Effect of subcooling and amount of hydrate former on formation of cyclopentane hydrates in brine

Desalination 278 (2011) 268–274

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Desalination j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / d e s a l

Effect of subcooling and amount of hydrate former on formation of cyclopentane hydrates in brine Djurdjica Corak a,⁎, Tanja Barth a, Sylvi Høiland b, Tore Skodvin a, Roar Larsen b, Tore Skjetne c a b c

University of Bergen, Norway SINTEF Petroleum Research, Norway Ecowat AS, Norway

a r t i c l e

i n f o

Article history: Received 11 January 2011 Received in revised form 12 May 2011 Accepted 13 May 2011 Available online 12 June 2011 Keywords: Desalination Cyclopentane gas hydrate Kinetics Effective hydrate number Hydrate mass

a b s t r a c t As a concept for a new water desalination technology, the use of gas hydrates is under development. In support of this work, experiments have been conducted to observe the behavior of cyclopentane hydrates and to provide data on thermodynamics, kinetics, the effective hydrate number and the purity of the water recovered from the hydrates. The cyclopentane hydrate formation experiments are performed at subcooling temperatures of 5.6 K and 3.6 K at atmospheric pressure. The brine used is 3 wt.% NaCl. The results show that the kinetics of hydrate formation at a subcooling of 3.6 K is significantly slower than the kinetics for a subcooling of 5.6 K. The effective hydrate number seems to be a function of the subcooling temperature, with 3.6 K subcooling giving a number close to the theoretical value. The quality of the desalinated water is strongly dependent on the experimental procedure and the general observation is that subcooling at 5.6 K provides better purification of the water. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Gas hydrates are naturally occurring crystalline compounds that consist of a network of water molecules which incorporates gas molecules [1]. Hydrates have recently received considerable interest in several research fields within environmental and industrial chemistry. Due to their high content of hydrocarbon gases, naturally occurring hydrates have become a point of interest as a possible future energy source [2]. In general, hydrate formation occurs when water and gas are mixed at low temperatures and high pressures. On a global basis, they are distributed in subsurface permafrost regions of the Arctic and at deep seafloors, e.g. along the Norwegian continental shelf [3]. Hydrates also represent a challenge for the oil industry since the pressure and temperature conditions required for hydrate formation may occur in pipelines during the transportation of oil and gas. Gas hydrates formation can lead to partial plugging and even complete blockage of the pipelines [4]. In addition to thermodynamic conditions, the formation and properties of gas hydrates depends on several factors, such as the water composition and the type of hydrate former (the inclusion compound), which typically could be a hydrocarbon with one to five carbons, or CO2. Based on the capability of gas hydrates to form a solid substance consisting of clean water and gas, the possibility of using hydrates for water desalination has been investigated during the last decade [5] , [6] , [7] and is actively being developed at industrial scale at present. Among ⁎ Corresponding author. Tel.: + 47 93827689; fax: + 47 55589490. E-mail address: [email protected] (D. Corak). 0011-9164/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.desal.2011.05.035

a number of possible applications, clean water for platforms and ships could help to reduce NOx emission due to the fact that by injecting water steam into turbine and combustion engines one can achieve NOx reduction to below 2 ppm without losing flame stability [8]. This water needs to be very clean to prevent damage to the machinery. One approach to remove water-soluble substances and producing ultrapure water using gas hydrates has recently been developed by Ecowat Company and tested in medium scale laboratory facilities at elevated pressure and low temperature [9]. The basis of this idea is to mix a hydrate former and polluted water under optimal temperature and pressure conditions in order to form gas hydrates. The hydrate solid phase is separated from the remaining concentrated polluted water and then melted. The final result of the whole process is pure water, concentrated polluted water and hydrate former, which may be recycled in the process. Gas hydrate formation and decomposition are exothermic and endothermic processes respectively, which can lead to their mutual inhibition during phase changes. However, the exothermic and endothermic processes also represent a possibility of optimizing the process in terms of energy consumption. By utilizing the heat from hydrate formation to melt the hydrates further down the process line, minimal energy consumption may be achieved. The aim of the proposed industrial process is desalination of large amounts of water over a short period of time with minimal energy use. An optimization of the process is thus needed. In this study, cyclopentane is chosen as hydrate former for sII (structure II) hydrates. The thermodynamics of cyclopentane hydrate have previously been investigated using differential scanning calorimetry

D. Corak et al. / Desalination 278 (2011) 268–274

269

Data acquisition system

Ultra turrax stirrer

Cooling bath

Thermometer

The level of cooling liquid

Reactor

Fig. 1. Schematic diagram of the experimental setup.

