Investigation of two-phase microchannel flow and phase equilibria in micro cells for applications to enhanced oil recovery

Transcription

1 Investigation of two-phase microchannel flow and phase equilibria in micro cells for applications to enhanced oil recovery by Hooman Foroughi A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Graduate Department of Chemical Engineering & Applied Chemistry University of Toronto Copyright by Hooman Foroughi 01

2 Investigation of two-phase microchannel flow and phase equilibria in micro cells for applications in enhanced oil recovery Abstract Hooman Foroughi Doctor of Philosophy Graduate Department of Chemical Engineering & Applied Chemistry University of Toronto 01 The viscous oil-water hydrodynamics in a microchannel and phase equilibria of heavy oil and carbon dioxide gas have been investigated in connection with the enhanced recovery of heavy oil from petroleum reservoirs. The oil-water flow was studied in a circular microchannel made of fused silica with an I.D. of 50 µm. The viscosity of the silicone oil (863 mpa.sec) was close to that of the gassaturated heavy oil in reservoirs. The channel was always initially filled with the oil. Two different sets of experiments were conducted: continuous oil-water flow and immiscible displacement of oil by water. For the case of continuous water and oil injection, different types of liquid-liquid flow patterns were identified and a flow pattern map was developed based on Reynolds, Capillary and Weber numbers. Also, a simple correlation for pressure drop of the two phase system was developed. In the immiscible displacement experiments, the water initially formed a core-annular flow pattern, i.e. a water core surrounded by a viscous oil film. The initially symmetric flow ii

3 became asymmetric with time as the water core shifted off centre and also the waves at the oilwater interface became asymmetric. A linear stability analysis for core-annular flow was also performed. A characteristic equation which predicts the growth rate of perturbations as a function of the core radius, Reynolds number, and viscosity and density ratios of the two phases was developed. Also, two micro cells for gas solubility measurements in oils were designed and constructed. The blind cell had an internal volume of less than ml and the micro glass cell had a volume less than 100 µl. By minimizing the cell volume, measurements could be made more quickly. The CO solubility was determined in bitumen and ashphaltene-free bitumen samples to show that ashphaltene has a negligible effect on CO solubility. iii

4 Acknowledgments I would like to thank my supervisor, Prof. Masahiro Kawaji, and my labmates, Mehrrad, Alireza, Dan and Kausik, for all their help. The committee members, Prof. Edgar Acosta, Prof. Axel Guenther, Prof. Ramin Franood, and Prof. Khellil Sefiane, kindly provided me with their insightful comments during my PhD program. I had helpful discussions with Prof. Charles Ward, Prof. Arun Ramchandran and Prof. Naser Ashgriz. My special thanks to my family and friends, Alireza, Sofia, Leila, Maryam, Pooya, Nima, and Hadi for their support. iv

5 Table of Contents Acknowledgments... iv Table of Contents... v List of Tables... ix List of Figures... x List of Appendices... xiv Nomenclature... xv Chapter 1: Introduction Viscous oil-water flows in a microchannel initially saturated with oil: flow patterns and pressure drop characteristics Immiscible displacement of oil by water in a microchannel: asymmetric flow behavior and stability analysis Gas solubility measurements by using micro-cells... 7 Chapter : Viscous oil-water flows in a microchannel initially saturated with oil: flow patterns and pressure drop characteristics Experimental details Materials Experimental facility Continuous liquid injection Fluid injection section Pressure Drop and Flow Rate Measurements Image capture Results and discussion Flow patterns Pressure Drop Measurements and Analysis for Slug, Annular and Annular- Droplet Flows... 5 v

6 Chapter 3: Immiscible displacement of oil by water in a microchannel: asymmetric flow behaviour and non-linear stability analysis Experimental details Materials Experimental Facility Flow Behaviour Stability analysis Chapter 4: A Miniature Cell for Gas Solubility Measurements in Oils and Bitumen Experimental Details Materials Experimental apparatus Solubility cell Pre-injection Cell Experimental Procedure Step 1: Liquid Injection into the Solubility Cell Step : Gas Injection Step -1: Gas Injection into the Pre-injection Cell Step -: Gas Injection from Pre-injection Cell into Solubility Cell Step 3: Solubility Measurements at 60 C Steps 4&5: Solubility Measurements at 35 C and C Step 6: Changing the Cell Temperature to Room Temperature for Next Gas Injection Results and Discussion Effect of gas dissolution on flow stability... 8 Chapter 5: Design of a micro glass cell apparatus for pure gas-nonvolatile liquid phase behavior study ) Experimental details vi

7 5-1-1) Materials ) Experimental apparatus ) Micro cell ) Gas line ) Liquid line ) Experimental procedure for systems with low viscosity liquids ) Vacuuming the cell ) Gas injection into the cell ) Liquid injection into the cell ) Temperature adjustment ) Mixing and reaching equilibrium conditions ) Experimental procedure for systems with highly viscous liquids ) Manual bitumen injection ) Gas injection ) Mercury injection ) Calculating reference CO solubility values in water from Henry s law ) Experimental results ) Error analysis ) Error due to the uncertainty in temperature and pressure measurements ) Error due to neglecting the liquid vapor pressure ) Error due to neglecting the gas diffusion through the needle Chapter 6: Conclusions Viscous oil-water two phase flow in a microchannel Immiscible displacement of oil by water in a microchannel: asymmetric flow behavior and stability analysis A miniature blind cell for solubility measurements vii

8 6.4. A micro glass cell for solubility measurements References Appendix I: Non-linear Stability analysis for core annular flow viii

9 List of Tables Table -1. Constants C 1 - C 4 in Eqs. 7 and 8 for the present and Salim et al. s (008) pressure drop data Table 3-1. Test conditions Table 3-. The initial ( a ) and last symmetric ( z ) wavelengths and wave speed. The f 1 experimental values are compared with the results of the non-linear ( ) and linear ( f ) analysis Table 4-1. SARA analysis of bitumen samples Table 4-. The effect of gas saturation on viscosity of Peace River bitumen ix

10 List of Figures Figure 1-1: Schematic of the CO and water injections into an oil reservoir Figure -1: Schematic of experimental apparatus... 1 Fig. -. Schematic of injection section Fig. -3. Effect of optical correction: a) without optical correction, b) with optical correction Fig. -4. Flows in the microchannel injection section: a) Single-phase oil flow (Q O =13 μl/min); b) Plug flow (Q O =13 μl/min, Q W =15 μl/min); c) Annular flow (Q O =13 μl/min, Q W =48 μl/min); d) Annular flow (Q O = μl/min, Q W =70 μl/min) Fig. -5. Flow patterns observed in viscous oil-water flow in a microchannel initially filled with oil: a) Droplet flow - water droplets in continuous oil phase (Q O =13 μl/min, Q W = μl/min); b) Plug Flow (Q O =46 μl/min and Q W =110 μl/min); c) Slug flow (Q O =46 μl/min, Q W =5 μl/min); d & e) Annular flow with sausage-shaped interfacial deformations (Q O =46 μl/min, Q W =530 μl/min); and f) Annular-droplet flow with smooth oil-water interface (Q O =46 μl/min and Q W =115 μl/min); g) Annular-droplet flow with wavy oilwater interface (Q O =46 μl/min, Q W =135 μl/min) Fig. -6. Flow pattern map for silicone oil-water flow in a 50 μm microchannel initially saturated with oil. The solid lines indicate the flow pattern transition boundaries Fig. -7. Pressure drop data for silicone oil-water flow in a microchannel. The constants in Eq. 8 are C 7648 and C Fig. -8. Prediction of Salim et al. (008) s pressure drop data for a glass microchannel by Eq. 8 with C and C Fig. -9. Prediction of Salim et al. (008) s pressure drop data for a quartz microchannel by Eq. 8 with C 11 and C Fig Linear variation of the water two-phase friction multiplier, Martinelli parameter, W, with Lockhart Fig Linear variation of the oil two-phase friction multiplier, O, with the inverse of 1 the Lockhart-Martinelli parameter, Fig A schematic of the experimental apparatus x

11 5 3 Fig. 3-. Flow patterns at Ca wi and Caw 9 10 observed in the middle of the channel (top view) at different times from the start of the water injection.: a) at t=0 sec, the channel was filled with oil; b) at t=50.7 sec, the water finger was displacing the oil at the core; c) at t=53.3 sec, the oil film was left evenly on the channel wall and the oil-water interface was smooth; d-1) at t=95.5 sec, symmetric perturbations formed at the interface; d-) at t=10.5 sec, the wavelength increased; e) at t=104., the water core shifted from the centre and the flow became asymmetric; f) at sec and g) at t=308.0, the water core touched one side of the channel; h) at t=550 sec, the oil was completely displaced Fig The initial water core thickness: the comparison of the experimental results with Equation Fig The water finger at Ca wi 10 observed in the middle of the channel, 714 sec after the start of the water injection. The oil film on the channel wall is too thin to be observed 4 Fig The variation of the pressure at the channel inlet with time Fig The water core fluctuation between the sides of the channel at Caw , a) at 9. sec; b) at 30. sec; c) 33.4 sec Fig Flow patterns at Ca wi and Caw 9 10, symmetric flow became asymmetric: a) at 10.0 sec; b) at 10.6 sec; c) at 103. sec Fig The variation of the maximum water core radius with time Fig The variation of the maximum oil film thicknesses on opposite sides of the channel with time Fig A stable water core broke up into droplets after the flow was stopped: a) asymmetric flow at Caw ; b) at 180 sec after the flow was stopped; c) at 740 sec after the flow was stopped Fig Dimensionless growth rate,, vs. dimensionless wave number, k, at * 5 l 1.03, ao 0.8, m 0.001, Re 0.007, Wew 0.8 and We o 3 10 : the system predicted by the non-linear analysis is more stable compared to the one predicted by the linear analysis Fig The ratio of the fastest growing wavelength to the water core radius vs. water Reynolds number. The results of the non-linear analysis (Eq. 9), linear analysis (Eq. 33), and the last symmetric wavelength in experiments ( z ) are compared: a) Experimental results are presented based on average velocities; b) Experimental results are presented based on interfacial wave speed. The values of the water core radius in Equation 9 are calculated by Equation Fig Density of bitumen samples and maltene extracted from sample 1 vs. temperature xi

12 Fig. 4-. Schematic of the experimental apparatus: 1) water bath 1 (WB1), ) thermocouple, 3) solubility cell, 4) magnetic mixer, 5) rotating magnetic field, 6) T-junction, 7) pressure transducer 1 (P1), 8) micro-valve 1 (V1), 9) pre-injection cell, 10) pressure transducer (P), 11) micro-valve (V), 1) purge valve, 13) gas regulator, 14) CO gas cylinder, 15) data acquisition system, 16) water bath (WB), 17) computer Fig Schematic of the solubility cell: 1) plug, ) compression fitting, 3) column end fitting, 4) magnetic mixer, 5) equilibrium cell, 6) micro-tube, 7) T-junction, 8) micro-tube connected to pressure transducer 1 (P1), 9) micro-tube connected to micro-valve 1 (V1) Fig Summary of the experimental procedure for solubility measurements Fig Formation of a liquid film inside the solubility cell Fig Changes in pressure and temperature of the solubility cell with time 7 Fig Variation of CO gas solubility in bitumen with pressure at C compared with solubility data reported by Mehrotra and Svrcek (1985b) for Peace River bitumen Fig Variation of CO gas solubility in bitumen with pressure at 35 C Fig Variation of CO gas solubility in bitumen with pressure at 60 C compared with solubility data reported by Mehrotra and Svrcek (1985b) for Peace River bitumen Fig Variation of CO gas solubility in bitumen sample 1 and maltene extracted from sample 1 with pressure at C. The recalculated solubility in maltene accounts for the amount of ashphaltene removed Fig Variation of CO gas solubility in bitumen sample 1 and maltene extracted from sample 1 with pressure at 35 C. The recalculated solubility in maltene accounts for the amount of ashphaltene removed Fig CO gas solubility data for bitumen sample 1 at C from three runs Fig The effect of swelling on CO solubility in bitumen sample Fig Maximum dimensionless growth rate predicted by linear stability analysis vs. dimensionless wave number, k, at l 1.03, a o 0.75, and * Re Figure 5-1. Schematic of the experimental apparatus consisting of three parts: the micro cell, gas line, and liquid line. The schematic is not to scale Figure 5-. The glass syringe used as the micro cell with a magnetic mixer and a bitumen plug inside.. 88 xii

13 Figure 5-3. Schematic of the gas line and the micro cell for gas injection process: a) The gas has been injected into the cell at pressure P g inj. and at room temperature; b) The valve V1 is closed and the gas line is vacuumed for the second time before the liquid injection Figure 5-4. Schematic of the liquid line and the micro cell for liquid injection. The liquid is injected at pressure P l inj. which is higher than the pressure of the gas injection Figure 5-5. Pressure change in the cell in each step for the solubility measurement by the pressure decay method Fig The micro cell for CO solubility measurements in bitumen: bitumen, CO, and mercury are injected into the cell before the start of the mixing Figure 5-7. The schematic of the solubility cell presented in Chapter Figure 5-8. CO solubility in water variation with pressure at temperatures of 31, 35, 40, and 50 o C. The solubility values measured in this study are compared with the reference values (Perry et al., 1997) and the values calculated from Henry s law (Equation 8) Figure 5-9. CO solubility in bitumen vs. pressure at o C. The experimental results of this work are compared with the results presented in Chapter Figure The schematic of the gas diffusion problem through the needle Figure I-1. Schematic of core-annular flow xiii

14 List of Appendices Appendix I. Nonlinear stability analysis for core annular flow xiv

15 Nomenclature A constant a water core radius a o unperturbed water core radius B constant Bo Bond number C constant (Chapter ); molar concentration (Chapter 5) Ca Capillary number D gl gas diffusion coefficient in liquid D channel diameter d water core diameter f fugacity G Gibbs energy H enthalpy h oil film thickness k wave number (Chapter 3); Henry constant (Chapter 5) L channel length (Chapter ); needle length (Chapter 5) xv

16 l water to oil density ratio M molecular weight m water to oil viscosity ratio (Chapter 3); mass (Chapters 4 & 5) N molar flux n number of moles P pressure P1-P pressure transducers Pˆ solute partial pressure Q volumetric flow rate R channel radius (Chapter 3); gas constant (Chapter 5) Re Reynolds number r radius S solubility (Chapter 4); entropy (Chapter 5) T temperature t time V velocity (Chapters &3); volume (Chapters 4&5) V1-V6 valves xvi

17 U dimensionless velocity W solubility W * characteristic velocity We Weber number x distance from the solubility cell z flow direction Greek symbols α constant β constant ε o oil to mixture volumetric flow rate ratio η constant for microchannel property λ dimensionless wavelength µ viscosity density φ Lockhart-Martinelli friction multiplier π pi constant xvii

