International Conference on Gas Hydrates (ICGH) (6th : 2008)

INVESTIGATION OF THE HYDROGEN STORAGE CAPACITY OF HYDRATES WITH MONTE CARLO SIMULATIONS Papadimitriou, Nikolaos I.; Tsimpanogiannis, Ioannis N.; Stubos, Athanassios K.; Peters, Cor J. 2008-07

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   INVESTIGATION OF THE HYDROGEN STORAGE CAPACITY OF HYDRATES WITH MONTE CARLO SIMULATIONS   Nikolaos I. Papadimitriou1,*  Ioannis N. Tsimpanogiannis1,**  Athanassios K. Stubos1  Cor J. Peters2  1 Environmental Research Laboratory National Center for Scientific Research “Demokritos” Patriarchou Grigoriou and Neapoleos, Agia Paraskevi 15310 GREECE  2 Physical Chemistry and Molecular Thermodynamics Laboratory Faculty of Applied Sciences, Delft University of Technology Julianalaan 136, 2628 BL Delft THE NETHERLANDS   ABSTRACT In the present work Grand Canonical Monte Carlo simulations are implemented in order to evaluate the hydrogen storage capacity of hydrates under a wide range of conditions. Hydrates of sII and sH type with or without promoter have been examined. Concerning hydrates of pure H2, our results show that sII hydrates can store up to 3.3 wt. % H2 and sH up to 3.6 wt. % in the pressure range examined (up to 500 MPa). The small cavities of the sII hydrate as well as the small and medium cavities of the sH hydrate are occupied by one H2 molecule at most. The occupancy of the large cavities of both types of hydrates highly depends on pressure. At 400 MPa, the average occupancy of the large cavity of the sII hydrate is 2.8 while the respective value for the sH hydrate is 5.5. Binary hydrates of H2 and promoter present a reduced H2 uptake (less than 1.1 wt. % for sII and less than 1.4 wt. % for sH hydrates). There rather limited values are attributed to the single occupancy of the cavities that are not occupied by the promoter molecules. Furthermore, the results of our simulations do not support the suggestion that the H2 uptake of the binary (sII) H2-THF hydrate can be “tuned” by adjusting the THF concentration in the equilibrium solution. Finally, binary sH hydrates with the promoter occupying the medium instead of the large cavities could be an alternative approach to increase hydrogen uptake.    * Corresponding author: Phone: +302106503416 FAX: +302106525004 e-mail: ** Visiting scientist: e-mail: INTRODUCTION Clathrate hydrates have been involved in a variety of industrial or scientific/academic applications [1, 2]. Primary interest in clathrate hydrates arises from their capacity to store large volumes of gas. Hydrates have been considered as an alternative material for storing and/or transporting energy-carrier gases like methane and hydrogen [3]. Until recently, it was believed that H2 was too small to stabilize the hydrate cages and therefore, could not form hydrates by itself [4]. This perception changed when initially Dyadin et al. [5] and later Mao et al. [6] synthesized pure H2 hydrate that was found to be of the sII type. Pure H2 hydrate is stable only at very high pressures or low temperatures (e.g. at 220 MPa and 280 K or at ambient pressure and 145 K [6]). Initial estimates of the H2 content of this new material reached 5.0 wt. % and this was considered a significant advancement in the field of hydrogen storage as it was very close to the U.S. DOE target (6 wt. % for year 2010) for application of H2 in transportation. This high H2 uptake was attributed to the occupancy of the cavities of the sII hydrate crystal by more than one H2 molecule. Specifically, the small cavities were believed to be occupied by two H2 molecules and the large ones by up to four H2 molecules [6]. These findings were also confirmed by results from Density Functional Theory simulations [7]. However, more recent experimental [8] and computational [9, 10] works questioned the double occupancy of the small cavities though confirming the quadruple occupancy of the large ones (at 77 K). While the actual H2 content of pure H2 hydrates was still an open issue, Florruse et al. [11] managed to stabilize a binary H2 hydrate at low pressures (down to 5 MPa) and at close-to-ambient temperature (274 K) using tetrahydrofuran (THF) as a promoter. THF molecules occupy the large cavities of the sII hydrate offering stability to the crystal but at the cost of a reduced H2 content since only the small