Investigation of Hydrate Formation in the System H2−CH4−H2O at a

11214

J. Phys. Chem. B 2007, 111, 11214-11220

Investigation of Hydrate Formation in the System H2-CH4-H2O at a Pressure up to 250 MPa Sergei S. Skiba, Eduard G. Larionov,* Andrey Y. Manakov, Boris A. Kolesov, and Viktor I. Kosyakov NikolaeV Institute of Inorganic Chemistry SB RAS, Akad. LaVrentieV AVenue 3, NoVosibirsk 630090, Russian Federation ReceiVed: April 11, 2007; In Final Form: June 13, 2007

Phase equilibria in the system H2-CH4-H2O are investigated by means of differential thermal analysis within hydrogen concentration range 0-70 mol % and at a pressure up to 250 MPa. All the experiments were carried out under the conditions of gas excess. With an increase in hydrogen concentration in the initial gas mixture, decomposition temperature of the formed hydrates decreased. X-ray diffraction patterns and Raman spectra of the quenched hydrate samples obtained at a pressure of 20 MPA from a gas mixture containing 40 mol % hydrogen were recorded. It turned out that the hydrate has cubic structure I under these conditions. The Raman spectra showed that hydrogen molecules are not detected in the hydrate within the sensitivity of the method, that is, almost pure methane hydrate is formed. The general view of the phase diagram of the investigated system is proposed. A thermodynamic model was proposed to explain a decrease in hydrate decomposition temperature in the system with an increase in the concentration of hydrogen in the initial mixture.

1. Introduction It is recognized at present that hydrogen, as an ecologically safe and high-energy fuel, can become one of the basic energy carriers of the future. One of the important questions of hydrogen power engineering is the storage of hydrogen in the form suitable for its further technological use and under technologically acceptable P-T conditions. Several methods of hydrogen storage are under consideration at present (in high-pressure cylinders, in liquefied form, adsorbed on various materials, or bound in the form of hydrides of some metals);1-3 each of these methods has its own advantages and shortcomings. The method involving hydrogen storage in the form of clathrate hydrates has been proposed not long ago4,5 However, development of this method is only at the initial stage and requires further investigation. Clathrate hydrates are crystal inclusion compounds in which the host framework is formed by water molecules connected through hydrogen bonds.6 The cavities of the framework are occupied by the guest molecules of appropriate size and molecular shape. The guest-to-host interaction in clathrate hydrates is purely Van der Waals. The hydrates formed by the guest components which are gaseous under normal conditions are usually called gas hydrates. As a rule, gas hydrates existing at not very high pressure (less than 100 MPa) belong to one of the three structural types: cubic structure I (sI), cubic structure II (sII), or hexagonal structure III (sH). Various aspects of the structural chemistry and physical chemistry of gas hydrates were considered in detail.7,8 Investigation of the gas hydrates of hydrogen has rather long history. At first, the authors of the work9 reported on the existence of solid solutions of hydrogen in ice Ih, then the existence of the solid solutions of hydrogen on the basis of ice II and Ic was discovered,10,11 and finally, when analyzing the * Corresponding author phone: (7-383) 339 13 46; Fax: (7-383) 330 94 89; e-mail: [email protected].

