Kinetic and Thermodynamic Aspects of Clathrate Hydrate Nucleation

Article pubs.acs.org/jced

Kinetic and Thermodynamic Aspects of Clathrate Hydrate Nucleation and Growth Judith M. Schicks* and Manja Luzi-Helbing Helmholtz Centre Potsdam GFZ German Research Centre for Geosciences, Telegrafenberg, 14473 Potsdam, Germany S Supporting Information *

ABSTRACT: In this study we present results of our investigations on simple CH4-hydrate and mixed hydrates during the initial steps of the hydrate formation process. In situ Raman spectroscopy, microscopic observation and in situ X-ray diffraction were used in our systematic studies. Although these techniques give only a limited view on the molecular level the combined results from the experiments reported here indicate that the labile cluster hypothesis can describe the initial hydrate formation process. Specifically, the guest molecules dissolve in the aqueous phase before they are encaged into single hydrate cavities which agglomerate to a solid phase. Results from Raman spectroscopic measurements suggest that the initially formed solid phase can be characterized by an excess of pentagonal dodecahedrons, whereas the formation of tetrakaidecahedrons or hexakaidecahedrons occurs as a subsequent step. At the time the tetrakaidecahedrons or hexakaidecahedrons are observed with Raman spectroscopy, corresponding X-ray diffraction experiments indicate the formation of a crystalline hydrate phase. Therefore, we assume that the solid phase formed at the very first state is not a hydrate phase in terms of a crystalline structure but some kind of an amorphous hydrate which transforms subsequently into a crystalline hydrate phase. Furthermore, the results suggest that the formation process and the properties of the resulting hydrate phase strongly depend on the properties of guest molecules.

1. INTRODUCTION Clathrate hydrates are ice-like crystalline solids composed of a three-dimensional network of hydrogen-bonded water molecules that confines guest molecules in well-defined cavities of different sizes.1,2 Preferred guest molecules in naturally occurring gas hydrates are nonpolar small gas molecules, such as light hydrocarbons (C1−C5) or CO2 or H2S. Depending on the size of the guest molecule, different structures are formed. Small molecules such as CH4, CO2, and H2S prefer the formation of structure I hydrates, whereas larger molecules like C3H8 form structure II hydrates. Even larger molecules such as 2-methylbutane form structure H hydrates in the presence of a helping gas like CH4 stabilizing the small cavities of this structure. However, when more than one guest molecule is present, the relationship between molecular size and formed hydrate structure is not always straightforward. Gas molecules which individually form structure I hydrates sometimes form structure II hydrates or both when they appear together in certain proportions. This effect could be observed among others for mixed hydrates formed from CH4−C2H6 gas mixtures.3,4 Coexisting metastable phases of simple hydrates as well as mixed hydrates were also observed during initial steps of hydrate formation, also, when the formation of hydrate crystals seemed to be finished, and even in natural systems.5−8 Therefore, the structure of the resulting hydrate phase(s) may depend not only on the size and shape of the guest molecule © XXXX American Chemical Society

but also on the nucleation and formation process itself. These processes have been investigated, and different hypotheses have been developed in the last decades. The most important approaches treat the nucleation of a hydrate crystal qualitatively on a molecular level. They assume that the guest molecule coexists as a free gas or liquid phase beside the water or ice phase. This is not necessarily the case because hydrates may also form from a gas saturated water phase without a coexisting free gas or liquid phase of the potential guest molecule.9 However, Long as well as Kvamme chose an approach where heterogeneous nucleation takes place at the interface between the water and the gas phase: gas molecules are transported to the interface and adsorb at the aqueous surface where they are at first partially and thereafter completely encased into water cavities. These clusters agglomerate and grow on the vapor side of the interface.10,11 The general observation of the formation of a hydrate film at the interface between gas and aqueous phase, for example, during a methane hydrate formation process, may support this hypothesis, though it is probably not a satisfying approach for those hydrates with a higher density Special Issue: In Honor of E. Dendy Sloan on the Occasion of His 70th Birthday Received: June 19, 2014 Accepted: November 12, 2014

A

dx.doi.org/10.1021/je5005593 | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Table 1. Composition of Gas Mixtures Used Given in Mole Fraction x mixture no.

xCH4

1 2 3 4 5 6 7 8

1.0 0.903 0.991 0.981 0.980 0.903 0.980 0.990

x of low-concentrated gas components CO2 H2S C3H8 C2H6 C2H6 2-methylpropane 2-methylbutane

