Download molecular dynamics studies of the stability of co2

Proceedings of the 7th International Conference on Gas Hydrates (ICGH 2011),
Edinburgh, Scotland, United Kingdom, July 17-21, 2011.
MOLECULAR DYNAMICS STUDIES OF THE STABILITY OF CO2 AND
CH4 HYDRATES IN THE PRESENCE OF UNDERSATURATED FLUIDS
Srinath Velaga1,2, Venkata Vedam1,2, Brian J. Anderson1,2*
1
National Energy Technology Laboratory
Morgantown, WV-26507, USA
2
Department of Chemical Engineering
West Virginia University
Morgantown, WV-26505, USA
ABSTRACT
Methane hydrates are globally distributed in sediments along the continental margins and
potentially contain more energy than all fossil fuel reserves. However, methane is also a potential
greenhouse gas which could play a major role in global climate change. Accurately
characterizing the stability of methane and CO2 hydrates in water can help us understand their
effects on earth’s environment and also fesibilty of long term CO2 sequestration in the sediments
under the ocean floor. Hydrate stability can be better predicted by understanding the phenomena
related to hydrate dissolution in water. Under hydrate stability conditions, the concentration
difference between the hydrate and water phases of hydrate-forming gases should be an
important factor affecting hydrate stability as oceanic hydrates are exposed to under-saturated sea
water. In this work, the dissolution of methane and CO2 hydrates have been studied and
compared to one another in the presence of water using molecular dynamics simulations. The
average lattice constant for structure I and II hydrate was calculated for two different potentials
of methane OPLS and GROMACS and compare to the experimental value for validation.
Methane hydrate dissociation in the presence of water was also studied using these two potentials
in addition to the Anderson et al. model. The Harris and Yung model for CO2 as well as our own
ab initio-derived CO2 potential were used in the simulations of CO2 hydrate in the study. In order
to provide comparison of the CO2 potentials, the reference chemical potentials, densities of pure
CO2 liquid and vapor, and solubility of CO2 in water were calculated using each of the potential
models.
Keywords: gas hydrates, stability, molecular dynamics, dissolution
NOMENCLATURE
ε
k
σ
Characteristic energy [kcal/mol]
Boltzmans constant [J/K]
Collision diameter [Å]
∆ Reference chemical potential [J/mol]
∆ Reference enthalpy [J/mol]
INTRODUCTION
Large deposits of CH4 hydrates are stored in
the permafrost and on the continental margins;
these could be potentially a source of energy if
recovered in an efficient way[1]. However,
methane is also a potent green house gas so the
destabilization of methane gas hydrates can affect
the ocean environment and geologic column along
*
with the atmosphere[2]. Additionally, the idea of
sequestrating the carbon dioxide in the oceanic
sediments to hold the increase in green house gas
in the atmosphere has been proposed[3]. Therefore
knowing the stability of methane and CO2 hydrates
in presence of water will help in predicting their
effects on earth’s environment and the feasibility
of long term storage of CO2 as hydrates in the
oceanic sediments. The stability of gas hydrates
depends not only on the temperature and pressure
but also, the composition of both water and gas.
Stability of gas hydrates in sea water is largely
influenced by two phenomena dissociation and
dissolution[4]. The process of decomposition of
hydrate caused due to the change in temperature
and pressure outside the hydrate stability field
Corresponding author: Phone: +1 304 293 9334 Fax: +1 304 293 4139 E-mail: Brian. [email protected]
(HSF) is called dissociation[4]. Alternately, gas
hydrates can be decomposed when there exists an
under-saturated liquid water phase surrounding the
hydrates within the HSF pressure and temperature.
This process can be called dissolution, as the
hydrate dissolves in to water and gas and thus the
saturated concentrations are reestablished[4-6].
Rehder et al.[6] first performed in situ
experimental studies to measure the dissolution
rates of pure synthetic samples of CH4 and CO2
hydrates directly on the sea floor at pressure and
temperature conditions which are well within
hydrate stability field (HSF). They proposed a
diffusive boundary layer model for the dissolution
process and the kinetics of which is a mass transfer
controlled. They concluded this because of the
finding that the ratio of the dissolution rates of
CH4 and CO2 are similar to their solubilities ratio.
