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Thermodynamics and kinetics of CO2 hydrate formation in the presence of cellulose nanocrystals Cendales, Jairo Eduardo 2021

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THERMODYNAMICS AND KINETICS OF CO2 HYDRATE FORMATION IN THE PRESENCE OF CELLULOSE NANOCRYSTALS  by  Jairo Eduardo Cendales  B.Sc., Universidad Nacional de Colombia (Bogotá), 2010  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF    MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Chemical and Biological Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)   February 2021  © Jairo Eduardo Cendales, 2021  ii  The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, a thesis entitled:  Thermodynamics and kinetics of co2 hydrate formation in the presence of cellulose nanocrystals  submitted by Jairo Eduardo Cendales in partial fulfillment of the requirements for the degree of Master of Applied Science  in Chemical and Biological Engineering  Examining Committee: Dr. Peter Englezos, Professor, Chemical and Biological Engineering, UBC Supervisor  Dr. Savvas G Hatzikiriakos, Professor, Chemical and Biological Engineering, UBC Supervisory Committee Member  Dr. John A Ripmeester, Adjunct Faculty Member, Chemical and Biological Engineering, UBC Supervisory Committee Member Dr. Nagu Daraboina, Assistant Professor, Chemical Engineering, University of Tulsa Additional Examiner   iii  Abstract The kinetics of gas hydrate formation are of interest in various energy and environmental applications of gas hydrates. One such example is the hydrate based gas separation (HBGS) as a possible method to capture CO2 from either pre-combustion or post-combustion gas mixtures present in integrated gasification combined cycle (IGCC) and conventional power plants respectively.  In such applications additives are included to improve the kinetics of gas hydrates. In this work, carbon dioxide hydrate was formed in aqueous suspensions of cellulose nanocrystals (CNC) and the induction time and rate of hydrate crystal growth was compared to data obtained with hydrates formed in pure water (blank). 24 runs were made for each group (blanks and CNCs). A suspension with a CNC concentration 0.75 wt% was employed to determine whether CNC could reduce the induction time and enhance hydrate growth rate as it has been reported for carbon nanotubes and other nanoparticle suspensions. Hydrate formation experiments were carried out in semi-batch mode setup in a high pressure crystallizer with overhead stirring. The temperature and the pressure were 274.15K and 2370 kPa respectively, this pressure is 1000 kPa above the equilibrium pressure of CO2 hydrates at the mentioned temperature. Statistical analysis was performed with the data gathered to establish whether there is an effect of CNC nanoparticles in hydrate kinetics. The results show that the CNC did not have a statistically significant impact on CO2 hydrate formation. This study also compared the results with data from the literature about the effect of other nanoparticles on gas hydrate formation.       iv  Lay Summary Clathrate hydrates or gas hydrates are nonstoichiometric inclusion compounds in which water (host) physically entraps guest molecules such methane, hydrogen, carbon dioxide, nitrogen or ethane in cages. Recently, carbon nanoparticles have been of interest as promoters of gas hydrates formation due to their good thermal conductivity and high surface area. Interest in the effect of nanoparticles is broader because in practice hydrate nucleation occurs under heterogeneous conditions due to the presence of impurities. In fact, the presence of impurities has been invoked to postulate a mechanism for heterogeneous nucleation, the memory effect, and its elimination by antifreeze proteins. In this work, the effect of cellulose nanocrystals (CNC) on CO2 hydrate equilibrium and kinetics is investigated. The hypothesis is that the presence of CNC nanoparticles will enhance the hydrate formation kinetics by reducing the induction time and enhancing the hydrate crystal growth rate. v  Preface This research was done under the supervision and tutelage of my supervisor Dr. Peter Englezos. As supervisor, he contributed in the literature review, hypothesis formulation, experimental design, experimental work, data analysis, writing of the present manuscript, peer review article publication and edition. I, Jairo Eduardo Cendales, was responsible for the literature review, preliminary experiments, main experimental design, experimental set up, main experimental work, data gathering, data analysis, conclusions, and the writing of the present manuscript. All the experiments were conducted in the Thermodynamics lab of the department of Chemical and Biological Engineering at the University of British Columbia (Vancouver, BC, Canada).  Additionally, Jackie Chow assisted with the literature review, lab training, he and Mingsi Yi also assisted me with the experimental design. The equipment used for all the experiments was designed and built by Dr. Hassan Sharifi who also provided insight and guidance for the experimental design and the experimental work. The analysis of the particle size of the nanoparticles was performed by Dr. Mehrnegar Mirvakili in the Pulp and Paper Centre at the University of British Columbia (Vancouver, BC, Canada), she also contributed with the experimental procedure for the sonication of the nanoparticles.  The data and analysis of this thesis was published in a peer-reviewed article. The authors were Jairo Eduardo Cendales, Mingsi Yin and Dr. Peter Englezos:  vi  Cendales, JE.; Yin, M.; Englezos, P.; Thermodynamics and Kinetics of CO2 Hydrate Formation in the Presence of Cellulose Nanocrystals with Statistical Treatment of Data, Fluid Phase Equilibria, 2021, 529, 112863.    vii  Table of Contents Abstract ......................................................................................................................................... iii Lay Summary ............................................................................................................................... iv Preface .............................................................................................................................................v Table of Contents ........................................................................................................................ vii List of Tables ..................................................................................................................................x List of Figures .............................................................................................................................. xii List of Symbols ........................................................................................................................... xiv List of Abbreviations ................................................................................................................. xvi Acknowledgements .................................................................................................................. xviii Chapter 1: Introduction to Gas Hydrates and Gas Hydrate CO2 Capture..............................1 1.1 Gas Hydrate Structures ................................................................................................... 1 1.2 Gas Hydrate Equilibrium ................................................................................................ 3 1.3 Gas hydrate formation kinetics ....................................................................................... 4 1.4 Stochastic nature of hydrate formation ........................................................................... 9 1.5 Memory effect ................................................................................................................. 9 1.6 Gas Hydrate Formation in the Presence of Nanoparticles ............................................ 10 1.7 Cellulose nanocrystals (CNC)....................................................................................... 13 1.8 Hydrate Based Gas Separation (HBGS) process .......................................................... 14 1.9 Thesis Objectives .......................................................................................................... 16 Chapter 2: Experimental setup...................................................................................................17 2.1 Materials ....................................................................................................................... 17 2.2 High pressure crystallizer system ................................................................................. 17 viii  2.3 Experimental procedure: Gas uptake method ............................................................... 20 2.3.1 Stirring rate ............................................................................................................... 22 2.4 Experimental procedure: Hydrate equilibrium measurements ..................................... 23 2.5 Experimental procedure: Preparation of CNC suspension ........................................... 24 2.6 Data recording ............................................................................................................... 25 2.7 Calculation of the gas consumed .................................................................................. 26 2.8 Error propagation .......................................................................................................... 28 2.9 CO2/N2 mixture ............................................................................................................. 30 Chapter 3: Results and Discussion .............................................................................................33 3.1 CNC characterization .................................................................................................... 33 3.2 CO2 hydrate equilibrium in pure water and in the presence of CNC............................ 33 3.3 Preliminary Experiments to Establish Experimental Pressure and Temperature Conditions ................................................................................................................................. 37 3.4 Kinetics of CO2 Hydrate formation in Pure water (blank). .......................................... 39 3.5 Kinetics of CO2 hydrate formation in the presence of CNC ......................................... 42 3.6 Plotted results ................................................................................................................ 45 3.6.1 Induction time ........................................................................................................... 45 3.6.2 Hydrate formation rate .............................................................................................. 46 3.7 Temperature and gas uptake profiles ............................................................................ 47 3.7.1 Blank: Temperature and gas uptake profiles ............................................................ 47 3.7.2 CNC 0.75% wt.: Temperature and gas uptake profiles ............................................ 48 3.8 Statistical hypothesis testing ......................................................................................... 49 3.8.1 Induction time ........................................................................................................... 50 ix  3.8.2 Gas uptake ................................................................................................................. 51 3.8.3 Hydrate formation rate .............................................................................................. 52 3.8.4 Plot - Induction time - statistics ................................................................................ 