0.097 0.009 0.019 0.010 0.049 0.020 0.010

± ± ± ± ± ± ±

0.00190 0.00018 0.00038 0.00020 0.00980 0.00040 0.00020

C3H8 C3H8

0.010 ± 0.00020 0.048 ± 0.00096

Christiansen and Sloan.13,18 These “blobs” persist in the aqueous solution and consist of gas molecules separated by half-cages of water molecules. After becoming a critical nucleus the water molecules of the “blob” order to clathrate cavities. The nucleus recruits more gas and water molecules from the solution resulting in an amorphous clathrate nucleus. Within the amorphous nucleus the water molecules are locally ordered but the gas molecules do not show the necessary order for a crystalline hydrate structure. In a third step, the amorphous clathrate nuclei rearrange to form a crystalline hydrate with elements of both, structure I and structure II.19 In situ Raman spectroscopic investigations on methane hydrate and mixed hydrates during the hydrate formation process may support the labile cluster hypothesis in general and the formation of an amorphous hydrate phase suggested by Jacobson et al.20−22 Naturally, the Raman experiments investigating the hydrate formation process were performed over a much longer period of time compared to the molecular dynamic simulations of the nucleation processes described in Walsh et al. and Jacobson et al. However, these experimental studies suggest that the incorporation of methane into the 512 cavities is a first step during the initial stage of hydrate formation and that the reconstruction of the water clusters to large cavities is an energy barrier for the methane hydrate nucleation. The Raman spectra also indicate the formation of a solid phase that does not correspond to a stable crystalline hydrate phase. It is questionable, if this solid phase which does not exhibit the characteristic Raman spectrum of a crystalline hydrate phase is a remaining amorphous hydrate phase which transforms over time into a crystalline hydrate structure with well-defined cavities. The in situ Raman investigations on mixed hydrates additionally indicate that feed gas composition and solubility of the gas molecules have some influence on the formation process and the resulting hydrate phase.22 This will be discussed in more detail based on experimental data in the following paragraphs.

compared to the density of water. Those hydrates show a preferential nucleation and growth on the subsurface which could be observed, for example, for CO2−SO2 hydrates.12 The labile cluster model developed by Christiansen and Sloan shows a higher universal validity since it can be applied for hydrate nucleation processes with or without a free gas or liquid phase of the guest molecule.13 Also, the formation of a hydrate phase subsurface can be explained with this hypothesis. One premise of the labile cluster hypothesis is that water molecules already form structures such as labile rings of pentamers and hexamers in the pure water phase without dissolved gas molecules. This assumption is supported by Pauling who already postulated the existence of clusters comprising 20 water molecules arranged in a pentagonal dodecahedron with one water molecule in the center in the pure water phase in 1964.14 Geiger et al. concluded from their simulations that water cavities existed in the pure water phase similar to those suggested by Pauling.15 More recently, Ludwig could show by means of ab initio calculations that besides tetrahedrally coordinated water molecules ring structures in the pure liquid water phase are very likely.16 Therefore, it seems to be likely that these structures of water molecules form labile clusters around dissolved gas molecules. The sizes of the labile clusters depend on the size of the dissolved gas molecule, for example, one methane molecule is surrounded by 20 water molecules.13 Clusters of dissolved gas molecules combine to form unit cells. For the formation of a unit cell, the coordination number of the water molecules surrounding the dissolved gas molecules has to be changed. This transformation of the cluster coordination number of the water molecules needs activation energy and therefore this step becomes a barrier in the formation process.13 Walsh et al. modeled with direct molecular dynamics simulations the spontaneous nucleation and growth of methane hydrate.17 They could show nucleation steps similar to the labile cluster hypothesis: pentagonal faces of water molecules exist in the water phase and arrange close to a dissolved methane molecule, partial cages form around the methane molecule and dissolve again. Small cages (coordination number of water molecules is 20) form around a methane molecule and additional methane molecules and partial water cages try to attach. At this point an extended growth of these partial cavities into face sharing pentagonal dodecahedrons around the central pentagonal dodecahedron is hindered by steric constraints. The coordination number of the water molecules has to be changed to build a structure I unit cell with well-defined cavities. An interesting outcome of this simulation is the formation of uncommon 51263 cavities during the formation process. Jacobson et al. described the nucleation of clathrate hydrates also using molecular dynamics simulations as a multistep mechanism and observed the formation of so-called “blobs” which are large analogues of the labile clusters proposed by

2. EXPERIMENTAL SECTION Materials. The hydrate formation process was studied starting from deionized water or freshly prepared ice. The ice was generated from deionized water that was frozen in a liquid nitrogen bath. The ice was powdered in a 6750 freezer mill (Spex CertiPrep) that was also cooled with liquid nitrogen. The diameter of these ice particles was determined with scanning electron microscopy (SEM ULTRA plus) and lies in between 10 and 20 μm. SEM images of the fresh prepared, foamy looking ice phase can be found elsewhere.22 Table 1 gives an overview of the used gas mixtures delivered as certified gas mixtures by Air Liquide. Raman Spectroscopic Measurements and Microscopic Observation. For the Raman spectroscopic measureB



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the Raman spectroscopic and the X-ray diffraction experimental setups simulates an unlimited gas reservoir which prevents the formation of coexisting hydrate phases due to a depletion of one component in the gas phase. Since the gas flow was regulated to 1 mL/min the incoming gas flow cooled down when it passed the cooled cell body before it entered the sample space.

