J. Phys. Chem. B 2006, 110, 17595-17599
17595
Highly Selective Encaging of Carbon Dioxide Molecules in the Mixed Carbon Dioxide and Nitrogen Hydrate at Low Temperatures Ji-Ho Yoon,*,† Taro Kawamura,‡ Michica Ohtake,‡ Satoshi Takeya,‡ Takeshi Komai,‡ Yoshitaka Yamamoto,*,‡ Hiroshi Emi,§ Mitsuhiro Kohara,§ Susumu Tanaka,| Osamu Takano,| and Kazuo Uchida⊥ Department of Energy & Resource Engineering, Korea Maritime UniVersity, Busan 606-791, Korea, National Institute for AdVanced Industrial Science and Technology, Ibaraki 305-8569, Japan, Osaka Gas Co. Ltd., Osaka 554-0046, Japan, Akishima Laboratories, Mitsui Zosen Inc., Akishima 196-0012, Japan, and NGH Project Department, Mitsui Engineering and Shipbuilding Co. Ltd., Tokyo 104-8439, Japan ReceiVed: March 24, 2006; In Final Form: July 11, 2006
The structural identification and guest compositions of the mixed CO2 and N2 hydrates at low temperature conditions were investigated by both theoretical predictions and experimental measurements. From the model calculations, at very low temperatures, the highly CO2-concentrated hydrates over 95 mol % CO2 on the basis of water-free concentration could coexist with the gas mixtures of low CO2 concentrations in equilibrium. X-ray diffraction measurements of the hydrates formed with the gas mixture of 3.16 mol % CO2 and balanced N2 indicate that the formed hydrates at all conditions considered in this study were identified as structure I, whereas the model predicts a structural transition to structure II around 220 K. However, it was also found that the formed hydrate samples contain a considerable amount of hexagonal ice resulting from incomplete conversion of ice to the hydrates. The compositional analysis suggests that a favorable encaging of CO2 in the mixed hydrate can be obtained by the hydrate formation at low temperatures and relative amount of CO2 molecules in the mixed hydrates increases with a decrease of temperature.
Introduction Clathrate hydrates are nonstoichiometric crystalline compounds formed by host-guest interactions between water and relatively small guest molecules occupied in the cavities of the crystal framework. Depending on the difference in the cavity shape and size of hydrates, they have been classified into three distinct structures I (sI), II (sII), and H (sH). The unit crystalline of cubic sI consists of two small 12-hedra (512) and six large 14-hedra (51262) cages, whereas cubic sII clathrate hydrate has 16 12-hedra (512) and eight 16-hedra (51264) cages.1 It is also well-known that hexagonal sH clathrate hydrate is composed of three types of cage, 12-hedra (512), 12-hedra (435663), and 20-hedra (51268) and require large guest molecules such as adamantane and methylcyclohexane with smaller help gas for cage stability.2,3 Recently, high-pressure experiments using a diamond anvil cell represented that a new structure of methane hydrate as a filled ice Ih could stably exit at pressures higher than 2 GPa and Ih methane hydrate layers in the ice mantle of Titan might be a plausible source of atmospheric methane.4,5 It has also been reported that a new clathrate hydrate structure shows bimodal guest hydration based on the stacking of structure cage layers, indicating that a wide variety of naturally occurring guest molecules, such as CH4, H2S, and CO2, can be incorporated in the new structure to form more stable hydrate layers.6 The identification of crystal structure of the clathrate hydrate * To whom correspondence should be addressed. E-mail:
[email protected] (J.-H.Y.) or
[email protected] (Y.Y.). † Korea Maritime University. ‡ National Institute for Advanced Industrial Science and Technology. § Osaka Gas Co. Ltd. | Mitsui Zosen Inc. ⊥ Mitsui Engineering and Shipbuilding Co. Ltd.