phase diagram within the pressure range 100-360 MPa, the existence of hydrogen hydrate of one of the classical polyhedral structures was assumed.12,13 Later, it was established that this hydrate has a cubic structure II.14 It was demonstrated15 that small 512 cavities (that is, polyhedrons with 12 pentagonal facets) in this structure are occupied by only one hydrogen molecule, while large 51264 cavities contain 4-2 hydrogen molecules, depending on temperature. Unfortunately, the gas hydrates of pure hydrogen can hardly be used to store hydrogen because this requires very high pressure and/or low temperature. For instance, at a temperature of -5.0 °C the hydrate is stable at a pressure of more than 100 MPa, whereas at a temperature of 1.2 °C it is stable at a pressure above 330 MPa.12-13 It is known that, as a rule, decomposition temperatures of the hydrates formed from mixtures of gases noticeably differing in size are higher than decomposition temperatures of the hydrates of individual components of these mixtures.16,17 Florusse at al.18 showed that decomposition temperature of hydrogen hydrate can be increased substantially if the large cavities in the hydrate of cubic structure II are filled with tetrahydrofuran molecules (THF). However, the hydrogen content of such a hydrate decreases substantially because only small 512 cavities are left for hydrogen; each of these cavities is occupied with only one hydrogen molecule.19,20 It seemed interesting for us to investigate the case when the initial gas mixture contains molecules smaller than THF in addition to hydrogen molecules. We chose the system H2CH4-H2O as the subject of investigation. Only scarce data on the decomposition curves of the hydrates formed in the system H2-CH4-H2O were available from literature;21 no data on the structures of these hydrates were available. It was shown previously that a part of the small 512 cavities in the hydrate of pure methane at low-pressure remains vacant,22 but with an increase in pressure the fraction of the vacant 512 cavities decreases sharply; it approaches zero at rather high pressure. It

10.1021/jp072821x CCC: $37.00 © 2007 American Chemical Society Published on Web 09/06/2007

Phase equilibria in the system H2-CH4-H2O are investigated seemed probable from the general considerations that at low pressure during the formation of the hydrate from a mixture of methane and hydrogen the vacant 512 cavities can fill with hydrogen molecules; each cavity contains only one hydrogen molecule. It is undoubtedly more favorable to fill a 512 cavity with a methane molecule because of more favorable Van der Waals guest-to-host interactions in this case; that is, it should be expected that an increase in pressure should be accompanied by hydrogen displacement from small cavities. However, it remains unclear which guest (CH4 or n × H2) would fill large cavities 51262 or 51264 (for the most probable structures sI and sII, respectively) in the hydrates formed in this system. It is only known15 that the large 51264 cavities in hydrogen hydrate contain (depending on temperature) 4-2 hydrogen molecules. Therefore, it may be assumed that there is a principal possibility of a competition between a separate methane molecule and several hydrogen molecules for large cavities during the formation of hydrates from a mixture of H2 and CH4 within a wide pressure range. In principle, one cannot exclude the formation of a double hydrate of hydrogen and methane. It is impossible to answer a priori whether this possibility is actually implemented in multiple filling of the cavities. It should be stressed that the experimental data available23-26 allow one to conclude that an increase in pressure promotes in clathrate hydrates with guest molecules; that is, to obtain a principal answer to the formulated question concerning the possibility of the formation of the double hydrate of hydrogen and methane, one should investigate the system until as high a pressure as possible. In the present paper, we describe our recent results on hydrate formation in the system H2-CH4- H2O at a pressure up to 250 MPa. 2. Experimental Methods Hydrate decomposition temperature was measured with by means of the differential thermal analysis under gas excess in a cell specially developed for the investigation of hydrate formation with a gaseous guest at high hydrostatic pressure.27 Hydrate decomposition temperature was measured with a chromel-alumel thermocouple calibrated with the startard reference compounds (the readings of this thermocouple are almost independent of pressure) with an accuracy of (0.3 K. Pressure was measured with Bourdon manometer. The accuracy of pressure measurement was not worse than 0.5%. The procedure was described in detail elsewhere.27,28 The gases used in the investigation contained not less than 99.95% of the main substance and were not further purified. Time of equilibrium establishment in the system at any pressure was about 30 min; it was determined in special experiments lasting for up to 24 h. The equilibrium was considered to be established if the ice melting peak was absent when the system was heated under the conditions of the excess of hydrate-forming gas. Hydrate samples for the investigation by means of powder diffraction and Raman spectroscopy were prepared as follows. Finely crushed ice powder was placed into a high-pressure cell. Then hydrogen and methane were supplied to the cell sequentially at a ratio of 40% mol. H2 and 60% mol. CH4 at the final pressure of 20 MPa. The sample was kept for 2-3 weeks in a freezing chamber at a temperature of -14 °C. The formation of the hydrate was monitored on the basis of pressure drop in the bomb. Then the bomb was cooled to the liquid nitrogen temperature and the hydrate was taken out of it. The quenched sample was divided into two parts to record X-ray powder diffractogram and Raman spectra.