Hester et al.[7] conducted in situ experiment on
two distinct natural samples for the dissolution
studies, unlike those done by Rehder et al.[6]
Their analysis gave similar results as those of
Rehder et al. and concluded that the dissolution is
mass transfer controlled. Nihous and Masutani[8]
proposed an elementary model on the dissolution
of pure hydrate in under-saturated sea water. They
applied this model to the experimental data of
Rehder et al. on dissolution rates and suggested
that the concentration of the hydrate guest species
at the interface between the desorption film and
diffusive boundary layer may be much lower than
ambient solubility. Lapham et al.[9] measured the
in situ pore water methane concentrations and
calculated the dissolution rates and these
dissolution rates are significantly less than
dissolution rates predicted for methane undersaturated pore-water in direct contact with pure
methane gas hydrate if equilibrium methane
concentrations exist immediately adjacent to the
hydrate surface.
Sea floor methane hydrate outcrops have
been found to show considerably longer life times
than the theoretical predictions[10]. An
understanding of the dissolution of gas hydrates in
contact with under-saturated water is important to
determine the long-term stability of gas hydrate
reservoirs. The concentration difference of the
hydrate forming gas between the hydrate and
water phases have a key role in the stability of the
hydrate.
Molecular dynamics (MD) computer
simulations can be used for studying the stability
of hydrates. Baez and Clancy[11] carried out MD
simulations to study the dissolution of spherical
methane hydrate crystal in presence of water using
non-polarizable SPC/E[12] model for water at 270
K and 40 bar, where the hydrate crystallite of
radius 12 Å had around 250 molecules of water
and 32 molecules of methane in the hydrate phase.
They found that the melting occurred in a stepwise
manner and the hydrate decay was governed by
the breakup of partial cages at the interface. They
also noted that the size of the crystallite, initially
or during the dissociation, did not affect the rate of
hydrate break up. English et al.[13] also studied
dissolution of spherical hydrate crystallites in
water at 277 K and 68 bar using TIP4P-FQ[14]
water model. They found that the crystallites
dissociate within 400 ps. The authors observed
that the dissolution rates were not affected by the
size of the crystallite and by the methane
composition of the hydrate phase between 80100%, but in contrast the empty hydrate clusters
were found to dissolve rapidly. Although the
liquid phase considered is unsaturated with respect
to methane, hydrate dissolution is supposed to be a
slow process and cannot occur in very short
timescales as those observed by these authors. So,
it is more likely that the dissolution occurred
because the crystallites considered were subcritical
in size. The critical size of a hydrate cluster for
nucleation has been estimated by Radhakrishnan et
al.[15] to be in between 10-14 Å in a linear
dimension. So, the size of the hydrate phase has to
be more than the critical size of nucleation to
remain stable and to have a continuous growth.
Myshakin et al.[16] performed molecular
dynamics studies on methane hydrate dissociation
at 277 K and 68 bar. They observed that the
dissociation rate depends on the hydration number
and found that a decrease in cage occupancy from
100% to 95% causes a greater change in the
dissociation rate than for a decrease from 95% to
85%, and also noted that the presence of empty
cages destabilizes the hydrate lattice and
stimulates the dissociation process.
There have been very few studies on CO2
hydrate using MD simulations. Hirai et al.[17]
studied the stability of CO2 hydrate using MD
simulations using an inter atomic potential
function based on a model given by Kumagai et
al.[18] for both CO2 and water. They found that it
is unstable compared to both empty and Argon
clathrate hydrates. This was attributed to the
destabilizing effect caused by the repulsive force
acting between the O atoms of CO2 and O atom in
H2O on the lattice structure. Kvamme et al.[19]
al.
performed MD simulations to study the CO2
hydrate-water
water interface at conditions within the
hydrate stability zone using the SPC/E[12]
SPC/E
water
model. They evaluated the steady state interface
thickness using different analyses like the
hydrogen density profiles and radial distribution
functions.
The objective of this work is to study and
compare the dissolution behavior of methane and
CO2 hydrates and understand the importance of gas
concentration in driving the hydrate dissolution
process. Also, the simulations were performed to
have the comparison of the CO2 potentials.
SIMULATION DETAILS
All the simulations in this work were done
in an NPT ensemble. In this study, the very
popular TIP4P[20] force field has been used for
water in both methane hydrate/water and CO2
hydrate/water simulations. Three different
potentials namely OPLS[21],, GROMACS
GROMACS[22] and
the Anderson et al.[23] model have been used for
methane in order to perform a comparison among
them with respect to the dissociation properties of
hydrates. The Harris and Yung[24] potential as
well as our own ab initio-derived
derived CO2 potential
were used for CO2 in the simulations. The charges
and the Lennard-Jones
nes parameters of methane or
CO2 for each of the potentials have been taken
from the corresponding references provided.