53 3.8.5 Plot – Hydrate formation rate - statistics .................................................................. 53 3.9 CO2/N2 hydrate kinetic experiments ............................................................................. 54 Chapter 4: Analysis and conclusions .........................................................................................55 4.1 Equilibrium data............................................................................................................ 55 4.2 Statistical analysis of the kinetic data ........................................................................... 55 4.3 Experiments with a mixture of CO2 and N2 .................................................................. 60 4.4 Conclusions ................................................................................................................... 60 4.5 Recommendations for further work .............................................................................. 61 Bibliography .................................................................................................................................62  x  List of Tables Table 1. Compilation of some results of research in gas hydrate kinetics using nanoparticles. ... 12 Table 2. Cellulose nanocrystals properties reported by provider Celluforce® (2019). ................. 17 Table 3. Results obtained for the propagation of uncertainty (error) in the calculation of the moles captured in the hydrate and dissolved phase (gas uptake). ........................................................... 30 Table 4. Experimental Hydrate equilibrium data obtained for CO2/N2 mixtures and TBAB-water solutions by different authors........................................................................................................ 31 Table 5. Experimental parameters for the gas mixture of CO2/N2 in TBAB-water and CNC-TBAB-water. ............................................................................................................................................. 32 Table 6. CNC characterization using a particle size analyzer. ..................................................... 33 Table 7. Incipient hydrate equilibrium pressure for CO2 in CNC 0.75% at different temperatures........................................................................................................................................................ 34 Table 8. Incipient hydrate equilibrium pressure for CO2 in CNC 0.75% at 274.1K and (L-H-V) compared with experimental data from different authors and the prediction model developed by Kamath. ......................................................................................................................................... 34 Table 9. Incipient hydrate equilibrium pressure for CO2 in CNC 0.75% at 276.2K and (L-H-V) compared with experimental data from different authors and the prediction model developed by Kamath. ......................................................................................................................................... 35 Table 10. Incipient hydrate equilibrium pressure for CO2 in CNC 0.75% at 277.5K and (L-H-V) compared with experimental data from different authors and the prediction model developed by Kamath. ......................................................................................................................................... 35 xi  Table 11. Incipient hydrate equilibrium pressure for CO2 in CNC 0.75% at 278.9K and (L-H-V) compared with experimental data from different authors and the prediction model developed by Kamath. ......................................................................................................................................... 36 Table 12. Experimental data obtained of induction time at 1°C for three driving forces. ............ 38 Table 13. Experimental parameters for the blank and CNC experiments. ................................... 39 Table 14. Results for the induction time, gas uptake at induction time, gas uptake 30 min. after induction time and hydrate formation rate in the first 30 min. of CO2 hydrates in water under the conditions in table 5. ..................................................................................................................... 41 Table 15. Results for the induction time, gas uptake at induction time, gas uptake 30 min. after induction time and hydrate formation rate in the first 30 min. of CO2 hydrates in a suspension of CNC 0.75%wt.-water under the conditions in table 5. ................................................................. 44 Table 16. Statistical results, induction time, blank and CNC 0.75% wt. ...................................... 50 Table 17. Statistical results, gas uptake at induction time and gas uptake 30 min. after induction time, blank and CNC 0.75% wt. ................................................................................................... 51 Table 18. Statistical results, hydrate formation rate in the first 30 min., blank and CNC 0.75% wt........................................................................................................................................................ 52 Table 19. Results for the induction time for the CO2/N2 mixture (0.132/0.868 mol) with the blank group and the CNC group. ............................................................................................................ 54  xii  List of Figures Figure 1. Gas hydrate structures. Image from Centre for Hydrate Research, Colorado School of Mines (Sloan, 2003). ....................................................................................................................... 2 Figure 2. CO2-Water hydrate experimental incipient hydrate equilibrium pressure at different temperatures (Lw-H-V). Data from different authors...................................................................... 4 Figure 3. A common hydrate equilibrium curve in a P vs. T diagram depicting the pressure driving force. ............................................................................................................................................... 7 Figure 4. Hydrate growth curve of gas consumption. Taken from Renault-Crispo and Servio (2017). ............................................................................................................................................. 8 Figure 5 Cellulose Nanocrystal structure. From CNC provider, Celluforce (2019). .................... 14 Figure 6. Pre-combustion and post-combustion CO2 capture with hydrates. Adapted from Linga et al., 2006. ........................................................................................................................................ 15 Figure 7. Piping and instrumentation Diagram (P&ID) of the apparatus. Only one crystallizer and one supply vessel are shown to simplify the diagram. System design by Sharifi et al. (2014). ... 18 Figure 8. Comparison of the incipient hydrate equilibrium pressure for CO2 in water and a suspension of water-CNC 0.75% from different authors.............................................................. 36 Figure 9. Results for the induction time of the blank and CNC 0.75wt. runs. .............................. 45 Figure 10. Results for the induction time of the blank and CNC 0.75wt. runs. ............................ 46  Figure 11. Blank, Run 1. Temperature vs. time. .......................................................................... 47  Figure 12. Blank, Run 1. Gas uptake vs. time. tind: hydrate formation time. ............................... 48  Figure 13. CNC 0.75% wt., Run 10. Temperature vs. time. ........................................................ 48 Figure 14. CNC 0.75% wt., Run 10. Gas uptake vs. time. tind: hydrate formation time. .............. 49 xiii  Figure 15. Statistical comparison of the induction time for the blank and CNC 0.75% wt. groups, │mean, ├┤95% confidence interval. ........................................................................................... 53 Figure 16. Statistical comparison of the hydrate growth rate for the blank and CNC 0.75% wt. groups, │mean, ├┤95% confidence interval. .............................................................................. 53  xiv  List of Symbols α: Probability Value (p-value). δ: Finite difference. ∂: Partial derivative. Δ: Difference between two points in time. G: Gas Phase. H: Hydrate Phase. H0: Null Hypothesis. Lw: Liquid Water Phase.  Min: minutes. nCR,t: Moles in the Crystallizer at a certain time. nCR,t: Moles in the Supply Vessel at a certain time. nG,t: Moles of Gas at a certain time. nH,t: Moles of Gas in the Hydrate Phase at a certain time. P: Pressure. Pc: Critical Pressure. Pr: Reduced Pressure Peq: Equilibrium Pressure. Pop: Operating Pressure.  T: Temperature. Tc: Critical Temperature. Teq: Equilibrium Temperature. xv  Tr: Reduced Temperature.  Top: Operating Temperature. tind: Induction Time. V: Vapour Phase. VCR: Volume Crystallizer. VSV: Volume Supply Vessel. ω: Acentric Factor. wt.: Weight percentage in suspension/solution (mass). z: Compressibility Factor. xvi  List of Abbreviations B1-#: Blank run (water). CI: Confidence Interval. CNC: Cellulose Nanocrystals (Also abbreviated NCC). CNT: Carbon Nanotubes. CR: Crystallizer. DAQ: Data Adquisition System. HGBS: Hydrate Based Gas Separation Process. MWCNT: Multi-walled Carbon Nanotubes. N1-#: CNC Suspension Run.  NPS: Nominal Pipe Size. OMWCNT: Oxidized Multi-walled Carbon Nanotubes. PCV: Pressure Control Valve. PG: Propylene Glycol. P&ID: Piping and Instrumentation Diagram. PID: Proportional Integral Derivative Controller. PIT: Pressure Indicator Transmitter. rpm: Revolution Per Minute SDS: Sodium Dodecyl Sulfate. SV: Supply Vessel. SWCNT: Single-walled Carbon Nanotubes. TBAB: Tetra-n-butyl Ammonium Bromide. TIC: Temperature Indicator Controller. xvii  TT: Temperature Transmitter.  xviii  Acknowledgements My deepest and everlasting gratitude goes to Dr. Peter Englezos who gave me the opportunity to do this research, supported me, guided me, encouraged me and counseled me throughout the research work presented on this thesis.   I also owe my gratitude to Jackie Chau and Mingsi Yi for their help during the experimental design, to Dr. Hassan Sharifi for his insight and support and Dr. Mehrnegar Mirvakili for her help and support with some of the experiments.  Additional thanks to Tina Raeisigahrooee and Marziyeh Danesh from Dr. Savvas Hatzikiriakos research group for their assistance.   I would also extend my gratitude to all the staff of the department of Chemical and Biological Engineering at the University of British Columbia for all their support during my program.   Special thanks to my parents, without their support none of this would have been possible.    1  Chapter 1: Introduction to Gas Hydrates and Gas Hydrate CO2 Capture Clathrate hydrates or gas hydrates, known since the early 1800s, are nonstoichiometric crystalline inclusion compounds in which water acting as the host molecule physically entraps the other (guest) molecule such methane, hydrogen, carbon dioxide, nitrogen or ethane in cages (Davidson, 1973; Englezos, 1993; Ripmeester, 2000; Sloan and Koh, 2007). Interest on gas hydrates has grown exponentially since the early 1990s based on the number of studies published started to grow exponentially (Babu et al., 2015; Nguyen et al., 2020). This was mainly due to the diverse potential applications like oil and gas pipeline plugging, high storage capacity and transportation (particularly natural gas), gas separation processes, CO2 sequestration, refrigeration processes and the large amounts of gas hydrates estimated in the crust of the earth, which is considered an important energy source but also an environmental risk for the amount of methane that could be liberated to the atmosphere. Methane is a potent greenhouse gas and its accidental release can further enhance warming and thus create a “runaway” greenhouse effect.   