J. Phys. Chem. B, Vol. 111, No. 38, 2007 11215 TABLE 1: Decomposition Temperatures for Clathrate Hydrogen Hydrates at High Pressure P MPa 86 90 140 160 184 225 258 290 336 338 364 T °C -6.3 -6.1 -3.5 -2.6 -1.6 -0.2 0.6 1.0 1.1 1.2 1.1

X-ray diffraction studies were performed with quenched samples of the hydrate using synchrotron radiation at the fourth beamline of the VEPP-3 storage ring (Budker Institute of Nuclear Physics SB RAS), at fixed wavelength of 0.3675 Å.29 The Debye-Scherrer scheme was applied. An imaging plate detector MAR345 (pixel dimension 100 µm) was used to register the diffraction pattern. The distance between the sample and the detector calibrated against the diffraction pattern of sodium chloride was 391.0 mm. A fine-ground hydrate sample was placed in an aluminum cell with two foam-coated holes for the primary beam and the outlet of diffracted radiation. Raman spectra were recorded with a Triplemate SPEX spectrometer equipped with a multichannel detector, LN1340PB, Princeton Instruments, in a back-scattering geometry. The spectral resolution was 5 cm -1. The 514 nm line of a 50 mW Ar ion laser was used for spectral excitation. All the spectra were recorded at a temperature near 77 K at atmospheric pressure. The hydrate taken out from the high-pressure chamber was put into a cell that was immersed in liquid nitrogen. This cell had a hole covered with glass plate. To exclude frosting of extraneous compounds on this glass, we maintained it under a flow of argon. The spectra were recorded within two wavenumber intervals: 2700-3000 cm-1 (recording C-H vibrations in methane molecule) and 4000-4200 cm-1 (recording H-H vibrations in molecular hydrogen). 3. Results and Discussion The decomposition curve of the individual methane hydrate at high pressure (above 5.0 MPa) was presented elsewhere.30,31 The data on decomposition temperature of the clathrate hydrates of pure hydrogen within the pressure range from 90 to 360 MPa were reported in the graphical form,12,13 the numerical data on this curve are presented in Table 1. At a pressure of 0.1-80 MPa for the system H2-H2O, the effects corresponding to the decomposition of solid solutions of hydrogen in Ih ice were observed; their decomposition temperature was only slightly (∼0.3°) above the ice melting point.12,13 The indicated effects were not observed with further pressure increase, because in the equilibrium state of H2-H2O system and under hydrogen excess the whole water passed into the hydrate. We observed the first effect corresponding to the clathrate hydrate of hydrogen at a pressure of 86 MPa and a temperature of -6.3 °C, which is about 1° higher than the melting point of ice at this pressure. The triple point: a solution of hydrogen in Ih ice-the clathrate hydrate of hydrogensliquid, determined as a point of intersection of the lines of melting of hydrogen solution in Ih ice and melting of the clathrate hydrate of hydrogen, is at about P ) 81 MPa and T ) -6.5 °C. The experimental data on decomposition temperatures of gas hydrates formed in the ternary system H2-CH4-H2O for 0-70% (mol) hydrogen content in the initial gas mixture are shown in Figure 1. For each of the experimental P-T curves obtained for the ternary system, leastsquares were applied to fit the coefficients of equation T (°C) ) A + B × P + C × P2 + D × P3 + E × lnP (P, MPa). The coefficients of polynomials approximating decomposition curves for the entire composition range of the ternary system are shown in Table 2. The decomposition curves of the hydrates formed in the system H2-CH4-H2O in the present investigation for different gas compositions differed from each other by different scattering

11216 J. Phys. Chem. B, Vol. 111, No. 38, 2007

Skiba et al.