Periodic boundary conditions were used in all the
directions for all the simulations. The LorentzLorentz
Berthelot[25] combination rules were used to
calculate the Lennard-Jones[25] parameters
between the water and gas molecules. The time
step of 1fs was used and the cutoff radius for the
LJ interactions was chosen to be 9 Å for all the
systems. Ewald summation[26] was used to
account for the long range electrostatic
interactions. The temperature and pressure was
controlled by Berendsen thermostat and barostat
respectively for dissociation and dissolution
simulations. The GROMACS package was used to
perform the MD simulations and Visual molecular
dynamics (VMD) was used to view the
simulations.
METHODOLOGY
Hydrate crystals for both CO2 and CH4
hydrates were constructed using the programs in
GROMACS package based on thee lattice structure
of unit cell of the hydrate for structure I (sI) and
structure II (sII). To study the dissociation of
hydrate in the presence of water, a 32 unit cell
(4×4×2) simulation box of sI methane hydrate was
constructed and a cell of 6917 water molecules
have been appended on one side of z-direction
z
making the simulation box of 4.7×4.7×7.2 nm as
shown in Figure 1. The simulations were
performed at a pressure of 1 bar and different
temperatures from 250 K to a time where it
dissociates completely. CH4 hydrate dissociation
in the presence of water was studied using the
OPLS, GROMACS and Anderson et al. potential
models. The dissociation process was studied
based on the number of gas molecules that moved
out of hydrate in to the water phase. To validate
the methane OPLS and GROMACS potentials
used for dissociation, simulations were performed
to calculate the lattice constants on an 8 unit cell
(2×2×2) simulation box each of sI and sII for 200
ps at a constant pressure of 1 bar and different
temperatures
res ranging from 250 K
K-400 K.
For the dissolution studies, a 64-unit
64
cell
(4×4×4) simulation box of sI hydrate was
constructed for both methane and CO2 and a cell of
6917 water molecules has been appended to it to
make it a simulation cell of dimensions 4.7×4.7×14
4.
nm as shown in the Figure 2. The hydrate phase
has 512 gas molecules (CO2 or CH4 in the
corresponding hydrates) and 2944 water
molecules. It was observed by the initial
simulations that a 32 unit cell hydrate phase
dissolved in 5ns compared to a 64 unit cell hydrate
which was stable even after 20 ns in same amount
of water. This might be because of the sub critical
size of 32 unit cell hydrate which has 24 Å in the
z-direction,
direction, compare to the critical size of
nucleation estimated by classical
classica theory as 32
Å[27].
Figure 1. 2-D
D view of a box with 32 unit cell (4×4×2)
of sI CH4 hydrate appended to 6917 water molecules in
z-direction.
Figure 2. Initial configuration of a simulation cell with
64 unit cell box of sI CO2 hydrate appended with 6917
water molecules in z-direction.
Different models of the simulation cells
have been constructed varying the concentration of
guest gas in the hydrate phase
se (cage occupancy)
and in liquid phase (under-saturation).
saturation). The effect
of cage occupancy was studied by varying the
small cage occupancy at 100%, 75%, 50%, 25%
and 0% for both CO2 and CH4 hydrates. The effect
of water phase undersaturation was studied by
varying
arying the gas saturation in the liquid phase at
100%, 75%, 50% and 0% for both 0% and 100%
cage occupancy of small cages. The details of all
different models constructed are listed in Table 1.
Simulations were carried out for longer timescales
of 36 ns. The Harris and Yung[24] potentials were
used for CO2 hydrate simulations.
Table 1.. Summary of the concentration of guest gas in
hydrate and liquid phasess for initial simulation box.