cavities remain available to the H2 molecules. Later, Lee et al. [12], and Kim et al. [13] suggested that the H2 content of the binary H2- THF hydrate can be “tuned” by suitably adjusting the THF concentration in the equilibrium solution. In this case, H2 content could reach up to 4.1 wt. % when an optimal THF concentration of approximately 0.15 mol % was used [12]. This “tuning” effect was also observed in other types of binary hydrates [14]. However, more recent experimental data based on a variety of experimental techniques (gas release measurements [15, 16], NMR spectroscopy [15] and Raman spectroscopy [17, 18]) did not confirm this suggestion. These works reported various values of H2 content ranging from 0.3 up to 1.0 wt. % but in all cases it was found to be constant regardless of the THF concentration in the solution. Also, recent results from Grand Canonical Monte Carlo (GCMC) simulations do not support the “tuning” concept [10]. The most recent advancement in H2 hydrates is the synthesis of sH hydrates by Strobel et al. [19], and Duarte et al. [20] by using several organic promoters including methyl-cyclohexane (MCH), 1,1-dimethyl-cyclohexane (DMCH), and methyl-tert-butyl-ether (MTBE). When 1,1- dimethyl-cyclohexane (DMCH) is used as the promoter, the sH H2 hydrate remains stable at pressures down to 60.1 MPa (at 274.7 K) [20]. The sH hydrate crystal contains three small cavities (512 with average radius 3.91 Å), two medium cavities (435663 with average radius 4.06 Å) and one large cavity (51268 with average radius 5.71 Å) per unit cell [1, 4]. The promoter molecules occupy the large cavities and H2 molecules enter the small and the medium ones. The size of the small and medium cavities of the sH hydrate is approximately the same as the size of the small cavity (512 with average radius 3.91 Å) of the sII hydrate. If single occupancy of the small and medium cavity is assumed, sH hydrates can reach a H2 uptake of 1.4 wt. %. This value is higher than the corresponding value of binary sII hydrates (1.1 wt. %), however, it remains low relatively to the U.S. DOE targets in order the hydrates to be considered as storage materials for practical application. To this day there is experimental evidence that pure H2 forms sII hydrate, however, no experimental evidence exists that it can form sH hydrate. Note, however, that other small molecules (sII hydrate formers), such as nitrogen [21] and argon [22], can form sH hydrates by themselves at higher pressures exhibiting a “sII-to-sH” structural transformation. In the case of a possible sH hydrate of pure H2, a gross estimate of the H2 content could reach up to 5.6 wt. % [19]. This content value is based on the size of H2 molecule relatively to the size of the large cavity of the sH hydrate. It can be expected that up to eight H2 molecules could possibly be accommodated in this cavity. Apart from pure H2 sH hydrate, another probable advancement could be the synthesis of binary H2 sH hydrates where the promoter molecules would occupy the medium instead of the large cavities. In this case, the expected H2 content would increase considering the fact that the medium cavities are occupied by just one H2 molecule while the large could be occupied with up to eight H2 molecule. The determination of the occupancy of each type of cavity in either sII or sH hydrates is an issue of crucial importance for the evaluation of the hydrogen storage capacity of hydrates. An accurate calculation of the H2 content of hydrates from experimental measurements is a demanding and difficult task. For this reason, molecular simulations could have an important contribution in this direction. The main objective of this work is to apply the Grand Canonical Monte Carlo (GCMC) methodology to calculate the H2 content of several hydrates of sII and sH type, either with or without promoter. GCMC method seems to be a very effective approach for the study of H2 content of hydrates. Contrary to the classical theory of Van der Waals and Platteeuw (VDWP) [23], there is no need for any assumptions concerning the number of gas molecules enclosed per cavity. VDWP theory is valid only when each cavity is occupied by one gas molecule at most. With GCMC simulations, the occupancy of each type of cavity occurs as a straightforward result. Moreover, the GCMC approach allows for