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Methane storage and transport via structure H clathrate hydrate Susilo, Robin 2008

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Methane Storage and Transport via Structure H Clathrate Hydrate  by  ROBIN SUSILO Bachelor of Engineering (Chem. Eng.), University of Indonesia, 2001 Master of Applied Science (Chem. Eng.), University of British Columbia, 2003  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Chemical and Biological Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) April 2008 © 2008 Robin Susilo  Abstract This thesis examines the prospect of structure H (sH) hydrate to be exploited for methane storage. The methane content in the hydrate, hydrate kinetics and conversion rates are areas of particular importance. Experiments and theory are employed at the macroscopic and molecular levels to study the relevant phenomena. sH hydrate was successfully synthesized from ice particles with full conversion achieved within a day when thermal ramping above the ice melting point was applied. It was found that a polar guest (tert-butyl methyl ether / TBME) wets ice more extensively compared to two hydrophobic guests (neo-hexane / NH and methyl-cyclohexane / MCH). TBME also has much higher solubility in water. Consequently, the system with TBME was found to exhibit the highest initial hydrate formation rate from ice particles or in water in a well stirred vessel. However, the rate with the hydrophobic guests was the fastest when the temperature exceeded the ice point. Thus, the applied temperature ramping compensated the slow kinetics below the ice point for the hydrophobic guests and allowed faster overall conversion than the polar guest. Structure, cage occupancy, composition and methane content in the hydrate were also determined by employing different techniques and the results were found to be consistent. It was found that the methane content in structure H hydrate with TBME was the smallest (103-125 v/v) whereas that with NH was 130-139 (v/v) and that with MCH was 132-142 (v/v). The methane content in structure II hydrate by using propane (C3H8) and tetrahydrofuran (THF) as the large guest molecule were also estimated. Optimal methane content was found at approximately 100 (v/v) for both C3H8 and THF systems with the large guest concentrations at 1% for C3H8 (10°C) and 1% for THF (room temperature). The gas content is of course lower  ii  than that for structure I hydrate (170 v/v) but one should consider the fact that the hydrate formation conditions are much lower (less than 1 MPa). Finally, MD simulations revealed for the first time the formation of defects in the cavities for the TBME/methane/water (sH hydrate) system which may affect hydrate stability and kinetics.  iii  TABLE OF CONTENTS Abstract.............................................................................................................................................  ii  Table of Contents .............................................................................................................................  iv  List of Tables .................................................................................................................................... viii List of Figures...................................................................................................................................  xi  Nomenclature ...................................................................................................................................xviii Acknowledgements .......................................................................................................................... xix Co-authorship Statement ................................................................................................................ xx CHAPTER-1: INTRODUCTION 1.1 Introduction to gas hydrates........................................................................................................  1  1.2 Significance of gas hydrate.........................................................................................................  4  1.3 Research area on gas hydrate......................................................................................................  6  1.4 Gas storage in hydrate................................................................................................................. 10 1.4.1 Economics.................................................................................................................... 12 1.4.2 Gas storage potential.................................................................................................... 14 1.5 Research objectives..................................................................................................................... 18 1.6 Thesis organization ..................................................................................................................... 19 1.7 References................................................................................................................................... 23 CHAPTER-2: LIQUID-LIQUID EQUILIBRIUM OF WATER WITH NEOHEXANE, METHYLCYCLOHEXANE, TERT-BUTYL METHYL ETHER, N-HEPTANE AND VAPOR-LIQUID-LIQUID EQUILIBRIUM WITH METHANE 2.1 Introduction................................................................................................................................. 31 2.2 Experimental procedure .............................................................................................................. 33 2.2.1 Liquid-liquid equilibrium (LLE).................................................................................. 33 2.2.2 Vapor-liquid-liquid equilibrium (VLLE)..................................................................... 34 2.2.3 Gas chromatography analysis ...................................................................................... 36 2.3 Results and discussion ................................................................................................................ 37 2.3.1 Binary liquid-liquid equilibrium .................................................................................. 38 2.3.2 Vapor-liquid-liquid equilibrium................................................................................... 42 2.4 Conclusions................................................................................................................................. 46 2.5 References................................................................................................................................... 48  iv  CHAPTER-3: HYDRATE KINETICS STUDY IN THE PRESENCE OF NON-AQUEOUS LIQUID BY NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY AND IMAGING 3.1 Introduction................................................................................................................................. 50 3.2 Experimental procedure .............................................................................................................. 54 3.3 Results and discussion ................................................................................................................ 55 3.3.1 Methane growth in the hydrate phase .......................................................................... 57 3.3.2 Methane diffusion in non-aqueous (NAL) liquid phase .............................................. 58 3.3.3 Hydrate conversion from fresh ground ice powder ..................................................... 60 3.3.4 Effect of thermal ramping on hydrate formation ......................................................... 62 3.3.5 Hydrate decomposition ................................................................................................ 64 3.3.6 Hydrate reformation..................................................................................................... 66 3.3.7 Ice-NAL wetting properties ......................................................................................... 67 3.3.8 Ice packing density ...................................................................................................... 70 3.4 Conclusions................................................................................................................................. 71 3.5 References................................................................................................................................... 72 CHAPTER-4: METHANE CONVERSION RATE INTO STRUCTURE H HYDRATE CRYSTALS FROM ICE 4.1 Introduction................................................................................................................................. 74 4.2 Experimental procedure .............................................................................................................. 75 4.3 Results and discussion ................................................................................................................ 76 4.3.1 Methane uptake with 200% LMGS synthesized at low pressure (P0=~4.3 MPa) ....... 80 4.3.2 Methane uptake with 50% LMGS synthesized at low pressure (P0=~4.3 MPa) ......... 81 4.3.3 Methane uptake with 200% LMGS synthesized at high pressure (P0=~8.1 MPa) ...... 82 4.3.4 Methane uptake with 50% LMGS synthesized at high pressure (P0=~8.1 MPa) ........ 83 4.3.5 Methane uptake with no LMGS synthesized at high pressure (P0=~8.1 MPa) ........... 84 4.3.6 Methane uptake with LMGS mixtures synthesized at low pressure (P0=~4.3 MPa)... 85 4.3.7 Correlation of conversion rate with crystallization models ......................................... 87 4.3.7.1 Correlation with the Avrami model .............................................................. 88 4.3.7.2 Correlation with the shrinking core model ................................................... 93 4.4 Conclusions................................................................................................................................. 95 4.5 References................................................................................................................................... 97  v  CHAPTER-5: CHARACTERIZATION OF GAS HYDRATES WITH PXRD, DSC, NMR AND RAMAN SPECTROSCOPY 5.1 Introduction................................................................................................................................. 98 5.2 Experimental procedure ..............................................................................................................100 5.3 Results and discussion ................................................................................................................102 5.3.1 X-Ray diffraction (XRD) analysis ...............................................................................102 5.3.2 Gas content measurement ............................................................................................104 5.3.3 Digital Scanning Calorimetry (DSC) analysis.............................................................106 5.3.4 Solid-state NMR analysis ............................................................................................108 5.3.5 Raman spectroscopic analysis......................................................................................116 5.4 Conclusions.................................................................................................................................122 5.5 References...................................................................................................................................123  CHAPTER-6: TUNING METHANE CONTENT IN GAS HYDRATES VIA THERMODYNAMICS MODELING AND MOLECULAR DYNAMICS SIMULATION 6.1 Introduction.................................................................................................................................126 6.2 Computational methodology.......................................................................................................128 6.2.1 Macroscopic modeling.................................................................................................128 6.2.2 Molecular dynamics (MD) method..............................................................................129 6.3 Results and discussion ................................................................................................................135 6.3.1 Storing methane in sII hydrates ...................................................................................135 6.3.1.1 Methane + propane system ...........................................................................136 6.3.1.2 Methane + THF system.................................................................................138 6.3.2 Storing methane in sH hydrate.....................................................................................144 6.3.2.1 The mechanical stability of pure sH methane hydrate..................................145 6.3.2.2 Free energy calculation of sH methane hydrate............................................149 6.3.2.3 Large guest (TBME) replacement with methane..........................................150 6.4 Conclusions.................................................................................................................................155 6.5 References...................................................................................................................................157  vi  CHAPTER-7: MOLECULAR DYNAMICS STUDY OF STRUCTURE-H CLATHRATE HYDRATE CONTAINING METHANE AND LARGE GUEST MOLECULES 7.1 Introduction.................................................................................................................................161 7.2 Computation methodology..........................................................................................................162 7.3 Results and discussion ................................................................................................................170 7.3.1 Preference of methane for occupying sH hydrate cages ..............................................170 7.3.2 Methane occupancy dependence on LMGS ................................................................172 7.3.3 Methane occupancy dependence with pressure ...........................................................174 7.3.4 Mechanical stability of the sH hydrate ........................................................................179 7.4 Conclusions.................................................................................................................................180 7.5 References...................................................................................................................................182 CHAPTER-8: INTERACTIONS BETWEEN STRUCTURE H HYDRATE FORMERS AND WATER MOLECULES 8.1 Introduction.................................................................................................................................185 8.2 Computation methodology..........................................................................................................186 8.3 Results and discussion ................................................................................................................191 8.3.1 Spatial distributions of water molecules near the solutes ............................................191 8.3.2 Spatial orientation of water molecules near LMGS molecule .....................................196 8.3.3 Solvation volume .........................................................................................................198 8.3.4 Solute diffusivity in aqueous solution..........................................................................199 8.3.5 Large guest-host (lattice) interactions..........................................................................201 8.3.6 Implications for clathrate formation ............................................................................203 8.4 Conclusions.................................................................................................................................207 8.5 References...................................................................................................................................208 CHAPTER-9: CONCLUSIONS, CONTRIBUTION TO KNOWLEDGE, AND RECOMMENDATIONS FOR FUTURE WORKS 9.1 Conclusions.................................................................................................................................211 9.2 Contribution to Knowledge.........................................................................................................214 9.3 Recommendations for Future Work............................................................................................215 9.4 References...................................................................................................................................217  vii  LIST OF TABLES Table 1.1. ...........................................................................................................................................  3  Hydrate structures and cage properties Table 1.2. ........................................................................................................................................... 12 Operating conditions for natural gas transport via LNG, CNG, and NGH technology. Table 1.3. ........................................................................................................................................... 15 Maximum gas storage capacities in hydrate with all cages fully occupied. Table 2.1. ........................................................................................................................................... 33 Chemicals used in this work. Table 2.2. ........................................................................................................................................... 38 LLE Data: Aqueous Phase Composition (mole fraction). Table 2.3. ........................................................................................................................................... 38 LLE Data: Non-Aqueous Phase Composition (mole fraction). Table 2.4. ........................................................................................................................................... 39 Parameters used to calculate the hydrocarbon solubility in water using equation (2.1) [8]. Table 2.5. ........................................................................................................................................... 40 Parameters used to calculate the water solubility in hydrocarbon using equation (2.2) [8]. Table 2.6. ........................................................................................................................................... 43 VLLE measurements (106x) for the methane-NH-water system at 275.5 K. Table 2.7. ........................................................................................................................................... 43 VLLE measurements (106x) for the methane-TBME-water system at 275.5K. Table 2.8. ........................................................................................................................................... 44 VLLE measurements (106x) for the methane-MCH-water system at 275.5K. Table 2.9. ........................................................................................................................................... 44 VLLE measurements (106x) for the methane-nC7-water system at 275.5K. Table 4.1. ........................................................................................................................................... 75 List of chemicals used in this work. Table 4.2. ........................................................................................................................................... 90 Avrami parameters; k is given in conversion/minuten. Table 4.3. ........................................................................................................................................... 94 Shrinking core model parameters.  viii  Table 5.1. ...........................................................................................................................................103 Lattice constants and unit cell volumes of synthesized hydrate at 82K. Table 5.2. ...........................................................................................................................................105 Amount of gas stored in hydrate with the final hydrate conversion achieved. Table 5.3. ...........................................................................................................................................107 Heat of fusion and hydration number of LMGS, ice, and sH hydrate. Table 5.4. ...........................................................................................................................................108 DSC summary of Methane + MCH hydrate formed at low pressure with 200% LMGS. Table 5.5. ...........................................................................................................................................112 Chemical shift of methane and LMGS in the hydrate and liquid phase obtained from 13C NMR referenced to adamantane at 298K. Table 5.6. ...........................................................................................................................................114 Cage occupancy values obtained by 13C MAS NMR. Table 6.1. ...........................................................................................................................................131 Coordinates of water molecules forming a unit cell of sH hydrate in Å units. Table 6.2. ...........................................................................................................................................149 Free energy per unit cell of hydrate (± 5 kJ/mol) calculation to determine the methane guest occupancy in the large cages of sH hydrate at 0.8 GPa. Table 6.3. ...........................................................................................................................................149 Free energy per unit cell of hydrate (± 5 kJ/mol) calculation to determine methane guest occupancy of the large cages of sH hydrate at 1.0 GPa. Table 7.1. ...........................................................................................................................................165 Atomic charges and Lennard-Jones interaction parameters for SPC/E water, large guest molecules (TBME, NH, MCH) and the methane molecule used in the MD simulations. Table 7.2. ...........................................................................................................................................170 Free energies of removing 20% of methane molecules from the small (512) cage only, medium (435663) cage only, and randomly from small and medium cages of sH hydrate at 274 K and 2 MPa. All values are in kJ/mol. Table 7.3. ...........................................................................................................................................171 The calculated values for supercritical methane molar volume at different pressures at 274 K using the Murad-Gubbins potential for methane and clathrate volumes at various methane occupancies. Table 7.4. ...........................................................................................................................................175 Free energy of removing methane from the small (512) and medium (435663) cages of sH hydrate at 274 K and 2 MPa. All values are in kJ/mol.  ix  Table 7.5. ...........................................................................................................................................175 Free energy of removing methane from the small (512) and medium (435663) cages of sH hydrate at 274 K and 6 MPa. All values are in kJ/mol. Table 7.6. ...........................................................................................................................................176 Free energy of removing methane from the small (512) and medium (435663) cages of sH hydrate at 274 K and 10 MPa. All values are in kJ/mol. Table 8.1. ...........................................................................................................................................198 Partial molar volume of water with TBME, NH and MCH.  x  LIST OF FIGURES Figure 1.1. ..............................................................................................................................  2  Burning methane hydrate. Photo was taken by the author at the Steacie Institute for Molecular Science, National Research Council (Ottawa, ON). Figure 1.2. ..............................................................................................................................  3  Hydrate cages and structure formulae based on complete occupancy. Figure 1.3. ..............................................................................................................................  5  Natural gas hydrates distribution worldwide, reprinted from [27], with permission from Elsevier. Figure 1.4. ..............................................................................................................................  9  Morphology of methane-propane hydrate (left) growing into the water phase (reprinted with permission from [81], copyright (2006) American Chemical Society) and carbon-dioxide hydrate (right) growing on water droplets exposed to a CO2 gas phase (reprinted from [85], with permission of John Wiley & Sons, Inc.). Figure 1.5. .............................................................................................................................. 11 Natural gas storage and transport from the gas fields to the market in the form of hydrate pellets, reprinted from [108] with permission from Mitsui Engineering & Shipbuilding Co., Ltd. Figure 1.6. .............................................................................................................................. 13 Estimated capital cost for natural gas storage and transport via various methods, reprinted from [109] with permission from Professor Gudmundsson. Figure 1.7. .............................................................................................................................. 14 Suitable technology for natural gas transport based on gas capacity in BCM (billion cubic meters) versus distance (km), reprinted from [109] with permission from Professor Gudmundsson. Figure 2.1. .............................................................................................................................. 32 Equilibrium hydrate formation conditions for sI and sH hydrates [7]. Figure 2.2. .............................................................................................................................. 35 Experimental apparatus for the ternary system, ‘A’ is shown in Figure 2.3. Figure 2.3. .............................................................................................................................. 36 Apparatus installed to collect the non-aqueous phase. Figure 2.4. .............................................................................................................................. 41 LLE data of water-neohexane (NH) system and correlation (solid or dashed line) using equations (2.1) and (2.2).  xi  Figure 2.5. .............................................................................................................................. 41 LLE data of water-methylcyclohexane (MCH) system and correlation (solid or dashed line) using equations (2.1) and (2.2). Figure 2.6. .............................................................................................................................. 42 LLE data of water-n-heptane system and correlation (solid or dashed line) using equations (2.1) and (2.2). Figure 2.7. .............................................................................................................................. 46 Krichevsky and Kasarnovsky plot at 275.5K. Figure 3.1. .............................................................................................................................. 51 Rates of hydrate formation and induction times versus driving force [1]. Figure 3.2. .............................................................................................................................. 56 Deuterium (2H) NMR spectra evolution of Ice+Neohexane+CD4 at 253K and ~4.5 MPa for 20 hours. The inset shows the acquired spectra at 0, 0.5, 1, 2, 3, 4, 6, 10, 15, 20 hours. Figure 3.3. .............................................................................................................................. 58 Normalized intensity of methane growth in the solid hydrate phase at 253K and ~4.5MPa. Figure 3.4. .............................................................................................................................. 59 Normalized intensity evolution of methane in the gas and dissolved in nonaqueous liquid phase at 253K and ~4.5MPa. Figure 3.5. .............................................................................................................................. 61 Ice to hydrate conversion obtained at 253K and ~4.5MPa. Hydrate conversion was calculated by assuming methane occupancy of 80% in the small and large cage in sH hydrate. Figure 3.6. .............................................................................................................................. 62 Ice to hydrate conversion obtained with temperature ramping to 274K after 20 hours isothermal at 253K. Figure 3.7. .............................................................................................................................. 65 Hydrate decomposition obtained at 253K and 1 atm for NH and MCH system. Figure 3.8. .............................................................................................................................. 66 Neohexane-CD4 mixed hydrates stability at 253K and ~0.5 MPa. The equilibrium pressure at 253K is ~0.48 MPa [18]. Figure 3.9. .............................................................................................................................. 67 Hydrate reformation (memory ice) obtained at 253K and ~4.5MPa after decomposing the previously formed hydrate (fresh ice) by releasing all the gas and kept at atmospheric pressure for 3 hours.  xii  Figure 3.10. ............................................................................................................................ 68 Distribution of LMGSs and diffusion of LMGS between ice particles observed by proton (1H) micro-imaging NMR for ice with MCH and TBME system. Figure 3.11. ............................................................................................................................ 70 Proton (1H) micro-imaging NMR of Ice+MCH system with different degree of ice packing: the left images correspond to highly packed ice and the right images correspond to system that is not highly packed. Figure 4.1. .............................................................................................................................. 77 Pressure drop profile during hydrate formation from ice + LMGS (~200%) + methane synthesized at low pressure (P0 = ~4.3 MPa). Figure 4.2. .............................................................................................................................. 78 Amount of methane uptake during hydrate formation from ice + LMGS (~200%) + methane synthesized at low pressure (P0 = ~4.3 MPa). Figure 4.3. .............................................................................................................................. 79 Hydrate conversion ratio of ice + LMGS (~200%) + methane synthesized at low pressure (P0 = ~4.3 MPa). Figure 4.4. .............................................................................................................................. 81 Pressure profile during hydrate formation from ice + LMGS (~50%) + methane synthesized at low pressure region (P0 = ~4.3 MPa). Figure 4.5. .............................................................................................................................. 83 Amount of methane uptake during hydrate formation from ice + LMGS (~200%) + methane synthesized at high pressure (P0 = ~8.1 MPa). Figure 4.6. .............................................................................................................................. 84 Amount of methane uptake during hydrate formation from ice+ LMGS (~50%) + methane synthesized at high pressure (P0 = ~8.1 MPa). Figure 4.7. .............................................................................................................................. 85 Amount of methane uptake during hydrate formation from ice without any LMGS synthesized at high pressure (P0 = ~8.1 MPa). Figure 4.8. .............................................................................................................................. 86 Amount of methane uptake during hydrate formation from ice + Neohexane (NH) and tert-butyl methyl ether (TBME) mixture (~200%) + methane, synthesized at low pressure (P0 = ~4.3 MPa). Figure 4.9. .............................................................................................................................. 89 Avrami plot for ice + LMGS (~200%) + methane systems. Hydrates were synthesized at low pressure (P0 = ~4.3 MPa).  xiii  Figure 4.10. ............................................................................................................................ 89 Avrami plot for ice + LMGS (~200%) + methane systems. Hydrates were synthesized at high pressure (P0 = ~8.1 MPa). Figure 4.11. ............................................................................................................................ 91 Hydrate conversion for ice + LMGS (~200%) + methane system synthesized at low pressure (P0 = ~4.3 MPa). Figure 4.12. ............................................................................................................................ 91 Hydrate conversion for ice + LMGS (200%) + methane system synthesized at high pressure (P0 = ~8.1 MPa). Figure 4.13. ............................................................................................................................ 92 Avrami plot for ice + methane systems (no LMGS). Hydrates were synthesized at high pressure (P0 = ~8.1 MPa). Figure 4.14. ............................................................................................................................ 94 Shrinking core model (SCM) plot for ice + LMGS (~200%) + methane systems. Hydrate was synthesized at low pressure (P0 = ~4.3 MPa). Figure 5.1. ..............................................................................................................................103 PXRD pattern of sH hydrate (TBME+Methane). Figure 5.2. ..............................................................................................................................106 DSC melting curve of (Methane+MCH) sH hydrate. Figure 5.3. ..............................................................................................................................109 13  C MAS-NMR spectra of (Methane+NH) sH hydrate, synthesized with 200% NH at low pressure condition (Final pressure ~17 bars at 274K).  Figure 5.4. ..............................................................................................................................109 13  C MAS-NMR spectra of (Methane+MCH) sH hydrate, synthesized with 200% MCH at low pressure condition (Final pressure ~17 bars at 274K). Figure 5.5. ..............................................................................................................................110 13  C MAS-NMR spectra of (Methane+TBME) sH hydrate, synthesized with 200% TBME at low pressure condition (Final pressure ~21 bars at 274K). Figure 5.6. ..............................................................................................................................110 13  C MAS-NMR spectra magnified around methane region obtained at 193K.  Figure 5.7. ..............................................................................................................................116 Raman spectra of (Methane+MCH) sH hydrate at ~85K. Figure 5.8. ..............................................................................................................................117 Raman spectra of (Methane+NH) sH hydrate at ~85K.  xiv  Figure 5.9. ..............................................................................................................................117 Raman spectra of (Methane+TBME) sH hydrate at ~85K. Figure 5.10. ............................................................................................................................118 Raman spectra of (Methane+TBME) sI+sH hydrate at ~85K. Figure 5.11. ............................................................................................................................119 Raman spectra around methane region obtained at ~85K. Figure 5.12. ............................................................................................................................120 Raman spectra during (CH4+TBME) hydrate formation at ~3.5 MPa. Figure 5.13. ............................................................................................................................121 Raman spectra during (CH4+TBME) hydrate decomposition at~3.5 MPa. Figure 6.1. ..............................................................................................................................137 Methane occupancy in the small (top) and large (bottom) cages of sII methanepropane mixed hydrates as a function of temperature and methane composition in the feed gas. Figure 6.2. ..............................................................................................................................138 Total methane gas stored in methane-propane mixed sII hydrates at STP as a function of methane composition in the feed gas and temperature. Figure 6.3. ..............................................................................................................................139 Three phase hydrate-liquid-gas equilibria of sI methane hydrate (black) and sII methane+THF mixed hydrate (color). The experimental data are obtained from the literature [11,46,47]. Figure 6.4. ..............................................................................................................................140 Methane occupancy in the small (top) and large (bottom) cages of sII methaneTHF mixed hydrates as a function of temperature and THF composition in water. Figure 6.5. ..............................................................................................................................142 Total methane gas content stored in methane-THF mixed sII hydrates at STP as a function of THF composition and temperature. Figure 6.6. ..............................................................................................................................143 Methane occupancy ratio (large to small cages) and hydrate equilibrium temperature at 2 MPa of methane-THF mixed sII hydrates as a function of THF concentration. Figure 6.7. ..............................................................................................................................145 Initial (top) and final (bottom) atomic configuration of 3×3×3 super-cell looking down along the c-axis during the hydrate stability simulation performed at 1 MPa and 300K. The distance from the cage center to its neighboring cage in a and baxis is approximately 12.3 Å, which is also the size of a unit cell of sH.  xv  Figure 6.8. ..............................................................................................................................147 Configuration energy profile during the simulation of sH methane hydrate. Figure 6.9. ..............................................................................................................................147 Phase diagram of methane-water system at high pressures. The experimental data was obtained from Dyadin et al. [55]. Figure 6.10. ............................................................................................................................151 Total methane gas content stored in sH methane when 0, 3, 9, 18, 24, and 27 TBME molecules out of 27 are replaced by methane at various quantities in the large cages at standard condition. Figure 6.11. ............................................................................................................................152 Configuration energy profile during the replacement of TBME with one to five methane molecules in the large cages at 0.8GPa and 300K. Figure 6.12. ............................................................................................................................153 Lattice constant changes during the replacement of TBME from the large cage of sH hydrate with one to five methane molecules at 0.8GPa and 300K. Figure 6.13. ............................................................................................................................154 Radial distribution function (RDF) of carbon of methane in the large cage with carbon of methane (top) and oxygen of host lattice (bottom). Figure 7.1. ..............................................................................................................................164 The atomic assignment for the Large Molecule Guest Substance (LMGS) employed in this study: TBME (top), MCH (bottom left) and NH (bottom right). The charges and Lennard-Jones parameter are given in Table 8.1. Figure 7.2. ..............................................................................................................................172 Lattice energy changes at 2 MPa and 274 K as 0.9, 0.8, 0.7, 0.6, and 0.5 occupancies of methane in small and medium cages of structure H (sH) hydrate are randomly removed. Figure 7.3. ..............................................................................................................................177 Lattice and total free energy (∆G) at 274 K and 2, 6, and 10 MPa as methane in small and medium cages of structure H (sH) hydrate are randomly removed from fully occupancy to 0.9, 0.8, 0.7, 0.6, and 0.5 occupancies. The average lattice energy is shown by the dashed-line. Figure 7.4. ..............................................................................................................................178 Variations of the unit cell volume and lattice constants with respect to LMGS, pressure, and methane occupancy in sH hydrate. The simulation (solid) is performed at 274 K and 2, 6, 10 MPa. The experimental results (not filled) are for atmospheric pressure and 82 K.  xvi  Figure 7.5. ..............................................................................................................................180 Snapshots during the simulation at 274 K and 2 MPa with the large cages filled with TBME and all methane molecules are removed from both small (512) and medium (435663) cages of sH hydrate. Figure 8.1. ..............................................................................................................................189 Coordinate assignment for the LMGS molecule as the reference. The atoms selected represent similar geometries. The colors for the carbon, oxygen, and hydrogen atoms are as follows: cyan, red, and white. Figure 8.2. ..............................................................................................................................191 The definitions of the orientation of water molecule relative to the reference atom (RA) at the origin. The water molecule is represented in red. Figure 8.3. ..............................................................................................................................192 Radial distribution function of water oxygen and solute reference atoms (O-water, O-TBME, C5-NH, and C2-MCH). Figure 8.4. ..............................................................................................................................194 Spatial oxygen and hydrogen distribution of water surrounding the LMGS molecule on XY-plane (z = 0). Figure 8.5. ..............................................................................................................................195 3-D illustration of water molecule positions with respect to the referenced molecule at selected distances. Figure 8.6. ..............................................................................................................................197 Spatial orientation distribution of water with respect to a reference atom normalized to the bulk water density. Figure 8.7. ..............................................................................................................................200 Mean square displacement (MSD) of TBME and NH in water over a time range of 60 ps. Figure 8.8. ..............................................................................................................................202 Snapshots of the large guest molecules inside the large cage of sH hydrate from the top and front side. The TBME inside the cage may induce a defect into the clathrate lattice due to the hydrogen bond formed.  