and guest distribution in hydrate cages plays a crucial role in studying thermodynamic phase behavior of the mixed hydrates and solid-state reactions. When the mixed clathrate hydrate forms with binary guests, two guest molecules compete with each other for better occupation and stabilization in hydrate cages. In the case of the mixed CO2-N2 hydrate, the crystal structure changes from sI to sII with increasing N2 content in the mixed clathrate hydrates, as N2 molecules stabilize small cages of sII hydrates and also occupy all of the large cages, while CO2 forms sI hydrates. Another aspect to be noted is that the structural transition of CO2-N2 binary hydrate occurs only in the region of very low CO2 content at normal temperature conditions.7 This indicates that even at low concentrations of CO2 in the gas phase the hydrate cages would be stabilized by relatively large amount of CO2 molecules, resulting in the formation of sI hydrate structure having a high concentration of CO2 in the hydrate phase. In the present study, we investigate a favorable encaging behavior of CO2 molecules in the mixed CO2-N2 hydrate at low-temperature conditions. To gain insight into the effect of temperature on the structural transition and cage occupation of the mixed hydrate, we provide theoretical calculations over a wide rage of temperature and concentration conditions. The powdered X-ray diffraction (XRD) was used to identify the structure of the mixed hydrates formed at several temperatures. The spectroscopic methods such as solid-state nuclear magnetic resonance (NMR) spectroscopy and Raman spectroscopy have also been used to identify the guest distribution in hydrate cages as well as formation of mixed hydrates. However, the XRD measurements provide the most promising results to determine crystalline structure of the mixed hydrates and its structural transition point.8 The selective encaging capacity of guest
10.1021/jp0618328 CCC: $33.50 © 2006 American Chemical Society Published on Web 08/12/2006
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molecules in the hydrate phase was investigated by compositional analysis of gas released on decomposition of the hydrates. Theoretical Background The chemical potential of water in the hydrate phase µHw is generally derived from statistical mechanics in the van der Waals and Platteeuw model,9
µHw ) µMT w + RT
νm ln(1 - ∑ θmj) ∑ m j
(1)
where the fractional occupancy θmj is determined by a Langmuirtype expression as follows
Cmj ˆf Vj
θmj )
1+
∑k
(2) Cmk ˆf Vk
where Cmj is the Langmuir constant of component j on the cavity of type m, and ˆfVj is the fugacity of component j in the vapor phase with which the hydrate phase is in equilibrium. The Langmuir constant represents the interactions between guest (gas molecules) and host (water molecules) in the hydrate cavities. Using the Lennard-Jones-Devonshire cell theory, the Langmuir constant has been expressed as a function of temperature
Cmj )
4π kT
∫0∞ exp
[ ]
-ω(r) 2 r dr kT
(3)
where ω(r) is the spherical-core potential. In the present study, the Kihara potential with spherical-core is used for the cavity potential function and given by
Γ(x) ) ∞,
x e 2a
σ 12 σ 6 Γ(x) ) 4 , x - 2a x - 2a
[(
)]
) (
x > 2a
(4)
When summing over all guest-water interactions in the cavity, the spherical-core potential is simply expressed as follows10
ω(r) ) 2z
[
)]
σ6 4 a 5 σ12 10 a 11 δ + δ + δ δ R R R11r R5r
(
)
(
(5)
where
δN )
1 r a -N r a -N 1- - 1+ N R R R R
[(
)
) ]
(
(6)
In previous work,11,12 we presented a new expression for the fugacity of ice related to that of pure liquid water.
(
fIw ) fLw exp -
∫TT 0
∆hfus w RT2
dT +
∫0P
)
∆υfus w dP RT
(7)
We note that this equation only uses the physical property difference between the ice and supercooled liquid water. Using this equation, we provide a final expression for the fugacity of water in the filled hydrate phase as follows
ˆf Hw
)
fLw
∫0
P
[
∆µw0
exp
RT
-
∫T
T
RT2
0
∆υMT-I + ∆υfus w w RT
∆hMT-I + ∆hfus w w
dP -
dT +
νm ln(1 + ∑Cmj ˆf Vj ) ∑ m j
]
(8)
Figure 1. “Micro-ice” used for formation of the mixed hydrates.