1.1 Gas Hydrate Structures Gas hydrates are crystalline materials and their structures are classified into three types: Structure I, Structure II and Structure H (Ripmeester et al., 1994; Ripmeester et al., 1987).  Hydrate structures are composed of five polyhedra formed by hydrogen-bonded water molecules as seen in figure 1 (Ripmeester et al., 1994; Sloan, 2003).  2   Figure 1. Gas hydrate structures. Image from Centre for Hydrate Research, Colorado School of Mines (Sloan, 2003).  Structure I hydrates have a unit cell with cubic symmetry with a 12Å lattice formed with 46 molecules of water. They consist of two types of polyhedral cages, a pentagonal dodecahedron (512) and a hexagonal truncated trapezohedron (62) and their ideal unit cell formula for structure I hydrates is 6(51262)-2(512)-46H2O (Jeffrey, 1984). Typical gases that form structure I hydrates are carbon dioxide and methane.  Structure II hydrates also have a unit cell with cubic symmetry, but its lattice is of 17.3Å and they have 136 molecules of water. They also form two types of cages, there are sixteen pentagonal dodecahedra (512) and eight hexadecahedra (64). Their ideal unit cell formula is 8(51264)-16(512)-136H2O (Jeffrey, 1984). Typical structure II hydrates are propane and iso-butane.  3  Structure H hydrates are hexagonal with a 12.2Å lattice, they consist of 34 molecules of water. They have three types of cages, three pentagonal dodecahedra (512), two 435663 polyhedra and one huge 51268 polyhedra. Their ideal unit cell formula is 1(51268)-3(512)-2(435663)-34H2O (Sloan and Koh, 2007). The formation of structure H hydrates requires two different guest molecules, one small and one large, for example methane + neohexene.   1.2 Gas Hydrate Equilibrium   Phase equilibrium data and methods to predict such equilibria are widely available for gas hydrate systems (Sloan and Koh, 2007). One important property for a hydrate forming system is the incipient equilibrium phase boundary separating stable hydrate solid phases form fluid phases. Experimentally, this is typically determined by the isothermal pressure search method (Englezos and Bishnoi, 1991) or isochoric methods (Sloan and Koh, 2007). Figure 2 below shows the incipient hydrate equilibrium conditions for CO2 hydrate. Carbon dioxide is a linear molecule, the length of the carbon-oxygen bond is 116.3 pm for a total length of 232.6 pm for the whole molecule. CO2 forms structure I hydrates and occupies both the small (512) and large (51262) cavities, it has the molecular formula CO2*nHH2O (nH=5.75 at maximum occupancy) (Sloan and Koh, 2007).  The CO2 hydrate phase equilibrium has been studied thoroughly; the following figure presents the experimental equilibrium pressure at different temperatures from various authors.   4   Figure 2. CO2-Water hydrate experimental incipient hydrate equilibrium pressure at different temperatures (Lw-H-V). Data from different authors.  The knowledge of this phase boundary facilitates the design of processes dealing with hydrates. It also aids the understanding of the kinetics of hydrate formation and dissociation as will be discussed below.  1.3 Gas hydrate formation kinetics One of the most challenging aspects of hydrates is the understanding of the kinetics of their formation and dissociation in pure water or in aqueous solutions containing dissolved chemicals that may influence the crystallization process. These phenomena being time dependent are more challenging than time independent phenomena (Sloan and Koh, 2007). Under suitable pressure 5  and temperature conditions the onset of hydrate formation refers to the moment in which hydrogen bonded molecules form detectable crystal nuclei with encaged gas molecules like CO2. The nuclei are detectable at a macroscopic level either visually or indirectly through a temperature signature. Hydrate crystal formation is an exothermic process. The onset of hydrate formation is also referred to as the nucleation point. Relevant to this term is the tern induction time that refers to the time it takes for the system to create the nuclei. Hydrate growth period is defined as the observation time after the induction time when hydrate particles continue to grow. Typically, an experiment proceeds to a point in the supply of hydrate forming gas is terminated or at a point at which agglomeration of the hydrate crystals is observed. This agglomeration causes a mass transfer resistance that reduces the hydrate growth (Englezos, 1996). In a similar manner, the dissociation time is the time that takes for a fully formed hydrate crystal to break into their initial gas and liquid phases.   Finally, hydrate inhibition refers to the process whereby a water soluble chemical is injected into the system so that the phase boundary is shifted to conditions outside the stable equilibrium region (thermodynamic inhibition) or the hydrate is allowed to form later in time (longer induction time) and then not allowed to agglomerate. The latter is called kinetic inhibition and typically is achieved with water soluble synthetic polymers or antifreeze proteins at low dosages (low dosage or kinetic hydrate inhibitors). Thermodynamic inhibitors include methanol and glycols. (Englezos, 1996; Sloan and Koh, 2007; Walker et al., 2015).    The kinetics of hydrates are typically studied experimentally at the macroscopic level with the gas uptake method (Englezos et al., 1987). In such a hydrate kinetic experiment, a crystallizer (high 6  pressure vessel) is filled with water (or any other hydrate forming liquid) and a hydrate forming gas.  The pressure is maintained using a supply vessel that transfers gas to the crystallizer as it is being consumed (semibatch operation). The experiment can be conducted in a batch mode as well (closed system). The experiment starts when the stirrer within the crystallizer is turned on, and the gas starts to dissolve in the water, but even with the system being at a temperature and pressure within the stable period hydrates do not form due to metastability (the tendency of a system to persist in a nonequilibrium state). The induction time is defined as the time elapsed between the start of the experiment (start of stirring) and the time when the hydrate nuclei reach a critical mass and the phase change becomes detectable. During the induction time gas dissolves in the water and builds a supersaturated environment that induces hydrate formation.   It is noted that the experimental pressure at a given temperature must lie above the equilibrium pressure at this temperature. The difference between the total pressure of the system (operating pressure) and the equilibrium pressure for hydrate formation at a certain temperature is called the pressure driving force (Pop-Peq), this can be seen in figure 3.    There is a direct relation between the driving force and the hydrate induction. Larger driving forces result in shorter induction times and higher gas uptakes for a particular system time (Englezos et al., 1987; Linga et al. 2007).  7   Figure 3. A common hydrate equilibrium curve in a P vs. T diagram depicting the pressure driving force.  Figure 4 shows the typical curve for gas consumption in a hydrate formation process (Renault-Crispo et al., 2017). The process is divided in three steps. The first involves the dissolution of the hydrate-forming gas into the liquid phase until in supersaturates it and reaches the point of three-phase equilibrium. The next step is the induction time in which the gas consumption decreases and pressure does not significantly change, this is due to the supersaturation of the first step. After the onset of hydrate crystallization, the gas consumption increases steadily until many crystals begin agglomeration.  PressureTemperature PeqTeq,TopPopDriving  force8   Figure 4. Hydrate growth curve of gas consumption. Taken from Renault-Crispo and Servio (2017).  As stated above, the method used to study hydrate formation in this work is the so called gas uptake method implemented by Englezos et al. (1987) and applied (with some modifications) by Lee and Englezos (2005) and Linga et al. (2007). This method established an isothermal and isobaric hydrate formation in a semi-batch operation. The temperature is maintained using a cooling bath with a circulation thermostat and the pressure is maintained using a supply vessel at a higher pressure that transfers gas through a control valve. The gas in the hydrate vessel is consumed to form hydrate and is dissolved in the water phase.    At a macroscopic scale, hydrates could be detected visually typically through Lexan or sapphire windows. Since hydrate formation is an exothermic process one may trace the nucleation and growth through temperature measurements (Sloan and Koh, 2007). As hydrates are formed the temperature increases and is detected with the use of thermocouples installed in the crystallizer. A 9  sudden temperature spike at the interface (and in the liquid phase) is typically observed. In addition, the mass of CO2 that is contributing to hydrate formation is determined from T, P measurements and mass balance (Linga et al., 2007; Sharifi, 2014).   1.4 Stochastic nature of hydrate formation  A stochastic process could be defined as one in which the observation of a certain variable (usually time dependant) is not certain but rather “most likely”, therefore, for an observation with a fixed set of conditions, it is expected to obtain a value within a probability distribution and not a fixed value like in a deterministic process. Hydrate formation kinetics is an example of an stochastic process, particularly at low driving forces, but the process becomes less stochastic at high driving forces (Sloan and Koh, 2007).     1.5 Memory effect It has been reported by several hydrate researchers that water from the melting of hydrates retains “memory” of the hydrate formation (Vysniauskas and Bishnoi, 1983; Servio and Englezos, 2003; Sloan and Koh, 2007). It has been observed that if a mixture of gas and water that has previously formed hydrates and was melted by a slight increase of temperature, will form hydrates more easily than a fresh mixture that has not formed hydrates before. When the temperature of a hydrate system is increased outside of its stable equilibrium zone, hydrates start to dissociate, but it appears that water retains some memory of the hydrate which facilitates the formation of hydrates  (Vysniauskas and Bishnoi, 1983). It was also observed that if a hydrate forming system is heated up way beyond its stable zone and a considerable amount of time has passed since the hydrates were dissolved, the memory effect will disappear from the water.    10   1.6 Gas Hydrate Formation in the Presence of Nanoparticles   Nanotechnology has become very significant because of its ability to control and manipulate matter at the atomic scale. Carbon nanoparticles have drawn considerable attention in the scientific and engineering community due to their extraordinary physical, chemical, optical, mechanical and thermal properties (Chandrasekaran et al., 2013). They are composed of pure carbon and therefore, they exhibit high stability, excellent conductivity and are environmentally favorable. Some of these properties are good electrical conductivity, good thermal conductivity and high surface area (CD Creative Diagnostics, 2020). Interest in the effect of nanoparticles is broader because in practice hydrate nucleation occurs under heterogeneous conditions due to the presence of impurities. In fact, the presence of impurities has been invoked to postulate a mechanism for heterogeneous nucleation, the memory effect, and its elimination by antifreeze proteins (Zeng et al., 2006).  