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Langmuir 2007, 23, 3440-3444
Phase Relations and Binary Clathrate Hydrate Formation in the System H2-THF-H2O Ross Anderson, Antonin Chapoy, and Bahman Tohidi* Centre for Gas Hydrate Research, Institute of Petroleum Engineering, Heriot-Watt UniVersity, Edinburgh, EH14 4AS, U.K. ReceiVed NoVember 1, 2006. In Final Form: December 21, 2006 Experimentally determined equilibrium phase relations are reported for the system H2-THF-H2O as a function of aqueous tetrahydrofuran (THF) concentration from 260 to 290 K at pressures up to 45 MPa. Data are consistent with the formation of cubic structure-II (CS-II) binary H2-THF clathrate hydrates with a stoichiometric THF-to-water ratio of 1:17, which can incorporate modest volumes of molecular hydrogen at elevated pressures. Direct compositional analyses of the clathrate phase, at both low (0.20 mol %) and stoichiometric (5.56 mol %) initial THF aqueous concentrations, are consistent with observed phase behavior, suggesting full occupancy of large hexakaidecahedral (51264) clathrate cavities by THF, coupled with largely complete (80-90%) filling of small dodecahedral (512) cages by single H2 molecules at pressures of >30 MPa, giving a clathrate formula of (H2)e2‚THF‚17H2O. Results should help to resolve the current controversy over binary H2-THF hydrate hydrogen contents; data confirm recent reports that suggest a maximum of ∼1 mass % H2, this contradicting values of up to 4 mass % previously claimed for comparable conditions.
Introduction Clathrate hydrates, or gas hydrates, are a group of ice-like, crystalline inclusion compounds that form through the combination of water and suitably sized “guest” molecules, typically under low temperature and elevated pressure conditions. Within the clathrate lattice, water molecules form a network of hydrogenbonded polyhedral cavity structures that enclose the guests, with the latter generally comprising single or mixed low-molecular diameter gases and/or organic liquids (e.g., methane, CO2, cyclopentane).1 Traditionally, it was believed that hydrogen could not form clathrate hydrates (structures I, II, and H), even in gas mixtures, as its molecular diameter was too small to stabilize cavities.1,2 However, in 1994, Udachin et al.3 reported that H2 could form binary clathrate hydrates with tetrahydrofuran (THF) at high pressures (∼350 MPa). THF is known to from simple (single guest), stoichiometric, cubic structure-II (CS-II) clathrates hydrates of formula THF‚17H2O (equivalent to complete large hexakaidecahedral (51264) cage occupancy), which are stable at atmospheric pressures below ∼278 K.4 The authors purported that single H2 molecules could enter the normally vacant small dodecahedral (512) cavities of these hydrates (up to 90% filling), stabilizing hydrogen in binary structure-II H2-THF clathrates. Subsequently, in 2002, Mao et al.5 found that hydrogen can form simple (single guest) CS-II clathrate hydrates at very high pressures (200 MPa at 280 K) or cryogenic temperatures (145 K). The authors estimated a maximum hydrogen storage capacity * To whom correspondence should be addressed. Phone: +44 131 451 3672. Fax: +44 131 451 3127. E-mail:
[email protected]. (1) Sloan, E. D. Clathrate Hydrates of Natural Gases, 2nd ed.; Marcel Dekker: New York, 1998. (2) Zhang, S.-X.; Chen, G.-J.; Ma, C.-F.; Yang, L.-Y.; Guo, T.-M. J. Chem. Eng. Data 2000, 45, 908-911. (3) Udachin, K.; Lipkowski, J.; Tzacz, M. Supramol. Chem. 1994, 3, 181. (4) Dyadin, Y. A.; Kuznetsov, P. N.; Yakovlev, I. I.; Pyrinova, A. V. Dokl. Akad. Nauk SSSR 1973, 208, 103-106. (5) Mao, W. L.; Mao, H.; Goncharov, A. F.; Struzhkin, V. V.; Guo, Q.; Hu, J.; Shu, J.; Hemley, R. J. Science 2002, 297, 2247-2249. (6) Lokshin, K. A.; Zhao, Y.; He, D.; Mao, W. L.; Mao, H. K.; Hemley, R. J.; Lobanov, M. V.; Greenblatt, M. Phys. ReV. Lett. 2004, 93, 125503.