Cage
CO2 molecules
CH4 molecules
occupancy
Hydrate
Liquid
Hydrate
Liquid
(small
phase
Phase
phase
Phase
cages)
100%
512
0
512
0
75%
480
0
480
0
50%
448
0
449
0
25%
416
0
416
0
0%
384
0
384
0
Varying the concentration in liquid phase
100% small cage occupancy
levels of
saturation
100%
512
52
512
9
75%
512
39
512
7
50%
512
26
512
5
0%
512
0
512
0
0% small cage occupancy
100%
384
52
384
9
75%
384
39
384
7
50%
384
26
384
5
0%
384
0
384
0
In order to have comparison of the CO2
potentials, Harris and Yung and ab initio
potentials as given in Table 2, simulations
imulations were
performed at constant temperature and pressure to
obtain the density of pure CO2 and solubility in
water at different temperatures.
temperat
Density
simulations were performed on 1000 pure CO2
(4.5Å×4.5Å×4.5Å) molecules and the solubility
calculations with 512 CO2 molecules appended
with 6917 H2O molecules. The temperature was
controlled by Nose-Hoover
Hoover thermostat
thermostat[28-29] and
the pressure by Parrinello-Rahman
Rahman[30] barostat.
Table 2. CO2 Intermolecular potentials used in
simulations. Bold atoms indicate specific atom-atom
atom
interactions.
L-J 6-12
This model
& Yung
Harris&
ε/k (K)
ε/k (K)
σ(Å)
Charge
σ(Å)
O2C – CO2
76.765
3.595
28.129
2.757
OCO –OCO
56.414
2.975
80.507
3.033
CO2
0.652
CO2
-0.326
RESULTS AND DISCUSSIONS
A time averaged value of lattice constant
was calculated after the equilibrium is reached for
different temperatures. The
he plot of average lattice
constant with respect to temperature for both the
potentials of methane is shown in the Figure 3 for
sI and sII. The lattice constant increases with
temperature and this effect was observed till the
hydrate dissociated completely.. Lattice constant of
sI methane hydrate at 273 K and 1 bar was noted
from Figure 3aa to be 1.187 nm for OPLS and
1.189 nm for GROMACS potential and was found
to be comparable to the experimental value[1]
value
of
1.2 nm. Lattice constant of structure II methane
hydrate at the same conditions were noted to be
1.68 nm for OPLS and 1.73 nm for GROMACS
potential, which were also comparable to the
experimental value[1] of 1.73 nm. This validates
the potentials considered for methane.
Dissociation
At 250 K and 1 bar, the hydrate was found
to be stable for the entire simulation run for 20 ns.
To see the effect of pressure, simulations were also
performed at temperature of 250 K and different
pressures between 1 bar and 50. It was found that
the dissociation
ociation rates of the hydrate were not
affected by a change in the pressure. At 255 K and
1 bar, the hydrate did not completely dissociate till
20 ns, but was found to be unstable and had a
higher dissociation rate compared to that of 250 K.
Number density of CH4
molecules
Lattice constant (nm)
1.210
opls
gmx
1.205
1.200
1.195
1.190
1.185
(a)
270
290
310
330
2ns
3ns
4ns
5ns
0
1.180
250
16
14
12
10
8
6
4
2
0
350
2
4
z- parameter of the cell (nm)
6
370
Temperature(K)
Lattice constant (nm)
1.740
opls
gmx
1.735
1.730
1.725
1.720
1.715
Figure 4. Density plot of CH4 molecules and a snapshot
of sI CH4-H2O system dissociated in 5 ns at 270 K. It is
clear from the snap shot that the hydrate is completely
dissociated.
1.710
(b)
1.705
1.700
250
270
290
310
330
Temperature (K)
350
370
Figure 3. Effect of temperature on lattice constant on
(a) sI and (b) sII for CH4 hydrate. gmx-Gromacs
potential, opls –OPLS potential.
A further increase in temperature to 260 K at same
pressure caused the hydrate to completely
dissociate within 20 ns. Hydrate at 265 K
dissociated in 15 ns, while it dissociated in 5 ns at
270 K. Increase in temperature has fastened the
dissociation rate. The density plot and
corresponding snapshot of the system of the
simulation at 270 K and 1 bar is shown in Figure
4. The dissociation temperature of methane
hydrate at 1 bar was noted to be 260 K. This was
for the Anderson et al. model of methane. These
simulations were also done using the other two
potentials for methane. Similar trends of
dissociation rates of hydrates were observed for all
the three potentials with changes in temperature
and pressure. The dissociation temperature was
noted to be 260 K for OPLS potential and 285 K
for GROMACS potential. Hydrate with
GROMACS potential for methane was found to
withstand higher temperatures compared to OPLS
and Anderson et al. model. The GROMACS
intermolecular potential for methane seemed to be
attractive for molecules in a hydrate compared to
other two potentials. Anderson et al.[23] model
was used for methane in all the simulations done
for dissolution of hydrates in water in this work.
