Isothermal Vapor–Liquid Equilibrium Data and Modeling for the

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Isothermal Vapor−Liquid Equilibrium Data and Modeling for the Ethane (R170) + Perfluoropropane (R218) System at Temperatures from (264 to 308) K Mulamba Marc Tshibangu,† Xavier Courtial,† Christophe Coquelet,‡,† Paramespri Naidoo,† and Deresh Ramjugernath*,† †

Thermodynamic Research Unit, School of Engineering, University KwaZuluNatal, Howard College Campus, Durban 4041, South Africa ‡ MINES ParisTech, CTPCentre Thermodynamique des Procédés, 35, Rue Saint Honoré, 77305 Fontainebleau, France ABSTRACT: Isothermal vapor−liquid equilibrium data are presented for the ethane (R170) + perfluoropropane (R218) binary system. Measurements were performed at five isotherms ranging from (264.05 to 308.04) K, with pressure ranging from (0.298 to 4.600) MPa. The measurements were undertaken using a “static-analytic” type apparatus, with sampling of the equilibrium phases via a mobile capillary sampler (ROLSI). The uncertainties in the measurements were within 0.06 K, 0.9 kPa, and less than 0.006 for temperature, pressure, and mole fraction, respectively. The full set of isothermal vapor−liquid equilibrium data was successfully correlated with the Peng−Robinson equation of state, incorporating the Mathias−Copeman alpha function, and the Wong−Sandler mixing rule with the Non-Random Two-Liquid (NRTL) activity coefficient model.

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given by Coquelet and Richon,8 as the vapor−liquid critical line links the critical points of the pure compounds.

INTRODUCTION Due to concerns about the effects of chlorinated refrigerants on the earth’s protective ozone layer, modifications were made to the Montréal Protocol which has prohibited the use of chlorofluorocarbons (CFCs). CFCs are now regarded as ozone-unfriendly fluids in industrialized nations. As a result, there has been a growing interest in the search for more effective and environmentally ozone-friendly fluids. Alternatives have been extended to include hydrocarbons, fluorocarbons, and their mixtures. To this end, isothermal vapor−liquid equilibrium (VLE) data for the ethane + perfluoropropane mixture are investigated in this study. Perfluoropropane has an ozone depletion potential (ODP) of zero and a global warming potential (GWP) of 6950.1 This work is a continuation of a previous study by Ramjugernath et al.2 which aims to investigate the capability of fluorocarbon and hydrocarbon mixtures as potential blended refrigerants, as well as the potential of fluorocarbons as extractive solvents for hydrocarbon separations. The measurements were undertaken at five isotherms for the system (four below and one above the critical temperature of ethane). The VLE data measured were correlated via the direct method using the Peng−Robinson3 equation of state (PR EoS) with the Mathias−Copeman (MC)4 alpha function and the Wong− Sandler (WS)5 mixing rule incorporating the Non-Random Two-Liquid (NRTL)6 activity coefficient model. This system corresponds to a type I or type II system according to the classification of van Konynenburg and Scott7 and the description © 2013 American Chemical Society

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EXPERIMENTAL SECTION Materials. Ethane (R170) (C2H6, CAS number: 74-84-0) and perfluoropropane (R218) (C3F8, CAS number: 76-19-7) were both purchased from Air Products with a certified purity greater than 99 % and 99.97 %, respectively. Both chemicals were used without further purification. Experimental Apparatus. The apparatus used in this work is based on the “static-analytic” method with sampling of both the vapor and liquid phases using a mobile ROLSI10 sampler. A schematic diagram of the experimental apparatus is shown in Figure 1. The main feature of the experimental apparatus is the equilibrium cell which was constructed from 316 stainless steel. The equilibrium cell consists of a cylindrical cavity with an internal diameter of 30 mm and a length of 85 mm which results in an internal volume of approximately 60 cm3. The equilibrium cell houses two sapphire windows and can withstand a maximum pressure of 20 MPa. The equilibrium cell was immersed in a thermo-regulated liquid bath. Accurate temperature measurement of the equilibrium cell was made with the aid of two platinum resistance thermometer probes (Pt-100) placed inside wells drilled into the Received: January 25, 2013 Accepted: March 22, 2013 Published: April 16, 2013 1316

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Figure 1. Flow diagram of the experimental equipment: BTC: bath temperature controller; DAU: data acquisition unit; GC: gas chromatograph; MC: mechanical circulator; PT: pressure transducer; RV: relief valve; V: valve.

