1. Shaunak PotdarDepartment of Chemical & Natural Gas Engineering Texas A&M University Kingsville Sangyong LeeDepartment of Chemical & Natural Gas Engineering Texas A&M University Kingsville

2. FORECAST Introduction to Gas Hydrates Gas Hydrate Structures Applications Phase Equilibrium Molecular Dynamic Simulation Results Conclusion 3. WHAT ARE GAS HYDRATES?HostNon-stoichiometric ,crystallineLatticemolecular complexes of water andlight gases (Argon, Methane,Ethane)Comprised of gas encaged byhydrogen bonding of watermoleculesStable at low T high P conditionsStructure I, Structure II, Structure HGuest Molecule 4. APPLICATIONS Energy source7 - Twice as much carbon as all other forms of fossil fuel combined Desalination of water11 Gas storage (Natural Gas, Hydrogen)8 Separation of Gas Mixtures9 CO2 sequestration (long term temporally storage) in the ocean107. Lee and Holder, Fuel Processing Technology, 71, 181 (2001)8. Zhong and Rogers, Chemical Engineering Science, 55, 4175 (2000)9. Barrer and Ruzicka, Trans. Faraday Soc., 58, 2289 (1962)10. S.-Y. Lee et al., Environmental Science & Technology J., 200311. Byk, S.M., Makogon, Yu.F., and Fomina, V.I., Gas ovye gidraty (GasHydrates), 1980 5. Hydrogen bondOxygen in Picture taken by USGS waterGas HydrateIndividual Cages Holder, G. D., Zetts, S. and N. Pradhan, Review in Chemical Engineering, 5., 1. 6. a=b=c ===90oSmallCavityLarge CavityLarge Cavity 512 6251262512 8X.46H2O 7. a=b=c ===90o24X.136H2O Small CavityLargeCavity 512512 64 8. When two or more phases are in equilibrium, thetemperature, pressure and chemical potential of a componentis the same for each phase At equilibrium, chemical potential of water in both phases is LHthe same, i.e. WW Using, the chemical potential of an unoccupied hydratelattice as a reference, we can rewrite as:W H L HWWand HW 9. PHASE EQUILIBRIUM DIAGRAMHydratesQuadruplePoint 10. Key Assumptions of the vdW model: Each spherical cavity contains at most one gasmolecule No interaction between gas molecules in differentcavities The interaction between guest (gas) and host(water) molecules described by a pair potentialfunction The gas molecules do not contribute to the freeenergy of the hydrate. (Rigid lattice assumption) 11. Each component has different cavity size Distortion modelfor calculating the effect oftemperature, pressure and composition on 3,4,5 WoWW TFhW PVWo 2dT dP ln awRTFRT ToRT 0RTF o and ho are the differences calculated at referencetemperature (273.15 K) and zero pressure for each typeof hydrate3. S.-Y. Lee and G. D. Holder, AIChE. J., Vol 48, 161-167 (2002)4. S.-Y. Lee and G. D. Holder, Gas Hydrates: Challenges for the Future, Ann. of the New York Academy of Science, Vol 912, 614-622 (2000)5. S. Zele, S.-Y. Lee and G. D. Holder, J. of Phy. Chem. B, Vol 103, 10250-10257 (1999) 12. Equations of motion are solved to studythe behavior of atoms and molecules Atomic movements are evaluated overlarger stepsto obtain macroscopicproperties Particle trajectories are developeddepending on the interaction betweenmolecules6 Program used for present study MOLDY76. M. P. Allen, T. J. Tildesley, Computer simulation of liquids, Oxford Press Publications7. K. Refson, Computer Physics Communications, Vol. 126 (3) 309-328, 2000. 