Some examples of carbon nanoparticles are graphene and carbon nanotubes (CNT), the latter are subdivided in single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs). Recently, MWNTs have been investigated for their potential to enhance the kinetics of hydrate formation. Amine functionalized and as produced MWCNTS were found to affect CO2 hydrate growth and this was attributed to the ability of the carbon nanotubes to enhance mass transfer (Pasieka, 2015). The high surface area and nanoscale nature of MWNTs facilitates the interaction between the diluted gas and the host molecules enhancing the formation of hydrate bonds. The concept is similar to what a solid catalyst does in a chemical reaction where it promotes the interaction between the reactants.  11   Previous studies have shown positive impact of nanoparticles in the rate of formation of hydrates. (Park et al., 2010) found that in the presence of multi-walled carbon nanotubes (MWCNTs) in water the amount of methane consumed was 300% higher and the hydrate formation time decrease at subcooling temperatures (Difference between the equilibrium temperature and the operational temperature) of 0.5K and 3.5K for equilibrium pressures between 3 and 9 MPa. It was concluded that carbon nanotubes played a seed role during hydrate formation and growth. The presence of multi-walled carbon nanotubes (9.5 ppm) in an aqueous solution of 40% Tetra-n-butyl ammonium bromide (TBAB) was found to increase the CO2 gas consumption rate for at a subcooling temperature of 3°C (Renault-Crispo, 2017). TBAB is a quaternary ammonium salt known to form semiclathrate hydrates with structures that are different from the three typical structures of gas hydrates (Shimada et al., 2005) The empty cages in semi-clathrate hydrates can trap molecules like CO2 or CH4. The presence of nanotubes was found that lower concentrations of MWCNT enhanced hydrate growth rate up to a maximum of 15% for induction times of less than one hour (Renault-Crispo, 2017), but this was not the case for higher concentrations because the initial nucleation event is more pronounced and caused heat and mass transfer limitations (Pasieka, 2015). These experiments were conducted at a temperature of 2 oC and a pressure of 2033 kPa (500 kPa driving force) and the hydrate growth rate increased by 8.37% for a concentration of 0.5 ppm with respect to water alone.    The influence of nanofluids in gas hydrates has also been studied (Said et al., 2016). The rate of dissolution and gas hydrate growth was also reported when hydrates formed from a 75/25 mol % (CH4/CO2) mixture at 274.15 K and 4,000 KPa in the presence of 0.1, 0.2 and 0.3 wt.% of SiO2, 12  Al2O3, Cu and Ag nanoparticles. The 0.3 wt % SiO2 nanofluid had the strongest effect. Two other nanofluids had a weaker effect (0.2 wt.% Al2O3 and 0.1 wt.% Cu) whereas the silver (Ag) nanofluid did not have any impact. Table 1 below summarizes some of the results obtained from different authors for the effect of nanoparticles on hydrate nucleation and growth.     Author System Temperature (K) Pressure (kPa) Driving force Induction time (min.) Renault-Crispo et al. (2017) CO2/TBAB (40% wt.) + MWCNT (9.5ppm) 287.15 2678 3.0°C * 54.9 Abedi-Farizhendi (2019) CH4/MWCNT (90 ppm) 274.15 4500 1915 kPa 7.0 CH4/MWCNT (360 ppm) 274.15 4500 1915 kPa 4.0 Park et al. (2010) CH4/MWCNT (0.004% wt.) 275.15 5006 5.0°C * 216.4 Montazeri et al. (2019) CO2/Boehmite (25 ppm) 274.15 2900 1500 kPa 22.5 CO2/Boehmite (75 ppm) 274.15 2900 1500 kPa 11.5 Lim et al. (2014) CH4/OMWCNT** (0.004% wt.) 275.15 4020 3.0°C * 239.8 Nashed et al. (2019) CH4/SDS (0.03% wt.) + MWCNT (0.1% wt.) 274.15 5100 2530 kPa 85.0 CH4/SDS (0.03% wt.) + COOH-MWCNT (0.1% wt.) 274.15 5100 2530 kPa 56.1 * In these experiments, subcooling was used as driving force instead of overpressure. ** Oxidized multi-walled carbon nanotubes. Table 1. Compilation of some results of research in gas hydrate kinetics using nanoparticles. 13   Additionally, a preliminary study of the potential effects of cellulose nanocrystals (CNC) on CO2 hydrate kinetics was conducted in our laboratory at UBC Yin (2019). Both batch and semi-batch experiments were done with a driving force of 1500 kPa and 1000 kPa respectively, the temperature was 2°C for all tests, and the concentrations were 0.13% weight for the semi-batch and 0.5% weight for the batch. It was observed that there was no statistically significant difference in the induction time but there was some positive impact on the hydrate growth rate. These results left open the possibility for the exploration of the effects of CNC in hydrate kinetics using higher concentrations, which is the goal of this study.   1.7 Cellulose nanocrystals (CNC) Cellulose nanocrystals (CNC) are unique nanomaterials derived from cellulose, the most abundant natural polymer. CNCs have large aspect ratio (surface area/volume), high tensile strength and elastic modulus. These materials have been considered in a diverse set of potential applications including adhesives, cements, inks, drilling fluids, polymer reinforcement, nanocomposites, transparent films, paper products, cosmetics, barrier/separation membranes, transparent-flexible electronics, batteries, supercapacitors, catalytic supports. The majority of CNCs are sourced from hard and soft wood, but algae, and bacteria also generate these materials (Foster et al., 2018; George and Sabapathi, 2015). Cellulose Nanocrystals are often abbreviated as CNCs or NCCs, in this work the former is used. 14   Figure 5 Cellulose Nanocrystal structure. From CNC provider, Celluforce (2019). CNCs are stiff, with spindle-like morphology of typical length 50–350 nm, width 5–20 nm, and aspect ratios of 5–30, where the surface chemistry, charge, and particle aspect ratio are determined by the hydrolysis conditions (Foster et al., 2018).   For hydrate kinetics, CNCs perhaps the most important property is the large surface area that can serve as heterogeneous nucleation site for hydrate formation. Besides, CNCs are environmentally friendly and can sustain high pressures without losing their structure. These properties make CNCs suitable as a hydrate mechanical additive and a potential kinetic promoter. It should be noted that In another study it was found that nanocellulose-based membranes have good separation performance for mixtures of CO2/N2 and CO2/CH4, pointing out their potential for advanced gas separation membrane-based technology (Ansaloni et al., 2017).    1.8 Hydrate Based Gas Separation (HBGS) process Capture of CO2 from flue gas mixtures arising from the combustion of fossil fuels and from fuel gas mixtures arising from the gasification of coal, natural gas and/or biomass represent very interesting cases of potential gas separations based on gas hydrates (Linga et al., 2007). The key 15  idea is illustrated in figure 6 (Linga et al, 2006) and is the fact that when gas hydrate crystals are formed from a binary gas mixture such as CO2/H2 (analogue for a fuel gas) or  CO2/N2 (analogue for a flue gas) at suitable pressure and temperature conditions the gas hydrate crystal phase is enriched with CO2 and the remaining gas (“unreacted” gas) is enriched in H2 or N2 respectively. Another remarkable property of gas hydrates is the fact that the concentration of CO2 in its hydrate state is 0.14 (mole fraction) whereas its solubility in water is 6.1 x 10-4 (mole fraction). Thus, the CO2 uptake capacity of water in the hydrate state is orders of magnitude more than that in liquid state.    Figure 6. Pre-combustion and post-combustion CO2 capture with hydrates. Adapted from Linga et al., 2006.  The following quantities have been proposed to assess the CO2 capture process (Linga et al, 2006; 2007a; 2007b). The CO2 recovery or split fraction (S.Fr.) of carbon dioxide in the CO2 rich stream 16  is calculated as the ratio of the molar flow rate in the CO-rich stream and the molar flow rate of CO2 in the feed. 𝑆. 𝐹𝑟. =𝑛𝐶𝑂2𝑅𝑖𝑐ℎ𝑛𝐶𝑂2𝐹𝑒𝑒𝑑    (1) Similarly, the Separation factor (S.F.) is calculated as follows: 𝑆. 𝐹. =𝑛𝐶𝑂2𝑟𝑖𝑐ℎ  𝑛𝑁2 𝑜𝑟 𝐻2𝑙𝑒𝑎𝑛𝑛𝑁2,𝑜𝑟 𝐻2𝑟𝑖𝑐ℎ   𝑛𝐶𝑂2𝑙𝑒𝑎𝑛   (2) Significant amount of effort has been devoted to the development of the HBGS process for pre-combustion and or post-combustion applications. The HBGS method uses water as a solvent instead of toxic or hazardous materials. Especially for pre-combustion applications the process is not as energy intensive because the pressure range of fuel gas is 5-7 MPa which is a suitable pressure for hydrate crystal formation (Babu et al., 2015).    1.9 Thesis Objectives The hypothesis of the proposed work is that the presence of CNC nanoparticles will enhance the hydrate formation kinetics by either reducing the induction time and/or increasing the hydrate growth rate. Therefore, the objectives of the work undertaken in the present study are as follows:  1. To determine the effect of CNCs dispersed in water on the nucleation and hydrate growth in a one component system. The CO2 was selected as the hydrate former. This choice is based on our desire to explore the application to CO2 capture processes. The analysis of the data will be done by proper statistical testing. 2. To determine the effect of CNC on the kinetics from a CO2/N2 mixture. 17  Chapter 2: Experimental setup 2.1 Materials The cellulose nanocrystals (abbreviated CNC) used for the experiments was purchased from Celluforce®. The provider reports the following properties:  Parameter (units) Value Nominal average length (nm) 150 Nominal average diameter (nm) 7.5 Aspect ratio   20 Nominal surface area per particle (nm2) 4500 Surface area (m2/g) 550 Table 2. Cellulose nanocrystals properties reported by provider Celluforce® (2019).  2.2 High pressure crystallizer system The high-pressure crystallizer set is shown in Figure 7 and is described in detail elsewhere (Sharifi et al., 2014). The apparatus consists of three stainless steel crystallizers of 211 mL capable to withstand pressures up to 20 MPa. Two of the crystallizers have two polycarbonate windows each, one in the front and one in the back. One crystallizer has a hydrophobic coating on the inside and has no windows. Each crystallizer has inside three thermocouples at three different positions to measure the temperature of gas, interphase and liquid respectively (uncertainty: 0.1K, Omega Engineering). The crystallizers are also equipped with baffles to control vortex formation when the mixture is stirred.  18    Figure 7. Piping and instrumentation Diagram (P&ID) of the apparatus. Only one crystallizer and one supply vessel are shown to simplify the diagram. System design by Sharifi et al. (2014).   The lid of the crystallizers is coupled with a gas induced impeller coupled with a hollow shaft which is rotated and controlled by a universal motor controller (Autoclave Engineers). The shaft speed is measured with a tachometer display.  19  The crystallizers are submerged in a Propylene glycol (PG)-water bath (15% wt. Propylene glycol) to keep the temperature constant. An external refrigerating/heating programmable circulating thermostat (VWR Scientific) is used to regulate the temperature of the Cooling bath.  Three stainless steel vessels of 300 mL are also submerged in the cooling bath and serve as supply vessels to the crystallizers. Nevertheless, to increase the volume of gas supply, the apparatus was modified and two additional stainless steel supply vessels of 1000 mL each were installed in a separate cooling bath with a separate circulating thermostat (Cole-Parmer) and the three 300 mL supply vessels in the main cooling bath serve as one supply vessel of 900 mL for the reactor with a hydrophobic coating. The separate cooling bath is an addition to the design by Sharifi et al. (2014) to install larger supply vessels.  