Formation of cyclopentane methane binary clathrate hydrate in brine solutions

Author’s Accepted Manuscript Formation of Cyclopentane Methane Binary Clathrate Hydrate in Brine Solutions Lichao Cai, Brian A. Pethica, Pablo G. Debenedetti, Sankaran Sundaresan www.elsevier.com/locate/ces

PII: DOI: Reference:

S0009-2509(15)00707-1 http://dx.doi.org/10.1016/j.ces.2015.11.001 CES12655

To appear in: Chemical Engineering Science Received date: 2 July 2015 Revised date: 17 September 2015 Accepted date: 1 November 2015 Cite this article as: Lichao Cai, Brian A. Pethica, Pablo G. Debenedetti and Sankaran Sundaresan, Formation of Cyclopentane Methane Binary Clathrate Hydrate in Brine Solutions, Chemical Engineering Science, http://dx.doi.org/10.1016/j.ces.2015.11.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Formation of Cyclopentane Methane Binary Clathrate Hydrate in Brine Solutions Lichao Cai, Brian A. Pethica, Pablo G. Debenedetti, Sankaran Sundaresan∗ Princeton University, Dept. of Chemical and Biological Engineering, NJ 08544, USA

Abstract Building on a our previous study on the kinetics of formation of cyclopentane (CP)-methane binary sII-type hydrate in wellagitated fresh water, analogous experiments have been performed in brine solutions at two salinities (3.5 % and 7.0 % NaCl, w/w) to investigate how salt affects this formation process thermodynamically and kinetically. The hydrate formation rate in salt water is found to be ∼2-3 times smaller than that in fresh water at small subcooling levels (ΔT < 4 K) but at higher subcooling levels, the two become comparable. The methane occupancy in the small cavities of the sII hydrate is also estimated to be ∼0.5 for methane pressures between 1 and 3 MPa under equilibrium conditions, as well as during growth at subcooled conditions (ΔT <∼ 7 K). Keywords: Binary clathrate hydrate, growth kinetics, mass transfer, brine solution, cyclopentane methane hydrate

1. Introduction A wide range of guest species methane, ethane, carbon dioxide etc. form clathrate hydrates of various structures (sI, sII and sH) with water[1]. Clathrate hydrates feature cages of various sizes formed by water molecules connected via hydrogen bonding. These cages are partially occupied by guest molecules that stabilize the structure, allowing hydrates to remain thermodynamically stable (often at elevated pressures) over a range of temperatures well above the ice melting point. Hydrates in oil pipelines can lead to flow assurance problems that motivated early extensive study to better understand and suppress their formation[1, 2]. More recently, clathrate hydrates have been proposed in several applications, including natural gas storage/transportation[3–7], carbon dioxide capture and sequestration [8–16] and desalination [17–25], and several of them could benefit from hydrate being produced at higher temperatures and/or lower pressures. A continuous hydrate-based desalination process would involve a crystallizer in which brine or seawater is mixed with appropriate hydrate formers – usually at sea surface level or at depth to take advantage of greater pressures[26], washing unit[18, 19, 25, 27, 28] to separate the salt-free hydrate particles from concentrated brine solutions, and a device to melt the hydrate to produce fresh water and recover hydrate former(s) as well as small amount of seed hydrate crystals to be returned to the crystallizer. These could be configured for both continuous and semi-continuous operation. The formation of hydrate is usually favored by lower temperatures and higher pressures; single component hydrates, as discussed in our earlier study[22], usually require either high pressures (such as methane hydrate) or low temperatures (such as cyclopentane hydrate and CH3 CCl2 F hydrate), and the cost ∗ Corresponding

author. Tel.:+1(609)258-4583 E-mail: [email protected] (S. Sundaresan)

Preprint submitted to Chemical Engineering Science

of refrigeration and/or pressurization is unfavorable to hydratebased desaliantion. The use of binary hydrate could be a potential solution to reduce such cost significantly. With their large and small cavities filled with different guest species of appropriate sizes, binary clathrate hydrates can form at combinations of higher temperatures and lower pressures, where neither of the corresponding single component hydrates are stable. Cyclopentane (CP) - methane binary hydrate, thermodynamically stable up to 22 ◦ C at a moderately elevated pressure of 2 MPa, conditions where neither methane nor CP hydrates are stable, is a typical candidate for desalination processes. However, the kinetics of its formation are less well understood. With four phases involved – a CH4 -rich vapor phase, a hydrocarbon-rich liquid, an aqueous phase and the hydrate solid phase – the formation and growth of this hydrate is likely to occur at the interfaces between the latter three. This suggests two possible mass transfer barriers: 1. Methane must be transferred from the vapor phase into and across one or both liquid phases to reach the vicinity of the hydrate growing sites. 2. If the aqueous phase is saline, the salt rejected upon hydrate formation must diffuse away. Its accumulation in the vicinity of the growing solid hydrate could lower the driving force for hydrate growth, the so-called concentration polarization effect. In our previous paper [22] the kinetics of the CP-methane binary hydrate growth with fresh water were studied in a wellstirred vessel, and analyzed to show that (CH4) transfer largely defines the overall hydrate growth rate, and that facilitating CH4 transfer would promote the hydrate growth rate. In order to assess the viability of hydrate-based applications such as desalination, which involve forming mixed hydrates from saline water, one must also quantify the effect of salt on hydrate growth rate. With this in mind, the present study examines the kinetics of formation of CP - CH4 hydrates in saline water. Salt Wednesday 4th November, 2015

2.1. Procedure for Measuring Hydrate Equilibrium Conditions The hydrate equilibrium conditions are determined experimentally by monitoring their formation/dissociation [1], which is sometimes achieved through visual observation[29] or using more sensitive apparatus such as a Quartz Crystal Microbalance [30]. As the vessel used in our experiments is not transparent, we followed an isochoric procedure based on monitoring P while varying T, which is analogous to that used by Ouar et al. [31] The reactor is first loaded with water or brine solution and liquid CP; after purging the air in the headspace, the helper gas CH4 is introduced up to the desired P. Starting from a temperature above the melting point (which is dictated by the selected P), the mixture is cooled down stepwise with very slow stirring, allowing a fixed time interval (30 min) following each step. The pressure at the end of each step is recorded (see the blue points in Figure 1); the modest decline in P with decreasing T seen in the figure reflects isochoric cooling of the vapor and

