Experimental Measurements and Modeling of the Dissociation

Article pubs.acs.org/jced

Experimental Measurements and Modeling of the Dissociation Conditions of Tetrabutylammonium Chloride Semiclathrate Hydrates in the Presence of Hydrogen Ayako Fukumoto,† Didier Dalmazzone,*,† Patrice Paricaud,† and Walter Fürst† †

ENSTA-ParisTech, UCP, 828 Boulevard des Maréchaux, 91762 Palaiseau, France ABSTRACT: Dissociation conditions of hydrogen semiclathrate hydrates with tetrabutylammonium chloride (TBAC) are measured using a differential scanning calorimeter at the TBAC weight fraction of 0.10, 0.20, 0.35, and 0.50 in the pressure range up to 15.5 MPa. The hydrogen storage capacity of TBAC semiclathrate hydrate is estimated with measured equilibrium data, dissociation enthalpies, and the Clapeyron equation. The amount of hydrogen stored in the semiclathrate hydrate is found to be 0.11 wt % at 15.5 MPa. The model proposed by Paricaud [J. Phys. Chem. B 2011, 115, 288−299] is applied to predict the dissociation condition of the H2 semiclathrate hydrate with TBAC. The parameters in the model have been determined by describing the liquid−vapor−hydrate three phase lines measured in this work and from the literature. The hydrogen storage capacity predicted by the model is in excellent agreement with the experimental value.

1. INTRODUCTION Clathrate hydrates are crystal compounds consisting of water and gas molecules such as CO2, N2, CH4, H2, etc. Water molecules form cage-like structures with hydrogen bonds, and gas molecules are trapped in the cages. Recently, clathrate hydrates, in particular, semiclathrate hydrates have been studied intensively for purposes of gas storage and gas separation. Classical gas hydrates are stable only at low temperature and high pressures. For instance, the liquid−vapor−hydrate (L−V−H) equilibrium of H2 hydrate is about 10 °C at 520 MPa.1 This is not favorable for an industrial application for gas storage/separation. Semiclathrate hydrates are formed by adding additives in water such as tetrabutylammonium bromide (TBAB). The equilibrium conditions of the semiclathrate hydrate are closer to ambient: they are at about 13 °C at 5 MPa2 for H2 semiclathrate hydrate with TBAB. Unlike clathrate hydrates, cage-like structures of semiclathrate hydrates consist not only of water molecules but also of the anions of the additives. Additionally, the cations of the additives are embedded in relatively large cages, and gas molecules are trapped in small cages.3 H2 semiclathrate hydrates have been investigated as possible hydrogen storage materials. The equilibrium conditions were investigated for systems of H2+H2O with TBAB,4−6 tetrabutylphosphonium bromide (TBPB),7 and tetrabutylammonium chloride (TBAC).7,8 However, the data are still limited and further studies are required to better characterize these systems. The purpose of our study is to develop a reliable thermodynamic model for the design of operation units involving gas semiclathrate hydrates for gas separation and storage applications. In this study, we focus on H2 semiclathrate hydrates with TBAC. The dissociation conditions of the semiclathrate hydrate are measured by a differential scanning © XXXX American Chemical Society

calorimeter. Hydrogen storage capacity is estimated using the measured equilibrium data, dissociation enthalpies, and the Clapeyron equation. The new data are described by the thermodynamic model proposed by Paricaud.9 Moreover, the hydrogen storage capacity is estimated as a function of the concentration of TBAC. This paper is organized as follows. First, experimental details are described. The thermodynamic approach is recalled briefly. Results of the experiment and modeling are found in section 4.

2. EXPERIMENTAL SECTION 2.1. Materials and Apparatus. TBAC monohydrate (w = 0.97) purchased from Fluka was used without further purification. The solutions were made with freshly distilled and degassed water. The samples were made at TBAC weight fraction (wTBAC) of 0.10, 0.20, 0.35, and 0.50. The mass of samples were measured with an electronic mass comparator with a precision of ± 0.01 mg. Hydrogen with a purity of 99.9999 % was purchased from Linde. The information on the substances used in the experiment is summarized in Table 1. Dissociation temperatures of semiclathrate hydrate were measured using a microdifferential scanning calorimeter (μDSC VII, Setaram). Schematic of experimental apparatus is shown in Figure 1. There were two hastelloy cells in the same temperature-controlled furnace equipped in the micro-DSC. Special Issue: In Honor of E. Dendy Sloan on the Occasion of His 70th Birthday Received: July 1, 2014 Accepted: September 12, 2014