The Soave-Redlich-Kwong equation of state13 incorporated with the modified Huron-Vidal second-order (MHV2) mixing rule14,15 is used to calculate the fugacity of all components in the vapor and liquid phases coexisting with hydrates. The modified UNIFAC group contribution model is also used as the excess Gibbs energy for the MHV2 model. A more detailed description for this model is given in our previous work.10 Experimental Section A high-pressure cell was used to synthesize the clathrate hydrates at low-temperature conditions. The maximum operating pressure of the cell is up to 15 MPa. The temperature and pressure in the cell were controlled within an accuracy of (0.1 °C and (0.02 MPa, respectively. To check the capability of selective encaging of CO2 molecules at low concentrations of CO2 in the gas phase, the gas mixture consisting of 3.16 mol % CO2 and balanced N2 was used to form the mixed hydrates. For the hydrate formation, finely pulverized “micro-ice” (∼10 µm) as shown in Figure 1 was exposed to the gas mixture in the high-pressure vessel at a given temperature and pressure for 2 days. To minimize the change of gas composition in the vapor phase during the hydrate formation, the gas phase was continuously refreshed with the gas mixture using a pressure control unit and a metering valve. For the XRD measurements, the hydrate samples were put in a quartz glass capillary cell and then mounted on the goniometer of the XRD apparatus. The crystalline structure of the mixed hydrate was determined by a diffractometer with Cu KR radiation (50 kV, 200 mA, Rigaku model Rint-2000) at 113 K and atmospheric pressure. The capillary cell was rotated 360° about the θ axis during each measurement to include all crystals in the capillary. For composition analysis of gas released from the hydrates, a gas chromatograph (Japan Aera M200) was used. Results and Discussion As shown in Table 1, the lattice and thermodynamic properties of empty hydrate lattice are used in the model calculation because the proposed values give a very good agreement between experimental and calculated hydrate dissociation pressures.16 In the present model, we did not take into account the compressibility of gas hydrate, and therefore the effect of pressure on the hydrate lattice was assumed to be negligible. Figure 2 shows the Langmuir constants of CO2 and N2 in small and large cages of the sI hydrates calculated by our proposed model. As expected, the Langmuir constants of both CO2 and N2 in hydrate cages increase with a decrease of temperature. We note that, for both small and large cages, the increase of the Langmuir constants of CO2 becomes larger than that of N2 at low temperature conditions. This indicates that the hydrate cages at low temperatures could be occupied dominantly by CO2 molecules, which is likely to prefer to
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J. Phys. Chem. B, Vol. 110, No. 35, 2006 17597
TABLE 1: Lattice and Thermodynamic Properties of Gas Hydrates Used in This Study ideal structurea number of water molecules/unit cell number of small cavities/unit cell number of large cavities/unit cell average radius of small cavities, Å average radius of large cavities, Å coordination number of small cavities coordination number of large cavities ∆µw0, J/mol ∆hMT-I , J/mol w ∆υMT-I , cm3/mol w fus ∆hw , J/mol 3 ∆υfus w , cm /mol a
structure I
structure II
3M1‚M2‚23H2O 46
M1‚2M2‚17H2O 136
2
16
6
8
3.95
3.91
4.33
4.73
20
20
24
28
1264 1151 3.0 -6011 1.6
883 808 3.4
M1 and M2 are large and small cavities, respectively.
Figure 2. Langmuir constants of CO2 and N2 molecules in hydrate cages.
stabilize the sI hydrates even when the amount of CO2 in the vapor phase is very small. Figure 3 represents the isothermal phase behavior of the mixed CO2-N2 hydrate at temperatures of 263.2, 203.2, and 123.2 K on the basis of water-free concentration. One can see that an abrupt change of phase behavior in this system could be expected at low-temperature regions. The composition of the mixed hydrates absolutely depends on not only the equilibrium temperatures, but also the hydrate structure formed at a given condition. At low temperatures, the gas phase containing only a small amount of CO2 coexists with the sI hydrates in equilibrium, indicating that the hydrate cages could be occupied by relatively large amount of CO2. In a point of view of practical application, especially focused on the separation process, the hydration with gas mixture containing 3 mol % CO2 and balanced N2 at 263 K provides the concentrated product (the mixed hydrate) of about 10 mol % CO2. When the temperature is decreased to 203.2 K, the amount of CO2 occupying the hydrate cages is drastically increased to 65 mol % CO2. Surprisingly, at a temperature of 123.2 K, the highly CO2-concentrated hydrate (∼97 mol %) can be obtained by a simple hydrate formation, as shown in Figure 3. It is clear that this drastic change is caused by the
Figure 3. Calculated isothermal phase behavior of the mixed CO2 and N2 hydrates on the basis of water-free concentration at (a) 263.2, (b) 203.2, and (c) 123.2 K. HI and HII stand for the sI and sII hydrates, respectively. The solid lines are the concentration of CO2 in the hydrate phase (sI or sII), whereas the dashed lines are the concentration of CO2 in the vapor phase at three-phase hydrate-ice-vapor (H-I-V) equilibrium conditions.
