Vapor–Liquid Equilibrium Measurements and Modeling for the Ethane

Article pubs.acs.org/jced

Vapor−Liquid Equilibrium Measurements and Modeling for the Ethane (R-170) + 1,1,2,3,3,3-Hexafluoro-1-propene (R-1216) Binary System Shalendra C. Subramoney,† Alain Valtz,‡ Christophe Coquelet,†,‡ Dominique Richon,† Paramespri Naidoo,† and Deresh Ramjugernath*,† †

Thermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, Howard College Campus, Durban, South Africa ‡ MINES ParisTech, CEP/TEPCentre Energétique et Procédés, 35 Rue Saint Honoré, 77305 Fontainebleau Cedex, France ABSTRACT: Novel isothermal (p−x−y) vapor−liquid equilibrium data are reported for ethane (R-170) + 1,1,2,3,3,3hexafluoro-1-propene (R-1216) mixtures at five temperatures in the (282.93 to 322.89) K range, at pressures up to about 4.6 MPa. The experimental data were measured using an apparatus based on the “static-analytic” method taking advantage of two electromagnetic capillary samplers for repeatable and reliable equilibrium phase sampling and handling. The experimental data are well-correlated with the “PR-MC-NRTL-WS” model constituted by the Mathias−Copeman α function, nonrandom two-liquid (NRTL) local composition model, and Wong− Sandler mixing rule introduced in the Peng−Robinson equation of state. The studied system did not exhibit azeotropic behavior nor liquid−liquid immiscibility over the range of investigated temperatures. Mixture critical points have been estimated from the experimental vapor−liquid equilibrium data via the extended scaling laws and the “PR-MC-NRTL-WS” model and are found to be in good agreement with the experimental isothermal phase envelopes.

■

INTRODUCTION This work is part of a continuing research program on the thermodynamic properties of fluorocarbons and their mixtures. The objective of this program is the development of an experimental property database for the investigation of novel fluorocarbon technologies. We have previously reported pure component saturated vapor pressures and densities for a perfluoroolefin1 and a perfluoroepoxide2 and vapor−liquid equilibria (VLE) for binary mixtures involving perfluoroalkanes3−5 or perfluoroolefins.6 In the present study, VLE data are reported for an alkane + perfluoroolefin mixture. The experimental determination of VLE data can be considered fundamental research7 necessary for the development and validation of thermodynamic models. Such models are central to the design of unit operations and chemical processes in modern process simulators. Furthermore, VLE data are required as “training” data for the development of Helmholtz energy equations of state (EoS) for refrigerant mixtures8 and group contribution methods such as the predictive Soave−Redlich−Kwong EoS (PSRK).9 Ethane (R-170) is commercially sourced from natural gas and is a basic raw material for the organic chemical industry. The benign environmental characteristics of R-170 and other © 2012 American Chemical Society

hydrocarbons renders such chemicals attractive as constituents of alternative refrigerant mixtures, despite their inherent flammability.10 1,1,2,3,3,3-Hexafluoro-1-propene, the fluorinated analogue of propylene, is used as a key intermediate for the manufacturing of high value perfluoroethers11 and perfluoroepoxides.12 In the context of refrigerants, binary mixtures of 1,1,2,3,3,3-hexafluoro-1-propene (R-1216) with chlorodifluoromethane (R-22)13 or low molecular weight hydrocarbons14 are known to form effective blends comparable to dichlorodifluoromethane (R-12) and 1,1,1,2-tetrafluoroethane (R-134a). Bibliographic studies reveal a scarcity of VLE data for perfluoroolefin mixtures. To the best of our knowledge, mixture data for R-170 + R-1216 have not been previously reported in the open literature. In this work, isothermal VLE data for R-170 + R-1216 mixtures are reported at five experimental temperaturestwo isotherms above the critical temperature of R-170 and three isotherms below this temperature. Pure component saturated vapor pressures for R-170 and R-1216 are also Received: April 12, 2012 Accepted: August 31, 2012 Published: October 4, 2012 2947

dx.doi.org/10.1021/je300431n | J. Chem. Eng. Data 2012, 57, 2947−2955

Journal of Chemical & Engineering Data

Article

Figure 1. Flow diagram of the “static-analytic” apparatus. B1 and B2: product cylinders, EC: equilibrium cell, GC: gas chromatograph, MS: magnetic stirrer, LS: liquid ROLSI sampler, LV1 and LV2: loading valves, LB: liquid bath, PP: platinum resistance thermometer probe, PC: personal computer, PT: pressure transducer, SC: ROLSI sampler control, SD: stirring device, TP: thermal press, TR: temperature regulator, VP: vacuum pump, VS: vapor ROLSI sampler, ST: sapphire tube, V1 and V4: 3-way shut off valves, V2, V3, and V5: 2-way shut off valves.