of ∼5 mass % based on double H2 occupancy of all 16 small dodecahedral cavities, and quadruple occupancy of large hexakaidecahedral cavities. The findings of Mao et al.5 have sparked considerable interest in clathrate hydrates as potential hydrogen storage materials.6-11 Certainly, the molecular storage of H2 in clathrates could potentially offer advantages in terms of ease of formation/regeneration, cost, and safety when compared with other media currently under investigation.7,8,12 However, the excessively high pressures (>200 MPa) required for pure H2 hydrate stability renders these compounds impractical for everyday use as hydrogen storage materials. In 2004, Florusse et al.7 demonstrated that the stability region of binary H2-THF clathrate hydrates extended to relatively low pressures at temperatures close to ambient (∼15 MPa at 10 °C). Powder X-ray diffraction confirmed clathrates to be of CS-II, with Raman and magic-angle spinning (MAS) NMR analyses agreeing with the findings of Udachin et al.,3 in that large hexakaidecahedral cavities are fully occupied by THF, with up to one H2 molecule per small dodecahedral cage. While the relatively low-pressure stability of this binary clathrate hydrate is promising with respect to hydrogen storage, THF occupies large cavities that might otherwise accommodate hydrogen, meaning stability is increased at the sacrifice of H2 content; one hydrogen molecule per small cage equals only 1 mass % H2. Recently, Lee et al.8 claimed to have circumvented this problem. These authors purported that the hydrogen content of binary H2-THF clathrates could be greatly increased (up to ∼4 mass % H2) at modest pressures (12 MPa) by “tuning” THF contents. Supported by Raman, MAS NMR, and volumetric measurements, (7) Florusse, L. J.; Peters, C. J.; Schoonman, J.; Hester, K. C.; Koh, C.; Dec, S. F.; Marsh, K. N.; Sloan, E. D. Science 2004, 306, 469-471. (8) Lee, H.; Lee, J.; Kim, D. Y.; Park, J.; Seo, Y.-T.; Zeng, H.; Moudrakovski, I. L.; Ratcliffe, C. I.; Ripmeester, J. A. Nature 2005, 434, 743-746. (9) Strobel, T. A.; Taylor, C. J.; Hester, K. C.; Dec, S. F.; Koh, C. A.; Miller, K. T.; Sloan, E. D., J. Phys. Chem. B 2006, 110, 17121-17125. (10) Rovetto, L. J.; Schoonman, J.; Peters, C. J. Proceedings of the 5th International Conference on Gas Hydrates (ICGH5), Trondheim, Norway, June 12-16, 2005; Tapir Academic Press: Trondheim, Norway, 2005; p 5031. (11) Hester, K. C.; Strobel, T. A.; Sloan, E. D.; Koh, C. A.; Huq, A.; Schultz, A. J. J. Phys. Chem. B 2006, 110, 14024-14027. (12) Berry, G. D.; Aceves, S. M. Energy Fuels 1998, 32, 49-55.