Figure 1. Decomposition temperatures of the three-component system H2-CH4-H2O for 0-70% (mol.) hydrogen concentration in the initial gas mixture.

TABLE 2: The Coefficients of Equations T (°C) ) A + B × P + C × P2 + D × P3+ E × lnP (P, MPa) That Approximate the Lines of Liquidus in the Hydrogen-Methane-Water System within Pressure up to 250 MPa with the Gas in Excessa CH2 % mol.

pressure range (MPa)

A

0.0 7.5 10.0 20.0 30.0 40.0 50.0 60.0 70.0

1.8-250 4.5-250 6.4-250 5.2-250 6.0-250 6.7-250 15.3-250 19.0-250 42.0-250

-11.1 -29.1 -31.2 -28.9 -28.5 -40.8 -35.1 -23.5 -15.3

B

C

-0.179 0.00131 -0.004 4.1 × 10-6 -0.003 3.8 × 10-6 -0.002 2.8 × 10-6 0.004 -1.4 × 10-6 -0.008 5.8 × 10-6 0.006 -3.5 × 10-6 -0.075 0.00057 0.027 -9.7 × 10-6

D

E

SD

-2.8 × 10-6 10.8 0.23 -8.5 × 10-10 8.8 0.26 -9.0 × 10-10 8.9 0.30 -6.4 × 10-10 8.2 0.28 1.8 × 10-10 7.5 0.55 -1.3 × 10-9 10.0 0.33 7.5 × 10-10 7.4 0.53 -1.2 × 10-6 9.3 0.53 1.4 × 10-9 0.9 0.62

a Hydrogen concentration is indicated for the initial gas mixture. SD, standard deviation of experimental points from the linear fit.

of the experimental values. The best convergence of the results was observed for the hydrates of pure methane and for the experiments in which the hydrogen content of the initial gas mixture did not exceed 40 mol %. At higher hydrogen concentrations, the differential peaks got smeared, and scattering of the experimental dots increased substantially. In our opinion, worsening of data convergence with an increase in hydrogen concentration is connected with broadening of the temperature range corresponding to the three-phase region lh1g, whereas hydrogen concentration increases in the gas mixture. The decomposition of the hydrate occurs within an increasingly broad temperature range, which results in worsening of the quality of thermograms. Because of this, we limited our measurements to the compositions in which the concentration of hydrogen in the gas-phase did not exceed 70 mol %; it turned out to be impossible to carry out the investigation with the help of our procedure at higher hydrogen concentration. To determine the structure of clathrate hydrates formed in the system under consideration, X-ray diffraction studies of a quenched hydrate sample were performed at a pressure of 20 MPa and 40 mol % hydrogen content of the initial gas mixture. The powder diffraction patterns is shown in Figure 2. One can conclude from Figure 2 that the investigated sample was a hydrate of CS-1 structure (cell parameter: 11.86 Å at 133 K), with a small amount of unreacted ice. The Raman spectra of the investigated hydrate sample are shown in Figure 3. One can see in this figure that two bands are observed within the

Figure 2. Synchrotron X-ray powder diffraction pattern of quenched hydrate, obtained at a wavelength of 0.3675 Å. Vertical tick-marks correspond to the calculated positions of reflections for the hydrate of cubic structure 1 (upper row) and of ice Ih (lower row). The diffractogram was recorded at a temperature of 133K and atmospheric pressure.