A

dx.doi.org/10.1021/je5006104 | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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shown in Figure 2. A negative peak exhibited in the flow obtained at wTBAC = 0.35 represents a dissociation of the semiclathrate

Table 1. Information of Substances Used in the Experiment name TBAC monohydrate hydrogen

chemical formula

purity

source

[CH3(CH2)3]4NClH2O

0.97 in mass

Fluka

H2

0.999999 in mole

Linde

One cell had the sample solution inside and the other was empty as a reference. Hydrogen was supplied from a cylinder to the sample cell via a simple stage pressure regulator, which was used to control pressure. Pressure was measured by a Druck gauge (0 MPa to 70 MPa) with an error of ± 0.04 MPa. A cooling bath was used to remove the heat from the micro-DSC during the measurements. The calibration of the micro-DSC was carried out in the temperature range from 233 K to 373 K using high purity gallium and naphthalene at heating rates of (0.2, 0.5, and 1.0) K·min−1. We used ice to determine the uncertainty of the measured phase change temperatures and enthalpies, which were found to be ± 0.04 K and ± 3 %, respectively. 2.2. Experimental Procedure. The sample cell, which contained about 50 mg of the solution, was flushed with hydrogen for three times to remove air, and pressurized up to the desired pressure. To maximize the production of semiclathrate hydrate in the system, a multicycle-crystallization method was adopted. Following are the processe steps of this method: (1) temperature of the furnace was cooled from room temperature to 253.15 K at a heating rate of −3 K·min−1. (2) The temperature was kept at 253.15 K for 10 min, and then increased to a temperature lower than the dissociation temperature of the semiclathrate hydrate at a heating rate of 4 K·min−1. (3) After being kept at the temperature for 10 min, the furnace was again cooled to 253.15 K at a heating rate of −3 K·min−1. Steps 2 and 3 were repeated for at least eight times. A detailed description of the method can be found in previous works.10−13 The dissociation temperatures were measured by two schemes; dynamic DSC and stepwise DSC for congruent and incongruent melting, respectively. For the samples which have congruent melting points, the dynamic method was adopted. A typical heat flow profile obtained by the dynamic method is

Figure 2. Dynamic DSC heating profile for the H2O+TBAC system at atmospheric pressure with different concentrations of TBAC. The heating rate is 0.5 K·min−1.

hydrate. The dissociation temperature, which corresponds to the onset temperature of the peak, was determined by an intersection point of a baseline and a tangent at an inflection point. For samples with incongruent meltings, this determination of the dissociation temperature requires further correction to give accurate results. A heat flow profile of a sample at wTBAC = 0.20, which melts incongruently, is shown in Figure 2. The first peak, which is at around 274 K, is the melting of the eutectic mixture of ice and TBAC semiclathrate hydrates, and the second one, which is at around 286 K, is due to the progressive melting of the semiclathrate hydrate. Since the phase transition is nonisothermal, the sample should be scanned at different heating rates to determine the dissociation temperature by the dynamic method. At each heating rate, the peak points or inflection points of the progressive peaks should be measured to plot them as a function of the heating rate. The extrapolation to null heating rate should be the best estimated dissociation temperature.14,15 Lin et al.16 investigated the accuracy of DSC measurements with

Figure 1. Schematic diagram of experimental apparatus. B



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cations, anions, and water, respectively. For TBAC semiclathrate hydrate, vC = vA = 1, and vw is the hydration number of the hydrate phase. Here, the semiclathrate hydrate can have different types of structures depending on the TBAC concentration in the solution. The hydration numbers of TBAC semiclathrate hydrate were reported by Aladko and Dyadin17 as vw = 32, 30, and 24. Δg0 can be expressed as

TBPB semiclathrate hydrate at atmospheric pressure with both schemes. They mentioned that despite the large time cost, the stepwise DSC has a higher accuracy than the dynamic DSC scheme for incongruent meltings. Therefore, we adopted the stepwise method for the samples which have incongruent melting points. Figure 3 shows temperature and heat-flow profile