2. Experimental method The experimental procedure has previously been described in Corak et al. [12] and will be briefly reviewed here. 2.1. Apparatus A simple experimental setup was used, consisting of a reactor, a round-bottomed three necked flask (500 ml), fitted with a paddle stirrer connected to an ultra turrax stirrer as shown in Fig. 1. Two temperature sensors are inserted into two of the necks in contact with the contents of the round-bottomed flask. In order to achieve a stable temperature in the reaction system, the flask is submerged in a thermostatted cooling bath Julabo F34 filled with a cooling liquid (50 vol.% glycol and 50 vol.% distilled water). The upper part of the flask was covered by thermal-insulation material since it was not submerged in the cooling liquid (see Fig. 1). However, there is a temperature gradient between the cooling medium and the flask, so the cooling bath was set at 0.4 °C and 2.4 °C in order to achieve stable subcooling temperatures in the flask of 5.6 K (1 °C thermometer readout) and 3.6 K (3 °C readout) . The temperature stability of the cooling bath was controlled by measuring the temperature of the bath over approximately 8 h. The temperature is continuously logged using a data acquisition system. 2.2. Experimental procedure Liquid cyclopentane (Sigma Aldrich, ≥99.5%) and brine (3 wt.% NaCl) are mixed in a specified ratio at 900 RPM, and then cooled down during continuous stirring to the specified temperature. The temperature must be within in the stable hydrate region of the corresponding phase diagram, i.e. below 6.6 °C, as shown in Fig. 2. In order to avoid variations in induction time and to achieve a better experimental reproducibility, a small piece of ice is added to the flask to initiate hydrate formation when the temperature specified for the experiment has been achieved and is stable. Hydrates then form at

a rate in accordance with their kinetics, while temperature vs. time data is continuously logged as showed in Fig. 3. When the temperature has re-stabilized, portions of the hydrate slurry are removed and filtered by vacuum suction in order to separate the hydrate phase and the brine. Excess water is then removed from portions of the hydrate phase using a cooled centrifuge (8000 RPM, 3 min, −5 °C). In order to determine an optimal centrifugation rate, several hydrate portions were centrifuged at 4500, 8000 and 11,500 RPM. The purity of the hydrate water was similar for rates 8000 and 11,500 RPM while results for rate of 4500 RPM showed higher NaCl contents. A cotton plug is placed in the bottom of each tube to collect the excess water. The remaining hydrate phase is collected, quantified by weight and left to melt. Cyclopentane is removed through evaporation using a water bath (50 °C, 1–2 h), and the mass of the pure water is quantified. Blank runs showed that water loss is between 1 and 2 wt.%. The purity of the hydrate water is determined by measuring the conductivity of the dilute solution assuming that only NaCl ions contribute to the conductivity since the electrical conductivity of hydrocarbons is not higher than 10− 18 Ω/cm [13]. 1.40

1.20

1.00

Pressure, bara

of cyclopentane/water emulsions [10] , [11]. In this work, particular attention is focused on how subcooling and cyclopentane quantity influence the hydrate formation process. The parameters under investigation are: The effective hydrate number, i.e. the ratio between water and hydrate former in the hydrate structure, the purity of the produced hydrate phase with respect to salt, the rate of the hydrate formation and the amount of hydrate produced.

x

x

0.80

0.60

0.40

0.20

0.00 0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

Temperature, ° C Fig. 2. Hydrate PT curve for 1.2 vol.% cyclopentane and 3 wt.% NaCl brine. Subcooling temperatures of 5.6 and 3.6 K are marked in hydrate region to the left and above the solid line.

