Experimental and Computational Investigation of the sII Binary He

ARTICLE pubs.acs.org/JPCB

Experimental and Computational Investigation of the sII Binary He-THF Hydrate Nikolaos I. Papadimitriou,† Ioannis N. Tsimpanogiannis,*,†,§ Athanassios K. Stubos,† Angel Martín,‡ Laura J. Rovetto,‡ Louw J. Florusse,‡ and Cor J. Peters‡ † ‡

Environmental Research Laboratory, National Center for Scientific Research “Demokritos”, 15310 Agia Paraskevi, Greece Laboratory of Process Equipment, Department of Process and Energy, Faculty of Mechanical Maritime and Materials Engineering, Delft University of Technology, Leeghwaterstraat 44, 2628 CA Delft, The Netherlands ABSTRACT: The objective of this work is to study the binary He-THF hydrate with both experimental and theoretical approaches. Experimental data for the hydrate equilibrium at pressures up to 12.6 MPa are reported for the binary He-THF hydrate with stoichiometric THF composition (i.e., 5.56 mol % THF). These data are used to calibrate a thermodynamic model [J. Phys. Chem. C 2009, 113, 422] for the prediction of hydrate equilibrium that is based on the van der Waals-Platteeuw statistical thermodynamic theory. Then this model is used to extrapolate the obtained experimental data to much higher pressures, and good agreement is observed with other available experimental data at pressures up to 150 MPa. This model is also capable of estimating the cavity occupancies for He and THF. The results show that the large cavities are completely occupied by THF molecules, whereas the small ones are partially occupied by He atoms. The He occupancy of the small cavities is less than 60%, even at high pressures (100 MPa). The occupancies predicted from this model are in close agreement with similar results from molecular simulations and a previously reported thermodynamic approach.

1. INTRODUCTION Clathrate hydrates are nonstoichiometric crystalline inclusion materials composed of hydrogen-bonded water molecules. The solid lattice of water molecules contains different types and sizes of cavities or cages stabilized by the enclathration of small “guest” molecules. The most common hydrate structures are sI, sII, and sH.1,2 Over 130 molecules (gas or liquid) are known to form hydrates.1 Hydrates have a substantial scientific interest due to the variety of natural and industrial processes in which they are involved. Pipeline blockage during oil or natural gas production, possible energy production from oceanic methane hydrate reserves, and storage of energy-carrier gases (e.g., methane or hydrogen) are the most important among them.2,3 Initially, it was believed that small gas molecules, such as hydrogen, helium, and neon could not form hydrates without the presence of a second hydrate former. The size of these molecules was thought too small to stabilize any type of hydrate cavity by themselves. Recently, however, hydrates of pure hydrogen4,5 and neon5 have been synthesized, and it was found that more than one gas molecules can be accommodated in the same cavity (multiple occupancy of cavities). Moreover, it has been experimentally shown that helium can be dissolved in several types of ice, such as Ih, Ic, and II.6-9 Theoretical and experimental studies have shown that the presence of helium increases the stability of such ice structures and slightly affects their geometrical characteristics.10-13 r 2011 American Chemical Society

Apart from filling interstitial spaces in several types of ice, He and H2 were also found to be the guest components of hydrates with promoter.14,15 A promoter is a substance that stabilizes the hydrate lattice by occupying some of the cavities while the rest of them can be occupied by gas molecules. The presence of the promoter significantly lowers the formation pressure of the hydrate compared with the hydrate of the pure gas. When tetrahydrofuran (THF) is used as the promoter, He can be enclathrated in the small cavities of the sII hydrate.15 The unit cell of this type of hydrate contains 136 water molecules forming two types of cavities: 16 small cavities with 12 pentagonal faces (512), and 8 large cavities consisting of 12 pentagonal and 4 hexagonal faces (51264). The molecular formula of this hydrate is 16S 3 8 L 3 136H2O, where S and L indicate the small and the large cavity respectively. THF occupies all of the large cavities, but it cannot enter the small ones, thus forming a hydrate that contains 5.56 mol % THF (stoichiometric hydrate). Udachin et al.15 were the first to report on binary hydrates of helium or hydrogen with THF. Experimental hydrate equilibrium data for the sII binary He-THF hydrate were also reported by Larionov et al.16 and Yeon et al.17 In a recent study, Papadimitriou et al.18 performed grand canonical Monte Carlo (GCMC) simulations on the sII Received: June 14, 2010 Revised: December 16, 2010 Published: January 21, 2011 1411

dx.doi.org/10.1021/jp105451m | J. Phys. Chem. B 2011, 115, 1411–1415

The Journal of Physical Chemistry B

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Figure 2. Experimental phase equilibrium conditions of the sII HeTHF binary hydrate in the pressure range 2-20 MPa. Lines are guides to the eye only.