compound confirmed the purities, and the chemicals were used as is. Equipment. A schema of the experimental apparatus is presented in Figure 1. The “static-analytic” VLE still used in this work is similar in concept to that of Laugier and Richon22 and identical to Valtz et al.;23 consequently only a brief description is given here. With “static-analytic” methods, equilibrium inside the cell is attained via rapid agitation or mixing, usually through efficient stirring, and vapor and liquid phases are carefully sampled and analyzed at equilibrium. In the present apparatus, VLE conditions are produced inside the thermo-regulated equilibrium cell (EC; V = 34 cm3). The equilibrium cell mainly consists of a sapphire tube (ST) held between two stainless steel flanges. Each flange contains valves and fittings for loading, discharging, degassing, and evacuation operations (LV1 and LV2) and provisions for temperature and pressure measurement. The equilibrium chamber contains an efficient stirring rod assembly (MS), driven by an external magnet attached to a stirring device (SD; Heidolph, Germany, RZR 2020). The cell is placed in a thermo-regulated liquid bath (LB) and maintained at desired operating temperatures. Two 100 Ω platinum resistance

reported over the temperature range of the VLE data. The measurements have been conducted on an apparatus based on the “static-analytic” method fitted with two electromagnetic capillary samplers15 for reliable equilibrium phase sampling and handling. The experimental data are represented using the following model: “PR-MC-NRTL-WS”, where the Mathias− Copeman16 α function (MC), the nonrandom two-liquid local composition model (NRTL),17 and the Wong−Sandler18 mixing rule (WS) are associated with the cubic Peng−Robinson19 equation of state (PR). Mixture critical points have been estimated from the experimental VLE data via the extended scaling laws20 and an EoS employing the algorithm of Stockfleth and Dohrn.21

■

EXPERIMENTAL SECTION Materials. 1,1,2,3,3,3-Hexafluoro-1-propene (C3F6, R-1216, CAS RN: 116-15-4) was supplied by Pelchem (South Africa), with a certified purity higher than 0.999 volume fraction. Ethane (C2H6, R-170, CAS RN: 74-84-0) was supplied by Messer-Griesheim (France), with a certified purity higher than 0.9995 volume fraction. Gas chromatographic analysis of each 2948

dx.doi.org/10.1021/je300431n | J. Chem. Eng. Data 2012, 57, 2947−2955

Journal of Chemical & Engineering Data

Article

Additional amounts of the lighter component (R-170) are introduced to the equilibrium cell, and a new equilibrium condition is established. This procedure is repeated until the entire composition range is covered for a desired isotherm. Thereafter, the equilibrium cell is evacuated and reloaded with fresh R-1216, and the procedure is repeated for new isothermal measurements. In some instances, the thermal press containing the lighter component R-170 is heated using a hot plate to facilitate charging from a higher pressure source. Calibrations and Uncertainties. The two 100 Ω platinum resistance thermometer probes were calibrated against a 25 Ω platinum resistance thermometer (TINSLEY Precision Instruments, U.K., type 5187A). The 25 Ω reference probe and its electronic multimeter have been calibrated by the Laboratoire National d’Essais (Paris) based on the 1990 International Temperature Scale (ITS 90). The calibration data for the 100 Ω platinum resistance thermometer probes were fitted to second-order polynomials by the method of least-squares. The maximum correlation error for both temperature probes is estimated as ± 0.02 K. The high pressure transducer was calibrated against a dead weight pressure balance (Desgranges & Huot, France, 5202S). The calibration data were fitted to a second-order polynomial, and the pressure correlation error is estimated as ± 0.006 MPa. The response of the TCD was calibrated for each pure component via a syringe injection technique. Syringes (SGE, Australia) of volumes ranging from (100 to 500) μL were used for both gaseous components. A sample of the pure component at a known syringe volume was withdrawn from the gas cylinder and the number of moles estimated by the ideal gas equation (n = pV/RT). The temperature and pressure for each injection were measured at the exit nozzle of the gas cylinder and were obtained from a digital barometer (DRUCK, DPI141) with a manufacturer stated uncertainty of ± 0.001 kPa and a calibrated Pt-100 probe (Leris, France) with a correlation error of ± 0.02 K. The syringe volume is read off the syringe via a specialized magnifying eyepiece. For multiple injections of each pure component at different syringe volumes, a graph of detector response (peak area) versus number of moles can be prepared. The calibration data for each pure component were fitted to second-order polynomials, and the maximum correlation errors on the mole numbers is estimated as ± 1 % for both R-170 and R-1216. The experimental uncertainties have been calculated taking into account the expanded uncertainties and coverage factor as described in Taylor and Kuyatt.24 Combined standard uncertainties on temperature, pressure, and composition were calculated from the error associated with the calibration procedures (correlation errors and non-negligible errors) and from standard deviations estimated from repeated readings over the course of the measurements. A detailed description of the uncertainty calculations for the static−analytic apparatus can be found in the thesis of Soo.25 The combined standard uncertainties are averaged over all data sets and are reported as expanded uncertainties with a coverage factor of 2 at a confidence level of approximately 95 %. The maximum expanded uncertainties on the experimental variables are estimated as (k = 2): U(T) = ± 0.03 K, U(p) = ± 0.007 MPa, U(x) = ± 0.007, and U(y) = ± 0.005.