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2.2

The calculated hydrate numbers are based on the experimental results, given as:

2.0

Temperature (° C)

cal

NH =

1.8

nexp H2 O

ð2Þ

nexp cp

where the experimentally estimated moles of water and cyclopentane are included. The calculated hydrate number thus represents the water/hydrate former ratio in the produced hydrate structure at the given experimental conditions. Experimentally the calculated hydrate number is found from:

1.6 1.4 1.2

exp

cal

1.0

NH =

mhw × Mwcp mexp cp

× MwH2 O

ð3Þ

0.8

Fig. 3. An example of recorded temperature data of cyclopentane hydrates formation.

exp where mhw is the mass of the purified hydrate water in the test sample, Mwcp and MwH2O are molecular masses of cyclopentane and exp water, respectively, and mcp is the mass of cyclopentane in the test sample. The mass of cyclopentane is found from:

2.3. Experimental variables

mcp = mhydrate −mH2O

0

10

20

30

40

Time (min)

exp

The experiments are conducted as a function of subcooling temperature and cyclopentane/brine ratio. The volume of brine is 400 ml in all cases while the cyclopentane volume is varied. In all the experiments, water is the excess phase. The cyclopentane/brine ratio is expressed in terms of wt.% converted water, when assuming that all the cyclopentane is forming hydrates to give the theoretical weight percentages of converted water which are varied from 15.1 to 40 wt.% of the total water mass. The range of conversion is determined based on preliminary runs showed that the conversion above 40 wt.% gives solid hydrate phase while the hydrate amount is too small for collection under 15 wt.%. The values shown in Table 1 are based on the theoretical hydrate number, i.e. the ratio of water molecules to cyclopentane molecules in the hydrate structure, of 17 for cyclopentane hydrate [1] meaning that all the large cages in the hydrate structure are occupied with cyclopentane molecules. The different cyclopentane/brine ratios in Table 1 were tested at the two subcooling temperatures 3.6 K and 5.6 K. The positions of these temperatures in the phase diagram of cyclopentane hydrates are shown in Fig. 2. 2.4. Output parameters 2.4.1. Calculated hydrate number The hydrate number NH is defined as the number of water molecules in the hydrate crystals divided by the number of hydrate former molecules (in this case cyclopentane), that occupy particular cavities in the water framework [1]: NH =

nH2 O

ð1Þ

ncp

where nH2O and ncp are moles of water and cyclopentane, respectively. Table 1 Experimental scheme of cyclopentane vs. water ratios. Sample No. 1 2 3 4 5 6

Theoretical water conversion(1) (wt %)

Mol % cyclopentane(2)

15.1 20.3 25.2 30.0 34.9 40.0

0.9 1.2 1.5 1.7 2.0 2.3

(1) Calculated from the theoretical hydrate number of 17, assuming all cyclopentane is converted to hydrate. (2) The amount of cyclopentane is expressed as a mole percentage of cyclopentane relative to the initial total number moles of cyclopentane and water.

exp

exp

ð4Þ

exp where mhydrate is the mass of the hydrate test sample. Loss of hydrates by melting during the work-up procedure is assumed not to systematically influence the values of the experimental hydrate numbers, since both water and cyclopentane will be removed as fluids.