effect of CO2 on the stability of sI hydrates at low temperatures, which results in favorable encaging of CO2 in most of the large cages and even part of the small cages of sI hydrate. Recently, it has been reported that an efficient recovery of more than 96
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Figure 5. Calculated and experimental CO2 mole fraction in the mixed hydrates formed with the gas mixture of 3.16 mol % CO2 and balanced N2. The experimental7 and calculated results at 272.1 K are presented for the mixed hydrate formed with the gas mixture of 3.3 mol % CO2 and balanced N2. Two-phase H-V equilibria (open circles) are also calculated at each corresponding experimental condition.
Figure 4. X-ray diffraction pattern of the mixed CO2 and N2 hydrate.
mol % CO2 from the gas mixture (10 mol % CO2 and balanced N2) can be achieved by a three-stage hydration process at a moderate temperature 272.1 K.17 We note that, from our model calculation, the gas mixture of 10 mol % CO2 and balanced N2 could be equilibrated with the hydrate phase dominantly occupied by 96 mol % CO2 at 155 K. To clarify the theoretical concept, several experiments for hydrate formation were carried out at low temperatures. We used the gas mixture of 3.16 mol % CO2 and balanced N2 and the formation conditions are 253.2, 243.2, 233.2, 213.2, and 143.2 K at pressures of 9.6, 7.0, 5.0, 2.4, and 0.1 MPa, respectively. At each temperature and corresponding CO2 composition in the vapor phase, three-phase hydrate-ice-vapor (H-I-V) equilibrium pressures are estimated to be 8.1, 6.0, 4.2, 1.8, and 0.006 MPa, respectively, which allows us to confirm that the formed hydrates are stable under the conditions of two-phase hydrate-vapor (H-V) equilibrium. The XRD analysis (Figure 4) indicates that the mixed hydrates definitely form the sI structure at higher temperatures than 203.2 K. Note that there are no characteristic XRD peaks reflecting the formation of hydrates at 143.2 K. Another aspect to be noted is that all formed hydrate samples mainly contain a considerable amount of hexagonal ice, resulting from incomplete conversion of ice to the hydrates. This implies that the formation rate of the mixed hydrates at low temperatures is very slow, and thus the hydrates are formed in part, specifically only on the surface layer of ice, even though finely powdered ice particles having an average size of 10 µm were used in this study. It is likely that incomplete conversion is attributed to significant shielding effects of the surface layer formed at low temperatures. For the formation of the mixed hydrates at lower temperatures than 150 K, it may be necessary to increase the system pressure over 0.1 MPa to enhance the nucleation of the hydrate structure, even though the H-I-V equilibrium pressures are far below 0.01 MPa. In addition, it is clear that binary CO2-N2 gas mixtures can form sII hydrate, which may occur in the region of very low CO2 content. As shown in the model calculation (Figure
3), the concentration range of CO2-N2 gas mixtures forming sII hydrates becomes narrower with a decreasing of temperature. These problems did not allow us to observe sII formation of the binary CO2-N2 hydrates at low temperatures. The compositional analysis (Figure 5) of released gas from the hydrate samples represents that the hydrate cages would favorably be governed by a considerable amount of CO2 molecules at low temperatures, and cage occupancy increases with decreasing temperature, which is in agreement with the model calculation. As mentioned previously, all mixed hydrate samples considered in this study are stable under two-phase H-V equilibrium conditions, as each experimental pressure at a constant temperature is far above the incipient hydrate formation pressure (H-I-V equilibrium pressure). Thus, it is clear that the ice should completely be converted to hydrates under the H-V equilibria when the growth rate could be accelerated by exposing the ice to the gas mixture for sufficient time. However, as shown in Figure 5, the calculated H-V equilibria at each corresponding experimental condition are nearly identical to three-phase H-I-V equilibria. This indicates that the effect of pressure on cage occupancy of guest molecules