the interactions between gas molecules themselves to be accounted for, in addition to the interactions between the gas molecules and the lattice of water molecules. However, the GCMC method, as applied in this work, cannot provide any information about the stability of the hydrate crystal, which must be explicitly assumed. In this work, the traditional and well- established GCMC approach developed by Metropolis et al. [24] has been used to study the hydrogen storage capacity of pure sII and sH hydrates and binary hydrates with promoters including THF and MCH. A detailed presentation of the method is beyond the scope of this paper and can be found in the book of Allen and Tildesley [25], as well as in published studies that utilized this method for simulations on hydrates [10, 26].  SIMULATION DETAILS Simulations on sII hydrates were performed on one unit cell with a lattice constant of 17.047 Å [6]. It has been shown [10, 26] that the use of one unit cell yields almost identical results as if eight (2×2×2) unit cells were used. Positions of the oxygen atoms of water molecules are taken from the X-ray diffraction data of Yousuf et al [27]. In the case of sH hydrates, a simulation box of 27 (3×3×3) unit cells was used that contained 918 water molecules in total. The lattice parameters used in this work were those proposed by Strobel et al. [19], i.e. a = 12.203 Å and c = 9.894 Å. In this work 3-D periodic boundary conditions were applied. In both sII and sH cases, among all proton configurations complying with the “ice rules”, the one with the minimum total dipole moment was selected for the simulations. For the case of sH hydrates we used the proton configuration proposed by Okano and Yasuoka [28] who have performed a dipole moment and potential energy minimization for more than 1.2×106 proton configurations. Water molecules are simulated with the SPC/E model [29]. This model has been accurately fitted to several water properties and it is the most widely used water model for simulations on hydrates [9, 10, 26, 30-32]. According to this model, each water molecule bears a Lennard-Jones interaction site on the oxygen atom to represent Van der Waals interactions, as well as partial charges to account for electrostatic interactions. Parameters of the SPC/E model are shown in Table 1. H2 molecules are represented by one Lennard- Jones site placed in the middle of the H-H bond and partial charges, two positive charges on each hydrogen atom and the double negative charge in the middle of the H-H bond. Interaction parameters for the H2 molecule have been derived from gas and solid phase experimental data [33] and are also shown in Table 1. Finally, the geometry of THF molecules has been optimized prior to the simulations using the AMBER force field [34] as proposed by Alavi et al. [30]. The MCH molecule was optimized using the Universal Force Field (UFF) [35]. Lennard-Jones parameters for interactions between different atoms were calculated using the Lorentz-Berthelot combining rules. The Ewald summation technique was used for the long-range electrostatic interactions and a cutoff distance of 20 Å was applied to both Van der Waals and electrostatic interactions. Each GCMC run includes 107 trial “moves” of creation, destruction or rotation of a H2 molecule, randomly selected with equal probability (33.3 % each). The maximum translation distance is set to 0.5 Å. After the run, every H2 molecule of each configuration examined is assigned to the  molecule atom σ (Å) ε (kJ/mol) charge (e) O 3.166 0.6502 -0.8476 H2O H 0.000 0.0000 +0.4238 H 0.000 0.0000 +0.4932 H2 middle of H-H bond 3.038 0.2852 -0.9864 Table 1. Interaction parameters and partial charges for each molecule.   