wavenumber range 2700-3000 cm-1, corresponding to the vibrations of C-H in methane molecule. The band at 2900 cm1 is assigned to methane molecules enclosed in large 51262 cavities of cubic structure I, the band at 2912 cm-1 corresponds to methane molecules enclosed in small 512 cavities.34 No bands were observed within the range 4050-4200 cm-1 where a band corresponding to H-H vibrations in hydrogen molecule had to appear. Our attempts to make a hydrate sample suitable for X-ray diffraction and spectroscopic examination at a higher hydrogen content in the initial gas mixture failed due to the limitations posed by the available instrumentation. (The highpressure cell for making a hydrate sample had a very small volume. An increase in the hydrogen content of the initial gas mixture at P ) const results in a decrease in the amount of methane in it. In turn, this causes (see below) a decrease in the amount of the hydrate formed; in the case of the high hydrogen content, this amount was insufficient to carry out spectroscopic investigations. We were unable to make an initial gas mixture at a pressure above 20 MPa). It was shown previously22 that methane molecules in the individual methane hydrate formed in the system CH4 - H2O at increased pressure almost completely occupy both the large 51262 and the small 512 cavities in sI structure. One can conclude from Figure 3 that methane molecules in the system H2-CH4-

Phase equilibria in the system H2-CH4-H2O are investigated

J. Phys. Chem. B, Vol. 111, No. 38, 2007 11217

Figure 3. Raman spectra of the quenched hydrate. Spectra were recorded at a temperature of 77 K and atmospheric pressure.

H2O, too, occupy all the cavities in the hydrate leaving no space for hydrogen molecules, at least within the concentration range 0-40% mol. H2 and at a pressure of 20 MPa (the conditions of X-ray and Raman experiments) and higher. This is likely because the H2 molecules are less complementary to 51262 and 512 cavities than CH4 molecules and, therefore, cannot be competitive for occupying cavities even in the case when more than one hydrogen molecule can be placed in the 51262 cavity. An indirect confirmation of these conclusions was reported by the authors of ref 21 who showed that at a pressure below 5.0 MPa and a temperature about 273 K methane-hydrogen mixtures can be efficiently separated due to the formation of methane hydrate. The transformations of isothermal-isobaric sections of the phase diagram of ternary system H2-CH4-H2O and the versions of polythermal sections at the pressures lower and higher than 81 MPa, respectively (the boundary of the region of existence of polyhedral hydrogen hydrate) are shown in Figure 4 and 5. Probable isobaric sections of the volume P-T-x phase diagram constructed taking into account our new experimental data on melting points of hydrates in H2-CH4-H2O system are shown in Figure 6. The solubility of methane in hydrogen hydrate and the solubility of hydrogen in methane hydrate were considered to be small. The sections depict the part of the full phase diagram in which hydrogen and methane hydrates decompose above the ice melting point. It is undoubtedly interesting to discuss the reasons of a decrease in the temperature of decomposition of the hydrate in equilibrium with the gas mixture while hydrogen concentration in the initial gas mixture increases. The statistical thermodynamic theory of ideal clathrate solutions was formulated by Van der Waals33,34 and developed in ref 35 for multicomponent systems. However, in the case under consideration, when the addition of the second gas (hydrogen) does not cause changes in the composition or structure of the initial methane hydrate, the effect of the added gas on decomposition temperature can be considered from the point of view of classical thermodynamics. In our opinion, the main part here is played by a decrease in thermodynamic activity of methane in the gas mixture. Let us consider the equilibrium between solid methane hydrate, gaseous solution of methane and hydrogen, and liquid water in which methane and hydrogen are dissolved. We assume that the solubility of hydrogen in solid hydrate is negligibly small. In this case, hydrogen does not take part in chemical processes, that is, acts as an inert gas affecting only total pressure in the system. Methane hydrate itself is assumed to be a