Δg 0 Δg 0(T0 , P0) Δh0 ⎛ T ⎞ Δv 0 = (P − P0) + ⎜1 − ⎟ + RT RT ⎝ T0 ⎠ RT RT0 (2)

by assuming that the difference of the heat capacity between hydrate and liquid phases is negligible. Here, Δv0 is a parameter which describes the effect of pressure on the melting point of the hydrate phase. It is given as Δv0 = −30 cm3·mol−1, which was the value previously determined for TBAB semiclathrate hydrate.9 Δh0 is an enthalpic parameter, and T0 is the melting point of the hydrate at congruent melting and at atmospheric pressure P0 = 0.101325 MPa. Δg0 (T0, P0) is a constant parameter which can be calculated by eq 1 and 2 at stiochiometric composition. The melting temperature of the semiclathrate hydrate at a given TBAC concentration and pressure P can be calculated by combining eq 1 and 2. The dissociation enthalpy per mole of TBAC (Δhdis) at P0 is given by

Figure 3. Temperature and heat flow profiles during the stepwise method at wTBAC = 0.20 and atmospheric pressure. Black line and gray line indicate temperature and heat flow, respectively. Gray dashed line is a baseline.

Δhdis = Δh0 − RT 2

during the stepwise method at wTBAC = 0.20. Each step has an endothermic peak, which was induced by the temperature increment and the dissociation of the semiclathrate hydrate. The step, at which the dissociation was entirely completed, was determined at 286.2 K. For the dynamic DSC scheme, temperature of the furnace was raised from 253.15 to 293.15 K at a heating rate of 0.5 K·min−1. To confirm the reproducibility, the measurement was conducted twice for each sample. For the stepwise DSC scheme, we first scanned the sample by the dynamic method to roughly estimate the approximate dissociation temperature, which corresponds to a peak point or inflection point of progressive melting. The sample was frozen again at 253.15 K, and then heated at 1 K· min−1 to a temperature which is at most 1 K lower than the roughly estimated dissociation temperature. Temperature was increased by 0.1 K with a time intervals of 3 h between each step.

+ νA ln(xAγA ) + νw ln(x wγw ))

(3)

The parameters T0 and Δh for the TBAC+H2O binary system were previously determined by Fukumoto et al.18 and are reported in Table 2. 0

Table 2. Parameters for TBAC Semiclathrate Hydratea vw

T0/K

Δh0/kJ·mol−1

ni

30 3 Vcell ij ·10 /m

εcell ij /k/K

32 30 24

287.5 288.1 287.8

170.5 154 130

2 2 1

0.013 0.013 0.013

1780 1780 2000

vw is hydration number, T0 and Δh0 are temperature at the congruent melting at atmospheric pressure and enthalpic parameter, respectively. ni is number of D cages per a TBAC molecule. Vcell ij is free volume of gas molecule j inside cavity i. εcell ij is the depth of the square-well cell potential. a

3. COMPUTATIONAL METHODS The thermodynamic model used in this study is identical to the model proposed in ref 9. Therefore, we only recall the main working equations of the model. The reader can find a detailed explanation of the model in ref 9. 3.1. Solid−Liquid Equilibrium (SLE) between the Electrolyte Solution and Hydrate Phases. Paricaud9 derived the SLE condition for semiclathrate hydrate by minimizing the total Gibbs free energy under the constraint that the composition of the hydrate phase is fixed. The SLE condition is expressed as

3.2. Thermodynamic Model for Gas Semiclathrate Hydrates. The Gibbs free energy of the semiclathrate hydrates, which are partially filled with gas molecules, per mole of TBAC can be written as19 g

Δg 0 = + νC ln(xCγC) + νA ln(xAγA ) + νw ln(x wγw ) RT RT

Δgdis

=0

∂ (νC ln(xCγC) ∂T

hyd,F

=g

hyd, β

Ncav

+ RT ∑ ni ln(1 − i=1

Ng

∑ Yij) j=1

(4)

where ghyd,F and ghyd,β are the Gibbs free energy of the filled and empty hydrate phases, respectively. ghyd,β can be calculated as the same way as presented in the previous section. ni is the number of cage-type i per mole of TBAC. Ncav and Ng are the number of types of cavity and gas, respectively. Yij is the occupancy fraction of cavity i by gas molecule j. In this study, it is assumed that one cage can only host one H2 molecule. Yij is expressed as