10.1021/la063189m CCC: $37.00 © 2007 American Chemical Society Published on Web 02/08/2007
Equilibrium Phase Relations for H2-THF-H2O
these authors argued that clathrate small cavities could accommodate two H2 molecules, and, at initial aqueous THF concentrations below the atmospheric eutectic composition (∼1.0 mol %), in the hydrate + ice + gas (H+I+G) region, clusters of four hydrogen molecules could replace THF in large cavities, thereby greatly increasing H2 content. While the results of Lee et al.8 offer significant promise for developing clathrate hydrates as hydrogen storage media, they have yet to be independently duplicated. Indeed, the most recent detailed study of H2-THF clathrate hydrogen contents directly contradicts the findings of these authors: Strobel et al.,9 similarly utilizing volumetric measurements in conjunction with Raman and MAS NMR data, concluded that small cavities can only accommodate single H2 molecules, and that, irrespective of initial aqueous THF concentration and/or formation conditions, large cavities are always fully occupied by THF. A maximum hydrogen content of around 1 mass % was reportedsa value considerably lower than that claimed by Lee et al.8 The result of such contradictory findings is that the true phase behavior of binary H2-THF hydrates remains the subject of some controversy. Part of the problem is that the phase diagram for the system H2-THF-H2O system is still poorly understood. To date, much effort has been placed on attempts to determine clathrate cage occupancies through advanced techniques such as Raman and NMR,5,7,8 with less emphasis being placed on traditional pressure-volume-temperature (PVT) studies. While the former offer great potential for investigating guest configurations, they can sometimes require considerable assumption in the interpretation of results, with spectral peaks on occasion being “assigned” based on theory instead of through calibration against samples of known composition. Furthermore, there is potential for error when relying solely on the integration of spectral intensities to determine hydrate compositions, and this may be the cause of conflicting results for THF-H2 clathrates.9 In contrast, traditional PVT methods, tried and tested over decades, offer a reliable, robust means to determine phase relations and clathrate composition with little assumption involved, thus providing an important tool for investigating hydrate systems. Some limited equilibrium data (at two single temperatures) have been reported by Rovetto et al.10 for different initial THF concentrations in the hydrate + liquid + gas (H+L+G) region. However, phase relations as a function of the aqueous molar fraction of THF for a wide range of PT conditions, particularly for lower aqueous THF concentrations below the binary THFH2O eutectic composition (where H2 enrichment apparently takes place),8 are still poorly understood. Such information is vital to understanding H2 enclathration phenomena, for validation of predictive models and for assessing the potential of clathrate hydrates for hydrogen storage. Here, we present the results of an experimental investigation into the phase behavior of the system H2-THF-H2O from 270 to 290 K at pressures up to 45 MPa. Using newly measured equilibrium and clathrate compositional data, we discuss the characteristics of H2-THF hydrate formation with particular focus on H2 uptake and clathrate stoichiometry.
Langmuir, Vol. 23, No. 6, 2007 3441
Figure 1. Example step-heating curve for a 0.2 mol % THF aqueous solution under H2 pressure. Points are equilibrium points (8-24 h equilibrium time at each step). Upon heating, pressure reduces as ice melts along the H+L+I+G quaternary eutectic line. Once ice melting is complete, pressure rises as gas is released during clathrate dissociation in the H+L+G region. Following the point of complete hydrate dissociation, conditions enter the L+G region. The dashed line is an extension of the L+G isochore serving to highlight the pressure drop associated with hydrate formation.
For reference, phase relations for the binary system THF-H2O were determined between 260 and 280 K for aqueous THF concentrations up to 5.9 mol % by a differential thermal analysis (DTA) technique based on that detailed by Anderson et al.13 The method relies upon the detection of the temperature difference
between a sample temperature (Ts) and reference (coolant/ environmental) probe temperature (Tr) while heating at a constant rate. During endothermic reaction (e.g., eutectic, clathrate melting), the sample temperature will lag behind the reference, holding at the transition temperature, before returning rapidly to follow the trend of the reference probe when the reaction is complete. Plotting this temperature deviation (Tr-Ts) versus sample temperature yields endothermic peaks corresponding to transition temperatures. The accuracy of the method, based on assessment using organic and inorganic liquids of known melting points (distilled water, decane, methanol aqueous solutions), is estimated to be (0.2 K. For the ternary system H2-THF-H2O, clathrate dissociation and ice melting PT conditions for various initial aqueous THF concentrations (0.20, 0.50, 1.00, 2.70, and 5.56 mol %) were determined by constant volume cell isochoric equilibrium step-heating techniques. This method, which is based upon the direct detection (from pressure) of bulk density changes occurring during phase transitions, produces very reliable, repeatable phase equilibrium measurements.14 Experiments were carried out in two setups with different configurations. In the first instance, a standard, large volume (650 cm3), cylindrical rocking equilibrium cell was used, with mercury being injected to control pressure (without changing bulk composition) and to aid mixing. To replicate the method of Lee et al.,8 a smaller volume (75 cm3), static cell was also used, with the liquid being dispersed on 0.1 mm inert silica beads. Both cells have been described in detail previously.13,14 In both cases, clathrates and/or ice were first formed by rapidly cooling THF solutions under hydrogen pressure. Systems were then left to equilibrate at a fixed temperature, before heating curves for the region of interest were measured in equilibrium steps, as illustrated in Figure 2. Heating curves were assessed for repeatability by heating/cooling along the curve a number of times. Both setups used yielded identical results, confirming that the different environment/means of hydrate formation had no effect on equilibrium conditions, as would be expected. Clathrate compositional analyses were carried out as follows. In the case of the stoichiometric 5.56 mol % THF solution (i.e., for complete filling of structure-II (s-II) large cavities), following complete conversion of the liquid phase to clathrates at 283 K and 30.3 MPa, the vapor phase was first removed at isobaric/isothermal conditions by controlled mercury injection. The system was then slowly depressurized to 1 atm at isothermal conditions until complete hydrate dissociation had occurred. The volume (and thus moles) of
(13) Anderson, R.; Llamedo, M.; Tohidi, B.; Burgass, R. W. J. Phys. Chem. B 2003, 107, 3507-3514.