18 σ interfacial tension χ Lockhart-Martinelli parameter ω dimensionless frequency Subscripts and superscripts a first eq. equilibrium c critical f fastest i initial inj. injection G gas (Chapter 4) g gas (Chapter 5) L liquid (Chapter 4) l liquid (Chapter 5) max maximum o oil xviii

19 TP two phase w water z last * characteristic parameter (Chapter 3); reference state ( Chapter 5) _ average / perturbations xix

20 1 Chapter 1 Introduction To enhance oil recovery, immiscible liquids such as water are injected into petroleum reservoirs in order to displace and push out oil towards the production wells (Figure 1-1). For recovery of highly viscous oils, such as bitumen, miscible gases such as CO can be injected before the immiscible (water) injection. The oil viscosity is significantly reduced as the gas is dissolved in the oil, which increases the oil flow rate (Simon et al., 1965; Jacobs et al., 1980). Knowledge of the oil-water flow characteristics and also gas solubility in oil is thus required to design and optimize the enhanced oil recovery process. In this study, the two-phase oil-water flow in a microchannel was investigated in connection with the flow of oil and water in petroleum reservoirs. The viscosity of the oil (863 mpa.s) used in the experiments was comparable to that of the gas saturated bitumen in reservoirs. The microchannel diameter (50 µm) was in the range of the pore size of porous media in oil reservoirs. Although the flow passages in petroleum reservoirs would be highly interconnected and not straight channels, the present experiments were performed to gain a basic understanding of the hydrodynamics of viscous oil-water in a well-defined microchannel geometry. Before each experiment, the microchannel was always initially saturated with oil. Two separate sets of experiments were performed to compare different flow conditions for oil recovery: in the first set of experiments, oil and water were simultaneously injected into the initially oil-saturated microchannel (Chapter ). Different oil-water flow patterns were identified some of which have not been reported in previous works, i.e. annular-droplet flow with a smooth or wavy interface. The interfacial tension, inertia, and viscous forces which would control the flow pattern were compared and a new flow pattern map was developed based on the dimensionless Capillary, Weber, and Reynolds numbers. The amounts of the oil displaced by the water in different flow patterns were also compared. The pressure drop data were collected and analyzed. A simple model was developed for the oil-water two-phase pressure drop in initially oil saturated microchannels. It is shown that this

21 model is applicable to systems of oil-water flows with different oil viscosity and also with different micorchannel geometries. In the second set of experiments referred to as the immiscible oil displacement experiments, the microchannel was filled with oil and then only water was injected into the channel to displace the oil (Chapter 3). The asymmetric flow behavior observed with time in the immiscible displacement experiments has not been reported in previous studies. The rates of the oil displacement under different experimental conditions were compared. A suggestion is made that intermittent water injection can improve the rate of oil recovery. A linear stability analysis was also performed on core-annular flows. The water core remained continuous in a stable system but tended to form a dispersed phase in an unstable system. This analysis allows us to determine the sensitivity of the flow stability to different fluid properties such as density and viscosity ratio of the two phases. For gas solubility measurements in heavy oil (bitumen) samples, two micro cells were designed and constructed: a miniature blind cell with a volume of less than ml (Chapter 4) and a micro glass cell with a volume less than 100 µl (Chapter 5). By minimizing the volume of the cell, the time required for the system to reach equilibrium which could take up to weeks or months in previous designs (Badamchi-Zadeh et al., 009) was reduced to less than 90 minutes with the glass cell and less than 10 minutes with the blind cell. The CO solubility measurements in bitumen and asphaltene-free bitumen were compared to find that ashphlatene had a negligible effect on CO solubility. Also, in Chapter 4, the effect of gas dissolution on the flow stability is discussed based on the results of the stability analysis presented in Chapter 3. Although the motivation behind the microchannel flow study is to understand the water-oil flow characteristics in petroleum reservoirs better, the discussion provided in Chapter may be generally applicable to liquid-liquid two-phase flows in microchannels for different applications. Also, the use of the solubility cells described in Chapters 4 and 5 is not limited to gas-oil systems and these cells can be used for a variety of gas-liquid mixtures.

22 3 Figure 1-1: Schematic of the CO and water injections into an oil reservoir. 1.1 Viscous oil-water flows in a microchannel initially saturated with oil: flow patterns and pressure drop characteristics Liquid-liquid flows are encountered in a wide range of applications in chemical engineering such as microreactors and a lab-on-a-chip (Gunther et al., 006), and petroleum engineering (Joseph et al., 1997). Numerous investigations have been carried out on liquid-liquid flows in conventional pipes with large hydraulic diameters. Many of these studies were performed in horizontal and vertical pipes as reviewed by Joseph et al. (1997) and Ghosh et al. (009). In microchannels with hydraulic diameters of µm, gas-liquid flows have been investigated extensively at the University of Toronto (Kawahara et al., 00; Chung and Kawaji, 004; Chung et al., 004; Kawahara et al., 005; Santos et al., 010). In the case of liquid-liquid flows in microchannels, many researchers have studied the formation of droplets in microfluidic devices (Thorsen et al.,

23 4 001; Anna et al., 003; Tice et al., 003; Cramer et al., 004; Garstecki et al., 006; Tan et al., 008; Baroud et al., 010), as well as the hydrodynamics and pressure drop of slug flow (Kashid and Agar, 007; Jovanovic et al., 011). However, only few flow pattern maps have been presented for liquid-liquid flows in microchannels (Zhao et al., 006; Dessimoz et al., 008; Salim et al., 008). The liquid-liquid flow patterns in microchannels are known to be influenced by the fluid properties including the wetting properties of the fluid and microchannel (Dreyfus et al., 003; Salim et al., 008), the geometry and size of the channel and the injection section (Kashid and Agar, 007; Dessimoz et al., 008) and the dominant forces which control the flow pattern (Zhao et al., 006; Dessimoz et al., 008). Liquid-liquid flow patterns and pressure drop correlations for microchannels, especially when one of the phases is highly viscous, however, have not been very well understood yet. Cramer et al. (004) experimentally studied the formation of droplets in rectangular capillaries by injecting the dispersed phase through a needle. Two different breakup mechanisms were distinguished: dripping and jetting. In dripping, the droplets were formed close to the injection section while in jetting the droplets were formed from an extended jet downstream. Guillot et al. (007) studied the stability of a jet in circular capillaries by performing a linear stability analysis. A stable system formed a continuous jet regime and an unstable jet broke up into droplets. The results of the stability analysis were presented based on the capillary number, viscosity ratio, unperturbed jet diameter and flow rates. Zhao et al. (006) studied the flow of water and kerosene in a T-junction microchannel. They observed different flow patterns and developed a flow pattern map based on a Weber number. The flow pattern map was divided into three zones: the interfacial tension dominated zone, the transition zone where inertia and interfacial tension were comparable, and the inertia dominated zone. They also studied the mechanism of droplet and slug formation at the T-junction. Kashid and Agar (007) investigated the flow pattern, slug size, interfacial area, and pressure drop for liquid-liquid slug flow in Y-junction mixing elements with various downstream capillaries. They showed that the slug size and interfacial area would change with the Y-junction and capillary dimensions. They also developed a theoretical model for predicting the pressure drop. The model

24 5 included individual terms for capillary pressure drop and hydrodynamic pressure drop. Dessimoz et al. (008) studied the flow pattern and mass transfer characteristics of water-toluene and water-hexane flows in T-junction and Y-junction microchannels. They developed flow pattern maps based on Reynolds and Capillary numbers and discussed how interfacial forces compete with viscous forces to change the flow pattern from parallel to slug flow. Salim et al. (008) studied the oil-water flow patterns and pressure drops in micro T-junctions. They used homogeneous flow and Lockhart-Martinelli correlations to interpret the measured pressure drops. The flow patterns and pressure drop were found to depend on the type of the fluid which was first injected into the channel and the channel material. Jovanovic et al. (011) studied the hydrodynamics and pressure drop of slug flow in circular microchannels. Two pressure drop models were presented: a stagnant film model and moving film model. Both models considered the formation of a thin film between slugs and the channel wall. They showed that the film velocity could be neglected and the stagnant film model could be used to predict the pressure drop data. In the case of viscous liquid-liquid flows in microchannels, Cubaud and Mason (006, 007, 008b, 009) investigated the flow behaviour of miscible fluids. Regarding the flow of immiscible liquids, they studied the flow of a viscous thread surrounded by a less viscous fluid in square microchannels (Cubaud and Mason, 008a). They developed a flow pattern map based on the capillary number of each fluid and distinguished five different flow regimes: threading, jetting, dripping, tubing, and displacement. In Chapter, the flow patterns and pressure drop for a mixture of highly viscous oil with a viscosity of 863 mpa.s and water flowing in a circular microchannel will be presented. The channel was initially saturated with the oil, and then water and oil were injected into the microchannel simultaneously. Video images of liquid-liquid flow patterns were analyzed to develop a flow pattern map. The amounts of the oil displaced by the water in different flow patterns were qualitatively compared. Also, pressure drop data were analyzed to develop a simple pressure drop correlation applicable to slug, annular and annular-droplet flows in a microchannel.

25 6 1. Immiscible displacement of oil by water in a microchannel: asymmetric flow behavior and stability analysis When a more viscous fluid is displaced by a less viscous fluid in a channel, the interface between the two fluids forms a finger. While the finger moves, it leaves a film of the more viscous fluid on the channel wall. This phenomenon is known as viscous fingering and was studied for the first time by Saffman and Taylor in a Hele-Shaw cell (Saffman et al., 1958). Viscous fingering frequently occurs in nature and in many engineering problems including the immiscible displacement of oil in petroleum reservoirs. The past studies have usually been conducted in Hele-Shaw cells or in microchannels to approximate the flow in petroleum reservoirs (Homsy et al., 1987; Aul et al. 1990). Viscous fingering has been studied extensively mainly to predict the thickness of the film deposited on the channel wall. The phenomenon has been well documented in this regard and some correlations have been developed for film thickness prediction (Bretherton et al., 1961; Taylor et al., 1961; Park et al., 1984; Aussillous et al., 000; Krechetnikov, 005). However, the thickness of the finger may not always match the predicted value and fluctuations in the finger width have been reported (Moore et al., 00). Perturbations at the interface were observed both in experiments (McCloud et al., 1995; Torralba et al., 006; Duclaux et al., 006) and in numerical simulations (Ledesma-Aguilar et al., 005; Quevedo-Reyes, 006). The stability of the viscous finger is also an important phenomenon to study. An unstable finger breaks up into droplets whereas a stable finger remains continuous and keeps growing (Aul, 1990). In Chapter 3, we studied the displacement of viscous silicone oil by water in a microchannel. The microchannel was initially saturated with oil and then only water was injected into the channel to displace the oil. The focus of the previous studies has been more on the motion of a viscous finger front. In the present work, we continued the immiscible displacement experiments until the oil was completely displaced and the water occupied the entire microchannel. The rates at which the oil was displaced by the water under different test conditions were compared.

26 7 In the experiments, after the water finger had reached the channel outlet, the flow regime changed from fingering to core-annular flow where the water core was surrounded by an oil film. Although initially the flow regime was symmetric, the displacing water core shifted towards one side of a channel and asymmetric perturbations were observed at the interface with time. To the best of our knowledge, such flow behaviour has not been reported in previous works. Under these experimental conditions, we have not observed any break up and droplet formation during injection of water in the core. We will also discuss the stability of the displacing fluid based on non-linear and linear stability analyses. 1.3 Gas solubility measurements by using micro-cells Since heavy oil samples from different reservoirs have different physical properties, the gas solubility in oil reservoirs should be measured for each production area (Mehrotra et al., 1985a, 1985b, & 1985c). Measuring the gas solubility in oil fractions and cuts would also be useful for developing models to predict gas solubility in oil as a mixture (Mehrotra et al., 1986). Methods used for gas solubility measurements in oil fall into two general categories: direct and indirect methods. Direct methods require taking samples from gas-liquid mixtures at equilibrium and measuring the amount of gas dissolved in each sample. Sampling introduces some uncertainty and makes measurements difficult and relatively expensive. In contrast, indirect methods do not involve any sampling which makes measurements more convenient. By using indirect methods, measurements can be done at higher pressures and temperatures (Cai et al., 001). The most commonly used indirect method is called the pressure decay method. This method was first used by Riazi (1996) for measuring the solubility of methane in n-pentane. In this method, gas solubility is calculated from pressure decay data. Pressure decays as a result of gas dissolution in liquid. Finally, the gas-oil system reaches a constant pressure which shows that the fluids in the cell are at equilibrium. Measuring gas solubility in oils in conventional cells with large internal volumes is always challenging. Reaching equilibrium conditions may take weeks to months (Badamchi-Zadeh et

27 8 al., 009). The dissolution of gas into bitumen samples is a very slow process because of the large internal cell volumes, relatively small gas-liquid interfacial area per unit volume, and slow gas diffusion into the sample liquid (Upreti et al., 000 & 00). Having homogeneous and uniform gas-liquid mixtures increases the mixing time due to the high viscosity of oils and bitumen. Leakage of gas over a long period of time at high pressures is also a concern. In contrast, experiments with gas-bitumen mixtures can be more easily conducted in a miniature cell for the collection of solubility data. By minimizing the sample volume, complete mixing would be achieved much faster. Also, the impact of accidental exposure to the gas is reduced, if toxic gases such as hydrogen sulphide are used. Furthermore, a small cell can be more easily sealed and experiments at high pressures and temperatures can be carried out. Unlike the conventional cells, the components of a miniature cell are readily available and inexpensive. In Chapter 4, a miniature stainless steel cell has been designed and constructed for gas solubility measurements in oils and bitumen. The cell had an internal volume of cc and only 0.4 cc of an oil sample was required for each set of measurements. The cell alone could be operated at pressures up to 4.7 MPa. In this cell, a large gas-liquid interfacial area was provided by spreading the liquid as a film on the cell inner wall which helped establish phase equilibrium sooner. The pressure decay method was used to evaluate the gas solubility in oil and bitumen samples. In each experiment, multiple gas injections were performed and gas solubility was measured at different pressures. Also, after each gas injection, the solubility was measured at different temperatures by changing the temperature of the solubility cell. In this way, a wide range of solubility data could be collected at different temperatures and pressures with one time liquid injection. The new technique was validated by measuring the CO solubility in bitumen and ashphaltene-free bitumen samples from the Peace River area in Alberta, Canada. In Chapter 5, a glass micro cell which uses an indirect method for phase behavior studies is described. The apparatus can be used for the phase behavior study of pure gas and nonvolatile liquid mixtures. A micro glass syringe with a volume of 100 µl is used as a constant volume cell. Two different experimental procedures are developed for gas solubility measurements in low

28 9 viscous and high viscous liquids. The experimental procedure for the systems with low viscosity liquids has been validated by measuring the solubility of CO in water. The cell pressure and the volume of the gas phase were controlled by the volume of the water injected into the cell. Under the experimental conditions tested in this study, the waiting time for the CO -water system to reach equilibrium was less than 8 minutes. The results are compared and found to be in a good agreement with the available literature data and also with reference values calculated from Henry s law. Also, the experimental procedure proposed for the systems with highly viscous liquids was tested by measuring the CO solubility in a bitumen sample from Peace River in Alberta, Canada. The bitumen sample was about 3,000 times more viscous than water at 50 o C. About a 90 minute mixing time was sufficient to bring the CO -bitumen mixture to equilibrium.