2100 2050 2000 1950 1900 1850

(1) Cooling

(2) Induction Period

o Hydrate Diss (5) Heating w/

He Di ating sso /H cia ydr tes ate

The equipment and schematics employed in this work are the same as in our previous study[22]. Briefly, the hydrates are formed in a 450 mL stainless steel reactor equipped with annular jacket through which a coolant is circulated. The coolant temperature is controlled by a Julabo thermostat. Multiple ports on the reactor head allow injection/discharge of selected hydrate formers (gas/liquid); a Resistance Temperature Detector (RTD) probe (1/10 DIN, OMEGA Eng. Inc., accuracy ∼0.04 ◦ C between 0 and 20 ◦ C) and a pressure transducer (Viatran 345, accuracy of 0.6% of full range 0 ∼ 4 MPa) are also installed and connected to multi-meters (Agilent 34410A) to allow continuous T and P measurements. Mechanical stirring is achieved via a magnetic drive without a rotating seal. The controllers/detectors for T , P and stirrer speed are managed by a LabVIEW program, which performs a series of pre-scripted experiments in a reliable and reproducible fashion. Additional details can be found in our earlier article[22].

ociation

Equilibrium T, P

(4)

2. Experimental Setup

(3) Hydrate Forms

1. Thermodynamically, the introduction of dissolved salt lowers the chemical potential of water in the aqueous phase, making it less favorable to form the hydrate. As a result, a lower temperature (T ) and/or a higher pressure (P) for the helper gas is needed to form the hydrate. In this study, the hydrate equilibrium temperatures corresponding to various methane pressures are measured at salinities of 3.5% and 7% (NaCl, w/w). 2. Kinetically, as noted above, the concentration polarization effect associated with NaCl rejection by the growing hydrates may limit the hydrate formation rate, even if hydrate formation in saline is allowed to occur at the same subcooling level as in the fresh water case. In this study, hydrate formation kinetics are measured over a range of T , P and salinities to assess the severity of concentration polarization.

higher methane solubility at lower T . One could easily reach up to ∼2 K below the melting point without forming hydrates, as both subcooling and active stirring are typically needed to trigger primary nucleation in our experiments. Next, a much lower coolant T is used, and intense agitation (600 RPM) is applied, in order to trigger hydrate formation, signaled by a sharp pressure drop, before raising the temperature back to ∼2 K below the melting point. Since part of methane is now clathrated, the pressure is significantly lower than that observed in the cooling process at the same T . In the melting sequence, represented by the red points in Figure 1, T is raised stepwise with a fixed time interval (120 min) between steps, and the ending pressures are recorded as shown in Figure 1. Before the system temperature reaches the melting point, each temperature rise results in partial melting of the existing hydrate, which releases methane into the headspace. As a result, pressure increases as indicated by stage (4) in Figure 1. Once T is above the melting temperature, all the hydrate crystals have dissociated completely and the P vs. T results for both cooling and heating experiments essentially overlap, as demonstrated by stages (1) and (5) in Figure 1. The intersection of stages (4) and (5) is taken as the hydrate equilibrium (melting) condition. After each cooling and heating cycle, additional methane is loaded to repeat the measurement at different pressures.

P/kPa

dissolved in the aqueous phase will affect both thermodynamic and kinetic aspects of hydrate growth:

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Figure 1: Determination of CP-CH4 hydrate four-phase equilibrium. Stage (1): The mixture is cooled down stepwise with very slow stirring, allowing a fixed time interval (30 min) following each step; the final system pressure is then recorded. Stage (2): The mixture could be cooled a few degrees below the equilibrium conditions without forming hydrates because of kinetic limitations. Stage (3): Hydrate formation consumes methane and leads to substantial pressure decline. Stage (4): The mixture is heated stepwise while maintaining intense stirring, allowing a fixed time interval (120 min) following each step; the system pressure is then recorded. Stage (5): Heating hydrate-free mixture in steps above the melting point.

Since it takes a long time for the hydrate to stabilize its composition by absorbing or releasing the guest molecules in response to the changing P and T , the ending pressures in stage (4) of Figure 1 do not represent equilibrium values (see Appendix A), even though the intersection of stages (4) and (5) does correspond to the equilibrium melting temperature at the given pressure (see below). In fact, the pressure would continue to change slowly even 18 hours after the temperature step, and 2

the red points in this section would move up slightly if a longer waiting period was allowed after each step change in temperature. We have ascertained through a series of tests that 120 minutes of conditioning time is adequate to get a good estimate of the melting condition (i.e. the intersection of stages 4 and 5) with an uncertainty no worse than that inherent in the experimental measurements of P and T .

3. Results and Discussions 3.1. Hydrate Equilibrium In Brine Solution Table 1 lists the four-phase CP-CH4 hydrate equilibrium conditions measured in this study over the pressure range from 1 MPa to 3 MPa. These results are also shown in Figure 3, and compared to literature values. The fresh-water data in this work agree well with those reported by Tohidi et al.[32], Sun et al.[33] and Chen et al.[34] However, the equilibrium data for NaCl solutions (with both 3.5% and 7% salinity) acquired in this work differ significantly from those reported by Chen et al.(3.5% and 7%)[34], which appears to be the only published article that reports such data. For instance, the equilibrium pressure for 289.2 K in 7% NaCl solution is 1.49 MPa in our experiments (see Table 1), in contrast to the 1.78 MPa at 289.14 K reported by Chen et al.(7%); the equilibrium pressure for 3.5% NaCl solution at 295.4 K is 3.03 MPa in Table 1, compared to 4.27 MPa at 295.8 K provided by Chen et al.(3.5%). The discrepancy is beyond the margin of experimental uncertainty. We point out that Chen et al. determined the equilibrium conditions through visual observation; at a constant temperature, the methane pressure is raised/lowered and hydrate formation/dissociation is detected solely by visual observation. Nevertheless, it is unclear how the two methods could yield closer results with fresh water but not for the brine solution. Figures 3a and 3b illustrate how the four phase CP-CH4 hydrate equilibrium curve changes with salinity. In the pressure range of ∼ 1 to 3 MPa, the melting point declines by ∼ 1 K from fresh water to 3.5% in NaCl, and ∼ 3 K from fresh water to 7% in NaCl. In comparison, Chen et al.(3.5%) find the shift introduced by 3.5% NaCl to be ∼3 K. Overall, the magnitudes of the melting point shifts due to salinity seen in our experiments are similar to those observed in the same pressure range for other hydrates formed with methane, ethane, propane, CO2 , etc.[35] Since seawater has a salinity close to a 3.5%(w/w) NaCl solution, approximately half of the feed seawater needs to be converted into hydrate before the residual aqueous phase salinity rises to 7%. Therefore, for a CP-CH4 hydrate-based desalination process that (1) uses seawater as feedstock and (2) does not require very high water conversions, the effect of NaCl on hydrate formation is a reduction of subcooling level of no more than 3 K.