ments the gas hydrates were synthesized in a pressure cell made of Hastelloy with a sample volume of ∼400 μL. The pressure cell could be used in a temperature range between 245 K and 350 K. The temperature of the sample cell was controlled by a thermostat, and the temperature was determined with a precision of ± 0.1 K. The applicable pressure range was between 0.1 MPa and 10.0 MPa. A pressure controller adjusted the sample pressure with a precision of 2 % relative. A quartz window permits microscopic observation and Raman spectroscopic investigations of the sample. The microscope is equipped with a digital camera (CC12, Soft Imaging System GmbH) to allow documentation of all processes in the cell. Raman spectra were taken using a confocal Raman spectrometer (LABRAM, HORIBA JOBIN YVON), which allowed the laser beam to be focused on a precise spot, for example, the surface of a hydrate crystal, thus ensuring that only the selected phase was analyzed. The instrument parameters are the following: grating, 1800 grooves/mm; entrance slit, 100 μm; confocal pinhole, 100 μm (according to HORIBA JOBIN YVON the effective measurement depth is 60 μm.), microscope objective, 20×; laser, external 100 mW diode-pumped solidstate laser with a wavelength of 532 nm. The Raman instrument was calibrated using silicium (521 cm−1) and diamond (1332 cm−1). More details regarding the experimental setup and sample preparation can be found elsewhere.6,22,23 The Raman measurements shown in this study were performed at pressures between 1.24 MPa and 3.1 MPa and the temperature was generally adjusted at 272 K. X-ray Diffraction Measurements. For the time-dependent powder X-ray diffraction (PXRD) measurements during hydrate formation a low-temperature−high-pressure cell that was integrated into a Bruker AXS D8 Discover microdiffractometer was used. The pressure cell is made from stainless steel with a hole of 0.5 cm diameter in its center, and it has a volume of ∼250 μL. Both sides of the cell body are sealed with beryllium plates and tightened with O-rings. The cell can be operated in a pressure range between 0.1 MPa and 4.0 MPa. The temperature is controlled by means of a Peltier-cooling device (Kryotherm model TB-119-1.4-1.15CH) that also contains a hole of 0.5 cm. The Peltier-cooling provides quick temperature changes and a precise temperature control of ± 1.0 K by use of an adjustable power source and a controlling device (West 4200, West Instruments Ltd.). The cell can be run in a temperature range between 253 K and 288 K. The cell was designed for the use in combination with a Bruker AXS D8 Discover microdiffractometer with Cu Kα radiation generated at 40 kV and 40 mA. The diffractometer has parallel beam optics (Goebel mirror) to optimize the beam intensity that enables the analysis of powder samples with a nonplanar surface. A monocapillary, which narrows the beam to a diameter of 300 μm, was applied. In consequence, small sample areas and small sample amounts of gas hydrate powder can be investigated in the micrometer range. The detection of the diffracted X-rays is carried out with GADDS (General Area Detection Diffraction System), which includes a Hi-Star area detector. A more detailed description of the experimental setup and the sample preparation can be found elsewhere.24,25 For the X-ray diffraction experiments reported here, pressures were chosen between 0.6 MPa and 2.8 MPa, and the temperature was generally adjusted at 267 K. It should be noted that the experiments were performed with a continuous gas flow to avoid changes in the gas composition during hydrate formation. This experimental feature for both

3. THEORETICAL BASIS In general, gas hydrates form under elevated pressure and low temperature conditions provided that sufficient amounts of gas and water are available. Hydrate formation is a phase change, that is, during the hydrate formation process no chemical bonds are formed or broken. However, a general chemical equation for the hydrate formation “reaction” can be formulated as follows: gas + n w H 2O ↔ gas·n w H 2O

(1)

where nw is the number of water molecules. As already mentioned in the paragraph introduction small clusters of water and gas are generated during hydrate nucleation which continue to form hydrate crystals when the clusters reached the critical size. According to Kashchiev and Firoozabadi the chemical potentials of the gas and the water molecules in aqueous W solution will be denoted as μW g and μw , respectively. If the expression gas·nwH2O from eq 1 is regarded as a building unit for a hydrate crystal, the chemical potential of this building unit in the water phase is denoted as μW h . Referring to the thermodynamic relation between chemical potentials in reaction equilibria the chemical potential of the hydrate building unit in an aqueous solution can be defined as26

μgW + n w μwW = μ hW

(2)

Kashchiev and Firoozabadi postulated that the driving force for the formation of the new phase is the difference between the chemical potentials of the old phase (aqueous solution) and of the new phase (hydrate crystal). Thereby, the chemical potential of a hydrate building unit (one gas molecule and nw water molecules) in the hydrate crystal is denoted as μh. Kashchiev and Firoozabadi called the driving force supersaturation, given as26 Δμ = (μgW + n w μwW ) − μ h = μ hW − μ h

(3)

In the case of supersaturation of the solution μW h > μh and Δμ > 0; nucleation and growth of the hydrate crystals are possible. A phase equilibrium in terms of a coexistence of dissolved and crystalline hydrate phases is reached if Δμ = 0. When Δμ < 0 the solution is undersaturated. In this case no nucleation of hydrates occurs and already existing hydrates may dissolve. Kashchiev and Firoozabadi pointed out that their concept for Δμ is also valid for the formation of hydrates from the ice phase and the decomposition of hydrates to gas and ice, respectively.26 At constant pressure and temperature the difference between the chemical potentials of the “reactants” and “product” corresponds to the Gibbs free energy change for the reaction as follows:27 ΔG = −(μgW + n w μwW ) + μ h C

(4)