29 10 Chapter Viscous oil-water flows in a microchannel initially saturated with oil: flow patterns and pressure drop characteristics Immiscible viscous liquid-liquid two-phase flow patterns and pressure drop characteristics in a circular microchannel have been investigated. Water and silicone oil with a dynamic viscosity of 863 mpa.s were injected into a fused silica microchannel with an inner diameter of 50 μm. As the microchannel was initially filled with the silicone oil, an oil film was found to always form and remain on the microchannel wall. Different flow patterns were observed and classified over a wide range of water and oil flow rates. A flow pattern map is presented in terms of Re, Ca, and We numbers. Two-phase pressure drop data have also been collected and analyzed to develop a simple correlation for slug, annular and annular-droplet flow patterns in terms of superficial water and oil velocities..1 Experimental details.1.1 Materials The working fluids used in this study were de-ionized water and silicone oil from Sigma Aldrich s 00 fluid series. The viscosity and density of silicone oil were 863 mpa.s and 970 kg/m 3 at 0 C, respectively. The water-to-oil viscosity ratio was 0.001, while the water-to-oil density ratio was close to unity (=1.03). The oil s surface tension and oil-water interfacial tension were measured to be 1 mn/m and 43 mn/m at 0 C, respectively. A circular microchannel from Polymicro Technologies was used in the present experiments. The microchannel made of fused silica was 7.0 cm long and had an inner diameter of 50 μm. The contact angles of oil and water with the microchannel wall were 5 and 36, respectively.

30 11.1. Experimental facility.1..1 Continuous liquid injection If syringe pumps are used for liquid injection, the volume of the liquid injected into the channel is limited to the volume of the syringe. Also, syringe pumps may not be forceful enough for injecting highly viscous liquids. By using pneumatic pumps, liquids can be continuously injected at high pressure for a sufficiently long time (Kawahara et al., 00). In this study, as shown in Figure -1, two pneumatic pumps were used to inject water and silicone oil separately. Each pump consisted of a cylindrical stainless steel vessel with a volume of 500 cm 3 and was partially filled with a liquid. One of the pneumatic pumps contained water and the other contained silicone oil. Both cylinders could be pressurized up to 17 MPa with a nitrogen gas from a cylinder. The pressures in the pneumatic pumps were adjusted to inject both liquids into the microchannel simultaneously. The pressure regulators on the nitrogen gas cylinders were adjusted to cover certain ranges of water and silicone oil flow rates. The minimum and maximum water flow rates were and 0 μl /min and the oil flow rate was varied between 3 and 57 μl/min..1.. Fluid injection section As shown in Figure -, the silicone oil was injected into a microchannel test section through a needle with an internal diameter of 100 μm and outer diameter of 10 μm. Silicone oil was injected at the centre of the microchannel through the needle, while water was injected through an annulus between the needle and the microchannel. In each experiment, the microchannel was always first filled with oil and then water and oil were continuously injected into the channel.

31 1 Figure -1: Schematic of experimental apparatus.1..3 Pressure Drop and Flow Rate Measurements A pressure transducer with an accuracy of 1.7 kpa (0.5 psi) was used to measure the pressure drop between the microchannel inlet and exit which was exposed to the atmosphere. Figure - shows how a cross junction connected the needle, water injection line, pressure transducer and microchannel. The oil flow rate was measured at the outlet of the needle at different injection pressures without the microchannel connected. The total oil-water mass flow rate was measured by collecting an oil-water mixture at the outlet of the microchannel in a beaker on a microbalance for a specific length of time. The water flow rate was calculated by subtracting the oil flow rate from the total oil-water flow rate. In the flow rate calculations, water injection into the channel

32 13 was assumed to have a negligible effect on the single-phase flow rate of oil through the needle. The oil reservoir was pressurized to a very high pressure for injecting the viscous oil through the needle such that the pressure drop across the needle was much greater than that in the microchannel at least by a factor of 10. To experimentally confirm this assumption, the oil-water mixture was collected at the outlet of the microchannel for a long time until the volume of the oil collected became measureable. The oil flow rates measured before and after connecting the microchannel were compared. This experiment was repeated over a wide range of oil and water flow rates and the results showed the maximum uncertainty of 7% in the oil flow rate. Fig. -. Schematic of injection section.1..4 Image capture A high speed video camera was used to capture images of the water-silicone oil flow at a frame rate of up to 15 frames per second. To minimize the entrance and exit effects on the flow patterns observed, images were captured in the middle of the channel at 3.5 cm or 140 diameters downstream of the tip of the needle used for water injection. Since a circular microchannel was

33 14 used, optical correction was necessary to capture undistorted and clear images of fluids across the entire inner cross section of the microchannel. To this end, the microchannel was sandwiched between two glass plates and the gap between the two plates was filled with oil to best match the index of refraction of the microchannel. Figure -3 shows the effect of optical correction on the images captured by the high speed video camera. In the image taken without optical correction, the edges of the channel wall could not be seen while in the case with optical correction, the edges can be clearly observed. Fig. -3. Effect of optical correction: a) without optical correction, b) with optical correction. Results and discussion..1 Flow patterns Flow patterns of oil-water flow in a microchannel strongly depend on the nature of the first fluid which wets the channel (Salim, 008). Different flow patterns could be observed depending on which fluid the channel was initially saturated with, silicone oil or water. In this work, the

34 15 channel was always saturated with silicone oil initially by injecting only the silicone oil first at a given flow rate. Then, water was injected into the microchannel at different flow rates while the oil flow rate was kept constant. Although the silicone oil was injected at the centre of the microchannel through a needle and water through an annular gap between the needle and the inner wall of the microchannel (Figure -), water formed the dispersed phase or core flow and oil was the continuous phase and formed an outer flow (Figures -4 & -5). Since the microchannel was initially saturated with the silicone oil, the oil wetted the channel inner wall and always formed a stable film. The formation of the oil film on the microchannel wall is contrary to the water-lubricated transport of heavy oil in pipes where the water flows in the high shear region along the wall and acts as a lubricant (Joseph et al., 1997). This shows that the wetting properties can significantly control the flow pattern in microchannels compared to the flow in large pipes. Figure -4 shows how oil and water flowed in the injection section of the microchannel. In Figure -4-a, only the oil was injected into the microchannel through the needle and the water flow rate was zero. The oil stream cannot be seen while it exited the needle since the microchannel was completely filled with the oil and the outer wall of the microchannel was also sandwiched between two glass plates and the gap between the two plates was filled with the same silicone oil for optical correction. As shown in Figures -4-b and -4-c, the water penetrated through a part of the annulus, channelled into the oil stream and formed a core flow surrounded by the oil film while both fluids were continuously being injected into the microchannel. In figure -4-d, with an increase in the water flow rate, the volume fraction of the water in the annular gap between the needle and the channel wall increased. Although it seems that the water flowed through the whole annulus in Figure -4-d, this was not the case since the oil continuously flowed out from the centre of the needle to form a liquid film on the inner channel wall. To develop a flow pattern map, care must be taken at which axial location the flow patterns are observed. Perturbations can grow or diminish while the interface moves through the microchannel and different flow patterns may occur at different axial locations. For example, Cramer et al. (004) showed that droplets can break up from an extended jet. The flow pattern

35 16 before the break up can be considered as annular flow while after the break up the flow pattern becomes droplet flow. Zhao et al. (006) developed two different flow pattern maps: one at the T-junction and the other further downstream in the microchannel. The chaotic thin striation flow they observed at the T-junction eventually evolved to annular flow in the microchannel downstream. In this study, as mentioned earlier, the images were captured midway between the needle tip and the microchannel exit such that the inlet and exit effects would be minimal. Figure -5 shows the different flow patterns observed in this system: droplet, plug, slug, annular and annular-droplet flows. In this work, water plugs and slugs were distinguished according to their lengths: if the average length of the water segments was equal to or less than 5 channel diameters (or 1.5 mm long), the flow was classified as a plug flow; but if the length was more than 5 channel diameters, the flow was classified as a slug flow. As mentioned earlier, for each experiment, the oil flow rate was kept constant, while the water flow rate was increased. At low water flow rates, the flow pattern was droplet flow (Figure -5-a). With an increase in the water flow rate, a transition occurred from droplet flow to plug flow (Figure -5-b) and then to slug flow (Figure -5-c). With a further increase in the water flow rate, the flow pattern changed to annular flow with sausage-shaped interface deformations (Figure -5-d & e). The linked sausage-shaped annular flow is simply referred to as annular flow in the present study. Finally, at the highest water flow rates tested, fine water droplets were observed within the oil film surrounding the water core (Figure -5-f & g). This type of flow is called the annular-droplet flow in this work. In this flow pattern, the oil-water interface could be smooth (Figure -5-f) or wavy (Figure -5-g). The occurrence of different flow patterns is attributed to the competition between interfacial, inertia, and viscous forces. The interfacial force tends to minimize the interfacial energy by decreasing the oil-water interfacial area, i.e., formation of droplets and plugs. The inertial force tends to extend the interface in the flow direction and keep the fluid continuous. Also, if there is a sufficient velocity difference across the interface, the interface could become wavy due to shear instability. The viscous force dissipates the energy of perturbations at the interface and tends to keep the oil-water interface smooth.

36 17 Fig. -4. Flows in the microchannel injection section: a) Single-phase oil flow (Q O =13 μl/min); b) Plug flow (Q O =13 μl/min, Q W =15 μl/min); c) Annular flow (Q O =13 μl/min, Q W =48 μl/min); d) Annular flow (Q O = μl/min, Q W =70 μl/min).

37 18 Fig. -5. Flow patterns observed in viscous oil-water flow in a microchannel initially filled with oil: a) Droplet flow - water droplets in continuous oil phase (Q O =13 μl/min, Q W = μl/min); b) Plug Flow (Q O =46 μl/min and Q W =110 μl/min); c) Slug flow (Q O =46 μl/min, Q W =5 μl/min); d & e) Annular flow with sausage-shaped interfacial deformations (Q O =46 μl/min, Q W =530 μl/min); and f) Annular-droplet flow with smooth oil-water interface (Q O =46 μl/min and Q W =115 μl/min); g) Annulardroplet flow with wavy oil-water interface (Q O =46 μl/min, Q W =135 μl/min).

38 19 Based on these forces competing to control the flow patterns in microchannels, Zhao et al. (006) and Dessimoz et al. (008) developed flow pattern maps based on dimensionless numbers representing the relative ratios of forces present in the system. In Figure -6, the flow pattern map for the present oil-water system is shown based on Reynolds, Capillary, and Weber numbers, V D i i Re i (1) i i V Ca i i () We i ivi D (3) where, is the density, is the viscosity, is the oil-water interfacial tension, and V i is the superficial velocity of phase i. V i Qi (4) 1 D 4 Here, Q is the volumetric flow rate and D is the microchannel diameter. The subscript i stands for either the water phase (W ) or the oil phase ( O ). The Reynolds number represents the ratio of inertia to viscous forces, the Capillary number the ratio of viscous to interfacial forces, and the Weber number the ratio of inertia to interfacial forces. The oil-solid interfacial tension played a very important role in all these experiments. The oil phase was more wetting compared to the water phase and the channel was always initially saturated with oil. A stable oil film always formed on the channel wall. Although the water was injected from an annular gap between the channel inner wall and a needle, it flowed in the core surrounded by the oil film. The oil film on the channel wall controlled the flow pattern and also

39 0 the two-phase pressure drop as it will be explained in Section... However, the Weber, Reynolds and Capillary numbers were not calculated based on the oil-solid interfacial tension since these numbers were used to compare the forces present in the system in different flow patterns. At all the flow rates tested in this study, an oil film was formed on the channel wall due to solid-oil interfacial tension. If there were additional flow patterns in which the channel was wetted by the water, then the oil-solid and water-solid interfacial tensions should be considered for comparison. Since the water and oil densities are close and the channel diameter is small, the Bond number, Bo, defined below is small (~ 4x10-4 ) which indicates the gravitational effects on the flow pattern can be ignored: g D Bo (5) where, is the difference between the densities of the two phases, and g is the gravitational acceleration. The ratio of the volumetric flow rates of water to the oil, Q Q W O, can also be used to describe the system. In the range of oil and water flow rates tested in this work, flow pattern transitions QW occurred mainly with the change in the water flow rate ( and 0. ReW 00 ). Q Figure -6 presents the flow pattern map for the oil-water two-phase flow in a microchannel initially filled with oil based on Re, Ca, and We. The flow pattern map can be divided into five different zones based on two criteria: discontinuity (zone I) or continuity (zone III) of the water phase as well as the smoothness (Zone III) or waviness of the oil-water interface (Zone V). The range of Re W in which both continuous and dispersed water phases (Zone II) or both smooth and wavy interfaces (Zone IV) exist can be considered as transition zones. The following five zones are distinguished in the flow pattern map: O

40 1 Zone I: Interfacial force dominant ( ReW 0, Ca W , We W 0. 03) The low values of Capillary and Weber numbers confirm that the interfacial forces dominated in zone I. Due to interfacial effects, water formed a dispersed phase of droplets, plugs, and slugs in the continuous oil stream. The water plugs and slugs had a bullet shaped nose (Figures -5-b & c) and were surrounded by the oil film. The viscous forces sheared and deformed the water droplets, plugs and slugs, preventing them from touching the channel wall. If the viscous forces were negligible, the dispersed phase could fill the entire cross section of the microchannel (Garstecki et al., 006). The formation of droplets, plugs, and slugs shows that these flow patterns are controlled by the interfacial tension. However, in the slug flow pattern, the inertia was also important since the slugs were long. The minimum slug length was five times the channel diameter and because of QW the high water to oil flow rate ratios in the slug flow region ( 4.8 3), water slugs of Q centimetre length scale were observed. O Fig. -6. Flow pattern map for silicone oil-water flow in a 50 μm microchannel initially saturated with oil. The solid lines indicate the flow pattern transition boundaries.