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2.2. Procedure for Hydrate Formation Kinetic Experiments A series of experiments were conducted over a range of operating conditions following the procedure developed in our earlier work[22]. A mixture with known amounts of water (usually 200 mL) and CP (22.0 g), plus methane at pressures ranging from 1 MPa to 3 MPa, is first loaded into the reactor. Then, the mixture is cooled to the desired T (typically below the hydrate melting point) by circulating the coolant through the reactor jacket, while maintaining no or very slow stirring. Vigorous stirring is then initiated to trigger hydrate formation and to provide active mixing. The temperature rises as heat is released by hydrate formation and the pressure declines as methane transfers into hydrate. The T and P are automatically logged by a computer for subsequent analysis. Figure 2 illustrates the data acquired during two hydrate formation experiments performed at the same coolant temperature (15.3 ◦ C), nearly the same starting pressure (∼2 MPa) and the same stirrer speed (600 RPM) but with different salinities (fresh water vs 7.0 % (w/w) NaCl solution). The differences between their T and P trajectories demonstrate that salt affects the hydrate formation rates at nearly identical operating conditions.

1800

1750 1500

Table 1: Four phase CP-CH4 hydrate equilibrium conditions measured in our experiments with (1) fresh water (2) 3.5% (w/w) NaCl solution (3) 7% (w/w) NaCl solution. Accuracy: ±0.1 K for temperature and ±0.02 MPa for pressure.

Figure 2: Temperature and pressure data for two hydrate experiments, one performed with fresh water (black) and one with 7.0 % (w/w) NaCl solution (blue). The same stirrer speed (600 RPM), same amount of cyclopentane (22.0 g) and the same volume of aqueous phase (200 mL of either fresh water or NaCl solution) are used in both cases.

Fresh Water

Through an energy balance analysis, the instantaneous hydrate growth rate on a water basis is recovered from the temperaturetime profiles. Analysis of the pressure data yields methane consumption rate. Aside from the necessary physical parameters adjusted for experiments conducted with brine solutions (e.g. the heat capacity of the aqueous phase; see Appendix B), the data analysis procedure in this work is the same as that applied in the previous work [22] and is therefore not repeated here. 3

3.5% NaCl

7% NaCl

T /K

P/MPa

T /K

P/MPa

T /K

P/MPa

290.6 292.0 292.7 293.6 294.5 295.1 296.0 296.9

1.09 1.32 1.54 1.79 2.07 2.32 2.67 3.08

290.0 291.0 291.9 292.8 294.0 294.8 295.4

1.26 1.48 1.73 2.01 2.39 2.72 3.03

288.5 289.2 290.3 291.2 291.8 292.3 292.8 293.2 293.6 294.2

1.33 1.49 1.76 2.04 2.24 2.38 2.62 2.80 3.00 3.26

3.50 3.00

P/MPa

2.50 2.00 1.50

(see Figure 3 for the 3.5% and 7% NaCl curves), this is a very reasonable assumption for the vapor phase. As indicated by Figure 3b, while a higher order regression will better represent the equilibrium data over a larger temperature range (the dashed curve in Figure 3), ln P measured in this work exhibits good linear dependence on 1/T in the temperature range covered in our experiments, and Δdis Hm(CH4 ) is readily found from the slopes and estimated values of Z. These enthalpy values can be used to estimate the methane occupancy level in the small cavities of the binary hydrate, by assuming that a constant ice-like hydrate dissociation heat (6.0 kJ/mol water) applies for the hydrates and that no methane goes into the large cavities of this sII binary hydrate which are fully occupied by CP. Noting the stoichiometric ratio for sII hydrates of 2 small cavities per 17 water molecules, the implied methane occupancy in small cavities along the equiim,eq librium curve, denoted by θ s,CH , is

Fresh water, this work Fresh water fitted Sun Tohidi Chen 3.5% this work 7.0% this work 3.5 % fitted 7.0 % fitted

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4

15.00

im,eq

θ s,CH = 4

ln(P/Pa)

14.00 13.00 12.00 11.00 10.00 0.00335

Fresh water, this work Fresh water fitted Fresh water, partial linear fit Sun Tohidi Chen 3.5% NaCl, this work 7.0% NaCl, this work 0.00340

0.00345

0.00350

(2)

Table 2: Four phase CP-CH4 hydrate equilibrium conditions measured in our experiments with (1) fresh water (2) 3.5% (w/w) NaCl solution (3) 7% (w/w) NaCl solution. Accuracy: ±0.1 K for temperature and ±0.02 MPa for pressure.

0.00355

1/(T/K)

Salinity

Range of T

(w/w)

(K)

0 3.5% 7.0%

290.6∼296.9 290.0∼295.4 288.5∼294.2

Range of Z

Δdis Hm(CH4 ) (kJ/mol)

0.969∼0.926 0.963∼0.924 0.962∼0.918

111.7∼116.9 105.6∼110.1 102.0∼106.9

im,eq

θ s,CH

4

0.437∼0.457 0.464∼0.484 0.478∼0.501

Table 2 indicates that addition of NaCl up to 7.0%(w/w) results in a modest decrease in Δdis Hm(CH4 ) and a small increase in im,eq θ s,CH at four-phase equilibrium in the temperature range stud4 ied. A similar trend in the enthalpy is reported by Chen et al. [34]. The trend is qualitatively as expected since the formation of clathrate hydrate is thermodynamically less favorable The occupancy changes reported here are quite small, which supports use of the Clausius-Clapeyron equation over the temperature and salinity ranges studied.