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Since the formation of hydrate is only possible if μW h > μh hydrate formation results in a diminishment of the Gibbs free energy.

encasement of CH4 into the pentagonal dodecahedrons. The induction time was determined as the first detectable signal for the enclathration of the gas molecule into a hydrate cavity via Raman spectroscopy. Figure 1 exhibits the determination of the enclathration of CH4 into a 51262 cavity after 90 min by a Raman band at 2902 cm−1. The Raman measurements were taken during the formation of a CH4−H2S mixed hydrate. The induction times may vary for the different hydrate formation experiments performed in this work; however, the trend for the cage filling is similar. In general, the experiments were repeated at the same temperature and similar or different pressures for selected gases/gas mixtures showing the same behavior for the encasement of the guest molecules. This observation can be explained by taking the composition of the feed gas and the approach of Kashchiev and Firoozabadi into account (see also section 3 “Theoretical Basis”). According to Kashchiev and Firoozabadi the driving force for the hydrate formation is the difference between the chemical potentials of the aqueous solution and the hydrate crystals. The aqueous solution has to be supersaturated to induce the hydrate formation:26

4. RESULTS AND DISCUSSION Our systematic Raman spectroscopic investigations on simple CH4-hydrate and mixed hydrates which predominantly contain CH4 show a preferential incorporation of CH4 in pentagonal dodecahedrons as a first step during initial gas hydrate formation processes. This observation is independent of the resulting hydrate structure and the molecular properties of an additional guest molecule besides CH4.22 A possible explanation for this phenomenon may be found in the nucleation process. Commonly, the nucleation process itself is a matter of nanoseconds. Although the time frame between the nucleation processes analyzed with molecular dynamics simulations as described in the literature and the formation processes observed in this study differs significantly, some similarities can be observed. According to the labile cluster hypothesis and the hydrate formation hypothesis of Jacobson et al. the dissolved CH4 molecule which is surrounded by 20 water molecules in the aqueous phase can easily transform into CH4 encased into a pentagonal dodecahedron, whereas the formation of other cavity types encasing CH4 is hindered because it requires the incorporation of additional water molecules. As mentioned before, by means of Raman spectroscopy we observed a preferred incorporation of CH4 into the pentagonal dodecahedrons on a time scale of several minutes during the hydrate formation process. This is most likely caused by the easy transformation of the hydration shell (including already 20 water molecules) surrounding a dissolved CH4 molecule into a defined hydrate cavity. In contrast, the reason for the retarded enclathration of the other guest molecules with different aqueous hydration numbers cannot be explained with these kinds of transformation processes. The coordination numbers of water molecules surrounding a dissolved gas molecule are 24 for CO2 and H2S, and 28 for both C3H8 and 2-methylpropane, respectively.28 Therefore, CO2 or H2S should be encased easily into a tetrakaidecahedron (51262, 24 water molecules) and C3H8 and 2-methylpropane into a hexakaidecahedron (51264, 28 water molecules), respectively. In fact, the Raman spectra indicate that CO2 and H2S are encased preferentially into tetrakaidecahedrons rather than pentagonal dodecahedrons, whereas C3H8 and 2methylpropanebased on their molecular sizecan only be encased into the hexakaidecahedrons. However, the induction times in Table 2, show that the enclathration of CO2, H2S, C3H8, and 2-methylpropane is hindered compared to the

Δμ = (μgW + n w μwW ) > μ h

For a system containing x = 0.98 to 0.99 CH4 and only x = 0.01 to 0.02 of an additional hydrate forming gas eq 5 is achieved easier for CH4 than for the additional gas molecules. In other words, the aqueous solution is faster supersaturated with CH4 rather than CO2, H2S, C3H8, and 2-methylpropane, even though a continuous gas flow was used in our experimental setup to avoid a depletion of the low concentrated component in the gas phase. This supersaturation of the aqueous solution with CH4 may induce the formation of a hydrate phase. But our studies show that this initially formed solid phase is characterized by an excess supply of CH4-filled pentagonal dodecahedrons as detected by Raman spectroscopy. When comparing the X-ray and Raman data of the formation process at similar pressure and temperature conditions, we noticed that during the first minutes of the formation of this solid phase no X-ray signals for a hydrate structure could be detected. The first X-ray signals of a defined hydrate structure were detected delayed in time compared to the Raman signals. This could be observed for all investigated systems independently if the resulting hydrate is a simple CH4 hydrate or a mixed hydrate. Figure 2a shows the real-time Raman spectra monitoring the enclathration of CH4 into the pentagonal dodecahedrons (2915 cm−1) of structure I directly after pressurization of the sample cell with CH4. The incipient enclathration of CH4 into the tetrakaidecahedrons (2905 cm−1) could be detected after about 15 min. Figure 2b shows the corresponding time-resolved X-ray diffraction pattern for the experiment performed at p = 2.5 MPa and T = 264 K. During the first 5 min after the ice phase was exposed to CH4 no hydrate structures could be detected. A first signal of structure I hydrate could be detected after 16 min when the subsequent X-ray measurements were started. Since both cavity types are necessary to form a structure I hydrate, this observation may indicate that the solid phase formed within the first minutes is not a crystalline hydrate phase but rather an amorphous phase. For hydrates formed from gas mixtures, this amorphous hydrate phase will continue to form a mixed hydrate when the aqueous solution is also supersaturated with the second component besides CH4. This is also true for the formation of hydrates from ice and a gas phase because,