41 Zone II: Interfacial force Inertia ( 0 ReW 46, Ca , and 0.03 We 0.17 ): W W Both slug and annular flows were observed in this zone. When the inertia controlled the flow pattern, the core flow was continuous. On the other hand, when the interfacial forces controlled the flow pattern, the core flow became discontinuous and dispersed. Occurrence of both continuous and discontinuous water flows in the core indicated that inertial and interfacial forces were comparable in Zone II. In annular flow, although the water core was continuous, sausageshaped deformations of the oil-water interface were seen (Figure -5-d). These deformations were frequently observed in all the annular flows and also in the case of long water slugs. The sausage-shaped interfacial deformation was caused by an interfacial tension effect in the injection section when water penetrated through a small channel in the annular gap into the oil stream (Figure -4-c). These deformations were stable and moved with the water core through the microchannel. In Zones II and III, the low values of Ca and We indicate that the interfacial tension effects were strong enough to disturb the interface at the injection section and form sausage-shaped deformations. W W In the work by Zhao et al. (006), the interfacial tension was dominant in the limit of We 1and dispersed flows were observed in this limit. However, in the annular flow in Zones II and III of QW this work, the water phase remained continuous due to its high flow rates ( ). Q Since the water core was surrounded and sheared by the viscous oil, it could not occupy the entire cross section of the microchannel. With an increase in the water flow rate, the only way for the water to increase its volume fraction was to elongate in the flow direction and form a continuous core. O The viscous oil film on the microchannel wall always restricted the water flow. The low values of ReO indicate that the viscous forces were always important in all the five zones. In the annular flow pattern, inertia tended to make the oil-water interface wavy due to shear instability, while the viscous effects kept the interface smooth (Figure -5-e). The growth of any perturbations or disturbances at the interface required the motion of the oil in the transverse

42 3 direction which was resisted by the viscous forces in the oil. Viscous forces also competed with the interfacial tension to keep the water core stable and continuous. For the water core to pinch off and break up into droplets, it was necessary for the viscous oil to flow radially towards the centre of the microchannel, but such radial flows were resisted by the high viscosity of the oil film. The transition from the dispersed plug and slug flow patterns to continuous annular flow with an increase in the Capillary number as shown in Figure -6 is consistent with the result of the stability analysis by Guillot et al. (007). They showed that an increase in the capillary number would shift the flow pattern from droplet regime to jet regime. Zone III: Viscous force > Inertia > Interfacial force ( 46 ReW 95, Ca , and 0.17 We ): W W In this zone, two different flow patterns were observed: annular flow and annular-droplet flow with a smooth oil-water interface. The annular-droplet flow in Zone III was the annular flow with addition of fine droplets in the oil film (Figure -5-f). The oil-water interface was smooth but showed sausage-shaped distortions due to interfacial tension effects. The smoothness of the interface indicated that the viscous forces were still controlling and the inertia was not sufficiently high to make the interface wavy. In the annular-droplet flow pattern, since the water flow rate was high, a portion of the water flowed as fine droplets in the oil film. Zone IV: Inertia Viscous force > Interfacial force ( 95 ReW 116, Ca , 0.73 We 1. 1) W W In this zone, annular flows and annular-droplet flows with smooth or wavy oil-water interface were observed. When the interface was smooth, the viscous force could be considered to be greater than the inertia. With an increase in the water flow rate, the inertia increased. Once the velocity difference between the oil and water became sufficiently high, inertia dominated the viscous effects and interfacial waves formed due to shear instability (Figure -5-g).

43 4 Zone V: Inertia dominant ( ReW 116, Ca , We W 1. 1) W In this zone, only the annular-droplet flow with a wavy water core was observed. Appearance of the wavy oil-water interface indicated that the inertia in the water phase was dominant and the velocity difference between the water core and oil film was sufficiently high so that the interface became wavy due to shear instability. This flow behaviour is similar to that of a water-glycerol jet from a 10 mm diameter nozzle injected into an oil at Re 430 (Webster et al., 001), where the Reynolds number was calculated from the jet exit velocity and the nozzle diameter. The jet became non axi-symmetric and there was no jet pinch-off at this Re number. Dessimoz et al. (008) and Zhao et al. (006) observed a parallel (stratified) flow pattern in liquid-liquid flows in microchannels while for the initially oil-saturated microchannel in this work, parallel flow was not observed. The viscous oil was more wetting compared to water and formed a stable film around the entire inner wall of the microchannel. The oil film kept the water flowing along the centre of the microchannel and if the water phase was continuous, annular flow pattern would form. Also, the oil and water could not form a stratified flow because of a small difference in the liquid densities and negligible effect of gravity on the flow. Comparison of the oil displacement by the water in different Zones: More oil was displaced by the water when the water formed a dispersed phase (unstable system) compared to when the water core formed a continuous phase (stable system). An unstable water core broke up into droplets, plugs or slugs. The oil was trapped between the water segments and displaced with the water flow stream. In other words, more oil was displaced by the water in Zone I where the flow patterns are controlled by the interfacial tension compared to the oil displaced by water in Zones III and V. When the water formed a continuous phase, in annular and annular-droplet flows, more oil was displaced by a wavy water core (Zone V) compared to a smooth water core (Zone III). When water was injected into a microchannel filled with oil, the flow of the water core displaced the oil at the centre of the channel while an oil film was left behind on the channel wall. In annular flow in the microchannel, the only oil displacement mechanism by the water was due to the shear

44 5 effects at the oil-water interface. The oil film resisted the displacement by water due to its high viscosity and no slip on the channel wall. When the interface became wavy, the oil was pushed by the waves and displaced faster with the interfacial wave motions... Pressure Drop Measurements and Analysis for Slug, Annular and Annular-Droplet Flows In this section, pressure drop measurements for slug, annular and annular-droplet flows in a microchannel initially saturated with a viscous oil are presented and discussed. Figure -7 shows the pressure drop data obtained in the present work and each curve represents a set of data obtained at a constant oil flow rate while the flow rate of water was increased. The pressure drop changed linearly as a function of the water flow rate for a given oil flow rate. As expected, the pressure drop also increased with an increase in the oil flow rate. Salim et al. (008) reported an increase and then a sharp decrease in pressure drop at low water flow rates for a 30 times less viscous oil than the present silicone oil. Such a variation in pressure drop data has not been seen in this work. The reason may be that the pressure drop data presented in Figure -7 were measured at water flow rates which were not sufficiently low to cause a sudden increase and decrease in the pressure drop. To correlate the present pressure drop data, the single-phase pressure drop was calculated for each phase by using the Hagen-Poiseuille correlation: P ( ) L i 3Vi D (6) where P ( ) L i is the pressure drop of phase i per unit length of the microchannel, D is the microchannel diameter, is the dynamic viscosity and Vi is the superficial velocity. Pressure drop data presented in Figure -7 show that the two-phase pressure drop in this system varies as a linear combination of the single-phase oil and water pressure drops:

45 6 P L P L ( ) TP C1 ( ) W C P ( ) L O (7) where C and 1 C are constants, P ( ) L TP is the two-phase pressure drop and P ( ) L W and P ( ) L are the water and oil single-phase pressure drops calculated by using Eq. 6 and superficial velocities of water and oil, respectively. By using Eq. 6, Equation 7 can be re-written as, O P ( ) TP C3 VW C L 4 V O (8) where C 3 and C 4 are constants, and V W and V O are the superficial water and oil velocities. The constants C1 C4 that best fit the present oil-water pressure drop data are given in Table -1. As shown in Figure -7, Eq. 8 can predict the pressure drop data for this system with a maximum error of 10%. It is noted that Eqs. 7 and 8 should be used only when the flow pattern is slug, annular or annular-droplet flow, and is not valid when the flow pattern is droplet or plug flow. Any pressure drop correlation for plug and droplet flows should reduce to that for a single-phase flow when the flow rate of the dispersed phase approaches zero. Equations 7 and 8 do not satisfy this limiting condition. In the range of flow rates tested in this work, mainly slug, annular and annular-droplet flows were observed and no pressure drop correlation is proposed for droplet and plug flow patterns. The experimental data from Salim et al. (008) were also used to validate the model proposed in this study. Equation 8 is correlated with their experimental results for slug and annular flows in microchannels initially filled with oil. However, Salim et al. (008) only reported slug flow pattern for their system and did not differentiate between plug and slug flows. They obtained and reported pressure drop data for oil-water flows in glass and quartz microchannels with hydraulic diameters of 667 and 793 μm, respectively. The viscosity and density of the oil used in their study were 30.6 mpa.s and 843 kg/m 3, respectively, and the oil-water interfacial tension was 30.1 mn/m. For their data, different values of the constants C1 C4 were obtained for the glass and

46 7 quartz microchannels as given in Table -1. As shown in Figures -8 and -9, the empirical pressure drop correlation given by Eq. 8 is also in good agreement with the experimental results of Salim et al. (008). The constants C3 and C 4 in Eq. 8 are inversely proportional to the channel diameter squared. The diameter of the microchannel used in this work was about 1/3 of those used by Salim et al. (008) resulted in higher values of the constants C3 andc 4. Also, the constant C 4 is directly proportional to the oil viscosity which was ~30 times higher than that used by Salim et al. (008). In the present experiments, after the microchannel was initially saturated with oil and water was injected into the channel, a viscous oil film was formed on the channel wall. The core flow of water surrounded by the oil film was similar to the single phase flow of water in a smaller diameter channel as the slowly moving viscous oil film effectively acted as a channel wall. In the slug, annular and annular-droplet flows in this work, the velocity ratio of water to oil QW was high ( ), and the oil phase could be considered as a stationary film. Under Q O these conditions the pressure drop changed linearly with the water velocity which is expected in a single-phase laminar flow. For a microchannel initially saturated with oil, Salim et al. (008) used the Lockhart-Martinelli correlation to predict the pressure drop which will be discussed later. For an initially water saturated microchannel, they proposed a linear equation for the two-phase pressure drop containing separate terms for individual pressure drops in each phase: P ( ) L TP P ( ) L W P o ( ) O (9) L Here, o is the ratio of the volumetric oil flow rate to the total oil-water flow rate and the parameter depends on the microchannel property. Equation 9 is similar in form to our pressure drop correlation given by Eq. 7, however, they cannot be directly compared since one of the coefficients in Eq. 9 includes the oil and water flow rate ratio while the coefficients in Eq. 7 are constant.

47 8 Table -1. Constants C 1 - C 4 in Eqs. 7 and 8 for the present and Salim et al. s (008) pressure drop data.

48 9 Fig. -7. Pressure drop data for silicone oil-water flow in a microchannel. The constants in Eq. 8 C and C are

49 30 Fig. -8. Prediction of Salim et al. (008) s pressure drop data for a glass microchannel by Eq. 8 C and C with

50 31 Fig. -9. Prediction of Salim et al. (008) s pressure drop data for a quartz microchannel by Eq. C and C with

51 3 In the works by Kashid and Agar (007) and Jovanovic et al. (011), the liquid-liquid slug flow pressure drop models included separate terms for the interfacial pressure drop and hydrodynamic pressure drop, whereas in this work, the effect of interfacial tension is not considered. The interfacial pressure drop accounts for the pressure drop in the flow direction due to the curvature of the oil-water interface. In the interfacial force dominant region, water droplets, plugs and slugs could be formed. Equations 7 and 8 cannot be used for droplet and plug flows. Also, QW because of the high water flow rate in the slug flow region ( 4.8 3), water slugs in the Q present work were long and the two phase pressure drop was due primarily to the contribution of hydrodynamic pressure drop. However, when Equation 8 was used to predict the experimental results of Salim et al. (008), the maximum error occurred in the limit of low water velocity in the slug flow regime (Figures -8 & -9). The error might be due to a sharp increase and then a decrease in the pressure drop in the limit of low water flow rates in their work or the fact that the interfacial pressure drop effects are ignored in Equation 8. O The pressure drop models presented by Kashid and Agar (007) and Jovanovic et al. (011) for slug flows are more elaborate than the simple model of Eq. 8. Also, the model of Salim et al. (008) (Equation 9) includes a flow rate ratio and is more complete than Eq. 8. However, the advantage of using Eq. 8 is its simplicity. Results presented in Figures -7, -9 and -9 show that Eq. 8 can be used to predict the pressure drop in an initially oil-saturated microchannel specifically when both liquids form continuous phases. Next, a Lockhart-Martinelli correlation was examined to see if it can also be used to describe the present oil-water two-phase pressure drop data. The two-phase friction multipliers and the Lockhart-Martinelli parameter are defined as: ( P / L) TP W (10) ( P / L) W ( P / L) TP O (11) ( P / L) O

52 33 W O (1) O ( P / L) ( P / L) W where W is the water-phase friction multiplier, O is the oil-phase friction multiplier and is the Lockhart-Martinelli parameter. By using Eqs. 7 and 1, Equations 10 and 11 can be written as: W C1 C (13) C1 O C (14) Equation 13 is comparable with the Lockhart-Martinelli model that Salim et al. (008) proposed for slug and annular flows: W 1 (15) where and are constants. Comparing Eqs. 13 and 15, the constant is zero in Eq. 13. When is zero, the two-phase pressure drop can be calculated from the individual pressure drop in each phase. The water-phase friction multiplier, W, the oil-phase friction multiplier, the Lockhart-Martinelli parameter, Figure -10, W is plotted against O, and the square of, were calculated from the present experimental data. In, while 1 O is plotted against in Figure -11 along with Eqs. 13 and 14. Equation 13 shows that W changes linearly with and Eq. 14 shows 1 that O is proportional to. Figures -10 and -11 show excellent agreement between both Eqs. 13 and 14 with the present viscous oil-water pressure drop data in a 50 µm diameter microchannel.

53 34 Fig Linear variation of the water two-phase friction multiplier, Martinelli parameter,. W, with Lockhart-

54 35 Fig Linear variation of the oil two-phase friction multiplier, O, with the inverse of the 1 Lockhart-Martinelli parameter,. Conclusion Inertia, interfacial tension and viscous forces compete to control the flow pattern. Inertia tends to keep the water core continuous while interfacial tension tends to break up the water core into droplets. Viscous forces damp any perturbations and keep the oil-water interface smooth. A flow pattern map was developed based on Capillary, Reynolds, and Weber numbers. The twophase pressure drop changed linearly with the water and oil superficial velocities.