Figure 3: (a) Four phase CP-CH4 hydrate equilibrium conditions for fresh water (black), 3.5% (w/w) NaCl solution (red) and 7.0% (w/w) NaCl solution (blue), compared to those reported by Sun et al.[33], Tohidi et al. [32] and Chen et al.[34] (b) Equilibrium conditions presented as ln(P/Pa) vs 1/T graphs. Solid lines are derived via linear regressions of ln(Peq /Pa) with 1/(T/K). The dashed curve corresponds to a quadratic fit of ln(Peq /Pa) as a function of 1/(T /K) that represents all the fresh water data. While the higher-order regression is necessary to capture the data trend across the wider range in the pure water case, the brine data are well represented by a linear regression.

3.2. Kinetics of Binary Hydrate Formation in Brine Solutions The process of forming CP-CH4 hydrate is complicated due to the number of phases and species involved, and the coupling of multiple mass transfer processes. Our previous work [22] gave several insights concerning the kinetics of formation of CP-CH4 hydrate in fresh water, including the following:

Given the four phase equilibrium conditions, the dissociation enthalpy on a methane basis can be estimated from the Clausius-Clapeyron equation: Δdis Hm(CH4 ) d ln P =− d(1/T ) ZR

17 Δdis Hm(H2 O) × 2 Δdis Hm(CH4 )

(1)

Here Z is the compressibility factor of CH4 vapor at the equilibrium condition, which is estimated using the Peng-Robinson equation of state[36] , and R is the gas constant. Strictly speaking, Eq. 1 requires the hydrate and the methane-rich vapor phases to maintain fixed compositions along the equilibrium curve. However, if it is assumed that the hydrate composition varies negligibly within the temperature range of our interest, Eq. (1) gives a first approximation of the hydrate formation enthalpy. Likewise, over the narrow temperature ranges explored 4

1. At a constant stirring speed, the CP-CH4 hydrate formation rate evolves over time as hydrate builds up. The instantaneous rate depends not only on the operating conditions (T , P and stirring speed) but also on the amount of hydrate already formed. 2. Subcooling level is a useful index for correlating growth rates obtained across a wide range of T and P, superior to alternatives such as excess pressure, and is a good measure of the thermodynamic driving force for rates observed under different operating conditions.

Here, subcooling level ΔT refers to the difference between the system temperature and the hydrate equilibrium temperature at the prevailing bulk methane pressure. Similarly the excess methane pressure is the difference between the prevailing methane pressure in the vessel and the equilibrium pressure corresponding to the system temperature. In general, both of these are only apparent quantities as the actual conditions at the growing hydrate crystals are different from the bulk conditions as a result of mass transfer resistance. As this mass transfer resistance is difficult to quantify precisely, the apparent values were used in our earlier study as metrics to compare growth rate at different conditions. The same procedure is followed in this study, as detailed below. Following the methods applied in the fresh water study, the percent water conversion over the first 20 minutes (Figure 4a) or 30 minutes (Figure 4b) after starting hydrate formation is used to characterize the hydrate growth rates at various ΔT levels. The filled and hollow symbols correspond to experiments performed at coolant temperatures of 15.3 ◦ C and 16.3 ◦ C, respectively. The figures summarize results for hydrate growth in fresh water (black), 3.5% NaCl solution (red) and 7% NaCl solution (blue). As readily seen from Figure 3, at a specified temperature, the methane pressure required to achieve a desired ΔT increases with salt concentration; as a result, experiments involving brine solutions have been done over higher ranges of pressures, as summarized in the caption of Figure 4. As the methane pressure decreases during the course of an experiment (e.g., see Figure 2) and the concentration of salt in the brine increases, ΔT decreases gradually with time; this variation is indicated by the error bars in Figure 4, with the points themselves denoting an average level. Comparison of the curves at different salinities indicates that at the same T and ΔT , there is only a modest change in the hydrate formation rate as the salinity increases from 0 to 7%, with the difference never greater than a factor of 2. For ΔT < 4 K, the hydrate formation rate in NaCl solution is smaller than that in fresh water. For ΔT > 4 K, the difference is less significant and the rates in NaCl solutions could sometimes even be higher than those in fresh water. To better understand this behavior, a closer look at the temporal evolution of the hydrate formation rates under different conditions is required. The energy balance analysis procedure is described in our previous work[22]. rw =

K CV dT + (T − T 0 ) L f dt Lf

Percentage Water Conversion after 20min

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Figure 4: Percent water conversion to CP-CH4 hydrate at various subcooling levels after (a) 20 minutes; (b) 30 minutes. The figures show results from experiments conducted at 15.3 ◦ C (solid symbols) and 16.3 ◦ C (empty symbols) at various pressures and salinity levels (black: fresh water; red: 3.5% in NaCl; blue: 7.0% in NaCl). The error bar accounts for the fact that pressure and salinity change during the course of an experiment, leading to a gradual shift in the subcooling level. The same stirrer speed (600 RPM), same amount of cyclopentane (22.0 g) and the same volume of aqueous phase (200 mL of either fresh water, 3.5% or 7.0% NaCl solution) apply to all experiments involved, but the pressures are higher in the cases of NaCl solutions at the same coolant temperature and ΔT . The pressure ranges covered by these tests are 1 MPa to 2 MPa for fresh water, 1.5 MPa to 3 MPa for 3.5% NaCl solution and 1.7 MPa to 3.3 MPa for 7.0% NaCl solution.

various times since the initiation of hydrate formation is shown in Figure 5a, along with the instantaneous apparent subcooling level. Clearly, the apparent subcooling levels are comparable throughout the course of the experiments, with a difference no greater than 0.5 K. The initial temperature increase and the rate of increase in the experiment with NaCl solution are generally lower than those with fresh water. According to Eq. (3), that translates to a lower hydrate formation rate in NaCl solution. As seen in Figure 5a, (T − T 0 ) in the experiment with NaCl solution is larger than that in fresh water experiment at later times, suggesting a higher hydrate formation rate. However, this comparison is deceptive as the cumulative amounts of hydrates formed in the two experiments are different. When the instantaneous growth rates (deduced from Eq. (3)) are plotted against the amount of hydrate formed (found by integrating the instantaneous hydrate growth rate), see Figure 5b, one finds that

