Experimental Measurements and Thermodynamic Modeling of

Article pubs.acs.org/jced

Experimental Measurements and Thermodynamic Modeling of Clathrate Hydrate Dissociation Conditions for Refrigerants R116, R23, and Their Mixture R508B Hamed Hashemi,† Saeedeh Babaee,† Paramespri Naidoo,† Amir H. Mohammadi,*,†,‡ and Deresh Ramjugernath*,† †

Thermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, Howard College Campus, King George V, Avenue, Durban, 4041, South Africa ‡ Institut de Recherche en Génie Chimique et Pétrolier (IRGCP), Paris Cedex, France ABSTRACT: Hydrate dissociation conditions for the refrigerants R116 (C2F6), R23 (CHF3), and their mixture R23/R116 (46:54 mass percent ratio) in the regions of hydrate−aqueous−vapor and hydrate−aqueous−liquid refrigerant equilibria were measured. The experimental measurements were performed within the pressure range of (0.45 to 9.2) MPa and the temperature range of (272.2 to 293.2) K. A thermodynamic model was developed for the prediction of the measured dissociation conditions. For this purpose, PRSV equation of state coupled with the MHV2 GE-EoS mixing rule along with the UNIFAC (original) activity coefficient and van der Waals−Platteeuw (vdW-P) models were applied for the fluid and hydrate phases, respectively. The results show satisfactory agreement between the experimental and predicted values. The Kihara potential parameters for the refrigerants investigated were also obtained and are reported in this article. distillation and reverse osmosis (RO).2,3,5,8−10 A group of new pure and mixed refrigerants has to date been considered as long-term alternatives for low-temperature refrigeration. The azeotropic mixture of the refrigerants R23 (CHF3) and R116 (C2F6) (46:54 mass percent ratio), with the ASHRAE number R508B, is an alternative to R503 and R13 (due to its zero ozone depletion potential). However, the formation of clathrate hydrates in such refrigeration systems is speculative as there is no data.11−13 Due to the motives/explanations presented, it is essential to study the dissociation conditions of refrigerant hydrates in search of feasible processes. Hence in this study, the dissociation conditions of clathrate hydrates of refrigerants including R116 (C2F6), R23 (CHF3), and their mixture R23/ R116 have been investigated. Furthermore, these dissociation conditions were measured at pressures above the upper quadruple point Q2 (hydrate−liquid water−vapor−liquid refrigerant). In this paper, to fully examine the hydrate phase behavior the dissociation conditions of the considered refrigerants have been studied in a wide range of temperatures and pressures from lower quadruple point to the pressures above the upper quadruple point. A thermodynamic model is proposed based on the van der Waals−Platteeuw (vdW-P)14 model to represent the hydrate phase, while the vapor and

1. INTRODUCTION The interaction between water and gas molecules of appropriate size and shape (molecular diameter normally less than 9 Å), at temperatures typically slightly higher than the freezing point of water, and at elevated pressures (usually higher than atmospheric pressure) result in the formation of an ice-like compounds, namely gas hydrates (clathrate hydrates).1−14 Gas hydrates first became a concern to the oil and gas industries when it was learned that their formation caused blockages in the transportation pipelines.1,2,5 Nowadays, these compounds have become an area of great research interest for scientists in many applications such as gas storage and transportation, cold storage technology in air conditioning systems, gas separation, and purification of saline water, etc.2−13 because of their outstanding properties. The ability of refrigerant hydrates to be used as phase-change materials (PCM) in cold storage applications in air conditioning systems has been well established.2,4−7,11,13 The favorable properties, such as, appropriate temperature of formation (278 to 285) K and high enthalpy of formation, are some of the reasons why these compounds are considered as replacements for conventional cold storage materials such as ice, eutectic salt, and water which suffer from the disadvantages of low formation temperature, small heat of fusion, and low density of storage, respectively.6,7 Furthermore, the cyclic formation and dissociation of refrigerant hydrates has been utilized as an alternative method for the purification of saline water instead of conventional approaches such as multistage flash (MSF) © XXXX American Chemical Society

Received: August 26, 2014 Accepted: October 7, 2014

A

dx.doi.org/10.1021/je5007955 | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