Each crystallizer and each supply vessel are coupled with a pressure transmitter (Rosemount smart, model 3051, uncertainty: 0.075% of span 0-15000kPa), the crystallizers are also coupled with an analog pressure gauge (Omega Engineering, uncertainty: 0.25% of span 0-20000 kPa) that serves as backup.    Each of the three crystallizer-supply vessels (CR-SV) has a control valve (Fisher, Baumann 5100, NPS ¼) to control the gas supply to the reactor. The control valve has its respective actuator and is coupled to a proportional, integral, derivative controller (PID).   All the pressure transmitters and thermocouples are linked to a data acquisition system (DAQ-9188, National Instrument) that receives the signals and transmits them to the computer using the 20  Labview full development system software (National Instruments). Labview exports and records the data using Microsoft Excel.  Of the three-reactor set, Reactor 2 was the only one used for all the experiments. Reactor 3 has a hydrophobic coating and does not allow for visual observations of hydrate formation, and Reactor 1 stirring arrangement was not functioning properly.  2.3 Experimental procedure: Gas uptake method For the kinetic experiments of hydrate formation were studied using the gas uptake method following the techniques used by Englezos et al. (1987), Lee and Englezos (2005) and Linga et al. (2007). For each experiment (run), the supply vessel is filled with hydrate forming gas (CO2) to a pressure at least 1000 kPa above the operating pressure set for the run. Preliminary experiments were conducted to help us find a suitable driving force so that leads to an induction period long enough to observe a possible reduction due to CNC and at the same time not long that it becomes impractical to conduct a reasonable number of experiments. The crystallizer is filled with 80 mL of liquid (distilled water or an aqueous solution/suspension). The air is flushed out of the crystallizer pressurizing it with gas from the supply vessel to at least 500 kPa and then depressurizing it just above atmospheric pressure (~30 kPa gauge), this procedure is repeated three times for each run.   The cooling bath was set to 294.15 K by adjusting the temperature of the circulating thermostat between 0.5-0.6K below the target temperature (293.5K).   21  The crystallizer is subsequently filled with the hydrate forming gas up to the operating pressure for the run. The operating pressure is the equilibrium pressure at the fixed temperature of the run plus the driving force pressure. Once it reaches the operating pressure the system is left to stabilize its temperature (between 2-5 minutes). The pressure of the crystallizer is maintained setting the control valve at the operating pressure.  Once temperature is stabilized the experiment is started by turning on the stirrer using the motor control of the respective crystallizer, the operation speed is set to 600 rpm. When the stirrer is turned on the experiment starts (time=0). The temperatures inside the crystallizer, of the bath, the chiller, the pressure of the supply vessel and the pressure of the crystallizer are constantly recorded and monitored using Labview as described in the previous section.  When the experiment starts, the temperature increases due to the dissolution of warm CO2 in the water, but then it decreases steadily to the set temperature. Hydrate formation is an exothermic process (release energy), therefore, the nucleation point (time when hydrates fully formed) in the system is detected by a temperature spike in both the liquid and the interphase. The nucleation is followed by the growth period. The system is left at least 1 hour after nucleation.   To finish the experiment the control valve is closed and the stirrer is turned off, then the gas is slowly released from the crystallizer to the vent. If a memory trial is going to be done (section 1.4), the pressure is reduced below the hydrate equilibrium pressure and therefore crystals are dissolved, but the pressure should never be below 0 gauge (atmospheric pressure), otherwise the memory of the solution might be affected. The stirrer could be left on at a low speed to avoid the formation 22  ice caused by the Joule-Thompson effect (isenthalpic expansion of a gas). For cases in which no memory solution is being used, all the gas must be released from the cell and the solution must be replaced for a new one.       2.3.1 Stirring rate Stirring is one of the key variables in macroscopic hydrate formation kinetics. The stirring enhances mass and heat transfer. In our case we have initially a gas/liquid water in a cylindrical vessel therefore stirring increases the dilution rate up to the point of saturation and if the pressure/temperature conditions are suitable, the hydrate formation. Stirring is necessary for proper mixing, but also, a high stirring rate can produce vortex, which is not desired because they start to decrease the mixing efficiency. In this case, the reactor has baffles that prevent vortex formation as described in section 2.2. Additionally, Renault-Crispo and Servio (2017) reported that each system has a maximum speed rate since the speeds above this point create gas bubbles in the liquid that drastically change the hydrodynamics in the system making the gas consumption rates unreliable. Moreover, more stirring requires more power, increasing the energy intensity of the gas hydrate kinetics.  Without stirring, hydrates would take a long time to form or not form at all within a time period depending on the driving force, and the amount of gas captured is not significant for an analysis and further application of the process at a large scale. For the equipment that is used in this work, several tests were done with different speed rates and a stirring rate of 600 rpm was establish as an adequate rate for the hydrate formation experiments. In a previous work of hydrate kinetics by Lee et al. (2005), it was established that there is a suitable stirring rate for each stirred crystallizer 23  arrangement. For the system used in this study it was determined that a speed above 600 rpm the system starts to form gas bubbles which makes the determined gas consumption rates unreliable as stated before.   2.4 Experimental procedure: Hydrate equilibrium measurements The incipient equilibrium measurements were performed following the isothermal pressure search method developed by Englezos and Ngan (1993) and Englezos and Hall (1994). The setup is similar to the one described in the previous section, for each experiment the crystallizer is filled with 80 mL of water,  the supply vessel is pressurized with the hydrate forming gas from the supply vessel up to 500 kPa and then the gas is released. This pressurization and release of gas is done three (3) times for each run to remove air from the system.     The desired cooling bath temperature is reached by setting the circulating thermostat between 0.5-0.6K below the target temperature for the crystallizer. Once the temperature inside the crystallizer reaches the point for the desired equilibrium measurement, it is slowly filled with hydrate forming gas from the supply vessel using the control valve, the pressure is set in intervals of 50-100 kPa to avoid sudden pressure increases within the crystallizer. For the equilibrium experiments the reactor pressure is increased at least 1.5 MPa beyond the estimated equilibrium pressure to form hydrates fast (high driving force). With a high driving force hydrates will start forming in the interface.   Once the target pressure is reached, a stabilizing period of 2 to 5 minutes is maintained to allow the crystallizer temperature to return to the fixed value, then the control valve is closed, and the experiment is started by turning on the stirrer system. Once small amount of hydrates is detected 24  visually, the pressure is quickly decreased down to 100 kPa above the estimated incipient hydrate equilibrium pressure by venting some of the gas within the cell. Then the system is left stirring at for four (4) hours. If there is a small amount of hydrates within the cell after the four hours and the pressure has not changed significantly, this is taken as the equilibrium pressure for the fixed temperature, but if no hydrates are present, the system is below the equilibrium pressure and it needs to be repeated but the pressure is reduced to 100 kPa above the previous experimental run.      2.5 Experimental procedure: Preparation of CNC suspension CNC (cellulose nanocrystals) are sparingly soluble in water. Therefore, in order to use it for hydrate formation it is necessary to achieve good dispersion in water. The CNC is initially weighted in a beaker to measure the amount that is necessary to achieve a specific concentration in 500 mL of distilled water. Then distilled water is added and the suspension is magnetically stirred (500 rpm) for at least 1 hour.   To ensure good CNC dispersion, a sonication treatment is applied (also called ultrasonic). Sonication has been proved to be effective to overcome dispersion issues (Beuguel, 2018). Ultrasonic processor model CL-18 (Qsonica Sonicators) with 1/8” diameter probe was used for applying the ultrasound energy. The procedure starts measuring 25 mL of CNC suspension in a graduated cylinder and then pouring it into a small glass tube. An ice bath is prepared and the glass tube is submerged in it to keep the CNC suspension from heating up and a subsequent thermal degradation (Guicquel et al., 2019). The ultrasonic transducer (probe) is introduced into the glass tube and in the control panel of the sonicator an amplitude of 50% is selected. The equipment is then started, and the sonication is let operating until the desired energy intensity per gram of CNC 25  is reached.  The sound energy used for the CNC dispersion is 1000 J/gCNC. After the procedure is stopped, the sonicated CNC suspension is transferred to a clean Erlenmeyer and ready to be used in the hydrate formation experiments. Since the sonication must be done in batches of 25 mL, this procedure should be repeated several times to prepare enough suspension for the hydrate experiments. Thus, for 500 mL of the magnetically stirred CNC suspension, the sonication procedure is repeated 20 times.   2.6 Data recording As stated in section 2.2, the high-pressure crystallizers thermocouples and pressure transmitters are linked to a data acquisition system that records the measurements on Labview and subsequently this data is exported to excel. The variables measured are the following: • Temperature of the gas phase in the crystallizers (top).  • Temperature of the interface in the crystallizers (middle). • Temperature of the liquid phase in the crystallizers (bottom). • Temperature of the cooling bath in which the crystallizers are submerged.  • Temperature of the chiller. • Temperature of the supply vessel. • Pressure in the crystallizer. • Pressure in the supply vessel. • 4-20 mA signal from the Pressure control valve of each reactor.  It is noted that all the above variables were recorded every five (5) seconds during every experiment run. 26   2.7 Calculation of the gas consumed The calculations of the gas consumed were carried following the procedure described by Linga et al. (2007). The system of Supply vessel (SV) and Crystallizer (CR) is a closed one once the experiment is started, therefore, the number of moles of gas within the system at any time (t) is constant throughout the experiment: 𝑛𝐶𝑅,𝑡 + 𝑛𝑆𝑉,𝑡 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 Where nCR,t and nSV,t represent the moles of gas within the crystallizer and supply vessel at any time t respectively. But the amount of gas in the crystallizer is the gas in the free space plus the gas in the liquid and hydrate phase (H): 𝑛𝐶𝑅,𝑡 = 𝑛𝐺,𝑡 + 𝑛𝐻,𝑡 So, the amount of gas that goes into either the liquid or hydrate phase (or both) within times t1 and t2 is determined as: 𝑛𝑆𝑉,𝑡1 + 𝑛𝐺,𝑡1 + 𝑛𝐻,𝑡1 = 𝑛𝑆𝑉,𝑡2 + 𝑛𝐺,𝑡2 + 𝑛𝐻,𝑡2 𝑛𝐻,𝑡2 − 𝑛𝐻,𝑡1 = (𝑛𝑆𝑉,𝑡2 − 𝑛𝑆𝑉,𝑡1) + (𝑛𝐺,𝑡2 − 𝑛𝐺,𝑡1) ∆𝑛𝐻,𝑡2−𝑡1=∆𝑛𝐺,𝑡2−𝑡1 + ∆𝑛𝑆𝑉,𝑡2−𝑡1 (𝐼) The moles of gas have in both the supply vessel (SV) and the crystallizer are calculated as: ∆𝑛𝐺,𝑡2−𝑡1 =𝑉𝐶𝑅𝑅[(𝑃𝑍𝑇)𝑡2− (𝑃𝑍𝑇)𝑡1]𝐺 (𝐼𝐼) ∆𝑛𝑆𝑉,𝑡2−𝑡1 =𝑉𝑆𝑉𝑅[(𝑃𝑍𝑇)𝑡2− (𝑃𝑍𝑇)𝑡1]𝑆𝑉 (𝐼𝐼𝐼) 27  Where VCR and VSV are the volumes of the crystallizer and the supply vessel respectively, R is the gas constant, and P, T and z are the pressure, temperature and compressibility factor of the crystallizer and supply vessel at times t1 and t2.   