Figure 4. (T1-T5) A schematic sketch of the transformation of isothermal-isobaric sections of the phase diagram of a three-component system H2-CH4-H2O with a decrease in temperature and at a constant pressure below 81 MPa. T1, the phases present in the system are g, (gas mixture); l, liquid-phase rich with water, and the region of coexistence of these phases is observed, l g. T2, with temperature decrease to T2, there appear the region of methane hydrate (h1), the regions of coexistence of methane hydrate with liquid (h1l) and with gas (h1g), and the region of the coexistence of methane hydrate with liquid and gas (h1lg). T3, further cooling of the system to temperature T3 causes ice crystallization (i) from phase l and the appearance of the regions il, ig, and ilg. T4, at temperature T4, due to the transition of a part of liquid into the solid phases, closure of fields il and h1l occurs, and hte field of coexistence of ice, methane hydrate, and liquid appears (ih1l). T5, System cooling to temperature T5 results in the complete disappearance of liquid (l) in the system and, as a consequence, the disappearance of regions of coexistence of the liquid with other phases. The regions of gas phase (g), ice (i), methane hydrate (h1) remain in the system, as well as the regions of their coexistence: ig, h1g and ih1g. Polythermal sections of the system methane-hydrogen-water are shown: A-A for the lack of gas, and B-B for gas in excess. It should be noted that in this system there are also the solutions of hydrogen in ice, which brings substantial complications to the diagrams under consideration; In the present work we do not consider their effect on phase equilibria to simplify rather complicated situation.

stoichiometric compound with 100% filling of both types of cavities. This assumption is confirmed by the results reported

11218 J. Phys. Chem. B, Vol. 111, No. 38, 2007

Skiba et al. correspond to temperature T and pressure P. Let us express the dependence of the right-hand part of this equation on pressure and temperature. In all the cases, the standard case will be chosen to be that at 273.15 K and 0.1 MPa; the corresponding values will be marked with subscript 0. The dependence of Gibbs energy of a phase and the dependence of the chemical potential of a component of the phase on temperature and pressure are determined by the following equations:

G ) H - TS ) G0 + ∆S0(T - 273.15) + ∆cP(T)P)0.1 T T dT + ∆cP(T)P)0.1dT - T 273.15 273.15 T ∂∆V(P) P T ∆V0 + 273.15 dT dP 0.1 ∂T T

∫

∫

∫

(

(

∫

) )

Equation 3 may be rewritten taking into account this dependence:

ln(Pγ(CH4)ga(H2O)ln) )

[G - ∆S (T - 273.15) + ∫ ∆c dT ∆c dT + ∫ (∆V + ∫ dT dP RT (4) (∂∆V T ∂T ) ) ] / T

0

Figure 5. Figure 5. (T1-T5) A schematic sketch of the transformation of isothermal-isobaric sections of the phase diagram of a threecomponent system H2-CH4-H2O with a decrease in temperature and constant pressure above 81 MPa. T1, methane crystallization started in the system (region h1). T2, in addition to methane hydrate, hydrogen hydrate appears in the system (region h2). T3, further cooling of the system leads to the start of ice crystallization from the liquid phase (region il). T4, the regions of coexistence of ice, liquid phase and the hydrates of methane and hydrogen appear in the system (regions ih1l and ih2l). T5, due to a decrease in the amount of the liquid-phase that is transformed to ice, a narrow region appears in which two hydrates are in equilibrium (region h1h2). Figure shows polythermal sections of the system methane-hydrogen-water: A-A for the lack of gas and B-B for gas in excess.

in ref 22. The degree of filling of the small cavities for 20 MPa determined in that work is about 0.9, whereas for 60 MPa it is almost 1. The reaction of methane hydrate formation is

CH4 + nH2O ) CH4‚H2O

(1)

Here n is hydrate number. The hydrate will be designated by h ) CH4‚nH2O. The condition of thermodynamic equilibrium for this reaction is

µ(CH4)g + nµ(H2O)l ) G (h) 0

(2)