xvii  NOMENCLATURE  Abbreviation  Full Form  C  carbon atom  EC  entropy correction contribution to the free energy  IG  ideal gas contribution to the free energy  LMGS  large molecule guest substance  MCH  methyl-cyclohexane  NAL  non-aqueous liquid  NH  neo-hexane  RDF  radial distribution function  RGC  real gas correction contribution to the free energy  TBME  tert-butyl methyl ether  SCM  shrinking core model  W  water  THF  tetra-hydrofuran  nC7  n-heptane  α  hydrate conversion ratio  α*  hydrate conversion ratio after time t*  fi  fugacity of component i  k1  rate of reaction from Avrami equation  k2  rate of reaction from SCM model  n  Avrami exponent  θS  occupancy of the small cage  θM  occupancy of the medium cage  θL  occupancy of the large cage  r  average radius of ice particles  t  time during the hydrate formation  t*  time at the point where the data deviate from Avrami equation  xi  solubility of component i  xviii  ACKNOWLEDGEMENTS This thesis is possible due to contributions from a number of people that are involved directly or indirectly. I want to express my sincere gratitude and special thanks to my supervisor Prof. Peter Englezos who has given me the opportunity, trust and wise advices to accomplish this challenging research project. I would also like to extend my grateful acknowledgement to Dr. John A. Ripmeester and Dr. Saman Alavi, who gave me the supports, fruitful discussions, inputs and guidance throughout this project. I have grown as a person both technically and socially throughout the course of my study. I learned to think positively in dealing with any issues and focus on finding the right solutions by incorporating the resources and using the tools around us. I become more open-minded and equipped myself with a set of valuable experimental and simulation techniques that are useful for my future career. It was a wonderful experience working with you all. I would also like to thank Natural Science and Engineering Research Council of Canada (NSERC) and the Institute of Applied Energy (IAE), Japan for their financial support for this project. The Canada Graduate Scholarship (CGS) scholarship from NSERC and Ph.D. award from UBC are highly appreciated. Finally, I would like to thank the members of hydrate research group at UBC and the Material Structure and Function (MSF) group at NRC for their accompanies, comments and suggestions. I take this opportunity to thank my family and all my friends who are patience, gave supports, motivations and encouragements during difficult times in order to complete my study.  xix  CO-AUTHORSHIP STATEMENT The content of this thesis is published or accepted for publication in seven articles. The authors include Susilo, R., Alavi, S., Lee, J.D., Moudrakovski, I.L., Lang, S., Ripmeester, J.A., and Englezos P. Professor Peter Englezos is my main supervisor at the University of British Columbia (UBC). Dr. John Ripmeester and Dr. Saman Alavi are my co-supervisors at the National Research Council Canada (NRC) in Ottawa, ON. During the course of my research, I was fortunate enough to get technical assistance from Dr. Judong Lee, who was a post-doctoral fellow at gas hydrate research group at UBC; Dr. Igor Moudrakovski, who is an expert in NMR related study; and Dr. Steve Lang, a technical officer at NRC. The literature review, experimental design, performing experiments, computer simulations and data analysis were done extensively by R. Susilo under supervision of Professor P. Englezos, Dr. J.A. Ripmeester, and Dr. S. Alavi. In some part of the work J.D. Lee, I.L. Moudrakovski, and S. Lang provides technical training and helpful discussions to complete the project.  xx  CHAPTER-1 INTRODUCTION 1.1 Introduction to gas hydrates Gas hydrates are non-stoichiometric crystalline compounds that can be found naturally or synthesized artificially at suitable pressure and temperature conditions [1-4]. They consist of host and guest molecules and are classified as true inclusion compounds [5]. They are also known as clathrates. The host is water molecules that are connected by hydrogen bonds forming cages or cavities to encapsulate the guest molecule. The key interaction between the host and the guest molecules is the weak van der Waals forces only. Hence the hydrate crystal is basically formed due to physical union between a suitable guest and host water molecules without any chemical reaction. The occupancy of the cages is essential to maintain the stability of the cages that would otherwise collapse. The guest molecules can be any molecules with suitable size and geometry that fit into the cage and do not interfere with the host cages. Any molecules smaller than ~10Å either in gas, liquid or solid state may act as a hydrate former. However hydrophobic and spherical molecules are generally favored with one guest molecule in a cage. Multiple guest molecules occupying a hydrate cage is possible only for molecules smaller than ~4.3Å such as nitrogen [7], hydrogen [8], and rare gases [9,10]. Natural gas components such as methane, ethane, propane, carbon dioxide, and hydrogen sulfide are the wellknown guest molecules associated with gas hydrates. Hence, the gas hydrate is also known as combustible ice [6], as shown in Figure 1.1.  1  Figure 1.1: Burning methane hydrate. Photo was taken by the author at the Steacie Institute for Molecular Science, National Research Council (Ottawa, ON)  Macroscopically, gas hydrates appear like ice or snow. However, the crystal structure is different because the water molecules in hydrate have to reorient themselves in order to accommodate guest molecules. There are three well-known hydrate structures: cubic structure I (sI) [11,12], cubic structure II (sII) [13,14] and hexagonal structure H (sH) [15]. Other structures have been reported as well but they are not commonly found. The cage properties for those three hydrate structures are given in Table 1.1 and illustrated in Figure 1.2. The cubic hydrate crystals (sI and sII) have 2-different cage sizes but the hexagonal one (sH) has 3-different cages. Generally, one type of guest molecules is enough to stabilize the hydrate, except for sH hydrate that requires two different sizes of guest molecules. There are more than 100 molecules identified as hydrate formers [16,17].  2  Table 1.1: Hydrate structures and cage properties Structure  I  II  H  Cubic Pm3n  Cubic Fd3m  a = 12A  a = 17.3A  2  2  Small/S (512) Large/L (51262)  Small/S (512) Large/L (51264)  Hexagonal P6/mmm a = 12.2 A c = 10A 3 Small/S (512) Medium/M (435663) Large/L (51268)  2S.6L.46H2O  16S.8L.136H2O  Cage radius  rS = 3.95A rL = 4.33A  rS = 3.91A rL = 4.73A  Coordination number  S = 20 L = 24  S = 20 L = 28  Crystal system Space group Lattice parameters Number of cage Cage identification Ideal unit cell formula  Small (S)  Medium (M)  Large (L)  -  3S.2M.1L.34H2O rS = 3.91A rM = 4.06A rL = 5.71A S = 20 M = 20 L = 36  Structure/Formula Structure I (sI)  512  51262 -  2S.6L.46H2O Structure II (sII)  512  51264  16S.8L.136H2O Structure H (sH)  512  435663  51268  3S.2M.1L.34H2O  Figure 1.2: Hydrate cages and structure formulae based on complete occupancy.  3  The cage sizes, geometries, and packing configurations are different among the three structures but they have a common basic cage, which is the small cage with 12pentagonal faces (512). A larger cage is created because this small cage cannot pack by itself to form a unit cell. The large cage has 12-pentagonal faces with 2-hexagonal faces (51262) for sI, 4-hexagonal faces (51264) for sII and 8-hexagonal faces (51268) for sH hydrate. An irregular cage with 3-quadrilateral faces, 6-pentagonal faces, and 3hexagonal faces (435663) is also formed for sH hydrate, which has similar size to the small cage (512). The size of the large cage increases on going from sI, sII to sH. Consequently, the stable hydrate structure is controlled by the size and geometry of the guest molecules.  1.2 Significance of gas hydrate Despite the fact that gas hydrate was discovered in 1810 by Sir Humphrey Davy’s [18], the intensive study on gas hydrate arose only around the mid 1930’s. It was due to the presence of solid material in gas transmission pipelines at temperatures above the icepoint which frequently plugged the pipelines [19]. That solid material was identified as gas hydrate, which was unwanted and created many technical and economical problems. As soon as the flow is blocked, the gas production and delivery will have to be stopped because it may damage the equipment and endanger the workers. It is not a trivial task to remove the hydrate and get the process back online. The hydrate may turn into a projectile if the pressure is released. Moreover, heating the pipelines or injecting chemicals to decompose the hydrate are costly. Hence gas hydrate was considered as an enemy to the oil and gas industry at that time.  4  The importance of gas hydrates to human welfare was marked after the discovery of naturally occurring gas hydrates in the Siberian permafrost regions [20]. Gas hydrates in the earth typically exist on the offshore of continental margins (marine sediments) and under the permafrost in the Arctic [6, 21-26]. The exact quantity of natural gas in hydrate form is not known accurately. It is estimated to represent 5 – 20 % of the global carbon budget. Hence it is significant and considered to be a huge potential unconventional energy source for the future [27,28]. The locations where natural gas hydrate has been inferred, recovered, and potentially exists in the world are marked in Figure 1.3.  Figure 1.3: Natural gas hydrates distribution worldwide, reprinted from [27], with permission from Elsevier. The hydrate reservoir properties are not fully understood and technologies available for conventional gas production are still too costly to recover the gas. The first production test of methane hydrate was conducted in the Mackenzie Delta in the Canadian Arctic in 2002. Two test wells were drilled where samples cores were collected to understand its characteristic and evaluate the possibility for successful gas production  5  [29]. Thermal and pressure stimulations were tested to measure both input conditions and reservoir responses that enabled the calibration and refinement of reservoir simulation models. The anticipated commercial production of gas hydrate is expected to begin sometime between 2015 and 2025 [30]. Besides the economic aspect that has to be taken into consideration, the impact on the environment, ecology, and geological stability are also important. The decomposition of natural hydrate may destabilize and alter the earth’s geological features [31-33] causing geohazards such as landslides, earthquakes, and even tsunamis if the mass movements are under water. On the other hand, current global warming may initiate the decomposition of natural hydrates [34,35]. Gas hydrate also offers opportunities to develop innovative technologies for gas storage and separation [36-39] as well as cool energy storage [40,41]. The applications include storing and transporting natural gas [38, 43-50], hydrogen storage for the hydrogen economy of the future [51-56], sequestration of carbon dioxide with in situ methane hydrate decomposition [57-59], separation of carbon dioxide from the flue gas [60-61], seawater desalination [63-66] and refrigeration [67-71].  1.3 Research on gas hydrates It is therefore indispensable to know how, when, and where gas hydrate forms and decomposes. The early research on gas hydrate was just a scientific curiosity where the focus was to identify the chemical compounds that were able to form hydrates. The study then evolved into a broad variety of research topics and applications, especially after recognizing the importance of gas hydrate to the oil and gas industry. The fundamental  6  research lines consist of thermodynamics and kinetics from the macro to micro level via experiments as well as computer simulations. Due to the complex behaviour of gas hydrates, research on gas hydrates involves chemical, mechanical and civil engineers and scientists from different backgrounds such as: chemistry, physics, biology, geology and geophysics. The study on thermodynamics is directed mostly towards determining the hydrate phase diagram. This work is motivated by the industrial need to assure the flow of hydrocarbons in pipelines. The need to explore oil and gas in deeper areas forces the oil and gas companies to deal with extreme conditions where hydrate formation in pipelines is more likely to be encountered. Hydrate formation conditions for most hydrocarboncontaining systems from single component to mixtures were studied extensively. A list with experimental data up until the late 1990s is available [3]. Thermodynamics modeling to predict the hydrate phase equilibria is also well established. New experimental data for mixed hydrate systems with additives and improved models to predict hydrate phase diagrams continue to appear, especially in relation to potential development of new technologies such as gas storage. It is very useful to find ways to shift the hydrate phase boundary. For example, for gas storage and gas separation applications via gas hydrate formation, a more stable hydrate at higher temperature and lower pressure is favoured for technical and economic reasons. However, the opposite is expected when the objective is to avoid hydrate plugging in pipelines. Hydrate studies at very high pressures have also been reported as a result of the recent interest in the outer solar system (icy satellites/planetary studies).  7  Kinetic studies on gas hydrates are concerned with the rate at which the phase transformation occurs and the identification of the factors affecting it. Gas hydrate formation is a crystallization process that is characterized by nucleation followed by crystal growth and agglomeration [72,73]. Hence kinetic studies involve induction time measurements for crystallization and the determination of hydrate crystal growth rate. Most gas hydrate kinetic studies have focused on the growth phase (hydrate crystal growth kinetics) by measuring mainly the rate of uptake of the hydrate forming substance [74,75]. This is because it is much more difficult to do online measurements of the solid hydrate phase. It is also noted that the rate of number hydrate crystal nuclei formed per unit time per unit volume (hydrate crystal nucleation kinetics) is extremely difficult to measure and to date no data are available. Bishnoi’s laboratory at the University of Calgary pioneered the kinetic studies on the macro-scale. They developed a mechanistic hydrate kinetics model based on gas uptake measurements [74,75] that was later improved [76]. Macroscopic measurement can also be coupled with measurement of the hydrate particle size distribution [77,78]. Another online macroscopic-type measurement is based on differential scanning calorimetry that measures the heat released during the formation [79]. The hydrate crystal growth rate generally increases with driving force, defined as the magnitude of the deviation of the pressure from the equilibrium one (overpressure) or the temperature from the equilibrium value (sub-cooling or under-cooling). Morphology studies at gas/waster interfaces may provide important information in order to elucidate the mechanistic aspects of hydrate formation [80-89]. A hydrate film growth model has also been derived from the observation of hydrate morphology [90-92].  8  Columnar or dendritic crystals were observed with growth from the interface towards the liquid water phase as shown in Figure 1.4 (left). The water may also migrate out through the hydrate layer due to capillary action. Hairy or needle-like crystal morphologies were observed on going from the interface towards the gas phase as seen in Figure 1.4 (rightbottom). Consequently, the water phase is depleted and a collapse is observed (Figure 1.4, right-top). Morphology studies also suggested that the crystal shape and dimension are influenced by the rate of hydrate formation that is controlled by the degree of subcooling [81,82,93] and the presence of hydrate inhibitors [94-96]. Hydrate film  1 mm  Figure 1.4: Morphology of methane-propane hydrate (left) growing into the water phase (reprinted with permission from [81], copyright (2006) American Chemical Society) and carbon-dioxide hydrate (right) growing on water droplets exposed to a CO2 gas phase (reprinted from [85], with permission of John Wiley & Sons, Inc.). Kinetics through gas uptake measurements and macroscopic techniques, in general, are in reality the “average kinetics” over the whole sample. The observation of gradual conversion in bulk samples only arises as a result of averaging over many local environments [97]. This raises a question how microscopic kinetics measurements are related to macroscopic ones. In addition, intermediate steps may also exist during the phase change into hydrate, which are not stable thermodynamically. For example a meta-  9  stable sII hydrate might be observed in the stability region of sI hydrate as reported for methane hydrate [98]. The occupancy of the cages may also change during their formation which further complicates the study of the kinetics. In order to get a complete picture of hydrate formation four microscopic techniques are employed. The techniques include X-Ray diffraction [99], Nuclear Magnetic Resonance (NMR) [100,101], micro-imaging (MRI) [61], and Raman spectroscopy [102]. Detailed information such as the crystal structure, relative cage occupancy and hydrate conversion during the “reaction” can be monitored. However the implementation of those techniques for gas hydrate studies is still limited due to the high pressure requirements for methane hydrate formation. Molecular Dynamics (MD) simulations are also employed recently to enable studies at conditions which are either difficult or impossible to access experimentally [103-106]. In spite of kinetic models that have appeared and aided the mechanistic understanding of hydrate growth, it is still difficult to come up with a generalized predictive model that will allow the prediction of the onset of hydrate formation and the rate of hydrate growth. Thus, there is a need to study particular hydrate forming systems with macroscopic and microscopic experimental techniques and theory.  1.4 Gas storage in hydrate Storing and transporting natural gas as hydrates from remote gas fields is one of the most promising applications of gas hydrates [36-39]. This is supported by the fact that more than 50% of the natural gas fields worldwide are considered as stranded and abandoned gas fields [107]. It is not profitable to recover the gas from gas fields where  10  the gas quantities are not sufficient and/or located in remote areas. It is too costly to transport the gas via pipelines or in liquefied form (LNG) due to extreme pressures or temperature requirements. Hence, there is a need for cost-effective technology in terms of capital and operational costs [37]. Figure 1.5 illustrates how gas hydrate technology can be implemented to store and transport natural gas.  Figure 1.5: Natural gas storage and transport from the gas fields to the market in the form of hydrate pellets, reprinted from [108] with permission from Mitsui Engineering & Shipbuilding Co., Ltd. The gas recovered from the reservoir is collected at the central gathering station where it is mixed with water to form hydrate at the hydrate production plant. The plant ideally should not be located too far away from the gas field and have easy access to water and a transport carrier such as ship or truck. The hydrate formed is then packed into pellets and is transported from the gas producing field (loading berth) to the energy users (unloading berth) at -20°C under atmospheric pressure. At the unloading site, the hydrate can be degasified for the gas turbine power plant to generate electricity. The decomposition of  11  hydrate releases the gas and water that can be accomplished easily by exposing it to higher temperature.  1.4.1 Economics The methods to store and transport natural gas include LNG (liquefied natural gas), GTL (gas to liquid), pipeline, CNG (compressed natural gas), GTW (gas to wire) and GTS (gas to solid) or NGH (natural gas hydrate) technologies. Hence natural gas can be stored and transported in various forms such as: liquid, syncrude (synthetic crude), compressed gas, electricity, and solid hydrate. Table 1.2 shows the operating conditions for three options: LNG, CNG, and NGH. The selected technology is obviously the one that is the most economical, which is controlled by two important factors: the capacity (amount of gas to be transported) and the distance to markets [109]. Table 1.2: Operating conditions for natural gas transport via LNG, CNG, and NGH technologies. Technology  Pressure [MPa]  Temperature [K]  0.1 >10 2-12  113 ~298 253  Liquefied Natural Gas (LNG) Compressed Natural Gas (CNG) Gas hydrate (NGH)  The approximate capital cost with transport distance is summarized in Figure 1.6. LNG is the most established technology with a high gas storage density. However, the capital cost for a LNG plant is the highest, and hence this technology is not a good candidate for transporting stranded gas. The cost for pipeline transport increases rapidly with distance, whereas gas-to-liquid technology (GTL) based on synthetic petroleum (syncrude) appears to be attractive for distances longer than 10,000 km. The estimated  12  capital cost is actually the lowest when the natural gas is transported via hydrate (NGH) except at very small distances.  Figure 1.6: Estimated capital cost for natural gas storage and transport via various methods, reprinted from [109] with permission from Professor Gudmundsson. Figure 1.7 actually shows a capacity (in billions of cubic meters) versus distance (in km) diagram which shows regions where a specific technology is preferable [109]. Natural gas transport via pipeline is good for large gas field located close to market. The capital cost to install pipelines is too expensive for remote gas fields. Hence the LNG technology is preferred at longer distances. However those two methods are not suitable for small capacity gas fields. Alternative technologies suggested include CNG, GTW, NGH, and GTL. NGH technology is considered to be appropriate for stranded gas at short distances up to 3000 km [109]. However NGH technology is not established yet and hence further cost reduction may be expected in the future. The area marked by dashed line is the region where a selection of technologies may overlap.  13  Figure 1.7: Suitable technology for natural gas transport based on gas capacity in BCM (billion cubic meters) versus distance (km), reprinted from [109] with permission from Professor Gudmundsson.  1.4.2 Gas storage potential Gas hydrate is being considered as an alternative technology. However, it is not well-established and thus further investigations are needed to determine the utility of this material in a variety of pressure and temperature conditions. Ideally, it is desirable to look for the most stable hydrate system with the maximum gas content so that the hydrate can be formed, stored and transported from the gas production field to the energy user close to room temperature and atmospheric pressure. The maximum gas storage capacities of hydrates per unit volume when gasified at standard temperature and pressure (STP) are summarized in Table 1.3. The gas content in each respective cage is distributed based on the stoichiometric hydrate formula for each structure with all the cages being singly and fully occupied. The gas content is reported as  14  volume of gas per volume of hydrate. Thus it depends on the hydrate molar density that is obtainable from the crystal dimension (lattice constants). Hence, the gas contents may differ slightly from the reported values in Table 1.3 due to contraction or expansion of the unit cells at different pressures and temperatures. The smaller unit cell volumes correspond to higher molar densities and thus greater hydrate storage capacity. Larger unit cell volumes lead to lower gas storage densities. Table 1.3: Maximum gas storage capacities in hydrate with all cages fully occupied. Hydrate structure  Lattice constant  Unit cell volume  Gas molar density (a)  sI sII  a = 12.0 Å a = 17.3 Å a = 12.2 Å c = 10.1 Å  1728 Å3 5178 Å3 1302 Å3  sH  Gas content (m3) per m3 hydrate(b) Small  Large  Total  7.7 mol/L 7.7 mol/L  43 115  129 57  172 172  6.4 mol/L  86 + 57 (c)  29n (d)  143 + 29n  (a) Assuming stoichiometric composition and full occupancy of all accessible cages. (b) Gas released at standard condition (1 atm and 25°C). (c) Refers to the medium cage for sH hydrate. (d) The large cage of sH hydrate is generally occupied by a large molecule (dvdw > 7 Å) only at low to moderate pressures (n = 0). Smaller molecule occupancy is possible only at high pressures (in the non-practical GPa range) where multiple numbers (n ≈ 2 to 5) molecules in a cage are needed to maintain the hydrate stability. It is noted that the maximum gas storage capacity in structure I and II is approximately equal at ~172 v/v when all cages are singly occupied with the specified lattice constants. The gas content is lower in sH hydrate (~143 v/v) because small gas molecules like methane are too small to interact efficiently with the large cage and maintain the stability of the lattice at low pressures (n =0). The occupancy of a small gas molecule in the large cage of sH hydrate under moderate pressure up to ~10 MPa has never been reported. Thus a larger molecule guest substance (LMGS) is required to fill the large cage and stabilize methane in sH hydrate. The large cage can accommodate the  15  small gas molecules only at a pressure in the range of GPa with multiple number of guests in a cage ranging from two to five. The maximum is five as the case for Argon hydrate [110]. Hence there is a potential to increase the gas content in sH hydrate, although it is not practical due to extreme pressure requirement. Obviously, the gas storage capacity in each hydrate depends on the occupancy of the cages. Hence, it is important to know the cage occupancies in order to assess the actual gas content in hydrate. The type of guest molecule(s) and the operating conditions at which the hydrate is synthesized control the cage occupancy. It is therefore very important to know how the guest(s) and host molecules interact and partition among the phases as well as within the hydrate phase itself. A tuning strategy is needed to fill the hydrate phase with the guest molecule of interest. The gas storage density in liquefied natural gas is actually higher (~600 v/v). However a cryogenic temperature is required which is very costly. Gas transport in pipelines requires pressures well above 10 MPa to match the gas density in hydrate, which is also costly and subject to safety issues and other issues such as political considerations. Hence storing gas in hydrate is attractive because the pressure and temperature conditions lie between the two extremes while keeping the gas density reasonably high. There are several challenges that have to be dealt with before gas hydrate storage and transport technology can be commercialized. Firstly, natural gas composition varies from gas field to gas field. The main component of purified natural gas generally is methane (~90 %+) along with other light hydrocarbons. If the natural gas contains only methane, the stable hydrate structure is sI. However the most stable hydrate structure is  16  more likely to be sII due to the presence of larger components that are sII hydrate formers such as propane, i-butane [111], and various combinations of ethane and methane also give sII hydrate [112-115]. The formation of sH hydrate is possible if the gas contains condensates. A mixture of hydrate structures may also be present. Another challenge is to be able to synthesize hydrates with the highest rate and conversion. There are several gas/water contacting modes reported in literature. However, most of them include only the initial reaction rates and neglect the hydrate conversion. This is mostly because hydrate is a solid material that may impede the contact between the guest and water molecule for subsequent growth. Moreover, hydrate formation is exothermic which generates heat that in fact may lower the driving force and hydrate formation rate if the heat is not removed from the system. The greatest challenge would be to establish a strategy on how to optimize the gas content and the hydrate formation rates and conversion while keeping the hydrate stable at the lowest possible pressure. A suitable help guest molecule may be selected as an additive to enhance the kinetics and/or stabilize the hydrate at a given concentration and operating condition. Hence, it would be helpful to know the relation between hydrate stability and the quantity of gas stored in hydrate phase for several hydrate systems. Japan leads the way in the effort to commercialize gas to solid (GtS) technology via gas hydrate. Mitsui Engineering and Shipbuilding Corp., Inc (MES) has completed a hydrate production pilot plant which is able to produce 600 kg of hydrate per day. The most recent interest to commercialize gas hydrate technology for natural gas storage and transport came from an Indian oil and gas company, which had reached an agreement  17  with Aker Kvaerner (AK) in 2004. AK is a Norwegian company that collaborates with the Norwegian University of Science and Technology (NTNU) and MES.  1.5 Research Objectives This thesis focuses on understanding methane hydrate formation in the presence of a large molecule guest substance (LMGS). The LMGS selected are neohexane (NH), tert-butyl methyl ether (TBME) and methyl-cyclohexane (MCH). Their selection was based mainly on cost and availability of hydrate equilibrium data. This is a model system with respect to the application of the gas hydrate as a means for natural gas storage and transportation. Methane is the most abundant component in natural gas and is the cleanest burning fuel among hydrocarbons and with the highest heating value. It is noted that produced natural gas also contains unwanted compounds such as hydrogen sulfide, carbon dioxide, and heavier hydrocarbons. Thus, one has to treat the gas first to meet the safety regulations before converting it into hydrate. Treated natural gas may still contain higher hydrocarbons such as ethane and propane. The simplified system avoids the complexities that may be encountered when working with gas mixtures [116]. Fortunately, fractionation during hydrate formation allows the gas phase to be split into a methane-rich stream and a heavier hydrocarbon one [117-119]. This enables the trapping of methane in hydrate after the fractionation. Methane hydrate formation in the presence of a LMGS is a multiphase (gas, aqueous liquid, non-aqueous liquid) crystallization process leading to formation of solid hydrate. This thesis concentrates on the kinetic and thermodynamic properties of gas hydrate at the macroscopic and microscopic level. More specifically, the objectives are:  18  1.  to determine the effect of the following parameters on the hydrate formation rate and conversion: (a) guest molecule(s) solubility in water; (b) non-aqueous liquid(s) wetting with ice particles; (c) gas diffusivity in non-aqueous liquid; and (d) temperature.  2.  to determine the rate of hydrate formation and conversion using liquid water or ice powder.  3.  to characterize the solid hydrate phase with respect to crystal structure and cage occupancy and determine the gas content.  4.  to determine the optimal conditions for gas storage in different sII hydrate systems and search for methods to increase methane content in sH hydrate.  5.  to gain insights on the gas hydrate formation from methane and a LMGS from a molecular perspective using molecular dynamics simulations.  1.6 Thesis Organization The basic information about gas hydrates is given in Chapter 1. This chapter also discusses the significance of gas hydrates towards human welfare and a variety of prospective applications involving gas hydrates. The current knowledge on hydrate research relevant to gas storage applications is also discussed. Chapter 2 reports the fluid phase equilibria relevant to sH hydrate systems at several pressures and temperatures. The concentrations of methane and/or LMGS in aqueous phase are determined. The material for this chapter is published. -  Robin Susilo, Judong Lee, Peter Englezos, Liquid-liquid equilibrium data of water with neohexane, methylcyclohexane, tert-butyl methyl ether, n-heptane  19  and vapor-liquid-liquid equilibrium with methane, Fluid Phase Equilibria, 231 (1), 20-26 (2005). Chapter 3 reports on the formation and decomposition of sH hydrate via Nuclear Magnetic Resonance (NMR) spectroscopy. The wetting of non-aqueous liquid with loose and packed ice particles are studied by micro-imaging NMR technique (MRI). The gas diffusivity in the liquid phase, the effect of temperature, and hydrate conversion rates from ice are also studied. An important recipe on how to synthesize sH hydrate is given. The material for this chapter is published. -  Robin Susilo, Igor L. Moudrakovski, John A. Ripmeester, Peter Englezos, Hydrate kinetics study in the presence of non-aqueous liquid by nuclear magnetic resonance spectroscopy and imaging, Journal of Physical Chemistry B, 110 (51), 25803-25909 (2006).  Chapter 4 reports the gas uptake rates of various sH hydrate systems grown from ice particles in a pressure vessel using the recipe suggested in Chapter 3. The hydrate conversion rates at various LMGS amount and pressures are compared to crystallization kinetics models. The material for this chapter is published. -  Robin Susilo, John A. Ripmeester, Peter Englezos, Methane Conversion Rate into Structure H Hydrate Crystals from Ice, AIChE Journal, 53 (9), 2451-2460 (2007).  Chapter 5 gives a complete solid-state analysis of the solid hydrate phase characterized by several independent measurements. The crystal structure, cage occupancy, and hydrate phase composition are reported. The material for this chapter is published.  20  -  Robin Susilo, John A. Ripmeester, Peter Englezos, Characterization of gas hydrates with PXRD, DSC, NMR and Raman Spectroscopy, Chemical Engineering Science, 62 (15), 3930-3939 (2007).  Chapter 6 provides correlations between methane content in sII hydrate and the hydrate stability via macroscopic modeling. The optimum condition to store methane in sII hydrate is suggested. The study is extended to look at the possibility of increasing the gas content in sH hydrate via molecular dynamics (MD) simulation. The material for this chapter is published. -  Robin Susilo, Saman Alavi, John A. Ripmeester, Peter Englezos, Tuning Methane Content in Gas Hydrates via Thermodynamics Modeling and Molecular Dynamics Simulation, Fluid Phase Equilibria, 263 (1), 6-17 (2008).  In Chapter 7 the dependence of methane occupancy on the nature of the LMGS and pressure are investigated via MD simulation. Moreover, the preference of methane molecules to occupy the small (512) or medium (435663) cages and the minimum cage occupancy required to maintain mechanical hydrate stability are examined. The material for this chapter has been submitted for publication in the Journal of Chemical Physics. -  Robin Susilo, Saman Alavi, John A. Ripmeester, Peter Englezos, Molecular Dynamics Study on Structure H Methane + Large Molecule Clathrate Hydrate, accepted for publication in Journal of Chemical Physics (March 21, 2008).  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[117] Uchida, T., Moriwaki, M., Takeya, S., Ikeda, I.Y., Ohmura, R., Nagao, J., Minagawa, H., Ebinuma, T., Narita, H., Gohara, K., Mae, S. AIChE J. 2004, 50 (2), 518-523. [118] Uchida, T.; Takeya, S.; Kamata, Y.; Ohmura, R.; Narita, H. Ind. Eng. Chem. Res. 2007, 46, 5080-5087. [119] Kumar, R.; Linga, P.; Moudrakovski, I.; Ripmeester, J.A.; Englezos, P. accepted for publication in AIChE J. (February 28, 2008).  30  CHAPTER-2 LIQUID-LIQUID EQUILIBRIUM OF WATER WITH NEOHEXANE, METHYLCYCLOHEXANE, TERT-BUTYL METHYL ETHER, N-HEPTANE AND VAPOR-LIQUID-LIQUID EQUILIBRIUM WITH METHANE1 2.1 Introduction It is well known that methane and water in the presence of neo-hexane or methylcyclohexane or tert-butyl methyl ether in water form a hexagonal hydrate structure (sH) instead of the cubic one (sI and/or sII) that methane forms with water alone [1]. Neohexane and the other substances are conveniently called Large-Molecule Guest Substances (LMGS) since they fit into the 20-faced cage (largest) of the structure H crystal [2]. The lower equilibrium pressure of sH hydrate than sI or sII hydrate has brought attention to many researchers in utilizing gas hydrate as a media for transportation and storage of natural gas [3]. Figure 2.1 shows that sH hydrate forms at a much lower pressure than the corresponding sI hydrate formation pressure [4-7]. For example, at 273.65 K sH hydrate forms at 1.17 MPa whereas sI forms at 2.76 MPa [7]. In a recent study, it was found that crystal growth is influenced by the amount of dissolved methane gas in the neohexane phase [8]. It was also found that the longer the induction time, the faster the rate of crystal growth due to higher saturation of gas in liquid. Thus, solubility of hydrate former in water plays an important role during the formation of structure H hydrate, as also suggested in other studies [9,10].  1  “A version of this chapter has been published. Susilo, R., Lee, J.-D. and Englezos, P., “Liquid-liquid equilibrium data of water with neohexane, methylcyclohexane, tert-butyl methyl ether, n-heptane and vapor-liquid-liquid equilibrium with methane”, Fluid Phase Equilibria, vol. 231 (1), 20-26, 2005.”  