nearest center of cavity. In this way, the average occupancy of every cavity is calculated. For the case of binary hydrates simulations, two different approaches have been followed depending on the solubility of the promoter in water. For MCH, which is practically insoluble in water, a GCMC simulation for the pure promoter at the conditions in question was carried initially and the lowest energy configuration was then used for the simulations of H2 adsorption. During the simulations the MCH molecules were considered fixed. On the other hand, THF is completely soluble in water and its concentration could have an important role in the adsorption process, if the concept of “hydrate tuning” is valid. In our simulations, THF dissolved in water is considered to be a second “adsorbed gas” (apart from H2) and the calculation of its fugacity is based on the theory of activity coefficient [36]:  1exp ( ) s Ps s LP f x P V p dp RT γ φ ⎛ ⎞= ⋅ ⋅ ⋅ ⋅ ⎜ ⎟⎝ ⎠∫  (1)  where γ is the activity coefficient, x the mole fraction of THF in the aqueous solution, Ps is the vapour pressure of pure THF at temperature T, φs is the fugacity coefficient of pure saturated gas THF at temperature T, R the gas constant, and VL is the molar volume of liquid THF as a function of pressure. The exponential term is the Poynting correction factor that accounts for the effect of high pressure on the fugacity of liquids. The activity coefficient is calculated from the NRTL equation [36], with parameters derived from VLE equilibrium data and recommended by Gmehling et al. [37]. For the analytical calculation of the integral in Eq. (1), THF density data of Back and Woolf [38] were fitted using the modified Tait equation that accurately describes the compressibility of liquids at high pressures [39]. It has been assumed that THF concentration in the solution remains constant and equal to the initial concentration during any simulation.  RESULTS AND DISCUSSION We have performed several series of GCMC simulations for sII and sH pure H2, and binary H2- promoter hydrates under a wide range of conditions (temperature, pressure, promoter concentration). The results will be presented and discussed in the following order: 1. sII and sH hydrates of pure H2. 2. Binary sII and sH hydrates of H2 with promoter at stoichiometric ratio. 3. Binary sII H2-THF hydrates with varying THF concentration (to investigate the so called “tuning effect”).  Pure H2 hydrates (sII and sH type) The H2 content of both sII and sH hydrates is presented in Figure 1. Within the pressure range examined (0.1 – 500 MPa) the sII hydrate cannot store more than 3.3 wt. % H2 while the sH hydrate no more than 3.6 wt. %. Although such values highlight the potential of these materials for application in hydrogen storage, they are still far from the requirements for use in practical applications (e.g. transportation). This deficiency becomes more pronounced if one considers the high pressures required in order those storage values to be achieved. Comparing the two types of hydrates, it is obvious that the sH hydrate presents an increased hydrogen storage capacity relatively to the sII hydrate. More specifically, the sH hydrate can store approximately 5 – 20 % larger amounts of H2 gravimetrically and up to 30 % volumetrically, than the sII hydrate. Apart from the overall H2 content, our GCMC simulations can provide information on the exact occupancy of each type of cavity. The small cavities of the sII hydrate are found to be singly occupied with virtually no occurrences of double occupancy. Although this type of cavity had been initially suggested [6] to be capable of  Figure 1. H2 content of pure H2 sII and sH hydrates as a function of pressure at 274 K.   Figure 2. Occupancy ratio (fraction of cavities occupied by the specified number of H2 molecules) of the medium cavities of the hypothetical pure H2 sH hydrate at 274 K.  accommodating two H2 molecules, the most recent experimental [8] and computational [9, 10] works do not give evidence in favor of double occupancy. Concerning the small and medium cavities of the sH hydrate, they are also found to be singly occupied. This fact is rather expected as these cavities are of about the same size as the small cavity of the sII hydrate. However, it should be mentioned that a small fraction (up to 5%) of doubly occupied medium cavities was observed, as shown in Figure 2, at high pressures (400 – 500 MPa) while the fraction of doubly occupied small cavities remained negligible (less than 0.1%).   Figure 3. Occupancy ratio of the large cavities of the pure H2 sII hydrate at 274 K.   Figure 4. Average occupancy of the large cavities of the hypothetical pure H2 sH hydrate at 274 K.  