The compressibility factor Z is calculated using the Pitzer equations (Smith et al., 2001): 𝑍 = 1 + 𝐵0𝑃𝑟𝑇𝑟+ 𝜔𝐵1𝑃𝑟𝑇𝑟;    𝑇𝑟 =𝑇𝑇𝑐;    𝑃𝑟 =𝑃𝑃𝑐  𝐵0 = 0.083 +0.422𝑇𝑟1.6  𝐵1 = 0.139 +0.172𝑇𝑟4.2  Pc, Tc, Pr, Tr and ω are the critical pressure, critical temperature, reduced pressure, reduced temperature and acentric factor for a determined substance.  For the experiments, a time lapse between measurements is set at 5 seconds, this lapse allows to detect significant changes in the system like the temperature spikes that arise when hydrates are formed and also avoids the gathering of excessive amounts of data (e.g. time lapses of 1 and 2 seconds). Equations I, II and III are used to calculate the total amount of moles that go either to the liquid phase (before induction time) or to the hydrate phase (after induction time) in the five (5) seconds lapses. The gas uptake profiles are presented as cumulative due to the noise present in the data. Additionally, the hydrate formation rate is calculated as the difference between the gas uptake at the induction time and the gas uptake 30 minutes after the induction time over the 30 minutes.    28  2.8 Error propagation Error propagation (or uncertainty) is present when a function f is based on various variables a, b,…,n. with uncertainties δa, δb,…, δn. These uncertainties propagate through calculation creating an uncertainty in f that can be calculated as follows (Taylor, 1997): 𝑓(𝑎, 𝑏, … , 𝑛) 𝛿𝑓 = √(𝜕𝑓𝜕𝑎𝛿𝑎)2+ (𝜕𝑓𝜕𝑏δ𝑏)2+ ⋯ + (𝜕𝑓𝜕𝑛δ𝑛)2 All the error in the equation above should be independent and random. The calculation of the gas consumed showed in the last section has a propagation uncertainty due to the independent uncertainties in temperature and pressure. As mentioned in section 2.2, the temperature measurement has and uncertainty of 0.1K and the pressure has an uncertainty of 0.075% from 0-15000kPa. The system in question operates at pressures within 1000 and 4500 kPa, so the uncertainties in the pressure measurements are between 0.75 and 3.375 kPa.  Applying the error propagation formula to the equation for the calculation of the gas moles either in the crystallizer or the supply vessel (equations II and III): δ𝑛 = √(𝜕𝑛𝜕𝑃δ𝑃)2+ (𝜕𝑛𝜕𝑇δ𝑇)2(𝐼𝑉) The partial derivatives of the number of moles with respect to P and T: 𝜕𝑛𝜕𝑃=𝑉𝑧𝑅𝑇 ; 𝜕𝑛𝜕𝑇=−𝑉𝑃𝑧𝑅𝑇2 Therefore: 29  δ𝑛 = √[(𝑉𝑧𝑅𝑇) δ𝑃]2+ [(−𝑉𝑃𝑧𝑅𝑇2) δ𝑇]2(𝑉) Where V is volume of the vessel (crystallizer or supply vessel) respectively, R is the gas constant, and P, T and z are the pressure, temperature and compressibility factor of the respective vessel. The compressibility factor is a function of T and P, but its uncertainty in the calculation of the error propagation in the number of moles is considered negligible in comparison to the effect of the explicit pressure and temperature variables in the equation.  The operating pressure of the supply vessel is different than the pressure in the crystallizer, thus the uncertainties in pressure are different for each case. It is necessary to calculate the uncertainties of the supply vessel and the crystallizer separately (using equation V) for each case and then calculate the total uncertainty for the moles in the hydrate phase (or dissolved): 𝛿𝑛𝐻 = √𝛿𝑛𝑆𝑉2 + 𝛿𝑛𝐶𝑅2  The results obtained for the propagation of uncertainty (error) in the calculation of the moles of gas consumed (gas uptake) are the following:  Parameter (units) Value Uncertainty in temperature measurement (K) 0.1 Uncertainty in pressure measurement supply vessel (kPa) 3 Uncertainty in pressure measurement crystallizer (kPa) 1.78 Uncertainty in the calculation of moles of gas in the supply vessel (moles) 0.001920 30  Parameter (units) Value Uncertainty in the calculation of moles of gas in the crystallizer (moles) 0.000136 Uncertainty in the calculation of moles of gas in the gas hydrate phase (or dissolved) (Gas uptake) (moles) 0.001925 Table 3. Results obtained for the propagation of uncertainty (error) in the calculation of the moles captured in the hydrate and dissolved phase (gas uptake).  2.9 CO2/N2 mixture Experiments with gas mixtures of carbon dioxide and nitrogen were also conducted using the same high pressure crystallizer system described in section 2.2 and following the same gas uptake method described in section 2.3. The mixture used had a composition of 13.2%mol of CO2 and 86.8%mol (Praxair), these concentrations are within the range of a typical flue gas mixture of a post combustion gas in an Integrated Gasification Combined Cycle (IGCC) power plants (Babu et al., 2015). Due to the low concentration of CO2 in the mixture, the equilibrium pressure for the mentioned mixture are considerably high making the number of experimental runs demanding in terms of gas consumption. For this reason, it is necessary to add Tetra-n-butyl ammonium bromide to both the blank and the CNC runs. This tetra-alkylammonium salt forms semi-clathrate hydrates at atmospheric pressure at temperatures between 2°C and 12°C (275.15K and 287.15 K respectively), the higher the concentration of TBAB, the lower the equilibrium temperature of the semi-clathrate hydrates at atmospheric pressure (Oyama et al., 2005). Additionally, several equilibrium experiments have been performed with different CO2/N2 mixtures, at different 31  temperatures and different TBAB concentrations. The following table summarizes some hydrate equilibrium data obtained for CO2/N2 mixtures and TBAB-water solutions:  Author CO2 concentration (%mol) TBAB concentration (%wt.) Temperature (K) Equilibrium Pressure (MPa) Belandria et al., 2012 15% 5% 282.4 1.93 Belandria et al., 2012 15% 5% 284.5 6.67 Belandria et al., 2012 40% 0% 275.6 4.92 Belandria et al., 2012 40% 30% 287.1 1.78 Mohammadi et al, 2012 40% 5% 277.1 1.12 Mohammadi et al, 2012 40% 30% 286.4 1.71 Meysel et al., 2012 50% 5% 282.3 1.96 Meysel et al., 2012 50% 10% 285.1 2.10 Meysel et al., 2012 50% 20% 287.1 2.11 Table 4. Experimental Hydrate equilibrium data obtained for CO2/N2 mixtures and TBAB-water solutions by different authors.  The TBAB 32%wt solution was prepared using solid TBAB (Sigma-Aldrich). For the CNC runs, the concentration used was the same used for the experiments with CO2. The CNC-TBAB-water suspensions were prepared and sonicated using the procedure described in section 2.5 to assure proper dispersion.  32  The kinetic experiments were run up to 6 hours (300 min). As it was stated for the experiments with pure CO2, it is impractical to run several runs with high induction times.  The parameters for the experimental runs with the CO2 /N2 mixture in Water-TBAB and Water-CNC-TBAB were the following:  Parameter (units) Value CO2 concentration (%mol) 13.2% TBAB concentration (%wt.) 32% CNC concentration (%wt.) 0.75 Number of tests 7 Temperatures (K) 280.2-282.2 Hydrate equilibrium pressure (kPa) Atmospheric Driving force (kPa) 2000 Operating pressure (kPa) 2000 Stirring speed (rpm) 600 Maximum operating time (min) 300 Table 5. Experimental parameters for the gas mixture of CO2/N2 in TBAB-water and CNC-TBAB-water.     33  Chapter 3: Results and Discussion 3.1 CNC characterization  Malvern Instruments Zetasizer (Model ZEN 3600) was used to measure the zeta potential and size of the CNC particles. The reported values are average of three measurements and the size of the particles is reported as the equivalent sphere diameter. For all the tests, the temperature was 25°C and the CNC concentration was 0.1% (wt.) The results are shown in the table below:   Test Average particle size (d.nm) Zeta potential (mV) 1 176.9 -58.8 2 191.0 -57.8 3 195.9 -57.8 4 188 -58.1 Table 6. CNC characterization using a particle size analyzer.  3.2 CO2 hydrate equilibrium in pure water and in the presence of CNC The incipient hydrate equilibrium pressure for CO2 hydrates in the CNC 0.75 wt. suspension was measured for six (6) temperatures following the procedure described in section 2.4. The results are shown in the following table:  34  Temperature (K) Incipient equilibrium pressure (kPa) 274.1 1392 275.2 1564 276.2 1751 277.5 2048 278.3 2273 278.9 2471 Table 7. Incipient hydrate equilibrium pressure for CO2 in CNC 0.75% at different temperatures.  The results were compared with the equilibrium pressure in water (no additives) predicted by Kumath (1984) and the experimental results of Englezos and Hall (1994) and Dholabhai et al. (1993):  Source Host Temperature (K) Incipient equilibrium pressure (kPa) This work CNC 0.75% wt. 274.2 1378 Kamath (1984) water 274.2 1347 Dholabhai (1993) water 273.2 1340 Table 8. Incipient hydrate equilibrium pressure for CO2 in CNC 0.75% at 274.1K and (L-H-V) compared with experimental data from different authors and the prediction model developed by Kamath.  35  Source Host Temperature (K) Incipient equilibrium pressure (kPa) This work CNC 0.75% wt. 276.2 1751 Kamath (1984) water 276.2 1765 Jeong-Hoon Sa et al. (2017) water 276.3 1767 Table 9. Incipient hydrate equilibrium pressure for CO2 in CNC 0.75% at 276.2K and (L-H-V) compared with experimental data from different authors and the prediction model developed by Kamath.  Source Host Temperature (K) Incipient equilibrium pressure (kPa) This work  CNC 0.75% wt. 277.5 2048 Kamath (1984) water 277.2 2018 Englezos and Hall (1994) water 277.7 2126 Jeong-Hoon Sa et al. (2017)  water 277.3 2029 Dholabhai (1993)  water 277.1 1987 Table 10. Incipient hydrate equilibrium pressure for CO2 in CNC 0.75% at 277.5K and (L-H-V) compared with experimental data from different authors and the prediction model developed by Kamath.  Source Host Temperature (K) Incipient equilibrium pressure (kPa) This work  CNC 0.75% wt. 278.9 2471 36  Source Host Temperature (K) Incipient equilibrium pressure (kPa) Kamath (1984) water 278.9 2528 Englezos and Hall (1994) water 279.2 2601 Jeong-Hoon Sa et al. (2017)  water 278.8 2435 Dholabhai (1993)  water 279.0 2520 Table 11. Incipient hydrate equilibrium pressure for CO2 in CNC 0.75% at 278.9K and (L-H-V) compared with experimental data from different authors and the prediction model developed by Kamath.  The results obtained in the equilibrium experiments are summarized in the following plot:   Figure 8. Comparison of the incipient hydrate equilibrium pressure for CO2 in water and a suspension of water-CNC 0.75% from different authors. 50010001500200025003000350040004500273 274 275 276 277 278 279 280 281 282 283Pressure (KPa)Temperature (K)Englezos and Hall (water, 1994) Breland and Englezos (water, 1996)Jeong-Hoon Sa et al. (water, 2017) Dholabhai (water, 1993)Kamath (1984) This work (CNC 0.75 %wt., 2020)37   3.3 Preliminary Experiments to Establish Experimental Pressure and Temperature Conditions After the establishment of the hydrate equilibrium conditions the next goal was to determine suitable pressure and temperature conditions to test the hypothesis of the effect of Cellulose Nanocrystals (CNC) on the gas hydrate kinetics.  The aim was to identify conditions such that the induction time is not short to make any difference between the water and the CNC suspension negligible and not too long to make the study somewhat impractical. Therefore, several experiments at different pressures were run with water alone. The temperature was set at 2°C (275.15K) based on both the Kamath gas hydrate prediction parameters (1984) and the experimental findings of Englezos and Hall (1994), Breland and Englezos (1994) and Jeong-Hoon Sa et al. (2017). A lower temperature allowed to formed hydrates at a lower pressure therefore reducing the amount of gas for each run and the chiller was capable to maintain this temperature with ease.  