Dissolution
Simulations on methane and CO2 hydrates
to study their dissolution phenomenon were
performed at a chosen temperature and pressure
conditions 275 K and 50 bar which are within the
hydrate stability zone for both the hydrates.
Different combinations of temperature and
pressure conditions were tried before choosing
these conditions. The temperature was chosen so
that it is within the hydrate stability zone but not
too far from the hydrate dissociation point at the
chosen pressure, so that considerable amount of
dissolution is observed with both methane and
CO2 hydrates. Hydrate dissolution was not found
to be sensitive to change in pressure between 2050 bar at 275 K. A pressure of 50 bar was chosen
because it is theoretically more stable pressure for
275 K.
Effect of cage occupancy
The effect of cage occupancies on the
dissolution rates were studied by varying the
percentage occupancy of small cages as given in
Table 1. A high amount of dissolution was found
to occur within the first 10 ns in the case of CO2
hydrate and a slow decrease in the overall rate of
dissolution was observed thereafter and for
methane hydrate it increases very slowly as given
in Figure 5. From Figure 6, it is evident that the
amount of dissolution in the case of methane
hydrate is lower compared to that of CO2 hydrates,
Number of gas molecules
dissolved in the water phase
200
150
100
CH4
CO2
50
0
0
20
40
Time (ns)
60
80
Figure 5. Dissolution rate of CO2 and CH4 with all
cavities completely occupied and water phase
completely unsaturated at the start of the simulation.
On the other hand, CO2 hydrate was found
to dissolve faster at 100% cage occupancy
compared to hydrate at other occupancies. The
dissolution rate was found to decrease with
decrease in cage occupancy till 0%. So, these
results imply a higher stability of CO2 hydrate at
lower cage occupancies. The symmetrical
structure of the CO2 hydrate at 0% cage occupancy
could be an added advantage for the hydrate to be
much stable compared to that at other occupancies.
This shows that CO2 hydrate is stable at lower
cage occupancies close to 0%.
Water phase undersaturation
The solubility of CH4 and CO2 in water was
estimated at 275 K and 50 bar for 20 ns to
construct the under-saturation of the liquid phase.
180
Number of gas molceules
dissolved in the liquid phase
in 35 ns
by a factor of 10 or greater. It was observed that
the amount of dissolution of methane hydrate is
lower at 100 % cage occupancy and increased with
decrease in occupancy till 25%. But methane
hydrate was found to be very stable at 0%
occupancy. A relatively higher stability or lesser
dissolution of hydrate at 100% or 0% cage
occupancy over hydrate at other occupancies can
be explained by their lack of defects in the
periodic crystal structure. At these occupancies,
the hydrate has a more symmetrical crystal
structure compared to other occupancies that
introduce crystal defects. This effect is observed
more in the case of methane hydrate than CO2
hydrate as the amount of methane hydrate
dissolution is also very low unlike the dissolution
in the case of CO2 hydrates. The regular increase
in the amount of methane hydrate dissolution with
decrease in cage occupancy shows that methane
hydrate is more stable at cage occupancy close to
100%.
160
CO2
140
CH4
120
100
80
60
40
20
0
100%
75%
50%
25%
0%
Percentage of cage occupancy
Figure 6. Comparing the effect of small cage occupancy
on the dissolution of CH4 and CO2 hydrates in water.
It was found from the density plots that 9
molecules of methane completely dissolved in to
water phase and 52 molecules of CO2 in 6917
water molecules. The corresponding molefractions
are 0.001322 and 0.007461, where as the
experimental values are 0.002334[16] and
0.01739[31] respectively.