The number of moles of component injected was calculated using the volume injected, temperature, and pressure in an equation of state such as the ideal gas or virial equation (virial coefficients obtained from Reid et al.11). A calibration plot was then made of the moles of component versus the GC peak areas. The uncertainty in the vapor and liquid phase concentration is estimated to be less than 0.006 mole fraction. Additional information regarding the uncertainty calculation method can be found in the National Institute of Standards and Technology (NIST) guide.9 Experimental Procedure. At room temperature, the equilibrium cell and its loading lines were initially evacuated. The cell was thereafter loaded with approximately 5 cm3 of perfluoropropane and the desired temperature set. Thermal equilibrium was assumed when the temperature measured by the two probes (inserted at two different locations of the cell corresponding to the vapor and liquid phases) were within the experimental uncertainty for temperature. After recording the vapor pressure of the pure perfluoropropane at the studied temperature, the more volatile component was introduced stepwise, leading to successive equilibrium mixtures of increasing overall ethane content. After each introduction of the lighter component, vigorous stirring was undertaken until the attainment of the equilibrium state. Thermodynamic equilibrium is assumed to be reached when, at constant temperature, the pressure is stable for at least 15 min within the experimental uncertainty for pressure. Thereafter, at least five samples of both

body of the cell, at levels corresponding to the vapor and liquid phases. Both Pt-100 probes were calibrated against a 100 Ω reference probe (CTH 6500, supplied and calibrated by WIKA). The equilibrium cell pressure was measured with a WIKA P-10 pressure transducer (certified accurate to within 0.1 %; range (0 to 10) MPa). The pressure transducer was intermittently calibrated against a reference transducer (CPT 6000 supplied and calibrated by WIKA). The uncertainties in the temperature and pressure measurements are estimated to be within 0.06 K and 0.9 kPa, respectively. Pressure and temperature data were recorded via a computer, linked to an Agilent Data Acquisition Unit (34970A) supplied with the BenchLink Data Logger 3 software (Agilent technologies, v.3.0.4). It provides a real time data display. Analysis of the equilibrium phase samples was carried out using a gas chromatograph (GC) (Shimadzu model GC-17A) equipped with a thermal conductivity detector (TCD) connected to a data acquisition system fitted with the GC Solution Analysis software (v.2.30.00). The analytical column used in the GC was a Porapak Q (length: 3 m, I.D.: 2.2 mm, 100/ 120 Mesh) which was maintained at 353 K, with a helium flow rate of 30 mL·min−1. The TCD used to detect all components was maintained at 473 K with a current intensity of 50 mA and was periodically calibrated. Calibration of the TCD consisted of injecting known volumes of each of the pure components into the GC injector using an SGE gastight syringe. For each volume, at least five samples were injected until the average absolute deviation for the corresponding peak areas were within 1 % error. 1317

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Article 2 ⎡ 100 ⎢ ⎛⎜ xexp − xcal ⎞⎟ + F= ∑ N ⎢⎢ ⎜⎝ xexp ⎟⎠ ⎣

phases (vapor and liquid) were withdrawn and sampled by means of the ROLSI 10 sampler and analyzed by a gas chromatograph.

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MODELING Table 1 lists the critical temperatures (Tc), critical pressures (Pc), and acentric factors (ω) for each of the two pure components.

a

ethane perfluoropropanea a

Tc/K

Pc/MPa

ω

305.40 345.05

4.884 2.680

0.098 0.326

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RESULTS AND DISCUSSION The measured pure component vapor pressures for perfluoropropane are listed in Table 2. The experimental data was Table 2. Experimentala and Calculated Vapor Pressure for Perfluoropropane

Values taken from ref 12.

The Peng−Robinson EoS3 (eq 1) with the Mathias−Copeman4 alpha function (eqs 2 and 3) and the Wong−Sandler mixing rules5 (eqs 3 to 6) incorporating the NRTL activity coefficient model6 (eq 7) were used to correlate the data. P=

a(T )α (T ) RT − 2 c v−b (v + 2bv − b2)

α(T ) = [1 + C1(1 −

Tr ) + C 2(1 −

(1)

Tr )2 + C3(1 −

Tr )3 ]2

if T < Tc

(2)

and Tr )]2

α(T ) = [1 + C1(1 −

if T > Tc

(3)

a b

where C1, C2, and C3 are the adjustable parameters unique to each component and are obtained from the regression of experimental vapor pressures.