Table 1. Pure Component Parameters for the CPA EoS Figure 1. Schematic of the experimental setup (Cailletet apparatus), adopted from ref 22.

b 105

a0

c1

εAB

β

water helium

1.4515 1.6278

0.12277 0.0347

0.67359 -0.0920

16655

0.0692

tetrahydrofuran

6.8339

1.5838

0.8159

substance

binary He-THF hydrate (at pressures up to 500 MPa) to determine the He content of this hydrate. This computational study reported the possibility of simultaneous occupancy of the large cavity by He and THF molecules. The objective of this work is the study of this binary He-THF hydrate. First, we report experimental data for hydrate equilibrium of the stoichiometric (5.56 mol % THF) binary He-THF hydrate in the pressure range 2.6-12.6 MPa. Then a thermodynamic model developed by Martín and Peters19 is used to correlate these data and predict the hydrate equilibrium at higher pressures. This model is based on the van der Waals-Platteeuw statistical thermodynamic theory20 and includes an accurate description of the fluid phases using the cubic-plus-association (CPA) equation of state. Furthermore, this model can calculate the occupancies of He and THF in each type of cavity. These occupancies are compared with similar results obtained from Monte Carlo simulations18 as well as from a different thermodynamic model based on the P-T equilibrium of the hydrate.21 Very good agreement between the three methods is obtained in the pressure range where single occupancy of the small cavities is dominant.

two sets of experimental data, it can be considered that they are in good agreement because the equilibrium pressure of hydrates is very sensitive to the temperature fluctuation. On the other hand, the equilibrium data reported by Yeon et al.17 present a different trend showing that the equilibrium pressures increases very slightly with temperature (within the temperature range 279-281 K), which is a behavior not observed in the other two experimental studies.

2. EXPERIMENTAL DETAILS We investigate the phase behavior of the binary system He-THF. The phase equilibrium transition H þ L þ V T L þ V (H, hydrate; L, liquid water; V, vapor or gas) is visually determined using a Cailletet apparatus (a schematic obtained from ref 22 is shown in Figure 1). At a given temperature, the pressure of hydrate formation/dissociation is measured with an accuracy of 0.005 MPa. The hydrate sample is prepared using a synthetic method in which the global composition of the system is known and equal to 5.56 mol % THF. The temperature of the system is controlled by a thermostat and measured by a platinum resistance thermometer (Pt 100) with an accuracy of (0.02 K. A dead weight pressure balance with accuracy of 0.03% of the reading was used to determine the equilibrium pressures. The experimental results are shown in Figure 2, along with previously reported experimental values from the literature16,17 in the pressure range up to 20 MPa. The results from our measurements present the same trend as those reported by Larionov et al.16 Although there is some deviation between these

3. THERMODYNAMIC CORRELATION The obtained experimental data has been correlated with a fugacity-based thermodynamic model based on the van der Waals-Platteeuw statistical thermodynamic theory.20 This model has been developed by Martín and Peters and is described in detail in ref 19. The CPA equation of state23 was used to calculate the fugacity in the fluid phases, with the pure component parameters and interaction coefficients summarized in Tables 1 and 2. Pure component parameters have been calculated from the critical and PVT properties of pure substances, and interaction coefficients have been obtained by correlation of binary vapor-liquid equilibrium (VLE) data. Since experimental VLE data is not available for the He-THF binary system, the CPA EoS had been correlated with data generated using the predictive Soave-Redlich-Kwong (PSRK) EoS.24 The Langmuir constants required for the calculation of the cage occupancies and the fugacity of the hydrate phase were calculated with the Lennard-Jones (LJ) 6-12 intermolecular potential (Table 3). The LJ parameters of water and THF are

Table 2. Binary Interaction Coefficients for the CPA EoS

a

1412

temperature

AAPD

binary system

kij

range (K)

and ref

H2O-He H2O-THF

-1263.2/T þ 5.5624 -0.35

292.65-296.15 298-373

3.2%36 10.1%37

He-THF

-477.46/T þ 2.2216

298

ref 24a

Correlated to data generated with the PSRK EoS.

dx.doi.org/10.1021/jp105451m |J. Phys. Chem. B 2011, 115, 1411–1415


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Table 3. Lennard-Jones 6-12 Potential Function Parameters ε/kb(K)

σ (Å)

ref

water

102.134

3.564

38

helium

10.23

2.556

18

substance

tetrahydrofuran a

649.27

Estimated with the method of Chung et al.