(1)

where Δgdis is the dissociation Gibbs free energy per mole of TBAC, which equals 0 at equilibrium. Here, R and T are the ideal gas constant and the temperature, respectively. v, x, and γ are stoichiometric coefficient, mole fraction, and the activity coefficient, respectively. The subscripts C, A, and w indicate C



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Table 3. SAFT-VRE Parameters for Pure Components and TBAC Salta compounds

m

σ·1010/m

ε/k/K

λ

H2O H2 TBA+/Cl−

1 1 1

3.036 2.52 3.55

253.3 24.94 450

1.8 1.5 1.2

C/K2

sites

εHB/k/K

kHB·1030/m3

ref

2H+2E no site

1365.92

1.0202

21, this work 18

1.0·105

m is number of chained hard spheres. σ, ε, and λ are diameter of a sphere, depth, and range of a square-well potential, respectively. εHB and kHB are the interaction energy of the sites and the bonding volume, respectively. C describes the temperature dependency of εw‑ion.

a

Yij =

of εw‑ion, which is adjusted on the SLE data of semiclathrate hydrate binary system. The parameters for TBAC were previously obtained by Fukumoto et al.,18 and are listed in Table 3. The square-well potential of depth εij, diameter σij, and range λij are used to describe the interaction between the segments of i and j. The Lorentz−Berthelot combining rules are used for εij and σij with a binary parameter kij. For λij, a simple combining rule is applied with another binary parameter lij.

Cijf j N

1 + ∑k =g 1 Cikfk

(5)

where Cij is the Langmuir constant, and f j is the fugacity of gas molecules j in the fluid phases. Cij can be calculated by approximating the potential between a cage and a gas molecule by square-well intermolecular potentials: Cij =

⎛ ε cell ⎞ 4π cell ij ⎟ V ij exp⎜⎜ ⎟ kT kT ⎠ ⎝

εij =

(6)

Here, Vcell ij is the free volume of a gas molecule j inside a cavity i, εcell is the depth of the square-well cell potential, and k is the ij Boltzmann constant. The equilibrium condition can be expressed as Ng

=

∑ ni ln(1 − ∑ Yij) − i=1

j=1

(7)

The compositions of the vapor and liquid phases are obtained by a flash calculation to solve the vapor−liquid equilibrium. The melting temperature of gas semiclathrate hydrate at a given pressure and composition is calculated by finding a L−V−H three-phase equilibrium. The compositions of the fluid phases are determined with the SAFT-VRE model at an initial temperature T. The obtained values are substituted for eq 7. T is changed iteratively until eq 7 is satisfied. Here, the mass of the semiclathrate hydrate phase is considered to be negligible at equilibrium. 3.3. SAFT-VRE Equation of State. The thermodynamic properties of fluid phases are obtained by the SAFT-VRE model.20 In this model, molecules i are described as chains of mi hard spheres of diameter σi. Ions are modeled as charged hard spheres. A water molecule is modeled as a hard sphere with four association sites in order to describe hydrogen-bonding. Two donor sites H and two sites E represent hydrogen atoms and the lone pairs of the oxygen, respectively. Further details of the description of water can be found elsewhere.9,21,22 The parameters for H2O and H2 are listed in Table 3. For simplicity of the model, the dispersion forces between ions are neglected, and only the Coulombic interactions are considered. Also, all electrolytes are assumed to be fully dissociated. The interaction of water−ion solvation is described by a short-range square-well potential of range λw‑ion, and depth εw‑ion. εw‑ion is given by ⎛1 1 ⎞ ⎜ ⎟ εw ‐ ion /k = εw(298) − ‐ ion / k + C ⎝T 298.15 ⎠