Table 2. Induction Times [min] Indicating the First Detectable Signal for the Encasement of a Gas Molecule into a Hydrate Cavity Obtained from Raman Spectroscopy: induction time [min] until first signal for gas molecule encased in the respective cavity type was detected 512

51262

51264 50 to 100

150 to 175

50 to 100 25 to 50 75

gas molecule CH4 CO2 H2S C3H8 2-methylpropane

0

(5)

25 to 50 10 to 15 D



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Figure 1. Real-time Raman spectra monitoring the formation of a CH4−H2S mixed hydrate (wavenumber (v)̅ versus intensity (I) versus time (t)). After 90 min a first Raman signal at 2902 cm−1 indicates the enclathration of CH4 into the 51262 cavities of a CH4−H2S mixed hydrate. Thus, the determined induction time for the enclosure of CH4 into the 51262 cavities in this experiment is 90 min. Experimental conditions: p = 2.3 MPa, T = 272 K.

Figure 2. (a) Real-time Raman spectra monitoring the encasement of CH4 into the 512 cavities (2915 cm−1) directly after pressurization of the sample (wavenumber (v)̅ versus intensity (I) versus time (t)). A first hint for the enclathration of CH4 into the 51262 cavities (2805 cm−1) can be detected after 15 min. (b) Corresponding time-resolved X-ray diffraction pattern (2 theta (2θ) versus counts versus time (t)) showing the first signal for a structure I hydrate phase after 16 min. Experimental conditions: p = 2.5 MPa, T = 264 K.

Supporting Information showing this transformation process in real time.) Figure 3 shows the pressure and temperature conditions for the observed transformation process (displayed as crosses within the greyish area) and the stability fields of the investigated hydrates. The phase equilibria data for the different investigated systems shown in Figure 3 are experimentally determined (data points) and calculated with CSMGem (solid lines).28,23 The uncertainty of the measured equilibrium temperature at a given pressure is about ± 0.5 K. At a given pressure, the observed temperature conditions for the transformation process are 5 K up to 10 K below the decomposition line of the mixed hydrates. The transformation process could be observed by moving toward the transformation zone in both directions. This transformation zone is defined by the experimental data (crosses) and marked as a greyish area in Figure 3. The lifetime of this transformation behavior (rapid crystal formation/decomposition) was a function of the chosen temperature. When the temperature was held within the

according to Sloan and Fleyfel, the mechanism for hydrate formation from ice passes through similar steps compared to the formation from water, assuming the presence of transient liquid water on a local scale.29 If the chosen pressure and temperature conditions for the formation of a mixed hydrate are also within the stability field of the simple CH4 hydrate, a structure I CH4 hydrate may form as coexisting phase besides the mixed hydrate phase. At pressure and temperature conditions close to the CH4 hydrate equilibrium line the formation and decomposition of a structure I CH4 hydrate could be observed for those systems containing C2H6 + C3H8, C3H8, and 2-methylpropane besides CH4 in the feed gas. We described this process that was first observed during the formation of CH4−C3H8 mixed hydrates as a transformation process.23 This transformation process was visually characterized by the rapid formation and dissociation of crystals. From the beginning of the transformation process, all crystals visualized in the cell immediately began to decompose and regrow. (Please find a short video sequence in the E



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The excess supply of CH4 compared to C3H8 and 2methylpropane in the aqueous solution on the one hand and the kinetic preference of CH4 hydrate formation compared to the mixed hydrate formation on the other hand may result in the formation of a CH4 hydrate phase besides the mixed hydrate phase, although the mixed hydrate phase should be thermodynamically preferred. If this formation of CH4 hydrate already starts at temperature and pressure conditions close to (but out of) the CH4 hydrate stability field, the formed crystals are unstable and decompose immediately as can be seen in the Supporting Information video. However, if the CH4 hydrate formation occurs at temperature and pressure conditions within the CH4 hydrate stability field this metastable structure I CH4 hydrate phase coexists besides the structure II mixed hydrate phase. Such a coexistence of structure I and structure II hydrates could be confirmed by Raman spectra taken from the solid phase formed, for example, from a CH4−C3H8 gas mixture and water at temperature and pressure conditions within the CH4-hydrate stability field.23 A coexistence of structure I CH4-hydrate and structure H CH4-2-methylbutane mixed hydrate could also be observed when studying the hydrate formation from a gas mixture containing 1 % 2-methylbutane in CH4 (mixture 8). The chosen pressure and temperature conditions were located within the stability field of structure I CH4 hydrate as well as structure H CH4-2-methylbutane hydrate (p = 2.81 MPa, T = 267 K). The time-resolved powder X-ray diffraction patterns presented in Figure 5 indicate a formation of structure I hydrate