Methane hydrate with 100% cage occupancy
in hydrate and 100% gas saturation in liquid phase
was found to be very stable. As, it has already
been seen that the methane hydrate is very stable
at 100% cage occupancy and 0% gas saturation, it
is expected that it should be much more stable at
100% gas saturation. But, it was interesting to
observe that the number of methane molecules in
the hydrate phase was found to increase past the
number that was present initially. In fact, this was
observed even with the simulation at 75% gas
saturation. This can be seen from the plot in Figure
7 where there are times at which the curve goes
above the black solid line in the case of 100% and
75% gas saturation. This might have occurred
because there is a possibility of the methane
molecules already present in the water phase
moving in to the hydrate phase, which again is an
indication that a hydrate growth is possible. At 0%
cage occupancy, the amount of dissolution was
found to show a similar trend with respect to
percentage gas undersaturation. But, the amount of
dissolution of methane molecules lowered by a
small amount when compared to that at 100% cage
occupancy. So, it seems that the dissolution is
driven by a difference between methane
concentration and its solubility in water phase. The
concentration of the guest species definitely plays
an important role in providing the necessary
concentration gradient as noted by Nihous and
Masutani[8] based on their model. This can be
Table 3. Effect of gas saturation on hydrate dissolution
Number of gas molecules that
moved in to the water phase
averaged over last 4 ns
gas
saturation
Number of gas
molecules
initially
present in the
liquid phase
100% small
cage
occupancy
0% small cage
occupancy
CH4
CO2
CH4
CO2
CH4
100%
1
145
-2*
88
75%
4
149
4
50%
11
154
0%
10
162
Total number of gas molecules in
the water phase averaged over
last 4 ns of simulation
100% small
cage occupancy
0% small cage
occupancy
CO2
CH4
CO2
CH4
CO2
9
52
10
197
7
140
96
7
39
11
188
11
135
7
101
5
26
15
180
12
127
8
111
0
0
11
162
8
111
*
seen from the Table 3.
In the case of CO2 hydrate, a high amount
of dissolution was found to occur within the first
10 ns followed by a slow increase in the number of
CO2 molecules moving in to the water phase and a
steady decrease in the dissolution rate. As the level
of gas saturation decreased from 100% to 0%, the
number of CO2 molecules moving in to the liquid
phase increased, but the increase was not
proportional to the decrease in the level of undersaturation. At 100% cage occupancy, the number
of CO2 molecules in the water phase was found to
be more than 3 times the number of molecules
required to saturate the water phase as per the
value of its solubility that has been obtained.
Number of CH4 molecules in hydrate
phase
516
514
512
510
508
506
504
100%
75%
50%
0%
502
500
498
0
10000
20000
Time (ps)
30000
Figure 7. Number of methane molecules in the hydrate
phase during the simulation, the initial number of
molecules is marked by a black solid line.
Number of CO2 molecules
moving in to the liquid phase
negative sign indicates the opposite direction of the movement.
180
160
140
120
100
80
60
40
20
0
100%
75%
50%
0%
0
10000
20000
Time (ps)
30000
Figure 8. Number of CO2 molecules moving in to liquid
phase during the simulation at 100% cage occupancy
It has already been seen that CO2 hydrate is
stable at 0% cage occupancy. So, the effect of
water phase under-saturation has also been studied
at 0% small cage occupancy and the results are
tabulated as shown in Table 3. At 0% small cage
occupancy, the number of CO2 molecules moving
in to the liquid phase was found to display a
similar trend with the change in percentage gas
saturation in the water phase. But, the amount of
dissolution was found to be much lower at 0%
cage occupancy than at 100% occupancy in all
different cases of water phase under-saturation.
Even in the case of 0% small cage occupancy, the
total number of CO2 molecules in the water phase
at the end of each simulation was found to be
much higher than that required to saturate the
water phase. However, the reason for the increase
in solubility of CO2 in water in the presence of a
hydrate is not clearly understood. This exceptional
behavior of high CO2 hydrate dissolution might be
because of the weak intermolecular potentials
given by Harris and Yung for CO2 in hydrate.
Density (Kg/m3)
1100
bar the ab initio potential predicted as in liquid
phase, where as it should be in vapor phase.
1200
1000
Density (kg/m3)
Comparison of CO2 potentials
Using the Harris and Yung potentials,
reference chemical potentials were calculated with
the van der Waals and Platteeuw[32] model frame
work. The reference parameters obtained were
∆ = 178.4 3 J/mol and ∆ = 95.8 12
J/mol.[33] for CO2 hydrates, where as the
reference parameters obtained using our own ab
initio-derived CO2 potentials were ∆ =
1204 3 J/mol and ∆ = 1190 12 J/mol.