20,23

4. RESULTS AND DISCUSSION 4.1. Experimental Results. 4.1.1. Dissociation Temperature. The heat flow profile of the TBAC+H2O system scanned by the Dynamic DSC method at different TBAC weight fraction and atmospheric pressure is shown in Figure 2. For wTBAC = 0.10 and 0.20, two endothermic peaks are observed: the first peak is located at around 274 K, which corresponds to the eutectic mixtures of ice and TBAC semiclathrate hydrates: The second peak is due to the progressive melting of the semiclathrate hydrate, and the corresponding melting temperature depends on the concentration of TBAC. As for wTBAC = 0.35, which is the stoichiometric composition of the TBAC semiclathrate hydrate, a congruent melting peak is observed at around 290 K. At wTBAC = 0.50, three peaks are observed at around a temperature of 267.5 K, 271 K, and 287 K. The third peak on the right of Figure 2 corresponds to the dissociation of the hydrate phase with hydration number 24 (H24) TBAC semiclathrate hydrate. The first and second peaks indicate the possibility that over phases of the semiclathrate hydrate exist at this concentration. The dissociation temperatures of the H2O+TBAC system at atmospheric pressure measured in this study are shown in Table 4 and Figure 4. Our measurements are consistent with the values

Δh0 ⎛ T⎞ ⎜1 − ⎟ RT ⎝ T0 ⎠

Δg 0(T0 , P0) Δv (P − P0) − RT RT0

(9) (10)

Details of the SAFT-VRE model can be found elsewhere.

0

−

σij = (σii + σjj)/2

λij = (σiiλii + σjjλjj)(1 − lij)/(σii + σjj)

νC ln(xCγC) + νA ln(xAγA ) + νw ln(x wγw ) Ncav

εiiεjj (1 − kij),

Table 4. Dissociation Temperatures of H2O+TBAC System at Atmospheric Pressure. Error of Temperature is 0.04 K wTBAC

T/K

0.10 0.20 0.35 0.50

282.11 286.23 288.19 286.73

in the literature.17,24,25 The average absolute deviations (AAD) among the literature are 0.17 K, 0.29 K, and 0.47 K from Sato et al.,26 Aladko and Dyadin,17 and Nakayama,24 respectively. Sun et al.27 reported dissociation temperatures that are 2.6 K, 1.8 K, and 0.14 K lower than our data at wTBAC = 0.1, 0.2, and 0.35, respectively. A solid line in the figure is drawn by the model for the binary system mentioned in section 3.1 with the parameters

(8)

ε(298) w‑ion

where is determined by fitting on the experimental activity coefficient and osmotic coefficient. C is temperature dependency D



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Figure 5. Pressure−temperature diagram of H2O+TBAC+H2 system. ■, this work at wTBAC = 0.10; ▲, this work at wTBAC = 0.20; ◆, this work at wTBAC = 0.35; ●, this work at wTBAC = 0.50; △, Makino et al.8 at wTBAC = 0.34; □, Deschamps and Dalmazzone28 at wTBAC = 0.34. The lines are calculated by the model. The dashed, solid, and dotted lines indicate hydrate phases with hydration number of 32, 30, and 24, respectively.

Figure 4. Temperature−composition diagram of the H2O+TBAC system. ●, this work; □, Sato et al.;26 ◇, Aladko and Dyadin;17 ▽, Nakayama,24 △, Sun et al.27 Solid line is the calculated SLE curve.

obtained by Fukumoto et al.18 From the model, it is predicted that hydrate at wTBAC = 0.1 is H32, wTBAC = 0.2 and 0.35 is H30, and wTBAC = 0.5 is H24. To confirm our prediction, further experiments should be carried out to observe the structures of the hydrates. The AAD between the calculation and our experimental data is 0.14 K. The dissociation temperatures of H2O+TBAC+H2 system measured in this study are shown in Table 5 and Figure 5. For comparison, the dissociation temperatures measured at wTBAC = 0.34 by Makino et al.8 and Deschamps and Dalmazzone28 are plotted in the figure. Our obtained data at wTBAC = 0.35 are close to that of Makino et al.8 Makino et al.8 conducted experiments using high-pressure cell by increasing the temperature step-by-

step by 0.1 K at a pressure range up to 5 MPa. Deschamps and Dalmazzone28 used a micro DSC at a heating rate of 1 K·min−1 at a pressure range up to 30 MPa. By linear approximation, the dissociation temperature of the literature deviates about 0.75 K at 4 MPa. It is found that stabilities of the semiclathrate hydrates in the pressure range up to 15.5 MPa increase, in order wTBAC = 0.10, 0.20, 0.50, and 0.35. 4.1.2. Enthalpy of Dissociation and Hydrogen Storage Capacity. The Dynamic DSC method, applied for the solution at wTBAC = 0.35, provides the enthalpy of dissociation per mole of water (ΔHHDSC ), which is listed in Table 6. Note that it is 2O