Figure 3. Observed pressure−temperature conditions for the transformation process (×) and stability fields of different (mixed) hydrates based on experimental data (data points). black ■, mixture 1 (pure CH4); red ●, mixture 4; orange ★, mixture 5; blue ⬟, mixture 6; green ▲, mixture 7. The composition of the gas mixtures is given in Table 1. Solid lines are the corresponding equilibrium lines calculated with CSMGem: black line, mixture 1; red line, mixture 4; orange line, mixture 5; blue line, mixture 6; green line, mixture 7.

transformation zone this transformation process could be observed for over 2 h until the experiment was halted. It should be noted that the transformation zone was observed at the same temperature and pressure conditions independent of the composition of the feed gas of the investigated systems. Recent investigations on the kinetics of hydrate formation may give some helpful information to explain the observed phenomenon. Luzi studied the kinetics of hydrate formation from ice and different gas mixtures at defined pressure and temperature conditions with X-ray diffraction.30,25 The experiments were conducted at the same temperature (267 K) and about 25 % above the equilibrium pressure of each gas mixture. The measurements show different hydrate formation rates during the first minutes for simple CH4 hydrate compared to mixed hydrates, containing C3H8 or 2-methylpropane besides CH4. Figure 4 shows the transformation rates of ice into hydrate over time. The results indicate that the formation of CH4 hydrate is faster during the first 40 min compared to the formation rate of CH4−C3H8-hydrate and CH4-2-methylpropane-hydrate, respectively.

Figure 5. Time-resolved PXRD pattern (2 theta (2θ) versus counts versus time (t)) showing the formation of structure I after 10 min (red XRD pattern) from hexagonal ice (black XRD pattern). After ca. 130 min a small shoulder starts to form at 18.3° 2θ which is assigned to structure H gas hydrates (green XRD pattern). Experimental conditions: p = 2.81 MPa, T = 267 K.

after 10 min (red XRD pattern) followed by the formation of a structure H hydrate after 130 min (green XRD pattern). The blue XRD pattern in Figure 5 proves the coexistence of a structure I and a structure H hydrate. Additional Raman spectroscopic investigations also confirm the coexistence of a structure I CH4-hydrate besides a structure H CH4-2methylbutane mixed hydrate.25 It should be noted, that these coexistences do not describe equilibrium states since the coexisting phases (structure I−structure II/H−gas phase) are not within chemical equilibria. Nevertheless, our observations confirm that during the hydrate formation process not only the

Figure 4. Transformation rates of ice into hydrate over time (t). Experimental conditions as follows: black ◆, mixture 1, p = 2.5 MPa, T = 264 K; red ●, mixture 4, p = 0.9 MPa, T = 267 K; green ■, mixture 7, p = 0.66 MPa, T = 267 K. F



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Table 4. Properties of the Gases Useda

thermodynamic stable hydrate phase may form but also metastable phases if they are kinetically promoted. We also observed that the composition of the resulting hydrate phases differs significantly from the composition of the feed gas. Although the composition of the mixed hydrates varied since they are nonstoichiometric solids, CH4 was depleted in the hydrate phase, whereas the additional gas component was clearly enriched compared to the feed gas composition. Table 3 gives an overview of the feed gas Table 3. Composition of Feed Gas and Gas Composition in the Hydrate Phase gas mixture CH4−CO2 CH4−H2S CH4−C2H6−C3H8

CH4−C3H8 CH4−2-methylpropane CH4−2-methylbutane

feed gas composition (mole fraction) 0.10 CO2 0.90 CH4 0.01 H2S 0.99 CH4 0.05 C2H6 0.05 C3H8 0.90 CH4 0.02 C3H8 0.98 CH4 0.02 2-methyl propane 0.98 CH4 0.01 2-methyl butane 0.99 CH4

average gas composition (mole fraction) in the hydrate phase 0.34 ± 0.08 CO2 0.66 ± 0.08 CH4 0.12 ± 0.04 H2S 0.88 ± 0.04 CH4 0.06 ± 0.01 C2H6 0.18 ± 0.03 C3H8 0.76 ± 0.04 CH4 0.19 ± 0.03 C3H8 0.81 ± 0.03 CH4 0.34 ± 0.02 2-methyl propane 0.66 ± 0.02 CH4 not determined

a

Molecular diameters were taken from Luzi;29 solubilities were taken from Air Liquide.32

continuous gas flow. Therefore, an enrichment of CO2 or H2S in the aqueous phase does not induce depletion of this component in the gas phase. A higher concentration of CO2 or H2S in the aqueous phase again results in an enrichment of these gases in the hydrate phase. (2). Size and Shape of the Molecule. C2H6, C3H8, 2methylpropane, and 2-methylbutane show almost the same or even lower solubility compared to CH4. Nevertheless, these gases are also enriched in the hydrate phase. This is probably caused by a better guest-to-cavity ratio of the additional component and the diverse cavity types of the different structures compared to CH4. The ratio of the guest diameter to cavity diameter helps to determine an upper and a lower size limit for a guest molecule to enter a specific cavity.28 In Table 5 the guest-to-cavity ratios for the gas components used in this study and the different cavities are listed. According to Lederhos et al. the guest-to-cavity ratio should be between 0.75 and 1.0 because in this case the gas molecule is large enough to stabilize the cavity and small enough to avoid any deformation of the cavity.31 For CH4 this is only the case if it is encased into the pentagonal dodecahedrons and the irregular dodecahedrons. For all other cavity types of the hydrate structures the guest-to-cavity ratio of CH4 is < 0.7. All other components used in our studies are larger molecules than CH4 (see also Table 4). Therefore, these molecules have a higher guest-to-cavity ratio and may stabilize the cavities better than CH4 which will result in a higher stability of the hydrate structure.