2.4.2. Amount of NaCl removed The purification efficiency is presented as wt.% removed NaCl as a percentage of the initial NaCl amount of 3 wt.%. 2.5. Reproducibility In order to check the reproducibility of the experimental results, each experiment has been performed at least twice. In general, the results show acceptable reproducibility in light of the simplified experimental set-up and procedures. The experimental errors are expressed in terms of % deviation from the mean value (see below). The % deviations are generally less than 10% between parallel experiments, though some of the results are associated with higher deviations. This is discussed in further detail below. 3. Results and discussion 3.1. The calculated hydrate number The variations in calculated hydrate numbers as a function of subcooling and cyclopentane/brine ratio (expressed in terms of mol % cyclopentane, see Table 1) are illustrated in Fig. 4 and given in Appendix A. The calculated hydrate numbers seem to be independent of the cyclopentane/brine ratio in the range that has been investigated, and are relatively constant with increasing amounts of hydrate former (i.e. as the theoretical maximum percentage of water conversion increases). However, the calculated hydrate number seems to be significantly dependent on subcooling temperature. The theoretical hydrate number for cyclopentane hydrates is 17 [1], and the calculated hydrate numbers are found to deviate from this, being approximately 11 and 19 for subcooling of 5.6 K and 3.6 K, respectively. A value of 19 means that there is less cyclopentane in the hydrate structure than ideally possible, i.e. not all the large cavities are filled with guests, which is quite as expected. A value of 11, however, means that the hydrate structure is associated with more cyclopentane than the theoretical ideal, which is less comprehensible. Such values can be obtained when more than one guest molecule occupies a cavity, as seen for nitrogen and argon hydrate [14]. However, the

D. Corak et al. / Desalination 278 (2011) 268–274

3.6 K 5.6 K ----- Theoretical hydrate number

Effective hydrate number

22 20 18 16 14 12 10 8 6 0.9

1.2

1.5

1.8

2.1

2.4

Cyclopentane (mole %) Fig. 4. Calculated hydrate numbers for experimental series of 3.6 K and 5.6 K subcooling.

size of a cyclopentane molecule makes this explanation less credible [4], and the value of 11 is more likely to be due to the presence of unconverted cyclopentane which is encapsulated both in hydrate shells formed around cyclopentane droplets and inside pores of the hydrate sample. The removal of encapsulated cyclopentane will require physical breakdown of the hydrate crystals, which makes it be less easy to remove by filtration and centrifugation than the free liquid phases. This probably contributes to the total measured cyclopentane mass in the hydrate samples. The presence of encapsulated cyclopentane is more probable in hydrates formed at the higher subcooling, because the crystallization is more rapid, while the slower crystallization at the low subcooling will give better conditions for formation of stochiometric crystals. The results of the parallel experiments for both experimental series show a degree of variation, as Fig. 4 shows, though the experiments performed at 3.6 K are associated with somewhat less experimental variation than the experiments performed at 5.6 K. For the 3.6 K series, the deviations from mean are generally less than 6%, but for the 5.6 K series deviations as high as 30% are observed. Since the results from the experimental series of subcooling 5.6 K are explained by the assumption that not all cyclopentane was converted, this would naturally give rise to experimental variation.

3.2. Desalination The results showing the purification efficiency in the experiments are graphically illustrated in Fig. 5, with specific values given in Appendix B. The results vary from less than 70% to close to 90% removal of NaCl.

Fig. 5. Purification efficiency for cyclopentane hydrates for initial subcooling temperatures 3.6 K and 5.6 K.

271

The purification efficiency is best in the experiments performed at subcooling 5.6 K, except when the amount of hydrate former is high (40% theoretical water conversion). The results vary from 89% to 73% removal of NaCl, with the best values obtained at low amounts of cyclopentane (15 and 20% water conversion). For the 3.6 K series, the results vary from 87% to 67% removal of NaCl, with the best results obtained at low cyclopentane amounts (15% water conversion) also for this series. For the 5.6 K series, there seems to be a weak decrease in purification efficiency as the amount of cyclopentane former is increased. For the 3.6 K series, this tendency is not observed, but rather a minimum value for purification efficiency is observed at 30% water conversion. The main reason for the difference in the purity of hydrates formed at subcoolings 3.6 and 5.6 K can be the concentration of salt in the excess water. Due to the larger mass of hydrate formed at subcooling 3.6 K, the quantity of the excess water is smaller with a high NaCl concentration. Thus any excess water which is not removed during the workup process causes higher residual salinity of purified hydrate water. The residual salinity is likely to be strongly related to the procedure for separating the solid hydrate phase form the residual brine. Adhesion measurements between cyclopentane hydrate particles show that adhesion forces increase linearly with increasing temperature [14]. These results suggest that the attractive force between hydrate particles formed at subcooling 3.6 K is stronger and more resistant to mechanical force like e.g. the centrifugal force is. For this reason it is possible to hypothesize that hydrate crystals grown at 3.6 K subcooling adhere to each other in a stronger framework than the ones grown at 5.6 K subcooling, and that may be enough to conserve more trapped brine between the crystals as the extraction procedure involving the centrifuging is performed. This remains speculation, however, and more data at a wider range of subcoolings would be needed to explore this further. The desalination efficiency shows relatively large standard deviations as shown in Fig. 5, partly due to variations in the conductometric measurements. However the average results show an acceptable consistency. 3.3. The rate of hydrate formation Kashichiev et al. [15] suggested that the driving force for an isobaric regime of gas hydrate formation is a function of subcooling, as shown in Eq. (5). Δμ = ΔSe ΔT