1−

(

∑i xi(ai / bi) RT

+

AE(T , P = ∞ , xi) CRT

)

b−

a = RT

⎛

∑ ∑ xixj⎜⎝b − i

j

a ⎞⎟ RT ⎠ij

a

(5)

⎛ ⎛ a ⎞⎟ 1 ⎡⎛ a ⎟⎞ a ⎟⎞ ⎤⎥ ⎜b − = ⎢⎜b − + ⎜b − (1 − kij) ⎝ RT ⎠ij 2 ⎢⎣⎝ RT ⎠i ⎝ RT ⎠ j ⎥⎦ (6)

(7)

where τji =

gji − gii RT

=

gji = exp( −αjiτji)

Δgji RT

Δpb/MPa

253.30 258.11 263.23 264.05 268.17 271.05 278.05 282.74 292.81 308.04 312.78 322.96

0.194 0.238 0.287 0.297 0.343 0.383 0.483 0.553 0.743 1.124 1.256 1.604

0.000 0.001 −0.001 0.000 −0.002 0.002 0.003 −0.002 −0.002 0.007 −0.002 −0.006

Expanded uncertainties (k = 2): U(T) = ± 0.06 K, U(p) = ± 0.9 kPa. (Δp = pexp − pcal).

coefficients

ethane8

perfluoropropanea

C1 C2 C3

0.531 −0.062 0.214

1.030 −3.229 15.487

Regressed from measured vapor pressure data.

The data measured at high temperatures could not be satisfactorily correlated with the model. It is common for there to be difficulties in correlating data in the region close to the critical point because of the weakness of most EoS models to describe the behavior in this vicinity. The vapor pressure data point measured at 303.04 K showed a pronounced deviation from the fitted vapor pressure correlation, and therefore it was not considered when regressing the Mathias−Copeman parameters. New experimental VLE data were measured at five isotherms at (264.05, 271.05, 278.05, 303.04, and 308.04) K. The VLE data along with the computed mole fraction uncertainties for the equilibrium samples are presented in Table 4, with a graphical comparison between the experimental data and model shown in Figure 2. The correlated model parameters are presented in Table 5. The temperature dependency of the model parameters are shown in Figures 3 and 4. The uncertainties in the equilibrium phase composition for both the vapor and liquid mole fractions were estimated to be less than 0.006, taking into consideration the uncertainties in the determination of number of moles for both pure ethane and

The calculation of the excess Gibbs energy gE(T,xi) function is based on the NRTL local composition model. gij − gjj and gji − gii are adjustable parameters, and αji = αij is the nonrandomness parameter. ⎡ τ G τ21G12 ⎤ GE = x1x 2⎢ 21 21 + ⎥ RT G12x1 + x 2 ⎦ ⎣ x1 + G21x 2

pexp/MPa

Table 3. Mathias−Copeman Coefficients (4)

with C = −0.62323

T/K

correlated with PR EoS with the Mathias−Copeman alpha function to obtain parameters which are presented in Table 3.

∑i ∑j xixj(b − a /RT )ij

b=

(10)

where N is the number of data points and (xexp,xcal) and (yexp,ycal) are respectively the measured and calculated liquid and vapor compositions at different fixed temperatures and pressures.

Table 1. Critical Parameters and Acentric Factors compound

⎛ y − y ⎞2 ⎤ exp cal ⎟ ⎥ ∑ ⎜⎜ ⎟⎥ y ⎝ ⎠ ⎥⎦ exp

(8) (9)

τii = αii = 0. αji was set to 0.3, but gij − gjj and gji − gii are adjusted directly to the measured VLE data through a modified simplex algorithm using the following flash-type objective function: 1318

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Table 4. Experimentala p−x−y Data for the Ethane (1) + Perfluoropropane (2) System p/MPa

nx

x1

U(x1)

ny

y1

U(y1)