composition and the gas composition in the hydrate phase calculated from the Raman spectra. For the calculations of the gas composition in the hydrate phase, the same routine was used as described in Beeskow−Strauch et al. in more detail.12 Usually, the composition of the guest molecules in the hydrate phase is given as relative percentage assuming that the corrected integrated intensities of the selected Raman bands for the guest molecules are set to 100 % which can be set as equivalent to a mole fraction of x = 1.0. The integrated band intensities were corrected with wavelength-independent cross section factors. It was assumed that the cross section factors do not vary with pressure, cage type, or the overall composition of the hydrate. Detailed information about the semiquantitative analysis of Raman spectra is given elsewhere.12,22 It should be noted that the hydrate phase was not necessarily in the equilibrium state when the composition was determined via Raman spectroscopy. However, the composition of the hydrate phase did not change over time. For the binary CH4-2methalbutane hydrate a guest molecule ratio could not be determined from Raman spectroscopy because there were no cross section values available for 2-methylbutane. To explain this observation, two approaches should be considered. (1). Solubility of the Different Gas Components. The solubilities of the different gas components are listed in Table 4. CO2 and H2S show a much better solubility in water than CH4. According to the labile cluster hypothesis the gas molecule is dissolved in the aqueous phase before it forms at first labile clusters which transform into hydrate cavities. A better solubility of CO2 or H2S results in higher concentrations of these gases in the aqueous phase compared to the gas phase. It should be noted that the experiments were performed with a

5. SUMMARY AND CONCLUSIONS In this study we present results of our investigations on simple CH4-hydrate and mixed hydrates during the formation process. We used in situ Raman spectroscopy, microscopic observation, and in situ X-ray diffraction for our systematic studies. The comparison and conjunction of the results we obtained from the different experiments may improve the understanding of hydrate formation also on a molecular level. The following points summarize the most important findings and conclusions: G



Article

Table 5. Guest-to-Cavity Ratio of the Used Gas Moleculesa guest diameter/cavity diameter structure I 12

cavity type→ guest molecule CH4 C2H6 C3H8 2-methylpropane 2-methylbutane H2S CO2 a

guest diameter

structure II 12 2

12

5

5 6

5

0.79 1.04 1.29 1.29 1.47 0.86 1.07

0.69 0.91 1.12 1.12 1.28 0.75 0.93

0.80 1.06 1.31 1.31 1.50 0.88 1.08

structure H 12 4

12

5 6

5

0.60 0.80 0.986 0.987 1.13 0.66 0.82

0.79 1.05 1.29 1.29 1.48 0.87 1.07

435663

51268

0.76 1.01 1.24 1.24 1.42 0.83 1.03

0.46 0.61 0.75 0.75 0.86 0.50 0.62

29

0.4018 nm 0.5323 nm 0.6568 nm 0.6572 nm 0.752 nm (gauche) 0.4396 nm 0.5436 nm

Guest diameters were taken from Luzi;29 cavity diameters were taken from Sloan and Koh.28

• In a first step at the initial hydrate formation process CH4 is incorporated into pentagonal dodecahedrons. This could be observed for all our investigated systems regardless of the composition of the feed gas and the structure of the resulting hydrate phase. • The formation of all other cavity types occurs later. This could also be observed for all investigated systems, independent if these cavities are occupied with CH4 or larger molecules, such as CO2, H2S, C3H8, 2-methylpropane, or 2-methylbutane. • Raman spectra indicate the immediate enclathration of CH4 into pentagonal dodecahedrons after pressurization of the sample cell with the chosen gas. In contrast, the detection of a hydrate structure with corresponding X-ray diffraction measurements was delayed in time. During the first minutes after pressurization of the sample cell with the chosen gas mixture no X-ray signal proving the formation of a crystalline hydrate structure could be detected. These observations from Raman spectroscopy and X-ray diffraction in combination may indicate that the solid phase formed within the first minutes is an agglomeration of hydrate cavities (preferentially CH4loaded pentagonal dodecahedrons) with an amorphous character rather than a crystalline hydrate structure. • Depending on the pressure and temperature conditions, a structure I CH4 hydrate phase forms besides the thermodynamically preferred mixed hydrate phase. The structure I CH4 hydrate phase may coexist as a metastable phase besides the mixed hydrate phase or disappear rapidly. • The composition of the gas encased into the hydrate phase differs from the composition of the feed gas. In all investigated systems the larger gas molecule compared to CH4 was enriched in the hydrate phase. This was already observed for mixed hydrates formed from a CH4− (C2H6)−C3H8 gas mixture by Kumar et al.33 From the results of the microscopic observation and Raman spectroscopic investigations it can be concluded that the guest molecule is dissolved in the water phase before it is encased into a hydrate cavity. Thereby, the water phase does not necessarily need to be liquid. As described by Wang et al. hydrate formation from ice does not require a conversion of ice into liquid water.34 The hydrate formation from ice may occur within a quasi-liquid layer, which exists between the forming hydrate layer and the surface of the unreacted ice particle. Since the guest molecules need to be dissolved first before they are enclathrated, the water phase is initially supersaturated with