(14) Tohidi, B.; Burgass, R. W.; Danesh, A.; Todd, A. C.; Østergaard, K. K. Ann. N.Y. Acad. Sci. 2000, 912, 924-931.
Experimental Equipment and Methods
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Anderson et al. Table 1. Experimental Ice Melting (Tmi), Clathrate Hydrate Dissociation (Tdc), and Eutectic (Te) Temperatures for the Binary System THF-H2O at Atmospheric Pressure (0.1 MPa)
Figure 2. Experimental incipient clathrate hydrate dissociation (H+L+G > L+G), ice melting (I+L+G > L+G), and eutectic (H+L+I+G) data for the system H2-THF-H2O for various initial aqueous THF concentrations. All data are from this work, with the exception of the points for 5.6 mol % from Lee et al.,8 as indicated. Filled squares show the sampling conditions for clathrate compositional analyses with appropriate initial THF aqueous concentrations for the sampled systems indicated.
mol % THF(aq)
Te/K
Tmi/K
0.00 0.10 0.20 0.20 0.50 0.70 0.80 0.96 1.00 1.50 2.70 3.50 4.31 5.56 5.90
272.1 272.1
273.2 273.1 273.2 273.1 272.8 272.6 272.5 272.3
272.1 272.2 272.1 272.1 272.1 272.2 272.2
H+L+G > L+G I+L+G > L+G/H+L+I+G (E)
0.20 0.50
1.00 2.70
H2 released during dissociation was determined using a precision gas volume meter. To determine H2 contents of clathrates formed from THF concentrations below the eutectic composition (∼1.0 mol % at 1 atm) in equilibrium with ice and gas (H+I+G conditions), the region purported by Lee et al.8 to be the site of H2 enrichment in H2-THF clathrates, hydrates were initially formed from a 0.2 mol % THF solution and stabilized in equilibrium with ice at 270 K and 30 MPa pressure (Figure 3). The vapor phase was then removed at isobaric/ isothermal conditions by controlled mercury injection before pressure was reduced to 1 atm at isothermal conditions. As conditions remained with the hydrate stability region for simple THF hydrates (binary THF-H2O system), to ensure complete clathrate dissociation following pressure reduction, the system was subsequently heated past the atmospheric THF-H2O eutectic temperature (272.1 K). Moles of gas released from hydrates during dissociation was again determined volumetrically using a precision gas volume meter.
272.4 274.1 276.8 277.6 278.0 278.2 278.1
Table 2. Experimental Ice Melting (I+L+G > L+G), Clathrate Hydrate Dissociation (H+L+G > L+G), and Eutectic (H+L+I+G) Temperatures (E) for the Ternary System H2-THF-H2O at Pressures up to 45 MPa T/K P/MPa mol % THF(aq) ((0.2) ((0.07)
Figure 3. Isobaric sections for binary THF-H2O and ternary H2THF-H2O systems as a function of aqueous THF concentration. Filled circles are experimental DTA data for the binary THF-H2O system at 1 atm. Ternary sections (open symbols) are derived from interpolated experimental data as presented in Figure 2 and Table 1. Phase relations show that, in the presence of hydrogen, irrespective of aqueous THF concentration, clathrates retain a THF-to-H2O stoichiometry of 1:17 (as indicated by consistent thermal stability maxima), although H2 is accommodated by, and lends stability to, the hydrate structure at elevated pressure.