13. TIP4P model for water Setting up the potential 12-6 Lennard-Jones pair potential 126(r ) [{ } { }]rr Temperature control Gaussian Time - step adjusted to obtain nearEquilibrium configurations 14. INPUT FILESCONTROLSYSTEM SPECIFICATIONUnit cell anglesNo. of unit cellsin each directionUnit cell dimensions 15. 3.00E+033000 Isobutane Pressure (Mpa) 2000Empty Isobutane Pressure (Mpa) 2.50E+03 Propane Pressure (Mpa) 1000 Equilibrium Total Energy (kJ/mol)Cyclopropane Empty Propane PressureEquilibrium Pressure (MPa)Hydrate @ 273K (Mpa) 2.00E+030 Cyclopropane Pressure (Mpa) -1000 Empty Cyclopropane 1.50E+03Pressure (Mpa) Propane Total Energy -2000Structure generated Empty Propane Total 1.00E+03 in MERCURY -3000 Energy Isobutane Total Energy -4000 Empty Isobutane Total 5.00E+02Energy Cyclopropane Total -5000 Energy Empty Cyclopropane 0.00E+00-6000 Total Energy0 10 203040 50 60 708090 Time (fs)SII CYCLOPROPANE, PROPANE AND ISOBUTANE HYDRATES 16. 3.00E+033000 Krypton Hydrate Pressure (Mpa) 2000Empty Krypton Pressure (Mpa) 2.50E+03 Equilibrium Total Energy (kJ/mol) Argon Hydrate Pressure 1000 (Mpa) Empty Argon PressureKrypton HydrateEquilibrium Pressure (MPa) 2.00E+030 (Mpa)@ 273 K NitrogenHydrate Pressure (Mpa) -1000 Empty Nitrogen 1.50E+03 Pressure (Mpa) -2000 Krypton Total Energy 1.00E+03Structure generated-3000 Empty Krypton Total in MERCURY Energy Argon Hydrate Total -4000 Energy 5.00E+02 Nitrogen Hydrate Total -5000 Energy Empty Nitrogen Total 0.00E+00-6000 Energy0 10 20 3040 50 60 70 80 Time (fs)SII ARGON, KRYPTON AND NITROGEN HYDRATES 17. 2500 Isobutane Error = 2.729%Reference Chemical PotentialReference Chemical Potential (J/mol) by MD Simulation 2000 1500 Reference Chemical Potential Propane by Lee - Holder model Error = -4.688% 1000 CyclopropaneError = -4.89%500Power (Reference Chemicaly = 3E-46x38.858 Potential by Lee - Holder model) 017.7517.817.8517.917.95 18Lattice Parameter ()SII CYCLOPROPANE, PROPANE AND ISOBUTANE HYDRATES 18. 1200 Argon Nitrogen Error = -3.588% Error = 3.842%Reference Chemical Potential (J/mol) Reference Chemical Potential by 1000 MD Simulation 800KryptonError = 4.704% Reference Chemical Potential by 600 Lee-Holder model 400 y = 1E+16x-10.54 200 Power (Reference Chemical Potential by Lee-Holder model) 017.4 17.4517.5 17.5517.617.6517.717.75Lattice Parameter () SII ARGON, KRYPTON AND NITROGEN HYDRATES 19. REFERENCE ENTHALPY PLOT h0 2000Argon 1800Error = -4.702 %Reference Enthalpy by MD Simulation 1600 KryptonError = 3.495 %Reference Enthalpy (J/mol) 1400 1200Reference Enthalpy by Lee-Holder 1000model Nitrogen 800 Error = 0.975 % 600 400Power (Reference Enthalpy by Lee-Holder model)200 y = 2.398x2.200 017.417.45 17.5 17.5517.6 17.65 17.7 17.75 Lattice Parameter ()SII ARGON, KRYPTON AND NITROGEN HYDRATES 20. REFERENCE ENTHALPY PLOT h0 1800 1600 Reference Enthalpy by MD Isobutane Simulation 1400Reference Enthalpy (J/mol) Error = - 1.576% Propane 1200 Error = -2.474%Cyclopropane 1000 Reference Enthalpy by Lee-Error = 0.423% Holder model 800 600 400y = 1E-33x28.76Power (Reference Enthalpy by Lee-Holder model) 200 017.7517.817.85 17.917.9518Lattice Parameter () SII CYCLOPROPANE, PROPANE AND ISOBUTANE HYDRATES 21. CLATHRATE PROPERTIESGuesto (J/mol) ho (J/mol) Cp(J/mol-K)Argon1075.333182593.867788Cyclopropane 1315.3851191.667130.9309Isobutane1918.1821675168.7388Krypton781.8182125016.96608Nitrogen 901 