31  Pressure (MPa)  9 8  CH4-H2O, Adisasmito et al. (1991) CH4-H2O-TBME, Hutz and Englezos (1996)  7  CH4-H2O-MCH, Mehta and Sloan (1993)  6  CH4-H2O-NH, This work  CH4-H2O-NH, Hutz and Englezos (1996)  5 4 3 2 1 0 272  274  276  278  280  282  284  Temperature (K) Figure 2.1: Equilibrium hydrate formation conditions for sI and sH hydrates [7]. A generalized equation has been established to calculate the solubility of binary alkane-water systems [11]. The mutual solubility of hydrocarbon and water are known to depend on carbon number and temperature [12,13]. The effect of pressure is small but positive [14]. Tsonopoulos [13] extensively discussed and reviewed the mutual solubility of normal alkanes (C5-C16), alkylcyclohexanes (C6-C12), alkylbenzenes (C6-C12) and 1alkenes (C5-C12) in water. General equations based on thermodynamic analysis were presented. It was found that the solubility of hydrocarbon in water generally decreases steeply as the carbon number increases and decreases to a minimum at about 298 K before going back up again as the temperature increases. The solubility of water in hydrocarbons is insensitive to carbon number but increases with increasing temperature. In this work, the mutual solubilities of methyl-cyclohexane (MCH), tert-butyl methyl ether (TBME), neo-hexane (NH) and n-heptane (nC7) in water phase as well as their concentration distribution in the presence of methane gas (three-phase system) are  32  investigated. n-heptane is not a LMGS but methane hydrate formation in the presence of this hydrocarbon serves as a model hydrate forming system involving three fluid phases. The mutual solubility data are also compared to available experimental data as well as model based calculated values [11].  2.2 Experimental Procedure All chemicals used in the experiment are listed in Table 2.1. Extra dry methanol (water content less than 50 ppm) was used as a solvent for preparing the calibration standard solution. Table 2.1: Chemicals used in this work Chemical neohexane (NH) tert-butyl methyl ether (TBME) methyl-cyclohexane (MCH) n- heptane (nC7) methane (C1) water (W)  Certified purity  Supplier  99.0 % 99.8 % ≥ 99.0 % ≥ 99.5 % UHP grade Distilled and deionized  Aldrich Chemical, Co. Inc. Aldrich Chemical, Co. Inc. Aldrich Chemical, Co. Inc. Fluka Chemika Praxair Technology, Inc.  2.2.1 Liquid-Liquid Equilibrium (LLE) The mutual solubility experiments were done in a 7-ml clear glass vial with teflon septum for syringe injection. LMGS or n-heptane and water, 3-ml of each, were placed in the vial, mixed for several minutes and put inside the water bath at the desired temperature. The vial was allowed to stay in the water bath for at least 6 hours to make sure equilibrium has been reached. Our preliminary results showed that there was no change in the solubility measurement after 6 hours. Two phases formed with the non-  33  aqueous phase on top because of the lighter density. The analysis of the non-aqueous phase was done by injecting a sample to the gas chromatograph (GC). The GC was calibrated previously with standard solution that was prepared in the laboratory. The water phase was transferred into another clean vial before taking a sample for injection to the GC for analysis. All liquid injections were done with a 10 µl syringe, but only 1 µl was injected to the column.  2.2.2 Vapor-Liquid-Liquid Equilibrium (VLLE) A stainless steel vessel that was immersed in a temperature controlled bath was used to carry out the three phase equilibrium experiment. The cell has two circular viewing windows on the front and back, made of plexi glass. Mixing was accomplished by a magnetic bar that was coupled to a set of rotating magnets. A copper-constantan thermocouple (Omega, ±0.10K accuracy) and a Rosemount smart pressure transducers, model 3051 (Norpac controls, Vancouver, BC) were also inserted in the vessel to monitor the temperature and pressure changes over time. The apparatus is a modification of the one described elsewhere [15], shown in Figure 2.2. 80-ml of LMGS or n-heptane (nC7) and 80-ml distilled de-ionized water were injected into the cell through the water phase line at the bottom. Methane gas was supplied from the reservoir which was also immersed in the water bath to ensure constant temperature (not shown in Figure 2.2). The cell was flushed three times with the methane gas to remove any air that might be trapped inside the cell before adjusting the pressure inside the cell to the desired pressure. Experiments at three different pressures (0.12, 1.00, and 2.00 MPa) were conducted. Once the desired system temperature and pressure  34  were reached, the gas and solution were mixed for an hour to ensure equilibrium. Usually there were no changes in pressure and temperature within the first 10 minutes after mixing. The mixing was stopped after an hour to collect the samples. Gas phase sampling line  Hydrocarbon phase sampling line  A PC/DA WATER BATH  PI Thermocouple  GAS FEED LINE  GAS PHASE  HYDROCARBON PHASE  TEMPERATURE CONTROLLER  MIXER WATER PHASE  Water phase sampling line  Rotating Magnet  Figure 2.2: Experimental apparatus for the ternary system, ‘A’ is shown in Figure 2.3 Three sampling lines were installed in the vessel to collect the gas, water and nonaqueous phase for analysis. Each sampling line is connected with a needle valve at each end. A teflon septum was inserted into the nut after the needle valve so that a microsyringe can collect the sample for analysis. The gas sample was taken first by a 100-µl gas tight syringe and injected to GC. Then the non-aqueous phase was taken for analysis followed by the water phase. Care was taken to avoid erroneous measurements due to the existence of a dead volume of 15 mL arising from the ¼” (6.35 mm) tubing at the water phase sampling line as seen in Figure 2.2. The liquid from the dead volume was  35  discarded. At atmospheric conditions, the non-aqueous phase was collected by sucking the liquid with a 60-ml syringe and locking the sample inside a tube with a valve on both ends. A straight tee connection was installed between the two valves for taking the sample from the non-aqueous phase through the septum as seen Figure 2.3. All liquid samples were taken by a 10-µl syringe but only 1-µl was taken and injected to the GC for analysis. At higher pressures, no sucking was required to collect the sample. The liquid that was injected from each phase at high pressures was locked at the desired volume and injected to GC immediately for analysis. For the non-aqueous and water phase, only 1-µl of liquid was taken and locked in the syringe and 100-µl for the gas phase. 8" septum  A 1/8" SS tube  1/8" vinyl tube needle valve  60 ml syringe  Figure 2.3: Apparatus installed to collect the non-aqueous phase 2.2.3 Gas Chromatography analysis A Varian GC model CX-3400 with a Thermal Conductivity detector (TCD) and a Flame Ionization detector (FID) were used. The TCD with a packed column (Porapak-N from Alltech) was used to analyze the water phase and the FID with a split injector and a capillary column was used to analyze the non-aqueous phase for the binary system. Only the capillary column was used for the ternary system. The capillary column was a PORAPLOT-U supplied from Varian (25 m length, 0.32 mm ID, and 10 µm film thickness). Both columns ran under the same operating condition to speed up the analysis time for the binary system, which was at 180°C. During the analysis, the temperatures of 36  the injector, TCD, and FID were set at 200, 140, and 250°C respectively. For the ternary system, the temperature was set lower due to the presence of methane gas. Temperature programming was applied. The column temperature was set at 120°C for 5 minutes before raising it to 180°C at a rate of 20°C per min for the gas phase and the non-aqueous phase analysis. For the water phase, column temperature was set at 80°C for 7 minutes before raising it to 180°C with rate of 40°C per min. For the gas phase, gas standards were prepared in the laboratory. The procedure followed the method described by Uyanik and Tinkilic [16]. This method assumes that vapors of volatile substances can be treated as ideal gases under common laboratory conditions. Basically, the analyte is dissolved in a solvent (methanol) to prepare a gas standard in the ppm level concentration. The calculation on how much analyte has to be dissolved is given by Uyanik and Tinkilic [16]. Then a small amount of liquid mixture of this analyte and solvent is evaporated in the gas bulb which has been flushed with inert gas (extra dry Helium) under room temperature and atmospheric pressure. Finally, the gas mixture in the bulb at a known concentration in ppm level is injected into gas chromatograph (GC). The peak area generated from this GC is used as the calibration curve. For the non-aqueous and water phase analysis, the standard solution was prepared by adding a known amount of analyte into a 25-ml volumetric flask which contained extra dry methanol as the solvent (Fisher Scientific).  2.3 Results and Discussion All measurements reported here are the average values of two to three injections. Standard deviations are given in parenthesis and shown in each table.  37  2.3.1 Binary Liquid-Liquid Equilibrium The mutual solubility measurements together with other data reported in literature and calculated values from an existing model [11] are given in Tables 2.2 and 2.3. Table 2.2: LLE Data: Aqueous Phase Composition (mole fraction) Compound  Temp [K]  NH MCH TBME nC7 NH MCH TBME nC7 NH MCH TBME nC7 Note:  275.50  283.15  298.15  This work 7.7 (0.3) 4.0 (0.2) 12541 (209) 1.5 (0.3) 6.2 (0.3) 3.6 (0.3) 11878 (235) 0.3 (0.1) 4.9 (0.2) 3.0 (0.2) 8901 (74) 0.2 (0.1)  106 x Correlation [11] 4.7 3.0 0.6 4.2 2.8 0.5 3.7 2.6 0.5  Other ref. 8.2* [17] 16963* [18] 0.8* [17] [17] 5.0 2.9 [19] 8584 [18] 0.6 [17]  superscript * refers to data obtained at 273.15K. The numbers in parenthesis are the standard deviations.  Table 2.3: LLE Data: Non-Aqueous Phase Composition (mole fraction) Compound  Temp [K]  NH MCH TBME nC7 NH MCH TBME nC7 NH MCH TBME nC7 Note:  superscript deviation  275.50  283.15  298.15 *  This work 331 (15) 158 (7) 56976 (2130) 310 (8) 521 (22) 328 (14) 65579 (2452) 466 (16) 722 (30) 405 (14) 68596 (2565) 562 (24)  106 x Correlation [11] 224 163 210 330 238 305 672 471 605  Other ref. 238* [17] 55703* [18] 211* [17] 60589 [18] 624 [17] 470 [19] 62060 [18] 667 [17]  refers to data obtained at 273.15K. The numbers in parenthesis are the standard  38  The equation to calculate the solubility of hydrocarbon (NH, MCH, and nC7) in the water phase is given below ln x HC = ln x min + c3b[Tmin T + ln (T Tmin ) − 1]  (2.1)  where xHC is the solubility of hydrocarbon in water in mole fraction and T is the temperature in [K]. The value of constant c3 is 0.376 mol/cm3 [11]. The other parameters in equation (2.1) are given in Table 2.4. The solubility of hydrocarbon in water reaches a minimum (xmin) at around room temperature (Tmin) because the positive heat of cavity formation due to solvation cancels the negative heat of hydrophobic interaction which results a zero value for heat of solution. The equation (2.1) is satisfactory up to the three phase critical temperature (T3c) [20]. Table 2.4: Parameters used to calculate the hydrocarbon solubility in water using equation (2.1) [11] Compound  ln x min  b  Tmin  NH MCH nC7  -12.52 -12.85 -14.58  114.3 118.8 142.3  306 298 306  The solubility of water in the hydrocarbon phase, xw, is calculated using the equation below [11]: 13  ln xW = d1 + d 2 (1 Tr − 1) + d 3 (1 − Tr ) + d 4 (1 − Tr )  (2.2)  where Tr = T T o , T is the temperature of interest in [K] and To is an adjustable temperature that usually corresponds to the three phase critical temperature (T3c) [20]. The other parameters in equation (2.2) are adjustable parameters given in Table 2.5. Equation (2.2) can be used up to temperatures about 40 K below To.  39  Table 2.5: Parameters used to calculate the water solubility in hydrocarbon using equation (2.2) [8] Compound NH MCH nC7  d1  d2  d3  d4  To  -1.299 -0.203 -0.633  -6.468 -6.277 -6.177  -0.056 -1.935 -0.846  -5.005 -1.695 -3.372  484.4 545.3 524.2  In general, it was found that the solubility of LMGS and nC7 (non-aqueous liquid) in water decreases as the temperature increases from 275.5K to 298.15K. The solubility order is as follows: nC7 < MCH < NH < TBME. As seen, TBME is the most soluble and n-heptane the least soluble in water. According to Tsonopoulos [12], the solubility of hydrocarbon in water reaches the minimum at about 298K before it goes back up at higher temperature, but few data were available at temperatures below 298K. In this work, we confirm that the solubility of hydrocarbon at temperature below 298K increases with decreasing in temperature. The solubility of water in non-aqueous liquid phase increases as the temperature increases from 275.5K to 298.15K. This trend is the opposite from the solubility of non-aqueous liquid in water phase at the same temperature range. The heat of solution of water in hydrocarbon is always positive so that the solubility always increases with temperature [12]. It was found that water is the least soluble in MCH followed by nC7, NH, and TBME. The data obtained in this work agree well with the calculated values using the equation given by Maczynski et al. [11] as well as data from other references. The comparisons between all our experimental data and the correlation from equation (2.1) and (2.2) for the water/NH, water/MCH and water/n-C7 system are shown in Figures 2.4 to Figure 2.6 respectively.  40  9  Mole fraction of NH in water wich phase (xNH) x 106  18000  x_NH data  16000  x_NH f rom equation (2.1) x_w data  8  14000  x_w f rom equation (2.2)  7  12000  6  10000  5  8000  4  6000  3 2  4000  1  2000  0 270  290  310  330  350  370  Mole fraction of water in NH rich phase (xw) x 106  10  0 390  Temperature / K  Figure 2.4. LLE data of water-neohexane (NH) system and correlation (solid or dashed line) using equations (2.1) and (2.2).  10000  x_MCH data  9  x_MCH f rom equation (2.1)  9000  8  x_w experimental data  8000  7  x_w f rom equation (2.2)  7000  6  6000  5  5000  4  4000  3  3000  2  2000  1  1000  0 270  290  310  330  350  370  Mole fraction of water in MCH rich phase (xw) x 106  Mole fraction of MCH in water wich phase (xMCH) x 106  10  0 390  Temperature / K  Figure 2.5. LLE data of water-methylcyclohexane (MCH) system and correlation (solid or dashed line) using equations (2.1) and (2.2).  41  14000  x_nC7 data  1.8  x_nC7 f rom equation (2.1)  1.6  x_w data  1.4  x_w f rom equation (2.2)  12000 10000  1.2  8000  1.0 0.8  6000  0.6  4000  0.4  2000  0.2 0.0 270  290  310  330  350  370  Mole fraction of water in nC7 rich phase (xw) x 106  Mole fraction of nC7 in water wich phase (xMCH) x 106  2.0  0 390  Temperature / K  Figure 2.6. LLE data of water-n-heptane (nC7) system and correlation (solid or dashed line) using equations (2.1) and (2.2). As seen in the those figures the slope of solubility x with respect to temperature T based on our measured values has the same sign as the slope based on the correlations reported by Maczyski et al [11]. Our motivation to carry out the work was to obtain phase equilibrium data in order to interpret gas hydrate kinetic data that we observed. Thus, we did not carry out measurements above 298 K. In retrospect, it would have been interesting to see if our experimental data would indicate a minimum in the solubility of NH or MCH or nC7 at 298 K as the correlations suggest.  2.3.2 Vapor-Liquid-Liquid Equilibrium The three phase equilibrium experiments involving methane, water and NH, TBME, MCH, or nC7 were conducted at 275.5 K and three pressures (0.12, 1.00, and 2.00 MPa). The compositions of all phases given in mole fraction are shown in Table 2.6 to 2.9. The hydrate equilibrium pressure of C1-TBME-W system is 2.06 MPa [5] and C142  nC7-W system is 3.29 MPa [21], which are above 2.00 MPa. However, the equilibrium pressure at 275.5 K for C1-NH-W system is 1.53 MPa [5] and for C1-MCH-W system is 1.58 MPa [4]. Thus the pressure of 2.00 MPa represents metastable conditions. The formation of sH hydrate at that pressure was possible but not observed. The induction time is longer than the time required to complete the experiment. Table 2.6: VLLE measurements (106x) for the methane-NH-water system at 275.5 K Phase Vapor Non-aqueous Water Note:  Methane  Water  Neohexane  Pressure[MPa]  888050 (774) 982274 (813) 990380 (383) 17182 (1194) 32778 (1484) 50485 (1053) 45 (12) 381 (28) 635 (59)  5921 (363) 1112 (81) 565 (22) 229 (34) 278 (8) 197 (28) 999949 (14) 999603 (31) 999342 (68)  106029 (411) 16614 (732) 9056 (361) 982589 (1160) 966944 (1475) 949318 (1025) 6 (2) 15 (3) 23 (5)  0.12 1.00 2.00 0.12 1.00 2.00 0.12 1.00 2.00  The numbers in parenthesis are the standard deviations.  Table 2.7: VLLE measurements (106x) for the methane-TBME-water system at 275.5K Phase Vapor Non-aqueous Water Note:  Methane  Water  TBME  Pressure[MPa]  881191 (16616) 981540 (2988) 986334 (796) 17151 (841) 23970 (547) 69140 (5050) 58 (6) 443 (21) 690 (34)  7417 (316) 782 (115) 707 (61) 73304 (4854) 61392 (4812) 63440 (5007) 996590 (84) 995295 (339) 994286 (435)  111392 (16300) 17678 (2873) 12959 (735) 909545 (5695) 914637 (5359) 867419 (10057) 3352 (90) 4262 (318) 5024 (406)  0.12 1.00 2.00 0.12 1.00 2.00 0.12 1.00 2.00  The numbers in parenthesis are the standard deviations.  The gas phase composition of non-aqueous liquids (NALs) and water in all four systems were found to decrease as the pressure increases. The solubility of methane in the  43  non-aqueous phase increases as the pressure increases but the water content remains practically constant. The methane concentration in non-aqueous phase increases in the order of: NH < TBME < nC7 < MCH. This trend implies that the methane content of the MCH-rich phase before the hydrate nucleation point is the highest. In the water phase, the solubility of NALs and methane increases with pressure. Table 2.8: VLLE measurements (106x) for the methane-MCH-water system at 275.5K Phase Vapor  Non-aqueous  Water Note:  Methane  Water  MCH  Pressure[MPa]  963407 (3129) 991842 (390) 993516 (214) 995508 (217) 18701 (1505) 102245 (2695) 110203 (7535) 149582 (8115) 37 (10) 265 (22) 502 (10) 779 (28)  7148 (154) 1735 (145) 1108 (113) 964 (65) 503 (32) 534 (42) 839 (103) 3421 (183) 999960 (1) 999727 (3) 999483 (57) 999201 (100)  29446 (3283) 6423 (245) 5376 (101) 3528 (152) 980797 (1537) 897221 (2737) 888958 (7432) 846996 (8298) 3 (1) 8 (2) 14 (1) 20 (2)  0.12 1.00 2.00 3.00 0.12 1.00 2.00 3.00 0.12 1.00 2.00 3.00  The numbers in parenthesis are the standard deviations.  Table 2.9: VLLE measurements (106x) for the methane-nC7-water system at 275.5K Phase Vapor Non-aqueous Water Note:  Methane  Water  Heptane  Pressure[MPa]  963987 (1230) 993456 (86) 994973 (150) 15111 (1045) 27014 (3322) 76446 (6872) 47 (9) 304 (33) 523 (43)  6800 (81) 1315 (102) 737 (3) 844 (20) 590 (20) 632 (26) 999953 (1) 999692 (1) 999466 (11)  29214 (1149) 5229 (16) 4291 (148) 984045 (1025) 972396 (3302) 922922 (6847) 1 (1) 4 (1) 11 (1)  0.12 1.00 2.00 0.12 1.00 2.00 0.12 1.00 2.00  The numbers in parenthesis are the standard deviations.  44  For the C1-MCH-W and C1-nC7-W system, the vapour composition of MCH and nC7 was found to be lower than C1-NH-W or C1-TBME-W system. This is because the volatilities of MCH and nC7 are less than NH and TBME. The vapour pressures of MCH and nC7 at 275.5K are 1.9 kPa and 1.7 kPa whereas the vapour pressures of NH and TBME are 16.4 kPa and 12.2 kPa respectively. The boiling points of MCH (101°C) and nC7 (98°C) are also higher than NH (50°C) and TBME (55°C). Based on our measurements TBME and water are the most mutually soluble. It is noted that TBME has been found to be best LMGS candidate for sH hydrate formation because the induction time was shortest and the hydrate growth rate was fastest [2]. Lee et al. [7] measured the induction time as well as the hydrate growth rate and found out that the rate of hydrate growth with TBME is the fastest followed by NH and MCH. However, there are two potential drawbacks. Although hydrate formation kinetics of C1TBME-W system is the fastest, the vapour composition of TBME is quite significant. The implication is that the amount of TBME needed as the LMGS would be more to make up the loss due to its volatility. Moreover, the equilibrium pressure for C1-TBME-W system is higher than the other two LMGS (MCH or NH). The Krichevsky and Kasarnovsky equation was employed to correlate the methane solubility data in the water phase, as given below [22]. ∞  (   f2  v 2 P − P1S   ln  = ln (H 2,1 ) + RT  x2   )  (2.3)  where f2 is the fugacity of solute gas in the vapor phase, x2 is the mole fraction of solute in the water phase, P is the total pressure, P1S is the partial saturation pressure of the water, which is assumed negligible in comparison to P. R is the gas constant, T is the  45  temperature, H2,1 is the Henry constant and v2∞ is the partial molar volume of the gas at infinite dilution. The fugacity was calculated by using the Peng-Robinson equation of state [23]. As seen in Figure 2.7 the data are correlated successfully with equation (2.3). 23.0 22.5  ln (f2/x2) [ln Pa]  22.0 21.5 MCH  21.0  n-Heptane nH  20.5  TBME Linear (MCH)  20.0  Linear (n-Heptane) Linear (nH)  19.5  Linear (TBME)  19.0 0  0.2  0.4  0.6  0.8  1  1.2  P/RT [mol/L]  Figure 2.7: Krichevsky and Kasarnovsky plot at 275.5 K  2.4 Conclusions Non aqueous-aqueous liquid equilibrium (LLE) data at atmospheric pressure and at 275.5, 283.15, and 298.15 K were obtained. The non-aqueous liquid was neo-hexane (NH), tert-butyl methyl ether (TBME), methyl-cyclohexane (MCH), or n-heptane (nC7). TBME was found to be the most soluble in water followed by NH, MCH, and nC7. The solubility of the NAL in water was found to decrease as the temperature increases whereas the solubility of water in the non-aqueous liquid phase increases. The distribution of methane in the two liquid phases was also measured at 275.5 K and 0.12,  46  1.00, and 2.00 MPa. Methane is highly soluble in the non-aqueous phase and its concentration increases with pressure. The solubility of methane and NALs in the water phase increases proportionally with pressure. Finally, the solubility of methane in water was found to follow Henry’s law.  47  2.5 References [1]  Ripmeester, J. A.; Tse, J., S.; Ratcliffe, C. I.; Powell, B.M. Nature 1987, 325, 135-136.  [2]  Tsuji, H.; Ohmura, R.; Mori, Y.H. Energy & Fuels 2004, 18, 418-424.  [3]  Khokhar, A.A.; Gudmundssond, J.S.; Sloan, E.D. Fluid Phase Equilibria 1998, 150-151, 383-392.  [4]  Metha, A. P; Sloan E.D.Jr. J. Chem. Eng. Data, 1993, 38, 580-582.  [5]  Hütz, U.; Englezos, P. Fluid Phase Equilibria 1996, 117, 178-185.  [6]  Adisasmito, S.; Frank, R. J.; Sloan, E. D. Jr. Chem. Eng. Data 1991, 36, 68-71.  [7]  Lee, J.D.; Susilo, R.; Englezos, P. Energy & Fuels 2005, 19, 1008-1015.  [8]  Servio, P.; Englezos, P. J. Cryst. Growth 2003, 3 (1), 61-66.  [9]  Mooijer-van den Heuvel, M.M.; Peters, C.J. Proc. 4th Int. Conf. Gas Hydrates  2002, 301-306. [10]  Ohmura, R.; Kashiwazaki, S.; Shiota, S.; Tsuji, H.; Mori, Y.M. Energy & Fuels  2002, 16, 1141-1147. [11]  Maczynski, A.; Goglowska, B.W.; Goral, M. J. Phys. Chem. Ref. Data 2004, 33 (2), 549-577.  [12]  Tsonopoulos, C. Fluid Phase Equilibria 1999, 156, 21-33.  [13]  Tsonopoulos, C. Fluid Phase Equilibria 2001, 186, 185-206.  [14]  Bradley, R.S.; Drew, M.J.; Munro, G.M. High Temp – High Pres. 1973, 5, 169.  [15]  Englezos, P.; Ngan, Y.T. Fluid Phase Equilibria 1994, 92, 271-288.  [16]  Uyanik, A.; Tinkilic, A. Chemical Educator 1999, 4, 141-143.  [17]  Polak, J.; Lu, B.C.-Y. Canadian Journal of Chemistry 1973, 51, 4018-4023.  48  [18]  Stephenson, R.M. J. Chem. Eng. Data 1972, 37, 80-95.  [19]  Price, L.C. Am. Assoc. Pet. Geol. 1976, 60, 213.  [20]  Economou, I.G.; Heidman, J.L., Tsonopoulos, C.; Wilson, G.M AIChE J. 1997, 43, 535.  [21]  Sloan, E. D. Jr. Clathrate Hydrates of Natural Gasses 1998, 2nd edition, Marcel Dekker, New York.  [22]  Lekvam, K.; Bishnoi, P.R. Fluid Phase Equilibria 1997, 131, 297-309.  [23]  Elliot, J.R. Jr.; Lira, C.T. Introductory Chemical Engineering Thermodynamics, Prentice-Hall, Upper Saddle River, New Jersey, 1999.  49  CHAPTER-3 HYDRATE KINETICS STUDY IN THE PRESENCE OF NON-AQUEOUS LIQUID BY NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY AND IMAGING2 3.1 Introduction Gas hydrate formation being a crystallization process is characterized by nucleation followed by growth and agglomeration. Gas hydrate kinetics is concerned with the rate at which the phase change occurs and the identification of the factors affecting it. The rate of nucleation e.g. number of hydrate crystal nuclei formed per unit time per unit volume is an extremely difficult measurement and to date there are no data reported. On the other hand the induction time marking the onset of crystallization is easily obtained experimentally. Gas hydrate kinetics studies have been carried out primarily through gas uptake measurements during which special care must be paid to the hydrodynamic conditions in the hydrate formation vessel [1]. The formation of sH hydrate rate with methane as guest substance along with neohexane (NH), tert-butyl methyl ether (TBME) and methyl-cyclohexane (MCH) as the LMGS was reported [1,2]. By employing the gas uptake experimental technique, the kinetics of structure H hydrate formation at a pressure ranging from 0.63 to 1.5 MPa above the hydrate equilibrium pressure were studied in Dr. Englezos’ laboratory at UBC [1]. The results of the kinetic measurements indicated that the rate of hydrate formation 2  “A version of this chapter has been published. Susilo, R., Moudrakovski, I.L., Ripmeester, J.A. and Englezos, P., “Hydrate Kinetics Study in the Presence of Non-Aqueous Liquid by Nuclear Magnetic Resonance Spectroscopy and Imaging”, Journal of Physical Chemistry B, vol. 110 (51), 25803-25809, 2006.”  50  depends on the magnitude of the driving force and the type of LMGS. The difference between the experimental pressure and hydrate equilibrium pressure is considered as the driving force. The correlations of the formation rate and the induction time with the driving force are shown in Figure 3.1. Although sH hydrate forms at a much lower pressure than the corresponding sI hydrate, the induction time is larger. It is seen from Figure 3.1 that the induction time is inversely proportional to the driving force but the  Rate of hydrate formation (mol/hr)  correlation is weak as expected due to the random nature of the nucleation process.  0.3  CH4-TBME-H2O  0.2  CH4-H2O 0.1  CH4-NH-H2O CH4-MCH-H2O  0.0  CH4-H2O  Induction time (min)  600  CH4-H2O-NH CH4-H2O-TBME CH4-H2O-MCH  400  200  0 0.3  0.6  0.9  1.2  1.5  1.8  Driving force (MPa)  Figure 3.1: Rates of hydrate formation and induction times versus driving force [1].  51  It was also noticed that the rate of hydrate formation is closely related to the mutual solubility of water and LMGS. The hydrate formation rate was the fastest when TBME was used, slower with NH and slowest with MCH. Furthermore, the rate of gas consumption in the hydrate formation with the TBME system is almost three times faster than that of the pure methane-water system at the same driving force. In the hydrate decomposition experiments, the decomposition rate with TBME as LMGS was also faster than the other two systems. The results of gas phase analysis showed that NH was more abundant in the gas phase than the other two LMGS during hydrate formation/ decomposition experiments. It should be noted that the kinetics through gas uptake measurements are in reality “average kinetics” over the whole sample because the conversion to hydrate is quite an inhomogeneous process and that the observation of gradual conversion in bulk samples only arises as a result of averaging over many local environments [3]. The question is how these “bulk” kinetics are related to kinetics obtained with microscopic techniques like NMR measurements. More specifically, how the intermolecular interactions may explain the results obtained from bulk measurements. The objective of the present study is to monitor the kinetics of sH methane hydrate formation involving the above mentioned LMGS at the microscopic level. This will enable a direct comparison with the previously reported macroscopic kinetic data from Lee et al. [1] as well as from Mori’s group [2]. It is noted that microscopic techniques to study hydrates have been carried out, but were restricted to simpler gasliquid water or gas-ice systems using Raman or NMR spectroscopy [4-6]. Hydrate kinetic studies reported in the literature using NMR spectroscopy have been limited to  52  129  Xe or  13  C NMR. Recently  19  F NMR was also employed to study the guest dynamics in  clathrates hydrate [7]. The low sensitivity of xenon, due mainly to long spin-lattice relaxation times, can be overcome by using hyper-polarized xenon [8]. Spectroscopy with enriched 13C was used in the kinetic study of methane-propane hydrate [5]. In this study, proton (1H) and deuterium (2H) NMR spectra were employed to distinguish the spectral contributions from LMGS and methane. Protons are abundant, have a high gyromagnetic ratio, and usually have short relaxation times so that short acquisition times can be achieved. Due to the small chemical shift range of protons (between -1 and 12 ppm), the identification of components in a multi-component system is generally difficult unless the signals are sharp so that chemically inequivalent protons can be resolved. Hence, deuterated-methane was used to separate the signal of methane from that of the non-aqueous liquid. The quantification of the broad contributions from the solid phase and the sharp contributions from the gas/liquid phase is then achievable without interference from other components. This work will be the first attempt to monitor structure H hydrate growth and decomposition kinetics using NMR spectroscopy. In addition, the effect of a non aqueous liquid (n-heptane) that does not participate in hydrate formation will be studied. Ice is chosen instead of liquid water to significantly reduce the waiting period due to induction time. Hydrate formed from liquid water without mixing requires a very long time for nucleation. The rate of methane hydrate growth, decomposition and the diffusion in NAL were monitored by deuterium (2H) Nuclear Magnetic Resonance (NMR) spectroscopy. The distribution of LMGS between ice particles was also observed by using 1H microimaging NMR.  53  3.2 Experimental Procedure The kinetics experiments were performed on a Bruker DSX 400 NMR instrument at the NMR facility located at the National Research Council of Canada (NRC), Ottawa, Ontario. A custom designed static sample 5 mm NMR probe for handling pressures up to ~ 350 bars was employed. The probe is connected to a gas feed line equipped with a pressure gauge. The temperature during each experiment was controlled by a Bruker BVT 3000 temperature control unit. The 1H and 2H NMR spectra were calibrated with a measured quantity of a mixture of H2O/D2O of known concentration at 298 K. The chemical shift of water was assigned to be 4.7 ppm. The probe was cooled before loading the ice and LMGS. Hydrates were formed from ~0.15 g of fresh ground ice particles loaded and packed into the NMR cell plus excess of LMGS. The zero time of the measurements was set when the cell was pressurized with 99%-deuterated methane (CD4). 1  H and 2H NMR spectra were recorded every 5 minutes for 20 hours. Spectra  were acquired with 16 scans and 3 s delay time. Spectra obtained from the gas and liquid phase appeared as sharp Lorentzian lines, whereas those from the solid phase appeared as broad Gaussian lines. Hence, the amount of methane in the gas/liquid phase and the solid phase can be quantified. Unfortunately, 1H NMR spectra are not able to distinguish the broad peaks from ice and LMGS in the solid hydrate phase as the nuclear dipolar broadening is much larger than the chemical shift range for 1H. However, the 2H NMR spectra took the form of sharp and broad peaks, which correspond to methane in the gas+ LMGS phases and the hydrate phase. The methane in the gas+LMGS phases appears as two sharp peaks which are very close to each other and hence are considered as one sharp  54  peak. The spectra were then analyzed with ‘dmfit’, a program provided by Massiot et al. (2002) for analysis of solid-state NMR spectra [9]. The distribution of LMGS between ice particles was also observed using the 1H micro-imaging NMR technique. This experiment was performed on a Bruker Avance 200 Spectrometer. Multi-slice spin-echo pulse sequences with Gaussian selective pulses were employed. In most experiments, three slices of 500- m thickness with a separation of 2 mm were acquired simultaneously in planes parallel to the axis of the cell. The 128 × 128 acquisition matrix with eight scans was accumulated to obtain good signal-to-noise ratio. The experiments were carried out in a cell capable of handling pressures up to ~350 bar connected to a high-pressure handling system. The experimental arrangement is described in detail elsewhere [3].  3.3 Results and Discussion The evolution of a typical 2H NMR spectrum for the Ice + Neohexane (NH) + CD4 system during hydrate formation at 253K and ~4.5 MPa over a 20 hour period is shown in Figure 3.2. The spectra appear as a sequence of sharp Lorenzian lines after the cell is pressurized at time t = 0, which corresponds to deuterated methane in the gas+LMGS phases. After the induction period, broad lines from methane-d4 trapped in the hydrate cages appear as shoulders on the sharp lines as ice is transformed into the solid hydrate phase. Due to the broad spectral contributions of the solid phase, the amplitude of the hydrate phase signal is much lower than that of the gas+LMGS phases. Hence the induction time and the early stages of hydrate growth are not so clearly visible in Figure 3.2, but the broad peak becomes evident as more hydrate is formed with time.  55  Ten spectra were selected and shown as the inset in Figure 3.2 to better visualize the growth of broad peaks due to hydrate formation. t = 20 hrs  Experimental time [hours]  t=0  20 15 10 5 0  Figure 3.2: Deuterium (2H) NMR spectra evolution of Ice+Neohexane+CD4 at 253K and ~4.5 MPa for 20 hours. The inset shows the acquired spectra at 0, 0.5, 1, 2, 3, 4, 6, 10, 15, 20 hours.  56  The areas below the peaks which correspond to the quantity of methane in the gas+NAL phases and the solid phase are then separated. Integration using ‘dmfit’ program gives the corresponding areas. The area is considered the intensity and is normalized to the maximum value [8]. The normalized intensity for the hydrate phase and the gas+NAL phase are shown in Figures 3.3 and 3.4 respectively.  3.3.1 Methane growth in the hydrate phase As seen in Figure 3.3, the amount of methane in the hydrate phase increases during the 20 hour period. An induction time was observed for NH (<60 min), nC7 (~2 hrs), and the MCH system (~2 hrs). No induction time was observed for the TBME system. Hydrate generally grows relatively quickly for the first ~5 hours before it slows down due to the formation of a hydrate film on the surface which hinders further contact between the ice, methane, and LMGS. The kinetics become slower with nC7 because nC7 does not form hydrate and its presence only creates a mass transfer resistance for the formation of sI hydrate. The hydrate growth rate with TBME is the largest followed by NH, and MCH. This trend is exactly what was observed in gas uptake measurements in a well-mixed semi-batch reactor [1] and spray system [2]. It is interesting to note that after the five hour period sI methane hydrate formation rate is the highest due to the accessibility of both cages to methane (ice-CD4 system). This indicates that more methane goes into sI hydrate compared to sH. The methane contents in sI and sH hydrates can be calculated from the cage occupancy values and the hydrate unit cell volume. If all accessible cages for methane are fully occupied, then the methane content at standard conditions (1 atm pressure and room temperature)  57  are ~172 v/v (gas/hydrate) and ~143 v/v for sI and sH hydrate respectively. It is obvious that the methane content in sI hydrate is higher than sH unless methane can fit into the large cage in sH, which has never been reported.  1.00 Ice-TBME-CD4 Ice-CD4 Ice-NH-CD4 Ice-MCH-CD4 Ice-nC7-CD4  Intensity  0.80  0.60  0.40  0.20  0.00 0  200  400  600  800  1000  1200  Time [min]  Figure 3.3: Normalized intensity of methane growth in the solid hydrate phase at 253K and ~4.5MPa.  3.3.2  Methane diffusion in the non-aqueous liquid (NAL) phase (LMGS or n-heptanerich liquid phase)  As seen in Figure 3.4, the quantity of methane in the gas+non-aqueous liquid phase increases during the first ~3 hours (except for the methyl-cyclohexane/MCH system) before it reaches a saturation level. After the NAL phase is saturated with methane, the intensity stays constant for some time before it drops slowly due to hydrate formation indicated by a pressure drop. It is important to note that methane diffusion in the NAL phase and hydrate formation may occur simultaneously. Thus, the methane intensity from  58  the gas+NAL phases corresponds to the amount of methane between that transferred by diffusion to the NAL phase and that consumed for hydrate formation. It is clearly seen from Figure 3.4 that methane diffuses relatively faster in NH and TBME, a little slower in nC7 and the slowest in MCH. Methane diffusion into the NAL phase appears to be faster than hydrate growth in most cases, as intensity continues to increase up to a saturation level. A “bump” in the rate was observed for the NH system for a short period after the nucleation (30 min).  1.00  Intensity  0.80  0.60  0.40 Ice-CD4 Ice-TBME-CD4 Ice-NH-CD4 Ice-nC7-CD4 Ice-MCH-CD4  0.20  0.00 0  200  400  600  800  1000  1200  Time [min]  Figure 3.4: Normalized intensity evolution of methane in the gas and dissolved in nonaqueous liquid phase at 253K and ~4.5MPa.  It is also interesting to investigate whether hydrate formation rates can be correlated with the methane concentration in the LMGS phase. As discussed earlier the hydrate formation rates correlates with the solubility of LMGS in water [1,10]. Methane solubilities in the NAL phase are within the same order of magnitude and found to increase with pressure [10]. Thus, the observed rates do not correlate with solubility of  59  methane in the NAL phase. Interestingly, methane solubility in MCH-rich phase is the highest among all LMGS studied. In the absence of NAL, gas diffusion was also observed, which suggests the presence of a gas film. A concentration gradient around the ice particles may exist so that the methane gas has to diffuse through the gas film until the gradient disappears. This is probably due to the presence of air trapped inside the NMR cell which was not evacuated prior to pressurization. The gas near the ice surface preferably goes into the hydrate phase which occurs relatively faster in the first 3-5 hours and maintains the concentration gradient for a while. This observation revealed that the methane gas might not necessarily be in contact with the ice particles instantaneously in the absence of a NAL phase.  3.3.3  Hydrate conversion from fresh ground ice powder The intensity values were calibrated so that the amount of methane in the hydrate  phase can be calculated. Hence, the conversion of ice into hydrate can also be calculated by assuming that the cage occupancy of LMGS in the large cage is 100% and the methane occupancy is 80% in both the small and medium cages of sH hydrate. Such occupancy values have been reported from  13  C solid-state NMR [11] and single crystal  X-Ray diffraction [12]. The methane occupancy in this study was not determined directly because of the very small amount of hydrate formed and difficulties in recovering the hydrate for 13C solid state NMR analysis. It is important to note that the occupancy values vary with operating conditions and hence the calculated conversion is strongly dependent on the methane occupancy. If the methane occupancy in the hydrate phase is less than  60  80%, then the actual conversion is higher than the reported value in this study. Higher methane occupancy lowers the conversion. 40  Hydrate Conversion [%]  35 30  Ice-TBME-CD4 Ice-NH-CD4 Ice-CD4 Ice-MCH-CD4 Ice-nC7-CD4  25 20 15 10 5 0 0  200  400  600  800  1000  1200  Time [min]  Figure 3.5: Ice to hydrate conversion obtained at 253K and ~4.5MPa. Hydrate conversion was calculated by assuming methane occupancy of 80% in the small and large cage in sH hydrate.  The conversion of ice into hydrate for all systems investigated is shown in Figure 3.5. As seen, the conversion is far below 100%. The maximum conversion achieved for sH hydrate was for the TBME system, which had ~35% conversion followed by NH (~19%) and MCH (~16%). For sI hydrate, the conversion was lower (~18% and ~8% without and with nC7). It is important to note that in sI hydrate methane can also fill the large cage so that its content is higher than in sH hydrate. Hence the actual conversion of ice into hydrate with the same methane content depends on the hydrate structure, which will be less for sI hydrate. The lower conversion of methane in sI hydrate is also due to a lower driving force because sI methane hydrate forms at higher pressure than sH. The  61  hydrate conversion obtained in this study for sI methane hydrate without nC7 is comparable to the kinetics results obtained from neutron diffraction technique [13,14].  3.3.4  Effect of thermal ramping on hydrate formation In the experiments with the NH and MCH, the temperature was ramped to a point  above the ice point (274 K) after the initial hydrate formation period (20 hours) at 253 K to see if the un-reacted ice can be further converted into hydrate by melting. The temperature reached a new steady state within a minute on going from 253K to 274K.  