(3)

Here rw is the water consumption rate, L f is the latent heat associated with the melting of hydrate (on a water basis), CV is the isochoric heat capacity of the hydrate pressure cell and contents, T 0 is the temperature of the circulating coolant plus a compensation term accounting for heat generated by agitation. K is (with dimension J/(K·s) is the product of wall heat transfer coefficient and the heat transfer area. Figure 5 presents results obtained in hydrate formation experiments in fresh water and 7.0% (w/w) NaCl solution with ΔT ∼ 3 K. The difference between reactor temperature and T 0 at 5

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Figure 5: (a) Temperature excursion and the evolution of subcooling level in two hydrate formation experiments done at similar nominal subcooling level of 3 K. The coolant temperature = 15.3◦ C. The stirrer speed (600 RPM), the amount of cyclopentane (22.0 g) and the volume of aquaous phase (200 mL) are kept the same in the two experiments. During the course of the fresh water experiments (black lines), the pressure drops from 1.5 MPa to 1.3 MPa. In the experiment with 7.0% NaCl solution (blue lines), pressure drops from 2.3 MPa to 2.1 MPa. (b) The instantaneous hydrate growth rates and subcooling levels of the same experiments are now plotted against the amount of hydrates formed (quantified by the number of water moles converted to hydrate)

Figure 6: (a) Temperature excursion and evolution of subcooling level in two hydrate formation experiments done at similar subcooling level of ∼6 K. The coolant temperature is 15.3 ◦ C, the stirrer speed (600 RPM) and the amount of cyclopentane (22.0 g) and the volume of aqueous phase (200 mL) are kept the same in the two experiments. During the course of the fresh water experiments (black lines), the pressure drops from 2.3 MPa to 2.1 MPa. In the experiment with 3.5% NaCl solution (red lines), pressure drops from 2.6 MPa to 2.4 MPa. (b) The instantaneous apparent hydrate growth rates and subcooling levels in the same experiments are now plotted against the amount of hydrates formed (quantified by the number of water moles converted to hydrate)

the hydrate growth rate in NaCl solution is systematically lower than that in fresh water at every conversion level. When experiments are repeated at higher subcooling levels, the difference between the rates in fresh water and NaCl solution becomes less pronounced. Figure 6 is similar to Figure 5, but compares the results obtained with fresh water and 3.5% NaCl solution at ΔT ≈ 6 K. The subcooling levels are very similar at all times (with a difference being less than 0.2 K); furthermore, the temperature profiles are very similar in the two experiments, indicating similar hydrate growth rates. At the very early stage, the hydrate forms at a slightly greater rate in NaCl solution than in fresh water. In order to rationalize these results, multiple factors need be recognized:

2. The apparent excess pressures may be taken as a measure of the driving force for methane transfer from the bulk gas phase to the growing hydrates crystals (defined aq aq as ΔP = f (T, P, cNaCl ) = P − P4-phase equil. (T, cNaCl )) . They are generally not the same between experiments conducted with fresh water and brine solutions, respectively, when fixing other factors to be the same or comparable (i.e. operating temperature T and subcooling level ΔT ) 3. The amount of CH4 pre-dissolved in the liquid phases can be different. For instance, at the same temperature the methane pressure needed to attain the same degree of subcooling is higher in the experiments with saline solutions, while the methane solubility in water is not significantly affected by salt concentration. Thus, more methane is pre-dissolved (in both the aqueous and CP phases) in the experiments with saline solution, which is readily available for hydrate growth at the early stage without need for immediate methane transfer from the vapor phase. This could give rise to faster initial growth rates in saline solutions when compared to fresh water.

1. As hydrates form and grow in saline solutions, they reject salt which results in an accumulation of salt near the growing crystals; the extent of salt accumulation depends on the hydrate growth rate and the rate at which the salt is transported away by diffusion and mixing.

6

For the low ΔT cases represented by Figure 5, evolutions of ΔT are similar for both the fresh water and salt water experiments, and the excess pressure ΔP – driving force of methane transfer – is larger for the 7%(w/w) NaCl solution case than the fresh water case (1.0 MPa vs. 0.75 MPa at the beginning of hydrate formation). Similarly, the pressure is also higher for the 7%(w/w) NaCl solution case (2.3 MPa vs 1.5 MPa at the beginning of hydrate formation), and that leads to a favorable greater amount of pre-dissolved methane. Nonetheless, the growth rate in the salt-water experiment is less than that in the fresh water experiment (see Figure 5b). Taken together, these observations suggest that the mass transfer resistance for the removal of NaCl rejected by the growing hydrates is likely to play a role in hindering the hydrate growth rate. On the other hand, our experiments at higher apparent subcooling levels suggest that, as presented in Figure 6, the growth rates in fresh water and salt water can become similar for the most part at comparable apparent ΔT levels. As in the low subcooling experiment in Figure 5, the apparent excess pressure is significantly higher in the salt-water case than in the fresh water one; however, the differential between the excess pressures is less significant during the two experiments shown in Figure 6. Furthermore, the growth rates at higher subcooling levels are larger than those at the lower subcooling level (indicated by the comparison between Figures 5b and 6b), which suggests that the salt concentration polarization associated with removal of NaCl from the hydrate surface must be greater in the salt-water experiments at higher ΔT levels. Yet, the growth rate in saltwater experiment is comparable to that in fresh water. Therefore, some other factors not resolved in the present study must be at stake as well. For instance, prior studies have indicated different morphologies of hydrate formed at various subcooling levels[37–39], which could potentially contribute to different mass transfer resistance. However, these are only hypotheses that could be probed in future studies.