5.090

Table 4. Interaction Parameters for Each Molecule Used in the GCMC Simulations molecule

atom

σ (Å)

ε (kJ/mol)

H2O

O

3.166

0.6502

He

H He

0.000 2.556

0.0000 0.0850

a

39

THF

C

3.400

0.4577

O

3.000

0.7113

H

2.471

0.0657

Figure 3. Comparison between experimental (b) and correlated (;) binary He-THF hydrate phase equilibrium pressures.

those reported in a previous work,25 whereas those of He are the same used in the Monte Carlo simulations reported in the study of Papadimitriou et al.18 Figure 3 presents a comparison between the hydrate equilibrium pressure predictions of the thermodynamic model and the experimental data measured in this study. The excellent results show that the CPA EoS is a suitable model to describe the phase equilibrium of the binary He-THF hydrate. The average deviation between the experimental and calculated pressures, calculated according to the definition presented in eq 1, corresponds to AAPD = 3.2%. calc exp P P i i Ndata 100 X ð1Þ AAPD ¼ exp Ndata i ¼ 1 Pi where Ndata is the number of experimental points, and the superscripts exp and calc denote the experimental and calculated pressure, P, respectively.

4. MONTE CARLO SIMULATIONS Grand canonical Monte Carlo (GCMC) simulations were performed to determine the distribution of He atoms in the cavities of the sII binary He-THF hydrate. A detailed description of the methodology and extended discussion on the results of these simulations can be found in our previous work.18 Only the most important simulations details are presented here. Simulations were performed on eight (2 2 2) unit cells of sII hydrate containing a total of 1088 rigid water molecules placed at fixed positions in the lattice. The lattice parameter (side length of the unit cell) has a value of 17.31 Å.26 The positions of the oxygen atoms of the water molecules are derived from the X-ray diffraction measurements of Yousuf et al.27 The SPC/E model28 was used to describe water molecules, and the LJ parameters are given in Table 4. The water molecules have a proton configuration with minimum dipole moment, consistent

Figure 4. P-T phase diagram of the sII binary He-THF hydrate. Model extrapolation (;) and comparison with the experimental data. Circles denote the experimental data of Larionov et al.,16 and triangles denote the experimental data obtained in this work.

with the Bernal-Fowler rules.29 3D periodic boundary conditions are applied. Helium molecules are represented by a LJ interaction site, with the parameters ε and σ reported by de Boer30 and given in Table 4. These LJ potential parameters had been previously used to describe the He-H2O interactions in lattice dynamics calculations,10,11 quantum Monte Carlo simulations31 and GCMC simulations.18 Due to its spherical shape and nonpolar nature, no electrostatic interactions were considered for He molecules in our calculations. Quantum effects of He were neglected since our simulations were performed at relatively high temperatures (274-285 K). Finally, the THF molecule is represented following the approach of Alavi et al.32 The LJ parameters of THF are shown in Table 4. Additional details on the application of the GCMC method to binary hydrates with THF can be found in our previous work on binary sII hydrates.33

5. RESULTS AND DISCUSSION The experimental hydrate equilibrium pressures obtained in this study (Section 2) are utilized for the development of a correlative thermodynamic model based on the van der WaalsPlatteeuw statistical theory20 as described in Section 3. In particular, the experimental data are used to calculate the parameters (model calibration) of the thermodynamic model. Once the parameters are available, they can be used to evaluate the predictive ability of the model at conditions outside the range of the parametrization (i.e., extrapolation of the experimental data). Figure 4 shows the results of the model to pressures up to 150 MPa. This pressure value is ∼1 order of magnitude higher than the maximum pressure (i.e., 12.6 MPa) used to obtain the model parameters. Shown also are the experimental data of Larionov 1413



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Figure 5. Average occupancy of the small cavity as a function of pressure (at the corresponding hydrate equilibrium temperature) for the sII binary He-THF hydrate. The dashed line denotes the contribution of only the single occupancy to the average occupancy of the small cavity.