Table 5. Dissociation Temperatures of H2O+TBAC+H2 System. Errors of Temperature and Pressure are 0.04 K and 0.04 MPa, Respectively wTBAC

T/K

P/MPa

0.10

282.31 282.51 282.81 283.01 283.11 283.41 286.43 286.63 286.83 286.93 287.03 287.13 287.44 288.55 288.64 288.77 288.97 289.24 289.72 289.75 287.03 287.23 287.34 287.54 287.64 287.84

2.27 3.61 4.59 6.6 8.51 10.73 2.06 3.10 4.07 5.47 7.35 8.34 11.00 2.45 4.27 5.01 7.27 9.73 15.55 15.47 2.12 4.34 6.23 7.39 9.54 11.22

0.20

0.35

0.50

Table 6. Dissociation Enthalpy and Hydrogen Storage Capacity of TBAC Semi-Clathrate Hydrate at wTBAC = 0.35 and Different Gas Pressuresa T K 288.19 288.55 288.64 288.77 288.97 289.24 289.75 289.72

m ·mol 3

MPa 0.10 2.45 4.27 5.01 7.27 9.73 15.47 15.55

ΔHHDSC 2O

Vgasc

P

−1

b

9.94 × 10−4 5.77 × 10−4 4.94 × 10−4 3.45 × 10−4 2.62 × 10−4 1.71 × 10−4 1.70 × 10−4

−1

kJ·mol

5.884 5.967 5.905 6.003 5.988 6.099 6.075 6.079

mH2·100 mgas hydrate 0.019 0.033 0.038 0.055 0.073 0.112 0.113

mH2·100 d

mgas hydratee 0.015 0.025 0.029 0.042 0.056 0.086 0.087

Vgas is the volume of hydrogen. ΔHHDSC is the enthalpy of dissociation 2O per mole of water. m indicates mass of each component. Errors of temperature, pressure, and enthalpy are 0.04 K, 0.04 MPa, and 3 %, respectively. bThe value “0.10” means measurement was done under air at atmospheric pressure. cCalculated by REFPROP ver. 9.0 from NIST. dCalculated with the Clapeyron equation. eCalculated with the Clausius−Clapeyron equation. a

considered that all the water molecules are converted into the hydrate since only one negative peak is detected. To confirm the validity of the measured value, the enthalpy at ambient pressure is compared with literature. The obtained value 5.88 kJ·mol−1 is consistent with values reported in the literature (5.23, 5.47, 5.78, and 5.99 kJ·mol−1 from Rodionova et al.,29 Nakayama,24 Mayoufi et al.,8 and Deschamps and Dalmazzone,28 respectively). E



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Hydrogen storage capacity is estimated by combining ΔHHDSC 2O and the enthalpy of dissociation per mole of hydrogen (ΔHCal H2 ). ΔHCal H2 can be estimated by the Clapeyron equation: ΔHHCal2 = T ΔV

dP dT

gas, but not on those of the hydrate or liquid phases. We have estimated the hydrogen storage also with the Clausius− Clapeyron equation, and found 0.087 wt % at 15.5 MPa. From the estimations, with either equation, it is found that the TBAC semiclathrate hydrate does not provide a sufficient value for the 2015 DOE (U.S. Department of Energy) hydrogen storage goal of 5.5 wt %. However, regarding the favorable equilibrium condition, it is possible to use it as a gas separation material. Since the storage capacity of H2 is low, it is recommended to take the volume of the hydrate and of the solution into account for the estimation. 4.2. Modeling Results. 4.2.1. The Liquid−Vapor−Hydrate Three-Phase Lines of the H2+H2O+TBAC System. The dissociation conditions of H2 semiclathrate hydrate with TBAC have been modeled by combining the van der Waals and Platteeuw theory19 and the thermodynamic model for semiclathrate hydrate binary system. The SAFT-VR pure component parameters of H2 have been fitted to PVT data over the temperature range from 270 K to 400 K, by assuming that quantum effects are negligible. We have used the REFPROP software (version 9) to generate pseudo-experimental data for H2. The H2 parameters are reported in Table 3. As shown in Figure 6, the experimental PVT data33 and the fugacity coefficients generated with REFPROP are very well described

