range of temperatures and pressures. This study is the first study to measure the diffusivity values for supercritical and liquid CO2 into bitumens and heavy oils. 105 8.3 Recommendations for future work There are many areas in the subject of bitumens and heavy oils which need to be addressed in the future. In particular, CO2-bitumen systems can be investigated into a higher depth in order to gain a better understanding of rheology applicable to reservoir engineering. A number of suggestions are as follows: 1- A study is required to understand the effect of CO2 on the interactions between different fractions of heavy oils and bitumens. Introducing CO2 can alter the interactions between fractions which leads to structural changes and hence variations in rheological response. 2- A study is needed to identify the capillary forces in the reservoirs for CO2-bitumen systems. This study can aim at mimicking actual reservoir conditions for these mixtures. Outcomes of this research can shed light on how the mixture flows at actual reservoir conditions. 3- Although there is a great deal of research performed on the structure of asphaltenes, the aggregation, agglomeration and break-up processes of asphaltenes at actual reservoir conditions are not yet understood. A study can clarify the mechanism of asphaltenes aggregation, agglomeration and break-up. 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The flow properties of bitumen in the presence of carbon dioxide Behzadfar, Ehsan 2014
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Title | The flow properties of bitumen in the presence of carbon dioxide |
Creator |
Behzadfar, Ehsan |
Publisher | University of British Columbia |
Date Issued | 2014 |
Description | The present dissertation discusses the flow behaviour of bitumens in the presence of CO₂. Firstly, the viscoelastic behaviour of bitumen is studied and an appropriate constitutive equation is identified to describe its rheological behavior. The K-BKZ constitutive equation has been shown to represent accurately the rheological properties of bitumen. Analysis of experimental results revealed that either the Papanastasiou or the Marucci form of the damping function can be used in the K-BKZ constitutive equation. Moreover, the damping function was found to be independent of temperature (0°C-50°C). Secondly, the effects of temperature, pressure, dissolved carbon dioxide and shear rate on the rheological response of bitumen are investigated by using the reduced variable method at the temperature range of –10°C to 180°C and pressures up to 15 MPa. The double–log model is found to be the most accurate equation in describing the effect of temperature on the viscosity of bitumen over a wide range of temperature while the Barus model with the temperature–dependent parameter is found to be the most appropriate correlation to represent the effect of pressure. The Fujita–Kishimato equation, resulting from the free volume concept modelling, is employed to account for the effect of dissolved CO₂ on the viscosity of the bitumen–CO₂ mixture. The results show that the viscosity is influenced by the temperature and saturation pressure. Thirdly, the combined pressure-decay technique with rheometry is developed to measure the diffusivity of CO₂ in bitumen at the temperatures of 30˚C, 50˚C, 70˚C, 90˚C and 110˚C and saturation pressures of 2, 4 and 10 MPa. The impact of temperature on the diffusivity of CO₂-bitumen systems can be described by the Arrhenius equation. The diffusivity increases with pressure at gaseous CO₂ state. The increase is more dominant at lower temperatures while the diffusivity increase is 53% at 30˚C compared to 25% at 70˚C. It is shown that changing the state of CO₂ impacts the diffusivity values of in bitumen while the diffusivity is higher for the liquid CO₂ compared to supercritical CO₂. |
Genre |
Thesis/Dissertation |
Type |
Text |
Language | eng |
Date Available | 2014-09-30 |
Provider | Vancouver : University of British Columbia Library |
Rights | Attribution-NonCommercial-NoDerivs 2.5 Canada |
DOI | 10.14288/1.0135569 |
URI | http://hdl.handle.net/2429/50496 |
Degree |
Doctor of Philosophy - PhD |
Program |
Chemical and Biological Engineering |
Affiliation |
Applied Science, Faculty of Chemical and Biological Engineering, Department of |
Degree Grantor | University of British Columbia |
Graduation Date | 2014-11 |
Campus |
UBCV |
Scholarly Level | Graduate |
Rights URI | http://creativecommons.org/licenses/by-nc-nd/2.5/ca/ |
Aggregated Source Repository | DSpace |
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