et al.16 The average deviation between the experimental and calculated pressures in this pressure interval is 26%. Given the extent of the extrapolation, the correlative model developed in this study gives very reasonable predictions of the hydrate equilibrium pressure. For an additional evaluation of the aforementioned model, we compare the resulting values for the occupancy of the small cavities with results obtained from GCMC simulations18 and from the thermodynamic model of Papadimitriou et al.21 The latter model calculates the gas content of promoter-stabilized binary hydrates from the equilibrium data of the binary hydrate and the hydrate of the promoter itself. It must be noted that the three methods are developed independently and have completely different theoretical bases. The comparison between the aforementioned approaches for occupancy of the small cavity (512) is presented in Figure 5, where the results are plotted as a function of pressure. At low pressures, very good agreement is observed between the three methods, giving essentially identical results for the average occupancy. As the pressure increases, GCMC simulations give higher occupancy values than those from the other two approaches. This deviation is attributed to the double occupancy of the small cavities. As determined by the GCMC simulations,18 double occupancy is negligible at low pressures (below 50 MPa), but it starts to become significant at higher pressures. For this reason, the discrepancy among the three approaches increases with pressure. In particular, the fraction of doubly occupied cavities is 1% at 50 MPa, 4% at 100 MPa, and reaches 9.5% at 150 MPa. For the pressure conditions of interest to this study (up to 150 MPa), no triply occupied small cavities were observed. A more detailed discussion for the small cavity occupancy at pressures up to 500 MPa is presented in ref 18. Recall that neither the correlative model proposed in Section 3 nor the model of Papadimitriou et al.21 account for the multiple occupancy of any type of cavity. Only the GCMC simulations are capable of predicting the occupancy of the cavities. GCMC simulations allow the separate calculation of the fraction of cavities that are occupied by 0, 1, or 2 gas molecules (assuming that higher occupancies do not occur). Let these fractions be ϑ0, ϑ1, and ϑ2, respectively. Obviously, ϑ0 þ ϑ1 þ ϑ2 ¼ 1 The average occupancy of the small cavity is θ ¼ ϑ1 þ 2ϑ2

ð2Þ ð3Þ

Equation 3 shows that the average occupancy of the small cavity is the sum of two different contributions (i.e., single and double occupancy). The dashed line in Figure 5 shows the contribution of the single occupancy,ϑ1, to the average occupancy, obtained from the GCMC simulations. In that case, excellent agreement with the correlative model is obtained. The difference between these two curves, θ - ϑ1 = 2ϑ2, denotes the contribution of the doubly occupied cavities to the small cavity average occupancy. As observed in Figure 5, this difference is zero for pressures lower than ∼50 MPa and, as expected, starts increasing at higher pressures. The phenomenon of multiple occupancy of hydrate cavities was discovered recently, and since then, it has attracted the attention of the scientific community.34,35 Cage occupancy by multiple guest molecules could have a major impact in terms of storage capacity of hydrate materials,4 since it can increase the gas storage capacity significantly. Concerning the large cavities, both the model of Martín and Peters19 and the GCMC simulations18 conclude that essentially all of them are occupied by one THF molecule. Note also that the model of Papadimitriou et al.21 has as an inherent assumption that all the large cavities are singly occupied by the promoter molecule.

6. CONCLUSIONS This study reported experimental data for the stoichiometric (i.e., 5.56 mol % THF) sII binary He-THF hydrate in the pressure range 2.6-12.6 MPa. A thermodynamic model based on the van der Waals and Platteeuw theory to describe hydrate equilibrium and the CPA equation of state to describe fluid phases was calibrated to correlate the experimental hydrate equilibrium data of the binary He-THF hydrate with excellent results within the pressure range of parametrization and reasonable behavior at extrapolation pressures. The correlative thermodynamic model was used to estimate the small cavity occupancies, and the results were compared with GCMC simulations18 and the recent thermodynamic model based on the P-T equilibrium of the hydrate21 and were found to be in very good agreement for the pressure range where single occupancy of the small cavities is dominant. Deviation in the small cavity occupancy increases as the contribution of double occupancy becomes more important. ’ AUTHOR INFORMATION Corresponding Author

*Fax: þ302106525004. E-mail: [email protected]. Notes §

Visiting scientist.

’ ACKNOWLEDGMENT Partial funding by the European Commission DG Research (Contract SES6-2006-518271/NESSHY) is gratefully acknowledged by the authors. ’ REFERENCES (1) Sloan, E. D.; Koh, C. A. Clathrate Hydrates of Natural Gases, 3rd ed.; Taylor & Francis, CRC Press: Boca Raton, FL, 2008. (2) Sloan, E. D. Nature 2003, 426, 353. (3) Koh, C. A. Chem. Soc. Rev. 2002, 31, 157. 1414



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Experimental and Computational Investigation of the sII Binary He

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