The experiments were run according to the gas uptake method procedure described in section 2.3. Driving forces of 500 kPa, 1000 kPa and 1500 kPa were chosen. Hydrate kinetics is a stochastic process, this means that for a set of conditions of a gas hydrate forming system the probability of observation is distributed over a range of values. So, values obtained for properties like the induction time are “most likely” (probabilistic) instead of absolute. Therefore, these results for the induction time are dispersed and one may say that they established a working zone for further experiments. 38  Driving force (kPa) Total Pressure (kPa) Experimental preliminary Induction time (min) 1500 2870 <1 1000 2370 ~30 500 1870 ~240 Table 12. Experimental data obtained of induction time at 1°C for three driving forces.  With a driving force of 1000 kPa is was possible to perform a significant amount of experiments in a reasonable amount of time for both the blanks and the CNC. The number of experiments is also important for hydrate kinetics. Even if you run two experiments in the exact same conditions, the results might differ significantly due to the stochastic nature of the process. Therefore, more tests allow a statistical analysis that leads to a better understanding of the phenomena of hydrate formation.  The parameters established for the experimental runs with blank and CNC were the following:  Parameter (units) Value Number of tests 24 Temperature (K) 274.15 Hydrate equilibrium pressure@1°C (kPa) 1370 Driving force (kPa) 1000 Operating pressure (kPa) 2370 39  Parameter (units) Value Stirring speed (rpm) 600 Table 13. Experimental parameters for the blank and CNC experiments.  3.4 Kinetics of CO2 Hydrate formation in Pure water (blank).  The kinetics experiments of hydrate formation for CO2 were first run with distilled water, these experiments are called blanks (B). The results for the experiments under the conditions in table 11 are the following:   40  Run Induction time (min) Gas uptake at induction time (mol) Gas uptake 30 min. after induction time (mol) Hydrate formation rate in the first 30 min. (mol/min) B1 25.8 0.13058 0.25828 0.00426 B2 10.8 0.05602 0.15731 0.00338 B3 52.5 0.16754 0.26803 0.00335 B4 27.4 0.08045 0.18019 0.00332 B5 9.3 0.04694 0.13031 0.00278 B6 19.3 0.10667 0.22918 0.00408 B7 16.8 0.05057 0.14765 0.00324 B8 9.6 0.07003 0.20354 0.00445 B9 12.3 0.07495 0.17840 0.00345 B10 53.1 0.15914 0.26157 0.00341 B11 8.0 0.02665 0.11183 0.00284 B12 73.6 0.27100 0.38373 0.00376 B13 15.2 0.08115 0.20738 0.00421 41  Run Induction time (min) Gas uptake at induction time (mol) Gas uptake 30 min. after induction time (mol) Hydrate formation rate in the first 30 min. (mol/min) B14 13.6 0.03804 0.12361 0.00285 B15 21.4 0.11399 0.23009 0.00387 B16 21.5 0.06156 0.14293 0.00271 B17 25.7 0.06852 0.16037 0.00306 B18 18.1 0.06217 0.18339 0.00404 B19 27.8 0.11791 0.22593 0.00360 B20 13.6 0.07298 0.19643 0.00412 B21 23.5 0.10337 0.21188 0.00362 B22 43.7 0.16443 0.27268 0.00361 B23 14.0 0.07420 0.19558 0.00405 B24 14.9 0.07778 0.20074 0.00410 Table 14. Results for the induction time, gas uptake at induction time, gas uptake 30 min. after induction time and hydrate formation rate in the first 30 min. of CO2 hydrates in water under the conditions in table 5.  42  3.5 Kinetics of CO2 hydrate formation in the presence of CNC The CNC suspension was prepared according to the procedure described in section 2.5. the concentration used was 0.75% by weight. The kinetic experiments were performed following the same procedure used for the blanks (section 2.3) and under the same conditions in table 11. The results are the following:                  43  Run Induction time (min) Gas uptake at induction time (mol) Gas uptake 30 min. after induction time (mol) Hydrate formation rate in the first 30 min. (mol/min) N1 37.0 0.11943 0.21255 0.00310 N2 15.4 0.07850 0.20575 0.00424 N3 11.5 0.07166 0.19977 0.00427 N4 13.8 0.03952 0.13743 0.00326 N5 13.0 0.03526 0.12880 0.00312 N6 14.7 0.04954 0.14529 0.00319 N7 10.5 0.03979 0.12764 0.00293 N8 13.1 0.04042 0.14091 0.00335 N9 70.1 0.23332 0.34373 0.00368 N10 14.3 0.05527 0.15041 0.00317 N11 11.3 0.04747 0.13986 0.00308 N12 22.4 0.06621 0.15597 0.00299 N13 9.0 0.05863 0.18332 0.00416 44  Run Induction time (min) Gas uptake at induction time (mol) Gas uptake 30 min. after induction time (mol) Hydrate formation rate in the first 30 min. (mol/min) N14 13.7 0.04491 0.13771 0.00309 N15 25.0 0.08007 0.18186 0.00339 N16 5.3 0.03332 0.13784 0.00348 N17 9.7 0.04469 0.12682 0.00274 N18 5.2 0.03670 0.11582 0.00264 N19 16.0 0.07819 0.20456 0.00421 N20 25.4 0.10354 0.21028 0.00356 N21 20.1 0.09435 0.20485 0.00368 N22 15.8 0.10464 0.27374 0.00564 N23 12.8 0.06317 0.18407 0.00403 N24 21.6 0.08572 0.20964 0.00413 Table 15. Results for the induction time, gas uptake at induction time, gas uptake 30 min. after induction time and hydrate formation rate in the first 30 min. of CO2 hydrates in a suspension of CNC 0.75%wt.-water under the conditions in table 5.  45  3.6 Plotted results  3.6.1 Induction time  Figure 9. Results for the induction time of the blank and CNC 0.75wt. runs.   051015202530354045505560657075800 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24Induction time (min.)RunBlank CNC 0.75%wt.46  3.6.2 Hydrate formation rate  Figure 10. Results for the induction time of the blank and CNC 0.75wt. runs.    2.50E-032.75E-033.00E-033.25E-033.50E-033.75E-034.00E-034.25E-034.50E-034.75E-035.00E-035.25E-035.50E-035.75E-036.00E-030 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24Hydrate fromation rate (mol/min)RunBlank CNC 0.75%wt.47  3.7 Temperature and gas uptake profiles  As was stated in section 2.3 the hydrate formation is determined by a temperature spike within the system due to the exothermic nature of the hydrate formation process. For each run the temperature and the gas uptake profiles were recorded with measurements every five (5) seconds, it is noted that after the temperature spike the gas uptake curve changes its slope. The following curves were obtained for some of the runs performed for both the blanks and the CNC:  3.7.1 Blank: Temperature and gas uptake profiles   Figure 11. Blank, Run 1. Temperature vs. time. 274.0274.2274.4274.6274.8275.0275.2275.4275.6275.8276.0276.2276.4276.6276.80 5 10 15 20 25 30 35 40 45 50 55Temperature (K)Time (min)48    Figure 12. Blank, Run 1. Gas uptake vs. time. tind: hydrate formation time. 3.7.2 CNC 0.75% wt.: Temperature and gas uptake profiles   Figure 13. CNC 0.75% wt., Run 10. Temperature vs. time. 0.0000.0250.0500.0750.1000.1250.1500.1750.2000.2250.2500.2750.3000 5 10 15 20 25 30 35 40 45 50 55Gas uptake  (mol)Time (min)tind274.0274.2274.4274.6274.8275.0275.2275.4275.6275.8276.0276.2276.40 5 10 15 20 25 30 35 40 45Temperature (K)Time (min.)49   Figure 14. CNC 0.75% wt., Run 10. Gas uptake vs. time. tind: hydrate formation time.  3.8 Statistical hypothesis testing  The data obtained for the CO2 kinetics were analyzed to established if there is a statistical difference in the induction time, gas uptake and gas uptake rate. The test of significance was performed using the student’s t-test function in Excel. The null hypothesis (H0) states that the results obtained with pure water (blanks) are statistically the same with those at a particular CNC concentration, temperature and driving force. The significance level alpha (α) is the probability of rejecting the null hypothesis (p-value), in this case, a p-value of 0.05 was assigned and it denotes a 5% probability of erroneously concluding that a difference exists when there is actually no difference.   0.0000.0250.0500.0750.1000.1250.1500.1750.2000 5 10 15 20 25 30 35 40 45Gas uptake  (mol)Time (min)tind50  3.8.1 Induction time Run  Induction time (min.) Blank CNC 0.75% wt. 1 25.8 37.0 2 10.8 15.4 3 52.5 11.5 4 27.4 13.8 5 9.3 13.0 6 19.3 14.7 7 16.8 10.5 8 9.6 13.1 9 12.3 70.1 10 53.1 14.3 11 8.0 11.3 12 73.6 22.4 13 15.2 9.0 14 13.6 13.7 15 21.4 25.0 16 21.5 5.3 17 25.7 9.7 18 18.1 5.2 19 27.8 16.0 20 13.6 25.4 21 23.5 20.1 22 43.7 15.8 23 14.0 12.8 24 14.9 21.6 Mean 23.8 17.8 Standard deviation 16.32 13.16 Variance 266.28 173.29 Sample size 24 24 α 0.05 Confidence interval (+/-) 6.89 5.56 p-value (t test) 0.16554 Table 16. Statistical results, induction time, blank and CNC 0.75% wt. 51  3.8.2 Gas uptake Run  Gas uptake at induction time (mol) Gas uptake 30min. after induction time (mol) Blank CNC 0.75% wt. Blank CNC 0.75% wt. 1 0.13058 0.11943 0.25828 0.21255 2 0.05602 0.07850 0.15731 0.20575 3 0.16754 0.07166 0.26803 0.19977 4 0.08045 0.03952 0.18019 0.13743 5 0.04694 0.03526 0.13031 0.12880 6 0.10667 0.04954 0.22918 0.14529 7 0.05057 0.03979 0.14765 0.12764 8 0.07003 0.04042 0.20354 0.14091 9 0.07495 0.23332 0.17840 0.34373 10 0.15914 0.05527 0.26157 0.15041 11 0.02665 0.04747 0.11183 0.13986 12 0.27100 0.06621 0.38373 0.15597 13 0.08115 0.05863 0.20738 0.18332 14 0.03804 0.04491 0.12361 0.13771 15 0.11399 0.08007 0.23009 0.18186 16 0.06156 0.03332 0.14293 0.13784 17 0.06852 0.04469 0.16037 0.12682 18 0.06217 0.03670 0.18339 0.11582 19 0.11791 0.07819 0.22593 0.20456 20 0.07298 0.10354 0.19643 0.21028 21 0.10337 0.09435 0.21188 0.20485 22 0.16443 0.10464 0.27268 0.27374 23 0.07420 0.06317 0.19558 0.18407 24 0.07778 0.08572 0.20074 0.20964 Mean 0.09486 0.07101 0.20254 0.17744 Standard deviation 0.05389 0.04247 0.05984 0.05278 Variance 0.00290 0.00180 0.00358 0.00279 Sample size 24 24 α 0.05 Confidence interval (+/-) 0.02275 0.01793 0.02527 0.02229 p-value (t test) 0.09574 0.13026 Table 17. Statistical results, gas uptake at induction time and gas uptake 30 min. after induction time, blank and CNC 0.75% wt.  52  3.8.3 Hydrate formation rate Run Hydrate formation rate in the first 30 min. (min.) Blank CNC 0.75% wt. 1 0.00426 0.00310 2 0.00338 0.00424 3 0.00335 0.00427 4 0.00332 0.00326 5 0.00278 0.00312 6 0.00408 0.00319 7 0.00324 0.00293 8 0.00445 0.00335 9 0.00345 0.00368 10 0.00341 0.00317 11 0.00284 0.00308 12 0.00376 0.00299 13 0.00421 0.00416 14 0.00285 0.00309 15 0.00387 0.00339 16 0.00271 0.00348 17 0.00306 0.00274 18 0.00404 0.00264 19 0.00360 0.00421 20 0.00412 0.00356 21 0.00362 0.00368 22 0.00361 0.00564 23 0.00405 0.00403 24 0.00410 0.00413 Mean 0.00359 0.00355 Standard deviation 0.00051 0.00067 Variance 0.0000003 0.0000004 Sample size 24 24 α 0.05 Confidence interval (+/-) 0.00022 0.00028 p-value (t test) 0.80852 Table 18. Statistical results, hydrate formation rate in the first 30 min., blank and CNC 0.75% wt. 53   3.8.4 Plot - Induction time - statistics  Figure 15. Statistical comparison of the induction time for the blank and CNC 0.75% wt. groups, │mean, ├┤95% confidence interval. 3.8.5 Plot – Hydrate formation rate - statistics  Figure 16. Statistical comparison of the hydrate growth rate for the blank and CNC 0.75% wt. groups, │mean, ├┤95% confidence interval. 0 20 40 60 80BlankCNC Induction time (min.)GroupBlankCNC0.0025 0.0030 0.0035 0.0040 0.0045BlankCNC Hydrate formation rate (mol/min.)GroupBlankCNC54   3.9 CO2/N2 hydrate kinetic experiments  For the results with the CO2/N2 mixture (13.2%mol-86.8%mol), the runs using the solution of water-TBAB (32%wt.) is defined as the blank, and the runs using the suspension of water-TBAB (32%wt.)-CNC (0.75%wt.) is defined as the CNC Run Temperature (°C) Blank Induction time (min) CNC Induction time (min) 1 9 >300 >300 2 9 7.5 >300 3 9 20.5 197 4 9 >300 >300 5 8 >300 >300 6 8 116 >300 7 8 >300 >300 Table 19. Results for the induction time for the CO2/N2 mixture (0.132/0.868 mol) with the blank group and the CNC group.   