Hydrate Conversion [%]  60 Ice-TBME-CD4 Ice-NH-CD4 Ice-CD4 Ice-MCH-CD4 Ice-nC7-CD4  50 40 30  T = 274 K  T = 253 K 20 10 0 0  300  600  900  1200  1500  1800  2100  2400  Time [min]  Figure 3.6: Ice to hydrate conversion obtained with temperature ramping to 274K after 20 hours isothermal at 253K. As seen from Figure 3.6 further conversion into hydrate was indeed achieved. The additional hydrate growth was instantaneous for the NH and MCH systems. This is probably due to over-saturation of the LMGS with methane and because better contact between water, LMGS, and methane was achieved. The solubility of methane in LMGS  62  is higher at lower temperature so that the excess of methane upon melting of the ice can dissolve in water and convert to hydrate without limitation from gas diffusion into the NAL phase to reach the melted ice. The melting of ice to water inside the hydrate shell causes a volume reduction and pressure drop inside the hydrate shell. This may decompose the hydrate slightly on the inside of the shell and may well crack the hydrate film. Hence, more gas can diffuse into the inside of hydrate shell because of the pressure gradient, creating new contact between water-LMGS and methane. The hydrate film may act to seed new hydrate which then allows rapid and instantaneous hydrate growth. The heat released from hydrate formation can also be balanced by the heat absorbed from the melting of ice. This may enhance the conversion. This phenomenon was well-documented from a 1H micro-imaging study of methane reacting with ice particles [15]. We also note that the continuous ice/water transformation into hydrate inside a hydrate-coated particle requires an expansion in volume because of the different densities of the various phases, which is approximately double the volume reduction from ice melting to water. This expansion may occur gradually or suddenly by rupture of the hydrate shell. The former is typically seen in the first stage of rapid hydrate growth after melting the ice. The conversion of hydrate was limited to ~40% and no further significant hydrate growth was observed afterward, likely because of pressure build-up inside the ice shell as ice converted to hydrate. However, an unexpected hydrate growth was observed in one experiment with the NH system at ~2000 minutes and further conversion was achieved quickly up to ~58% (See Figure 3.6). This phenomenon was probably due to rupture of the hydrate layer because of internal pressure creating new access sites for the  63  occluded water to be converted into hydrate. It is noted that similar behavior was observed in the gas uptake experiments, but with MCH [1]. Temperature ramping was not performed with the TBME system because the hydrate kinetics was already the fastest and further hydrate conversion was limited by tight ice packing at about 40% as discussed later. In a separate hydrate formation experiment from gas uptake in a pressure vessel with loosely packed ice, the instantaneous hydrate growth from TBME system was not seen, unlike for the NH or MCH systems. The melting of ice does indeed enhance more transformation into hydrate. However, it occurs at a slower rate than for the NH or MCH systems [16].  3.3.5  Hydrate decomposition The decomposition of the hydrate was also monitored for a three hour period for  the systems with NH and TBME by lowering the pressure to atmospheric. As seen in Figure 3.7, the hydrate decomposed very quickly during the first hour especially with TBME as guest. A small amount of residual methane, corresponding to methane dissolved in the NAL phase, was also seen (not shown in the figure). It was also observed that the hydrate with TBME decomposed completely. The system with NH did not dissociate completely in three hours. A very slow decomposition rate was observed after the initial fast period. This is probably due to larger hydrate content of the NH system (~60%) as compared to TBME (~35%) so some hydrate in the core may be isolated by the formation of ice film that preserves it longer. However it is clearly seen in Figure 3.8 that the decomposition rate of the TBME system is faster than that of the NH system.  64  70  Hydrate content [%]  60  NH-CD4 hydrate TBME-CD4 hydrate  50 40 30 20 10 0 0  30  60  90  120  150  180  Time [min]  Figure 3.7: Hydrate decomposition obtained at 253K and 1 atm for NH and MCH system  It is also noted that the so called ‘self-preservation effect’ was not seen in this study [17]. The majority of the hydrate dissociates in less than an hour after the pressure is released. Hence storing and transporting sH hydrates containing methane below the hydrate phase equilibrium at 253K and atmospheric conditions are not possible without reducing the hydrate surface exposure to the atmosphere. This kind of hydrate has to be densely packed to have an ice coating on the outside of the hydrate that limits decomposition by control of the heat flow to hydrate. In one experiment, the stability of hydrate formed from memory ice in the NH system was also studied at 253K and ~0.5 MPa, as shown in Figure 3.8. Memory ice is defined as ice that has experienced hydrate formation and decomposition. The pressure and temperature conditions are slightly above the equilibrium conditions for the methaneNH sH hydrate. The equilibrium hydrate pressure at 253K is approximately 0.48 MPa  65  (obtained by fitting the data reported by Ohmura et al. [18]). As seen in Figure 3.8, the hydrate was relatively stable as it decomposed slowly under those conditions with only ~9% of its content decomposed in 15 hours. This indicates that storing hydrate for longer time requires sufficient pressure above the hydrate phase equilibrium line. 80  Hydrate content [%]  70 60 50 40 30 20 10 0 0  200  400  600  800  1000  Time [min]  Figure 3.8: Neohexane-CD4 mixed hydrates stability at 253K and ~0.5 MPa. The equilibrium pressure at 253K is ~0.48 MPa [18].  3.3.6  Hydrate reformation In one experiment with neohexane (NH), hydrate was reformed using ice that had  experienced hydrate formation. This reformation experiment followed the previous experiment reported above for the NH system, which had formed hydrate but decomposed by releasing all of the gas at 253K for 3 hours. The reformation of hydrate from ‘memory ice’ proved to speed up the kinetics, as seen in Figure 3.9. Memory effects also were reported on Xenon hydrate reformation experiments [8]. It is unclear whether  66  residual hydrate structure still exists in ice particles. However one thing that is certain is that the system has been saturated with methane so even though small amount of methane is left dissolved in LMGS or even in the hydrate phase the effect on hydrate growth seems to be significant.  Hydrate Conversion [%]  30 25 20  Memory Ice-NH-CD4 Fresh Ice-NH-CD4  15 10 5 0 0  30  60  90  120  150  180  210  240  270  300  Time [min]  Figure 3.9: Hydrate reformation (memory ice) obtained at 253K and ~4.5MPa after decomposing the previously formed hydrate (fresh ice) by releasing all the gas and kept at atmospheric pressure for 3 hours.  3.3.7  Ice-NAL wetting properties The degree of wetting of the ice by the LMGS may play an important role on  hydrate formation, especially in a non-stirred system. For this purpose, 1H micro-imaging NMR was employed to image the proton density in the ice/LMGS/methane system. The ice 1H NMR resonance line is extremely broad because of strong dipolar couplings, whereas 1H in LMGS liquids has very sharp resonances as the dipolar couplings are averaged completely by molecular motion. Because of instrumental limitations, the ice  67  1  Hs are invisible in the standard micro-imaging experiment, hence the liquid LMGS 1H  spin density can be observed selectively during hydrate formation. 1H spin density from liquids appears as a bright area in the image, whereas ice and the hydrate are invisible (dark).  Figure 3.10: Distribution of LMGSs and diffusion of LMGS between ice particles observed by proton (1H) micro-imaging NMR for ice with MCH and TBME system. As seen in Figure 3.10, the distribution of TBME is reasonably homogeneous, in contrast to that of NH and MCH. The image shows that TBME fills the empty spaces between ice particles whereas the interaction/contact of NH and MCH with the ice particles is poor. Figure 3.10 shows that after 20 hours without pressurization some ice particles are still isolated from MCH. NH and MCH preferably stay on the top of the sample or near the wall of the sample tube (not clearly seen because the image is smaller than the actual cell size). It appears that TBME has a strong affinity towards ice that will play an important role in speeding up the formation kinetics, unlike the other NALs that  68  are hydrophobic. The measurements on liquid-liquid equilibria between NAL and water also indicated strong affinity of TBME for water [10]. A theory that correlates surface wetting and solubility has been reported [19]. A Hansen solubility parameter (HSP) describes three major types of cohesive energy in volatile liquids due to non-polar dispersion interactions, permanent dipole-permanent dipole interactions, and hydrogen bonding interactions. A combination of each type allows the characterization and prediction of preferable interaction in terms of solubility, surfaces (wetting), and diffusion among the materials involved. A liquid with low cohesion energy spreads spontaneously on a surface with no contact angle and hence better wetting properties. The relative energy difference (RED number) between the solute and solvent indicate the affinity and hence the solubility. A lower RED number (less than one) indicates stronger affinity and hence higher solubility. TBME must fall into the lower cohesion energy with low RED number category (similar to ice because both are polar) so that it has better wetting with ice than NH or MCH system. The differences in LMGS wetting towards ice may explain further the observed phenomena during the hydrate kinetic measurements. Hydrate formation rate in the TBME system is the fastest because TBME wets ice more effectively compared to NH and MCH. Hence the intensity of methane dissolved in TBME is also the highest. Although the diffusion rate of methane in NH is almost of the same magnitude as in TBME, the hydrate growth is slower due to poor wetting of the ice. The MCH system has the highest mass transfer resistance, as it does not wet ice particles well.  69  3.3.8  Ice packing density Mass transfer resistances may also be attributed to the ice packing density, as seen  in Figure 3.11. Ice particles that are densely packed create a mass transfer barrier for the LMGS and the methane gas to diffuse. The distribution of all LMGS becomes relatively homogeneous after the system is pressurized with methane unless the degree of ice packing is very high. In the latter case, ice particles may well sinter, thus isolating the ice phase, especially those molecules that are situated in the middle of the cell. Hence, the conversion of ice into hydrate is further limited. This is a likely reason why the hydrate conversions achieved in this NMR study did not reach 100%, even after ramping the temperature.  Figure 3.11: Proton (1H) micro-imaging NMR of Ice+MCH system with different degree of ice packing: the left images correspond to highly packed ice and the right images correspond to system that is not highly packed Less dense ice packing proves to increase conversion of ice into hydrate, as observed from the gas uptake measurements [16]. It is also important to note that particle sizes can also affect the kinetics, and hence ice conversion. Smaller particles are better  70  for contacting the liquid and gas guest phases. It is noted that all ice particles used in this study were ground ice powders with the smallest size that could be obtained by quick freezing and grinding in liquid nitrogen. The surface area of powdered ice prepared in that way was reported [8]. It was found to be 5.1 ± 0.8 m2/g corresponding to a particle size of ~1.3 ± 0.1 µm.  3.4 Conclusions Nuclear Magnetic Resonance (NMR) spectroscopy and imaging (MRI) were employed to monitor the dynamics of structure I and H methane (CD4) hydrate growth and decomposition. The hydrate growth rate obtained by NMR spectroscopy was found to agree with the results from gas uptake measurements, with tert-butyl methyl ether (TBME) exhibiting the fastest kinetics. Good agreement was also found with the reported conversion rates of methane sI hydrate studied by neutron diffraction. It was also found that temperature ramping above the ice point improved the conversion. Another important finding was the role of temperature and the contact between the LMGS and the ice particles. Increasing the temperature above the ice melting point was found to enhance the hydrate conversion. The contact of TBME with the ice particles was found to be reasonably homogeneous, but not so for the neo-hexane (NH) and methyl-cyclohexane (MCH). This explains the fastest kinetics for the TBME system. The degree of packing of ice particles also plays a role and “loosely-packed” ice is preferable to avoid mass transfer resistances. Finally, the major portion of hydrate was found to decompose very quickly at atmospheric conditions. However, complete hydrate crystal dissociation was not achieved for the system with NH.  71  3.5 References [1]  Lee, J.-D.; Susilo, R.; Englezos, P. Energy & Fuels 2005, 19 (3), 1008-1015.  [2]  Tsuji, H.; Ohmura, R.; Mori, Y. H. Energy & Fuels 2004, 18, 418-424.  [3]  Moudrakovski, I. L.; McLaurin, G. E.; Ratcliffe, C. I.; Ripmeester, J. A. J. Phys. Chem. B 2004, 108, 17591-17595.  [4]  Komai, T.; Kang, S.-P.; Yoon, J.-H.; Yamamoto, Y.; Kawamura, T.; Ohtake, M. J. Phys. Chem. B 2004, 108, 8062-8068.  [5]  Kini, R.; Dec, S. F.; Sloan, E. D. Jr. J. Phys. Chem. A 2004, 108, 9550-9556.  [6]  Yoon, J.-H.; Kawamura, T.; Yamamoto, Y.; Komai, T. J. Phys. Chem. A 2004, 108, 5057-5059.  [7]  Ripmeester, J. A.; Ratcliffe, C. I.; Cameron, I. G. J. Phys. Chem. B 2004, 108, 929-935.  [8]  Moudrakovski I. L.; Sanchez, A. A.; Ratcliffe, C. I.; Ripmeester, J. A.., J. Phys. Chem. B 2001, 105, 12338-12347.  [9]  Massiot, D.; Fayon, F.; Capron, M.; King, I.; Le Calve S.; Alonso, B.; Durand, JO.; Bujoli, B.; Gan, Z.; Hoatson, G. Magnetic Resonance in Chemistry 2002, 40, 70-76.  [10]  Susilo, R.; Lee, J. D.; Englezos, P. Fluid Phase Equilibria 2005, 231, 20-26.  [11]  Seo, Y.-T.; and Lee, H. Kor. J. Chem. Eng. 2003, 20 (6), 1085-1091.  [12]  Udachin, K. A.; Ratcliffe, C. I.; Ripmeester, J. A. Proc.4th Int. Conf. Gas Hydrates, 2002, 604-607.  [13]  Staykova, D. K.; Kuhs, W. F.; Salamantin, A. N.; Hansen, T. J. Phys. Chem. B  2003, 107, 10299-10311.  72  [14]  Wang, X.; Schultz, A. J., Halpern, Y. Proc.4th Int. Conf. Gas Hydrates, 2002, 455-460.  [15]  Moudrakovski, I. L.; Ratcliffe, C. I.; McLaurin, G. E.; Simard, B.; Ripmeester, J. A. J. Phys. Chem. A 1999, 103 (26), 4969-4972.  [16]  Susilo, R.; Ripmeester, J. A.; Englezos, P. AIChE J. 2006, 53 (9), 2451-2460.  [17]  Takeya, S.; Shimada, W.; Kamata, Y.; Ebinuma, T.; Uchida, T.; Nagao, J.; Narita, H. J. Phys. Chem. A 2001, 105 (42), 9756-9759.  [18]  Ohmura, R.; Matsuda, S.; Uchida, T.; Ebinuma, T.; Narita, H. J. Chem. Eng. Data  2005, 50, 993-996. [19]  Hansen, C. M. Progress in Organic Coatings 2004, 51, 55-66.  73  CHAPTER-4 METHANE CONVERSION RATE INTO STRUCTURE H HYDRATE CRYSTALS FROM ICE3 4.1 Introduction Significant research efforts have been devoted to study the possibility of storing methane as sH hydrate. However, few studies have addressed the kinetics compared to studies on phase equilibria. Moreover, hydrate conversion from the feed water/ice used in the experiment is seldom reported. Our earlier work through gas uptake measurements [1] and NMR spectroscopy [2] revealed that the kinetics depend on the chosen large molecule guest substance (LMGS) and the driving force, which is essentially the deviation of the formation pressure from the equilibrium pressure at a given temperature. Unfortunately, in both studies the maximum hydrate conversions obtained were approximately 40% which is still far from completion. As discussed in the previous chapter, forming hydrate from ice offers higher hydrate conversion especially with thermal ramping across the ice point. It was also reported in Chapter 3 that the wetting of LMGS on ice and ice packing density influence the hydrate conversion rate. Hence, the objective of this study is to follow up on the previous NMR work and to form hydrate in bulk samples in order to examine if full hydrate conversion can be achieved in a reasonable time. Fresh-ground ice powder with loose ice packing density was used to synthesize hydrates. Methane uptake during hydrate formation was measured and the conversion rates were correlated to crystallization kinetics models. Two different 3  “A version of this chapter has been published. Susilo, R., Ripmeester, J.A. and Englezos, P., “Methane Conversion Rate into Structure H Hydrate Crystals from Ice”, AIChE Journal, vol. 53 (9), 2451-2460, 2007.” 74  hydrate formation pressures and two different LMGS amounts were chosen to see how they may influence the kinetics. In addition, a mixture of LMGSs was also studied.  4.2 Experimental Procedure Hydrates were synthesized from fresh-ground ice particles (~1.3 µm) that were poured by gravity into a 50 ml pressure vessel. Approximately ~10 g of ice powder was used with the LMGS sprayed by a syringe from the top after loading the ice powder. The loading procedure was performed in a freezer at ~253K to prevent melting of the ice. It was noted that ice particles almost filled the vessel completely. The LMGS amount was varied to be 200% (excess) and 50% of the calculated stoichiometric amount, which is approximately ~2 ml. Additional experiments were also conducted by adding tert-butyl methyl ether (TBME) as a polar guest to a hydrophobic guest (NH) with relative concentrations of 1:6 and 1:3. The list of chemicals/LMGSs used in this study is summarized in Table 4.1.  Table 4.1: List of chemicals used in this work Chemical  certified purity  Supplier  Methane tert-butyl methyl ether (TBME) neohexane (NH) methyl-cyclohexane (MCH) n-heptane (nC7) Water  UHP grade 99.9% 99%+ 99%+ 99%+ distilled  Praxair Sigma Aldrich Sigma Aldrich Sigma Aldrich Omnisolv  The vessel was then immersed in a constant temperature water bath and connected to a valve and pressure transducer. The time zero of the measurement was recorded as the  75  vessel was pressurized to the desired pressure. All measurements were performed at 253K for about 20 hours. At the end of the 20-hour period the temperature was increased to a point above the icepoint (274K) within 5 minutes to enhance the ice conversion into hydrate. It is well known that temperature ramping enhances the hydrate conversion [2,3]. Two starting pressure conditions (P0) were chosen, ~4.3 (low pressure condition) and 8.1 MPa (high pressure condition) which would give final pressures at the end of the experiment well below and above the equilibrium condition for sI methane hydrate at 274K (Peq = ~2.9 MPa). The starting pressures were well above the stability region of sI hydrate to ensure there was sufficient methane to convert ice into hydrate. This is because the experiment was conducted in a pressure vessel without replenishment of the gas supply, so the pressure kept dropping as the hydrate formed. The experiments were stopped when a significant pressure drop was no longer observed (almost full hydrate conversion was achieved). The moles of methane uptake over time were calculated from the pressure drop profile in the vessel with respect to the starting pressure, taking the gas compressibility into account. The equations used are given elsewhere [1]. The expected total moles of methane uptake if ice was fully converted to hydrate is ~82 mmol for sH hydrate and ~97 mmol for sI hydrate when all cages are fully occupied. The gas amount has to be adjusted accordingly when the methane occupancies in the hydrate cages are not complete.  4.3 Results and Discussion A typical pressure profile recorded during hydrate formation is shown in Figure 4.1. The pressure dropped relatively quickly in the first few hours indicating rapid  76  hydrate formation. This period is denoted arbitrarily as stage I. During this period ice surfaces were in contact directly with the LMGS liquid so that methane diffusion in LMGS controlled hydrate formation. A noticeable induction time was not observed for any of the systems investigated. Following stage I the pressure drop slowed considerably, presumably because a hydrate film covered the ice surface. This period is denoted arbitrarily as stage II. The hydrate formation is probably limited by the diffusion of methane and LMGS across the hydrate film.  Reaction stages I  3  III  MCH NH  3.5  -2  Ice + TBME + methane Ice + NH + methane  o  Pressure / MPa  4.0  II  -7  Ice + MCH + methane Temperature  3.0  Temperature / C  4.5  TBME  -12  2.5 -17  2.0  Temperature  1.5  -22 0  10  20  30  40  50  60  Experimental time / h  Figure 4.1: Pressure drop profile during hydrate formation from ice + LMGS (~200%) + methane synthesized at low pressure (P0 = ~4.3 MPa).  The end of stage II is marked by a temperature change (temperature ramping). As seen the ramping of temperature above the ice point caused an increased in pressure for  77  about 5-10 minutes and then pressure started decreasing again. The thermal ramping enhanced the transformation of the unreacted ice core towards complete transformation (stage III) into hydrate. The pressure drop data were then used to calculate the moles of methane gas in the hydrate phase, as shown in Figure 4.2. Rapid methane gas uptake is seen in stage I followed by a slower uptake in stage II due possibly to mass transfer resistance. The melting of un-reacted ice inside the hydrate shell is accompanied by further reaction (hydrate formation) towards completion (stage III).  Reaction stages 80  I  II  3  III  -2 o  60  Temperature / C  Methane uptake / mmol  70  50  -7  TBME  40  Ice + TBME + methane  30  -12  Ice + NH + methane  20 10  NH  Ice + MCH + methane  MCH  Temperature  -17  Temperature  0 0  10  -22 20  30  40  50  60  Experimental time / h  Figure 4.2: Amount of methane uptake during hydrate formation from ice + LMGS (~200%) + methane synthesized at low pressure (P0 = ~4.3 MPa). The conversion ratio of ice/water into hydrate can also be calculated if the hydrate structure formed and cage occupancy values for methane and LMGS in the hydrate phase  78  are known. Hence it is important to have such information. A detailed solid phase analysis of hydrates synthesized in this study is reported in the next chapter [4]. Table 5.6 in chapter 5 shows a summary of the cage occupancy values and Table 5.2 in the same chapter the gas content in the hydrate phase [4]. The solid-state analysis at the end of the experiment revealed the presence of methane in sH hydrate for all systems that used an excess amount of LMGS (200 %). A mixture of sI and sH hydrate was observed only for the systems with LMGS amounts less than stoichiometric (50 %). Figure 4.3 shows the conversion versus time calculated from the gas uptake data showed in Figure 4.2.  Reaction stages I  II  III  3  80%  -2 o  TBME  60%  -7 Ice + TBME + methane  40%  -12  Ice + NH + methane NH  20%  Ice + MCH + methane Temperature  MCH  -17  Temperature  0% 0  10  Temperature / C  Hydrate conversion ratio  100%  -22 20  30  40  50  60  Experimental time / h Figure 4.3: Hydrate conversion ratio of ice + LMGS (~200%) + methane synthesized at low pressure (P0 = ~4.3 MPa). The conversion ratio is calculated by dividing the moles of methane consumed (Figure 4.2) by the total number of moles of methane that would be enclathrated if all 79  ice/water that is present in the system is fully converted into hydrate. The latter is known because the amount of ice and the methane occupancies from NMR (see Chapter 5) are known. It is important to note here that the hydrate structure and cage occupancies were assumed to remain the same throughout the experiments. This assumption is reasonable when the system has excess LMGS because the hydrate formed is sH only. However, the calculated conversions may be under or over estimated for the mixed sI and sH hydrates. It is not known how and when the mixed hydrate is formed, whether simultaneously or subsequently after the shortage of LMGS. In this case we took into account the final hydrate composition.  4.3.1  Methane uptake with 200% LMGS synthesized at low pressure (P0=~4.3 MPa) Examination of the results in Figures 4.2 and 4.3 reveals two types of hydrate  growth behavior. The systems with NH and MCH have similar hydrate growth trends. The observed kinetics was relatively slow at 253K, but then rapid hydrate growth followed and almost full hydrate conversion was achieved immediately after the unreacted ice was melted. A slight delay was observed in one MCH system as seen in Figure 4.3. However, it was not observed in any other experiments. The hydrate growth for the TBME system was reasonably fast at 253K, but the effect of temperature ramping was not so drastic as in the case of the NH and MCH systems. This is probably due to the strong affinity between polar guest molecules like TBME with water/ice as indicated by the solubility and wetting properties [2,5]. The strong interaction of TBME with water molecules makes it more difficult (higher energy barrier) for water molecules to reorientate and form hydrate cages, resulting in slower kinetics when there is no mixing.  80  4.3.2  Methane uptake with 50% LMGS synthesized at low pressure (P0=~4.3 MPa) Figure 4.4 shows the pressure profiles when the LMGS amount is less than the  stoichiometric (50%). As seen, similar pressure profiles are observed as those with excess LMGS amounts. Rapid hydrate growth in “stage I” is seen to be followed by slower growth at stage II. The pressure profiles for the NH and MCH systems from Figure 4.4 are compared with those in Figure 4.1. It is seen that when only 50% of LMGS is used, the corresponding hydrate growth is faster during stage II (Figure 4.4). This is likely caused by the formation of sI hydrate. Some ice particles may be exposed directly to methane gas due to the insufficient amount of LMGS. It is also noted that TBME still exhibited the fastest kinetics (stages I and II) followed by the NH and MCH systems.  Reaction stages I  4.0  II  III  3  3.8 MCH NH  -2 o  3.4  Temperature / C  Pressure / MPa  3.6  3.2  -7  3.0  TBME  2.8  -12 Ice + TBME + methane Ice + NH + methane  2.6 2.4 Temperature  2.2  -17  Ice + MCH + methane Temperature  2.0  -22 0  10  20  30  40  50  60  Experimental time / h  Figure 4.4: Pressure profile during hydrate formation from ice + LMGS (~50%) + methane synthesized at low pressure region (P0 = ~4.3 MPa).  81  Upon melting the unreacted ice, the pressure increased for a few minutes (2-3 min) and then dropped quickly indicating fast hydrate formation, but then it rose back up and stayed at the equilibrium pressure of sI methane hydrate at 274K (~2.9 MPa). This suggests that most of the hydrate formed was a mixture of sI and sH hydrates. However, sI hydrate is not stable at pressures below ~2.9 MPa. Consequently, it decomposed as indicated by an increase in pressure. The solid state analysis showed that the solid phase contained mostly sH hydrate with a significant amount of unreacted ice and a small amount of sI hydrate. The hydrate yield was determined by dissociating the samples. It was found to be only ~15-25% for the NH and TBME systems although there was sufficient LMGS to convert up to ~50% theoretically. The yield for the MCH system was ~45% but it consisted of mixed sI and sH hydrates. The sH hydrate content was ~20%. This emphasizes the need to have excess LMGS to fully convert ice/water into hydrate. It is not known why the MCH system behaved differently.  4.3.3  Methane uptake with 200% LMGS synthesized at high pressure (P0=~8.1 MPa) The methane uptake data are shown in Figure 4.5. As seen the initial hydrate  formation (stage I) is faster than at the low pressure condition. Hence, stage I period is shorter. Stage II is similar to that of low pressure. Further hydrate formation during stage III is also observed upon melting of the unreacted ice. However, the rates are much slower than those observed at the low pressure condition. Hydrate conversion was also calculated and it was found that it took a week to achieve ~90% conversion at the higher pressure condition whereas only several hours at the low pressure one. The solid-state NMR revealed that the methane occupancy was higher when the hydrate was synthesized  82  at the high pressure. It is unclear whether the slower methane uptake rate is the result of higher occupancy or due to the competition between sI and sH hydrate formation. sI hydrate may form quickly at first, then convert to sH hydrate at a slower rate.  Reaction stages I II  3  Temperature  TBME  60  -2  NH  MCH  o  Methane uptake / mmol  70  III  Temperature / C  80  50  -7  40  Ice + TBME + methane  30  Ice + NH + methane  -12  Ice + MCH + methane  20  Temperature  -17  10 0 0  50  100  150  200  -22 250  Experimental time / h  Figure 4.5: Amount of methane uptake during hydrate formation from ice + LMGS (~200%) + methane synthesized at high pressure (P0 = ~8.1 MPa).  4.3.4  Methane uptake with 50% LMGS synthesized at high pressure (P0=~8.1 MPa) Figure 4.6 shows the methane uptake profile. The growth rates in stage I were  similar to those observed in the previous systems. As seen the MCH curve crossed over the NH curve after approximately one hour. This is most likely due to the formation of a mixture of sI and sH hydrates. This resulted in an increase of the methane uptake. During stage II the uptake rate slows as observed previously, but there is more hydrate growth  83  compared to the systems at same pressure but with excess of LMGS. After melting the unreacted ice core, slow and irregular methane uptake profiles were seen, especially for the NH and MCH systems. Higher overall methane uptake was also obtained, possibly due to the presence of sI hydrate. In fact the solid state analysis confirmed the presence of sI hydrate, as discussed in Chapter 5.  Reaction stages I  100  II  III  3  Temperature  80  -2 o  70  Temperature / C  Methane uptake / mmol  90  60  -7  50 40  Ice + TBME + methane  TBME MCH NH  30 20  -12  Ice + NH + methane Ice + MCH + methane Temperature  10 0  -17 -22  0  20  40  60  80  Experimental time / h  Figure 4.6: Amount of methane uptake during hydrate formation from ice+ LMGS (~50%) + methane synthesized at high pressure (P0 = ~8.1 MPa).  4.3.5  Methane uptake with no LMGS synthesized at high pressure (P0=~8.1 MPa) Methane uptake data for sI hydrate for the system with n-heptane (nC7) is shown  in Figure 4.7.It is known that n-heptane is not a hydrate former and hence there is no LMGS present in this system. In addition, data for the methane/ice system are shown  84  (absence of nC7). A noticeable lower methane uptake was observed in comparison to those from sH hydrates systems especially during stage I. The slope in stage II for the icemethane system is relatively greater than the slopes for the sH hydrate systems except for the system with TBME. Rapid hydrate growth is also observed in stage III. The overall methane uptake for sI hydrate is higher than for sH hydrate due to higher methane storage capacity.  Reaction stages I  100  II  III  3  Temperature  Ice/methane only  70  -2 o  80  nC7  60  Temperature / C  Methane uptake / mmol  90  -7  50  Ice + methane  40  Ice + nC7 + methane  30  Temperature  -12  20  -17  10 0  -22 0  10  20  30  40  50  Experimental time / h  Figure 4.7: Amount of methane uptake during hydrate formation from ice without any LMGS synthesized at high pressure (P0 = ~8.1 MPa).  4.3.6  Methane uptake with LMGS mixtures synthesized at low pressure (P0=~4.3 MPa) It is clear that the hydrate formation rate for the systems containing LMGS  depends on temperature ramping above the ice point. At temperatures below the icepoint  85  where water molecules are relatively immobile, the LMGS which has the highest interaction/affinity towards water is expected to show faster kinetics than a hydrophobic guest. This is clearly seen from the uptake rate of the TBME system that is superior to that of the NH and MCH systems during stage I and II. However, the strong affinity turns out to be a disadvantage when the water is in its liquid state. In this case, water soluble guest molecule (TBME) appears to inhibit the hydrate growth. The most plausible explanation for this is the absence of any mixing of the phases and the affinity of TBME and water as discussed in section 4.3.1.  Reaction stages 80  I  II  III  3  -2 o  60  Temperature / C  Methane uptake / mmol  70  50  -7  TBME  40  TBME system 3NH+1TBME 6NH+1TBME  3:1 6:1  30 20  NH system Temperature  NH  10  -12  -17  Temperature  0 0  10  -22 20  30  40  50  Experimental time / h  Figure 4.8: Amount of methane uptake during hydrate formation from ice + Neohexane (NH) and tert-butyl methyl ether (TBME) mixture (~200%) + methane, synthesized at low pressure (P0 = ~4.3 MPa). A mixture of TBME with NH at different concentrations was also studied in order to seek the optimum condition in terms of kinetics and methane occupancy. The idea was  86  to see if the slow kinetics at the low temperature region (253K) of the NH system could be enhanced by the addition of a small amount of TBME while maintaining the fast conversion rates at 274K and high gas storage capacity in hydrate. The methane uptake curve that was obtained is shown in Figure 4.8. As seen, the addition of TBME improves the rate at 253K (stage I and II). It is also seen that higher TBME concentration shifts the uptake curve closer to that for the TBME system. On the other hand, adding TBME slows the rate during stage III. It is interesting to note that methane occupancy was reduced at higher TBME concentration, as seen in Tables 5.2 and 5.6 in Chapter 5. Similar results were obtained with the TBME/MCH mixtures but are not shown here. Hence, adding TBME into a hydrophobic guest does not necessarily improve the rate overall. In addition the gas content is reduced. Therefore the TBME/MCH or TBME/NH system is not necessarily better than pure NH or MCH in terms of storage potential. Based on the above findings the total reaction time could be reduced while reaction time for stage I is sufficient. The time spent in growth stage II can be minimized. Rapid hydrate growth towards full conversion is achievable with thermal ramping (stage III) for another ~5 hours. Hence, the total conversion of ice into sH hydrates with maximum methane occupancy can be reached within ~8 hours.  4.3.7  Correlation of conversion rate with crystallization models Hydrate conversion was introduced in section 4.3. The conversion data such as  those shown in Figure 4.3 were correlated with the Avrami equations [6-8] and the shrinking core model (SCM) [3,9]. It is noted again that the hydrate conversion, α, is  87  determined by dividing the moles of methane consumed at time t by the moles consumed if all ice/water is fully converted into hydrate. The model equations are given below: Avrami model:  α = 1 − exp(− k1t n ) or ln[− ln(1 − α )] = n ln t + ln k1  SCM model:  (1 − α )1 3 = −  (2k 2 )1 2 r  (t − t *)1 2 + (1 − α *)1 3  (4.1) (4.2)  where α is the hydrate conversion ratio at time t, α * is the hydrate conversion ratio when diffusion though hydrate film starts at time t * , k is the rate constant with the subscript indicating the growth stage, n is the Avrami exponent and r is the radius of ice particle (~0.65 µm [10]).  4.3.7.1 Correlation with the Avrami model The low pressure data in Figure 4.9 indicate that the Avrami model for TBME and NH correlate the data up to a certain time t* which corresponds to a conversion α*. The values for t* and α* are given in Table 4.3 and discussed below. However, for the MCH it is clear that the Avrami model fails at the beginning but it fits the subsequent data up to time t* and conversion α*. At high pressure, the Avrami model correlates the conversion data for the TBME system but fails at the beginning for the NH and MCH systems, as shown in Figure 4.10. The differences in observed intercepts from both Avrami plots correspond to different rate constants k1. The higher the k1 values, the faster the hydrate conversion. TBME systems always appear at the top because they have the fastest kinetics, followed by NH and MCH systems. The slopes are ~0.5 for all systems with the  88  exception for the TBME system at high pressure. The regressed k1 and n values are given in Table 4.2. 3  3  2  ln [-ln(1-α )]  o  Temperature / C  -2  1 0  -7  -1  TBME  -12  -2  NH  -3 -4  -17  Temperature profile  MCH  -5  -22 1  2  3  4  5  6  7  8  ln (t/[min])  Figure 4.9: Avrami plot for ice + LMGS (~200%) + methane systems. Hydrates were synthesized at low pressure (P0 = ~4.3 MPa). 2  3  1  ln [-ln(1-α )]  o  0 -7 -1  Temperature / C  -2  TBME  -12  -2  NH -3 MCH  -17  Temperature profile  -4  -22 1  3  5  7  9  ln (t/[min])  Figure 4.10: Avrami plot for ice + LMGS (~200%) + methane systems. Hydrates were synthesized at high pressure (P0 = ~8.1 MPa). 89  Table 4.2: Avrami parameters; k is given in conversion/minuten. LMGS system/amount  Pressure  k1 A  nB  Ice + methane Ice + methane + nC7  high high low high low high low high low high low high low high  0.0067 0.0043 0.0649 0.0331 0.0640 0.1358 0.0272 0.0299 0.0278 0.0378 0.0158 0.0167 0.0157 0.0205  0.40 0.51 0.46 0.54 0.52 0.28 0.52 0.51 0.52 0.47 0.50 0.51 0.50 0.49  50% TBME 200% TBME 50% NH 200% NH 50% MCH 200% MCH  ‘A’ The maximum standard error of k1 is 5 %, ‘B’ The maximum standard error of n is 0.1. It is well known that the Avrami equation considers the crystallization process as “free” growth [11-13]. Thus, the Avrami exponent n indicates the dimensionality of crystal growth front, starting with unity for a linear growth up to three for a threedimensional growth. Diffusion controlled growth reduces the Avrami exponent n typically by a factor of two [11]. Since the hydrate growth here is probably controlled by the methane diffusion in the LMGS phase, hence the actual hydrate growth front is actually linear in one dimension (needle-like crystal) after multiplying the n value by two. The deviation from the model at the beginning of hydrate growth shown in Figure 4.9 and 4.10 suggest there is a different hydrate growth mechanism. Regarding the low pressure data, this may be ascribed to the slow diffusion of methane in the MCH phase. The NMR study confirmed the slow methane diffusion in MCH [2]. In addition, the deviation at high pressure may also be attributed to the fact that sI methane hydrate may  90  also form. The fitting parameters in Table 4.2 are used to compare the model with the actual conversion as plotted in Figure 4.11 and 4.12. Ice + TBME + Methane Avrami correlation-TBME Ice + NH + Methane Avrami correlation-NH Ice + MCH + Methane Avrami correlation-MCH  80%  Hydrate conversion  70% 60% 50% 40% 30% 20% 10% 0% 0  1  2  3  4  5  Experimental time / h  Figure 4.11: Hydrate conversion for ice + LMGS (~200%) + methane system synthesized at low pressure (P0 = ~4.3 MPa). 80%  Hydrate conversion  70%  Ice + TBME + methane Avrami correlation-TBME Ice + NH + methane Avrami correlation-NH Ice + MCH + methane Avrami correlation-MCH  60% 50% 40% 30% 20% 10% 0% 0  1  2  3  4  5  Experimental time / h  Figure 4.12: Hydrate conversion for ice + LMGS (200%) + methane system synthesized at high pressure (P0 = ~8.1 MPa). 91  As seen in Figures 4.11 and 4.12, the model predicts reasonably well up to a certain conversion α* at time t*. The value of α* is around 20% for both NH and MCH system and slightly higher (30%) for the TBME system. The t* values vary between 10 minutes to three hours depending on the hydrate formation rate. The model slightly overpredicts the data at low pressure for the MCH system and under-predicts the data at high pressures for the NH and MCH systems. 2  3  1  ln [-ln(1-α )]  o  0  Temperature / C  -2  -7  -1  Ice only -2  -12  n-heptane  -3  -17  -4  Temperature profile  -5  -22 1  2  3  4  5  6  7  8  ln (t/[min])  Figure 4.13: Avrami plot for ice + methane systems (no LMGS). Hydrates were synthesized at high The Avrami plot for non-LMGS systems (sI hydrate) is also shown in Figure 4.13 for comparison. The n value obtained is 0.4 which suggest the presence of diffusion. Since there is no LMGS, this suggests that there is a resistance in the gas phase (gas film). This gas film was also observed from the NMR study [2]. It is unknown whether the gas film is also present with LMGS. The expected slope would be lower than without  92  LMGS if the gas film is also present due to the additional resistance. However this was not seen and hence the existence of gas film is unlikely or insignificant. Consequently, the observed rates with the presence of liquid LMGS are not necessarily lower than those without one although additional liquid layer is present. A lower n value for sI hydrate in the initial reaction agrees with the lower slopes observed in the LMGS systems where the hydrate is synthesized at high pressure and less than stoichiometric LMGS amounts. The presence of liquid n-heptane is expected to behave in the same way as the LMGS. Hence the expected n-value is ~0.5, which is indeed the value obtained.  4.3.7.2 Correlation with the shrinking core model The conversion data after time t* (conversion α*) were correlated with the SCM model because there is already a product (hydrate) layer covering the ice particles. The presence of the hydrate layer on the ice surfaces limits the mass transfer so that the subsequent hydrate growth becomes much slower. A typical SCM plot is shown in Figure 4.14. As seen, the model fits the data well. A slight deviation is observed for the first few data points, as also indicated by Wang et al. [3]. The values of α*, t* and the rate constant k2 are given in Table 4.3. It is noted that the values for α* and t* were obtained from plots like Figures 4.9 and 4.10.  93  0.95  0.94  0.91 0.90  0.80  0.89  (1-α )  0.75  0.88  TBME  0.87  0.70  1/3  NH  0.85  (1-α )  0.92  1/3  / for TBME  MCH  / for NH and MCH  0.93  0.90  0.86  0.65  0.85 0  5  10  15 1/2  (t-t*)  / min  20  25  30  1/2  Figure 4.14: Shrinking core model (SCM) plot for ice + LMGS (~200%) + methane systems. Hydrate was synthesized at low pressure (P0 = ~4.3 MPa).  