Tdc/K
5.56
5.90
275.7 274.5 273.2 273.5 275.4 278.4 282.0 275.1 278.1 281.3 278.2 278.7 280.2 282.6 284.6 286.1 281.2 282.8 286.0 288.2 279.6 281.3 282.5 284.1 285.0
42.85 37.51 31.68 12.76 18.69 29.47 45.00 7.59 16.14 28.48 39.50 5.26 10.18 18.52 26.23 33.39 8.69 14.46 28.15 38.58 5.10 10.58 14.72 20.74 24.55
T/K ((0.2)
P/MPa ((0.07)
272.0 271.0 (E) 269.8 (E) 272.4 271.5 (E)
14.57 26.96 (E) 41.23 (E) 6.12 18.96 (E)
Results and Discussion Equilibrium data determined for binary THF-H2O and ternary H2+THF+H2O systems are reported in Tables 1 and 2 and presented in Figures 2 and 3. THF is known to form stoichiometric CS-II clathrates of composition THF‚17H2O (or 5.56 mol % THF aqueous) with a maximum thermal stability of ∼278.4 K at 1 atm.4 DTA data presented in Figure 3 are consistent with this. For initial THF concentrations greater than 5.56 mol %, clathrates grow in equilibrium with an increasingly THF-rich liquid, tending toward a eutectic below 173 K. For THF concentrations lower than the stoichiometric value, clathrates exist in equilibrium with an increasingly water-rich liquid (H+L region) until a eutectic (H+L+I) is reached at around 1.0 mol % THF (measured as ∼0.95 mol % in this work) and 272.1 K. For THF concentrations lower than this eutectic, ice is initially the more stable phase (I+L region), while, below the eutectic transition, for all THF concentrations less than 5.56 mol %, ice
Equilibrium Phase Relations for H2-THF-H2O
is in equilibrium with stoichiometric THF clathrates (H+I region). As the density of THF clathrate is slightly less than that of its parent liquid, hydrate dissociation conditions in the binary THFH2O system are reduced to lower temperatures under increasing pressure in a similar pattern to that seen for hexagonal ice.4 As shown in Figure 2, when hydrogen is introduced to the THF-H2O system, in contrast to binary phase relations, H+L+G phase boundaries show a strongly positive slope. Florusse et al.7 previously reported this behavior for a single THF concentration (unfortunately the actual concentration was not specified, but data suggest it was close to the stoichiometric composition) and attributed it to H2 incorporation into, and stabilization of, the THF clathrate structure. As detailed, the authors concluded that, as for simple THF clathrates, these binary H2-THF clathrates were of CS-II, with a stoichiometric THF-to-water ratio of 1:17, and a maximum of one H2 molecule per small cavity, giving the formula 2H2‚THF‚17H2O. The authors did not go further to assess phase relations, particularly the effect of initial aqueous THF concentration on hydrate composition, with, as noted, data being confined to a single aqueous THF solution of unspecified concentration. In this work, for the stoichiometric 5.56 mol % THF initial concentration, H2-THF clathrates showed maximum thermal stability (see Figures 2 and 3), with dissociation typified by essentially congruent decomposition on the phase boundary for the system, i.e., a clathrate of composition XH2‚THF‚17H2O was formed, confirming previous studies. Consistent with congruent clathrate dissociation, cooling into the hydrate stability region away from the phase boundary for the stoichiometric composition resulted in complete conversion of liquid to hydrate (H+G conditions). As discussed, phase relations for the H2-THF-H2O system as a function of aqueous THF concentration have not previously been investigated to any great extent, particularly for lower aqueous THF concentrations at temperatures below the eutectic. In Figure 3, data for 0.20, 0.50, 1.00, and 2.70 mol % THF aqueous solutions show that, as is the case for the binary THFH2O system (Figure 2), reducing the initial aqueous THF concentration reduces binary H2-THF-H2O clathrate stability to lower temperatures at any given pressure. The close relationship between binary and ternary phase behavior is clear from Figure 2: for compositions equal to or higher than the binary eutectic composition (e.g., 1.00, 2.70, and 5.56 mol %), H2-THF hydrate phase boundaries intersect with binary THF-H2O clathrate melting conditions at 1 atm. This strongly suggests that hydrogen does not alter the THF-to-water stoichiometry of clathrates, but rather can be accommodated by, and lends stability to, the THF hydrate structure. For concentrations lower than the eutectic (e.g., 0.2 and 0.5 mol % THF), ice is initially the more stable phase at lower pressures, with H+L+G regions emerging at higher pressures. This behavior is similarly consistent with binary