calculated uncertainties in the temperature and pressure measurements are ± 0.1 K and ± 0.005 MPa, respectively. 2.3. Procedure. The equilibrium cell was washed with distilled water, drained, and thereafter placed under vacuum before starting the measurements. After introducing an appropriate amount of distilled water (approximately 16 cm3) to the cell, it was once again evacuated to ensure that all gases were removed. The hydrate dissociation conditions of the refrigerants investigated were measured using the isochoric pressure search method.4,5,19 The main reason for selecting this method is its accuracy compared to visual methods.5 After pressurizing the equilibrium cell to a desired pressure, the thermostat temperature was set to a value below the anticipated hydrate formation temperature (which was found according to the fact that most refrigerants can form hydrate at the temperature range of (278.15 K to 288.15 K)). To pressurize the cell to pressures above the upper quadruple point, Q2, (hydrate−liquid water−liquid refrigerant region) a hydraulic hand pump was used. Hydrate formation was confirmed by the abrupt depression in the cell pressure. After the formation of an appropriate amount of hydrate (the pressure drop was significant) and after the pressure of the cell stabilized, the temperature was increased stepwise. At the beginning of the heating steps, the temperature of the cell was increased rapidly in 0.5 K steps. As the heating curve approached the final dissociation point, the temperature was increased slowly (0.1 K steps). At each step the pressure was allowed to stabilize (approximately 1 h duration). The final dissociation point was taken as the equilibrium dissociation condition at which a sudden change in the slope of the heating curve was observed (see Figure 2).

liquid phases were modeled using the modified Peng− Robinson (PR) equation of state (EoS)4,15 along with the MHV2 GE-EoS mixing rule4,16,17 coupled with the UNIFAC activity coefficient model.18 The results show reasonable agreement between the experimental and predicted values.

2. EXPERIMENTAL SECTION 2.1. Materials. The suppliers of the chemicals used in this study, as well as their purities are reported in Table 1. The reported purities are as stated by the suppliers in their product certificates. Table 1. Chemical Purities and Details of the Suppliers of the Chemicals Used in This Study formula

puritya

supplier

H2O CHF3 C2F6 0.46 CHF3 + 0.54 C2F6c

0.998 0.998 0.998

UKZN A-gas A-gas A-gas

chemical distilled water R23 R116 R508B

b

a

Mole fraction as stated by the supplier. bUltrapure Millipore Q water with an electrical conductivity of 18 MΩ·cm. cMass fraction.

2.2. Apparatus. A schematic diagram of the experimental apparatus used in this study is shown in Figure 1. The main part of the experimental setup consists of a high pressure stainless steel equilibrium cell with an internal volume of approximately 40 cm3 which can withstand pressures up to 20 MPa. The contents of the cell are agitated using a mechanical stirrer which is connected to a stirrer motor at the top of the cell. The stirrer speed was fixed at 650 rpm for all experiments. The temperature of the cell is controlled using a thermostated bath with a stability ± 0.1 K. A Pt100 (platinum temperature probe) is used for measurment of the cell temperature. The Pt100 was calibrated using a WIKA primary temperature probe which is connected to a WIKA CTH 6500 multimeter. The pressure of the cell is measured using a WIKA pressure transducer with an uncertainty of ± 0.05 % of full scale. The

3. THERMODYNAMIC MODELING The equality of fugacities in the neighboring phases has been used as the equilibrium criteria in this study, which follows as (ignoring water content of the vapor phase): f wL = f wH

(1)

Figure 1. Schematic diagram of the apparatus used in this study: C, cell; CF, coldfinger; DAS, data acquisition system; GC, gas cylinder; MJ, mechanical jack; MS, mechanical stirrer; R, regulator; PT, pressure transmitter; TP, temperature probe; TPC, temperature programmable circulator; V-i, valve; VP, vacuum pump;. B



Article

k 0 = 0.378893 + 1.489715ω − 0.17131ω 2 + 0.01965ω3 (8)

where parameter k1 is unique or specific for each compound. The pure component parameters Tc, Pc, ω, and k1 of the PRSV EoS,15 are given in Table 3. The EoS mixture parameters, a and Table 3. Pure Component PRSV EoS Parameters Used in This Study

where f Lw is the fugacity of water in the liquid phase and f Hw represents the fugacity of water in the hydrate phase. 3.1. Hydrate Phase. The fugacity of the water in the hydrate phase was obtained using the solid solution theory of van der Waals and Platteeuw14 as follows:19,21

a

(2)

where the definition of each term in eq 2 is given elsewhere. The transition parameters from water to hydrate which have been used in the thermodynamic model are listed in Table 2.

Ia IIb

1297 883

Δh0w/J·mol−1 liquid

ice

liquid

ice

1151 808

4.6 5.0

3.0 3.4

a

(3)

⎛ RT ⎞ bi = 0.077796⎜ c ⎟ ⎝ Pc ⎠

(5)

α(T ) = (1 + k(1 − Tr)0.5 )2

(6)

k = k 0 + k1(1 − Tr0.5)(0.7 − Tr)

(7)

group

subgroup

Rk

Qk

7 40 53

H2O CF2 CHF3

H2O CF3 CHF3

0.9200 1.4060 1.6335

1.400 1.380 1.608

Obtained from ref 25.

(9)

7 H2O

40 CF2

53 CHF3

0.00 0.00 −109.52

0.00 0.00 36.99

203.54 118.65 0.00

Obtained from ref 25.