Table 4.3: Shrinking core model parameters α* [conversion] Ice only high 0.10 200% nC7 high 0.08 low 0.22 50% TBME high 0.27 low 0.33 200% TBME high 0.25 low 0.23 50% NH high 0.17 low 0.20 200% NH high 0.23 low 0.17 50% MCH high 0.21 low 0.20 200% MCH high 0.21 A ‘ ’ The maximum standard error of k2 is 3 %. LMGS system/amount  Pressure  94  t* [h] 7 7 0.5 0.5 0.5 0.5 1 1 1 1 3 3 3 3  k2 A [nm2/h] 42 11 400 194 399 189 41 7 12 6 51 10 3 7  As seen the TBME system has the highest α* (~30%) and k2 values (~400 nm2/h) implying a strong interaction between ice and TBME. For the system with 50% LMGS, the k2 values are affected by the formation of sI hydrate. The k2 value for the methane-ice system is higher than for NH and MCH systems, but lower than for TBME. Thus the k2 values increase for NH and MCH system, but decrease for the TBME system when sI hydrate coexists with sH hydrate in this region.  4.4 Conclusions Structure H (sH) hydrate was synthesized from freshly-ground ice powder. Three sH hydrate formers were selected in this study: tert-butyl methyl ether (TBME), neohexane (NH), and methyl-cyclohexane (MCH). The number of moles of methane consumed (gas uptake) were measured and used to determine the hydrate conversion. The hydrate crystallization “reaction” was allowed to proceed for 20 hours at 253K before ramping the temperature to 274K. The hydrate synthesis procedure followed temperature ramping above 0°C to 1°C enabled nearly full hydrate conversion (90% conversion) within a short time and without mixing. The gas uptake rates were found to depend on the amount of LMGS, the temperature and pressure at which the hydrate was synthesized. An excess amount of LMGS was required to maintain sH hydrate formation. The rate with TBME is the fastest below the ice point, but the slowest above. The effect of pressure is more noticeable above 0°C. In fact, the uptake rates are faster at the low pressure condition (P0 = ~4.3 MPa). Adding TBME into NH or MCH may help enhance the rate at 253K, but not at 274K.  95  The Avrami model was found to correlate the TBME data up to time t* and conversion α* (approximately 30%). The data after t* were correlated well with the SCM model. The Avrami model correlates the NH and MCH data up to α* (approximately 20%) except at the very beginning.  96  4.5 References [1]  Lee, J.D.; Susilo, R.; Englezos, P. Energy & Fuels 2005, 19, 1008-1015.  [2]  Susilo, R.; Moudrakovski, I.L.; Ripmeester, J.A.; Englezos, P. J. Phys. Chem. B  2006, 110, 25803-25809. [3]  Wang, X.; Schultz, A.J.; Halpern, Y. J. Phys. Chem. A. 2002, 106, 7304–7309.  [4]  Susilo, R.; Ripmeester, J.A.; Englezos, P. Chem. Eng. Sci. 2007, 62 (15), 39303939  [5]  Susilo, R.; Lee, J.D.; Englezos, P. Fluid Phase Equilibria 2005, 231, 20-26.  [6]  Avrami, M. J. Chem. Phys. 1939, 7, 1103-1112.  [7]  Avrami, M. J. Chem. Phys. 1940, 8, 212-224.  [8]  Avrami, M. J. Chem. Phys. 1941, 9, 177-184.  [9]  Fujii, K.; Kondo, W. J. Am. Cer. Soc. 1974, 57, 492-497.  [10]  Moudrakovski, I.L.; Sanchez, A.A.; Ratcliffe, C.I.; Ripmeester, J.A. J.Phys. Chem. B 2001, 105, 12338-12347.  [11]  Gedde, U.W. Polymer physics: Crystallization Kinetics. London: Chapman and Hall, 169-199, 1995.  [12]  Marangoni, A.G. Fat crystals network: Crystallization Kinetics. New York: Marcel Dekker, Inc., 21-83, 2005.  [13]  Shaples, A. Introduction to polymer crystallization. London: Edward Arnold, Inc., 44-59, 1966.  97  CHAPTER-5 CHARACTERIZATION OF GAS HYDRATES WITH PXRD, DSC, NMR AND RAMAN SPECTROSCOPY4 5.1 Introduction Powder X-Ray diffraction (PXRD), Raman and Nuclear Magnetic Resonance (NMR) spectroscopy are well-known tools used for solid structural analysis of gas hydrate [1-4]. Such techniques are required to obtain information on crystal structure, crystal dimension/volume, and composition/occupancy values of the cages. A thermal analysis technique such as Differential Scanning Calorimetric (DSC) may also be employed [5-7]. However a combination of all instrumental methods to characterize the hydrate phase has not been reported. Interpreting the experimental data from PXRD and NMR for methane hydrate in all hydrate structures is already well established and often the measurement from each instrumental method may explain the results independently. However, Raman spectroscopy still requires attention, especially in determining hydrate structure and the composition for complex systems like sH hydrate. Both Raman and NMR spectroscopy have been successfully employed to study gas hydrates at a molecular level [8-11]. These instrumental methods are based on different principles and hence have different advantages and limitations. Raman is more convenient for in-situ measurement, but so far is less diagnostic for structure and composition, whereas NMR is more sensitive to changes in local environment and hence of greater diagnostic value. A direct comparison between the two is required to establish 4  “A version of this chapter has been published. Susilo, R., Ripmeester, J.A. and Englezos, P., “Characterization of gas hydrates with PXRD, DSC, NMR and Raman Spectroscopy”, Chemical Engineering Science, vol. 62 (15), 3930-3939, 2007.” 98  a common understanding in the interpretation of the spectra. Both NMR and Raman gave comparable cage occupancy values for methane in structure I (sI) hydrate [12,13], yet a discrepancy was reported for a mixed hydrate with carbon dioxide [13]. Methane occupancy in sH hydrate also has been reported from NMR and single crystal diffraction study [14-16]. However, it is still unsure if Raman can also be used to obtain such occupancy values, although the identification of methane signals was reported [17-20] and occupancy values were suggested [20]. Both Raman and NMR show that gas/liquid signals are shifted when a molecule is encaged in hydrate phase. For the encaged methane molecule, its signature in all three hydrate structures is shifted to a lower frequency in Raman [18] and lower field in NMR [14, 21]. Generally the shifts in Raman spectra are not structure specific, and a large cage/small cage intensity ratio has to be interpreted. Hence one has to be more careful in determining the hydrate structure and its composition from Raman. The  13  C NMR shift  for methane is more structure specific so that the ambiguity is less. However the chemical shifts of methane in the small cage of all the hydrate structures are similar due to the similar chemical environment. Hence the signals of methane in 512 and 435663 cages of sH hydrate are expected to be very close to each other, and may even be indistinguishable. Surprisingly, it was reported recently that both methane signals are distinguishable from their Raman measurements [20]. Most Raman spectra reported previously in the literature for sH hydrate showed only one broad peak at around ~2913-2918 cm-1 (temperature dependent) that corresponds to methane in both small and medium cages [17-19]. None of them shows a distinct peak between the two except the last published spectra. So it is interesting to investigate this puzzle.  99  The objective of this study is to present a direct comparison of the three solidstate analytical tools (PXRD, NMR and Raman) plus DSC for sH hydrate characterization. In addition, the presence of n-heptane (nC7) as a non-hydrate former will also be studied along with a system without LMGS added. The structural information from PXRD will be linked to both NMR and Raman shifts. The signals from NMR and Raman will be used to identify the corresponding molecules in each phase and to determine the cage occupancy. The occupancy values obtained from spectroscopy will be compared with the gas content measured by decomposing the hydrate.  5.2 Experimental Procedure Hydrates were synthesized from freshly ground ice particles that were poured by gravity into a 50 ml pressure vessel. Approximately ~10 g of ice powder was used with the LMGS sprayed on top of the ice by a syringe after loading the ice powder. The LMGS amount was varied from 200% (excess) to 50% of the stoichiometric composition. The list of chemicals/LMGS used in this study is summarized in Table 4.1. The loading procedure was performed in a freezer at ~253K to prevent the melting of the ice. The vessel was then immersed in a constant temperature water bath containing watermethanol mixture and connected to a valve and pressure transducer. The time zero of the measurement was recorded as the vessel was pressurized to the desired pressure. All measurements were performed at 253K over about 20 hours. At the end of the 20-hour period the temperature was increased to a point above the ice point (274K) within 5 minutes in order to enhance the conversion of ice into hydrate. It is well known that temperature ramping enhances the conversion to hydrate [22]. Two starting pressure  100  conditions were chosen, ~4.3 and 8.1 MPa which would give final pressures well below and above the equilibrium condition for sI methane hydrate at 274 K (Peq = ~2.9 MPa). The hydrate samples were collected under liquid nitrogen temperature (77 K) at the end of the experiment after no significant pressure drop was observed (almost full hydrate conversion was achieved). The recovered hydrate samples were kept in liquid nitrogen for subsequent analysis. Crystal structures and lattice constants were obtained from powder X-Ray Diffraction (PXRD). The PXRD patterns were recorded at ~85K on a Rigaku Geigerflex diffractometer (λ=1.79021) in the θ/2θ scan mode. The XRD experiments were carried out in step mode with a fixed time of 5 s and a step size of 0.05° for 2θ=5-50° with a total acquisition time of ~75 minutes for each hydrate sample. The crystal structure was then correlated to results from  13  C magic angle spinning (MAS) NMR at 193 K and Raman  spectroscopy at liquid nitrogen temperature. A Bruker DSX 400 MHz NMR spectrometer was used to analyze the hydrate structure and cage occupancies of methane and LMGS. Prior to the NMR measurements, hydrate samples were ground under liquid nitrogen and packed in a 7 mm zirconia rotor, which was loaded into a variable temperature probe. All 13  C NMR spectra were recorded at ~2 kHz spinning rate. A single pulse excitation (90° of  5 µs) and pulse repetition delay of 300 s under proton decoupling were employed. The cross polarization technique was also employed to distinguish the signals arising from the solid phase from those of the liquid phase. Adamantane was assigned as the external chemical shift reference at 298 K and 38.56 ppm. An Acton Raman spectrograph with fiber optics and equipped with a 1200 grooves/mm grating and a CCD detector was used in this study. An Ar-ion laser was used as the excitation source emitting at 514.53 nm.  101  The laser was focused on the sample by 5x microscope objective. The spectrograph was controlled with a computer and the spectra were recorded with a 1s integration time over 5 to 30 scans. All spectra were referenced to methane gas at 2918 cm-1. The amount of hydrate, unreacted ice and unreacted LMGS were determined by DSC. Hydrate samples were sealed in an aluminum pan under liquid nitrogen and placed in the DSC cell at -150°C. The sample was equilibrated at that temperature for ~10 minutes before heating to 30°C with the rate of 5°C/min. The samples were all frozen at 150°C so that a phase change due to melting appeared at the melting point of the LMGS, hydrate and ice. The areas for each phase transition peak correspond to the energy absorbed due to decomposition or melting. The amount of the corresponding phase can be calculated by calibrating the peak area with the heat of fusion values given in literature [23,24]. The dissociation enthalpy of hydrate was calculated from the hydrate phase equilibria data using the Clausius-Clapeyron equation [25]. Hence the amount of unreacted ice and LMGS can be calculated from the mass balance. The hydrate conversion and the gas stored in the hydrate were also cross-checked by measuring the gas release while decomposing the hydrate in a vacuum line of a known volume.  5.3 Results and Discussion 5.3.1  X-Ray diffraction (XRD) analysis All synthesized hydrate samples were analyzed by PXRD first to confirm the  presence of hydrate and to verify the crystal structure. A typical PXRD pattern of sH hydrate is shown in Figure 5.1. The pattern was fitted to a standard sH hydrate pattern  102  (space group P6/mmm) to obtain the lattice constants and unit cell volumes, which are summarized in Table 5.1.  Intensity  1 0 2 1 0 1  10  0 0 2  2 1 2  3 0 1  2 0 1  3 1 0  2 2 0 2 1 0  *  20  2 0 12 0 10 3 2  *  1 0 3  30  2 0 3  2 2 2 3 3 1 2 1 0 32 3 *  40  2 0 4  3 2 2 1 2 4  50  2θ θ [Degrees]  Figure 5.1: PXRD pattern of sH hydrate (TBME+Methane) Table 5.1: Lattice constants and unit cell volumes of synthesized hydrate at 82K System  Hydrate structure  Lattice constants  Unit cell volume  CH4 + H2O CH4 + H2O + nC7  I I  1665 A3 1665 A3  CH4 + H2O + TBME  H  CH4 + H2O + NH  H  CH4 + H2O + MCH  H  a = 11.85 A a = 11.85 A a = 12.16 A c = 10.10 A a = 12.18 A c = 10.08 A a = 12.16 A c = 10.13 A  1294 A3 1295 A3 1297 A3  The unit cell volumes were found to increase slightly on going from TBME, NH, to MCH. The presence of ice is indicated by the asterisk in Figure 5.1. The intensity of the ice peaks for the sample corresponded to the amount of unreacted ice and some ice  103  resulting from condensation of moisture in the air, which was found to be minimal for most samples. For those hydrates that were synthesized with an amount of LMGS that was less than stoichiometric, the conversion of hydrate was very low at low pressure (sH stability region) as the intensity of ice peaks was predominant. Some ice particles that were not exposed to LMGS formed sI hydrate at higher pressures. Consequently, sI and sH hydrate were detected by PXRD. Hydrates synthesized without LMGS or n-heptane as a non hydrate former form sI hydrate. Once the PXRD confirmed that the solid phase contained hydrate, the gas stored in the hydrate phase was measured and the sample was further analyzed to obtain the hydrate composition and unreacted ice content by NMR, Raman spectroscopy and DSC.  5.3.2  Gas content measurement Table 5.2 summarizes the amount of gas stored in the hydrate as measured by  decomposing the hydrate under vacuum. The volume ratio (v/v) of gas stored in hydrate phase that is relevant to practical interest is reported in the table. The ratio of gas per volume of water generated upon decomposition is also given, which is slightly higher due to higher water density than hydrate phase. Synthetic hydrate made with n-heptane or without LMGS store the same amount of methane gas (173 v/v). The addition of LMGS lowers the hydrate formation pressure by forming sH hydrate so it is favourable for methane storage and transport application. However, as a result the gas storage capacity in the hydrate phase decreases. The amount of methane gas stored in sH hydrates was found to be approximately 20-40% lower (103142 v-gas/v-hydrate, depending on the methane occupancy) than in sI hydrate. This is due  104  to the accessibility of both small and large cages of sI hydrate towards methane, whereas only the small and medium cages are accessible for sH hydrate. A methane molecule is too small to fill the large cavity of sH hydrate so that the LMGS is preferred.  Table 5.2: Amount of gas stored in hydrate with the final hydrate conversion achieved. System (LMGS amount) No LMGS nC7 (200%) TBME (50%) TBME (200%) NH (50%) NH (200%) MCH (50%) MCH (200%) 3NH:1TBME (200%) 6NH:1TBME (200%)  PressureE  Structure  Vgas/Vhydrate  Vgas/Vwater  Conversion A  high high low high low high low high low high low high low high  sI sI sH sI +sH sH sH sH sI +sH sH sH sI +sH sI +sH sH sH  173 173 32 131 D 103 125 20 144 D 130 139 72 D 157 D 132 142  210 210 41 166 131 160 26 184 166 177 92 200 168 181  85% 85% 22% B 98% C 99% 96% 14% B 96% C 98% 91% 45% B,C 99% C 98% 87%  low  sH  109  139  99%  high  sH  123  157  96%  ‘A’  The conversion was calculated from the total methane uptake divided by the uptake if all ice/water is converted into hydrate taking methane occupancies into account B ‘ ’ The conversion was obtained from the gas content measurements ‘C’ The conversion was calculated from total methane uptake divided by the uptake if all ice/water is converted into hydrate taking methane occupancy into account for both sI and sH hydrate. D ‘ ’ The hydrate phase was calculated using lattice constants from sH hydrate “E” “high” and “low” denote a final pressure of 6 MPa and 2 MPa respectively at 274 K The gas stored in sH hydrate depends on the type of LMGS used and on the pressure at which the hydrate is synthesized. The systems with MCH and NH have higher methane content than TBME. Higher hydrate formation pressure increases the amount of methane stored for all systems. Hydrate synthesized with 50% LMGS at lower pressures  105  has the least methane content due to limited hydrate conversion. At higher pressures, the methane content increases due to the formation of sI hydrate.  5.3.3  Differential Scanning Calorimetry (DSC) analysis Figure 5.2 shows a DSC plot obtained from hydrate formation in the presence of  MCH. Similar plots were obtained for the other hydrate forming systems. The melting curve obtained shows that three distinct phases melt at different temperatures. All phases are solid at the initial temperature at -150°C. As the temperature was increased, the unreacted LMGS melted first, followed by hydrate and finally ice.  Temperature [C] -140 0  Heat Flow [mW]  -10  -120  -100  -80  -60  Excess MCH (282 mJ)  -40  -20  0  20  40  sH hydrate (3200 mJ)  -20  Ice (6831 mJ) Unreacted ice plus dissociated from hydrate  -30 -40 -50 -60  Figure 5.2: DSC melting curve of (Methane+MCH) sH hydrate The first endothermic peak appeared at the melting point of LMGS, which were at -126°C, -109°C, and -100°C for MCH, TBME, and NH respectively. Hydrate started to  106  dissociate at the corresponding hydrate equilibrium temperature at 1 atm, which were approximately -70°C, -60°C and -55°C for TBME, MCH, and NH respectively. The ice melting peak that appeared at 0°C consisted of unreacted ice and ice from hydrate decomposition. Therefore, the ice that originated from the dissociated hydrate needed to be determined first to obtain the amount of unreacted ice in the sample and hence the hydrate conversion. This was obtained by multiplying the amount of dissociated hydrate with the hydration number which was acquired from NMR measurements. It depends on the cage occupancy and varies between ~5.67 to 7.00. The amount of unreacted ice was then calculated by subtracting the total amount of melted ice from that of the hydrate.  Table 5.3: Heat of fusion and hydration number of LMGS, ice, and sH hydrate System  Heat of fusion  TBME NH MCH Ice (CH4 + TBME) hydrate (CH4 + NH) hydrate (CH4 + MCH) hydrate  7.60 kJ/mol 0.58 kJ/mol 6.75 kJ/mol 6.01 kJ/mol 16.21 kJ/mol 18.47 kJ/mol 17.93 kJ/mol  ‘A’ ‘B’ ‘C’  Hydration number A 7.00 B 6.30 B 6.18 B  6.19 C 5.71 C 5.67 C  Hydration number was calculated from occupancy values obtained by NMR. Values reported correspond to the system at low pressure with 200% LMGS. Values reported correspond to the system at high pressure and 200% LMGS. The amount of unreacted LMGS, hydrate, and ice (in moles) were calculated by  calibrating the peak areas with the corresponding heat of fusion. The relevant heat of fusion data and hydration numbers are given in Table 5.3. The peak area and the corresponding amount of each phase from Figure 5.2 are given in Table 5.4 for the MCH system synthesized at lower pressure. The hydrate conversion for that particular sample  107  was found to be 97%. This number is comparable to the total conversion value calculated from the gas uptake taking into account the cage occupancy and also from directly measuring the gas content in hydrate phase, as given in Table 5.2.  Table 5.4: DSC summary of Methane + MCH hydrate formed at low pressure with 200% LMGS Phase  Integrated area  Amount from melting  Amount from hydrate  Conversion into hydrate  MCH  282 mJ  0.042 mmol  0.032 mmol  0.032 ×100 = 44% 0.032+ 0.042  (CH4 + MCH) hydrate  3200 mJ  0.179 mmol  Ice/water  6831 mJ  1.137 mmol  1.105 mmol  1.105 ×100 = 97% 1.137  5.3.4  Solid-state NMR analysis Figures 5.3 to 5.5 show  13  C magic angle spinning (MAS) NMR spectra obtained  at 193K with ~2 kHz spinning rate. Table 5.5 summarizes the chemical shifts. The spectra were acquired by both cross-polarization and high power proton decoupling program to distinguish the signal from the liquid (excess LMGS) and hydrate phases. The signals acquired from cross-polarization refer to the hydrate (solid) phase only. It is noted that due to rapid motion of TBME in the hydrate phase, the cross-polarization spectrum has weak intensity and hence the identification of signals from the liquid phase is obtained from the high power decoupling spectrum of pure liquid TBME. Figure 5.6 shows the magnified spectra in the methane region for sI, sI+sH, and sH. The signature of the methane signals from sH hydrate is obvious at around -4.4 ppm. The sample with 50% LMGS formed at high pressure showed the appearance of another methane signal at -6.5 ppm. This is the signature of methane in the large cage of sI hydrate, as seen from  108  pure sI methane hydrate (no LMGS) signals. The methane signal from the small cage at 4.1 ppm is not clearly seen because it overlaps with sH signals. High power decoupling (hydrate+liquid) Cross-polarization (hydrate only)  Methane in hydrate  Intensity  NH in hydrate NH in liquid NH in hydrate  NH in hydrate  50  40  NH in liquid  30  20  10  0  -10  -20  Chemical Shift [ppm]  Figure 5.3:  13  C MAS-NMR spectra of (Methane+NH) sH hydrate, synthesized with 200% NH at low pressure condition (Final pressure ~17 bars at 274K) High power decoupling (hydrate+liquid) Cross-polarization (hydrate only)  Methane in hydrate  Intensity  MCH  50  40  30  20  10  0  -10  -20  Chemical Shift [ppm]  Figure 5.4:  13  C MAS-NMR spectra of (Methane+MCH) sH hydrate, synthesized with 200% MCH at low pressure condition (Final pressure ~17 bars at 274K)  109  High-power decoupling (hydrate+liquid) Liquid TBME  Intensity  Methane in hydrate TBME  80  60  40  20  0  -20  Chemical Shift [ppm] Figure 5.5:  13  C MAS-NMR spectra of (Methane+TBME) sH hydrate, synthesized with 200% TBME at low pressure condition (Final pressure ~21 bars at 274K)  No LMGS (sI) NH (sI+sH) TBME (sI+sH) TBME (sH) MCH (sH) NH (sH) 0  -2  -4  -6  -8  -10  -12  Chemical Shift [ppm]  Figure 5.6:  13  C MAS-NMR spectra magnified around methane region obtained at 193K.  110  Methane molecules in the small and medium cages of NH and MCH systems are not distinguishable because the peaks overlapped. Hence the occupancies of methane in the small and medium cage for the NH and MCH systems are reported as the average occupancy between the two cages. Interestingly the previously reported NMR spectra indicated the existence of a doublet even for the NH [14] and MCH [26] systems whereas no doublet was seen in this study. This is not due to lower spinning rate (2 kHz-in this study as opposed to 3 kHz-in their study), but rather because of the temperature differences during the measurements. It was found that a 2 kHz spinning rate is high enough that further increasing the rate would not improve the resolution. However, there is a huge temperature difference (50 K) reported in this study (T=193 K) and that of Seo and Lee (T=243 K) [14] and Yeon et al. [26]. The acquired spectrum requires a minimum of an hour to obtain a good signal-to-noise ratio due to long relaxation time and low natural abundance of 13C. Hence, low temperature at 193K was employed in this study to prevent hydrate decomposition during the experiments. It has been reported that the host water molecules begin to re-orientate faster at temperature above 200K [27]. Hence the dynamic on time average at higher temperatures gives isotropic line-shape that is narrower with sharper features than at low temperatures. This explains the differences observed for the 13C NMR spectra of methane in sH hydrate in this study and that of Seo and Lee [14] and Yeon et al. [26]. Methane peak broadening with NH and MCH in our measurements was purely due to the nature of the sample. At such a low temperature, the guest molecules experienced different re-orientation motion that gives a distribution of individual line-shape resulting in line-broadening. On the other hand, the signal from the TBME system is much sharper than those of the NH or MCH  111  systems where a split peak was seen at -4.3 and -4.7 ppm. The intensity ratio of the signals at -4.3 and -4.7 ppm is approximately 3:2, which corresponds to methane in the small cage and medium cage. The better resolution for methane signals in sH hydrate with TBME may be related to the nature of the guest in the hydrate cage. The TBME molecule has an oxygen atom which is able to inject Bjerrum defects into the host lattice. It has been reported that hydrate kinetics with polar guest such as ether is reasonably fast, even at such low temperatures where very little activity was observed with the non-polar guest [28]. The unusual mobility for the system with a polar guest is attributed to the induced defect to the host lattice. As a result the motion of water molecules becomes faster which gives the cages their true crystallographic symmetry resulting in sharper resonances [27].  Table 5.5: Chemical shift of methane and LMGS in the hydrate and liquid phase obtained from 13C NMR referenced to adamantane at 298K Hydrate phase System Liquid phase Small cage Medium cage Large cage CH4 hydrate (CH4 + TBME) hydrate (CH4 + NH) hydrate  (CH4 + MCH) hydrate  ‘A’ ‘B’ ‘C’  -4.10  -  -4.30  -4.70  -4.40 A  -6.50  -  26.91 48.41 73.14 8.53 29.20 30.27 36.91 B  27.29 49.37 72.47 9.60 29.46 31.04 36.95 23.88 26.95 27.31 33.72 36.09  23.49 27.24 B, C 33.71 B 36.08 B  -4.40 A  Methane signals from the small and medium cages overlap. The chemical shift for these signals overlapped with the liquid phase (fairly close). The number given is just approximate. Two MCH signals from the hydrate phase at ~27 ppm are too close to be separated.  112  The summary of chemical shifts from methane and LMGS in the hydrate and liquid phases are summarized in Table 5.5. Since the LMGS molecule has more than one carbon atoms, several peaks appear on the  13  C spectra. The number of peaks is  determined by the symmetry of the molecule. For example, TBME has three signals because there are three carbon atoms with different symmetry, which are: (1) the three methyl groups that are connected to the carbon atom; (2) the carbon atom that is connected to three methyl groups and oxygen atom; and (3) a methyl group that is attached to the oxygen. The LMGS signals from the hydrate phase are generally shifted to the higher field from the corresponding liquid signals. A few exceptions were observed where the signal did not shift much from the liquid signals (MCH), or, where it is shifted to lower field in the case of TBME at ~73 ppm. The intensity of the LMGS signals from the hydrate phase that were indistinguishable from that of the liquid phase was assigned from the corresponding molecular formula and the other signal that was distinguishable, generally the methyl group. The intensity ratio of methane and LMGS peaks from the hydrate phase was then used to calculate the cage occupancy after taking into account the number of molecules per cage and carbon atoms per molecule. It is generally safe to assume that the large cages have to be completely full to maintain hydrate stability. Hence the determination of methane occupancy was taken directly from the intensity ratio. For the TBME system, the cage occupancy was calculated from the statistical thermodynamics equation for the hydrate phase:  − ∆µ wo =  RT [3 ln(1 − θ S ) + 2 ln(1 − θ M ) + ln(1 − θ L )] 34  (6.1)  The value of ∆µ wo was 1187.5 J/mol [29]. Two more equations are needed to solve three variables, which are obtainable from NMR: θ S θ L and θ M θ L . 113  Table 5.6: Cage occupancy values obtained by 13C MAS NMR LMGS amount/ System  Pressure  No LMGS 200% nC7  high high low high low high low high low high low high low high low high  50% TBME 200% TBME 50% NH 200% NH 50% MCH 200% MCH 3NH:1TBME (200%) 6NH:1TBME (200%)  Hydrate structure I I H HA H H H HA H H HA HA H H H H  θS  θM  θL  0.87 0.87 0.78 0.92 0.78 0.97  0.74 0.63 0.76 0.79  1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00  0.84 B 0.94 B 0.88 B 0.99 B 0.91 B 0.99 B 0.90 B 1.00 B 0.76 B 0.88 B  ‘A’  The presence of methane in sI hydrate was also seen. The intensities of the methane in the small cage of sI and sH hydrate were overlapped, hence the contribution from sI was calculated with the assumption that its occupancy was the same as sI methane hydrate by itself and subtracted from the total amount. The occupancy values which belong to sH hydrate only are reported.  ‘B’  The spectra from NMR do not distinguish the methane in the small and medium cages due to very close chemical shift and broader peak than TBME system. Hence the average occupancy from the two cages is reported. All cage occupancy values and hydrate structures formed at the end of the  synthesis are summarized in Table 5.6. In the stability region of sI hydrate, the stable structure is sH hydrate when excess LMGS is present. A mixture of sI and sH hydrate was encountered when less LMGS was used, as seen in Figure 5.6. The amount of LMGS did not seem to affect the methane occupancy. Methane occupancy was found to increase with pressure for all systems. The methane occupancy varies with LMGS and hydrate formation pressure in the following order: MCH (0.90), NH (0.88), and TBME (0.77).  114  This is interesting because the rate of hydrate formation obtained from the kinetics experiment through gas uptake and spectroscopy indicated the opposite trend [30,31]. Thus, the kinetics and cage occupancy of hydrates do not necessarily correlate with each other although the kinetics is correlated with the solubility of the LMGS in the water phase [32]. Lower methane occupancy for the TBME system may be associated with the lower driving force applied during the hydrates synthesis. The driving force here is defined as the difference between the experimental and equilibrium pressure at a given temperature. Since all hydrates were synthesized under the same pressure and temperature conditions, the most stable system with the lowest equilibrium pressure has the highest driving force. Among all systems investigated, the NH and MCH systems are much more stable than the TBME system. Hence, the methane occupancies for the NH and MCH hydrates are higher than for the TBME system. However, it is also important to note that the occupancy values reported here are based on non-isobaric and nonisothermal hydrate synthesis. Hence, the cage occupancy may change during the formation as the pressure and temperature is not maintained at the same condition. The methane occupancy for the MCH system was also reported from a single crystal study [15,16]. The reported occupancy was ~0.80, which is lower than the measured values in this study. This is likely due to the difference in the driving force during the synthesis. The methane occupancy values obtained from NMR are also consistent with the gas contents measured by decomposing the hydrates. However, they are significantly lower than the suggested ones [33]. Apparently Khokhar et al. [33] overestimated the possible gas content in sH hydrate.  115  13  It is clear at this point that  C MAS NMR is capable of identifying hydrate  structure and cage occupancy. The hydration number can be calculated from the occupancy values, as given in Table 5.3. The chemical shift of methane is specific and clear for each hydrate structure and the intensity ratio can be used to determine the cage occupancy.  5.3.5  Raman spectroscopic analysis Hydrate samples were also analyzed with Raman spectroscopy, as shown in  Figures 5.7 to 5.10. There are many signals observed in the Raman spectra. However, the intense ones are those in the region of C-H and O-H bond, stretching between 2800 and 3500 cm-1. The C-H stretching signals from the methane and LMGS overlap. However, the intensity of the methane peak is much higher than those of the LMGS. CH4 in hydrate  MCH liquid Methane + MCH (sH hydrate)  MCH in liquid  Intensity  MCH in hydrate  O-H from ice/hydrate  2800  2900  3000  3100  3200  3300 -1  Wavenumber [cm ]  Figure 5.7: Raman spectra of (Methane+MCH) sH hydrate at ~85K  116  3400  3500  CH4 in hydrate  NH liquid Methane+NH (sH hydrate)  NH in liquid  Intensity  NH in hydrate  O-H from ice/hydrate  2800  2900  3000  3100  3200  3300  3400  3500  -1  Wavenumber [cm ]  Figure 5.8: Raman spectra of (Methane+NH) sH hydrate at ~85K  CH4 in hydrate  TBME liquid Methane+TBME hydrate (sH hydrate)  TBME in liquid Intensity  TBME in hydrate  O-H from ice/hydrate  2800  2900  3000  3100  3200  3300  3400  3500  -1  Wavenumber [cm ]  Figure 5.9: Raman spectra of (Methane+TBME) sH hydrate at ~85K and TBME liquid.  117  CH4 in sH CH4 in sI  TBME liquid  TBME in liquid  Methane+TBME (sI+sH) hydrate  Intensity  TBME in hydrate  O-H from ice/hydrate  2800  2900  3000  3100  3200  3300  3400  3500  -1  Wavenumber [cm ]  Figure 5.10: Raman spectra of (Methane+TBME) sI+sH hydrate at ~85K Figure 5.11 shows the magnified spectra in the methane region. There is only a single and strong methane signal which appears at ~2913 cm-1 that corresponds to sH hydrate. No peak splitting was seen, unlike those from the  13  C methane NMR signal in  TBME hydrate. Another methane signal appears at ~2904 cm-1 for the hydrate formed at high pressure and 50% LMGS. The intensity ratio for the signals at 2913 cm-1 and 2904 cm-1 is ~3:2, which coincides with the number ratio of small to medium cages. One may interpret this spectrum as methane in sH hydrate with the signal at 2904cm-1 assigned to the medium cage. However the PXRD and NMR measurements do not support this idea (Table 5.2 and figure 5.6), suggesting that the signals arise from a mixture of sI and sH hydrate. Hence the signal at 2904cm-1 is actually from the large cage of sI hydrate because it is exactly at the same location as the signal from pure sI hydrate. Uchida et al. [20] argued that two methane signals from sH hydrate were observed, the methane peak  118  in the medium cage being at 2901.5 cm-1 and at 2911.0 cm-1 for the small cage, however this study does not support this assignment.  No LMGS (sI) TBME (sI+sH) TBME (sH) MCH (sH)  NH (sH)  2880  2890  2900  2910  2920  2930  2940  2950  -1  Wavenumber [cm ]  Figure 5.11: Raman spectra around methane region obtained at ~85K Due to the complexity and low intensity of the LMGS signals, it is very difficult to quantify the LMGS from the hydrate phase. Hence it is impossible to determine the cage occupancy from Raman spectroscopy. Besides, an excess or unreacted LMGS is always present in the sample making it more difficult to separate the signals from the hydrate phase. Full LMGS conversion or single crystals may be required to eliminate the liquid signal interference. Raman spectra from the LMGS liquids are also shown in the figures. Generally, the LMGS signals from the hydrate phase are shifted slightly to a higher wavenumber. The O-H stretching signals from sH hydrate are comparable to those from ice or sI hydrate with the most intense part of the signal at ~3100 cm-1. Thus one has to be careful to determine the hydrate structure from the O-H signals especially for solid  119  mixtures because it is not that simple as suggested previously [34]. Raman spectra for methane-containing hydrate without additional data generally do not offer much information in terms of crystal structure and cage occupancy, especially when more than one guest molecule is present. A combined analysis with PXRD and/or NMR is therefore required to interpret the Raman spectra. The peak positions of all hydrate structures are fairly close to each other and the natural line widths are large so that relating the Raman shift to hydrate structure is not straightforward.  o t = 0 min at -5 C  Intensity / a.u.  o t0 = 120 min at -5 C o t = (t0 + 15) min at 5 C  2890  2900  2910  2920  2930  2940  2950  Wavenumber / cm-1 Figure 5.12: Raman spectra during (CH4+TBME) hydrate formation at ~3.5 MPa. An extra experiment was performed to further verify the arguments presented above on peak assignment. Hydrate was formed in a pressure cell with a quartz window for in-situ Raman analysis during hydrate formation and decomposition. The design of the Raman cell is given elsewhere [35]. Hydrate was grown from ice powder with excess  120  TBME sprayed on top at -5°C and ~3.5MPa. The hydrate was allowed to grow for 2 hours before ramping the temperature to 5°C for further conversion (20 min). A spectrum was recorded every minute by accumulating 5 scans (5s). Figure 5.12 shows three spectra.  Intensity / a.u.  o td = 0 min at 8 C o td = 3 min at 10 C o td = 4 min at 10 C  2890  2900  2910  2920  2930  2940  2950  Wavenumber / cm-1 Figure 5.13: Raman spectra during (CH4+TBME) hydrate decomposition at~3.5 MPa. The LMGS signals were invisible due to the few scans acquired and very low signal intensity. Initially, only methane gas was seen at ~2918 cm-1 and then another signal grew at ~2913 cm-1 which corresponded to hydrate formation. No other signal was observed in this spectral region. The hydrate was then decomposed by increasing the temperature above the phase equilibrium line (10°C). Figure 5.13 shows the disappearance of the signal at ~2913 cm-1 leaving the gas phase alone which further supports the fact that methane molecules in small and medium cages of sH hydrate are not distinguishable from Raman.  121  5.4 Conclusions Structure I and structure H gas hydrate samples were synthesized, characterized and analyzed with PXRD, DSC, NMR, and Raman spectroscopy. The hydrate structure, conversion, and gas content in the hydrate phase obtained from the different techniques are consistent. The stable crystal structure is sH hydrate whenever there is an excess of the large molecule guest substance (LMGS). The presence of n-heptane as a non-hydrate former does not change the methane hydrate structure and methane occupancy. The methane content in sH hydrate increases in the following order: TBME<NH<MCH. The gas storage capacity in sH hydrate varies with LMGS and is approximately 20-40% less than that of sI methane hydrate (170 v/v). Methane and LMGS signals could be identified by Raman and NMR spectroscopies. However, the hydrate composition can only be acquired through NMR. Misinterpretation of the observed Raman spectra used to determine cage occupancy of sH hydrate that was reported in the literature is clarified in this study.  122  5.5 References [1]  Ripmeester, J.A.; Ratcliffe, C.I. J. Phys. Chem. 1988, 92 (2), 337-339.  [2]  Ripmeester, J.A.; Ratcliffe, C.I.; J. Struct. Chem. 1999, 40 (5), 654-662.  [3]  Sloan, E.D. J. Chem. Thermodynamics 2003, 35, 41-53.  [4]  Tulk, C.A.; Ripmeester, J.A.; Klug, D.D. Ann. NY Acad. Sci. 2000, 912, 859-872.  [5]  Dalmazzone, D.; Kharrat, M.; Lachet, V.; Fouconnier, B.; Clausse, D. J. Thermal Anal. Cal. 2002, 70, 493-505.  [6]  Giavarini, C.; Maccioni F.; Santarelli, M.L. J. Thermal Anal. Cal. 2006, 84, 419424.  [7]  Parlouër, P.L.; Dalmazzone, C.; Herzhaft , B.; Rousseau, L.; Mathonat, C. J. Thermal Anal. Cal. 2004, 78, 165-172.  [8]  Kini, R.; Dec, S.F.; Sloan, E.D. Jr. J. Phys. Chem. A 2004, 108, 9550-9556.  [9]  Komai, T.; Kang, S.-P.; Yoon, J.-H.; Yamamoto, Y.; Kawamura, T.; Ohtake, M. J. Phys. Chem. B 2004, 108, 8062-8068.  [10]  Pietrass, T.; Gaede, H.C.; Bifone, A.; Pines, A.; Ripmeester, J.A. J. Am. Chem. Soc. 1995, 117, 7520-7525.  [11]  Yoon, J.-H.; Kawamura, T.; Yamamoto, Y.; Komai, T. J. Phys. Chem. A 2004, 108, 5057-5059.  [12]  Uchida, T.; Takeya, S.; Wilson, L.D.; Tulk, C.A.; Ripmeester, J.A.; Nagao, J.; Ebinuma, T.; Narita, H. Can. J. Phys. 2003, 81, 351-357.  [13]  Wilson, L.D.; Tulk, C.A.; Ripmeester, J.A.; Proc. 4th Int. Conf. Gas Hydrates  2002, 2, 614-618. [14]  Seo Y.-T.; Lee, H. Kor. J. Chem. Eng. 2003, 20, 1085-1091.  123  [15]  Udachin, K.A.; Ratcliffe, C.I.; Ripmeester, J.A. Proc. 4th Int. Conf. Gas Hydrates  2002a, 2, 604-607. [16]  Udachin, K.A.; Ratcliffe, C.I.; Ripmeester, J.A. Supramol. Chem. 2002b, 2, 405408.  [17]  Chou, I.-M.; Sharma, A.; Burruss, R.C.; Shu, J.; Mao, H.-K.; Hemley, R.J.; Goncharov, A.F.; Stern, L.A.; Kirby, S.H. Proc. Nat. Acad. Sci. U.S.A. 2000, 97 (25), 13484-13487.  [18]  Sum, A.K.; Burruss, R.C.; Sloan, E.D. J. Phys. Chem. B 1997, 101, 7371-7377.  [19]  Sun, Q.; Duan, T.-Y.; Zheng, H.-F.; Ji, J.-Q.; Wu, X.-Y. J. Chem. Phys. 2005, 122 (2), 024174.  [20]  Uchida, T.; Ohmura, R.; Ikeda, I.Y.; Nagao, J.; Takeya, S.; Hori, A. J. Phys. Chem. B 2006, 110, 4583-4588.  [21]  Subramanian, S.; Kini, R.A.; Dec, S.F.; Sloan, E.D. Jr. Chem. Eng. Sci. 2000, 55, 1981-1999.  [22]  Wang, X.; Schultz, A.J.; Halpern, Y. J. Phys. Chem. A 2002, 106, 7304-7309.  [23]  Anderson, G. K. J. Chem. Thermodynamics 2004, 36, 1119-1127.  [24]  Linstrom, P.J.; Mallard, W.G. NIST Chemistry WebBook, NIST Standard Reference Database 2005, Number 69, June, National Institute of Standards and Technology, Gaithersburg MD, 20899 (http://webbook.nist.gov).  [25]  Yoon, J.-H.; Yamamoto, Y.; Komai, T.; Haneda, H. Ind. Eng. Chem. Res. 2003, 42, 1111-1114.  [26]  Yeon, S.-H.; Seol, J.; Lee, H. J. Am. Chem. Soc. 2006, 128 (38), 12388-12389.  [27]  Collins, M.J.; Ratcliffe, C.I.; Ripmeester, J.A. J. Phys. Chem. 1990, 94, 157-162.  124  [28]  Gulluru, D.B.; Devlin, J.P. J. Phys. Chem. A 2006, 110, 1901-1906.  [29]  Mehta, A.P.; Sloan, E.D. A. I. Ch. E. J. 1996, 42, 2036-2046.  [30]  Lee, J.-D.; Susilo, R.; Englezos, P. Energy & Fuels 2005, 19, 1008-1015.  [31]  Susilo, R.; Moudrakovski, I.L.; Englezos, P.; Ripmeester, J.A. J. Phys. Chem. B  2006, 110, 25803-25809. [32]  Susilo, R.; Lee, J.D.; Englezos, P. Fluid Phase Equilibria 2005, 231(1), 20-26.  [33]  Khokhar, A.A.; Gudmundsson, J.S.; Sloan, E.D. Fluid Phase Equilibria 1998, 150, 383-392.  [34]  Schicks, J.M.; Erzinger, J.; Ziemann, M.A. Spectrochimica Acta Part A 2005, 61, 2399-2403.  [35]  Schicks, J.M.; Ripmeester, J.A. Angew. Chem. Int. Ed. 2004, 43, 3310-3313.  125  CHAPTER-6 TUNING METHANE CONTENT IN GAS HYDRATES VIA THERMODYNAMICS MODELING AND MOLECULAR DYNAMICS SIMULATION5 6.1 Introduction The maximum gas storage capacities of hydrates at standard temperature and pressure (STP) when all cages are singly occupied are summarized in Table 1.3. The gas content in each respective cage is distributed based on the hydrate formula of each structure. Obviously the realistic gas storage capacity in each hydrate depends on the occupancy of the cages with the guest molecule of interest. Methane can fit into all of hydrate cages. Under moderate pressure conditions, it is well-known that methane forms a stable sI hydrate with both 512 and 51262 cages occupied [1]. Methane in sII or sH hydrate is stable only if a larger guest molecule is present or at extremely high pressures [2-5] where multiple methane molecules occupy the large cages. Methane sI hydrate is stable above 2.65 MPa at 0°C [6]. The hydrate phase equilibria of sI methane hydrate and the occupancy values in the small and large cages are readily available. Methane occupancy in the large sI cages is almost complete (97% and up) whereas about 85-95% occupancy in the small cage has been reported, depending on the pressure and temperature at which the hydrate is synthesized [1, 7]. Thus the total methane content in sI hydrate is approximated as anywhere between ~160 to ~170 v/v, which is the highest among all hydrate structures. 5  “A version of this chapter has been published. Susilo, R., Alavi, S., Ripmeester, J.A. and Englezos, P., “Tuning Methane Content in Gas Hydrates via Thermodynamics Modeling and Molecular Dynamics Simulation”, special edition of Fluid Phase Equilibria, 263 (1), 6-17, 2008.” 126  The motivation for storing methane in sII and sH hydrate is to lower the hydrate stability pressure at a given temperature so that it becomes safer to handle and more economical to transport. One way of achieving this is to introduce a second guest molecule that is a much more stable hydrate former in a mixture with methane. The stability of the binary guest hydrate can be determined by the hydrate phase boundary for these guests. However, it is not straightforward to determine the methane cage occupancy/content in mixed hydrates. Therefore, it is important to obtain strategies on how to tune hydrate properties by optimizing the methane gas storage density versus hydrate stability. Larger molecular guest substances form stable methane-containing sH hydrates at lower pressures than sI hydrate, but with ~20% lower methane content [8]. Hence, there is a trade-off between hydrate stability and methane content for different hydrate systems/structures. It has been reported that at pressures above 0.6 GPa, the large cages of the sH hydrate accommodate multiple methane molecules without the need of the large guest molecules [2]. The initial analysis of the solid state X-ray and neutron diffraction data suggested that there were five methane molecules per large cage [4]. However, further analysis indicates that this result may need revision (Klug, D.D., personal communication, 2007). Only 2-3 methane molecules were suggested from Raman spectroscopy to fit the large cage of sH hydrate [5]. Molecular dynamics (MD) was employed to further study the methane occupancy in pure sH methane clathrates [9]. It was found that the predicted number of methane molecules occupying the large cages depends critically on the methane potential chosen. Potentials with stronger attractions among methane molecules allow the large cage to accommodate more methane, up to  127  five molecules per cage. It should be pointed out that methane storage in sH clathrates with multiple methane occupancies is only of theoretical interest as the required pressure is about 0.5GPa or higher. The goals of this study are to determine optimum hydrate formation conditions and/or methane content in sII and sH hydrate. The methane occupancies in all hydrate cages are determined for several hydrate systems at the equilibrium conditions so that the gas content can be inferred. A macroscopic approach using the van der Waals-Platteeuw model is employed to obtain a correlation between gas content in the hydrate and the stability for singly occupied hydrate cages in binary methane sII hydrates with propane and tetrahydrofuran (THF). MD simulations are employed for all sH hydrates systems to determine the stability of multiple methane occupancy in the large cages. Free energy calculations are performed to determine the number of methane molecules in the large cage of the most stable hydrate at a given temperature and pressure. The possibility of storing more methane in sH hydrate by replacing the large sH forming molecule with methane is also discussed. The simulation results are compared with available experimental data reported in the literature.  6.2 Computational Methodology 6.2.1  Macroscopic modeling  At equilibrium, the chemical potential of host water in the hydrate phase (µH) and the liquid water (µW) or ice phase (µI) are equal as given in equation (6.1). Since the temperature of interest in our study is above 273 K (6.1)  µ H = µW  128  The chemical potential of water in the hydrate phase is obtained from the statistical thermodynamical model of van der Waals and Platteeuw [10]. The occupancy of guest molecules in the hydrate cages were calculated from the Langmuir constants utilizing the Kihara potential [11]. The chemical potential of water in the liquid phase can be calculated following the method suggested by Holder et al. [12]. The solubility of methane and propane were calculated by using the Krichevsky and Kasarnovsky equation based on modified Henry’s law [13]. For THF, which is completely miscible in water, the activity coefficient was calculated from the modified UNIFAC model, with all UNIFAC parameters obtained from Reid et al. [14]. The SRK (Soave-Redlich-Kwong) equation of state was used for gas phase fugacities. For the system with THF, a flash calculation is performed to account for the THF volatility. At equilibrium the fugacity of each component in each phase has to be equal. In the THF containing system, the fugacity was calculated by using the modified Huron-Vidal (MHV-2) mixing rule incorporated with the modified UNIFAC [15-17]. A program was written to predict the hydrate phase equilibrium pressure and cage occupancies at a given temperature.  6.2.2  Molecular dynamics (MD) methods The macroscopic statistical thermodynamics approach of the last section is based  on several assumptions that do not allow multiple guest occupancy in a cage. The partition function and the cell potential function of the van der Waals – Platteeuw theory have to be re-formulated to take into account multiple guest occupancy. Alternatively, molecular dynamics simulations are employed to provide insight into the feasibility of  129  enhancing methane storage in sH hydrates. The method applied in this study has been reported in previous publications on hydrogen [18-20], rare gases [21], and recently carbon dioxide [22] and methane [9] hydrate. A periodic 3×3×3 replica of the sH hydrate unit cell was used in simulations with initial dimensions set at 36.99 × 36.99 × 29.76 Å3. The initial positions of water-oxygen atoms of the hydrate lattice were obtained from the crystallography of sH hydrate [2326]. The disordered water hydrogen atoms were attached to water oxygen sites subjected to the constraints of the Bernal-Fowler ice rules [27] via a Monte Carlo calculation. The hydrogen configuration with minimum total dipole moment of the unit cell of the sH lattice was chosen as the initial state for the molecular dynamics simulations. The water coordinates of a unit cell of the sH hydrate lattice are given in Table 6.1. The small and medium cages in all simulations are occupied by one methane molecule. The large cage is filled with tert-butyl methyl ether (TBME) or one to five methane molecules. All molecules are placed randomly, with the center of mass at the center of the cage. The position of each molecule is equilibrated at the beginning of the simulation. . The extended simple point charge (SPC/E) model is used to describe the potential for water [28]. This potential allows the modeling of many features of water and water solutions under various conditions and has also been extensively used in simulations of structure II N2 [29-31] and H2 clathrates [18-20]. The SPC/E model properly predicts the lattice constants of these clathrate phases at experimental temperatures and pressures. As a result, we expect the SPC/E model to correctly capture the features of the sH methane clathrates. The SPC/E model, however estimates the  130  melting point of water to be 215 K [32] and as a result may also underestimate the clathrate decomposition conditions. The TBME molecule is considered flexible, with the initial structure determined by optimization using density functional theory at the B3LYP/6-311++G(d,p) level [33] with the GAUSSIAN 98 suite of programs [34].  Table 6.1: Coordinates of water molecules forming a unit cell of sH hydrate in Å units. O x 0.000 0.000 0.000 2.269 -2.269 2.269 0.000 -2.269 -2.367 2.367 0.000 3.739 7.479 3.722 -3.722 4.733 -3.739 3.739 7.479 -2.367 2.367 -3.739 4.733 8.375 3.837 2.384 9.828 6.106 6.106 6.106 8.375 3.837 6.106 6.106  y 7.050 7.050 4.430 8.361 8.361 8.361 4.430 8.361 4.099 4.099 2.753 6.477 0.000 9.200 9.200 0.000 6.477 6.477 0.000 4.099 4.099 6.477 0.000 2.215 2.215 1.377 1.377 6.146 7.823 6.146 2.215 2.215 3.526 3.526  H z 1.402 8.741 2.259 2.259 2.259 7.884 7.884 7.884 3.651 3.651 0.000 3.651 3.651 0.000 0.000 3.651 3.651 6.492 6.492 6.492 6.492 6.492 6.492 2.259 2.259 0.000 0.000 2.259 0.000 7.884 7.884 7.884 1.402 8.741  x -0.010 0.010 -0.856 1.468 -2.788 1.451 -0.029 -2.795 -2.423 1.504 -0.008 3.211 6.493 3.192 -3.170 4.698 -3.211 3.181 7.803 -1.510 2.282 -3.822 5.733 8.051 3.315 2.396 10.736 5.296 6.106 5.259 8.916 3.282 6.933 6.926  y 6.101 7.044 4.311 7.859 8.644 7.888 5.375 7.723 4.032 4.236 3.391 7.161 0.000 8.913 8.883 0.087 7.161 7.192 -0.820 4.214 3.953 6.466 -0.004 1.414 1.914 0.377 1.795 6.282 7.266 6.297 2.884 2.873 3.060 3.052  131  H z 1.718 9.741 2.762 1.933 1.452 8.211 8.209 7.322 4.647 3.166 -0.770 3.148 3.482 0.798 -0.771 4.647 3.148 6.912 6.964 6.994 5.506 5.495 6.489 2.763 1.461 0.012 0.000 2.829 0.831 7.375 7.375 7.375 1.718 8.419  x -0.827 -0.820 0.000 1.972 -1.966 2.808 0.847 -2.007 -2.954 2.918 0.864 3.243 7.648 4.593 -4.599 4.393 -3.243 3.681 7.794 -2.870 2.860 -4.643 4.404 8.891 4.662 2.932 9.920 6.929 6.106 6.135 8.905 4.670 6.116 6.096  y 7.516 7.524 3.834 9.179 9.171 8.672 4.279 9.153 3.403 3.420 2.249 5.609 0.000 8.709 8.719 0.841 5.609 6.551 0.813 4.963 4.953 6.357 0.800 1.917 2.692 1.708 0.381 6.278 7.225 5.201 1.881 2.662 4.475 3.532  z 1.718 8.419 1.456 2.751 2.762 8.666 7.375 7.333 3.237 3.166 0.007 3.653 4.637 -0.016 0.002 3.231 3.653 5.496 6.982 6.489 6.661 6.903 6.995 1.456 1.956 -0.768 0.000 2.812 -0.802 8.209 8.663 8.209 1.718 9.741  Electrostatic charges on TBME are estimated from the Charges from Electrostatic Potential, Grid (CHELPG) [35] method as implemented in the GAUSSIAN program. The van der Waals intermolecular interaction parameters of atoms from the TBME molecule are obtained from the general AMBER force field (GAFF) [36] as reported in our previous study [20]. The performance of several methane potentials were demonstrated in our previous work [9]. Simulations with the Murad-Gubbins (MG) potential [37] suggest that the large cage may accommodate two to three methane molecules due to weak attraction between methane and methane, in agreement with Raman measurements and thus employed in this study. The van der Waals interactions among guest-guest and guest-host molecules are based  on  Lennard-Jones  (12-6)  potential.  The  standard  combining  rules,  ε ij = (ε ii ε jj ) and σij = (σii+ σjj)/2 are used to derive Lennard-Jones potential parameters 1/ 2  between unlike atom-type force centers i and j from the values of the parameters between similar atom types. All intermolecular interactions are calculated with the cut-off distance of 13 Å. Coulombic interactions between point charges qi and qj located on the atomic nuclei i and j are used to model the electrostatic intermolecular interactions. Long-range electrostatic interactions were calculated using the Ewald summation method [38] with a precision of 1×10-6. The intermolecular potential is given by   σ  ij V (inter ) = ∑∑  4ε ij    rij i =1 j >i    N −1 N  12 6   σ ij   qq   −   + i j    rij   4πε 0 rij       (6.2)  Free energy calculations were performed to determine the number of methane molecules occupying the large cage of sH hydrate that provide the most stable hydrate. The initial calculation was carried out with five methane molecules placed inside the  132  large cage. Subsequently (x) methane molecules are removed randomly from the clathrate one by one until there is only one methane left (n = 1) in each large cage. The methane removal from a cage is represented by the following equation. clathrate [(n+x) CH4]  clathrate [(n) CH4] + fluid (x) CH4  (6.3)  where n + x is the number of methane molecules in a simulation cell and x is the number of methane molecules removed from the simulation cell. The numbers n and x are integers. The total change in free energy ∆GTotal for the reaction is the summation of the free energy change of the clathrate phase ∆GClathrate and the evolution of methane into the fluid phase ∆GGas as given in equation (6.4). (6.4)  ∆GTotal = ∆GClathrate + ∆GGas  The free energy of the clathrate phase consists of two parts, which are the lattice free energy ∆G Lattice due to removal of (x) methane molecule from the clathrate lattice and the entropy correction ∆G EC due to indistinguishability of the methane molecules in the cage that is not taken into account by MD. The free energy of the lattice change is calculated via MD by using thermodynamic integration [39] based on the Kirkwood coupling parameter method [40]. The free energy of the clathrate phase and the entropy correction factor to the free energy ∆G EC are given in equations (6.5) and (6.6). ∆GClathrate = ∆G Lattice + ∆G EC  (6.5)   (n + x )!   ∆G EC = −kT ln n ! x !    (6.6)  133  The methane removed from the cage is considered to be a real gas at the pressure and temperature of the simulation. Hence the gas contribution to the free energy ∆GGas consists of an ideal gas ∆G IG contribution and a real gas correction ∆GRGC , ∆GGas = ∆G IG + ∆G RGC .  (6.7)  The ideal gas part is calculated using the statistical mechanics relation [41] taking into account the translational and rotational degrees of freedom of the molecule.  ∆G IG  π 1/ 2  2πmkT  3 / 2 kT   kT = − kT ln  − ln   2 p    σ  h   T   Θ rot      3/ 2   ,   (6.8)  where m = 16.0 ×10-3 kg/mol is the mass of the methane molecule, p = 0.8, 1.0 GPa is the pressure of the reaction, σ = 12 is the symmetry number of the methane molecule, Θrot = 7.54 K is the characteristic rotational temperature of methane, and h is Planck’s constant. The real gas correction factor due to non-ideality is obtained from thermodynamic tables [42]. ∆G RGC = G ( p, T ) − G (1 atm, T )  (6.9)  G ( p, T ) is the Gibbs energy at p and T calculated from the volumetric data (G = H - TS). We assume that the gas is ideal at atmospheric pressure and the temperature T. The entropy correction, ideal gas, and real gas correction contributions to the free energy are calculated separately. The lattice free energy is the only part that is calculated via MD. The annihilation of methane from the clathrate lattice is performed is such a way that the methane molecule is removed gradually by introducing two coupling parameters  λ1 and λ2 for the electrostatic and van der Waals interaction. Hence, the potential energy of the system can be written as follows [9], U n + x (λ1 , λ 2 ) = U n + U elec (λ1 ) + U vdW (λ 2 )  134  (6.10)  where λ1 couples the electrostatic interactions and λ2 couples the van der Waals interactions of the (n+x) guest in the large cages to the (n) guest system. The lattice free energy calculations are performed with potential energies for states with values of λi between 0 and 1 in 0.1 increments [9, 43]. The free energy difference between the (n+x) guest and (n) guest occupancies is given in equation (6.11). The ensemble averages of the potential energy as a function of λ1 and λ2 are determined from MD simulations. The average total potentials U(λ1, λ2) are used to determine the derivatives numerically with respect to the λi and these functions are used in evaluating the integrals of Eq. (6.11).  1  n+ x→n ∆G Lattice = ∫ dλ1 0  ∂U (λ1 , λ 2 ) ∂λ1  1  + ∫ dλ 2 NPT , λ1 ,λ2 =1  0  ∂U (λ1 , λ 2 ) ∂λ 2  (6.11) NPT ,λ1 = 0 ,λ2  Further details of the free energy calculations can be found in references [9] and [43].  6.3 Results and Discussion 6.3.1  Storing methane in sII hydrate Methane with additional sII hydrate formers forms a stable sII hydrate at lower  pressures than pure methane sI hydrate. However, little is known about the methane occupancy/content in the binary clathrate. Macroscopic modeling is employed in this sII hydrate system and a comparison to the binary hydrate phase diagram reported in the literature is made. Propane and THF are chosen as the sII forming guests because they are known to have a strong hydrate stabilizing effect as evident from the hydrate phase diagram [44-47].  135  6.3.1.1 Methane + propane system The predicted hydrate phase equilibria of methane-propane mixtures at different concentrations and the experimental data [44] are reported in the literature [11]. It is well known that methane in sII hydrates with propane is much more stable than in sI hydrate. However, the stabilizing effect of propane is not as significant when its concentration exceeds ~10%. The maximum temperature is also limited to 283.2 K due to the presence of an upper quadruple point. The occupancies of methane in the small and large cages as a function of temperature for different methane concentrations in the initial gas are shown in Figure 6.1. Generally the occupancy increases slightly with temperature corresponding to higher pressure. It is clear that the stabilizing effect of propane lowers the methane occupancy in both cages. The higher propane concentration in the system lowers the methane occupancy even further. However, this effect is more pronounced in the methane occupancy of large cages where essentially only propane is present. 1  100%  0.9  99.0% 97.4% 95.2%  Methane occupancy in small cage / θ S  0.8 0.7  88.3%  0.6  71.2%  0.5 0.4  36.2%  0.3 0.2 0.1 0 273  275  277  279  281  T emperature / K  136  283  285  Methane occupancy in large cage / θ L  1  100%  99.0% 0.1  97.4% 95.2% 88.3%  0.01  71.2%  36.2%  0.001 273  275  277  279  281  283  285  T emperature / K  Figure 6.1: Methane occupancy in the small (top) and large (bottom) cages of sII methane-propane mixed hydrates as a function of temperature and methane composition in the feed gas. The methane occupancy in the large cage is almost negligible when the system has more than 10% propane. Methane is able to enter the large cage only when the gas phase is rich with methane (95% or higher). The maximum methane occupancy in the large cage is ~25% when there is only 1% of propane. Propane does not fit into the small cages of sII hydrate. It is noted that the total large cage occupancy between methane and propane is very close to unity, which is essential for maintaining the structure. Methane occupancy in the small cage in 40% methane + 60% propane gas mixture was suggested to be ~25% [45] with the assumption that all large cages were fully occupied by propane. The predicted occupancy in this work has also confirmed the measured the methane occupancy. The methane storage density in hydrate (v/v) is then computed from the occupancy values relative to full occupancy values from Table 1.2. The total methane  137  content from both cages as a function of methane gas composition in the feed and temperature is given in Figure 6.2. As seen, the methane content in the mixed hydrate is much lower than in sI methane hydrate. The temperature/pressure increases the methane storage to some extent, but not so significantly. However the methane composition in the feed gas has a drastic effect on the storage capacity. The maximum methane content is ~100 to 110 v/v when the feed gas is enriched (99%) with methane. This is a considerable reduction (~40%) of the methane content in comparison to sI methane hydrates. Higher propane concentration (10% or more) in the feed gas lowers the methane content even further.  Total methane content in hydrate [V CH4 /V hydrate ]  175 150 125 100  Temperature increases from 273.2K to 283.2K with 2K increment  75 50 25 0 0%  20%  40%  60%  80%  100%  Feed composition of methane  Figure 6.2: Total methane gas stored in methane-propane mixed sII hydrates at STP as a function of methane composition in the feed gas and temperature.  6.3.1.2 Methane + THF system The hydrate phase diagram for the methane-THF system is shown in Figure 6.3. The predicted results and the experimental data [46,47] are in good agreement. The  138  presence of THF reduces the hydrate equilibrium pressure significantly (even lower than propane) at a given temperature. The hydrate can also be formed and stored at higher temperatures, which was impossible for the mixed hydrate with propane. The lowest hydrate formation pressure at a given temperature is when the THF concentration in the feed liquid phase is near the stoichiometric composition for full occupancy of the large cages by THF, which is ~5.6 mol % THF. 0% 0.01%  16  0.1% 0.5%  Pressure / MPa  14  1%  12  3%  10  5%  8 6 4 2 0 273  278  283  288  293  298  303  T emperature / K Figure 6.3: Three phase hydrate-liquid-gas equilibria of sI methane hydrate (black) and sII methane+THF mixed hydrate (color). The experimental data are obtained from the literature [11,46,47]. A higher concentration than the stoichiometric does not improve the hydrate stability [47]. In fact, it may slow down the kinetics due to the inhibiting effect of THF by lowering the water activity. The pressure reduction is quite significant when the THF concentration in the feed liquid phase is higher than 3% mol, but the phase boundary becomes closer to the sI methane hydrate when the THF concentration is lowered below 1%.  139  Methane occupancy in small cage / θ S  1 0.9  0%  0.8  0.01%  0.7  0.1%  0.6  0.5%  0.5  1%  0.4 0.3  3%  0.2  5%  0.1 0 273  278  283  288  293  298  303  T emperature / K 1  0% 0.01%  Methane occupancy in large cage / θ L  0.9 0.8  0.1%  0.7 0.6 0.5 0.4 0.3 0.2  0.5% 1% 3% 5%  0.1 0 273  278  283  288  293  298  303  T emperature / K  Figure 6.4: Methane occupancy in the small (top) and large (bottom) cages of sII methane-THF mixed hydrates as a function of temperature and THF composition in water. The predicted methane occupancies in small and large cages of the binary sII methane + THF clathrate are shown in Figure 6.4. Generally the occupancy values increase at lower THF concentration and higher temperatures/pressures. The occupancy in the small cage is a strong function of temperature at THF concentrations close to  140  stoichiometric. This can be correlated to the phase diagram in Figure 6.3 where an exponential increase in pressure is observed at higher temperatures. This result suggests that the occupancy values have a strong dependence on the pressure. In addition, THF is also a volatile compound so that its concentration in the liquid phase is lowered at higher temperatures and pressures. Hence performing flash calculations is particularly important at higher temperature/pressure and and/or lower THF concentrations. A simplified calculation by assuming zero THF concentration in the vapor phase was presented earlier [47]. They reported higher deviation between their prediction and experimental data at lower THF concentration, possibly due to inappropriate assumptions. The total occupancy of the large cages in this system is also very close to unity. However methane occupancy in the large cage is very limited especially at THF concentration above 1% as shown in Figure 6.4. Obviously, this is because THF is much more favored to occupy the large cage than methane. Methane occupies the large cage of sII hydrate only when the THF amount is very small so that it is essentially driven by the high methane pressure. The methane storage density in the hydrate phase as a function of THF concentration in the feed liquid phase and temperature is shown in Figure 6.5. It is clear that the gas content in hydrate increases significantly when the THF concentration is lowered below 1% mol. There is also a strong dependency with respect to temperature mainly due to the pressures as mentioned earlier. The optimum conditions are actually working with higher temperatures (close to room temperature) and higher THF concentration (~1% to 3% mol) because reasonably high methane content in hydrate can be maintained (~85 to 100 v/v) without dealing with high pressure (less than 5 MPa).  141  Total methane content in hydrate [V CH4 /V hydrate ]  175 150 125 100  299K 294K 289K  75  284K  50  279K  25  274K  0 0  1  2  3  4  5  T HF concentration / % mol  Figure 6.5: Total methane gas content stored in methane-THF mixed sII hydrates at STP as a function of THF composition and temperature. The comparison between methane occupancy ratio from the large and small cage obtained experimentally and predicted in this study is shown in Figure 6.6. The predicted hydrate equilibrium temperature at 2 MPa of methane pressure is also given. The prediction suggests an exponential increase in the occupancy ratio as the THF concentration decreases below 1% at the expense of lower temperature to maintain the hydrate stability. The predicted values are in good agreement with the data reported earlier [48]. However the most recent data published [49] indicate a much higher deviation from the prediction. This is may well be due to the volatility of the THF and the inhomogeneity of the hydrate (perhaps a non-equilibrium state) when synthesized and collected. Thus, although the initial feed composition of THF is reported, the actual composition in the local environment may differ. Some of the THF evaporates or stays in the hydrate phase with the small cages unoccupied. This becomes very important, especially at low THF concentration because the methane in the hydrate phase observed  142  from NMR spectroscopy may correspond to a THF concentration that is actually lower than the reported one. Consequently higher occupancy values were measured. Temperature profile at 2MPa 290  0.9 0.8 Prediction at P = 20 bar Seo et al. (2005) Kim et al. (2006) / 4 mm probe Kim et al. (2006) / 7 mm probe T eq at P = 20 bar  0.7 0.6 0.5  286 282  0.4  278  0.3 0.2  Temperature / K  Methane occupancy ratio [ θ L /θ S ]  1.0  274  0.1  Predicted occupancy ratio  0.0 0  1  2  3  270 4  5  T HF Concentration / % mol Figure 6.6: Methane occupancy ratio (large to small cages) and hydrate equilibrium temperature at 2 MPa of methane-THF mixed sII hydrates as a function of THF concentration. The other interesting issue is regarding the critical guest (THF) concentration (CGC) which limits the methane occupancy in the large cage [49]. Based on the data, methane occupancy in the large cages reaches the maximum at the CGC and subsequently decreases and diminishes at THF concentrations lower than the CGC. For the methane and THF system the CGC was reported at 0.2 mol% THF [49]. The macroscopic statistical thermodynamics model however does not indicate the presence of a CGC. The predicted results suggest that the occupancy ratio would go all the way up to ~0.84 at 0.01%THF. The methane occupancy ratio eventually increases up to ~1.1 at ~ 0%mol THF where the sI methane hydrate would form instead of sII hydrate. Hence it is still a question why NMR spectroscopy does not detect methane in the large cages at THF  143  concentrations lower than the CGC. It would be interesting to see the ratio of the NMR intensities for methane and THF to see the relative composition of methane and THF in the hydrate phase. Unfortunately only the intensity ratio of methane in different cages is reported but not that for the THF.  6.3.2  Storing methane in sH hydrate Methane with large molecular guest substances (LMGS) such as tert-butyl methyl  ether (TBME), neohexane (NH) and methyl-cyclohexane (MCH) forms sH hydrates at moderate pressure. The relevant fluid phase equilibria, kinetics studies at macro and micro-level and solid phase properties were reported in our previous studies [50-54]. It was found that the average methane occupancy from both small and medium cages varies slightly depending on the LMGS used and pressure at which the hydrate is formed [53]. Lower methane occupancy was reported for polar LMGS ~77% (TBME) than hydrophobic LMGS ~90% (NH and MCH) at pressures below the stability of pure sI methane hydrate. Higher pressure increases the occupancy. This suggests that methane storage capacity in sH hydrate at moderate pressures (2-6 MPa at 274K) is approximately ~100-140 v/v, which is ~20% to 40% lower than in sI hydrate. Hence putting methane in the large cage is the only way to increase the methane content in sH hydrate. MD simulations are employed to study the substitution of the LMGS by methane.  6.3.2.1 The mechanical stability of pure sH methane hydrate The mechanical stability (not thermodynamic stability) of the pure sH methane hydrate with five methane molecules placed inside the large cages was studied by a set of  144  simulations run at different pressures and temperatures. The SPC/E potential used for water is known to underestimate the melting point of ice [32] and therefore the nominal temperatures of the simulation of the sH methane hydrate may not correspond to the experimental temperatures. A separate study will be needed to “calibrate” nominal temperatures used in the simulation and the SPC/E and MG potentials for water and methane with the experimental temperatures. Such a study remains for future work.  ~12.3Å  b  a  ~12.3Å  Figure 6.7: Initial (top) and final (bottom) atomic configuration of 3×3×3 super-cell looking down along the c-axis during the hydrate stability simulation performed at 1 MPa and 300K. The distance from the cage center to its neighboring cage in a and b-axis is approximately 12.3 Å, which is also the size of a unit cell of sH. 145  The simulation for other methane occupancies in the large cage was not attempted due to the very long simulation times required to find out if the hydrate is mechanically stable or not at a given pressure and temperature. Even so the indication of the reliability of MD for such studies is demonstrated. The initial atomic configuration at the beginning of the simulation and a snapshot of the final configuration when the hydrate is fully decomposed are shown in Figure 6.7. The simulations were run until the hydrate decomposed or 3 ns of simulation time had been reached, whichever came first. Decomposition of the structure in less than 3 ns implies the mechanical instability of the clathrate, but a hydrate that has not decomposed in simulations up to 3 ns cannot with certainty be designated as stable. The water forms a droplet as the hydrate decomposes and the methane occupies all the space in the gas phase. The decomposition of the hydrate can also be observed from the configuration energy and volume profiles along the simulation trajectory. The configuration energy increases and the volume decreases as the hydrates melt. Simulations at the nominal temperature of 300 K and a range of pressures from 1 MPa to 1 GPa were performed. The configuration energy profile during the simulation is shown in Figure 6.8. The first 30 ps of the simulation is for thermal equilibration. As seen, the equilibrated configuration energy decreases with increasing pressure. Generally the simulation time when the hydrate starts to decompose increases with pressure. At pressures lower than 0.5 GPa, a sudden jump is observed in the configuration energy during the simulation. This corresponds to hydrate mechanical instability. Hence the hydrate is mechanically stable only at 0.5GPa or higher pressures, which is fairly close to the measured experimental  146  pressure. The lower pressure boundary reported for sH methane hydrate at room temperature is between 0.6 GPa to 1.0 GPa [2,3,5]. Simulation time / ps 1  10  100  1000  10000  -3.8E+04  1MPa  -4.0E+04  E config / kJ/mol  50MPa -4.2E+04  0.1GPa 0.2GPa 10MPa  -4.4E+04  -4.6E+04  0.5GPa 1.0GPa  -4.8E+04  -5.0E+04  Pressure / kbar  Figure 6.8: Configuration energy profile during the simulation of sH methane hydrate.  20 18 Ice VI 16 14 12 10 8 6 4 sI hydrate 2 0 280 290 300  sH hydrate  Liquid water  310  320  330  340  Temperature / K Figure 6.9: Phase diagram of methane-water system at high pressures. The experimental data was obtained from Dyadin et al. [55].  147  The simulation was also performed at higher temperatures (>340 K) at 0.5 GPa and 1 GPa where the hydrate was found to decompose as well. It is important to note that the fluctuation in the pressure and temperature in the simulation are ±50MPa and ±5K. The hydrate phase diagram with experimental data from [55] and simulation results is depicted in Figure 6.9. The green diamond is the quadruple point where sI hydrates, sH hydrates, liquid water and fluid methane are in equilibrium. The grey line is the boundary expected for methane hydrate transition from sI to sH. The stars are the data points from the simulation. The “yellow stars” refer to hydrate instability at that temperature or higher. The “blue star” refers to hydrate instability at that pressure or lower. The “red stars” are the pressures where sH methane hydrate are found to be stable at 300K.  6.3.2.2 Free energy calculation of sH methane hydrate The free energy calculations at 0.8 GPa are summarized in Table 6.2. The free energy contribution from the lattice, entropy correction (EC), ideal gas (IG), and real gas correction (RGC) are given. The lattice energy and total free energy have similar trends. The lattice energy is negative and decreases upon methane removal from 5 to 2. However, an increase is observed when there is only one methane molecule in the cage. Eventually the hydrate decomposes when the simulation is run longer with only a single methane occupying the large cage. The ideal gas contributions are also negative due to molecular motions, but the real gas corrections are positive due to work required to compress the gas. The more methane is released from the hydrate lattice towards the gas phase, the more negative is the ideal gas contribution, but positive for the real gas correction. The overall gas contribution, ∆GGas , is positive. The total free energy change  148  indicates that two to three methane molecules in the large cage provide the most stable hydrate depending on the temperature. Higher methane occupancy is observed at lower temperature. At lower temperature (280 K), three methane molecules seem to be preferred. At 300 K and higher, the large cage may accommodate 2 to 3 methane molecules without a significant free energy difference.  Table 6.2: Free energy per unit cell of hydrate (± 5 kJ/mol) calculation to determine the methane guest occupancy in the large cages of sH hydrate at 0.8 GPa. ∆G lattice  θCH4  ∆G IG  ∆G  ∆G RGC  ∆G total  280K  300K  320K  EC  280K  300K  320K  280K  300K  320K  280K  300K  320K  5 to 4  -13  -12  -14  -4  -31  -34  -37  39  41  43  -8  -9  -12  5 to 3  -24  -27  -28  -5  -62  -68  -74  79  82  86  -13  -19  -22  5 to 2  -27  -32  -36  -5  -93  -102  -111  118  123  128  -8  -17  -24  5 to 1  -13  -15  -14  -4  -124  -136  -148  157  164  171  16  9  5  Table 6.3: Free energy per unit cell of hydrate (± 5 kJ/mol) calculation to determine methane guest occupancy of the large cages of sH hydrate at 1.0 GPa. ∆G lattice  θCH4  ∆G IG  ∆G  ∆G RGC  ∆G total  280K  300K  320K  EC  280K  300K  320K  280K  300K  320K  280K  300K  320K  5 to 4  -9  -11  -12  -4  -31  -34  -37  45  47  49  +1  -2  -4  5 to 3  -22  -26  -26  -5  -62  -68  -74  90  94  98  +1  -5  -8  5 to 2  -26  -27  -30  -5  -93  -102  -111  136  141  146  +11  +6  0  5 to 1  -10  -12  27  -4  -124  -136  -148  181  188  195  +43  +36  +71  The free energy calculations at 1.0 GPa are summarized in Table 6.3. The lattice energy is also negative as the methane content is reduced from 5 to 2 and becomes positive when there is only one methane molecule in the cage that eventually decomposes. The entropy correction and ideal gas contribution to the total free energy is the same as at 0.8 GPa. However, the real gas correction term is larger due to higher 149  pressure. Hence the total free energy indicates that higher occupancy (three to five methane molecules) is more favored. At 280K, there is no large energy penalty for the system when the large cages accommodate three to five methane molecules. At higher temperatures (300 K and 320 K), three methane molecules are preferred. It is also important to note that there is an error associated with the free energy values, which arises from the fluctuation in the configuration energy from the simulation. The error is in the range of ~4-6 kJ/mol. Hence the conclusions drawn from the total energy values should take this error margin into account.  6.3.2.3 Large guest (TBME) replacement with methane TBME is chosen as the large guest molecule. Initially all 27 large cages of the simulation cell are occupied with TBME and subsequently 3, 9, 18, 24, and 27 of them (1/9, 1/3, 2/3, 8/9, 1) are substituted by methane at 300 K and 0.8 GPa. Each TBME is replaced by one to five methane molecules inside a cage. Hence the total methane content stored in sH hydrate is increased from ~143 v/v up to ~286 v/v as shown in Figure 6.10. The change in the configuration energy of the hydrate (sum of van der Waals and electrostatic energy) is shown in Figure 6.11. As seen, the system configurational energy increases when the TBME is replaced by methane. Surprisingly, one methane molecule is preferred to replace the TBME when the TBME content in the total simulation cell is two-thirds or higher. There is a minimum (see Figure 6.11) when the number of TBME molecules replaced is less than 9 (1/3). This is interesting because if this is true, the methane storage capacity in sH hydrate can be increased from ~143 v/v to ~153 v/v without any energy penalty. The system energy increases as more TBME molecules (one-  150  third or more) are replaced with methane. In that case two methane molecules per large cage are preferred instead of one to maintain the hydrate stability (see Figure 6.11 and Table 6.2 where the ∆Gtotal is the least). It should be noted that the full free energy (hydrate+guest) calculations and not only for the hydrate are needed in principle to determine the relative stability of the sH clathrate with partial or full substitution of the TBME in the large cages with methane molecules. This would require developments of new methodology to convert the complex TBME molecule to smaller and multiple methane molecules and as such is beyond the scope of the present work  300 5 CH4  280  4 CH4 260  3 CH4  Gas content [V/V]  2 CH4 240  1 CH4  220 200 180 160  13  140 0  3  6  9  23 12  15  18  1 21  24  27  Number of TBME replaced out of 27  Figure 6.10: Total methane gas content stored in sH methane when 0, 3, 9, 18, 24, and 27 TBME molecules out of 27 are replaced by methane at various quantities in the large cages at standard condition.  151  Number of TBME replaced out of 27 0  3  6  -1770  9  12  15  18  23  13  21  24  27  1  -1790 5 CH4 4 CH4  E config / kJ/mol  -1810  3 CH4 2 CH4 1 CH4  -1830  -1850  -1870  -1890  Figure 6.11: Configuration energy profile during the replacement of TBME with one to five methane molecules in the large cages at 0.8GPa and 300K. Both lattice constants a and c increase as the TBME is replaced by three methane molecules or more. The lattice constants change during the replacement process are summarized in Figure 6.12. The more TBME is replaced with methane, the larger the lattice constants are due to repulsion among methane molecules in a cage. The lattice constants do not change much when two methane molecules replace the TBME. A slight decrease was observed when one methane molecule replaces less than one-third of TBME (9 out of 27). Large changes in lattice constants are observed when all TBMEs are replaced by methane. The lattice constant a increases whereas the c constant decreases. Hence the large cage apparently becomes larger at the equator, but shorter along the polar axis.  152  (a) 4 CH4  (a) 3 CH4  (a) 2 CH4  (a) 1 CH4  (c) 5 CH4  (c) 4 CH4  (c) 3 CH4  (c) 2 CH4  (c) 1 CH4  10.8  12.5  10.7  12.4  10.6  12.3 Lattice constant a / A  (a) 5 CH4  10.5  Lattice constant a  12.2  10.4  12.1  10.3  12.0  10.2  11.9  10.1  Lattice constant c  11.8  Lattice constant c / A  12.6  10.0  11.7  9.9  13  11.6 0  5  23  10  15  1 20  9.8  25  Number of TBME replaced out of 27  Figure 6.12: Lattice constant changes during the replacement of TBME from the large cage of sH hydrate with one to five methane molecules at 0.8GPa and 300K.  