55 36 Chapter 3 Immiscible displacement of oil by water in a microchannel: asymmetric flow behaviour and non-linear stability analysis The immiscible displacement of oil by water in a circular microchannel was investigated. A fused silica microchannel with an I.D. of 50 µm was initially filled with a viscous silicone oil. Then, only water was injected into the channel. We describe our flow observations based on the two dimensional images captured in the middle of the channel. The water finger displaced the oil, left an oil film on the channel wall. Eventually, the water finger reached the channel exit and formed a core-annular flow pattern. The water flow rate and inertia increased with the change in flow regime to core annular flow since the flow resistance decreased. The wavelength of waves formed at the oil-water interface also increased with the increase in inertia. The initially symmetric interfacial waves became asymmetric with time. Also, the water core shifted from the centre of the channel and left a thinner oil film on one side. Under all flow rates tested in this study, as long as the water was continuously injected, the water core was stable and no break up into droplets was observed. We also discuss the flow stability based on non-linear and linear stability analyses performed on the core-annular flow Experimental details Materials Silicone oil from Sigma Aldrich s 00 fluid series and De-ionized water were used as the working fluids. The oil s surface tension and oil-water interfacial tension were 1 mn/m and

56 37 water 43mN/m at 0 C, respectively. The densities of the two fluids were close ( 1.03at 0 water C), while the oil was highly viscous compared to water ( at 0 C). oil oil A circular fused silica microchannel (Polymicro Technologies) used in the experiments was 7.0 cm long and had an inner diameter of 50 μm. Both fluids were wetting and the contact angles for the oil-channel and water-channel were 5 and 30, respectively. A schematic diagram of the apparatus is given in Figure Experimental Facility The microchannel was first filled with silicone oil and then only water was injected into the microchannel to displace the oil. As shown in Figure 3-1, a pneumatic pump was used to inject water into a previously oil-saturated microchannel. The pump consisted of a nitrogen gas cylinder and a cylindrical stainless steel water reservoir. The reservoir was partially filled with water and was pressurized at the top by using a compressed nitrogen gas for water injection into the microchannel. A pressure transducer measured the pressure at the microchannel inlet and the channel outlet was open to the atmosphere. A video camera was used to capture images of the water-silicone oil flow. To minimize the entrance and exit effects on the flow patterns observed, all images were captured in the middle of the channel at 140 diameters (3.5 cm) downstream of the channel inlet.

57 38 Fig A schematic of the experimental apparatus. 3.. Flow Behaviour Figure 3- shows the flow regimes observed in one experiment. All the images were captured in the middle of the channel at different times from the start of the water injection. The channel was first filled with oil (Figure 3--a), and then water was injected into the channel. The water finger displaced the oil at the centre of the microchannel and left a continuous oil film on the channel wall (Figure 3--b). Here, we define the initial Capillary, Reynolds, and Weber numbers of the water phase based on the actual velocity of the water finger: Ca wi µ V w wi (1) Re V D w wi wi () µ w

58 39 We wi V D w wi (3) where µ w is the viscosity of the water, V wi is the velocity of the finger nose at the centre of the channel, is the liquid-liquid interfacial tension, w is the density of the water, and D is the channel diameter. Table 3-1 gives the initial Capillary, Reynolds and Weber numbers of the water phase for the experiments carried out in this study. The results presented in Figure 3- is for 5 Ca wi Table 3-1. Test conditions.

59 40 Fig. 3-. Flow patterns at Ca wi and Caw 9 10 observed in the middle of the channel (top view) at different times from the start of the water injection: a) at t=0 sec, the channel was filled with oil; b) at t=50.7 sec, the water finger was displacing the oil at the core; c) at t=53.3 sec, the oil film was left evenly on the channel wall and the oilwater interface was smooth; d-1) at t=95.5 sec, symmetric perturbations formed at the interface; d-) at t=10.5 sec, the wavelength increased; e) at t=104., the water core shifted from the centre and the flow became asymmetric; f) at sec and g) at t=308.0, the water core touched one side of the channel; h) at t=550 sec, the oil was completely displaced. 5

60 41 The unperturbed water core was thicker at lower water flow rates. This is consistent with the Bretherton scaling which predicts the oil film thickness to increase with the increased speed of the finger nose (Bretherton et al., 1961). As shown in Figure 3-3, the initial dimensionless radius of the water core, a 0, can be predicted by the semi-empirical correlation (Equation 4) suggested in Aussillous et al. (000) with 3 % error. The radius of the water core was divided by the channel radius, R, to be made dimensionless. a o / kai 1 (4) ka /3 i where µv o wi kai is the Capillary number of the form were µ o is the viscosity of the displaced fluid, i.e. oil. Under the conditions tested in this study, the dimensionless and 1. a o varied between 0.7 Fig The initial water core thickness: the comparison of the experimental results with Equation 4.

61 4 The minimum film thickness we were able to determine from the images was 3 µm and films thinner than this limit were not visually observable. At the lowest flow rate tested in this work at 6 Ca wi 10, the water core occupied the entire channel and the film left on the wall was too thin to be observed (Figure 3-4). To reach such a low water flow rate, the nitrogen gas cylinder was removed from the pneumatic pump and thus, the only pressure applied for water injection was hydrostatic, created by the height of the water column in the reservoir and the water flowed into the channel by gravity. Fig The water finger at Ca wi 6 10 observed in the middle of the channel, 714 sec after the start of the water injection. The oil film on the channel wall is too thin to be observed. The resistance against the water flow was higher at the beginning of the experiments while the water displaced the oil at the centre of the channel (Figure 3--b) which resulted in an initially low water velocity. This is primarily because the water had to displace a column of highly viscous oil out of the channel. The water flow rate increased once the water core reached the channel outlet and formed a fully core-annular flow. Figure 3-5 shows the time variation of the pressure at the channel inlet under different test conditions. The initial sharp decrease in the pressure drop, which was more noticeable at higher flow rates, was due to the oil displacement by the finger nose at the centre of the channel. After the water finger reached the channel outlet, the pressure drop changed more smoothly with time. Since the resistance against the flow decreased, the water flow rate increased which resulted in higher Capillary, Reynolds and Weber numbers. Here, we define a second group of dimensionless numbers for the water phase based on the average superficial velocity of the water, V w, after the finger nose reached the channel exit:

62 43 Ca µv w w w (5) VD (6) µ w w Rew w We w wv w D (7) Assuming that the oil velocity is negligible compared to the water velocity, the average superficial velocity of the water can be calculated by dividing the mixture of the oil and water flow rate, Q m, by the channel cross sectional area: V w Qm (8) 1 D 4 values of 3 The results presented in Figure 3- were at Caw As given in Table 3-1, the Ca w are two orders of magnitude higher than that of Ca wi. At first, the water core was uniform (Figure 3--c), but perturbations started to grow at the oil-water interface with time and formed travelling waves at the interface (Figure 3--d). The time required for the initiation of perturbations is given in Table 3-1. The initiation and growth of perturbations took place earlier and faster, respectively, at higher water flow rates. Also, the speed at which waves travelled along the oil-water interface increased with an increase in the water flow rate (Table 3-). The maximum wave speed we were able to measure in our image analyses was 140 mm/s. Also, the maximum wavelength we were able to measure was 5 mm ( R =40). The 1 wavelengths and wave speeds at Caw and Caw 10 were higher than this limit and are not reported in Table 3-.

63 44 Table 3-. The initial ( a ) and last symmetric ( z ) wavelengths and wave speed. The experimental values are compared with the results of the non-linear ( f 1 ) and linear ( f ) analysis. Fig The variation of the pressure at the channel inlet with time.

64 45 In each experiment, the interfacial wavelength increased with time. The first wavelength, a, and also the last symmetric wavelength observed at the interface -d-1 and 3--d-. Also, as given in Table 3-, the ratios of z z, are shown in Figures 3- a are less than one which shows that the wavelength increased with time (compare Figures 3--d-1 & 3--d-). The wave speed also increased with time (Table 3-). The increase in the wavelength and wave speed could be due to the increase in the water flow rate after the water finger reached the channel outlet. This observation is in agreement with the results of the non-linear stability analysis which will be discussed later. Based on the result of this analysis, the fastest growing wavelength increases with an increase in inertia (see section 3.3 for the stability analysis). It should be noted that all descriptions of the flow pattern given are based on the two dimensional images captured from the system. Although the initiation of disturbances was symmetrical (Figure 3--d), these perturbations did not uniformly grow and the oil-water interface became asymmetric (Figure 3--e). Also, the water core tended to shift towards one side of the channel and leave a thicker oil film on the other side. At low water flow rates ( the water core remained closer to one side (Figure 3--f), while at high flow ( rates, the core position fluctuated between the sides of the channel (Figure 3-6). 5 Ca wi ), 4 Ca wi ) It is possible that interfacial perturbations may be caused by fluctuations in injection pressure as shown by Torralba et al. (008). However, the pressures of the pneumatic pumps in this study were regulated and kept constant by a double-stage gas regulator which was connected to a high pressure nitrogen gas cylinder. In these experiments, the oil-water interface was initially smooth and perturbations were formed at the interface with time. If the pneumatic pump was responsible for the interfacial instability, perturbations could be formed at any time and the interface might not be initially smooth. Compared to other injection methods, pneumatic pumps can supply fluids at a constant injection pressure. For example, in syringe pumps, the injection pressure keeps changing while the flow rate is constant.

65 46 The asymmetric flow behaviour was not due to gravity since the top and side views of the 4 flow exhibited similar behaviour. The low value of Bond number ( Bo 4 10 ) defined below confirms that the gravity was negligible compared to other forces in the present system: gd Bo (9) where acceleration. is the difference between the densities of the two fluids, and g is the gravitational Fig The water core fluctuation between the sides of the channel at Caw , a) at 9. sec; b) at 30. sec; c) 33.4 sec. Once the water core became off-centre, the drag forces were not uniform all around the interface and this could result in the asymmetric nature of the waves. Figure 3-7 shows how symmetric deformations at the interface were dragged and sheared at different rates and became asymmetric. Also, the interface may become wavy due to shear instability at high water flow

66 47 rates ( Rew 95 ) (Chapter ). Once the velocity difference across the interface becomes sufficiently large, the interface can become unstable and wavy. Understanding the asymmetric flow behaviour of the water core requires further experimental and numerical investigations. However, the shift of the water core towards one side of the channel might be due to drag force minimization. As experimentally shown in Tudose et al. (1999), the drag force on a bubble placed in a liquid stream in a vertical tube decreased when the bubble was displaced from the tube axis. Similarly, in the current experiments the shift of the water core from the centre could decrease the overall drag force acting on the interface. Fig Flow patterns at Ca wi and Caw 9 10, symmetric flow became asymmetric: a) at 10.0 sec; b) at 10.6 sec; c) at 103. sec. The water core displaced the oil by pushing and dragging it at the oil-water interface. The oil film thickness diminished and the water core diameter increased with time. Figure 3-8 shows how the maximum water core diameter, d max, changed with time under different test conditions.

67 48 At the beginning of the experiments when water was displacing a large oil volume in the core, the water finger was initially thicker at lower flow rates and the finger nose displaced a larger oil volume. However, at higher flow rates the water finger displaced less oil volume but at a higher rate. Also, the drag force at the lateral oil-water interface was higher at higher flow rates and more oil was dragged at the interface. As shown in Figure 3-8, the complete displacement of the oil occurred faster at the higher water flow rates. Fig The variation of the maximum water core radius with time. To show how the oil film thickness changed with time, the maximum film thicknesses on both sides ( h 1,max and h,max where h1,max h,max ) were measured and the results are presented in Figure 3-9. Initially, when the water core was at the centre of the channel, h1,max and h,max were equal. The maximum film thickness increased when the perturbations formed at the interface (compare Figure 3--c with 3--d). Then h1,max and h,max decreased while the oil was being dragged and pushed out by the water. Once the water core was shifted from the centre, it left a

68 49 thinner oil film on one side and the values of h1,max and h,max became different (Figure 3--e). As shown in Figure 3-9, the difference was larger at lower water flow rates, implying that the eccentric flow behaviour became more noticeable at lower water flow rates. Fig The variation of the maximum oil film thicknesses on opposite sides of the channel with time.

69 50 The wave height decreased faster on the thinner oil film (Figure 3--e) and the water core first touched the side of the channel where the film was thinner (Figure 3--f). The wave height on the thicker oil film also decreased with time while the film was dragged (compare Figure 3--f with 3--g). Finally, the water completely displaced the oil layer and occupied the entire microchannel (Figure 3--h). At all the flow rates tested in this study, as long as the water was continuously injected into the channel, the water core was always stable. No water core break up was observed and the water always formed a continuous phase. However, in similar experiments carried out in Aul et al. (1990) at in a microchannel with an I.D. of 54 µm, the water core 6 5 Ca wi break up always took place. Generally, the interfacial forces competed with inertia to make the water core unstable (Chapter ). The interfacial tension forces tend to minimize the energy by breaking the water core into droplets and decreasing the interfacial area between the two fluids. On the other hand, the inertia tended to keep the water core continuous. At low values of Ca wi in Aul et al. (1999), the interfacial forces were dominant and the water core break up occurred. In this study, after the water finger reached the channel outlet, the water flow rate and inertia increased and the capillary number changed from Ca wi to Ca w. The increase in the inertia was sufficiently large to keep the water core stable and also made the system asymmetric. This indicates that inertia can have an important effect on the stability and also morphology of immiscible displacement (Chevalier et al., 006; Dias et al., 011). Generally, the system may remain stable while the water flow is maintained, but if the flow is stopped, the water core break up can occur due to a capillary instability. In one experiment, after the observation of the asymmetric flow behaviour in the system, the water flow was stopped The symmetric perturbations appeared again and then the water core broke up. The results of this experiment are shown in Figure 10. This suggests that the asymmetric behaviour is one of the flow characteristics. The force due to interfacial tension was always present in the system. Once the water flow was stopped, there was no inertia to resist the interfacial tension and viscous forces. The symmetric deformations of the oil-water interface caused by thick for the break up of the core to take place interfacial tension finally broke up the water core into droplets. However, the surrounding oil film needs to be sufficiently.

70 51 Fig A stable water core broke up into droplets after the flow was stopped: a) asymmetric flow at Caw ; b) at 180 sec after the flow was stopped; c) at 740 sec after the flow was stopped Stability analysis Here, we perform a non-linear stability analysis on core-annular flow to predict the wavelength of perturbations formed at the oil-water interface. The derivations of the non-linear analysis are given in Appendix I in details. Most of the previous analytical studies of coreannular flow stability analysis were linear (Guillot et al., 007). In the case of non-linear coreannular flow stability analysis, the problem is usually solved numerically (Hu and Joseph, 1989) or by making the formulation weakly non-linear. In the analysis presented in the thesis which is purely analytical, the non-linear terms in the Navier-Stokes equations are considered. An averaging technique by integrating the equations across the cross-section of the channel has been used in this work which makes the analysis very simple. The present analysis deals with average velocities which are only functions of flow direction and time while the velocity profiles are a function of radius as well.