ð5Þ

ΔSe is the hydrate dissociation entropy per hydrate building unit at equilibrium temperature andΔTis the subcooling. This relation is in agreement with the result obtained in this work, i.e. more subcooling causes stronger driving force. The difference in rates of formation for subcoolings of 3.6 K and 5.6 K is illustrated in Fig. 6. Sakamoto et al. [16] also reports significantly faster kinetics of cyclopentane hydrate formation at larger subcooling. Since the hydrate formation is an exothermic process, the rise, decrease and stabilization of the temperature during this process provide information of kinetics and thermodynamics of hydrate growth. However, in many experiments it was difficult to determine the start and end point for the hydrate formation process. Therefore the kinetics of the cyclopentane hydrate formation was evaluated in terms of the steepest gradient of temperature increase during hydrate formation (i.e. the inflection point of the derivative of the temperature rise as a function of time, (δT/δt)). The steepest gradients for both experimental series are graphically illustrated in Fig. 7, and specified in Appendix C. The results show that the kinetics of the hydrate formation are dependent on subcooling temperature, as expected, due to the difference in the driving forces for hydrate formation which is higher

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D. Corak et al. / Desalination 278 (2011) 268–274

4.0

3.6 K 5.6 K

3.6 K 5.6 K

220

3.5

180

Hydrate mass (g)

Temperature (° C)

200 3.0 2.5 2.0 1.5

160 140 120 100 80

1.0

60 0

50

100

150

200

250

300

40

350

Time (min)

0.9

1.2

1.5

1.8

2.1

2.4

Cyclopentane (mole %) Fig. 6. The temperature changes during cyclopentane hydrate formation for subcooling of 3.6 K and 5.6 K. The theoretical water conversion for both subcoolings is 25.2 wt.%.

for 5.6 K subcooling. The values in Fig. 7 are higher for 5.6 K than for 3.6 K, indicating significantly faster kinetics at subcooling 5.6 K. Increased amounts of cyclopentane causes steeper gradients for both subcoolings (3.6 K and 5.6 K), meaning that faster growth is observed, though the effect of amount of hydrate former is significant for 5.6 K whereas only weakly increasing the rate for 3.6 K. The dependence of kinetics on volume of cyclopentane is as expected, since increased amounts of hydrate former lead to better mass transport, less diffusion resistance and increased number of nucleation sites for hydrate formation. For the 5.6 K series, the effect of the amount of cyclopentane seems to level off at the higher volumes, 35 and 40% water conversion. This reflects the fact that at some specific volume (in this case, approximately 30% water conversion), further increase of cyclopentane amount will not enhance the mass transport due to other limitations of the set-up, such as the stirring rate. 3.4. Quantification of the total hydrate mass In the simple experimental setup that was used, it was not possible to collect and quantify the entire hydrate phase, but it was visually observed that the volumes of cyclopentane hydrates formed at subcooling 3.6 K were significantly larger than the volumes formed at subcooling 5.6 K. However, quantitatively it can roughly be estimated using the effective hydrate number, assuming that all 3.6 K 5.6 K

Steepest gradient

0.25

Fig. 8. The calculated masses of the cyclopentane hydrates for subcooling of 3.6 K and 5.6 K.