Here µ(CH4)g and µ(H2O)l are chemical potential values for methane in the gas phase and for water in liquid solution, G0(h) is Gibbs energy of the hydrate. All these values relate to temperature T and pressure P. The equation for the equilibrium constant of reaction (1) is

ln(Pγ(CH4)ga(H2O)nl ) )

∆G0 RT

(3)

Here ∆G0 is standard Gibbs energy of reaction (1), P is methane pressure, γ(CH4)g is fugacity coefficient of methane in the gas mixture, a(H2O)l is activity of water in the aqueous solution containing methane and hydrogen. All the values

T

T ∫273.15

0

273.15

P

P

0.1

P

T

0

273.15

∆G0 ) G0(h)s - G0(CH4)g - nG0(H2O)l is the difference of Gibbs energies of the solid hydrate and gaseous methane with liquid water at 273.15 K, 0.1 MPa; ∆S0 ) S0(h)s - S0(CH4)g - nS0(H2O)l - the same for entropy; ∆V0 ) V0(h)s - V0(CH4)g - nV0(H2O)l - the same for molar volume; ∆cP )cp(h)s - cp(CH4)g - ncp(H2O)l - the same for thermal capacities at 0.1 MPa; ∆V ) V(h)s - V(CH4)g - nV(H2O)l - volume change during reaction, which depends on temperature and volume. If we assume that a mixture of methane with hydrogen is an ideal gaseous solution within the whole pressure range under consideration, and neglect partial pressure of water vapor, methane fugacity in it will be equal to f ) xγP, where x is the molar fraction of methane in gas mixture, P is total pressure in the cell. Taking this into account and rearranging the terms we obtain

ln(xP) ) -

∆S0 +

∆G0 - ∆S0T0 +

∫

T ∫273.15

T

273.15

∆cP dT + R(γ(CH4)ga(H2O)nl ) T + R

∆cPdT +

∫

P

0.1

dT dP (∆V + ∫ (∂∆V ∂T ) ) T

0

273.15

RT

(5) So, the equation under consideration has been transformed to the following kind:

ln(xP) ) A +

B T

(6)

In the region of rather high pressure, where the density of gaseous methane is rather large, whereas the difference in compressibility of the hydrate, methane and water is relatively small (which is characteristic of condensed molecular phases),

Phase equilibria in the system H2-CH4-H2O are investigated

J. Phys. Chem. B, Vol. 111, No. 38, 2007 11219

Figure 6. Isobars of the phase diagram for hydrogen-methane-water at pressures 40, 80, 150, and 250 MPa. o, experimental data; h1, methane hydrate; h2, hydrogen hydrate; l, aqueous solution with gas; g, gaseous phase.

coefficient B may be assumed to be nearly linearly dependent on pressure, that is,

ln(xP) ) A +

B′ + CP T

(7)

In the general case, coefficients A, B’, and C depend on pressure and temperature but are independent of the composition of the gas mixture. The temperature and pressure range under consideration corresponds to 273-313 K and 0.1-200 MPa. It is reasonable to assume that changes in the coefficients will be not large within this temperature range, whereas the dependence on pressure will be more clearly exhibited. Indeed, as a rule, the thermal capacity of the hydrate is very close to the sum of thermal capacities of the corresponding amounts of gaseous methane and ice,36 so the value of ∆cP in eq 5 should be close to ∆cP for the transformation of ice into liquid water, that is, to 39.2 J/(mol‚K). Estimations of the integrals incorporated into coefficients A and B of eq 5 in this case lead to the values 0.64 and 189 K, respectively. It will be shown below that these contributions are at a level of experimental errors for the corresponding values. In addition, one can see in eq 4 that the terms under consideration compensate each other to a great extent; their final contribution into the ln(xP) value should be small. Since substantial compression of liquid water and hydrate is achieved within pressure range 0.1-200 MPa (about 6 and 2% of the initial volume, respectively),37,22 one may expect a noticeable change in the activities of the components of these phases, that is, a systematic change in coefficient A. The dependence of coefficient B on pressure has already been discussed above. So, the isobaric dependencies of hydrate decomposition temperatures in the system under investigation on the composition of the gas mixture should become straight lines when plotted as ln(xP) versus 1/T, and coefficients A and