(11)

Here, T is temperature, ΔV is the volume change caused by the dissociation per mole of gas. dP/dT can be determined from the phase equilibrium data measured in this study. A simple linear interpolation is used for dP/dT, which is estimated as 10.465 DSC Cal DSC MPa·K−1. ΔHCal H2 and ΔHH2O are related as ΔHH2 = αΔHH2O , where α = nH2O/nH2. The dissociation can be written as TBAC·n H2OH 2O·n H2 H 2(s) → (TBAC + n H2OH 2O)(l) + n H2 H 2(g)

where nH2O and nH2 represent the number of moles of H2O and H2 per TBAC molecule in the hydrate, respectively. Here, the solubility of H2 in water is so low that its impact on the volume change is considered to be negligible. ΔV in eq 11 is given as ΔV = Vgas + α(Vliquid − Vhydrate)

(12)

where Vgas/liquid/hydrate represents a volume of each phase. Vgas is obtained from REFPROP version 9.0 published by the National Institute of Standards and Technology (NIST). To our knowledge, the density of TBAC solution is not available. Therefore, one can estimate Vliquid as Vliquid = (30vH*̅ 2O + v∞ ̅ BA+ + T ∞ 3 −1 − = 22.7 cm3· v∞ and v −)/30, where v + = 267.26 cm ·mol C ̅ l ̅ BA ̅ l C T mol−1 are the apparent partial molar volumes of the ions TBA+ and Cl− around 289 K taken from the literature.30,31 Such an approximation is accurate for TBAB solutions; we found the density of the TBAB solutions as 1.02 g·cm−3 at 298.15 K, which agrees well with Sinha et al.32 We found Vliquid = 27.68 cm3 per mole of water for TBAC solutions. Rodionova et al.29 reported that the structure of the semiclathrate hydrate (TBAC·30H2O) is tetragonal-I with unit-cell dimensions of a = 23.733 Å and c = 12.513 Å. Since one unit cell includes five TBA cations,29 it is estimated that 150 water molecules are in the cell. As a consequence, Vhydrate (m3 per mole of water) is obtained as Vhydrate = =

VunitNA n Hunit 2O (23.733·10−10)2 ·12.513·10−10 ·6.022·1023 150

= 2.83·10−5

(13)

Here, Vunit, NA, and nHunit represent the volume of the unit cell, the 2O Avogadro constant, and the number of H2O in the unit cell, DSC respectively. By substituting the equations for ΔHCal H2 = αΔHH2O , DSC α is obtained. Note that the original data of ΔHH2O is scattered due to the experimental errors; the values obtained from the linear approximation (118.66 T − 28287) are assigned instead. In Table 6, we report the predicted hydrogen storage capacity in weight fraction (mH2/mgas hydrate). It is estimated that 0.11 wt % of H2 is stored in the semiclathrate hydrate at 15.5 MPa. Deschamps and Dalmazzone28 estimated the storage capacity as 0.12 wt % at 14.9 MPa with the Clausius−Clapeyron equation (with the assumption Vliquid − Vhydrate = 0). This equation is based on the assumption that ΔV only depends on the volume of the

Figure 6. Thermodynamic propeties of pure dihydrogen: (a) pressure vs density at fixed temperature; (b) fugacity coefficients vs density at fixed temperature. The symbols are experimental data from ref 33. The solid lines correspond to SAFT-VR calculation. The dotted lines are calculated with REFPROP ver. 9.0 (NIST). F



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by the SAFT-VR model. The water−H2 binary parameters have been determined as kij = −0.3 and lij = −0.1 by fitting the solubility of H2 at temperatures close to ambient temperatures. As shown in Figure 7, the SAFT-VR can describe reasonably well

Figure 8. Predicted hydrogen storage capacity versus TBAC concentrations: ■, hydrogen storage in weight fraction (wH2); ○, hydration number of the hydrate phase (vw). The calculation is made at 5 MPa along the liquid−vapor−hydrate three-phase equilibrium.

of the equilibrium temperature leads to the higher hydrogen storage when wTBAC is between 0.4 and 0.55.