5 5 5 5 5 5 7 5

0.000 0.386 0.599 0.721 0.775 0.814 0.842 0.873 0.901 1.000

0.004 0.006 0.004 0.004 0.005 0.003 0.003 0.002

5 5 5 5 5 5 6

0.000 0.350 0.537 0.662 0.720 0.770 0.824 0.928 1.000

T/K = 264.05 0.298 0.473 0.713 0.938 1.117 1.266 1.402 1.550 1.693 1.862

5 5 5 5 5 5 5 5

0.000 0.064 0.158 0.250 0.356 0.443 0.541 0.659 0.781 1.000

5 5 5 5 5 5 6

0.000 0.055 0.141 0.246 0.331 0.437 0.569 0.866 1.000

0.002 0.004 0.004 0.004 0.005 0.005 0.004 0.004 T/K = 271.05

0.383 0.569 0.791 1.069 1.256 1.461 1.693 2.112 2.275

0.007 0.004 0.004 0.005 0.005 0.006 0.003

Figure 2. Plot of p−x−y data for the ethane (1) + perfluoropropane (2) system: ◊, 264.05 K; ■, T = 271.05 K; ●, T = 278.05 K; □, T = 303.04 K; ⧫, T = 308.04 K; , model.

0.005 0.005 0.004 0.004 0.003 0.003 0.001

Table 5. Model Parameters Regressed for the Peng−Robinson EoS with Mathias−Copeman Alpha Parameters and the Wong−Sandler Mixing Rule Incorporating the NRTL Activity Coefficient Model T/K

T/K = 278.05 0.483 0.772 0.930 1.231 1.451 1.675 1.865 2.068 2.331 2.498 2.700

5 5 5 5 5 5 5 5 5

0.000 0.086 0.138 0.238 0.319 0.418 0.519 0.622 0.766 0.866 1.000

5 5 5 5 5 6 6 5 5 6

0.000 0.143 0.221 0.290 0.371 0.484 0.578 0.687 0.836 0.877 0.920 1.000

0.002 0.003 0.004 0.005 0.006 0.006 0.008 0.003 0.002

parameters 5 5 5 5 5 5 5 5 5

0.000 0.389 0.499 0.623 0.689 0.738 0.784 0.825 0.878 0.921 1.000

0.004 0.005 0.004 0.005 0.005 0.003 0.003 0.002 0.002

5 5 5 6 5 5 5 5 5 5

0.000 0.367 0.494 0.556 0.615 0.675 0.719 0.770 0.841 0.883 0.924 1.000

0.004 0.005 0.005 0.005 0.004 0.004 0.003 0.004 0.002 0.001

(g12 − g22) (J·mol−1) (g21 − g11) (J·mol−1) k12

264.05

271.05

278.05

303.04

308.04

2028

2915

3337

2867

3926

342.47

276.67

113.30

270.15

−123.18

0.34

0.28

0.26

0.28

0.27

T/K = 303.04 0.995 1.656 1.981 2.255 2.556 2.973 3.295 3.690 4.149 4.334 4.467 4.600

0.002 0.003 0.004 0.004 0.005 0.005 0.004 0.003 0.004 0.003

Figure 3. Plot of the NRTL model parameters versus the temperature for the five isotherms measured (⧫, (g12 − g22); ◊, (g21 − g11); - - -, critical temperature of ethane).

T/K = 308.04 1.124 1.534 1.858 2.221 2.630 3.028 3.416 3.685

5 5 5 6 5 5 5

0.000 0.081 0.153 0.235 0.331 0.431 0.524 0.599

0.002 0.002 0.004 0.004 0.005 0.005 0.005

5 5 5 5 5 5 5

0.000 0.230 0.356 0.457 0.547 0.619 0.662 0.694

perfluoropropane and the repeatability in the VLE data measurements. Deviations between the experimental and the calculated liquid and vapor mole fractions were determined from the MRDU (eq 11) and BIASU (eq 12) calculations. The results obtained are shown in Table 6.

0.004 0.004 0.006 0.005 0.005 0.004 0.004

MRDU(%) = (100/N ) ∑ |(Ucal − Uexp)/Uexp|

(11)

BIASU(%) = (100/N ) ∑ ((Uexp − Ucal)/Uexp)

(12)

where N is the number of data points and U = x1 or y1. The relative volatility is determined using the following equation:

a Expanded uncertainties (k = 2): U(T) = ± 0.06 K, U(p) = ± 0.9 kPa. x, y: liquid and vapor mole fraction; nx, ny: number of samples taken; U(x1), U(y1): liquid and vapor mole fraction uncertainties.