71 5 We use a similar approach as Funada et al. (00) to make the equations dimensionless. * The following scales were used: channel radius, R, as the characteristic length, W as R R characteristic velocity, * W as characteristic time and * * P ow as characteristic pressure. Generally, in the notations, we use V as the velocity and U as the dimensionless velocity. Also, V and U are the average velocities. The dimensionless Navier-Stokes equations for both phases are: o Uw Uw dpw m 1 Uw l( U w ) ( r ) * t z dz Re r r r (10) U o o o 1 1 o U U dp o ( r U ) * t z dz Re r r r (11) where subscripts w and o represent water and oil, respectively, z is the dimensionless coordinate in the flow direction, U is the dimensionless z-component of velocity, P is the dimensionless pressure, * Re is the dimensionless Reynolds number of the form µ * o WR o, l w is the density o ratio and µ m µ w o is the viscosity ratio, t is the dimensionless time and r is the dimensionless * radius ( Re =0.007, l 1.03, m in this work). The notation used in this analysis is for the case where the more viscous fluid is the outer fluid and the value of m is less than one. In the case that the more viscous fluid is the inner fluid, the subscripts w and o should be interchanged in Equations 10 and 11. Also, m, l, and * Re should be replaced with ˆm, ˆl, and Reˆ* where 1 ˆm, m ˆl 1 and l Reˆ* * wwr ( Funada et al., 00). µ w

72 53 The velocity profiles of the two fluids for core-annular flow are ( a r ) m 1 a Uw Uw 0 r a a m1 a r 1 Uo Uo a r 1 1 a 1 (1) (13) where U w and U o are the dimensionless cross section-averaged water and oil velocities, respectively. a is the dimensionless radius of the water core, which could be a function of time. At the interface, the oil and water velocities are equal, i.e. Uw Uoat r a. Since Equations 1 and 13 satisfy this condition, one can find the relation between the averaged oil and water velocities, U w and U o. We substitute Equations 1 and 13 into Equations 10 and 11 and then integrate Equation 10 with respect to r dr from r 0 to r a and integrate Equation 11 with respect to r dr from r ato r 1. Integrating the equations allows us to work with average velocities instead of velocity profiles (Johnson et al., 1991). The integrated Navier-Stokes equations are: a 1 a dpw a m a l Uw l Uw ( ) U ( ) * w t z dz Re a m(1 a ) (14) 1 a 1 1 a dp 1 a 4 U U U t z dz Re o o o ( ) * o (15) The mass conservation equations for the two fluids are

73 54 d d ( Uwa ) ( a ) dz dt (16) d (1 d ( U ) o a a dz dt (17) Following Johnson et al. (1991), we use the perturbations of the form o a a [1 exp t ikz ] (18) w U υ exp t ikz (19) w o U υ exp t ikz (0) o where ao is the radius of the unperturbed water core, is the dimensionless growth rate, k is the dimensionless wave number and is the dimensionless wavelength. The primes denote the perturbations. υ w and into Equations 16 and 17. υ o can be found in terms of, a o and by inserting Equations 18-0 Also, the dimensionless normal stresses must balance at the interface: 1 a a ( Pw Po) ( ) z We z a z * o (1) where * We is the Weber number of the form W * o R and is equal to 1. Equation 1 couples Equations 14 and 15 since it gives the relation between the perturbations in pressures of the two fluids. After introducing the perturbations into Equations 14, 15, and 1, Equations 14

74 55 and 15 can be combined into a single equation by using Equation 1. Ignoring all the imaginary terms, this single equation results in the following dispersion equation for the growth rate: A B C 1 0 () where the constants A, B, and C 1 are a Al 1 o ao (3) 8 a B Re 1 m o * ao a (1 o m ao ) (4) a 1 a C1 k l U U k We We a o 4 o ( ) * * w o (5) ao 1 o or 1 4 ( 1 1 ao 1 ) * (1 ) ) C aok Wew Weo k We ao ao (6) Where * We 1and We V D w w w and We o V D o o are the Weber numbers calculated by the water and oil properties. respectively. V w and V o are the water and oil average velocities, Between the two roots of Equation, we choose the one which gives the asymptotic solution where goes to zero when k goes to zero. The solution to Equation is

75 56 B B C ( ) 1 (7) A A A The critical wavelength, c1, at which the growth rate is zero and the fastest growing wavelength, f 1, at which the growth rate is maximum can be given by Equations 8 and 9: c 1 ao ao 1 ( We w 1 a Weo 1 o ao ) (8) f1 ao 1 ao ao 1 ( Wew Weo ) 1 a o (9) In the limit of low Re number, the Stokes approximation can be used to describe the system (Currie, 003; Guillot et al., 007). In Stokes equations the inertia terms, i.e. the second terms in Equations 10 and 11, are neglected and the analysis becomes linear. If one redo the analysis using Stokes equations the following dispersion equation can be found for the core-annular flow: A B C 0 (30) where the constant C is C a ( ) * ok k We ao (31)

76 57 From Equation 30, the following critical and also the fastest growing wavelength can be found in the limit of low Re number where inertia is negligible: a (3) c o f ao (33) The results of the linear analysis given by Equations 3 and 33 are in agreement with the results of the classical theory of the capillary instability of a cylindrical interface (Lord Rayleigh, 1878). This critical wavelength is also the same as the one given in the analysis of viscous potential flow presented in Funada et al. (00). Also, these results are in agreement with the results of previous analyses of core-annular flows in channels (Hu et al., 1989). In Aul et al. (1990), for the system of thin film, it was shown that the fastest growing wavelength would be different from Equation 33 by a factor of 1 1 CV, where C V is the ratio of van der Waals forces to interfacial tension forces. Also, as experimentally shown in Duclaux et al. (006), when the effect of gravity becomes considerable, the fastest growing wavelength would be different from Equation 3 by a factor of 1 1.5Bo. Here we compare the results of the non-linear analysis which considers the effect of inertia with those of the linear analysis in which the effect of inertia is neglected. In the linear analysis, the * growth rate is a function of the unperturbed water core radius, Re number ( Re ), the density and viscosity ratios, and the wave number (Equation 30). In the non-linear analysis, the growth rate is a function of all these parameters as well as the oil and water Weber numbers (Equation ). Figure 3-11 compares the stability of a system predicted by the two analyses. The growth rate predicted by the linear analysis, in which the effect of inertia is neglected, is unstable over a

77 58 wider range of wave numbers. Also, for a given unstable wavelength, the growth rate of the linear analysis is higher than that of the non-linear analysis. This indicates that considering the inertia effects makes the system more stable which is in agreement with the experimental results. Generally, inertia tends to keep the water core continuous (Chapter ). As mentioned earlier, under the experimental conditions tested in this study, as long as the water was injected into the channel, inertia kept the water core stable. The water core break up only took place when the flow was stopped. Fig Dimensionless growth rate,, vs. dimensionless wave number, k, at * l 1.03, a 0.8, m 0.001, Re 0.007, We 0.8 and o w We o : the system predicted by the non-linear analysis is more stable compared to the one predicted by the linear analysis.

78 59 Based on the results of the linear analysis (Equations 3 and 33), the critical and the fastest growing wavelengths are only a function of water core radius while in the non-linear analysis (Equations 8 and 9), these wavelengths are a function of the oil and water Weber numbers as well. The wavelengths predicted by the non-linear analysis have higher values by a factor of 1 ao 1 ( Wew We a o ) 1 o ao compared to the values given by the linear analysis. This is in qualitative agreement with the experimental results where the interfacial wavelengths increased with an increase in inertia. A quantitative comparison between the results of Equations 9 and 33 is also made. Recalling that the relation between the average oil and water velocities is given by Equations 1 and 13 at the interface, two sets of Weber numbers for the oil and water phases were calculated for each experiments: the initial Weber numbers based on the velocity of the water finger at the centre of the channel and also the Weber numbers based on the average water and oil velocities after the water finger reached the channel exit. For the experimental conditions tested in this study, the factor of ao o 1 ( Wew We a o ) 1 a 1 o in Equation 9 calculated based on the initial values of the Weber numbers was very close to unity with a difference less than In other words, both analyses predict the same results in the limit of low initial Weber numbers. Also, in Figure 3-1-a, the results of the linear and non-linear for the system of oil and water used in this study are compared with the last symmetric wavelengths observed in the experiments. As shown in Figure 3-1-a, the results of both analyses give the same values of wavelengths in the limit of low Reynolds numbers ( 60 Re w ). This suggests that ignoring the inertia terms is a valid assumption for systems with low Reynolds and Weber numbers. However, as given in Table 3-, the results of the two analyses are different when the wavelength in Equation 9 is calculated by the Weber numbers based on the water and oil velocities after the water finger reached the channel exit. In the case of linear analysis, the ratio of the last symmetric wavelengths in experiments to the one given by the analysis, i.e. z f, is more than one which indicates that the

79 60 linear analysis underestimates the wavelength when the effect of inertia is not negligible. In the case of non-linear analysis, as shown in Figure 3-1-a, with an increase in the water velocity and consequently the Weber and Reynolds numbers, the non-linear analysis predicts higher wavelengths compared to the linear analysis ( 60 Rew 180 ). With further increase in the Reynolds number (180 Re w ), the wavelength predicted by the non-linear analysis approaches infinity which shows that averaging the inertial terms by integrating Equations 10 and 11 resulted in an overestimation of the fastest growing wavelength in this limit. Fig The ratio of the fastest growing wavelength to the water core radius vs. water Reynolds number. The results of the non-linear analysis (Eq. 9), linear analysis (Eq. 33), and the last symmetric wavelength in experiments ( z ) are compared: a) Experimental results are presented based on average velocities;

80 61 Conclusion In the immiscible displacement experiments, interfacial wavelengths were sensitive to inertia. Inertia made the flow asymmetric and kept the water core continuous. Non-linear and linear analyses were performed for the system of core-annular flow. Compared to a linear analysis, a non-linear analysis predicts the stability of the system more accurately.

81 6 Chapter 4 A Miniature Cell for Gas Solubility Measurements in Oils and Bitumen A miniature cell has been designed and constructed to measure gas solubility in crude oils and bitumen. The cell was made of stainless steel with a total internal volume of cc and only an oil sample of 0.4 cc was required for one set of measurements at different pressures. By using this small cell, the waiting time for reaching equilibrium was less than 10 minutes. The technique was validated by measuring CO gas solubility in two bitumen samples. The results were compared and found to be in very good agreement with available data. The apparatus was also used to study the effect of ashphaltene on CO solubility in bitumen. It was shown that ashphaltene had a negligible effect on CO solubility in bitumen. 4.1 Experimental Details Materials The CO solubility was measured in two bitumen samples obtained from Peace River and provided by Shell Canada Limited. Research grade CO with % purity was purchased from Linde. The densities of bitumen samples were measured by using a density meter (Anton Paar, Model DMA38) at temperatures up to 40 C as shown in figure 4-1. The density of sample at 60 C was extrapolated by assuming a linear variation of density with temperature. The SARA (Saturates, Aromatics, Resins, and Ashphaltene) composition of bitumen samples was determined by using the thin layer chromatography with flame ionization detection (TLC-FID) method (Carbognani et al., 007). The SARA composition of both samples is given in table 4-1. To make ashphaltene-free samples, ashphaltene was removed from a bitumen sample 1 by following the method developed by Alboudwarej et al. (00) and using n-heptane as a solvent.

82 63 temperature. Fig Density of bitumen samples and maltene extracted from sample 1 vs.

83 64 Table 4-1. SARA analysis of bitumen samples. Fraction Sample 1 (Weight%) Sample (Weight%) Saturates Aromatics Resins Ashphaltene Experimental apparatus The experimental apparatus is shown in figure 4-. The experimental apparatus consisted of a solubility cell and pre-injection cell. An oil or bitumen sample was injected into the solubility cell, in which an equilibrium condition was established between the gas and liquid. The pre-injection cell was used to accurately inject gas into the solubility cell. Two pressure transducers were used to measure the pressures of the solubility cell and the pre-injection cell. A micro-valve was used to connect the solubility cell to the pre-injection cell and another microvalve connected the pre-injection cell to a high pressure gas cylinder containing CO. All the components of the apparatus were connected using stainless steel micro tubes (VICI, Model T5C5D) with an O.D. of cm and I.D. of cm. The total internal volume of microtubes connected to the solubility cell was 1.9x10-3 cc which was negligibly small compared to the internal volume of the cell. To control the gas-liquid mixture temperature, the solubility cell was placed in a water bath equipped with a temperature controller. This water bath is labelled as WB1 in figure 4-, and its temperature was measured with a type-t thermocouple calibrated by using a thermistor thermometer. The accuracy of the thermocouple was 0.03 C. In one experiment, to determine

84 65 how fast the temperature of the gas-liquid mixture inside the cell would respond to a change in the temperature of the water bath, a thermocouple was placed inside the solubility cell. The temperature of the water bath changed from room temperature to 60 C in about 9 minutes. The temperature of the solubility cell also changed with a 30 second time lag with respect to the temperature of the bath. The change in the cell temperature was quick, since the cell was made of a thermally conductive metal and its volume was small. Another water bath, labelled as WB in figure 4-, was used to control the temperatures of the pressure transducers and the pre-injection cell. The temperature of WB was also measured by a calibrated thermocouple with an accuracy of 0.03 C. The temperature of WB was always kept constant to eliminate any effect of room temperature variations on the pressure transducer readings. A PC-based data acquisition system with Labview software was used to monitor and record the pressure readings in the solubility and pre-injection cells and the temperatures of the water baths Solubility cell The solubility cell was an empty cylinder made of stainless steel with a length of 5.01 cm and I.D. of cm. A rod-shaped magnet with a length of 3.47 cm and O.D. of 0.44 cm was placed inside the solubility cell as a mixer. A rotating magnetic field was used from outside the cell to vibrate the magnet inside the cell. The total free internal volume of the solubility cell was cc. The apparatus was designed in such a way that all components connected to the solubility cell had very small internal volumes compared to that of the solubility cell. Only the volume of the solubility cell was considered in solubility calculations and the dead volume of all elements connected to the solubility cell was neglected.