Next, we examine the occupancy of the large cavities of sII and sH hydrates. The results of our simulations are shown in Figures 3 and 4. In both cases, the occupancy is highly dependent on pressure. For sII hydrate, the majority of the large cavities seem to be doubly occupied at pressures below 340 MPa while triply occupancy becomes dominant at higher pressures as shown in Figure 3. A significant fraction of quadruply occupied cavities is also present. These results are in very good agreement with the GCMC results of Katsumasa et al. [40]. However, they do not confirm the initial hydrogen storage estimates of Mao et al. [6]. At a pressure of 200 MPa, Mao et al. had reported double occupancy of the small cavities and quadruple of the large ones.  Number of H2 molecules per cavity Pressure (MPa) 0 1 2 3 4 5 6 7 8 50 2.9 22.0 44.7 25.8 4.4 0.2 0.0 0.0 0.0 100 0.2 4.7 26.2 44.3 21.9 2.7 0.1 0.0 0.0 200 0.0 0.1 2.8 21.6 46.2 26.3 2.9 0.0 0.0 300 0.0 0.0 0.1 3.8 27.3 50.2 17.5 1.1 0.0 400 0.0 0.0 0.0 0.4 8.1 41.1 42.2 8.1 0.2 Table 2. Occupancy ratios (%) of the large cavity of the hypothetical pure H2 sH hydrate at several pressures.  At this pressure, according to the results of the present work, the fraction of quadruply occupied large cavities is just 0.2 % with the majority of the cavities (65 %) being doubly occupied, some of them being singly (22 %) and triply (12 %) occupied and a minor fraction (0.4 %) being empty. With such occupancy of the large cavities and 95 % filling of the small ones, the H2 content of this hydrate is 2.4 wt. % which is half of the value calculated by Mao et al. (4.8 wt. %) [6]. Finally, we investigate the occupancy of the large cavity of the sH hydrate that is the largest cavity, among all cavities that are used as building blocks in sI, sII, and sH hydrates. Although the sH hydrate of pure H2 has not been experimentally stabilized yet, this numerical study can give important information on the possible hydrogen storage efficiency of this hydrate. As can be seen in Figure 4, the average occupancy of this cavity reaches the value of 6.0 at about 470 MPa. Due to its shape and size, this cavity was assumed to be able to accommodate up to eight H2 molecules [41]. However, a more accurate investigation of the possible H2 occupancy had not been carried out previously, although Alavi et al. [42] had used Molecular Dynamics simulations to examine the stability of sH hydrates of noble gases with several numbers of guest molecules per cavity. Table 2 offers a more detailed description of the number of H2 molecules encaged in this cavity at various pressures. In the pressure range under examination (up to 500 MPa), the large cavity of sH hydrate has been observed to accommodate even eight H2 molecules.  Binary sII and sH hydrates with promoters at stoichiometric ratio In this Section, we examine binary sII and sH hydrates where a promoter is used to stabilize the material at lower pressures than in the case of pure hydrates. Binary H2-THF hydrate (sII type) has been found to be stable at pressures above 5 MPa (at 274 K) [11]. The H2 content of the binary H2-THF hydrate, as a function of pressure, as calculated by our GCMC simulations, is shown in Figure 5. Unfortunately, this material cannot store more than 1.1 wt. % H2. This reduced H2 uptake is completely justified because the large cavities are exclusively occupied by THF molecules. What can be concluded from Figure 5 is that the “adsorption isotherm” of this material is a Langmuir type curve with a plateau at 1.1 wt. %. This value corresponds to the scenario where all small cavities are occupied by just one H2 molecule. This behavior does not change even at higher pressures up to 350 MPa. So, our results confirm recent works [17, 18, 30] reporting that the small cavities of the sII hydrate are unable to accommodate more than one H2 molecule. Similar simulations were performed for a binary sH hydrate where MCH was used as the promoter. The results are also presented in Figure 5 and reveal a similar behavior as in the case of H2-THF hydrate. H2 content does not exceed 1.4 wt. % which corresponds to all small and medium cavities occupied by one H2 molecule. This finding is consistent with recent Molecular Dynamics simulations of Alavi et al. [43]. This value of H2 content also confirms the estimations of Strobel et al. [19]; however, an experimental measurement of the actual H2 content of this hydrate is still required. From the GCMC simulations of this work we find that the binary H2-MCH sH hydrate presents an increased H2 content by up to 35 %, when compared with the binary H2-THF sII hydrate. This finding is in agreement with the estimates by Strobel et al. [19] who stated that the binary sH hydrate could be up to 40 % more efficient than the binary sII hydrate in storing hydrogen. However, both of these materials seem to have limited prospects of being used for hydrogen storage.  