4. RESULTS AND DISCUSSION Hydrate phase equilibrium for the refrigerants R23, R116, and their mixture R23/R116 within equilibrium regions of hydrateliquid water-vapor (H−Lw−V) and hydrate-liquid water-liquid refrigerant (H−Lw−LR) have been measured and are reported in Figure 3 and Table 6. To the best of our knowledge, in the case of R116 and R508B there is no experimental data in the open literature; hence this constitutes new hydrate dissociation data. For R23 hydrates, several experimental data from literature are also compared with the data obtained in this study. The Kihara potential parameters obtained for the aforementioned refrigerants are reported in Table 7 using minimization of the following objective function:

where

(4)

main

7 H2O 40 CF2 53 CHF3

3.2. Fluid Phases. The fugacity of water in the liquid phase in eq 1 was obtained using the PR EoS modified by Stryjek and Vera (PRSV):15

⎛ R2T 2 ⎞ c ⎟ α (T ) ai(T ) = 0.457235⎜ ⎝ Pc ⎠

22 23 24,

Table 5. UNIFAC Group Interaction Parameters, amn/K, Used in This Studya

It is assumed that R23 forms structure I. bIt is assumed that R116 and R508B form structure II.

RT a − 2 V−b V − 2bCV − b

ref

0.00535 0.00000

in which the temperature-independent group interaction parameters a and b are listed in Table 5. More details regarding the thermodynamic model used in this study and the definitions of each term and parameter are given elsewhere.4

a

P=

k1

0.265 0.229

⎡ ⎛ a ⎞⎤ Ψmn = exp⎢ −⎜ mn ⎟⎥ ⎣ ⎝ T ⎠⎦

Δv0w/cm3·mol−1

−4858 −5201

ω

4.836 3.042

listed in Table 4. The interaction parameters of the UNIFAC activity model between main groups are given by

Table 2. Phase Transition Parameters between the Empty Hydrate Lattice and Liquid Water Used in This Study19 Δμ0w/J·mol−1

Pc/MPa

299.07 293.04

Table 4. UNIFAC Volume and Surface Area Parameters Used in This Studya

4

structure

Tc/K

R23 R116

b, were calculated using the MHV2 EoS-GE mixing rule as mentioned earlier.16,17 For the calculation of the activity coefficient of refrigerants and water, the UNIFAC activity model (original) was applied as pointed out earlier.4,18 The UNIFAC volume and surface area parameters, Rk and Qk, are

Figure 2. Primary heating and cooling curve for R508B hydrate obtained in this study.

⎛ −Δμ β‐ H ⎞ w ⎟⎟ f wH = f wβ exp⎜⎜ RT ⎝ ⎠

refrigerant

C



Article

Table 7. Optimized Kihara Potential Parameters Obtained in This Study refrigerant

a, nm

σ, nm

ε/k, K

R23(CHF3) R116(C2F6)

9.1 10.8

31.0 27.9

200 230

model results. The maximum and minimum absolute deviation (AD) between the experimental data and model results are 0.9 and 0, respectively. It is found that the addition of R23 to R116 shifts the hydrate dissociation curve to higher temperatures (at a specific pressure) region.

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CONCLUSIONS Equilibrium hydrate dissociation data for refrigerants R116, R23, and their mixture R23/R116 within the equilibrium regions of hydrate−aqueous phase−liquid refrigerant and hydrate−aqueous phase−vapor were measured and are reported. It was attempted in this study to cover a wide temperature and pressure range of refrigerant hydrate dissociation conditions. Hence, the measurements were performed from the lowest possible pressure in which the corresponding refrigerant could form hydrate above the freezing point of water to pressures above the upper quadruple point. The experimental measurements were carried out in the temperature range of (272.2 to 293.15) K and at pressures up to 10 MPa. A thermodynamic model was developed based on the van der Waals−Platteeuw (vdW-P) model14 for the hydrate phase, while the fluid phase was modeled using PRSV EoS15 coupled with the MHV2 GE-EoS mixing rule16,17 along with the UNIFAC (original) activity coefficient model.4,18 The Kihara potential function was employed to consider the interaction between the hydrate former and water in the hydrate cavities. The Kihara potential parameters were obtained for the refrigerants considered and reported. The model predictions show satisfactory agreement with the experimental data. The

Figure 3. Hydrate dissociation conditions of the refrigerants studied in this work: ●, R23 (this work); ▼, R23 (ref 26); ▲, R116 (this work); ★, R508B (this work); Q2, upper quadruple point (H−Lw−LR−V); solid lines, model predictions. R508B is an azeotropic mixture of the refrigerants R23 and R116. NDP