Apparent Methane Occupancy

1.00

Water 1.05 MPa Water 1.95 MPa 3.5% 1.47 MPa 3.5% 2.65 MPa 7.0% 2.57 MPa

0.80

Water 1.25 MPa Water 2.19 MPa 3.5% 1.71 MPa 7.0% 2.18 MPa 7.0% 2.73 MPa

3.3. Occupancy Derived From Kinetic Data The actual hydrate formation rate on methane basis cannot be determined solely from T and P data of the kind shown in Figure 2, as data on evolution of methane concentrations in the liquid phases are also needed. However, by introducing a quasisteady state assumption, the methane consumption rate can estimated from the T and P data, following the procedure used in our earlier study[22]. Further assuming that all the large cavities of the hydrate are occupied by cyclopentane and that methane can only occupy small cavities, the ratio of the rates inferred on water and methane bases indicates the fraction of small cavities being occupied by methane:  r(CH4 ) 2 ap (4) θ s,CH = 4 r(H2 O) 17 ap

Figure 7 shows θ s,CH estimated in this manner for several 4 different hydrate formation experiments performed at the same coolant temperature of 15.3 ◦ C. All the trajectories reveal low apparent occupancy levels at the beginning of hydrate formation, gradually rising to 0.5 ± 0.1; however, as discussed in our earlier study [22], only the values estimated for the later times reasonably characterize the composition of the hydrate. At the early stage, the hydrate formation mainly consumes the excess methane pre-dissolved in liquid phases, at a faster rate than methane being supplied from the vapor phase; as a result, our analysis based on pressure response and quasi-steady state asap sumption underestimates both r(CH4 ) and θ s,CH at early times. 4 It is clear from Figure 7 that, at the later stages of hydrate forap mation, θ s,CH ∼ 0.5 in all the experiments at this temperature. 4 A salinity up to 7% does not appear to have any systematic (or significant) effect on methane occupancy of the smaller hydrate cavities. Moreover, these values are commensurate with those listed in Table 2 (0.4 ∼ 0.5), which were estimated from the enthalpy of hydrate formation on a methane basis (see equations 1 and 2). The analysis in this section, taken together, sheds some light on the key question that motivated this study, namely, to what extent does the salt impact the kinetics of binary hydrate formation and processes based on them. It is clear from our experiments that, at any given operating condition, the presence of salt in the range relevant for seawater desalination decreases the subcooling level by up to ∼3 K; this can be compensated by a modest increase in methane pressure. Further, at comparable subcooling levels, the overall hydrate growth rate is of the same order of magnitude as in fresh water, smaller by a factor of 2∼3 at low subcooling levels, and comparable at higher subcooling levels. These results encourage further efforts to develop desalination processes based on binary hydrates.

Water 1.47 MPa Water 2.50 MPa 3.5% 1.97 MPa 7.0% 2.34 MPa

0.60 0.40 0.20 0.00 0

500

1000

1500

2000

Duration (s)

4. Conclusions Experimental data on four-phase equilibrium conditions for CP-CH4 hydrate at three salinity levels (0, 3.5% and 7.0% (w/w) in NaCl) and within the pressure range of 1 to 3 MPa are reported. The equilibrium methane occupancy of the small hydrate cavities in the cyclopentane-methane binary hydrate is estimated to be ∼0.5 in the 15 to 20 ◦ C range. The kinetics of

Figure 7: Evolution of apparent methane occupancy in hydrate formation experiments conducted at various salinity levels (black symbols: fresh water; red: 3.5% (w/w) NaCl solution; blue: 7% (w/w) NaCl solution) and initial pressures (specified in the legend). The same coolant temperature (15.3 ◦ C), stirrer speed (600 RPM), amount of cyclopentane (22 g) and volume of aqueous phase (fresh water or NaCl solutions) are used in every experiment. The apparent occupancy is estimated using Eq. (4)

7

hydrate formation were followed by measuring the evolution of temperature and pressure. Such measurements were carried out for different salinity and subcooling levels. The occupancy levels estimated from our kinetic experiments are also ∼ 0.5. The amounts of hydrate formed in 20 and 30 minutes were used as metrics to estimate the effect of salinity on the hydrate growth rates at different subcooling levels. At low subcooling levels (ΔT < 4 K), the growth rates were smaller in saline solutions than in fresh water by a factor of ∼2-3, which is attributed to concentration polarization associated with salt rejection by the hydrate. At higher subcooling levels, the growth rates in saline solutions were found to be comparable to or sometimes larger than those in fresh water. This is likely due to the complex interplay between concentration polarization stemming from slow removal of NaCl from the growing hydrate and mass transfer associated with the supply of methane to the hydrate

Table 3: Physical properties for fresh water and brine solutions at 285 K and 1 atm. [40]

Appendix A. The use of dissociation point as the equilibrium point

P/kPa

2,500 2,000

Fresh Water Fresh Water Fitted 3.5% NaCl 7% NaCl 3.5 % Fitted 7.0 % Fitted Non-Equilibrium Pressures

1,500 1,000 500 0 5.00

10.00

15.00

T/ oC

20.00

CV /(103 J/kg·K)