in the hydrate phase is negligible, whereas the encaging capacity significantly depends on the formation temperature. It is interesting to be noted that the model predicts a structural transition point around 220 K, and thus the sI hydrate is stable only at lower temperatures than 220 K. In contrast, as described above, the XRD pattern indicates that only sI hydrates are stable at all experimental conditions of H-V equilibrium. Also noted is that there are some differences in the composition of the hydrate phase between experimental results and model calculations as shown in Figure 5. At 213.2 K and 2.4 MPa, the model predicts 55 mol % CO2 in the hydrate phase, whereas the evolving gas from the hydrate sample has the composition of 38 mol % CO2 at the pseudo-equilibrium state. These differences may be caused by inadequate model parameters for N2 because the Kihara potential parameters of N2 were fitted using the experimental dissociation data only at high temperatures ranging from 268 to 305 K.11 However, both experimental and theoretical results allow us to confirm that, even at low CO2 concentrations in the vapor phase, highly selective encaging of CO2 molecules in the hydrate phase could be achieved at the region of low temperatures. These findings provide new means for
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Acknowledgment. We thank S. Higuchi, Y. Tsukada, T. Hirayama, and K. Morishita (AIST, Tsukuba) for their technical assistance in the experimental work.
x ) central distance between two molecules z ) coordination number of the cavity ) Kihara energy parameter Γ(x) ) Kihara potential function ) difference in chemical potential of water be∆µMT-H w tween empty and filled hydrate lattice ∆µw0 ) difference in chemical potential of water between empty hydrate lattice and water at T0 and zero absolute pressure νm ) the number of cavities of type m per water molecule in the hydrate lattice σ ) Kihara size parameter θmj ) fraction of cavities of type m occupied by component j ω(r) ) spherical-core potential function Superscripts and Subscripts 0 ) reference state fus ) fusion H ) hydrate j, k ) component I ) ice L ) liquid water m ) cavity type m MT ) empty V ) vapor w ) water
Nomenclature
References and Notes
a ) Kihara hard-core parameter Cmj ) Langmuir constant of component j on the cavity of type m fIw ) fugacity of ice fLw ) fugacity of pure water in liquid phase ˆfHw ) fugacity of water in hydrate phase ˆfVi ) fugacity of component i in vapor phase ∆hfus w ) molar enthalpy difference between water and ice ) enthalpy difference between empty hydrate lat∆hMT-I w tice and ice k ) Boltzmann’s constant P ) pressure R ) gas constant R ) average radius of the cavity r ) radius of distance from the cavity center T ) temperature T0 ) reference temperature, 273.15 K ∆υfus w ) molar volume difference between water and ice ∆υMT-I ) volume difference between empty hydrate lattice w and ice
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studying technological applications of gas hydrates such as natural gas transportation and separation/recovery processes at low temperatures. A further analysis of the effect of the sample morphology such as the annealing condition and granular size of ice particles on the formation rate will be required for a complete understanding of the kinetic problems of hydrate formation at low temperatures. Conclusions In the present study, we provide both theoretical calculations and experimental results for selective encaging of CO2 molecules in the hydrate cages formed at low-temperature conditions. From the model calculation with the gas mixtures of low CO2 concentrations, highly selective encaging of CO2 molecules in the hydrate phase could be obtained by a simple hydrate formation at low-temperature conditions. At the pseudo-equilibrium conditions, the experimental results indicate that the mixed hydrates formed at all temperatures reveal the sI hydrate structure and have the CO2-concentrated compositions. However, more treatments of ice particles such as a variation of the particle size (∼submicron) to enhance the formation rate should be considered for technological applications, as the formation reaction at low temperatures is very slow.