The RDF plots of methane guests in the large cages for the sH clathrate with different occupancies are shown in Figure 6.13 (top). If the large cage accommodates one methane molecule only, the methane–methane distance is large with a broad distribution and the most probable separation of neighboring methane guests in large cages is ~12 Å. This separation roughly corresponds to the separation of the centers of two large cages in the a and b lattice directions, as shown in Fig. 6.7. If the large cage accommodates two or more methane molecules, the most probable separation between methane molecules in the same cage is in the range of ~3.5 Å to 3.7 Å. The relative position or distribution of a methane molecule with the other methane molecules within a cage can be seen from the peak(s) that appear(s) between 5 to 8 Å. Peaks near 10 and 12 Å correspond to  153  correlations among nearest neighbor large cages in the c and (a,b) lattice directions, respectively.  Carbon (methane) – Carbon (methane) 16 14  1 CH4 2 CH4  12  3 CH4  g (r)  10  4 CH4 5 CH4  8 6 4 2 0 0  2  4  6  8  10  12  14  Distance / A Carbon (methane) – Oxygen (water)  3.0  1 CH4 2 CH4  2.5  3 CH4 4 CH4  g (r)  2.0  5 CH4  1.5 1.0 0.5 0.0 0  2  4  6  8  10  12  14  Distance / A Figure 6.13: Radial distribution function (RDF) of carbon of methane in the large cage with carbon of methane (top) and oxygen of host lattice (bottom). 154  The radial distribution functions (RDF) between carbon of methane in the large cage and oxygen of water in the sH clathrates are shown in Figure 6.13 (bottom). As seen, the methane distribution in the large cage is broad when only single methane is inside and becomes sharper as more methane molecules are encaged. The distance between methane and the host lattice varies between ~3.5 Å to 4.7 Å. A smaller distance closer to the cage wall is seen as the large cage contains more methane.  6.4 Conclusions Statistical thermodynamics and molecular dynamics (MD) simulations are employed to assess the storage potential of methane in all gas hydrate structures. Under moderate pressure conditions, methane in sI hydrate has the highest storage density due to the accessibility of both cages and high occupancy values. The presence of propane and tetrahydrofuran (THF) as hydrate stabilizer (sII hydrate formers) reduces the hydrate stability pressure at a given temperature depending on the composition. Higher propane and THF concentration up to the stoichiometric amount increases the hydrate stability. However, it may not be practical due to much lower methane content. The methane content and hydrate stability are optimized when the concentrations sII hydrate formers are 1% for propane (~283 K) and 3% for THF (298 K). The free energy calculations from MD suggest that the methane storage capacity may be increased when methane molecules are placed inside the large cage of sH hydrate. The number of methane molecules in the large cages was found to depend on the pressure and temperature. The large cage may accommodate up to five methane molecules at higher pressures and lower temperatures. The accommodation of two is favorable at  155  lower pressures and higher temperatures. It should be pointed out that methane storage in sH hydrates with multiple methane occupancies is only of theoretical interest as the required pressure is about 0.5GPa or higher. It has also been demonstrated that methane may replace large guest species (TBME) in the large cage. Surprisingly, hydrate is predicted to be more stable when less than a third of the TBME in the simulation cell are replaced by a single methane molecule per TBME molecule. Experimental studies are required to verify this prediction. 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Gas Hydrates 2005, June 12-16, Trondheim, Norway. [49]  Kim, D.-Y.; Park, J.; Lee, J.-W.; Ripmeester, J.A.; Lee, H. J. Am. Chem. Soc.  2006, 128, 15360-15361. [50]  Susilo, R.; Lee, J.D.; Englezos, P. Fluid Phase Equilibria 2005, 231, 20-26.  [51]  Lee, J.-D.; Susilo, R.; Englezos, P. Energy and Fuels 2005, 19, 1008-1015.  [52]  Susilo, R.; Moudrakovski, I.L.; Englezos, P.; Ripmeester, J.A. J. Phys. Chem. B  2006, 110, 25803-25809. [53]  Susilo, R.; Englezos, P.; Ripmeester, J.A. Chem. Eng. Sci. 2007, 62, 3930-3939.  [54]  Susilo, R.; Englezos, P.; Ripmeester, J.A. AIChE J. 2007, 53, 2451-2460.  [55]  Dyadin, Y.A.; Aladko, E.Y.; Larionov, E.G. Mendeleev Communications 1997, 7, 34-35.  160  CHAPTER-7 MOLECULAR DYNAMICS STUDY OF STRUCTURE-H CLATHRATE HYDRATE CONTAINING METHANE AND LARGE GUEST MOLECULES6  7.1 Introduction This chapter is a continuation of our previous experimental [1-5] and computational [6,7] studies. Experimental measurements employing macroscopic (gas uptake, fluid phase equilibria, calorimetric) and microscopic (X-Ray diffraction, NMR and Raman spectroscopy) techniques were combined to obtain a more complete picture of the thermodynamic and kinetic properties of sH hydrates and the two approaches were in good agreement. It is found that the rates of hydrate formation and the methane occupancies depend on the large guest molecule (LMGS) and pressure. For the three sH forming guest species methyl-cyclohexane (MCH), neo-hexane (NH), and tert-butyl methyl ether (TBME), the initial rates of hydrate formation, either starting from solid ice particles or liquid water with mixing, increased according to the following trend: MCH < NH < TBME [2,3] whereas the methane occupancy/content in the hydrate phase increases as follows: TBME < NH < MCH [4]. Initial hydrate formation rates are well correlated by the solubility of guest molecule in water [1], gas diffusion in liquid and wetting property of LMGS and ice [3]. The system with better contact between the water/ice and guest molecules (methane/TBME) has faster kinetics. Surprisingly, the method of synthesis employed may also lead to different kinetic profiles. The hydrate conversion rate with TBME 6  “A version of this chapter has been accepted for publication. Susilo, R., Alavi, S., Ripmeester, J.A. and Englezos, P., “Molecular Dynamics Study of Structure H Clathrate Hydrate Containing Methane and Large Guest Molecules”, Journal of Chemical Physics (accepted March 21, 2008).” 161  became the slowest when the temperature was ramped above the ice-point whereas the other two systems with NH and MCH proceed quickly towards full conversion [5]. Moreover, methane occupancy/ content also varies with the LMGS and pressure [4]. It is unknown whether different methane occupancy values observed are due to thermodynamics, kinetics or a combination of both. In this work, we use molecular dynamics (MD) simulations to obtain further insight on sH clathrate formation. Free energy calculations are performed to determine hydrate stability and any dependency of methane occupancy in sH hydrate with respect to the LMGS and pressure. The preference of methane molecules to different cages (512 or 435663) and the minimum methane occupancy required to maintain hydrate stability are also studied.  7.2 Computation Methodology The DL_POLY molecular dynamics simulation package version 2.14 was employed in this study [8]. Calculations are performed with the NPT ensemble using the Nosé-Hoover thermostat-barostat algorithm [9,10] and the modification of Melchionna et al. [11] with thermostat and barostat relaxation times of 0.5 and 2.0 ps, respectively. The equations of motion were solved by using the Verlet leapfrog algorithm with a time step of 1 fs [12,13]. The simulations were performed for a total time of 100 ps where the initial 30 ps was used to equilibrate the system. A 3×3×3 sH hydrate simulation cell with periodic boundary conditions is used. The initial hydrate lattice dimensions are 36.99 × 36.99 × 29.76 Å3 with the oxygen atom positions obtained from the crystallography of sH hydrate [14-17]. The hydrogen atoms  162  were distributed at the oxygen sites subject to the constraints of the Bernal-Fowler ice rules [18] via a Monte Carlo simulation. The hydrogen positions that give the smallest unit cell dipole moment were chosen. The sH unit cell has 34 water molecules arranged in one large 20-sided (51268) cage, two “medium” sized 12-sided cages (435663), and three small 12-sided cages (512) and can be represented by (S)3(M)2(L)1·34H2O, where S, M, and L represent the small, medium, and large cages, respectively. Methane molecules occupy both small and medium sH cages, whereas larger molecules (LMGS) are placed in the large clathrate cages. The LMGSs studied are tert-butylmethylether (TBME), neohexane (NH) and methyl-cyclohexane (MCH). Guest molecules are initially placed at the center of the cages and equilibrated before collecting the data. The extended simple point charge (SPC/E) model is used to describe the potential for water [19]. The structure of the LMGS are determined by energy optimization using density functional theory at the B3LYP/6-311++G(d,p) level [20] with the GAUSSIAN 98 suite of programs [21]. The electrostatic charges are estimated from “charges from electrostatic potential grid” (CHELPG) [22] method as implemented in the GAUSSIAN 98 program and the van der Waals interactions of atoms and force constants for the internal degrees of freedom are obtained from the general AMBER force field (GAFF) [23]. The atomic assignments of LMGS molecules are illustrated in Figure 7.1. The Murad-Gubbins (MG) [24] potential for methane is used. The van der Waals interactions among guest-guest and guest-host molecules are based on the Lennard-Jones (12-6) potential with a cut-off distance of 13 Å. The cut-off distance was selected at a point where the attraction and repulsion forces are no longer influence the molecular interaction. Coulombic interactions between point charges qi and  163  qj located on the atomic nuclei i and j are used to model the electrostatic intermolecular interactions. The standard combination rules, ε ij = (ε iiε jj )1 / 2 and σij = (σii+ σjj)/2 are used to derive Lennard-Jones potential parameters between unlike atom-type force centers i and j from the values of the parameters between similar atom types. The intermolecular potential is given by Eq. 6.2 with the parameters listed in Table 7.1. H5 H7  H6  C3 H4  H8  C4 C2  O  H3  H9 H10  C1 C5 H2  H12 H1  H11 H2  H9  H7  H3 C1  H2  H3  H12 C3 C2  H4  C4  C4  H14  H13  H8 C5  C6 H10  H8  H10  H13 H9  H11  H6  H7  H6  C5 C6 H1  C3  C2  C7  H13  C1  H4  H5 H5  H1  H12 H11  Figure 7.1: The atomic assignment for the Large Molecule Guest Substance (LMGS) employed in this study: TBME (top), MCH (bottom left) and NH (bottom right). The charges and Lennard-Jones parameter are given in Table 8.1.  164  Table 7.1: Atomic charges and Lennard-Jones interaction parameters for SPC/E water, large guest molecules (TBME, NH, MCH) and the methane molecule used in the MD simulations.  Atom (assignment)  Molecule  q (e)  σ ii (Å)a  ε ii (kJ/mol) a  O H C1 (C3) H1-H3 (H1) O (OS) C2 (C3) C3-C5 (C3) H4-H12 (HC) C1 (C3) C2 (C3) C3-C4 (C3) C5-C6 (C3) C7 (C3) H1-H3 (HC) H4 (HC) H5-H6 (HC) H7-H8 (HC) H9-H10 (HC) H11-H12 (HC) H13-H14 (HC) C1-C3 (C3) C4 (C3) C5 (C3) C6 (C3) H1-H12 (HC) H13-H14 (HC) Cb Hb Cc Hc  water water TBME TBME TBME TBME TBME TBME MCH MCH MCH MCH MCH MCH MCH MCH MCH MCH MCH MCH NH NH NH NH NH NH methane methane methane methane  −0.8476 +0.4238 0.1027 0.0256 -0.5405 0.7721 -0.3474 0.0701 -0.3848 0.3597 -0.0520 0.0441 0.0265 0.0765 -0.0722 -0.0110 -0.0050 -0.0231 -0.0150 -0.0174 -0.3298 0.6173 0.0564 -0.1818 0.0475 -0.0362 -0.56 +0.14 −0.572 +0.143  3.166 0.000 3.3996 2.4714 3.0000 3.3996 3.3996 2.6496 0.4577 0.4577 0.4577 0.4577 0.4577 2.6495 2.6495 2.6495 2.6495 2.6495 2.6495 2.6495 3.3996 3.3996 3.3996 3.3996 2.6495 2.6495 3.64 3.35 2.61  0.6502 0.0000 0.4577 0.0657 0.7113 0.4577 0.4577 0.0657 3.3997 3.3997 3.3997 3.3997 3.3997 0.0657 0.0657 0.0657 0.0657 0.0657 0.0657 0.0657 0.4577 0.4577 0.4577 0.4577 0.0657 0.0657 1.365 0.42566 0.07176  a  The intermolecular potential parameters between unlike atoms are determined from combination rules. b From Tse, Klein, and McDonald [25,26]. c From Murad and Gubbins [24].  165  Free energy calculations were performed to determine the relative stability of sH hydrates at several methane occupancy values. The calculations were carried out with all large cages fully occupied by the LMGS and, initially, all small and medium cages in the simulation cell (27×5=135 cages altogether) are also fully occupied by methane molecules. Subsequently, in each stage (x) methane molecules are removed/annihilated randomly from both small and medium cages to reduce the methane guests occupancy. The methane occupancy fraction of the small and medium cages in the simulation cell is varied from 1.0 to 0.5 with 0.1 increments. The methane removal from the clathrate at temperature T and pressure p is represented by the following equation. clathrate [(n+x) CH4] → clathrate [(n) CH4] + x CH4 (fluid)  (7.1)  where n and x are integers representing the number of methane molecules that remain in a simulation cell and the number of methane molecules randomly removed from the simulation cell, respectively. Chemical equilibrium will be established between the two phases when methane in the clathrate and fluid phases have the same chemical potential. Initially there are 135 methane molecules (n+x) when the cages are fully occupied because there are 5 cages accessible for methane in each of the 27 unit cells of the simulation supercell. The number of methane molecules annihilated (x) are 14, 27, 41, 54, and 68 which correspond to 0.9, 0.8, 0.7, 0.6, and 0.5 methane occupancy of the small and medium cages in the sH hydrate. Two additional simulations were also conducted with methane molecules removed only from the small cages or only from medium cages. This is to determine whether there is any preference for the methane molecule to occupy a particular type of cage.  166  The total change in free energy ∆GTotal for the methane annihilation in equation (7.1) is the sum of the free energy change of the clathrate phase ∆GClathrate and the free energy change of the methane in the gas phase ∆GGas ,  ∆GTotal = ∆GClathrate + ∆GGas .  (7.2)  where (Gn+x – Gn) is the free energy of n methane molecules in the clathrate hydrate phase (-∆GClathrate). For methane in the gas phase, the free energy is the sum of ideal gas and residual contribution,  ρ ( gas, T , p)   + xµ resid ( gas, T , p ) , GGas = xkT ln   q methane   (7.3)  where ρ(T, p) is the number density, qmethane is the partition function for methane internal degrees of freedom and µresid(gas) is the residual (or excess) chemical potential of gas methane at T and p. The residual chemical potential is determined from direct calculations from MD simulations by using the thermodynamic relation, µ resid ( gas, T , p ) =  p  ∫ [V ( p, T ) − V 1  ig  ( p, T )] dp ,  (7.4)  where V ( p ,T ) is fluid molar volume calculated from MD simulations and Vig = RT / p is the ideal gas molar volume at the same pressure and temperature. The free energy of methane in the clathrate phase (Gn+x – Gn) can be written as,   ρ (clathrate, T , p )   + xµ resid (clathrate, T , p ) + ∆G EC (7.5) Gn+ x − Gn = xkT ln q methane   where ρ(clathrate,T,p) is the number density of methane confined in the simulation cell with volume determined by the clathrate phase and µresid(clathrate) is the residual chemical potential for a methane molecule from the clathrate phase. The µresid(clathrate)  167  will be obtained by using the method of thermodynamic integration as discussed below. The entropy correction, ∆G EC is free energy associated with the possible ways for distributing n methane molecules among a total of n + x small and/or medium cages in the simulation cell,   (n + x )!   . ∆G EC = kT ln  n! x!   (7.6)  The total free energy change for the methane annihilation reaction in Eq. (7.1), is the difference between the free energies of methane in the gas phase and methane in the clathrate phase,  ρ ( gas, T , p)   + xµ resid ( gas, T , p) − xµ resid (clathrate, T , p) − ∆G EC (7.7) ∆G total = xkT ln  ρ (clathrate, T , p)   The  methane  residual  chemical  potential  in  the  clathrate  phase,  µresid(clathrate,T,p) is calculated by using thermodynamic integration [12] based on the Kirkwood coupling parameter method [25,26]. This technique has been used in previous calculations of the free energy of clathrate guest substitution and annihilation reactions [6,7,27]. The annihilation of the x methane molecules from the clathrate lattice is achieved by gradually weakening the intermolecular potentials of the x methane molecules by introducing two coupling parameters λ1 and λ2 for the electrostatic and van der Waals interactions, respectively. The potential energy of the clathrate system can be written as [6],  U n + x (λ1 , λ 2 ) = U n + U elec (λ1 ) + U vdW (λ 2 ) ,  (7.8)  where λ1 couples the electrostatic interactions and λ2 couples the van der Waals interactions of the x guests in the cages to the rest of the clathrate[(n)CH4] system. For the electrostatic interactions we have [27], 168  ( λ q )( λ q ) ( λ1qi )q k +∑ 1 i 1 l , 4πε o ril i ,k 4πε o rik i ,l  U elec ( λ1 ) = ∑  (7.9)  where the first summation represents electrostatic interactions of one of the x guests to an atom of the clathrate[(n)CH4] system and the second summation represents the electrostatic interaction of two guests from the x subsystem. For Lennard-Jones type of van der Waals interactions [27],  1  U vdW ( λ2 ) = ∑ 4ε ij  i, j  0.5(1 − λ 2 ) 2 − ( rij / σ ij )6     −  (7.10) 0.5(1 − λ2 ) 2 − ( rij / σ ij )6   1  2  where the function smoothly transforms the Lennard-Jones interaction to an interaction with a soft-core and diminishing potential well [28]. The annihilated methane molecules with λ1 = λ2 = 0 no longer interact with each other or with other remaining particles in the simulation, but remain in the clathrate simulation cell volume as ideal gas molecules at the density of the clathrate. The  µresid(clathrate,T,p) calculations are performed with potential energies Un+x(λ1,λ2) for states with values of λi between 0 and 1 in small increments [6,27]. The residual clathrate chemical potential is calculated from, xµ( clathrate,T , p ) = ∫ 1 dλ1 0  ∂U ( λ1 ,λ2 ) ∂λ1  + ∫ 1 dλ2 NpT ,λ2 =1  0  ∂U ( λ1 ,λ2 ) ∂λ2  (7.11). NpT ,λ1 =0  The derivatives of the total potential U(λ1, λ2) with respect to the λi are evaluated numerically [27] and these functions are used in calculating the integrals of Eq. (7.11). Simulations were also performed to determine the minimum methane occupancy required to maintain the mechanical stability of sH hydrate at the nominal conditions of the simulation (274 K and 2 MPa). TBME was chosen as the LMGS. The simulation was  169  run until the hydrate cage structure collapsed or up to a maximum of 10 ns simulation time. Initially, small and medium cages in these simulations were empty and then progressively more methane molecules were added if the previous lower occupancy was mechanically unstable.  7.3 Results and Discussion 7.3.1 Preference of methane for occupying sH hydrate cages Free energy calculations were performed to determine whether there is small or medium cage preference for methane molecule occupancy. Methane molecules from the hydrate cages were removed from the small cages, medium cages, or randomly from both small and medium cages. The different contributions to the free energies for removing 20% of the methane molecules from the clathrate are summarized in Table 7.2.  Table 7.2: Free energies of removing 20% of methane molecules from the small (512) cage only, medium (435663) cage only, and randomly from small and medium cages of sH hydrate at 274 K and 2 MPa. All values are in kJ/mol. θCH4 Small Medium Random  kT ln  ρ fluid ρ clath  -8.2 -8.2 -8.2  xµresid(fluid,T,p)  -∆GEC  -xµresid(clath,T,p)  ∆Gtotal  -0.3 -0.3 -0.3  -4 -3 -5  +19 +18 +16  +7 +7 +3  The entropy correction was determined as follows. There are a total of 27 unit cells in the simulation cell for a total of 27×3 small cages and 27×2 medium cages. A total of 27 methane guests are to be removed out of the 135 methane guest molecules originally in the clathrate, which is equivalent to ~20% annihilation. For the methane removal from the small cages only, 27 of the 81 methane guests in the small cages are  170  annihilated. In this case, the entropy correction cell is −kTln[81!/(27!54!)] = 112 kJ for the total simulation (27 unit cells). Since our calculations are based per one unit cell, this value is divided by 27, giving ∆GEC = -4 kJ/mol. The molar volumes of methane gas and the calculated volumes of the clathrate phase are given in Table 7.3. These values are used in calculating the first two terms on the right hand side of Eq. (7.7).  Table 7.3.  The calculated values for supercritical methane molar volume at different pressures at 274 K using the Murad-Gubbins potential for methane and clathrate volumes at various methane occupancies.  p / kPa  V(fluid) / m3 mol-1  Cage occupancy  V(clathrate) / Å3  100 500 1000 2000 6000 10000  2.27 × 10-2 4.50 × 10-3 2.22 × 10-3 1.08 × 10-3 3.38 × 10-4 1.91 × 10-4  1.0 0.9 0.8 0.7 0.6 0.5  1307 1305 1303 1301 1299 1295  The values of -xµresid(clathrate,T,p) for the three methane annihilation cases are given in Table 7.2. The electrostatic contribution to µresid(clathrate,T,p) in Eq. (7.11) is smaller in comparison to the van der Waals contribution. The residual clathrate contribution to the free energy increases slightly if the methane is removed only from one particular type of cage. The total free energy calculation indicates that random methane removal from both small and medium cages is preferred over removal from only one type of cage. In subsequent simulations methane molecules are removed randomly from both small and medium cages.  171  7.3.2 Methane occupancy dependence on LMGS The free energy calculations of pure sH methane clathrate were reported earlier [6]. It was found that the CH4 potential used in the simulation affected the prediction of the number of CH4 molecules that were incorporated in the large cages. Using the MG potential, two to three CH4 molecules in the large cage were determined to be the most stable configuration which agrees with the experimental observation. Hence, the MG potential is selected for CH4 in this study.  − µ res (clathrate) / kJ/mol  45  43 42  40  34 32 27 34  35 30  25  25  17 24  20 15 10  41  9  9  8 16  16  5 0 1.0 to 0.9 1.0 to 0.8  1.0 to 0.7 1.0 to 0.6 1.0 to 0.5  TBME NH MCH  Methane occupancy Figure 7.2: Lattice energy changes at 2 MPa and 274 K as 0.9, 0.8, 0.7, 0.6, and 0.5 occupancies of methane in small and medium cages of structure H (sH) hydrate are randomly removed. The clathrate residual free energy contribution -xµresid(clathrate,T,p) increases linearly upon removing methane from the small and medium cages of sH hydrate for all the three LMGS at 274 K and 2 MPa as plotted in Fig. 7.2. The clathrate residual free energy calculations at higher pressures (6 and 10 MPa) show similar trends. The linearity shows that there are no strong collective interactions associated with the methane guests  172  in small and medium cages. The hydrate lattice is less stable when the small and medium cages are empty. Experimentally, it is observed that the measured methane occupancy from synthetic sH hydrate depends on the LMGS [4]. The hydrate from those experiments were collected under the final equilibrium conditions at 274 K and ~2 MPa and stored at liquid nitrogen temperature (77 K). The solid state-analysis with NMR spectroscopy indicated that the small and medium cage occupancies increased as follows: TBME (~77%) < NH (~88%) < MCH (~90%). Similar cage occupancy values were also reported from single crystal diffraction studies [29]. If the methane occupancy dependence on LMGS were driven by thermodynamics, the lattice energy values obtained from the simulation should increase following the same trend as for the measurements. However, as shown in Fig. 7.2, within simulation uncertainties there is no noticeable difference in lattice energy among all LMGS studied and the experimental variation of methane occupancy with different LMGS is not observed in the MD simulation. This discrepancy may be related to the difference in the kinetics of methane incorporation during clathrate formation for the different LMGSs [5]. Compared to NH or MCH, the TBME sH clathrate shows rapid hydrate formation when synthesized from solid ice without mixing or from liquid water with efficient mixing. However, the rate of clathrate formation with TBME becomes slower when the unreacted ice inside the hydrate shell is melted as the temperature is ramped above the ice-point without applying any mixing whereas rapid hydrate transformation occurs for the NH and MCH system. The simulations are performed under equilibrium conditions whereas the clathrates are not synthesized under constant pressure and temperature conditions. This can be a  173  possible explanation for the discrepancy between the experiments and the equilibrium MD simulations. The hydrate is not formed at equilibrium and the measured methane occupancies may be influenced by the clathrate formation kinetics although it may be expected to be at equilibrium when it is collected at the end of the experiment. The free energy differences for different methane occupancies are not large, so the occupancies may well be controlled by the clathrate growth rate. The change in the kinetics profile for the TBME system is not well-understood and hence further study is needed. The structures of the LMGS solution and clathrate cages are given in Chapter 8.  7.3.3 Methane occupancy dependence on pressure Under given pressures and temperatures, methane molecules may partition between the gas and hydrate phases and it is important to calculate the overall/total free energy of clathrate formation to determine the stability of a hydrate system. The methane molecules removed from the hydrate lattice enter the gas phase as shown in Eq. (7.1). The free energy contribution from the lattice, entropic correction, ideal, and real gas corrections for various occupancies are summarized in Tables 7.4 to 7.6 for the sH hydrate system at 274 K and 2, 6, and 10 MPa. The residual clathrate free energy increases linearly upon methane removal from the clathrate cages and within simulation uncertainty seems to be unaffected by increasing pressure. This may be due to the low compressibility of the lattice with pressure. In all cases, the entropy correction is a small negative number and dependent only on the cage occupancy. The clathrate entropy increases when the cages are not full due to the greater number of configurations for methane distribution among the cages. As seen from Tables 7.4 to 7.6, gas contributions  174  to the total free energy, i.e. first two terms in Eq. (7.7), are strongly pressure dependent. The values are negative at low pressures but become more positive at higher pressures due to work required to compress the methane gas. Hence, the total free energy is fully dependent on the cage occupancy and pressure.  Table 7.4: Free energy of removing methane from the small (512) and medium (435663) cages of sH hydrate at 274 K and 2 MPa. All values are in kJ/mol. xµresid(gas,T,p)  -xµresid(clath,T,p) θCH4  −∆GEC  TBME  NH  MCH  1.0 → 0.9  +8  +9  +9  -4  1.0 → 0.8  +17  +16  +16  1.0 → 0.7  +27  +25  1.0 → 0.6  +34  1.0 → 0.5  +41  + kT ln  ρ fluid  ∆Gtotal  TBME  NH  MCH  -7  -3  -2  -2  -5  -8  +4  +3  +3  +24  -7  -9  +11  +9  +8  +32  +34  -7  -10  +17  +15  +17  +42  +43  -8  -11  +22  +23  +24  ρ clath  Table 7.5: Free energy of removing methane from the small (512) and medium (435663) cages of sH hydrate at 274 K and 6 MPa. All values are in kJ/mol. xµresid(gas,T,p)  -xµresid(clath,T,p) θCH4  −∆GEC  TBME  NH  MCH  1.0 → 0.9  +9  +9  +9  -4  1.0 → 0.8  +16  +16  +17  1.0 → 0.7  +26  +22  1.0 → 0.6  +34  1.0 → 0.5  +40  + kT ln  ρ fluid  ∆Gtotal  TBME  NH  MCH  -4  +1  +1  +1  -5  -6  +5  +5  +6  +24  -7  -7  +12  +8  +10  +33  +33  -7  -8  +19  +18  +18  +43  +43  -8  -8  +24  +27  +27  175  ρ clath  Table 7.6: Free energy of removing methane from the small (512) and medium (435663) cages of sH hydrate at 274 K and 10 MPa. All values are in kJ/mol. xµresid(gas,T,p)  -xµresid(clath,T,p) θCH4  −∆GEC  TBME  NH  MCH  1.0 → 0.9  +8  +10  +8  -4  1.0 → 0.8  +18  +17  +16  1.0 → 0.7  +27  +24  1.0 → 0.6  +34  1.0 → 0.5  +42  + kT ln  ρ fluid  ∆Gtotal  TBME  NH  MCH  -3  +1  +3  +1  -5  -5  +8  +7  +6  +23  -7  -6  +14  +11  +10  +33  +34  -7  -7  +20  +19  +20  +43  +43  -8  -8  +26  +27  +27  ρ clath  The averaged residual chemical potential for the clathrate and the total free energies of the system at pressures ranging from 2 MPa to 10 MPa are plotted in Fig. 7.3. The residual clathrate energy is independent of pressure but the relationship between the total free energy and methane occupancy is pressure dependent, but not linear. At the lowest pressure (2 MPa) close to equilibrium pressure, calculations predict that the total free energy of the reaction shown in Eq. (7.1) is negative only when the hydrate cages go from full methane occupancy to 90% methane occupancy. This is in good agreement with the experimental cage occupancies measured from 13C solid state NMR spectroscopy [4]. Thus, lower methane occupancies in the hydrate cages are favored near ambient conditions, as observed in natural sI clathrate samples [30-32]. Further removal of methane molecules from the hydrate phase to the gas phase leads to an increase in the total free energy that eventually decreases the hydrate stability and ultimately decomposes the hydrate. At higher pressures, the total free energy of methane annihilation increases quickly, which indicates that full cage occupancies are preferred at high pressure. This observation is in good qualitative agreement with the idea of the  176  Langmuir isotherms for gas adsorption which emphasize that higher pressure increases the methane occupancy.  − µ res (clathrate )  ∆ G Total / kJ/mol  45  10 MPa 6 MPa 2 MPa  35 25 15 5 -5 1.0  0.9  0.8  0.7  0.6  0.5  Cage occupancy  Figure 7.3: Lattice and total free energy (∆G) at 274 K and 2, 6, and 10 MPa as methane in small and medium cages of structure H (sH) hydrate are randomly removed from fully occupancy to 0.9, 0.8, 0.7, 0.6, and 0.5 occupancies. The average lattice energy is shown by the dashed-line. Figure 7.4 shows the lattice constants and unit cell volumes as a function of methane occupancy, LMGS, and pressure. It is clear that higher methane occupancy increases the lattice constants and the greater number of guest molecules in the clathrate cages leads to an expansion of the unit cell. The agreement with the measured values from powder XRay diffraction [4] is satisfactory. The calculated lattice constants and unit cell volumes increase slightly in the order NH < TBME < MCH, but decrease slightly with pressure due to compression. However, the unit cell volumes for the three LMGSs are still equal within the simulation uncertainty (~±5 Å3). The similar lattice constants for the different LMGSs are consistent with equal lattice energies among the three LMGS.  177  1318  MCH TBME  1313  Unit cell volume / A  3  NH 1308  Average  1303 1298  1293 1288 0.45  0.55  0.65  0.75  0.85  0.95  1.05  Methane occupancy  10.18  Lattice constant a / A  12.22  10.16  12.20 10.14 12.18 10.12 12.16 10.10  12.14 12.12 0.45  0.55  0.65  0.75  0.85  0.95  Lattice constant c / A  12.24  10.08 1.05  M ethane occupancy  Figure 7.4: Variations of the unit cell volume and lattice constants with respect to LMGS, pressure, and methane occupancy in sH hydrate. The simulation (solid) is performed at 274 K and 2, 6, 10 MPa. The experimental results (not filled) are for atmospheric pressure and 82 K.  178  7.3.4 Mechanical stability of the sH hydrate It is important to know the effect of small and medium cage occupancy in maintaining sH clathrate mechanical stability. We performed a set of simulations at the nominal conditions of 274 K and 2 MPa. TBME is chosen as the large guest molecule in these simulations and varying amounts of methane were placed in the small and medium cages. It was found that the hydrate decomposes after ~750 ps simulation time when both small and medium cages are empty. Without guests in the small and medium cages, there are no repulsive forces from these cages to maintain the open hydrate cage structure. Snapshots during the simulation are shown in Fig. 7.5 with mechanically unstable areas of the lattice marked by the ellipse. The breaking of the water network usually “nucleates” at a particular site which then initiates the breaking of the adjacent neighboring hydrogen bonding network. The hydrate decomposes completely within ~1.25 ns. Simulation was also performed with 20% methane occupancy and it was found that the hydrate also decomposes at this methane occupancy. However, it takes a much longer simulation time to initiate the hydrate decomposition (~2.7 ns) and to decompose the hydrate completely (~3.2 ns). The hydrate decomposes at the sites of adjacent empty cages. When 40% of the cages were occupied by methane molecules the hydrate was found to be mechanically stable up to 10 ns total simulation time. It is important to note that the intermolecular potentials employed in this study are not optimized for this particular clathrate system. The results give a qualitative picture of the clathrate decomposition at the molecular level but are not quantitative. The findings support the fact that the stability of sH clathrates requires partial occupancy of small and  179  medium cages. By custom fitting the methane, TBME, and water intermolecular potential parameters to reproduce the experimental lattice constants of the sH clathrate with known occupancy, we can better evaluate the amount of methane required to maintain the clathrate stability quantitatively.  0.75 ns  0.85 ns  host network breaking  Start of decomposition  0.95 ns  1.25 ns  hydrate has decomposed  Figure 7.5: Snapshots during the simulation at 274 K and 2 MPa with the large cages filled with TBME and all methane molecules are removed from both small (512) and medium (435663) cages of sH hydrate.  7.4 Conclusions The methane occupancy dependence on the large molecule guest substance (LMGS) and pressure are investigated through molecular dynamics (MD) simulations. Methane in sH hydrate was found to have similar occupancies in the small and medium cages. Energetically, the hydrate lattice becomes more stable when both the cages are  180  fully occupied by methane. However, the negative free energy contribution from methane in the gas phase controls the methane occupancy in the hydrate cages and not all the cages are fully occupied when the pressure is near the equilibrium condition. These findings are in good agreement with occupancies of naturally occurring and synthetic hydrates. Full methane occupancy is favored at higher pressures. Contrary to experiments, methane occupancy dependence with LMGS was not observed by MD simulation in this study. This may be due to kinetic effects during the synthesis of hydrate that are not taken into account in the MD simulation. Finally, 40% or more of the small and medium cages have to be filled with guest molecules in order to maintain clathrate mechanical stability. The clathrate collapses when all the methane molecules are removed from the cages.  181  7.5 References [1]  Susilo, R.; Lee, J.D.; Englezos, P. Fluid Phase Equilibria 2005, 231, 20-26.  [2]  Lee, J.-D.; Susilo, R.; Englezos, P. Energy & Fuels 2005, 19, 1008.  [3]  Susilo, R.; Moudrakovski, I.L.; Ripmeester, J.A.; Englezos, P. J. Phys. Chem. B  2006, 110, 25803. [4]  Susilo, R.; Ripmeester, J.A. Englezos, P. Chem. Eng. Sci. 2007, 62, 3930.  [5]  Susilo, R.; Ripmeester, J.A. Englezos, P. AIChE J. 2007, 53, 2451.  [6]  Alavi, S.; Ripmeester, J.A.; Klug, D.D. J. Chem. Phys. 2007, 126, 124708.  [7]  Susilo, R.; Alavi, S.; Ripmeester J.A.; Englezos, P. Fluid Phase Equilibria 2008, 263, 6-17.  [8]  Forester T. R.; Smith, W. DLPOLY 2.14, CCLRC, Daresbury Laboratory, 1995.  [9]  Nosé, S. J. Chem. Phys. 1984, 81, 511.  [10]  Hoover, W.G. Phys. Rev. A 1985, 31, 1695.  [11]  Melchionna, S.; Ciccotti, G.; Holian, B.L. Mol. Phys. 1993, 78, 533-544.  [12]  Frenkel, D.; Smit, B. Understanding Molecular Simulation, Academic, San Diego, 2000.  [13]  Allen, M.P.; Tildesley, D.J. Computer Simulation of Liquids, Oxford Science, Oxford, 1987.  [14]  Davidson, D.W.; Gough, S.R.; Handa, Y.P.; Ratcliffe, C.I.; Ripmeester, J.A.; Tse, J.S. J. Phys. (Paris) 1987, 48, C1-537.  [15]  Ripmeester, J.A.; Tse, J.S.; Ratcliffe, C.I.; Powell, B.M. Nature (London) 1987, 325, 135.  182  [16]  Pratt, R.M.; Mei, D.-H.; Guo, T.-M.; Sloan, E. D. Jr. J. Chem. Phys. 1997, 106, 4187.  [17]  Udachin, K.A.; Ratcliffe, C.I.; Enright, G.D.; Ripmeester, J.A. Supramol. Chem.  1997, 8, 173. [18]  Bernal, J.D.; Fowler, R. H. J. Chem. Phys. 1933, 1, 515.  [19]  Berendsen, H.J.C.; Grigera, J.R.; Straatsma, T.P. J. Phys. Chem. 1987, 91, 6269.  [20]  Becke, A.D. J. Chem. Phys. 1993, 98, 5648.  [21]  Frisch, M.J.; Trucks, G.W.; Schlegel, H.B. et al., GAUSSIAN 98, Revision A.7, Gaussian, Inc., Pittsburg, PA, 2001.  [22]  Breneman, C.M.; Wiberg, K.G. J. Comput. Chem. 1990, 11, 361.  [23]  Cornell, W.D.; Cieplak, P.; Bayly, C.; Gould, I.R.; Merz, K.M. Jr.; Ferguson, D.M.; Spellmeyer, D.C.; Fox, T.; Caldwell, J.W.; Kollman, P.A. J. Am. Chem. Soc. 1995, 117, 5179.  [24]  Murad, S.; Gubbins, K.E. in Computer Modeling of Matter, edited by P. Lykos, American Chemical Society, Washington, DC, pp. 62, 1978.  [25]  Kirkwood, J.G. J. Chem. Phys. 1935, 3, 300.  [26]  McQuarrie, D.A. Statistical Mechanics, Harper & Row, New York, 1976.  [27]  Yezdimer, E.M.; Cummings, P.T.; Chialvo, A.A. J. Phys. Chem. A 2002, 106, 7982.  [28]  Beutler, T.C.; Mark, A.E.; van Schnaik, R.C.; Gerber, P.R.; van Gunsteren, W.F. Chem. Phys. Lett. 1994, 222, 529-539.  [29]  Udachin, K.A.; Ratcliffe, C.I.; Ripmeester, J.A. J. Supramol. Chem. 2002, 2, 405408.  183  [30]  Ripmeester, J.A.; Lu, H.; Moudrakovski, I.L.; Dutrisac, R.; Wilson, L.D.; Wright, F.; Dallimore, S.R. Geol. Surv. Can. Bull. 2005, 585, 106.  [31]  Lu, H.; Moudrakovski, I.L.; Riedel, M.; Spence, G.; Dutrisac, R.; Ripmeester, J.A.; Wright, F.; Dallimore, S. J. Geophys. Res. 2005, 110, B10204.  [32]  Hester, K.C.; Dunk, R.M.; White, S.N.; Brewer, P.G.; Peltzer, E.T.; Sloan, E.D. Geochim. Cosmochim. 2007, 71, 2947.  184  CHAPTER-8 INTERACTIONS BETWEEN STRUCTURE H HYDRATE FORMERS AND WATER MOLECULES7 8.1 Introduction Structure H clathrates have the largest cage among all clathrate structures and require two different sized guest molecules to stabilize the crystal [1]. The large cages accommodate large guest molecules, whereas the smaller cages are filled with smaller molecules such as methane, xenon, and carbon dioxide. In the presence of these small molecules, the sH clathrates form at lower pressures than the regular sI hydrates. The formation of sH clathrates involves at least three different molecules in three separate phases, adding to the complexity of these systems. The sH clathrate formers also known as large molecule guest substances (LMGS) that are generally poorly miscible in water and the smaller guest molecules are commonly present in the gas phase. Hence the gas, non-aqueous liquid (LMGS), and aqueous phase have to be in contact in order for the sH clathrate to form [2,3]. Previous experimental studies on methane storage in sH hydrates found that the formation rates and methane occupancies differ among the three LMGS studied: tertbutyl methyl ether (TBME), neo-hexane (NH), and methyl-cyclohexane (MCH). The initial rate of clathrate formation grown from solid ice powder with no mixing [4,6] and liquid water with efficient mixing [3] were found to increase in the order: MCH < NH < TBME. The system with TBME showed the fastest clathrate growth rate which is 7  “A version of this chapter has been accepted for publication. Susilo, R., Alavi, S., Lang, S., Ripmeester, J.A. and Englezos, P., “Interactions between Structure H Hydrate Formers and Water Molecules”, Journal of Physical Chemistry C (accepted April 1, 2008).” 185  consistent with the fact that TBME is much more soluble in water than NH and MCH [2] and TBME wets ice much better than the other two liquids [3]. Surprisingly, the hydrate composition determined by solid-state NMR and the gas content measured by decomposing the clathrate revealed that the methane content with TBME was the smallest, followed by NH and MCH [6]. The methane pressure required to form a stable sH clathrate with TBME is also higher than with NH or MCH [7,8]. The selection of appropriate LMGS is therefore essential to ensure that the clathrate has the requirements for gas storage applications, which are high gas content and faster hydrate formation rate. Experimental observations and measurements motivate us to study the molecular-level aqueous solvation of the LMGS and guest-host interaction within the clathrate cages. More specifically, the spatial distributions and orientations of water surrounding the LMGS molecule are studied. The volumes of solvation and solution density are also reported. The results are related to the solubility and wetting properties of LMGS, rates of hydrate formation, the occupancy of the cages and stability of the clathrate crystal.  