Figure 5. Hydrogen content as a function of pressure for the stoichiometric (5.56 mol % THF) binary H2-THF sII hydrate, and the binary H2-MCH sH hydrate at 274 K. Dashed lines denote the content of a sII hydrate with all small cavities singly occupied (red line) or a sH hydrate with all small and medium cavities singly occupied (blue line).   Figure 6. Hydrogen content as a function of pressure (at 274 K) for a hypothetical binary H2-promoter sH hydrate with the promoter (MW: 20, 50, 100) encaged in the medium cavities.  Another conclusion that can be drawn from Figures 1 and 5 is that the presence of the promoter in the large cavities hardly affects the occupancy of the remaining cavities. Probably, the interactions between H2 and promoter molecules are insignificant comparatively to the interactions between H2 molecules and the solid lattice of water molecules. This fact can lead to the assumption that the gravimetric H2 content of the hydrate depends mostly on the molecular weight of the promoter and not on its chemical structure.  Figure 7. H2 content of the binary H2-THF hydrate as a function of THF concentration, at 274 K and 12 MPa.  Based on this assumption, we have attempted a parametric analysis of a hypothetical binary sH hydrate where a promoter (of varying molecular weight) occupies the medium instead of the large cavities. A promoter of suitable size to fit the medium cavity is expected to have a molecular weight of approximately 20-100. The results are shown in Figure 6. This hydrate obviously presents a higher H2 content than the binary H2-MCH hydrate (where the promoter is in the large cavities) but it is considerably lower than that of the pure H2 sH hydrate. Assuming a promoter with a molecular weight of 50, one should expect a H2 content of 2.0 wt. % at 220 MPa.  Non-stoichiometric binary H2-THF hydrate Finally, we have investigated the possibility of “tuning” the H2 content of the binary H2-THF hydrate. This concept was suggested by Lee et al. [12] and Kim et al. [13] who claimed that if the THF concentration in the formation solution is less than the stoichiometric (5.56 mol %), then a binary hydrate is formed where THF molecules occupy only some of the large cavities and the rest of the large cavities can be occupied by H2 molecules. This effect could increase the H2 uptake up to 4.1 wt. %. However, our results do not confirm this concept and give evidence in favor of the recent experimental data of Strobel et al. [15], as shown in Figure 7. This binary hydrate seems to have a constant H2 content of 0.3 wt. % at 274 K and 12 MPa regardless of the THF concentration. Until a concrete experimental confirmation of this “tuning effect” occurs, the binary H2-THF hydrate should be considered a material with limited hydrogen storage capacity.  CONCLUSIONS We have utilized Grand Canonical Monte Carlo simulations to evaluate the hydrogen storage capacity of several pure and binary hydrates under a wide range of conditions. In this approach, hydrate formation is treated as a process of gas adsorption in a solid. According to our results, both sII and sH hydrates of pure H2 present a significant H2 uptake (3.3 and 3.6 wt. % respectively) that justifies further research and development towards the use of the specific materials for hydrogen storage. Note, however, that pressures as high as 400 MPa are required in order these materials to achieve such values of H2 content. On the other hand, binary (sII or sH) hydrates with promoters, seem to have very limited prospects of application in hydrogen storage in the future because the presence of the promoter sets an upper limit to their H2 uptake that is far below the target value. In particular the upper limit is 1.1 wt. % for sII and 1.4 wt. % for sH hydrates (with single occupancy of the small/medium cavities). However, a promising advancement could be the synthesis of binary sH hydrates with the promoter occupying the medium instead of the large cavities. 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