The reference parameters obtained using Harris
and Yung potentials are well outside the range
obtained by earlier researchers either numerically
or experimentally given in Table 1 of Anderson et
al.[23] for structure I hydrate. This shows the
inability of the Harris and Yung potentials to
accurately model carbon dioxide hydrates using
the van der Waals and Platteeuw[32] model frame
work. When used with the ab initio derived
potentials the reference potentials were well in the
range and were also able to accurately calculate
the phase equilibrium and cage occupancy of CO2
hydrate.
The average density was calculated after the
equilibrium was reached. The densities obtained
are given in Figure 9 and Figure 10 for ab initio
potential and Harris and Yung potentials
respectively. When compared to the experimental
800
50 bar H&Y
50 bar
100 bar-H&Y
100 bar200 bar H&Y
200 bar500 bar H&Y
600
400
200
0
255
265
275
285
Temperature(K)
295
305
Figure 10. Densities obtained using Harris and Yung
potential for pure CO2. Experimental-solid lines, Harris
and Yung[24]-points
Simulations were carried out to calculate the
solubility of the carbon dioxide at a temperature
and pressure. The simulation box contains 512
CO2 molecules and 6917 H2O molecules appended
to it. The simulation box was allowed to
equilibrate in NVT ensemble for 15 ps and then in
NPT ensemble for 12 ns. The solubilites were
obtained by averaging over the last 4ns using
density plots. The solubilities obtained using ab
initio CO2 potentials are compared to experimental
data[35] and shown in Table 4. The snapshot and
density plot of CO2-water system at 275K and 20
bar is given in Figure 11.
900
50 bar
50 bar100 bar
100 bar200 bar
200 bar500 bar
500 bar-
700
500
300
100
255
265
275
285
295
Temperature
(K)
Pressure
(bar)
20
Simulation.
(g CO2/kg
H2O)
51.24
Exp[35]
(g CO2/kg
H2O)
55.410
274
275
20
54.084
53.533
275
50
59.789
81.678
280
50
73.78
76.188
305
Figure 9. Densities obtained using ab initio potentials
for pure CO2 . Experimental-solid lines, ab initio-points.
Table 4. Solubilites obtained using ab initio-derived
CO2 potentials.
data obtained from equation of state[34], the
Harris and Yung potentials under predicted the
densities in liquid phase. For 275 K and 50 bar, the
Harris and Yung model predicted as vapor, 90
kg/m3, compare to the experimental value of 928
kg/m3 which is in liquid phase. The densities
obtained using ab initio potentials are in good
agreement to experimental values compare to
Harris and Yung potential. But, for 300K and 50
The Harris and Yung potentials predicts the
critical point and VLE for CO2 accurately[24], but
it fails when applied to CO2 hydrates. The ab
initio-derived potentials well predicted the cage
occupancies and reference properties of CO2
hydrate, but it fails to predict the vapor density. So
there is a need of intermolecular potential which
can work in all three phases.
laboratory’s on-going research in methane
hydrates under the RES contract DEFE0004000.
Number density of CO2
molecules across the box
40
35
30
25
20
15
10
5
0
0
1
2 3 4 5 6 7 8 9 10 11 12 13
z-parameter of the simulation box (nm)
Figure 11. Density plot of CO2 molecules along the
length of the box and snap shot of CO2-water system at
275 K and 20 bar.
CONCLUSIONS
Dissolution of CH4 and CO2 was studied at
275 K and 50 bar and it was observed that the CO2
hydrate dissolves at much higher rate in
comparison to CH4 hydrate. For CH4 hydrates the
amount of dissolution was found to be lower at
100% cage occupancy and increase with decrease
in cage occupancy, but for CO2 hydrate the
dissolution was higher at 100% occupancy and
decreases with decrease in cage occupancy. The
effect of gas under-saturation on hydrate
dissolution of CH4 and CO2 hydrates was studied
at 100% and 0% cage occupancies. The amount of
dissolution was found to be proportional to the
level of under-saturation in the water phase in the
case of CH4 hydrate. In the case of CO2 hydrate,
the amount of dissolution of CO2 molecules in to
the water phase was found to be higher than the
saturation value. The higher dissolution rates in
CO2 hydrate might be because of the repulsive
nature of the potentials in the hydrate phase.
Density and solubility calculations were performed
for CO2 using Harris and Yung potentials and ab
initio-derived intermolecular potentials. The ab
initio-derived potentials predicted the densities and
solubilities at higher pressures well compare to the
Harris and Yung intermolecular potentials.
ACKNOWLEDGEMENTS
This technical effort was performed in
support of the National Energy Technology
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