101580.6616Propane1609.0911452.941117.154 22. TEMPERATURE EFFECT ON HYDRATE SIZE58505800 IsobutaneUnit Cell Volume (3)57505700 Propane56505600 Cyclopropane5550 240 245 250 255 260 265 270 275 280 Temperature (K) 23. TEMPERATURE EFFECT ON HYDRATE SIZE56505600 Krypton Hydrate55505500Unit Cell Volume (3)5450 Argon Hydrate540053505300 Nitrogen Hydrate52505200 140 160 180 200 220240260 280 300 320 Temperature (K) 24. THERMAL EXPANSION COEFFICIENT1 V V1 V0 [1 (T1 T0 )]V0T P GuestTemperature (K) (oK-1) Argon148.8 - 291 0.044602 Krypton202.9 283.2 0.00065 Nitrogen 285.63 295.61 0.000642 Cyclopropane 258.09 2730.000412 Propane251.4 275.2 0.000639 Isobutane243.4 273.150.000594 25. SUMMARY Reviewed physical properties of clathartes Hydrate reference properties based on the lattice distortion theory of gas hydrates Comparison with experimental results Increase in unit cell volume with temperature 26. Using MD simulation, equilibrium conditions of structure II gas hydrates attained Validated the Distortion model Demonstrated thermal expansion of hydrate lattice 27. Gaussian Thermostat Set by control parameter: const temp = 2 It rescales the atomic velocities at each time step, to obtainthe desired value of average temperature 28. Nose Hover ThermostatSet by control parameter: const temp = 1The system is coupled to a fictitious heat bathIt allows the temperature to fluctuate about an average valueIt oscillates for systems not in equilibrium, hence, notrecommended 29. EWALD SUM Long range electrostatic forces are evaluated using this technique 30. LINK CELL Short range interactions are computed using the linkcell method The MD cell is divided into a number of smaller cellscalled subcells 31. CUT OFF (Rc)Rc Used to minimize total number of calculations Molecules close to the molecule of interest contribute most to the potential energy and forces acting on it Interactions amongst molecules within Rc considered 32. ho The temperature dependence of enthalpy is given by2 TF 0h WhW CPW dT To CPw is the heat capacity difference between theoreticalempty lattice and water20 CPWCPW b(T T0 ) CoPw is the reference heat capacity b is an empirical constant fitted to experimental data22. S.-Y. Lee and G. D. Holder, AIChE. J., Vol 48, 161-167 (2002). 33. ArgonTf < T0Tf263.2 System TemperatureT0 273.15 Reference TemperatureR 8.314 Gas ConstantVw3.39644 Constant for SIIref chem pot (0) 1075.333 MDref enthalpy 1825 MDexp pot () 1038.078 Experimentalexp enthalpy 1647.531 ExperimentalP6940 MD(/RTf) = (0/RT0) -[hw/R(T0-T)]+ [(V wP/RTf)]0.474388606 0.473513 -[hw/R(T0-T)]+ 10.7717809[hw/R(T0-T)] = 10.77091Therefore,hw = 891.0156Therefore,Cpw =93.86778 J/(mol-K) 34. 200 Krypton Hydrate Simulated Pressure Krypton Hydrate Experimental PressureEquilibrium Pressure (MPa) 150 (Kpa) Argon Hydrate Simulated Pressure 100 Argon Hydrate Experimental Pressure50 Nitrogen Hydrate Simulated Pressure Nitrogen Hydrate Experimental Pressure0 190 210 230 250 270 290 310 Temperature (K) 35. 0.3Isobutane Hydrate SimulatedPressure 0.25Isobutane Hydrate ExperimentalEquilibrium Pressure (MPa)Pressure0.2Propane Hydrate Simulated Pressure 0.15Propane Hydrate ExperimentalPressure0.1Cyclopropane Hydrate SimulatedPressure 0.05Cyclopropane Hydrate ExperimentalPressure 0240 245 250255260 265 270 275 280Temperature (K) 36. CyclopropaneHydrate @ 273K