cyclopentane is converted to hydrate according to this water/ cyclopentane ratio. This means that the total hydrate mass can be expressed in terms of the total cyclopentane mass (mcp) plus the mass of converted water calculated by the use of the calculated hydrate number NHcal: total

cal

mhydrate = mcp + NH ncp MwH2 O

ð6Þ

where ncp is the moles of cyclopentane in the total sample. The results are shown in Appendix D, and graphically illustrated in Fig. 8. As can be seen, the total hydrate mass increases with increasing amount of cyclopentane as expected. Since the calculated hydrate number is closer to the theoretical value, the amount of hydrates produced at 3.6 K is larger than at 5.6 K, which corresponds with the visual observations. It should be noted that due to the slow kinetics, the hydrates at 3.6 K are allowed to grow over a longer period of time, which ultimately may give hydrate amounts closer to the theoretical value. From the discussion of the effective hydrate number results (see Section 3.1), it was indicated that the 5.6 K series contained some level of encapsulated and unconverted cyclopentane. This corresponds well with the observation that lower amounts of hydrates are formed at 5.6 K, since the encapsulated cyclopentane is unavailable for hydrate formation. The reason is likely to be related to the kinetics (see Section 3.3) and morphology, as fast growth may tend to encapsulate liquids if the mixing is insufficient, limiting the mass transfer and hence the hydrate growth in the system.

0.20

4. Conclusion 0.15

0.10

0.05

0.00 0.9

1.2

1.5

1.8

2.1

2.4

Cyclopentane (mole %) Fig. 7. Steepest gradients of temperature increase for cyclopentane hydrates formation at initial subcooling temperatures 3.6 K and 5.6 K.

Cyclopentane hydrate formation was investigated at atmospheric pressure for subcoolings 3.6 K and 5.6 K. The mole percent of cyclopentane of total liquid was varied from 0.9 to 2.3 while the water quantity and salinity were unchanged for all the experiments. The results show that the effective hydrate numbers, desalination, the rate of cyclopentane hydrate formation and the hydrate mass are predominantly functions of subcooling, while the cyclopentane quantity does not affect these results in a large degree. The effective hydrate numbers for subcooling of 3.6 K are close to the theoretical one while subcooling of 5.6 K causes seemingly lower values. The desalination is more effective and the rate of hydrate formation is significantly higher for subcooling of 5.6 K. In a desalination perspective, the high degree of subcooling seems to overall yield the

D. Corak et al. / Desalination 278 (2011) 268–274

best results, with rapid formation of the hydrates and the higher degree of desalination, even though the amounts that are formed are significantly lower than the theoretical maximum.

273

Appendix C. Steepest gradients and percent deviation from the mean for subcooling 3.6 K (15 data points) and subcooling 5.6 K (17 data points).

Acknowledgments 3.6 K

This work is a part of The Innovation Program Maroff which is supported by The Research Council of Norway (NFR). The authors would like to gratefully acknowledge NFR, Sintef Petroleum Research, Ecowat AS and University of Bergen for their financial and professional support. Appendix A. Calculated hydrate numbers and percent deviation from the mean for subcooling 3.6 K (15 data points) and subcooling 5.6 K (17 data points).

3.6 K

Cyclopentane Exp. Calculated Mean Deviation Calculated Mean Deviation from the from the hydrate mole % numb. hydrate mean (%) mean (%) number number 0.9