Fobj =

⎛ 1 ⎞ ⎜ ⎟∑ ⎝ NDP ⎠ k=1

⎛ |Texp − Tcal| ⎞ ⎜⎜ ⎟⎟ Texp ⎝ ⎠k

(10)

in which Texp and Tcal are the experimental and calculated hydrate dissociation temperatures, respectively, and NDP is the number of data points. The entire experimental data set for each refrigerant was used for the optimization of the Kihara potential parameters. In the optimization procedure, the initial guesses were taken from other refrigerants (with structures similar to the refrigerants considered in this study) of which the Kihara potential parameters are reported.4 The results from the model are also compared graphically with the measured data in Figure 3. Table 6 shows the absolute deviations (|Texp − Tcal|) between the experimental data obtained in this study and the Table 6. Hydrate Dissociation Data Obtained in This Studya R23 Pexp MPa 0.450 0.647 0.713 0.956 1.010 1.133 1.350 1.566 1.819 1.988 2.544 2.727 3.440 4.49 6.49 9.15 a

T K

R508B (Azeotropic mixture of R23 and R116) Tcalc. K

H−Lw−V 275.4 276.3 278.3 279.2 279.2 279.9 281.7 282.2 282.1 282.7 283.3 283.5 284.6 284.8 285.8 285.9 286.9 286.9 287.8 287.5 289.3 289.1 290.1 289.5 292.0 292.1 H−Lw−LR 292.3 292.2 292.8 292.5 293.2 292.9

Pexp AD

b

0.9 0.9 0.7 0.5 0.6 0.2 0.2 0.1 0.0 0.3 0.2 0.6 0.1

MPa 0.527 0.830 1.090 1.458 1.744 2.082 2.415 2.923 3.360 4.890 7.164 8.957

T

Tcalc.

K

K

H−Lw−V 272.2 272.9 276.5 276.1 278.5 278.1 280.8 280.1 281.9 281.4 283.3 282.6 284.3 283.5 285.7 284.9 286.5 285.6 H−Lw−LR 286.4 286.2 286.5 286.7 286.6 286.9

R116 Pexp

T

Tcalc.

AD

MPa

K

K

0.7 0.4 0.4 0.7 0.5 0.7 0.8 0.8 0.9

0.521 0.595 0.811 0.944 1.225 1.784

b

2.600 3.906 7.371

H−Lw−V 273.6 273.8 274.3 274.4 275.9 275.7 276.5 276.4 277.9 277.4 278.7 278.7 H−Lw−LR 279.2 279.3 279.6 279.5 280.1 280.0

ADb 0.2 0.1 0.2 0.1 0.5 0.0 0.1 0.1 0.1

0.2 0.2 0.3

0.1 0.3 0.3

Overall uncertainties: u(T) = 0.1 K; u(P) = 0.005 MPa. bAD = |Texp − Tcal|. D



Article

(19) Mohammadi, A. H.; Anderson, R.; Tohidi, B. Carbon monoxide clathrate hydrates: Equilibrium data and thermodynamic modeling. AIChE J. 2005, 51, 2825−2833. (20) Holder, G.; Corbin, G.; Papadopoulos, K. Thermodynamic and molecular properties of gas hydrates from mixtures containing methane, argon, and krypton. Ind. Eng. Chem. Fundam. 1980, 19, 282−286. (21) Anderson, F.; Prausnitz, J. Inhibition of gas hydrates by methanol. AIChE J. 1986, 32, 1321−1333. (22) Proust, P.; Vera, J. PRSV: The Stryjek−Vera modification of the Peng−Robinson equation of state. Parameters for other pure compounds of industrial interest. Can. J. Chem. Eng. 1989, 67, 170− 173. (23) Ramjugernath, D.; Valtz, A.; Coquelet, C.; Richon, D. Isothermal vapor− liquid equilibrium data for the hexafluoroethane (R116) + propane system at temperatures from (263 to 323) K. J. Chem. Eng. Data 2009, 54, 1292−1296. (24) Orbey, H.; Sandler, S. I. Equation of state modeling of refrigerant mixtures. Ind. Eng. Chem. Res. 1995, 34, 2520−2525. (25) Kleiber, M. An extension to the UNIFAC group assignment for prediction of vapor-liquid equilibria of mixtures containing refrigerants. Fluid Phase Equilib. 1995, 107, 161−188. (26) Mooijer-van den Heuvel, M. M.; Sawirjo, N. M.; Peters, C. J. Influence of fluoroalkanes on the phase behaviour of methane gas hydrate systems. Fluid Phase Equilib. 2006, 241, 124−137.

results from this study would be essential information required in refrigeration systems and in hydrate-based processes.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected], [email protected]. *E-mail: [email protected]. Funding

This work is based upon research supported by the South African Research Chairs Initiative of the Department of Science and Technology and National Research Foundation. Notes

The authors declare no competing financial interest.

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REFERENCES

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Experimental Measurements and Thermodynamic Modeling of

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