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CONCLUSIONS This paper presents isothermal VLE data and modeling for the ethane + perfluoropropane binary system at temperatures ranging from (264 to 308) K. This system, to our knowledge, has not previously been reported in the literature. The data were measured using a static-analytical method, with sampling of the equilibrium phases using a mobile ROLSI. The uncertainties in the measurements were within 0.06 K, 0.9 kPa, and less than 0.006 for temperatures, pressures, and equilibrium mole fractions, respectively. The experimental vapor pressures for perfluoroethane were correlated with the PR EoS incorporating the MC alpha function. The measured VLE data were satisfactorily modeled via the direct method using the PR EoS with the MC alpha function and the WS mixing rules incorporating the NRTL activity coefficient model.

Figure 4. Plot of the EoS binary interaction parameter (k12) versus temperature for the five isotherms measured (- - -, critical temperature of ethane).

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BIAS x %

MRD x %

BIAS y %

MRD y %

264.05 271.05 278.05 303.04 308.04

−0.14 −0.79 −0.23 −1.01 0.20

0.60 1.81 1.04 1.01 1.18

0.49 1.33 0.93 0.53 −1.28

0.82 1.48 1.04 0.94 1.92

αij =

y /xi yi /xi Ki = i = Kj yj /xj (1 − xi)/(1 − yi )

AUTHOR INFORMATION

Corresponding Author

Table 6. Relative Deviation of MRDU and BIASU Obtained in Fitting Experimental VLE Data with the PR EoS with the Mathias−Copeman Alpha Function and WS Mixing Rule Incorporating the NRTL Model T/K

Article

*E-mail: [email protected]; tel.: +27 31 260 3128. Fax: +27 31 260 1118. 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. The authors acknowledge the support of Pelchem and Department of Science and Technology-Fluorochemical Expansion Initiative. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Simpson, C. R.; Mendicino, L.; Rajeshwar, K.; Fenton, J. M. Environmental Issues in the Electronics/Semiconductor industries and Electrochemical/Photochemical Methods for Pollution Abatement; The Electrochemical Society, Inc.: Pennington, NJ, 1998. (2) Ramjugernath, D.; Valtz, A.; Coquelet, C.; Richon, D. Isothermal vapour-liquid equilibrium data for the hexafluoroethane (R116) + propane system at temperatures from (263 to 323) K. J. Chem. Eng. Data 2009, 54, 1292−1296. (3) Peng, D. Y.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 1976, 15, 59−64. (4) Mathias, P. M.; Copeman, T. W. Extension of the Peng-Robinson Equation of State to Complex Mixtures: Evaluation of the Various Forms of the Local Composition Concept. Fluid Phase Equilib. 1983, 13, 91−108. (5) Wong, D. S. H.; Sandler, S. I. Theoretically Correct Mixing Rule for Cubic Equations of State. AIChE J. 1992, 38, 671−680. (6) Renon, H.; Prausnitz, J. M. Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures. AIChE J. 1968, 14, 135− 144. (7) Van Konynenburg, P. H.; Scott, R. L. Critical Lines and Phase Equilibria in Binary Van Der Waals Mixtures. Philos. Trans. R. Soc. 1980, 298, 495−539. (8) Coquelet, C.; Richon, D. Experimental Determination of phase diagram and modeling: Applications to refrigerant mixtures. Int. J. Refrig. 2009, 32, 1604−1614. (9) http://www.nist.gov/gov/pml/pubs/tn1297/index.cfm. (10) Guilbot, P.; Valtz, A.; Legendre, H.; Richon, D. Rapid on-line sampler injector: a reliable tool for HT-HP sampling and on-line GC analysis. Analysis 2000, 28, 426−431. (11) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The properties of gases and liquids, 4th ed.; McGraw-Hill Book Company: New York, 1987. (12) Dortmund Data Bank (DDB); DDBST Software and Separation Technology GmbH: Oldenburg, Germany, 2002.

(13)

where x and y are liquid and vapor mole fractions for either components i or j. The calculation of the relative volatility was undertaken for the measured, as well as the modeled data. Figure 5 shows a plot of the relative volatility versus the liquid mole fraction. The estimated error bands for the relative volatility, based on the measured data, are 7.5 %. There is generally good agreement between the relative volatility computed from experimental data and that predicted from the model.

Figure 5. Plot of the relative volatility versus the liquid mole fraction for the ethane (1) + perfluoropropane (2) system. ◊, 264.05 K; ■, 271.05 K; ●, 278.05 K; □, 303.04 K; ⧫, 308.04 K; ―, model. Error bands: ± 7.5 % for the measured data. 1320

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