0 3.5% 7.0%

0.9998 1.0232 1.0486

4.19 4.01 3.84

[1] E. D. Sloan Jr, C. Koh, Clathrate hydrates of natural gases, CRC press, 2007. [2] D. Sloan, C. Koh, A. K. Sum, A. L. Ballard, J. Creek, M. Eaton, J. Lachance, N. Mcmullen, T. Palermo, G. Shoup, L. Talley, Natural Gas Hydrates in Flow Assurance, Gulf Professional Publishing, Boston, 2011. doi:http://dx.doi.org/10.1016/B978-1-85617-945-4. 00013-3. URL http://www.sciencedirect.com/science/article/pii/ B9781856179454000133 [3] J. S. Gudmundsson, V. Andersson, O. I. Levik, M. Parlaktuna, Hydrate concept for capturing associated gas (1998). doi:10.2118/50598-MS. [4] S. Thomas, R. Dawe, Review of ways to transport natural gas energy from countries which do not need the gas for domestic use, Energy 28 (14) (2003) 1461–1477, cited By (since 1996)77. doi:10.1016/S0360-5442(03)00124-5. URL http://www.scopus.com/inward/record. url?eid=2-s2.0-0141674779&partnerID=40&md5= 89bd967e8d1ccb5c12342eb323b089d1 [5] A. Khokhar, J. Gudmundsson, E. Sloan, Gas storage in structure h hydrates, Fluid Phase Equilibria 150 (0) (1998) 383 – 392. doi:10.1016/S0378-3812(98)00338-0. URL http://www.sciencedirect.com/science/article/pii/ S0378381298003380 [6] R. Kumar, P. Linga, I. Moudrakovski, J. A. Ripmeester, P. Englezos, Structure and kinetics of gas hydrates from methane/ethane/propane mixtures relevant to the design of natural gas hydrate storage and transport facilities, AIChE Journal 54 (8) (2008) 2132–2144. doi:10.1002/aic. 11527. URL http://dx.doi.org/10.1002/aic.11527 [7] E. D. Sloan, Fundamental principles and applications of natural gas hydrates, Nature 426 (6964) (2003) 353–363. [8] A. Yamasaki, M. Wakatsuki, H. Teng, Y. Yanagisawa, K. Yamada, A new ocean disposal scenario for anthropogenic co2 : Co2 hydrate formation in a submerged crystallizer and its disposal, Energy 25 (1) (2000) 85–96. doi:10.1016/S0360-5442(99)00036-5. URL 10.1016/S0360-5442(99)00036-5 [9] A. Saji, H. Yoshida, M. Sakai, T. Tanii, T. Kamata, H. Kitamura, Fixation of carbon dioxide by clathrate-hydrate, Energy Convers. Manage. 33 (5) (1992) 643–649. [10] M. K. Mondal, H. K. Balsora, P. Varshney, Progress and trends in co2 capture/separation technologies: A review, Energy 46 (1) (2012) 431–441. doi:10.1016/j.energy.2012.08.006. URL http://www.sciencedirect.com/science/article/pii/ S0360544212006184 [11] L. C. Ho, P. Babu, R. Kumar, P. Linga, Hbgs (hydrate based gas separation) process for carbon dioxide capture employing an unstirred reactor with cyclopentane, Energy 63 (0) (2013) 252–259. doi:10.1016/j.energy.2013.10.031. URL http://www.sciencedirect.com/science/article/pii/ S0360544213008827 [12] H. J. Lee, J. D. Lee, P. Linga, P. Englezos, Y. S. Kim, M. S. Lee, Y. D. Kim, Gas hydrate formation process for pre-combustion capture of carbon dioxide, Energy 35 (6) (2010) 2729–2733. doi:10.1016/j.energy.2009.05.026. URL http://www.sciencedirect.com/science/article/pii/ S0360544209001960 [13] P. Babu, R. Kumar, P. Linga, Pre-combustion capture of carbon dioxide in a fixed bed reactor using the clathrate hydrate process, Energy 50 (0) (2013) 364 – 373. doi:10.1016/j.energy.2012.10.046.

Financial support through the Grand Challenges Program and Project X Innovation Fund at Princeton University is greatly appreciated.

3,000

ρ/(103 kg/m3 )

References

5. Acknowledgments

3,500

Salinity (w/w)

25.00

Figure 8: Non-equilibrium ending pressures obtained at the melting stage of hydrate equilibrium measurement. Each determined equilbrium pressure (solid marks) is accompanied by the corresponding non-equilibrium pressures

B. Physical properties of fresh water/brine solutions used in the data analysis Different parameters for the fresh water and brine solutions are needed when deriving rw via Eq. (3), a procedure developed in the earlier paper [22], and they are summarized below. While these properties vary slightly within the pressure and temperature ranges in this studied, the deviation is neglected without introducing significant error. 8

[14]

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

[24]

[25]

[26]

[27]

[28]

URL http://www.sciencedirect.com/science/article/pii/ S0360544212008262 P. Linga, R. Kumar, P. Englezos, The clathrate hydrate process for post and pre-combustion capture of carbon dioxide, Journal of Hazardous Materials 149 (3) (2007) 625–629. doi:http://dx.doi.org/10.1016/j.jhazmat.2007.06.086. URL http://www.sciencedirect.com/science/article/pii/ S0304389407009557 P. Linga, R. Kumar, P. Englezos, Gas hydrate formation from hydrogen/carbon dioxide and nitrogen/carbon dioxide gas mixtures, Chemical Engineering Science 62 (16) (2007) 4268–4276. doi:10.1016/j.ces. 2007.04.033. URL http://dx.doi.org/10.1016/j.ces.2007.04.033 P. Babu, P. Linga, R. Kumar, P. Englezos, A review of the hydrate based gas separation (hbgs) process for carbon dioxide pre-combustion capture, Energy 85 (2015) 261 – 279. doi:http://dx.doi.org/10.1016/j.energy.2015.03.103. URL http://www.sciencedirect.com/science/article/pii/ S0360544215004120 R. W. Bradshaw, J. A. Greathouse, R. T. Cygan, B. A. Simmons, D. E. Dedrick, E. H. Majzoub, Desalination utilizing clathrate hydrates, Report, Sandia National Laboratories (2007). R. A. McCormack, G. A. Niblock, Build and operate a clathrate desalination pilot plant, Report 31, Thermal Energy Storage, Inc., 6362 Ferris Square, Suite C, San Diego, Caliifornia 92121, USA (1998). R. A. McCormack, G. A. Niblock, Investigation of high freezing temperature, zero ozone, and zero global warming potential clathrate formers for desalination, Report 59, Thermcal Energy Storage, Inc. (2000). R. McCormack, J. Ripmeester, Clathrate desalination process using an ultrasonic actuator, uS Patent App. 14/347,228 (Aug. 14 2014). URL http://www.google.com/patents/US20140223958 J.-H. Cha, Y. Seol, Increasing gas hydrate formation temperature for desalination of high salinity produced water with secondary guests, ACS Sustainable Chemistry & Engineering 1 (10) (2013) 1218–1224. L. Cai, B. A. Pethica, P. G. Debenedetti, S. Sundaresan, Formation kinetics of cyclopentaneˆa??methane binary clathrate hydrate, Chemical Engineering Science 119 (0) (2014) 147 – 157. doi:http://dx.doi.org/10.1016/j.ces.2014.08.025. URL http://www.sciencedirect.com/science/article/pii/ S0009250914004436 K. nam Park, S. Y. Hong, J. W. Lee, K. C. Kang, Y. C. Lee, M.G. Ha, J. D. Lee, A new apparatus for seawater desalination by gas hydrate process and removal characteristics of dissolved minerals (na+ , mg2+ , ca2+ , k+ , b3+ ), Desalination 274 (2011) 91 – 96. doi:http://dx.doi.org/10.1016/j.desal.2011.01.084. URL http://www.sciencedirect.com/science/article/pii/ S0011916411001111 K. C. Kang, P. Linga, K. nam Park, S.-J. Choi, J. D. Lee, Seawater desalination by gas hydrate process and removal characteristics of dissolved ions (na+ , k+ , mg2+ , ca2+ , b3+ , cl− , s2 o2− 4 ), Desalination 353 (2014) 84 – 90. doi:http://dx.doi.org/10.1016/j.desal.2014.09.007. URL http://www.sciencedirect.com/science/article/pii/ S0011916414004731 S. Han, J.-Y. Shin, Y.-W. Rhee, S.-P. Kang, Enhanced efficiency of salt removal from brine for cyclopentane hydrates by washing, centrifuging, and sweating, Desalination 354 (2014) 17 – 22. doi:http://dx.doi.org/10.1016/j.desal.2014.09.023. URL http://www.sciencedirect.com/science/article/pii/ S0011916414004986 M. Max, Land-based desalination using positively buoyant or negatively buoyant/assisted buoyancy hydrate, uS Patent 6,531,034 (Mar. 11 2003). URL https://www.google.com/patents/US6531034 H. F. Wiegandt, R. L. Von Berg, J. P. Leinroth, Piston bed and its design, Industrial & Engineering Chemistry Process Design and Development 11 (3) (1972) 404–414. arXiv:http://dx.doi.org/10.1021/ i260043a013, doi:10.1021/i260043a013. URL http://dx.doi.org/10.1021/i260043a013 H. Wiegandt, R. V. Berg, P. Patel, The crossflow piston bed, Desalination 25 (3) (1978) 303 – 324. doi:http://dx.doi.org/10.1016/ S0011-9164(00)80328-8. URL http://www.sciencedirect.com/science/article/pii/