phase relations, with ice being the more stable phase for these concentrations at 1 atm. With the exception of the 5.56 mol % THF system, which gives an essentially congruently melting clathrate as discussed, phase relations indicate that cooling drives H+L+G conditions toward a quaternary eutectic line (1 degree of freedom), where all phases (H+L+I+G) can coexist in equilibrium. At temperatures below this eutectic, complete conversion of the liquid phase to solid results in H+I+G conditions, as indicated by proportionate (to excess water) pressure rises associated with ice formation observed on heating curves (Figure 1). From interpolated PT data (Figure 2), we can construct approximate isobaric sections as a function of aqueous THF
Langmuir, Vol. 23, No. 6, 2007 3443
concentration for the H2-THF-17H2O system at various pressures. It is possible to interpret data in a binary sense in this case, as only at very low (limiting) or high (where H2O and/or THF loss to the vapor phase could be an issue) H2 fractions would phase relations be expected to deviate from that observed. As can be seen, isobaric sections demonstrate the formation of two solids: water ice (hexagonal ice would be expected at these conditions) and a clathrate of stoichiometric 1:17 THF-to-water ratio, with the formula XH2‚THF‚17H2O. No other solid phases are observed. Again the similarity between binary THF-H2O and ternary H2-THF-17H2O systems is strongly apparent: isobaric sections in the presence of H2 are almost identical in form (in terms of phases present at TX and degrees of freedom) to those of the binary system, with the principal difference being an increase in clathrate thermal stability due to the uptake of H2. As noted, Lee et al.8 claimed that, for initial aqueous THF concentrations lower than the binary eutectic (∼1.0 mol %), at low pressures (12 MPa) in the H+I+G region, ice and THF‚ 17H2O clathrates would convert to binary H2-THF hydrates increasingly rich in H2. This was purported to be achieved through double H2 molecule occupancy of small dodecahedral s-II cavities, coupled with increasing co-occupancy of large hexakaidecahedral by four H2 molecules, with the ratio of 4H2 to THF in the latter increasing as THF concentration is reduced. The following formula was proposed for this reaction:
THF·17H2O(H) + H2(G) + H2O(L) f (2H2)2‚(4H2)x‚THF(1-x)‚17H2O(H) (1) The problem with the results of Lee et al.8 is that they have not been successfully repeated to date. The results presented here do not support the conclusions of these authors, in that the data strongly suggest the consistent formation of clathrates with a stoichiometric THF-to-water ratio of 1:17; that is, large cavities are ubiquitously filled by THF, irrespective of initial aqueous THF concentration. We have found no evidence for H2 entering and stabilizing the large s-II cavity under the conditions tested. Instead, phase relations indicate that, as aqueous THF concentration is reduced, the THF-to-water stoichiometry is retained with merely less clathrate formed, with all remaining free water being present as ice at equilibrium below the eutectic. Clathrate hydrates formed in the system H2-THF-H2O do, however, in agreement with the findings of others, host significant volumes of H2. With all large cavities filled by THF, only small dodecahedral cages should be available for the accommodation of hydrogen. Lee et al.8 suggested that these cavities could host two H2 molecules at pressures within the range tested here. While small cage occupancy ratios cannot be determined from the phase relations presented here so far, compositional analysis can provide information on this. As detailed, we have directly measured the composition of clathrates by a reliable Hg isolation technique. Compositional analyses were carried out on hydrates formed from a stoichiometric (5.56 mol %) THF solution in the H+G region, and a 0.2 mol % solution in the H+I+G region. Data are reported in Table 3. For the 5.56 mol % analyses at 283 K and 30 MPa, clathrates were found to be of the composition 1.8H2‚ THF‚17H2O. This is consistent with a 90% filling of small s-II dodecahedral cavities by single H2 molecules and is equivalent to 0.95% H2 by mass. For compositional analyses of the clathrate formed from the 0.2 mol % THF solution, the ice phase could not be separated from the hydrate during mercury injection. Thus, upon depressurization and gas release, only the number of moles of hydrogen released from all solid (ice and hydrate) phases could be measured.