55  Chapter 4: Analysis and conclusions 4.1 Equilibrium data As presented in table 7, six (6) CO2 hydrate equilibrium experiments with a suspension of CNC 0.75% at 6 different temperatures were conducted. The resulting incipient equilibrium pressures at their respective temperatures were compared with previous equilibrium data in pure water from the literature at close (or same) temperatures. Tables 8, 9, 10 and 11 show the equilibrium points obtained with the CNC suspension fall within the same range of the data from the literature with a difference of 5% at most with the furthest equilibrium data point for the cases analyzed in each table and therefore there is no effect of the CNC suspension in the hydrate equilibrium. It must be taking into account that there are small temperature differences within the equilibrium points compared. These results were expected because CNC particles do not affect the activity of water. The CNC particles were proposed as a mechanical promoter to enhance heterogeneous hydrate formation, but nonetheless, the equilibrium data was collected to validate this statement.  4.2 Statistical analysis of the kinetic data As seen in tables 14 and 15, the data collected for both the blank and the CNC 0.75% wt. shows a significant variability. The variability was expected due to the stochastic nature of gas hydrate formation as stated in section 1.4.   The Student’s t-test was used for the analysis, the established null hypothesis (H0) states that the data in pure water are statistically the same with the data in 0.75% wt. CNC concentration for a fixed temperature and driving force. The two sets of data were considered as a two-tailed distribution, a significant level alpha value(p-value) of 0.05 was pre-assigned and the data were 56  assumed to have unequal variances.  The alpha value is the probability of rejecting the null hypothesis when it is true. In this case, the 0.05 denotes a 5% risk of concluding that a difference exists when there is no difference. If the returned p value is greater than the pre-assigned alpha value, the null hypothesis is accepted.   The mean and 95 % CI (confidence interval) for the induction times are 17.8 ± 5.6 (min) for the pure water group and 23.8± 6.9 (min) for the 0.75% wt. CNC group as seen on table 14. The mean induction time in the CNC suspension is 25% (6 minutes) lower than the mean in pure water and it could be promptly concluded that the CNC reduces the induction time of CO2 hydrates, but an in-depth statistical analysis of the data gives that the returned (calculated) p-value of 0.166. Thus, the null hypothesis is valid and there is no statistical difference between the two sets of data under the established set parameters. Moreover, the 95% CI of the two sets overlaps.   Regarding the potential effect of CNC on hydrate growth rate the mean and 95 % CI are 0.00359 ±0.00022 (mol/min) for the pure water group and 0.00355 ± 0.00028 (mol/min) as seen on table 18, this is for the first 30 minutes after the induction time. The returned p-value is 0.809 and therefore, the null hypothesis is also valid and there is no statistical difference between the two sets of data. accepting the null hypothesis that there is no significant effect of the CNC at the conditions tested. The CIs based on the standard error of the mean are also shown in table 18 and indicate the range within which the true mean of the formation rate is contained at 95 % probability, moreover, the CIs overlap to a very large extent.    57  Table 17 shows the data for the gas uptake at induction time and at 30 minutes after induction time. The returned p-values calculated are 0.096 and 0.13 respectively leading to conclude that the is no statistical difference between the two groups. It must be stated that in these cases the amount of gas captured depends on the induction time (reference point) and comparing the data on table 16 and table 17, in most cases longer induction times lead to more moles captured, but the point of reference is different in each case, therefore the gas uptake is not a valid parameter for comparison between the two groups.     In summary, the above hydrate data have significant variability and suggest that there is no effect of the CNC on the induction time and on the CO2 hydrate growth rate at the conditions tested. It is noted that the significant variability in gas uptake for hydrate growth was also reported for CO2 hydrates by Renault-Crispo and Servio (2017). As the authors pointed out, this is a significant finding for CO2 hydrate studies that report a singular gas uptake rate to make conclusions.  Interestingly, all the studies which were reviewed in the introduction section reported the effect on nanoparticles by relying on very small samples. It is well known that the smaller the sample size the broader is the range of the uncertainty (Cendales et al., 2020).   In addition, there is no report of any statistical testing of significance. For example, the effect of Ag and SDS was investigated based on nine experiments at 273.65 and pressures ranging from 2.05 to 3.24 MPa while doing only one or two experiments at a particular concentration (Mohammadi et al., 2014). The authors concluded based on two data points that a mixture of Ag and SDS affects the kinetics of CO2 hydrate.  They did not report any impact on the induction time. In another study the presence of synthesized Boehmite (AlOOH) nanoparticles was found to 58  influence the induction time and the kinetics of CO2 hydrate as it was stated in the introduction (Montazeri et al., 2019). In this case, the conclusion was based on one experiment in pure water, five experiments at 2.9 MPa varying concentrations of the nanoparticle and four more experiments at constant concentration but varying stirring rate and pressure. The authors did not do any statistical analysis and given the many variables tested and the very small sample size of their data, the variability is expected to render the data statistically inconclusive (Cendales et al., 2020).  The data for graphite nanoparticles also claim an effect (Zhou et al., 2014). In this work, data at 2.5, 3.5, 4.5, 5.5 and 6.5 MPa for CO2 hydrate at 277.15 k are used to compare induction times in pure water and with the nanofluid. Again, the sample size is very small and heterogeneous (the data at 4.5 MPa and above are from liquid CO2). At each pressure they claim to have done three runs and plotted the average value. This means that their sample size at a given driving force is three data points. For the comparison of the growth rates they report just two experiments, one in pure water and one with the nanofluid. Unless we have misunderstood these data, there is in our view lack of statistical evidence to support the claim for an effect on hydrate growth rate.  On the other hand, a study on the effect of MWCNTs on CO2 hydrate reported the average value and confidence intervals for experiments in pure water and at five different concentrations (Pasieka et al., 2015).  Each measurement was repeated five times to obtain the mean and the confidence interval (CI). The study concluded that the variability was found to be significant and there is no effect on the induction time and the rate of dissolution (Pasieka et al., 2015). However, the authors reported an effect on the growth (figure 7 of Pasieka et al., 2015). This claim was based on five measurements (sample size is five points) in pure water and taking the average and the confidence interval and comparing with measurements at each of the five concentrations of MWCNTs. 59  Because there is no overlap in the CIs the authors concluded that carbon nanotubes affect the kinetics. It is tacitly assumed that the 95 % CIs were computed based on the t-statistic t4,95=2.77 (mean± t4,95 x standard deviation) which gives a broader CI than that from the normal distribution. We carried out the t test on these data and the p value was 0.29 which indicates acceptance of the hypothesis that the data are not significant (Cendales et al., 2020).  The reported effects of nanofluids on CO2 hydrate growth rate in the literature were concluded based on limited evidence (very small sample sizes) and without statistical analysis. We consider that these small data sets without statistical treatment are inconclusive. In section 1.4 it was stated that the hydrate formation and growth processes though time are stochastic rather than deterministic, therefore induction times and hydrate growth rates for a particular system should be establish as a probabilistic space. This means that there is an inherit uncertainty in hydrate kinetics, but it can be reduced considerably collecting larger data sets and then analyze them properly using statistical tools.  The work of Cox et al. (2018) employed neutron scattering experiments and molecular dynamics simulations to investigate the impact of natural and synthetic nanoparticles on the kinetics of hydrate formation. The study concluded that the formation of methane hydrates is not affected by the presence of these natural and synthetic nanoparticles. These results show that these nanoparticles like carbon nanocrystals in this work have no effect the kinetics of gas hydrates.  Perhaps, further work based on a suitable experimental design and statistical analysis may resolve the issue of suspended nanoparticles influence on hydrate formation. Finally, the above analysis 60  suggests that the uncertainties in the induction time and the hydrate growth rate measurements should be reported when such data are presented (Cendales et al., 2020).  4.3 Experiments with a mixture of CO2 and N2 Most of the runs with the mixture of CO2/N2 (0.132/0.868 mol) showed a considerable variability as shown in table 19. Of the seven (7) blank runs, just in three (3) the semi-clathrate was formed within 6 hours, two of them at 282.2 and one at 281.2. In the CNC runs, just one nucleated within 6 hours. The wide range of variability observed within the groups and between the groups lead to inconclusive results and no trend can be established.   4.4 Conclusions Based on the collected data and its correspondent analysis, cellulose nanocrystals (CNC) suspended in water (0.75% wt.) were found not have any effect on either the induction time or the hydrate formation rate (first 30 minutes). These results are not in agreement with recent data in the literature on carbon nanotubes and other nanofluids which reported positive effects on the CO2 hydrate kinetics. It is noted that the literature claims on the reported effects of nanoparticles on hydrate growth were based on very small samples sizes which imply broad uncertainties. Moreover, there was no statistical analysis of the data done. It is therefore possible that reported effects may not be statistically significant. In addition to studying the effects of carbon nanocrystals the present study contributes a proper methodology to assess the impact of additives on gas hydrate formation and to gas hydrate kinetics in general. Specifically, the analysis of the kinetics should be based on statistical treatment on large data sets that lead to the establishment of probabilistic spaces with minimum uncertainties.  61   4.5 Recommendations for further work The potential effect of nanoparticles is should be explored further to settle the question about the existence of an effect or not. It is recommended that the effect of carbon nanotubes be investigated based on the statistical method followed in this work, in addition the effect of some nanoparticles that were studied by neutron scattering and molecular dynamics is also recommended.                  62  Bibliography Abedi-Farizhendi, S; Iranshahi, M.; Mohammadi, A.; Manteghian, M.; Mohammadi, AH. 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