CH4 (in case of a mixed feed gas including CH4). This supports our observations that, depending on the pressure and temperature conditions, the formation of a structure I CH4 hydrate phase besides the mixed hydrate phase is kinetically favored, although the formation of a mixed hydrate which is in chemical equilibrium with the surrounding phases should be thermodynamically preferred. However, the dissolution of the guest molecules may also affect the composition of the hydrate phase. Guest molecules showing good water solubility such as CO2 or H2S enrich in the hydrate phase. Additionally the composition of the hydrate phase seems to be affected by other molecular properties of the hydrate forming gas such as the size. The coordination numbers of water molecules surrounding these gas molecules are 24 for CO2 and H2S, and 28 for both, C3H8 and 2-methylpropane, respectively. Similar to CH4 (coordination number 20) which is easily encased into a pentagonal dodecahedron (512, 20 water molecules), CO2 or H2S should be incorporated simply into a tetrakaidecahedron (51262, 24 water molecules), whereas C3H8 and 2-methylpropane should be encased into a hexakaidecahedron (51264, 28 water molecules). Since H2S does not only occupy the tetrakaidecahedrons but also the pentagonal dodecahedrons of a structure I CH4−H2S mixed hydrate, the enrichment of the larger molecules (compared to CH4) in the hydrate phase is most likely also triggered by the higher stability of the hydrate phase due to a better guest-to-cavity ratio: gas molecules with a guest-to-cavity ratio close to 1.0 may stabilize the cavities much better which in turn leads to a higher stability of the resulting hydrate phase. The reported results show that numerous aspects have to be taken into account to understand the hydrate formation process. Particularly for the formation of mixed hydrates both thermodynamic and kinetic aspects have to be considered.

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ASSOCIATED CONTENT

S Supporting Information *

This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. H



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Article

(21) Uchida, T.; Okabe, R.; Mae, S.; Ebinuma, T.; Narita, H. In situ Observations of Methane Hydrate Formation Mechanisms by Raman Spectroscopy. Ann. N.Y. Acad. Sci. 2000, 593−601. (22) Schicks, J. M.; Luzi-Helbing, M. Cage occupancy and structural changes during hydrate formation from initial stages to resulting hydrate phase. Spectrochim. Acata, Part A 2013, 115, 528−536. (23) Schicks, J. M.; Naumann, R.; Erzinger, J.; Hester, K. C.; Koh, C. A.; Sloan, E. D. Phase transitions in mixed gas hydrates: Experimental observations versus calculated data. J. Phys. Chem. B 2006, 110 (23), 11468−11474. (24) Luzi, M.; Girod, M.; Naumann, R.; Schicks, J. M.; Erzinger, J. A high pressure cell for kinetic studies on gas hydrates by powder X-ray diffraction. Rev. Sci. Instrum. 2010, 81, 125105. (25) Luzi, M.; Schicks, J. M.; Naumann, R.; Erzinger, J. Systematic kinetic studies on mixed gas hydrates by Raman spectroscopy and powder X-ray diffraction. J. Chem. Therm. 2012, 48, 28−35. (26) Kashchiev, D.; Firoozabadi, A. Driving force crystallization of gas hydrates. J. Chrys. Growth 2002, 241 (1−2), 220−230. (27) Atkins, P. W. Physikalische Chemie, 3rd ed.; Wiley-VCH Verlag GmbH: Weinheim, Germany, 2001. (28) Sloan, E. D.; Koh, C. A. Clathrate Hydrates of Natural Gases, 3rd ed.; CRC Press Taylor and Francis Group: Boca Raton, FL, 2008. (29) Sloan, E. D.; Fleyfel, F. A molecular mechanism for gas hydrate nucleation from ice. AIChE J. 1991, 37, 1281−1292. (30) Luzi, M. Kinetic Studies of Mixed Gas Hydrates. Ph.D. Thesis, University of Potsdam, Germany, 2012. (31) Lederhos, J. P.; Christiansen, R. L.; Sloan, E. D. A first order method of hydrate equilibrium estimation and its use with new structures. Fluid Phase Equilib. 1993, 83, 445−454. (32) Das 1 × 1 der Gase; Air Liquide Deutschland GmbH: Dusseldorf, Germay, 2009. (33) Kumar, R.; Linga, P.; Moudrakovski, I.; Ripmeester, J. A.; Englezos, P. Structure and kinetics of gas hydrates from methane/ ethane/propane mixtures relevant to the design of natural gas hydrate storage and transport facilities. AlChE J. 2008, 54, 2132−2144. (34) Wang, X.; Schultz, A. J.; Halpern, Y. Kinetics of methane hydrate formation from polycrystalline deuterated ice. J. Phys. Chem. A 2002, 106 (32), 7304−7309.

ACKNOWLEDGMENTS The authors thank Rudolf Naumann for the technical support and the staff of the GFZ workshops for the construction of the pressure cells.

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