8.2 Computation Methodology The DL_POLY molecular dynamics (MD) simulation package version 2.14 was employed in this study [9]. Constant temperature and pressure (NPT) simulations were performed at 274 K and 2 MPa with the Nosé-Hoover thermostat-barostat algorithm [10,11] and the modification of Melchionna et al. [12] with thermostat and barostat relaxation times of 0.5 and 2.0 ps, respectively. The equations of motion were solved by using the Verlet leapfrog algorithm with a time step of 1 fs [13,14]. Energy conservation  186  and configurational energy convergence criteria were used to test the appropriateness of this time step. The aqueous solution structures were determined at constant temperature and pressure (NPT) and the mean square displacements (MSD) were obtained at constant volume and energy (NVE) simulations. The extended simple point charge (SPC/E) model is used to describe the intermolecular potential for water [15]. Water molecules are considered rigid and are treated with the SHAKE [14] algorithm. The fixed-charge SPC/E model has been used in clathrate simulations and gives qualitatively and semi-quantitatively correct predictions regarding the behaviors of these inclusion compounds. The use of polarizable potential models for water [16,17] leads to a more accurate representation of molecular dipole and charge polarization enhancements in the methane hydrate. The calculated vibrational spectrum of methane hydrate in the water libration region was also found to depend sensitively on the nature of the water potential used in the classical force field. The AMOEBA [18], COS/G2 [19], SWM4-NDP [20], and GCPM [21] are among polarizable water models that have been used to predict the properties of solvation and hydrogen bonding in aqueous solutions more accurately. By allowing a degree of charge mobility around the atoms, polarizable potentials provide a more accurate representation of the interactions between the non-bonded electron pairs of the oxygen atoms and the protons of water. Consequently, it is more difficult to implement those polarizable water potentials in MD are and hence the fixed-charge model is used, which is good enough to get qualitative prediction. All LMGS molecules are considered flexible with the initial structure determined by energy optimization using density functional theory at the B3LYP/6-311++G(d,p)  187  level with the GAUSSIAN 98 suite of programs [22]. The electrostatic charges are estimated from the electrostatic potential grid (CHELPG) [23] method as implemented in the GAUSSIAN program and the van der Waals interactions of atoms are obtained from the general AMBER force field (GAFF) [24]. The point charges and van der Waals Lennard-Jones potential parameters are provided in Table 7.1 [25]. Intramolecular force constants for the bond stretches, the angle bending and the dihedral interactions are taken directly from the GAFF tables. The van der Waals interactions among guest-guest and guest-host molecules are based on Lennard-Jones (12-6) potential. Coulombic interactions are used to model the electrostatic intermolecular interactions between point charges qi and qj located on the atomic nuclei i and j. Long-range electrostatic interactions were calculated using the Ewald summation method [13,14] with a precision of 1×10-6 and all intermolecular interactions in the simulation box were calculated within a cutoff distance of Rcutoff = 13.0 Å. The standard combining rules, εij = (εii εij)1/2 and σij = (σii+ σjj)/2 are used for LennardJones potential parameters between unlike atom-type force centers i and j. The intermolecular potential is given by Eq. (8.1),   σ  ij V (inter ) = ∑∑  4ε ij    rij i =1 j >i     12 6   σ ij   qq   −   + i j  .   rij   4πε 0 rij       (8.1)  The simulations for aqueous solution were performed for a minimum total time of 250 ps where the initial 50 ps was used to equilibrate the system. The solution consists of 918 water molecules and a single solute (LMGS) molecule with periodic boundary and initial dimension of 33.7 × 33.7 × 28.0 Å3. Snapshots of the solution are collected at every 0.2 ps interval and 1000 snapshots of the solutions were used to acquire structural  188  data for analysis. For the hydrate phase, a 3×3×3 sH clathrate simulation cell with periodic boundary conditions is used with initial dimensions of 36.99 × 36.99 × 29.76 Å3. The coordinates of the clathrate lattice are given in Table 6.1 [26]. The hydrates are fully occupied with methane in the small and medium cages and the LMGS in the large cages. The hydrates where equilibrated for 500 ps and their structure and host – guest interactions studied for a further 500 ps.  Y C6  C1  C1 C5  Z  X  O  Z  C4  NH  Y  Y  C2  TBME  C2  X  X  Z C3  MCH  Figure 8.1: Coordinate assignment for the LMGS molecule as the reference. The atoms selected represent similar geometries. The colors for the carbon, oxygen, and hydrogen atoms are as follows: cyan, red, and white The spatial data from each snapshot is projected onto the reference coordinate systems shown in Fig. 8.1. The C1-O-C2 atoms for TBME, C1-C2-C3 atoms for MCH,  189  and C6-C5-C4 atoms for NH atoms are selected to define the reference axes. See Figure 7.1 for a complete description of the atomic labels. The two end carbon atoms define the Y-axis in each case. The X-axis is drawn perpendicular from the Y-axis through the central atom (oxygen atom from the TBME molecule or analogous carbon atoms in NH and MCH). The Z-axis faces outwards perpendicular to the XY-plane. The reference axes are chosen to arrange analogous structural features of the solutes in a similar manner. A rotation and translation matrix based on the reference LMGS molecules is used to transform the coordinates of the water molecules in the simulation. The LMGS studied are considered as flexible molecules and hence vibrational motions are allowed for the atoms that are not used in defining the coordinate axes. The water spatial distributions are obtained by analyzing all the snapshots after transforming the coordinates to the reference system based on the LMGS molecules. The water molecule positions are stored in 3-dimensional bins 0.5 Å per side. The atomic (hydrogen or oxygen) densities in each box are normalized to a pure bulk water simulation. Water molecular distributions and orientations up to 10 Å away from the solute are analyzed. Figure 8.2 illustrates the definitions of the water orientation (µ) and radial distribution (R) vectors and the angle (ω) between these two vectors. The water orientation vector µ is drawn from the oxygen atom along the bisector of the HOH angle. The angle ω determines the angular orientations of water molecules with respect to the referenced atom. The water orientation distribution is also normalized relative to the orientation of water molecules in the bulk phase.  190  µ Y  ω R  Z  X  RA  Figure 8.2: The definitions of the orientation of water molecule relative to the reference atom (RA) at the origin. The water molecule is represented in red. The guest-host interactions in the hydrates were examined by looking at the snapshots of the large cages with the LMGS. The snapshots along the ac- and bc-planes are chosen to represent the structures. These two side-views allow clear visualization of the guest molecule orientations inside the hydrate as well as the cage distortions due to guest molecule motions.  8.3 Results and Discussions 8.3.1  Spatial distributions of water molecules near the solutes The radial distribution functions (RDFs) of the reference-atom from the LMGS  (O-TBME, C5-NH, and C2-MCH) with oxygen-water and hydrogen-water are plotted in Figure 8.3. For comparison, the corresponding RDFs of pure water are also plotted. The water-water interactions clearly indicate the presence of hydration shells. The strong first O-O water shell appears at less than 3.3 Å (or less than 2.5 Å for O-H atoms) that is the typical hydrogen bond distances between the reference water molecule and the nearest neighbour shell of waters. The second hydration shell is centered at ~4.5 Å for O-O  191  atoms (or ~3.8 Å for O-H atoms) and is broader and less structured than the first shell. The water molecules in the second hydration shell are mostly those that are hydrogen bonded to the first hydration shell. A weak third hydration shell is also visible between 5.7 to 7.7 Å (O-O).  g (r)  3  Water TBME NH MCH  2  1  0 0  2  4  6  8  10  12  14  Distance / A 2.0 Water TBME NH MCH  g (r)  1.5  1.0  0.5  0.0 0  2  4  6  8  10  12  14  Distance / A  Figure 8.3: Radial distribution function of water oxygen and solute reference atoms (Owater, O-TBME, C5-NH, and C2-MCH). 192  A strong signal in the first hydration shell (below ~3 Å) is also seen in the TBME solution, indicating the presence of hydrogen bonding between the water and oxygen from TBME, but this is absent for the other two solutes. TBME also has a broad peak in the range of 4 – 7 Å, which represents the solvation sphere of the hydrophobic parts (methyl groups) of the molecule. The NH and MCH solutions have broad peaks in the range of 4 – 7 Å representing the solvation sphere of the hydrophobic molecules. There are only weak longer range peaks for these solutes. The RDF plots provide the radial distribution of water molecules around the solute. However, a more detailed analysis cannot be obtained. In order to gain more insight on the solvation process and its relationship with clathrate formation and stability, information on the water spatial distribution and orientation with respect to the solutes is needed. The spatial distributions of water oxygen and hydrogen atoms near the solutes in the XY-plane at Z = 0 are shown in Figure 8.4. The oxygen and hydrogen density maps are similar and the water spatial distribution function near the solute shows a density that is approximately twice that of the bulk water phase. The solute hydrophobic groups interact weakly with the water molecules. Consequently, the water molecules in the hydration sphere attract each other more strongly so as to minimize the energy loss due to hydrophobic moiety – water interactions. This high density water in the hydration shell was also reported for water-methane [27], water-cyclohexane, and water-benzene systems [28]. The thickness of this high density hydration shell is less than ~1 Å. The strong interaction between the oxygen of TBME and hydrogen of water distorts the hydration shell.  193  R/Å  R/Å  R/Å  Oxygen density  10 8 NH 6 4 2 0 -2 -4 -6 -8 -10-10 -5 10 8 TBME 6 4 2 0 -2 -4 -6 -8 -10 10 8 MCH 6 4 2 0 -2 -4 -6 -8 -10 -10 -5  Hydrogen density 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2  0  5  10  -10  -5  0  5  10  1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0  5  10 -10  R/Å  -5  0  5  10  R/Å  Figure 8.4: Spatial oxygen and hydrogen distribution of water surrounding the LMGS molecule on XY-plane (z = 0). Figure 8.5 illustrates the 3-dimensional spatial distribution of water oxygen atoms surrounding the reference molecule at 2.7 Å (green), 4 Å (white), and 5 Å (grey). The shortest distance (2.7 Å), corresponds to water molecules that interact with other water  194  molecules and TBME, so these are characteristic of hydrogen-bonding in these systems. The “hydrogen bonds” of water are present as two caps above the hydrogen atoms of the reference water and there is a wide distribution at the oxygen site (right hand side) [29]. The latter is also observed in the water-TBME system. At a distance 4 Å away from the reference atom, the water molecules begin to form a shell that encapsulates the hydrophobic parts of the LMGS. The LMGS molecules are almost completely enclosed by a water molecule network at 5 Å except for the hydrophobic part on the lower left for both TBME and NH molecule and on the lower right for the MCH molecule.  2.7A  water  4A  5A  TBME  NH  MCH  Figure 8.5: 3-D illustration of water molecule positions with respect to the referenced molecule at selected distances.  195  The cavity size increases on going from TBME, NH, and MCH. The TBME and NH molecule are rather similar in profile and molecular weight and hence a comparison between the two is particularly interesting. The only difference between the two is that the oxygen atom in TBME is replaced by a CH2 group in NH. It is clear from Figure 8.5 that water encloses the TBME molecule to a greater extent than the NH molecule at the same distance from the reference atom due to the stronger attraction between TBME and water molecules. The solvation volume with MCH is the biggest because of solute size.  8.3.2  Spatial orientation of water molecules near LMGS molecule The orientation density maps of water around the solutes are shown in Figure 8.6.  The orientational density is normalized to the orientational correlations in the pure water system. In the water solvent, at a separation of ~ 2.5 Å, water molecules have their preferential orientational densities approximately 18 times larger than the random distribution in the bulk phase. The water molecules which accept a hydrogen from reference water mostly face away from the reference atom (cos ω ≈ -1). The protondonating water molecules preferably face in the reference atom with angles between 4555° (cos ω ≈ +0.6 to +0.7). Water molecules in the second hydration shell (~ 4 Å) are mostly oriented either facing towards (H-donor, cos ω ≈ +1), away from (H-acceptor, cos ω ≈ -1), or tangential to (cos ω ≈ 0) the reference atom. The water molecules in the bulk  phase (R > 6 Å) have no preferred orientation. The proton–donor water molecules at ~ 3 Å that are hydrogen-bonded to the oxygen atom of TBME face toward the reference atom with angles ω ≈ 45-55° angles. The water orientation density is a factor of six higher than the bulk water phase, but three  196  times lower than the water-water system. The water molecules up to ~6 Å from TBME are preferentially oriented away from the reference atom by 90-125° (cos ω ≈ 0 to -0.6) due to the hydrophobic nature of the methyl groups. The NH and MCH have orientational densities similar to the hydrophobic part of TBME but in a broader range, from 50-135°. There is no preferred orientation for water molecules that are further than 7 Å from the  Cos ω  Cos ω  reference atoms in all LMGS. 1.0 Water 0.8 0.6 18x 0.4 0.2 0.0 2x -0.2 -0.4 -0.6 -0.8 18x -1.0  2x  TBME  1.8  6x  1.6 1.4 1.2 1.0 0.8 0.6 0.4  3x 2x  1.0 0.8 NH 0.6 0.4 0.2 0.0 -0.2 3x -0.4 -0.6 -0.8 -1.0 0 2 4  0.2  MCH  1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4  3x  0.2  6  8  10  R/Å  0  2  4  6  8  10  R/Å  Figure 8.6: Spatial orientation distribution of water with respect to a reference atom normalized to the bulk water density.  197  8.3.3  Solvation volumes The volumes of pure solvent (water), pure solutes (LMGSs), and the LMGS-water  solution are summarized in Table 8.1. The volumes reported correspond to the number of molecules indicated in the bracket. The volume change differences between the solution volume and the sum of the separate solute and solvent volumes are generally small negative values for all systems.  Table 8.1: Partial molar volume of water with TBME, NH and MCH. Component / number of molecule  Volume (Å3)  ρ calc. a (g/cc)  ρ expt. b (g/cc)  Water (918) TBME (1) NH (1) MCH (1) Water (918) + TBME (1) Water (918) + NH (1) Water (918) + MCH (1)  27196 ± 208 197 ± 7 204 ± 5 210 ± 5 27390 ± 196 27364 ± 192 37375 ± 197  1.009 ± 0.008 0.742 ± 0.027 0.700 ± 0.017 0.776 ± 0.020 1.007 ± 0.007 1.008 ± 0.007 1.008 ± 0.007  1.000 0.741 0.644 0.769  a b  Density values from the simulation Density values from the literature [30] Although the quantification of molar volume change is not possible due to the  small number of solute molecules present in the system studied, the decrease in molar volume for hydrophobic solutes such as methane, ethane, propane and benzene has been reported in several studies via experiments [31] and theory [32]. The volume reduction can be attributed to stronger hydrogen bonds between the solvating water molecules in order to minimize the hydrophobic effect. Hence, the water molecules are expected to be more structured when solvating the non-polar solutes. The density of the pure solute and solvent from the simulation are comparable to literature values [30]. The density of all  198  solutions is slightly lower than the water density due to the presence of the LMGS molecule. It should be noted that the magnitudes of the volume reductions in the solutions given in Table 8.1 are semi-quantitative. To get better quantitative estimates for the volume of solution, more accurate potentials using polarizable models for water (such as TIP4P-FQ [33,34]) and the LGMS (CHARMM-FQ [35]) should be used. The use of polarizable models would additionally lead to a more accurate representation of hydrogen bonding in the solvation shell of the LGMS.  8.3.4  Solute diffusivity in aqueous solution The dynamics of LMGS molecules as solutes in water can be observed from the  mean square displacement (MSD) plot, which determines the diffusion coefficient. Figure 8.7 shows the time variation of the MSD of the TBME and NH molecules. The MSD profiles of TBME and NH show similar structures but differ in quantitative features. For time scales < 1 ps, the MSD increases rapidly (proportional to t2) as the solute moves inside the solvent “cage”. This is the ballistic motion regime of the MSD. For intermediate time scales, the slope of the MSD decreases as the solute must break the solvent cage in order to further diffuse from its initial starting point. This intermediate motion regime lasts until ~ 2 ps for TBME, and up to ~ 20 ps for NH. The time required to break the solvent cage is longer for the hydrophobic NH. The TBME molecule, on the other hand, forms hydrogen bonds with the solvent water molecules and does not have a rigid solvent cage structure and thus completes the intermediate motion regime much quicker. The diffusive regime where MSD ∝ t begins after about 5 ps for TBME and after  199  about 20 ps for NH. The solute diffusion coefficient in water is calculated from the slope of the linear segment of the MSD curve. TBME molecule has larger diffusion coefficients than NH. The diffusivity of MCH in water is similar to that of NH. 30  TBME solution NH solution  MSD / A  2  25 20 15 10 5 0 0  10  20  30  40  50  60  Simulation time / ps Figure 8.7: Mean square displacement (MSD) of TBME and NH in water over a time range of 60 ps. The differences in LMGS diffusion in water can be explained with reference to the nature of LMGS solvation in water as shown in Fig. 8.4. For TBME molecule as the solute, the water cage is already distorted due to the hydrogen bond that is formed between oxygen-ether and water molecules. In this case, less energy may be required to break or move the TBME molecule from the hydration shell. On the other hand, it is harder for hydrophobic guests to break the solvation shell because of the high water density/internal pressure surrounding the solute. Consequently, the diffusivity of NH and MCH as solute/guest molecule are limited.  200  8.3.5  Large guest-host (lattice) interactions The snapshots of guest molecule positions and orientations in the sH large cages  are shown in Figure 8.8. Generally the LMGS molecules are located near the center of the cage with their long axes oriented along the c-axis. The motion of the guests is restricted within the confined space of the cage. The molecular motions of LMGS are generally confined to librations (irregular rotation and wobbling/precessional motion inside the cage) of the molecules about the c-axis. The TBME molecule is the only LMGS that is seen to flip in the cage and this may be due to the distortion of the water cage as a result of the interactions with the TBME oxygen. The TBME molecule also rotates faster than the NH or MCH. The MCH molecule shows the least rotational mobility because of its larger effective size and rigid geometry. The hydrophobic part of the guest molecule provides the necessary repulsive forces to maintain the clathrate lattice from collapsing. Hence, the lattice geometry of the large cages is generally not greatly distorted in the NH and MCH clathrates. The hydrogen atoms from the water molecules generally participate in hydrogen bonding with other water molecules from neighboring cages. However, the presence of the ether oxygen in TBME may distort the clathrate lattice structure and also may induce defects in the clathrate lattice by inducing a hydrogen bond. An adjacent water in the clathrate cage then rotates to face the ether oxygen and this water molecule is moved inward. The top view is on the a-b plane looking down along the c-axis. The front view is on the a-c plane looking through the b-axis. Upon looking down from the top, the large cage consists of two hexagonal rings. The ring at the center represents two hexagonal faces on the poles sides (top and bottom) and the other one on the outside represents six  201  hexagonal faces on the equatorial plane. The outside ring looks like a perfect 12-sided from the top-view when no defect is seen. However, a distortion on the outside ring is seen as marked by the yellow dashed ellipse due to hydrogen bond that is formed between ether-TBME and host-water molecule.  NO DEFECT  DEFECT  a  a b  b  c  c  a  a  Figure 8.8: Snapshots of the large guest molecules inside the large cage of sH hydrate from the top and front side. The TBME inside the cage may induce a defect into the clathrate lattice due to the hydrogen bond formed. The front view provides better illustration on the hydrate cage structure. As seen on the lower part in Fig. 8.8, each hexagonal faces on the equatorial plane (six in total) is connected to a medium cage which shares the square face. When no defect is formed, all square faces are seen from all the six hexagonal faces. This square face is the boundary  202  between neighboring medium cages that are attached to the same large cage. However, this square face is altered when a defect forms. A hydrogen bond is missing on the hostcage due to the stronger attraction from the ether-TBME. Consequently, two medium cages appear as one larger cage. Hence, it is expected that the hydrate cage is less stable and less effective in enclosing the methane molecules. The presence of a guest – water hydrogen bond leaves a vacant hydrogen bond in the lattice, similar to a negative Bjerrum defect in ice [36]. However, unlike Bjerrum defects in ice, where negative (N-empty hydrogen bond) and positive (P-doubly occupied hydrogen bond) pairs of defects are always formed, in this case, just a single N defect is formed. The defects appear to be long lived and may alter the stability of the lattice since they increase the size of neighboring cage faces and may lead to a reduction in their methane holding capability. The formation of this defect is not permanent and the water molecule may rotate back into position in the cage lattice. The defects form and move from one cage water molecule to another. However, the defects are primarily limited to water molecules near the equatorial region of the large cages.  8.3.5  Implications for clathrate formation The spatial and orientational distributions of water molecules clearly show that  there is a strong interaction between water and the oxygen atom in TBME. On the other hand, only hydrophobic interactions between water and NH or MCH are seen as expected. The diffusivity of TBME in water is also faster than NH or MCH. This explains the experimental observations in which it was found that TBME has higher solubility in  203  water, better contact with ice surfaces and faster initial hydrate formation rate in liquid water and from ice particles [2-5, 37]. Hydrate conversion can be enhanced significantly by increasing the temperature of the mixture above the ice melting point to initiate renewed guest-water contacts to facilitate hydrate growth as discussed in earlier chapters [4,38,39]. The melting of ice inside the hydrate shell often breaks the shell and in fact the later may act as a clathrate seed for continued growth. Moreover, the non-aqueous liquid phase is already supersaturated by methane. Hence, full and faster hydrate conversion for the hydrophobic guests is observed within one hour immediately after the temperature exceeds 0°C [5]. However, this was not the case for TBME system for which the full conversion was achieved at a much lower speed (within 30 hours). The water spatial density distribution map indicates higher density surrounding the solute LMGS, especially for NH and MCH due to hydrophobic effects. The change in molar volume due to incorporation of LMGS in the solution is negative for all three LMGS guests. Hence, it is expected that the hydrogen bonding network enclosing the LMGS in the solution provides a structural template for hydrate formation. Consequently, in a system with ice particles, rapid clathrate formation towards complete conversion is expected to be achieved after temperature ramping. However, the strong guest-host interactions between TBME and water distorts the cavity and may turn to be a disadvantage during hydrate nucleation and growth. A higher energy barrier may exist for breaking the hydrogen bond between TBME and water in order to form the clathrate cage. As a result, the rate of hydrate formation with TBME is the slowest when hydrate is grown from melted ice in a non-stirred system.  204  This may be the reason why the rate of hydrate formation with TBME is the slowest when hydrate is grown from melted ice. However, as was seen in previous Chapter (3), TBME has the highest growth in a stirred vessel. Those findings do not contradict the above interpretations because in the case of the stirred vessel good mixing and solubility were probably the main reason, whereas in the melted ice case there is no mixing in the vessel content. The mixing may overcome the energy barrier to hydrate formation. The rate of clathrate formation with temperature ramping in the presence of ice does not seem to be the same as that is a stirred liquid water system. The number of water - guest contacts and the mobility of the available water may not be the same in those two cases and this could lead to different kinetics. Strong guest-host interactions between the polar guest (TBME) and water molecules require the clathrate cages to be flexible in order to avoid breaking the clathrate-lattice due to defect formation. The neighbouring large cage is opened partially as well due to the missing hydrogen bond that completes the cavity. This may be related to the adjacent small cages (512 and 435663) being less occupied in the TBME clathrate than in the clathrates with purely hydrophobic guests (NH, MCH) [6]. Thus, higher pressure is required to maintain the crystal stability for the TBME system, as is also evident from the phase diagram [7]. The strength of the hydrogen bonds of the water molecules in the hydration cell can also be determined by evaluating the rotational relaxation times of the water molecules in solvation shell. The water molecules of the solvation shell have weak interactions with hydrophobic solutes and form strong solvent – solvent hydrogen bonds. These water molecules are expected to have longer rotational relaxation times when  205  compared with the water molecules of the solvation cell of TBME. The strong hydrogen bonding with TBME will cause the breaking of some solvent – solvent hydrogen bonds and give the water molecules in the solvation shell a greater mobility. Elucidating the details of this process will be the subject of future work. The defect identified by modeling may play important roles in hydrate kinetics as well as in stability considerations. Interestingly, the defect is not permanent and its detection may not seem straightforward, especially from experimental measurements. We note that molecular dynamics free energy simulations could not predict the methane occupancy dependence with LMGS variation [26]. It is possible that the kinetics during clathrate formation are important for the determination of clathrate stability and cage occupancy. A quantitative examination of the guest-host interactions and guest motions inside the clathrate lattice are in progress. In addition to the geometric characterizations presented above, it is important to determine the solvation energy of the TBME and hydrophobic LGMS solutes in aqueous solution in order to understand their different behaviors. The interaction energies between the solute – surrounding solvation shell, solute – individual water molecules, solvation shell – solvation shell can be determined by averaging intermolecular potential terms between these groups of molecules in snapshots of the MD simulation. These calculations would allow us to better rationalize the differences in the behaviors observed for the aqueous solutions. Such calculations remain for future work.  206  8.4 Conclusions Molecular dynamics simulations were employed to generate atom-scale snapshots of the solutions and the clathrate structure for the sH methane hydrate with tert-butyl methyl ether (TBME), neo-hexane (NH), and methyl-cyclohexane (MCH). Water molecules were found to solvate the solute (MCH, NH, and TBME). The water spatial distribution density around the solute was found to increase by a factor of two. The shape of the cavity follows the solute geometry and the water molecules are oriented mostly tangentially away from the solute for the hydrophobic solutes. On the other hand, strong attraction between the oxygen of TBME and the hydrogen of water is observed due to hydrogen bonding, and thus the cavity shape for the TBME solute is distorted. The strong interaction between TBME and water explains higher solubility of TBME in water, better wetting of ice. Higher solubility and more extensive wetting then lead to faster initial hydrate formation rate. The hydrophobic interaction between NH or MCH and water limits guest-host contact, resulting in slower initial hydrate formation kinetics. Finally, the work identified a defect in the TBME structure H hydrate system.  207  8.5 References [1]  Ripmeester, J.A.; Tse, J.S.; Ratcliffe, C.I.; Powell, B.M. Nature 1987, 325, 135136.  [2]  Susilo, R.; Lee, J.D.; Englezos, P. Fluid Phase Equilibria 2005, 231, 20-26.  [3]  Lee, J.-D.; Susilo, R.; Englezos, P. Energy and Fuels 2005, 19, 1008-1015.  [4]  Susilo, R.; Moudrakovski, I.L.; Ripmeester, J.A.; Englezos, P. J. Phys. Chem. B  2006, 110 (51), 25803-25909. [5]  Susilo, R.; Ripmeester, J.A.; Englezos, P. AIChE J. 2007, 53 (9), 2451-2460.  [6]  Susilo, R.; Ripmeester, J.A.; Englezos, P. Chem. Eng. Sci. 2007, 62 (15), 39303939.  [7]  Hütz, U.; Englezos, P. Fluid Phase Equilib. 1996, 117, 178-185.  [8]  Ohmura, R.; Matsuda, S.; Uchida, T.; Ebinuma, T.; Narita, H. J. Chem. Eng. Data  2005, 50, 993-996. [9]  DLPOLY 2.14, edited by Forester T.R. and Smith, W. CCLRC, Daresbury Laboratory, 1995.  [10]  Nosé, S. J. Chem. Phys. 1984, 81, 511.  [11]  Hoover, W.G. Phys. Rev. A 1985, 31, 1695.  [12]  Melchionna, S.; Ciccotti, G.; Holian, B.L. Mol. Phys. 1993, 78, 533-544.  [13]  Frenkel, D. and Smit, B. Understanding Molecular Simulation. Academic, San Diego, 2000.  [14]  Allen, M.P.; Tildesley, D.J. Computer Simulation of Liquids. Oxford Science, Oxford, 1987.  208  [15]  Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. J. Phys. Chem. 1987, 91, 6269-6271.  [16]  English, N.J.; MacElroy, J.M.D. J. Comput. Chem. 2003, 24, 1569-1581.  [17]  Jiang, H.; Jordan, K. D.; Taylor, C. E. J. Phys. Chem. B 2007, 111, 6486-6492.  [18]  Ren, P.; Ponder, J. W. J. Phys. Chem. B 2003, 107, 5933-5947.  [19]  Yu, H.; van Gunsteren, W. F. J. Chem. Phys. 2004, 121, 9549-9564.  [20]  Lamoureux, G.; Harder, E.; Vorobyov, I. V.; Roux, B.; MacKerell, A. D., Jr. Chem. Phys. Lett. 2005, 418, 245-249.  [21]  Paricaud, P.; Predota, M.; Chialvo, A. A.; Cummings, P. T. J. Chem. Phys. 2005, 122, 244511.  [22]  Frisch, M.J.; Trucks, G.W.; Schlegel, H.B. et al. GAUSSIAN 98, Revision A.7, Gaussian, Inc., Pittsburg, PA, 2001.  [23]  Breneman, C.M.; Wiberg, K.G. J. Comput. Chem. 1990, 11, 361-373.  [24]  Cornell, W.D.; Cieplak, P.; Bayly, C.; Gould, I.R.; Merz, K.M. Jr.; Ferguson, D.M.; Spellmeyer, D.C.; Fox, T.; Caldwell, J.W.; Kollman, P.A. J. Am. Chem. Soc. 1995, 117, 5179-5197.  [25]  Susilo, R.; Alavi, S.; Ripmeester, J.A.; Englezos, P. J. Chem. Phys. 2008, accepted for publication on March 21, 2008.  [26]  Susilo, R.; Alavi, S.; Ripmeester, J.A.; Englezos, P. Fluid Phase Equilibria 2008, 263, 6-17.  [27]  Buchanan, P.; Aldiwan, N.; Soper, A.K.; Creek, J.L.; Koh, C.A.; Chem. Phys. Lett. 2005, 415, 89-93.  [28]  Raschke, T.M.; Levitt, M.; PNAS 2005, 102 (19), 6777-6782.  209  [29]  Kusalik, P.G.; Svishchev, I.M. Science 1994, 265 (5176), 1219-1221.  [30]  Chemfinder, Reference database (http://www.chemfinder.com), CambridgeSoft Corporation, 2004.  [31]  Masterton, W.L. J. Chem. Phys. 1954, 22 (11), 1830.  [32]  Imai, T.; Hirata, F. J. Chem. Phys. 2005. 122, 094509.  [33]  Rick, S.W.; Stuart, S.J.; Berne, B.J. J. Chem. Phys. 1994, 101, 6141-6156.  [34]  Rick, S.W. J. Chem. Phys. 2001, 114, 2276-2283.  [35]  Patel, S.; Mackerell, A.D., Jr.; Brooks, C.L., III J. Comput. Chem. 2004, 25, 15041513.  [36]  Bjerrum, N. Science 1952, 115, 385-390.  [37]  Tsuji, H.; Ohmura, R.; Mori, Y.H.; Energy & Fuels 2004, 18, 418-424.  [38]  Moudrakovski, I. L.; Ratcliffe, C. I.; McLaurin, G. E.; Simard, B.; Ripmeester, J. A. J. Phys. Chem. A 1999, 103 (26), 4969-4972.  [39]  Moudrakovski, I. L.; McLaurin, G. E.; Ratcliffe, C. I.; Ripmeester, J. A. J. Phys. Chem. B 2004, 108, 17591-17595.  210  CHAPTER-9 CONCLUSIONS, CONTRIBUTION TO KNOWLEDGE, AND RECOMMENDATIONS FOR FUTURE WORK  9.1 Conclusions This thesis examined structure H hydrate formation from the methane/LMGS (methyl-cyclohehane, tert butyl methyl ether and neo-hexane)/water systems. In addition methane hydrate formation with and without n-heptane (a non hydrate former) was studied. The scope of the study was to determine the factors that affect the kinetics of hydrate formation [1-5], the cage occupancy [6] and the methane gas content [7,8] in the hydrate. The motivation was to examine the possibility of storing and transporting methane as structure H hydrate. This is a technology under consideration for development because it is believed that the economics are favorable under certain capacity (gas flow rate)-distance from the gas field to the market conditions. The conclusions are as follows: 1. The initial rate of gas hydrate formation from ice particles was found to increase in the following order: MCH<NH<TBME [1,2]. While the hydrate formation pressure for TBME is the highest and one may attribute this difference to a higher “overpressure” or driving force this trend was also observed in experiments where hydrates formed from liquid water in a well stirred vessel at the same “overpressure” (driving force) conditions. Thus, overpressure alone is not the reason. These two independent experiments are in agreement, and the results in the stirred vessel correlate well with the solubility trend of the LMGS in water, and those from ice particles correlate with the extent of wetting of the ice surface 211  by the LMGS. It should also be noted that in the experiments with ice the methane that goes into the hydrate phase was measured directly by NMR spectroscopy, whereas in the stirred vessel the rate was inferred from methane gas uptake measurements. The latter is a customary macroscopic technique for hydrate kinetics. Thus, microscopic kinetics is in agreement with macroscopic ones which are average kinetics. 2. When hydrate is formed from liquid water, the hydrate conversion is limited by occlusion of water within hydrate crystal agglomerates. Limitations to hydrate conversion exist when hydrate is formed from ice particles. However, in the latter case it was found that full conversion to structure H hydrate was achieved by ramping the temperature up to 1 oC [3]. Two additional important observations were also made in this case [4]. First, the rate of hydrate growth after ice melting was very fast from the two hydrophobic guests (MCH and NH), but considerably slower for the polar one (TBME). Second, when temperature ramping is applied during hydrate formation from MCH or NH, one may compensate for the slow kinetics below the ice point with the fast kinetics above and achieve full conversion within a time period that is less than for the TBME. 3. Structure, cage occupancy, composition and methane content in the hydrate were also determined by employing different experimental techniques. The results from the different techniques were found to be consistent [6]. It was also shown that hydrate composition cannot be achieved by Raman spectroscopy because this technique cannot distinguish between methane molecules in the small and medium  cages  of  structure  H  212  hydrate.  This  finding  resolved  an  inconsistency/ambiguity in the literature. It was found that the methane content in structure H hydrate with TBME was the smallest (103-125 v/v), whereas that with NH was 130-139 (v/v) and that with MCH was 132-142 (v/v). Thus, the maximum methane content is achieved with one of the hydrophobic guests (MCH). 4. The methane content in structure II hydrate by using propane and tetrahydrofuran (THF) as the LMGS was also estimated by thermodynamics-based simulations. The methane content was found to be dependent on the large guest concentration for both CH4/C3H8 hydrate and CH4/THF hydrate [7]. Optimal methane content was found at approximately 100 (v/v) for both C3H8 and THF systems with the large guest concentrations at 1% for C3H8 (10°C) and 1% for THF (room temperature). The gas content is of course lower than that for structure I hydrate (170 v/v) but one should consider the fact that the hydrate formation conditions are much lower (less than 1 MPa). 5. Enhancement of the methane content in structure H hydrate by including methane in the large cages can be achieved at pressures in the GPa range and thus it is only of theoretical interest. 6. Based on the findings of this thesis it is pointed out that from a process design point of view one has to be very careful to not rely on kinetic data from one source alone, especially when those are gas uptake measurements. Moreover, one has to take into account hydrate conversions. If full hydrate conversion is desired, then hydrate should be formed from ice with temperature ramping and not in a stirred vessel requiring mechanical agitation. The LMGS of choice based on  213  kinetics and conversion is the NH or MCH, but TBME can also be considered. If one considers the methane content into the hydrate then the choice again is the hydrophobic guest. Interestingly, the thermodynamic stability conditions (hydrate formation pressure at a given temperature) are most favorable for MCH. 7. Finally, MD simulations provided insight into the guest (MCH, NH, TBME)/host (H2O) interactions and facilitated understanding of the experimental observations [5,8]. These simulations revealed for the first time formation of a defect in the cavities for the TBME/methane/water (sH hydrate) system which may affect hydrate stability and kinetics.  9.2 Contribution to Knowledge This thesis provides new insights on the guest-host interaction that is crucial in understanding the kinetic and thermodynamic properties of gas hydrates especially on structure H (sH). More specifically the contributions are as follows: 1. Methane content and the formation and decomposition rate of sH hydrate depends on the chosen LMGS, temperature and pressure. 2. The solubility, diffusivity, and wetting properties of guest molecules (LMGS, methane) with water molecules determine the formation rate of sH hydrate. 3. Hydrate synthesized from loosely packed ice powder with temperature ramping allows full sH hydrate conversion within relatively short time. 4. Methane storage capacity in sH hydrate ranges between 100 v/v to 140 v/v, which is approximately 20% to 40% less than that of sI hydrate (170 v/v), but only half of the methane pressure is required during the synthesis.  214  5. The methane occupancy may be controlled by the hydrate growth rate in addition to thermodynamics conditions. 6. Hydrophobic guests are preferred to maintain hydrate stability, higher occupancy of the cages and overall conversion rate into hydrate at the expense of slower initial formation rates due to poor contact with water/ice. 7. Polar guests show stronger interactions with water molecules that enable them to have a rapid initial hydrate formation rate due to higher solute concentration in water, better wetting properties and a higher collision probability in the solution. 8. Strong guest-host interactions may distort the cavity formation, induce defects in the hydrate lattice and limit the guest molecule occupancy that eventually slow down the hydrate conversion at a later stage.  9.3 Recommendations for Future Work The following are suggested to further establish the gas-to-solids technology: 1. Use a treated natural gas instead of methane only and determine the kinetics, the hydrate stability, structure, cage occupancy and storage potential. 2. Study the guest (LMGS) – host dynamics via NMR spectroscopy to understand how the guest molecule interacts with the cage and how it influences the hydrate stability, kinetics and cage occupancy. 3. Confirm the inclusion of methane in the large cage of the sH hydrate in addition to the presence of LMGS at lower pressure reported from the pure sH methane hydrate as suggested from the MD simulation results.  215  4. Simulate the methane sH hydrate formation process theoretically via molecular dynamics to see if the change in kinetics profile between a hydrophobic and polar guest can also be observed and insights at a molecular level can be attained. 5. Determine how to control the decomposition of sH hydrate and to see whether the self preservation property of sI methane hydrate can be applied to the sH hydrate as well by forming a hydrate pellet. This is especially useful for longer term storage. 6. Study the crystal morphology differences between the polar and hydrophobic guest to see if the defect can be observed macroscopically.  216  9.4 References [1]  Susilo, R.; Lee, J.D.; Englezos, P. Fluid Phase Equilibria 2005, 231, 20-26.  [2]  Lee, J.-D.; Susilo, R.; Englezos, P. Energy and Fuels 2005, 19, 1008-1015.  [3]  Susilo, R.; Moudrakovski, I.L.; Ripmeester, J.A.; Englezos, P. J. Phys. Chem. B  2006, 110 (51), 25803-25909. [4]  Susilo, R.; Ripmeester, J.A.; Englezos, P. AIChE J. 2007, 53 (9), 2451-2460.  [5]  Susilo, R.; Alavi, S.; Lang, S.; Ripmeester, J.A.; Englezos, P. J. Phys. Chem. C  2008, accepted for publication on April 1, 2008. [6]  Susilo, R.; Ripmeester, J.A.; Englezos, P. Chem. Eng. Sci. 2007, 62 (15), 39303939.  [7]  Susilo, R.; Alavi, S.; Ripmeester, J.A.; Englezos, P. Fluid Phase Equilibria 2008, 263, 6-17.  [8]  Susilo, R.; Alavi, S.; Ripmeester, J.A.; Englezos, P. J. Chem. Phys. 2008, accepted for publication on March 21, 2008.  217  

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