1.2

1.5

1.7

2.0 2.3

1 2 3 1 2 3 1 2 3 1 2 3 4 1 2 1 2 3

16.9 18.5 20.1 19.2 22.0 19.8 20.2 21.3 19.7 20.0 17.9

20.2 19.3 19.2 19.2

18.5

20.3

20.4

18.9

19.7 19.2

− 8.6 0.0 8.6 − 5.5 8.2 − 2.7 − 0.9 4.4 − 3.5 5.5 − 5.5

2.4 − 2.4 0.0 0.0

10.2 9.3 12.0 10.2 7.4 13.0 11.7 10.4

− 3.1 − 11.4 14.5 10.2 0.2 − 27.6 27.4 11.02 14.7 1.7

13.6 13.0 7.8 13.5 11.2 10.8 13.6 11.5 12.8

12.0

10.5

11.0 12.6

1.2

1.5

1.7

2.0 2.3

1 2 3 1 2 3 1 2 3 1 2 3 4 1 2 1 2 3

1.5

2.0 2.3

81.6 87.0 79.0 84.2 69.7 78.5 82.8 72.7 68.6 67.2 68.2

82.5

78.1 69.5 83.7 71.5

73.8

77.5

74.7

67.7

77.6

− 1.1 5.4 − 4.3 8.7 − 10.0 1.3 10.8 − 2.7 − 8.1 − 0.7 0.7

5.8 − 5.8 7.9 − 7.9

3.02 2.43 2.43 3.05 3.05 3.64 3.64 3.64 3.05 3.64 3.64

3.64 4.23 4.23 4.27

2.62

3.25

3.44

3.64

3.93 4.25

15.0 − 7.5 − 7.5 − 6.0 − 6.0 12.1 5.7 5.7 − 11.4 0.0 0.0

− 7.5 7.5 − 0.4 0.4

3.6 K

88.5 81.8 89.4 86.9 87.4 87.4 82.1 83.5

86.5

82.0 75.0 77.6 79.6 79.3 82.2 54.6 73.1 85.7

78.5

87.2

82.8

0.954 0.971 0.971 1.21 1.41 1.51 1.58 1.46 2.43 2.12 1.82 2.06 2.06 2.31 2.18 2.06 2.13

0.965

1.38

1.52

2.11

2.20 2.12

− 1.2 0.6 0.6 − 12.1 2.3 9.8 4.0 − 4.0 15.1 0.7 − 13.6 − 2.1 − 1.8 1.8 2.8 − 2.9 0.1

Appendix D. Calculated hydrate mass and percent deviation from the mean for subcooling 3.6 K (15 data points) and subcooling 5.6 K (17 data points).

5.6 K

Cyclopentane Exp. Removed Mean Deviation Removed Mean from the NaCl mole % numb. NaCl mean (%) (wt.%) (wt.%) 0.9

1.2

1 2 3 1 2 3 1 2 3 1 2 3 4 1 2 1 2 3

23.7 18.2 − 29.6 22.9 − 6.7 − 9.7 23.2 4.1 16.5

Appendix B. Desalination and percent deviation from the mean for subcooling 3.6 K (15 data points) and subcooling 5.6 K (17 data points). 3.6 K

0.9

1.7

5.6 K

5.6 K

Cyclopentane Exp. Steepest Mean Deviation Steepest Mean Deviation mole % numb. gradient (×10−2) from the gradient (×10− 1) from the (×10−2) mean (%) (×10− 1) mean (%)

Deviation from the mean (%) 2.2 − 5.5 3.3 − 0.4 0.2 0.2 − 0.8 0.8

4.4 − 4.5 − 1.1 1.3 80.8 − 1.8 1.8 71.1 − 23.3 2.7 20.5

5.6 K

Cyclopentane Exp. Calculated Mean Deviation Calculated Mean Deviation from the from the hydrate mole % numb. hydrate mean (%) mean (%) mass (g) mass (g) 0.9

1.2

1.5

1.7

2.0 2.3

1 2 3 1 2 3 1 2 3 1 2 3 4 1 2 1 2 3

73.9 79.6 85.3 111.0 124.3 113.7 143.4 149.9 140.3 169.9 155.0

79.6 − 7.1 0.0 7.1 116.3 − 4.6 6.9 − 2.2 144.5 − 0.8 3.7 − 2.9 162.4 4.6 −4.6

199.1 191.4 217.9 217.9

195.3

2.0 − 2.0 217.9 0.0 0.0

49.9 46.8 56.5 67.7 54.1 81.0 92.7 84.8 124.6 120.2 82.8 123.9 124.6 121.6 164.7 144.8 157.8

− 2.3 − 8.3 10.6 67.6 0.1 − 20.0 19.9 88.8 4.5 − 4.5 51.1

112.9

10.4 6.5 − 26.7 9.8 123.1 1.2 − 1.2 155.7 5.7 5.7 1.3

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