85 66 Fig. 4-. Schematic of the experimental apparatus: 1) water bath 1 (WB1), ) thermocouple, 3) solubility cell, 4) magnetic mixer, 5) rotating magnetic field, 6) T-junction, 7) pressure transducer 1 (P1), 8) micro-valve 1 (V1), 9) pre-injection cell, 10) pressure transducer (P), 11) micro-valve (V), 1) purge valve, 13) gas regulator, 14) CO gas cylinder, 15) data acquisition system, 16) water bath (WB), 17) computer. As shown in figure 4-3, two reducing unions (Swagelok, Model SS ZV) with zero dead volume were used as the cell end fittings to connect the solubility cell to its neighboring components. These end fittings were compression fittings made of stainless steel, with which the cell could be easily sealed. The cell alone could withstand a high internal pressure of up to 4.7 MPa at temperatures below 93 C and 3.4 MPa at temperatures below 537 C. Also, with these compression fittings, the cell could be readily detached from the apparatus for cleaning. A plug was used to close one end of the solubility cell while the other side was connected to a T-junction (Swagelok, Model SS-1F0-3GC), which had a negligible dead volume

86 67 of.8x10-4 cc compared to the volume of the solubility cell. The T-junction connected the solubility cell to a pressure transducer (Omega, Model PX 5500) and micro-valve (VICI, Model SFVO) which are labelled as P1 and V1, respectively, in figure 4-. The accuracy of the pressure transducer was 7 kpa and it could operate at pressures up to 6.89 MPa. To reduce the internal dead volume of the pressure transducer to zero, the pressure transducer was first vacuumed and then filled with mercury. The micro-valve, V1, had an internal volume of x10-3 cc which was again negligibly small compared to the internal volume of the solubility cell Pre-injection Cell To accurately control the amount of gas injected into the solubility cell, the gas was first injected into the pre-injection cell and then into the solubility cell. The pre-injection cell was an empty cylinder made of stainless steel. From one end, the pre-injection cell was connected to the solubility cell via a micro-valve, V1. From the other end, the pre-injection cell was connected to another pressure transducer (P) and micro-valve (V) by using exactly the same type of end fittings, T-junction and micro tubes used for the solubility cell. The total internal volume of the pre-injection cell and pressure transducer (P) was 7.15 cc. V and P were the same models as V1 and P1. V connected the pre-injection cell to a purge valve and a high pressure gas cylinder. Fig Schematic of the solubility cell: 1) plug, ) compression fitting, 3) column end fitting, 4) magnetic mixer, 5) equilibrium cell, 6) micro-tube, 7) T-junction, 8) micro-tube connected to pressure transducer 1 (P1), 9) micro-tube connected to micro-valve 1 (V1).

87 Experimental Procedure The solubility of CO was measured in two bitumen samples from Peace River at, 35, and 60 C for the first sample and at and 35 C for the second sample. Six steps were followed to measure solubility values as summarized in figure Step 1: Liquid Injection into the Solubility Cell Liquid samples were injected into the solubility cell before the cell was placed in the water bath, WB1. First, a plug from one end of the solubility cell was removed. To remove air from the cell, both micro-valves, V1 and V, were opened and the cell was purged with CO at a pressure slightly higher than atmospheric pressure. Although the CO gas in the cell at the purge pressure contacted the bitumen sample, the contact time was short and the solubility of CO in the sample at this low pressure was neglected. The vacuum was not applied since light hydrocarbons might evolve under vacuum and change the liquid sample composition. An oil sample, 0.4 cc in volume, was manually injected into the cell by using a glass syringe. Liquid samples were injected uniformly all around the top side of the cell while the cell was kept vertical. The sample injected slid down and wetted the inner wall of the cell. After the liquid was injected, the cell was kept horizontally so that the liquid did not accumulate at the bottom of the cell. Figure 4-5 shows how a liquid film was formed inside the cell. Because of gravity, the thickness of the liquid film on the lower side wall of the cell was thicker than that of the upper part. The formation of the thin liquid film reduced the waiting time for equilibrium by reducing the diffusion resistance and providing a very large gas-liquid interfacial area. The plug was replaced to make the solubility cell closed and sealed. Then the cell was placed in the water bath, WB1, and its temperature was set to the room temperature.

88 Fig Summary of the experimental procedure for solubility measurements. 69

89 70 Fig Formation of a liquid film inside the solubility cell Step : Gas Injection Step -1: Gas Injection into the Pre-injection Cell The temperature of the water bath, WB, in which the pressure transducers and pre-injection cell were placed, was always kept constant at room temperature. For CO gas injection, the valve V1 was closed while V was left open. The purge valve connected to the gas cylinder was only used to better adjust the pressure at which the gas was injected into the pre-injection cell when needed. The gas was first injected into the pre-injection cell from a high pressure gas cylinder and then V was closed. For calculations, the gas density was obtained using a data base from the National Institute of Standards and Technology (see for NIST data base). In this data base, the density of carbon dioxide is calculated by using the equation of state developed by Span and Wagner (1996). This equation of state considers the non-ideal behavior of carbon dioxide and is widely used for calculating the properties of carbon dioxide from its triple point temperature to 1100 K at pressures up to 800 MPa. To determine the mass of the gas injected into the pre-injection cell, m G,1, the internal volume of the pre-injection cell, V Pre-cell, was multiplied by the gas density, ρ G,1, at the pressure and temperature of the pre-injection cell after the gas was injected into the pre-injection cell.

90 71 m G,1 =V Pre-cell ρ G,1 (1) Step -: Gas Injection from Pre-injection Cell into Solubility Cell To inject the gas from the pre-injection cell to the solubility cell, V1 was opened and closed. The amount of gas left in the pre-injection cell, m G,, was calculated from the CO density, ρ G,, at the pressure and temperature of the pre-injection cell after the gas had been injected into the solubility cell. m G, =V Pre-cell ρ G, () The difference between the amounts of gas in the pre-injection cell before and after gas injection into the solubility cell was the amount of gas injected into solubility cell, m G,inj. m G,inj =m G,1 -m G, (3) The measured variables to calculate solubility were temperature and pressure of the pre-injection and solubility cells. Figure 4-6 shows the changes in the pressure and temperature of the solubility cell with time Step 3: Solubility Measurements at 60 C After the gas was injected into the solubility cell, the temperature of the water bath WB1 was set to 60 C. As shown in figure 4-6, the pressure in the solubility cell first increased as a result of an increase in the temperature but after the solubility cell reached 60 C, the pressure started to decay as a result of the gas dissolution into the bitumen sample. Finally, the solubility cell reached a constant pressure indicating the system had reached an equilibrium condition. The volume of the liquid phase, V L, was determined by dividing the mass of liquid injected into the solubility cell, m L, by the liquid density, ρ L, at equilibrium temperature.

91 7 V L =m L / ρ L (4) The volume of the gas phase, V G, was determined by subtracting the volume of the liquid at each equilibrium temperature, V L, from the total internal volume of the solubility cell, V Cell. V G =V Cell -V L (5) The mass of CO in the gas phase was calculated by, m G,eq =V G ρ G,eq (6) where m G,eq is the mass of CO in the gas phase and ρ G,eq is the CO density at the equilibrium condition. The difference between the initial mass of CO injected, m G,inj, and that remaining in the gas phase at equilibrium, m G,eq, was the amount of gas dissolved in oil, m G, dissolved. m G, dissolved = m G,inj - m G,eq (7) Finally, the solubility, S, at equilibrium condition was calculated: S= m G, dissolved / ( m L + m G, dissolved ) (8) Fig Changes in pressure and temperature of the solubility cell with time.

92 Steps 4&5: Solubility Measurements at 35 C and C The same procedure as in step 3 was followed after changing the temperature of the water bath WB1 and the solubility cell to 35 C and finally to C. In this way, the solubility of CO gas in the same bitumen sample was measured at three different temperatures for each gas injection Step 6: Changing the Cell Temperature to Room Temperature for Next Gas Injection To measure the gas solubility at different pressures and temperatures in the same run, multiple gas injections were performed. For the second time gas injection, the temperature of the solubility cell was changed to the room temperature. More gas at a higher pressure than in the previous gas injection was injected to the solubility cell by following the same gas injection procedure. The total amount of gas injected into the solubility cell was the sum of the amounts of gas injected into the cell in current and previous injections. After each additional gas injection, the temperature of the solubility cell was set to 60 C again, and then to 35 C and finally to C. At each temperature, the solubility was measured at equilibrium. Then the temperature of the solubility cell was again set to the room temperature and another gas injection was performed. This procedure was repeated and gas at different pressures was injected into the cell and a wide range of solubility data at different pressures and three temperatures were collected after injecting the bitumen sample only once. After the last solubility measurement, the solubility cell was taken out of the water bath and one of the end plugs was removed to depressurize the cell. To clean the cell, it was first detached from the apparatus. Toluene was used as a solvent to wash out the bitumen sample from the cell and the cell was left in a fume hood for 4 hrs to be completely dry and ready for the next experiment. For the bitumen samples studied in this work, a 10 minute waiting time was found to be sufficient for the system to reach a constant equilibrium pressure. Although the gas-bitumen mixtures reached equilibrium in less than 10 minutes, the system was left at equilibrium

93 74 condition for at least one hour to make sure that the pressure did not change with time. This waiting time for equilibrium is much shorter than that needed for larger cells which may take up to weeks. However, the new cell used in this work had some minor disadvantages. Although the cell alone could withstand pressures up to 4.7 MPa, the maximum operating pressure was limited to the pressure of the gas cylinder used to feed the cell. Since the volume of the cell was fixed, the gas inside the cell could not be compressed and reach higher pressures above the gas injection pressure. One other problem was the swelling effect. Oil samples swell as a result of gas dissolution. Since the solubility cell was opaque, the swelling ratios could not be measured Results and Discussion The CO solubility was measured at and 35 C for sample 1 and at, 35 and 60 C for sample. Figures 4-7, 4-8 and 4-9 show the CO solubility data for the two bitumen samples. The solubility decreased with an increase in temperature, and increased with increasing pressure. Both bitumen samples had close solubility values since they were obtained from reservoirs in the same area and their SARA compositions were quite similar. In figures 4-7 and 4-9, the CO solubility data measured in this study are also shown to be in good agreement with the solubility values for Peace River bitumen reported by Mehrotra and Svrcek (1985b). The effect of ashphaltene on CO solubility was also studied. The ashphaltene-free bitumen is called maltene and the CO solubility in maltene is shown in Figures 4-10, 4-11, and 4-1. As shown in Table 4-1, 11% of the bitumen sample 1 was ashphaltene. To compare the CO solubility in samples with and without ashphatene, the solubility in maltene was recalculated by including the amount of ashphaltene which was removed from the sample injected into the cell. Although only maltene was injected into the solubility cell, when equation 8 was used to recalculate the solubility in maltene, the total mass of maltene and removed ashphaltene was considered as the mass of the liquid phase, m L. As shown in Figures 4-10 & 4-11, the recalculated solubility values for maltene and the values for bitumen containing ashphaltene are very close. This confirms that ashphaltene has a negligible effect on CO solubility, which is consistent with a very small effect of ashphaltene on the solubility of CO in oil as previously reported by Kokal et al. (1993).

94 75 For an error analysis, the CO solubility results from three runs for sample 1 at C are compared in Figure 4-1. Since the pressure of the solubility cell decayed as a result of gas dissolution in bitumen, measurements could not be repeated at exactly the same equilibrium pressure. But measurements from different runs can be compared by interpolation. By using interpolation and comparing data from three different runs, the results are found to be reproducible within 3%. One source of error in these measurements was the swelling effect. At each equilibrium condition, the volume of the gas phase was equal to the volume of the equilibrium cell minus the volume of the liquid. As a result of gas dissolution, the liquid could have swelled and changed its volume inside the cell resulting in a smaller volume of the gas phase. Since the equilibrium cell was a blind cell, swelling ratios could not be measured. To analyze the error caused by the swelling effect, the swelling ratio of sample 1 as a result of CO dissolution at C and at 5.4 MPa was measured by using a glass cell and found to be 1.0. Since the solubility values reported in this study for sample 1 at C were measured at equilibrium pressures less than 5.4 MPa, the swelling ratios for all these measurements should be smaller than 1.0. As shown in Figure 4-13, the solubility values measured at C in one run were recalculated by assuming a swelling ratio of 1.0. The recalculated solubility values were higher than the values obtained without considering the swelling effect with a maximum error of.9%.

95 76 Fig Variation of CO gas solubility in bitumen with pressure at C compared with solubility data reported by Mehrotra and Svrcek (1985b) for Peace River bitumen.

96 Fig Variation of CO gas solubility in bitumen with pressure at 35 C. 77

97 78 Fig Variation of CO gas solubility in bitumen with pressure at 60 C compared with solubility data reported by Mehrotra and Svrcek (1985b) for Peace River bitumen.

98 79 Fig Variation of CO gas solubility in bitumen sample 1 and maltene extracted from sample 1 with pressure at C. The recalculated solubility in maltene accounts for the amount of ashphaltene removed.

99 80 Fig Variation of CO gas solubility in bitumen sample 1 and maltene extracted from sample 1 with pressure at 35 C. The recalculated solubility in maltene accounts for the amount of ashphaltene removed.

100 Fig CO gas solubility data for bitumen sample 1 at C from three runs. 81

101 8 Fig The effect of swelling on CO solubility in bitumen sample Effect of gas dissolution on flow stability As a result of the gas dissolution in oil, the oil viscosity would be significantly reduced and the oil-water viscosity ratio would approach unity. Table 4- compares the viscosities of bitumen and gas saturated bitumen from Peace River measured by Mehrotra et al. (1985b). The gas dissolution resulted in a significant viscosity reduction. Figure 4-14 shows the effect of µ w viscosity ratio, m, on the linear stability of the system. The maximum growth rate µ o

102 83 predicted by the linear stability analysis of the core-annular flow (Equation 30 in Chapter 3) vs. the water to oil viscosity ratio is plotted in this Figure. The maximum growth rate decreases with an increase in the viscosity ratio which shows that the system becomes more stable with an increase in the viscosity ratio. Since the gas injection in oil reservoirs results in an increase in the water to oil viscosity ratio, the gas injection makes the immiscible displacement more stable. This is in agreement with the result of Guillot et al. s (007) analysis, where the flow pattern may change from droplet regime to jet regime with an increase in m. Table 4-. The effect of gas saturation on viscosity of Peace River bitumen (source: Mehrotra et al., 1985b). Bitumen CO Saturated Bitumen Temperature ( C) Pressure (MPa) Viscosity (Pa.s) Temperature ( C) Pressure (MPa) Viscosity (Pa.s) 0.1 >

103 84 Fig Maximum dimensionless growth rate predicted by linear stability analysis vs. dimensionless wave number, k, at l 1.03, a o 0.75, and * Re Conclusion A micro cell with a volume less than ml has been developed for solubility measurements in bitumen. The available CO solubility data in bitumen in literature have been reproduced in much shorter times, typically less than 9 minutes. Solubility measurements in ashphaltene free bitumen showed that ashphaltene has little effect on CO solubility in bitumen.