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Anderson et al.
Table 3. Experimental H2-THF Clathrate Hydrate Compositional Data sampling conditions mol % THF(aq)
T/K ((0.1)
P/MPa ((0.07)
5.56 0.20
283.0 270.0
30.30 30.00
a
mol % mol % THF-to- mass % liquid liquid as water H2 as ice clathrate ratio ((0.1) 0.0 96.4
100.0 3.6
1:17 1:17a
0.95 0.83
Assumed, based on evidence for stoichiometry from phase relations.
This means that an assumption must be made regarding the composition of the clathrate in terms of THF-to-water ratio. As discussed, phase relations indicate that clathrates are consistently stoichiometric in this respect, having a THF -to-water ratio of 1:17. Using this ratio, compositional data yields a hydrate of formula 1.6H2‚THF‚17H2O. This equals an 80% occupancy of small cages and gives a clathrate of 0.83% H2 by mass. The validity of the assumption used above is confirmed when we look at the alternative options. First, we can consider the theory of Lee et al.,8 in that, as aqueous THF concentration is reduced, so is the THF factional cage occupancy in hydrates below the eutectic. If we assume this to be the case, then the total number of moles of hydrate in the system would be higher, which of course would mean an even lower measured hydrogen content for the clathrate phase. On the other hand, it could be assumed that some THF was still present as a liquid phase. If this was the case, then the hydrate would be more H2-rich. However, this would introduce a new phase into the system, reducing the degrees of freedom to 1, and so the observed H+I+G region (2 degrees of freedom) below the eutectic, as described in this work and highlighted by Lee et al.8 as the region of clathrate H2 enrichment, could not exist. Rather, equilibrium conditions for such a combination of phases should follow a univariant line. As seen in Figures 2 and 3, no such behavior is observed. We thus conclude that measured hydrate compositions represent, within experimental error, true values at the conditions studied. Values for hydrates formed from the two initial THF concentrations analyzed (5.56 and 0.2 mol %) are in good agreement and support only single H2 molecule occupancy of small s-II cavities, with large cavities completely occupied by THF. This is consistent with observed phase relations for the system, with single H2 occupancy of small cages being further supported by recent high-pressure neutron diffraction studies of simple (single guest) and binary H2-THF s-II clathrates.6,11 Our results thus strongly suggest that the Lee et al.8 “tuning” concept (i.e., that reducing THF concentration increases H2THF clathrate hydrogen contents) is not viable, and instead the data generated in this work support the conflicting conclusions of Strobel et al.9 who, as discussed, determined maximum hydrogen contents of only ∼1 mass % under comparable conditions. These authors reached the same conclusion as reported here; small cavities can accommodate one H2 molecule only, with large cavities ubiquitously occupied by THF, irrespective of initial aqueous THF concentration. According to Strobel et al.,8 gas uptake by clathrates as a function of H2 fugacity follows a Langmuir absorption-like trend, approaching maximum H2 filling of small cavities above 30 MPa, with the latter case giving a binary clathrate hydrate formula of (H2)2‚THF‚17H2O. Figure 4 shows measured hydrate mass percent H2 as a function of pressure for the two samples studied here compared with values determined by Strobel et al.8 Data are in very good agreement, particularly for the 0.2 mol % THF (initial) solution for which hydrate gas content was measured at similar conditions in the H+I+G region below the eutectic.
Figure 4. H2-THF clathrate mass percent hydrogen as a function of pressure for the two samples analyzed in this work compared to the data of Strobel et al.9 The sample analyzed here in the H+I+G region (0.2 mol % THF aqueous initial concentration) agrees very well with data reported by Strobel et al. for similar conditions.
In light of the above, we can outline the principal reactions occurring in the system for the conditions tested, correcting formula (1): For 5.56 mol % THF(aq), L+G f H+G:
H2O-THF(L) + H2(G) f (H2)e2‚THF‚17H2O(H) + H2(G) (2) For