Figure 7. Solubility of H2 in water (VLE) at different temperatures: ▲, T = 298.0 K; ○, T = 323.15 K; ■, T = 373.1 K. The solids are the SAFT-VR calculations. The experimental data (symbols) are from Kling and Maurer34 and Purwanto et al.35

5. CONCLUSIONS The dissociation conditions of TBAC semiclathrate hydrate in the presence of hydrogen are measured with a differential scanning calorimeter at four different weight fractions of TBAC (wTBAC): 0.10, 0.20, 0.35, and 0.50 and at a pressure up to 15.5 MPa. The stepwise DSC method is adopted for samples which have incongruent melting, as it enables a greater accuracy. For wTBAC lower than 0.35, the semiclathrate hydrate becomes more stable as the TBAC concentration increased, but it destabilizes as we keep increasing wTBAC beyond 0.35. Hydrogen storage capacity is estimated with the Clapeyron equation, the measured phase equilibrium data, and enthalpies of dissociations. The amount of hydrogen stored in the semiclathrate hydrate is estimated as 0.11 wt % at 15.5 MPa. This capacity is too low for a possible use of TBAC semiclathrate hydrates as H2 storage material. However, such hydrates can be used for the separation of mixtures H2 + CO2, as CO2 would be captured much more into the hydrate phase. The thermodynamic model proposed by Paricaud9 is applied to calculate the dissociation condition of H2 semiclathrate hydrate with TBAC. The SAFT-VRE equation of state is used to compute the thermodynamic properties of the fluid phase. The parameters Δh0 and T0 obtained by Fukumoto et al.18 are used to calculate the Gibbs free energy of the empty hydrate. A very good agreement between the new data and the model is found. The predicted hydrogen capacity at 15.5 MPa is also very close to the experimental value.

the solubility of H2. The model predicts that the solubility increases as the temperature is increased, in agreement with Kling an Maurer’s data.34 Note that the experimental data at 298 K from Purwanto et al.35 are not consistent with Kling an Maurer’s data34 at 323 K and 373 K. It is not clear if this is due to experimental uncertainty or if the solubility of H2 goes through a minimum. In our case, this is not an issue, as the value of the water−H2 kij parameter does not have a large effect on the predicted dissociation conditions of H2 semiclathrate hydrates. Those conditions mainly depend on the fugacity of H2 in the vapor phase at fixed T and P and on the hydrate parameters. The L−V−H three phase lines are determined by fitting the cell parameters of Vcell ij and εij to the experimental dissociation conditions obtained in this study. The number ni of empty cages per TBAC molecule is set to 2 for the hydrate phase with hydration number 32 and 30 (H32 and H30). This is based on the structural study reported by Rodionova et al.29 ni for H24 is assumed to be 1 comparable to TBAB semiclathrate hydrate.18 The fitted parameters for H2+H2O+TBAC system are listed in Table 2. The lines in Figure 5 are the result of the fitting. It is observed that H32 is the most stable at wTBAC = 0.10, while H30 is the most stable at wTBAC = 0.35 and 0.20. Only H24 is observed at wTBAC = 0.50. Theoretical H2 storage capacity is predicted by our model as Yij·ni·MH2/(MTBAC + vw·MH2O + Yij·ni·MH2), where M is a molecular weight of each component. It is predicted that 0.12 wt % of hydrogen can be stored in TBAC semiclathrate hydrate at wTBAC = 0.35 MPa and 15.5 MPa, which agrees well with our estimation from experimental data. The hydrogen storage capacity along the L−V−H three-phase equilibrium is predicted at different TBAC concentrations and 5 MP. As can be seen in Figure 8, the hydrogen storage capacity slowly decreases until wTBAC = 0.35. This is mainly due to the increment in the equilibrium temperature, which results in the decrease of the Langmuir constant. Although H24 only has one empty cage per TBAC molecule, the storage capacity increases at wTBAC = 0.40. This is because that the Langmuir constant of H24 is about 2.2 times bigger than that of H30/32 (at T = 288.15 K). The decrease

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

The authors thank AREVA for financial support as part of the nuclear and engineering funding of Areva-ParisTech. Notes

The authors declare no competing financial interest.

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REFERENCES

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Experimental Measurements and Modeling of the Dissociation

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