TABLE 3: The Coefficients of Equation ln(xP) ) A + B/T for the Isobaric Sections of the Investigated Part of the Surface of Liquidus in the System Methane-Hydrogen-Water. P Values are in Pa, T is in K pressure, MPa

A

B, K

R2

SD

n

10 20 40 60 80 100 140 180 220

31.4 ( 1.5 32.5 ( 0.9 31.6 ( 0.9 32.5 ( 0.9 33.6 ( 0.6 34.4 ( 0.5 34.9 ( 0.4 35.5 ( 0.6 36.1 ( 0.5

4378 ( 436 4583 ( 262 4199 ( 267 4395 ( 259 4665 ( 184 4886 ( 142 4999 ( 125 5152 ( 184 5307 ( 155

0.962 0.981 0.973 0.976 0.976 0.994 0.996 0.991 0.997

0.042 0.049 0.074 0.068 0.068 0.034 0.029 0.042 0.034

6 8 9 9 9 9 9 9 9

a 2 R , correlation coefficient; SD, standard deviation of experimental points from the linear fit; n, number of experimental points.

B should change systematically with an increase in pressure. Let us consider our experimental data from this point of view. Using the primary experimental data, we recalculated the isobaric sections of liquidus surface for the pressure of 20, 60, 100, 140, 180, and 220 MPa. It turned out that indeed the resulting curves became straight when plotted as ln(xP) versus 1/T (Table 3, Figure 7). The value of coefficient A changes with an increase in pressure relatively weakly; the pressure dependence of coefficient B is rather complicated; however, at a pressure above 100 MPa this dependence is close to a straight line (Figure 8). The shape of the curve at lower pressure is likely to depict a complicated character of changes in pV with pressure for methane. A more detailed analysis of the obtained values seems impossible due to the lack of quantitative data on the parameters incorporated into coefficients A and B. So, the real behavior of the system under consideration corresponds to the predictions

11220 J. Phys. Chem. B, Vol. 111, No. 38, 2007

Skiba et al. Acknowledgment. Financial support from the Center for Hydrate Research, Department of Chemical Engineering, Colorado School of Mines is gratefully acknowledged. References and Notes

Figure 7. Dependence of ln(xP) values on reciprocal temperature for a pressure of 20 MPa (triangles) and 220 MPa (squares).

Figure 8. Dependence of coefficient B on pressure.

of the thermodynamic theory assuming the absence of hydrogen inclusion into the hydrate framework and explaining a drop in the hydrate decomposition temperature with an increase in hydrogen content by a decrease in thermodynamic activity of methane in the gas mixture. 4. Conclusions 1. Experimental data on decomposition temperatures of gas hydrates in the system H2-CH4-H2O at a pressure up to 250 MPa were obtained. Decomposition temperature of the formed hydrates decreases with an increase in hydrogen concentration in the initial gas mixture, for any pressure. 2. A general view of the phase diagram of the system H2CH4-H2O is proposed for a wide range of temperature, pressure and concentrations. 3. X-ray powder diffractograms and Raman spectra of the hydrates formed in the system under investigation were recorded. 4. It is shown that for the hydrogen content of the initial mixture within the range from 0 to 70 mol % and at a pressure of 20 MPa and higher the hydrates formed from this mixture have sI structure in which all the cavities are occupied by methane molecules, while hydrogen molecules are not incorporated into the hydrate. Therefore, the system H2-CH4-H2O cannot be used to store hydrogen in the form of gas hydrate. 5. A thermodynamic model was proposed to explain a decrease in hydrate decomposition temperature in the system with an increase in the concentration of hydrogen in the initial mixture.

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