The document provides an overview of gas hydrates including their structure, applications, phase equilibrium modeling, and molecular dynamic simulations. Gas hydrates are crystalline structures formed when gas molecules like methane are trapped within a lattice of water molecules. They are stable under conditions of low temperature and high pressure. The document discusses gas hydrate structures, applications in energy storage and transport, modeling of phase equilibria, and results from molecular dynamic simulations validating distortion models of gas hydrate properties.

1. Shaunak Potdar
Department of Chemical & Natural Gas Engineering
Texas A&M University – Kingsville
Sangyong Lee
Department 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?
Host
Non-stoichiometric ,crystalline Lattice
molecular complexes of water and
light gases (Argon, Methane,
Ethane…)
Comprised of gas encaged by
hydrogen bonding of water
molecules
Stable at low T high P conditions
Structure I, Structure II, Structure H
Guest
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
ocean10
7. 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., 2003
11. Byk, S.M., Makogon, Yu.F., and Fomina, V.I., Gas ovye gidraty (Gas
Hydrates), 1980

5. Hydrogen bond Oxygen in Picture taken by USGS
water
Gas
Hydrate
Individual Cages
Holder, G. D., Zetts, S. and N. Pradhan, Review in Chemical Engineering, 5., 1.

6. a=b=c
α =β=γ=90o
Small
Cavity
Large Cavity
Large Cavity
512 62
5126
2
512
8X.46H2O

7. a=b=c
α =β=γ=90o 24X.136H2O
Small
Cavity
Large
Cavity
512
512 64

8.  When two or more phases are in equilibrium, the
temperature, pressure and chemical potential of a component
is the same for each phase
 At equilibrium, chemical potential of water in both phases is
L H
the same, i.e. W W
 Using , the chemical potential of an unoccupied hydrate
lattice as a reference, we can rewrite as:
W H
L H
W W and H W

9. PHASE EQUILIBRIUM DIAGRAM
Hydrates
Quadruple
Point

10.  Key Assumptions of the vdW model:
 Each spherical cavity contains at most one gas
molecule
 No interaction between gas molecules in different
cavities
 The interaction between guest (gas) and host
(water) molecules described by a pair potential
function
 The gas molecules do not contribute to the free
energy of the hydrate. (Rigid lattice assumption)

11.  Each component has different cavity size
 Distortion model for calculating the effect of
temperature, pressure and composition on 3,4,5
W
o ' '
W W
TF hW P VW
o 2
dT dP ln aw
RTF RT To RT 0 RTF
 ∆µo and ∆ho are the differences calculated at reference
temperature (273.15 K) and zero pressure for each type
of hydrate
3. 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 study
the behavior of atoms and molecules
 Atomic movements are evaluated over
larger steps to obtain macroscopic
properties
 Particle trajectories are developed
depending on the interaction between
molecules6
 Program used for present study – MOLDY7
6. M. P. Allen, T. J. Tildesley, Computer simulation of liquids, Oxford Press Publications
7. 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
12 6
(r ) [{ } { }]
r r
 Temperature control – Gaussian
 Time - step adjusted to obtain near
Equilibrium configurations

14. INPUT FILES
CONTROL SYSTEM SPECIFICATION
Unit cell angles
No. of unit cells
in each
direction
Unit cell
dimensions

15. 3.00E+03 3000
Isobutane Pressure (Mpa)
2000 Empty Isobutane
Pressure (Mpa)
2.50E+03
Propane Pressure (Mpa)
1000
Equilibrium Total Energy (kJ/mol)
Cyclopropane
Empty Propane Pressure
Equilibrium Pressure (MPa)
Hydrate @ 273K (Mpa)
2.00E+03 0
Cyclopropane Pressure
(Mpa)
-1000 Empty Cyclopropane
1.50E+03 Pressure (Mpa)
Propane Total Energy
-2000
Structure generated
Empty Propane Total
1.00E+03
in MERCURY® -3000 Energy
Isobutane Total Energy
-4000 Empty Isobutane Total
5.00E+02 Energy
Cyclopropane Total
-5000
Energy
Empty Cyclopropane
0.00E+00 -6000 Total Energy
0 10 20 30 40 50 60 70 80 90
Time (fs)
SII CYCLOPROPANE, PROPANE AND ISOBUTANE HYDRATES

16. 3.00E+03 3000
Krypton Hydrate
Pressure (Mpa)
2000 Empty Krypton Pressure
(Mpa)
2.50E+03
Equilibrium Total Energy (kJ/mol)
Argon Hydrate Pressure
1000
(Mpa)
Empty Argon Pressure
Krypton Hydrate
Equilibrium Pressure (MPa)
2.00E+03 0 (Mpa)
@ 273 K
NitrogenHydrate
Pressure (Mpa)
-1000
Empty Nitrogen
1.50E+03
Pressure (Mpa)
-2000
Krypton Total Energy
1.00E+03
Structure 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 Energy
0 10 20 30 40 50 60 70 80
Time (fs)
SII ARGON, KRYPTON AND NITROGEN HYDRATES

17. 2500
Isobutane
Error = 2.729% Reference Chemical Potential
Reference Chemical Potential (J/mol)
by MD Simulation
2000
1500
Reference Chemical Potential
Propane by Lee - Holder model
Error = -4.688%
1000 Cyclopropane
Error = -4.89%
500 Power (Reference Chemical
y = 3E-46x38.858 Potential by Lee - Holder
model)
0
17.75 17.8 17.85 17.9 17.95 18
Lattice Parameter (Å)
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
800
Krypton
Error = 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)
0
17.4 17.45 17.5 17.55 17.6 17.65 17.7 17.75
Lattice Parameter (Å)
SII ARGON, KRYPTON AND NITROGEN HYDRATES