104 85 Chapter 5 Design of a micro glass cell apparatus for pure gas-nonvolatile liquid phase behavior study A micro syringe is used as a constant volume cell for gas-liquid equilibrium (GLE) study. The cell is made of glass and has a volume of less than 100 µl. It can operate at pressures up to 13 MPa and temperatures up to 115 o C. Two different experimental procedures are presented for systems with non-volatile low and high viscosity liquids. A micro magnetic stir bar is used to mix the gas-liquid mixtures inside the cell. Since the internal volume of the cell is small, a short mixing time is sufficient for the gas-liquid mixtures to reach equilibrium. The solubility values are measured by using the pressure decay method. The experimental procedures are validated by measuring the carbon dioxide (CO ) solubility in water and highly viscous bitumen. The experimental results are in good agreement with the available literature data which shows that the technique works well. 5-1) Experimental details 5-1-1) Materials Research grade carbon dioxide (CO ) with % purity was used as the gas phase. Water and bitumen were used as the low viscosity and highly viscous liquid phases, respectively. To prepare the water sample, de-ionized water was boiled under vacuum and degassed before it was injected into the micro cell. The bitumen sample from Peace River was provided by Shell Canada Limited. The SARA (Saturates, Aromatics, Resins, and Ashphaltene) composition of the bitumen sample was determined by using the thin layer chromatography with flame ionization detection (TLC-FID) method (Carbognani et al., 007). The bitumen sample contained 5. % saturates, 56.8 % aromatics, 7.0 % resins, and 11.0 % ashphaltene. The density of the bitumen sample was 0.99g/cm 3 at o C and its viscosity was 1.6 Pa.sec at 50 o C.

105 ) Experimental apparatus The experimental apparatus consisted of three parts: 1) micro cell, ) gas line, and 3) liquid line. The schematic of the apparatus is shown in Figure 5-1. Figure 5-1. Schematic of the experimental apparatus consisting of three parts: the micro cell, gas line, and liquid line. The schematic is not to scale.

106 ) Micro cell In this apparatus, a gas-tight glass syringe (Hamilton Syringe, Model 1710) with a volume of 100 µl was used as the micro glass cell (Figure 5-). The length of the syringe was 6 cm and its bore size was mm. The syringe could operate at temperatures up to 115 C. For the solubility measurements in low viscosity liquids, the standard needle of the glass syringe with an inner diameter of 0.4 mm (Hamilton Removable Needle, Gauge ) was replaced with a thinner needle (Hamilton Needle, Gauge 34) which had an inner diameter of 0.05 mm and a length of 38 mm. The internal volume of this needle was µl. The outer diameter of the needle was only 0.16 mm and a 1/16 inch stainless steel tube was used as a support to keep the needle straight. The needle was inserted into the tube and glued to it. To prevent leakage at high pressures, the plunger of the syringe was glued to the inner cell wall using an epoxy glue. After the plunger was glued, the micro cell was tested to be gas tight at pressures up to 13 MPa. The volume of the cell was constant, since the plunger could not be moved. A miniature magnetic stir bar with a volume of µl was placed inside the cell as a mixer. A magnet placed outside the cell was used to move the stir bar up and down inside the cell. The free volume of the cell, V cell, was calculated by subtracting the volume of the stir bar, V stirr bar, from the volume of the syringe, V syringe. As shown in Figure 5-1, the temperature of the cell was controlled by a cooling or heating fluid from a constant temperature bath circulated through a glass jacket placed around the cell. To thermally isolate the cell, all the components connected to the cell at both ends were insulated. Two type T thermocouples were used to measure the temperature of the coolant or the heating fluid at the inlet and outlet of the jacket. These thermocouples had an accuracy of 0. ºC and were calibrated by using a thermistor thermometer. To ensure that the cell temperature could be precisely controlled by the jacket temperature, the plunger was replaced with a thermocouple in a set of experiments. In each experiment, the thermocouple was placed at a different height in the cell and then the cell was sealed. The cell temperature was compared with the temperature of the

107 88 jacket. All the readings were found to be in excellent agreement (with a maximum difference of ±0. ºC) which shows that the glass jacket uniformly controlled the cell temperature. The needle of the micro cell was connected to a micro valve (VICI, Model SFVO) by using one piece fused silica adapters (VICI, Models FS1.8 and FS1.). This micro valve, which is labeled as V 1 in Figure 5-1, was used as an on/off valve to isolate the cell. The internal volume of the valve V 1 is µl which is negligible compared to the volume of the cell. A 3-way valve, labeled as V in Figure 5-1, connected the micro cell and the micro valve to the gas and liquid lines. The 3-way valve was either switched to the gas line or the liquid line. Figure 5-. The glass syringe used as the micro cell with a magnetic mixer and a bitumen plug inside ) Gas line As shown in Figure 5-1, the gas line consisted of 1) a high pressure gas cylinder with a gas regulator, ) a vent valve, 3) a pressure transducer, and 4) a vacuum pump with a shut off valve. The vacuum pump was used to initially make the micro cell air free. The high pressure gas cylinder was used for gas injection into the cell. The pressure of the gas line was measured by using a pressure transducer (Omega, Model PX 5500) with an accuracy of 7 kpa. This pressure transducer is labeled as P1 in Figure 5-1. The pressure transducer also measured the pressure of

108 89 the main cell when the cell was connected to the gas line. The vent valve, V 5 in Figure 5-1, was only used to better adjust the pressure of the gas line if it was required ) Liquid line The liquid line is composed of 1) a stainless steel syringe with a manual stage, ) a liquid reservoir with an on/off valve and 3) a pressure transducer. The stainless steel syringe (KD Scientific, Model ) was used for liquid injection into the micro cell. The plunger of the stainless steel syringe was supported and moved by the manual stage. The stainless steel syringe was filled with liquid from the liquid reservoir. The pressure of the liquid line was measured by the pressure transducer (Omega, Model PX 5500), labeled as P in Figure 5-1. This pressure transducer also measured the pressure of the micro cell when the 3-way valve was switched to the liquid line ) Experimental procedure for systems with low viscosity liquids Five steps were followed to measure the gas solubility (CO ) in the low viscosity liquid (water). In the first step, the cell was vacuumed. Then, in step, the gas was injected into the micro cell at room temperature. In step 3, liquid was injected into the cell. After the gas and liquid injections, in step 4, the temperature of the cell was changed from the room temperature to the temperature at which the solubility was measured. Finally, in step 5, the gas and liquid inside the cell were mixed and brought to equilibrium and the solubility was measured at the equilibrium pressure ) Vacuuming the cell In the first step, the micro cell was vacuumed to eliminate air. The lowest pressure that could be achieved with the vacuum pump was 40 kpa. Since lower pressure was not reachable, the residual air was diluted with the gas from the high pressure cylinder after the vacuuming, and then the cell was vacuumed for the second time. This process was repeated at least three times to make the cell air free.

109 ) Gas injection into the cell A cooling or heating fluid at room temperature, T room, was circulated through the jacket surrounding the micro cell. This way, the temperature of the cell was kept constant at room temperature for gas injection. The pressure of the gas regulator was adjusted to the pressure, inj. P g, at which the gas would be injected into the cell. The micro valve V 1 was opened and the 3- way valve connected the micro cell to the gas line. The valve V 3 was also opened and the gas was injected into the cell (Figure 5-3-a). The pressure transducer P1 measured the pressure of the gas line and also the micro cell. After the pressure of the cell became stable and equal to inj. P g, the micro valve V 1 was closed. The amount of the gas injected into the cell was calculated from, m inj. inj. g Vcell g (1) where cell, and inj. m g is the mass of the gas injected into the micro cell, V cell is the volume of the micro inj. g is the density of the gas at room temperature and at the gas injection pressure, inj. P g. For calculations, the gas density was obtained from the National Institute of Standards and Technology (NIST) database (See for NIST database). After the gas was injected and V 1 was closed, the gas line was vacuumed for the second time (Figure 5-3-b). This prevented the liquid, which would be injected in the next step, from introducing additional gas into the cell ) Liquid injection into the cell The 3-way valve was switched to the liquid line. The stainless steel syringe was first filled with liquid from the liquid reservoir. The pressure transducer P indicated the pressure of the liquid line. The pressure of the micro cell at this point was inj. Pg and the liquid should be injected at a pressure higher than the cell pressure. Before injecting the liquid into the cell, the pressure of the liquid line was increased to a pressure, inj. P l, higher than inj. P g by pushing the plunger of the stainless steel syringe forward while the micro valve V 1 was closed. After the pressure of the liquid line was increased, V 1 was opened and the liquid was injected into the micro cell (Figure

110 91 5-4). The injected gas could not escape from the cell while liquid was being injected, since the pressure of the liquid line was higher than the pressure of the cell. The pressure transducer P also measured the pressure of the cell while the 3-way valve was switched to the liquid line and V 1 was opened. Figure 5-5 shows the change in the pressure of the cell in each step. Figure 5-3. Schematic of the gas line and the micro cell for gas injection process: a) The gas has been injected into the cell at pressure P g inj. and at room temperature; b) The valve V1 is closed and the gas line is vacuumed for the second time before the liquid injection.

111 9 Since the volume of the cell was constant, the gas volume and pressure inside the cell were controlled by injecting more sample liquid into the cell. In other words, the liquid sample was used as a piston to pressurize the gas-liquid mixture inside the cell. By using the stainless steel syringe for sample liquid injection in the liquid line, it was possible to inject the liquid at a sufficiently high pressure into the cell. Figure 5-4. Schematic of the liquid line and the micro cell for liquid injection. The liquid is injected at pressure P l inj. which is higher than the pressure of the gas injection ) Temperature adjustment As mentioned earlier, the temperature of the cell was controlled by circulating a constant temperature coolant or heating fluid through the glass jacket surrounding the cell. After the gas and the liquid were injected into the cell, the temperature of the cell was changed from the room

112 93 temperature, T room, to the temperature at which the solubility was measured, T experiment. The pressure of the cell changed due to the change in temperature (Figure 5-5). The pressure increased with an increase in temperature and decreased if the temperature was decreased. Figure 5-5. Pressure change in the cell in each step for the solubility measurement by the pressure decay method ) Mixing and reaching equilibrium conditions The gas and liquid phases inside the cell were mixed by moving a miniature magnetic stir bar inside the cell. The pressure transducer on the liquid line measured the pressure of the cell. As a result of the dissolution of gas in the liquid, the pressure decayed until the system reached an equilibrium condition. At equilibrium, the pressure remained constant. This method of solubility measurement is known as the pressure decay method (Chapter 4). In this method, the equilibrium pressure cannot be set a priori at a specific value as the equilibrium pressure depends on the solubility. The amount of gas inside the cell was calculated at equilibrium:

113 94 m eq. eq. eq. g Vg g () where eq. m g is the mass of the gas at equilibrium, eq. V g is the volume of the gas phase at eq. equilibrium, and g is the density of the gas at equilibrium condition. In this calculation, it is eq. assumed that the liquid vapor pressure was negligible compared to the gas pressure and g was equal to the pure gas density. Ren et al. (007) experimentally showed that this assumption is valid for high pressure gas-liquid systems by comparing their solubility results for decane-co mixtures with the data obtained by using analytical methods. However, this assumption may not be valid for vapor-liquid equilibrium (VLE) studies and also for systems including highly volatile liquids. Also, this method cannot be used for gas mixtures since the composition of the gas at equilibrium is unknown. The error introduced by neglecting the liquid vapor pressure will be calculated and discussed later. While the gas was being dissolved in the liquid and the gas-liquid mixture was reaching equilibrium, the cell was opened to the liquid line. Since the cell was not isolated, the gas could also diffuse through the needle. The total amount of the gas dissolved in the liquid inside the cell, dissolved m g, is given by the difference between the initial amount of the gas injected into the cell, inj. m g, and the sum of the amount of the gas at equilibrium, diffused through the needle, diffused m g. eq. m g, and the amount of the gas that m dissolved g m inj. g m eq. g m difussed g (3) The gas solubility in the liquid sample, W, at the equilibrium pressure and temperature was calculated by dividing the amount of the gas dissolved in liquid, liquid injected into the cell, ml and dissolved m g. dissolved m g, by the sum of the W m m m l dissolved g dissolved g (4) The molar concentration of the gas in the liquid at equilibrium, C eq. g, can also be calculated by,

114 95 C dissolved dissolved eq. ng ( mg / M g ) g eq. eq. Vl Vl (5) where dissolved ng is the number of moles of the gas dissolved in the liquid, eq. Vl is the volume of the liquid phase at equilibrium and M g is the gas molecular weight. The amount of the gas diffused through the needle was assumed to be negligible compared to the amount of the gas dissolved in the liquid inside the cell and was not considered in the solubility calculations. The error caused by neglecting the gas diffusion through the needle will be discussed later ) Experimental procedure for systems with highly viscous liquids The method presented above may not be applicable to systems comprised of highly viscous liquids. To minimize the gas diffusion through the needle, a very thin needle with an inner diameter of 0.05 mm (gauge 34) was used as the cell end connection. It may not be possible to inject a highly viscous liquid such as bitumen through this needle into the cell at high pressures. Also, in the solubility measurements in low viscous liquids, the gas diffusion through the needle is neglected. This error may become considerable for the systems with highly diffusive gases and also for the systems with highly viscous liquids which require a long mixing time. However, the experimental procedure can be modified in a way that uses the same experimental apparatus even for viscous liquids. To validate the modified experimental procedure, the solubility of CO in a bitumen sample from Peace River was measured. For these experiments, a gauge needle with an inner diameter of 0.4 mm was used as the cell end connection. The cell was mounted horizontally. Also, the liquid lines in Figure 5-1 were completely filled with mercury instead of the test liquid. The steps for solubility measurements in the bitumen were as follows: ) Manual bitumen injection First, the plunger of the cell (syringe) was removed so one end of the cell was open while the other end was connected to the gas and the mercury lines. Vacuum could not be applied to make the cell air free since light components of bitumen might evolve under vacuum and change the

115 96 bitumen composition. Instead of using vacuum, the cell was purged with gas (CO ) to push the air out prior to the bitumen injection. Then, a known amount of liquid, m l, was manually injected from the plunger side into the purged cell. The plunger was then placed inside the cell and glued to prevent leakage. The plunger pushed the injected bitumen and formed a bitumen plug inside the cell (Figure 5-6). Fig The micro cell for CO solubility measurements in bitumen: bitumen, CO, and mercury are injected into the cell before the start of the mixing ) Gas injection After the bitumen injection, the gas was injected into the cell from the high pressure gas cylinder. If the gas was suddenly injected into the cell at a high pressure, the gas could finger into the bitumen plug. To avoid perturbing the bitumen plug, the discharge pressure of the gas cylinder and consequently the cell pressure were slowly increased until they reached the set injection pressure. The free volume of the cell for gas injection was equal to the total cell volume, V cell, minus the injected liquid volume, calculated as follows. inj. V l, so the mass of the gas injected could be m ( V V ) (6) inj. inj. inj. g cell l g