S0011916400803288 [29] W. M. Deaton, J. Frost, E. M., Hydrates and Their Relation to the Operation of Natural-Gas Pipe Lines, U. S. Bureau of Mines Monograph 8, 1946. [30] A. H. Mohammadi, B. Tohidi, R. W. Burgass, Equilibrium data and thermodynamic modeling of nitrogen, oxygen, and air clathrate hydrates, Journal of Chemical & Engineering Data 48 (3) (2003) 612– 616. arXiv:http://dx.doi.org/10.1021/je025608x, doi:10. 1021/je025608x. URL http://dx.doi.org/10.1021/je025608x [31] H. Ouar, S. Cha, T. Wildeman, E. Sloan, The formation of natural gas hydrates in water-based drilling fluids, Chemical engineering research & design 70 (A1) (1992) 48–54. [32] B. Tohidi, A. Danesh, A. Todd, R. Burgass, K. Østergaard, Equilibrium data and thermodynamic modelling of cyclopentane and neopentane hydrates, Fluid Phase Equilibria 138 (1ˆa??2) (1997) 241 – 250. doi:10.1016/S0378-3812(97)00164-7. URL http://www.sciencedirect.com/science/article/pii/ S0378381297001647 [33] Z. G. Sun, S. S. Fan, K. H. Guo, L. Shi, Y. K. Guo, R. Z. Wang, Gas hydrate phase equilibrium data of cyclohexane and cyclopentane, Journal of Chemical and Engineering Data 47 (2) (2002) 313–315, iSI Document Delivery No.: 532KY Times Cited: 16 Cited Reference Count: 13 AMER CHEMICAL SOC WASHINGTON. doi:10.1021/je0102199. URL ://000174475100035 [34] Z.-Y. Chen, Q.-P. Li, Z.-Y. Yan, K.-F. Yan, Z.-Y. Zeng, X.-S. Li, Phase equilibrium and dissociation enthalpies for cyclopentane + methane hydrates in nacl aqueous solutions, Journal of Chemical & Engineering Data 55 (10) (2010) 4444–4449. arXiv:http://dx.doi.org/10.1021/ je100597e, doi:10.1021/je100597e. URL http://dx.doi.org/10.1021/je100597e [35] A. H. Mohammadi, W. Afzal, D. Richon, Gas hydrates of methane, ethane, propane, and carbon dioxide in the presence of single nacl, kcl, and cacl2 aqueous solutions: Experimental measurements and predictions of dissociation conditions, The Journal of Chemical Thermodynamics 40 (12) (2008) 1693 – 1697. doi:http://dx.doi.org/10.1016/j.jct.2008.06.015. URL http://www.sciencedirect.com/science/article/pii/ S0021961408001432 [36] D.-Y. Peng, D. B. Robinson, A new two-constant equation of state, Industrial & Engineering Chemistry Fundamentals 15 (1) (1976) 59–64. [37] Y. Ishida, Y. Takahashi, R. Ohmura, Dynamic behavior of clathrate hydrate growth in gas/liquid/liquid system, Crystal Growth & Design 12 (6) (2012) 3271–3277. arXiv:http://dx.doi.org/10.1021/ cg300416x, doi:10.1021/cg300416x. URL http://dx.doi.org/10.1021/cg300416x [38] R. Ohmura, S. Matsuda, T. Uchida, T. Ebinuma, , H. Narita, Clathrate hydrate crystal growth in liquid water saturated with a guest substance: observations in a methane + water system, Crystal Growth & Design 5 (3) (2005) 953–957. arXiv:http://dx.doi.org/10.1021/cg049675u, doi:10.1021/cg049675u. URL http://dx.doi.org/10.1021/cg049675u [39] R. Ohmura, S. Kashiwazaki, Y. H. Mori, Measurements of clathratehydrate film thickness using laser interferometry, Journal of crystal growth 218 (2) (2000) 372–380. [40] D. G. Archer, R. W. Carter, Thermodynamic properties of the nacl + h2o system. 4. heat capacities of h2o and nacl(aq) in coldstable and supercooled statesˆa?, The Journal of Physical Chemistry B 104 (35) (2000) 8563–8584. arXiv:http://dx.doi.org/10.1021/ jp0003914, doi:10.1021/jp0003914. URL http://dx.doi.org/10.1021/jp0003914

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