19. REFERENCE ENTHALPY PLOT ∆h0
2000
Argon
1800
Error = -4.702 % Reference Enthalpy by MD Simulation
1600 Krypton
Error = 3.495 %
Reference Enthalpy (J/mol)
1400
1200
Reference Enthalpy by Lee-Holder
1000
model
Nitrogen
800
Error = 0.975 %
600
400 Power (Reference Enthalpy by Lee-
Holder model)
200
y = 2.398x2.200
0
17.4 17.45 17.5 17.55 17.6 17.65 17.7 17.75
Lattice Parameter (Å)
SII ARGON, KRYPTON AND NITROGEN HYDRATES

20. REFERENCE ENTHALPY PLOT ∆h0
1800
1600
Reference Enthalpy by MD
Isobutane Simulation
1400
Reference Enthalpy (J/mol)
Error = - 1.576%
Propane
1200
Error = -2.474%
Cyclopropane
1000
Reference Enthalpy by Lee-
Error = 0.423% Holder model
800
600
400
y = 1E-33x28.76 Power (Reference Enthalpy by
Lee-Holder model)
200
0
17.75 17.8 17.85 17.9 17.95 18
Lattice Parameter (Å)
SII CYCLOPROPANE, PROPANE AND ISOBUTANE HYDRATES

21. CLATHRATE PROPERTIES
Guest ∆μo (J/mol) ∆ho (J/mol) Cp(J/mol-K)
Argon 1075.333 1825 93.867788
Cyclopropane 1315.385 1191.667 130.9309
Isobutane 1918.182 1675 168.7388
Krypton 781.8182 1250 16.96608
Nitrogen 901 1015 80.6616
Propane 1609.091 1452.941 117.154

22. TEMPERATURE EFFECT ON HYDRATE SIZE
5850
5800 Isobutane
Unit Cell Volume (Å3)
5750
5700 Propane
5650
5600 Cyclopropane
5550
240 245 250 255 260 265 270 275 280
Temperature (K)

23. TEMPERATURE EFFECT ON HYDRATE SIZE
5650
5600
Krypton Hydrate
5550
5500
Unit Cell Volume (Å3)
5450
Argon Hydrate
5400
5350
5300
Nitrogen Hydrate
5250
5200
140 160 180 200 220 240 260 280 300 320
Temperature (K)

24. THERMAL EXPANSION COEFFICIENT
1 V V1 V0 [1 (T1 T0 )]
V0 T P
Guest Temperature (K) α (oK-1)
Argon 148.8 - 291 0.044602
Krypton 202.9 – 283.2 0.00065
Nitrogen 285.63 – 295.61 0.000642
Cyclopropane 258.09 – 273 0.000412
Propane 251.4 – 275.2 0.000639
Isobutane 243.4 – 273.15 0.000594

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 obtain
the desired value of average temperature

28. Nose – Hover Thermostat
•Set by control parameter: const – temp = 1
•The system is coupled to a fictitious heat bath
•It allows the temperature to fluctuate about an average value
•It oscillates for systems not in equilibrium, hence, not
recommended

29. EWALD SUM
 Long range electrostatic
forces are evaluated
using this technique

30. LINK CELL
 Short range interactions are computed using the link
cell method
 The MD cell is divided into a number of smaller cells
called 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
' 0 '
h W hW CPW dT
To
 ∆C’Pw is the heat capacity difference between theoretical
empty lattice and water2 ' 0
CPW CPW b(T T0 )
 ∆CoPw is the reference heat capacity
 b is an empirical constant fitted to experimental data2
2. S.-Y. Lee and G. D. Holder, AIChE. J., Vol 48, 161-167 (2002).

33. Argon Tf < T0
Tf 263.2 System Temperature
T0 273.15 Reference Temperature
R 8.314 Gas Constant
Vw 3.39644 Constant for SII
ref chem pot (∆μ0) 1075.333 MD
ref enthalpy 1825 MD
exp pot (∆μ) 1038.078 Experimental
exp enthalpy 1647.531 Experimental
P 6940 MD
(∆μ/RTf) = (∆μ0/RT0) - [hw/R(T0-T)] + [(V wP/RTf)]
0.474388606 0.473513 - [hw/R(T0-T)] + 10.7717809
[hw/R(T0-T)] = 10.77091
Therefore,
hw = 891.0156
Therefore,
Cpw = 93.86778 J/(mol-K)

34. 200
Krypton Hydrate Simulated Pressure
Krypton Hydrate Experimental Pressure
Equilibrium Pressure (MPa)
150 (Kpa)
Argon Hydrate Simulated Pressure
100
Argon Hydrate Experimental Pressure
50 Nitrogen Hydrate Simulated Pressure
Nitrogen Hydrate Experimental Pressure
0
190 210 230 250 270 290 310
Temperature (K)

35. 0.3
Isobutane Hydrate Simulated
Pressure
0.25
Isobutane Hydrate Experimental
Equilibrium Pressure (MPa)
Pressure
0.2
Propane Hydrate Simulated Pressure
0.15
Propane Hydrate Experimental
Pressure
0.1
Cyclopropane Hydrate Simulated
Pressure
0.05
Cyclopropane Hydrate Experimental
Pressure
0
240 245 250 255 260 265 270 275 280
Temperature (K)

36. Cyclopropane
Hydrate @ 273K