Table 1. Pure Component Parameters for R170 and R1216 CAS RN, critical parameters, and acentric factora R-170 CAS RN Tc/K Pc/MPa ω

c1 c2 c3

R-1216

74-84-0 116-15-4 305.32 358.93 4.872 3.136 0.099 0.353 Mathias−Copeman parametersb R-170

R-1216

0.563 −0.173 0.302

0.895 −0.387 1.568

a

R-170 parameters from REFPROP,26 R-1216 parameters from Coquelet et al.1 bR-170 and R-1216 parameters regressed from experimental data measured in this work.

thermometer probes (PP; Actifa, France) are located inside wells drilled on the top and bottom stainless steel flanges. The VLE still is equipped with a high pressure transducer [Druck, U.S.A., PTX611, (0 to 6) MPa]. The pressure transducer was maintained at a constant temperature above the highest temperature of the measurements through a heating resistance connected to a PID controller (TR; WEST, U.S.A., model 6100). The signals from the temperature and pressure sensors are transmitted to a data acquisition unit (Agilent, U.S.A., HP34970A) connected to a personal computer system (PC) for real time data logging. Two Monel capillary tubes extend into the equilibrium cell from the top stainless steel flange and are positioned to allow independent sampling of the vapor and liquid phases. The capillaries are connected to two electromagnetic ROLSI samplers (LS and VS) supplied by ArminesTransvalor, France. A helium carrier gas line is connected to each ROLSI sampler that transports the equilibrium samples to a gas chromatograph (GC; Perichrom, France, PR-2100) for analyses. The GC unit is equipped with a thermal conductivity detector (TCD) and fitted with a packed column (Restek, France, 5 % Krytox on CarboBlack B, stainless steel, 60/80 mesh). All transfer lines are insulated and heated to ensure that the analyzed samples are representative of the equilibrium cell contents. The electromagnetic ROLSI samplers are actuated using a dedicated control box (SC) that allows specification and control of the ROLSI opening time with a 0.01 s resolution. For a given equilibrium cell pressure, the mass of sample withdrawn by ROLSI samplers can be adjusted by varying the opening time through the SC control box. GC peak area analysis and integration are performed with the commercial data acquisition software WINILAB III (Perichrom, France, Version 4.6). Experimental Procedure. The equilibrium cell and all lines are evacuated using a vacuum pump (VP). The heavier component (R-1216) is introduced first from a cylinder (B2) via the loading valve (LV2), and the liquid bath thermostat is set to the desired temperature. The lighter component (R-170) is charged to the cell through LV1, via a thermal press (TP), to a cell pressure corresponding to the desired pressure of the first measurement. Adequate stirring is maintained throughout the cell. Phase equilibrium is assumed when the pressure transducer and temperature probes have stabilized to within their instrument uncertainty. For each equilibrium condition, a minimum of five samples for both the vapor and the liquid phases are withdrawn using the ROLSI samplers. The resulting samples are analyzed to check for measurement repeatability. Average values are considered to correspond to the equilibrium value for each phase.

■

CORRELATIONS The experimental VLE data were correlated with in-house thermodynamic software developed at the CEP/TEP laboratory. 2949

dx.doi.org/10.1021/je300431n | J. Chem. Eng. Data 2012, 57, 2947−2955

Journal of Chemical & Engineering Data

Article

Table 2. Experimental and Calculated Pure Component Vapor Pressures for R-170, Expanded Uncertainties (k = 2): U(T) = ± 0.03 K and U(p) = ± 0.007 MPa, and Calculated Data via the PR EoS with the MC α Function and the Reference EoS for R-17031 from REFPROP26 REFPROP

PR-MC

Texp/K

pexp/MPa

pcal/MPa

pexp − pcal/MPa

10 (pexp − pcal /pexp)

pcal/MPa

pexp − pcal/MPa

102(pexp − pcal /pexp)

279.82 282.49 285.1 287.43 290.31 292.81 296.02 297.72 300.21 302.13 304.65

2.793 2.970 3.155 3.324 3.542 3.735 4.003 4.154 4.379 4.560 4.806

2.795 2.972 3.153 3.322 3.540 3.738 4.005 4.152 4.377 4.557 4.804

−0.002 −0.002 0.002 0.002 0.002 −0.003 −0.002 0.002 0.002 0.003 0.002

−0.08 −0.07 0.06 0.07 0.06 −0.07 −0.04 0.04 0.06 0.08 0.05 AADP = 0.06 %

2.793 2.972 3.154 3.323 3.541 3.739 4.006 4.153 4.378 4.558 4.806

0.000 −0.002 0.001 0.001 0.001 −0.004 −0.003 0.001 0.001 0.002 0.000

0.00 −0.06 0.04 0.04 0.03 −0.09 −0.06 0.02 0.03 0.05 0.00 AADP = 0.04 %

2

Table 3. Experimental and Calculated Pure Component Vapor Pressures for R-1216, Expanded Uncertainties (k = 2): U(T) = ± 0.03 K and U(p) = ± 0.007 MPa, and Calculated Data via the PR EoS with the MC α Function and the Wagner Equation with Fitted Parameters from Literature1 Wagner

PR-MC

Texp/K

pexp/MPa

pcal/MPa

pexp − pcal/MPa

10 (pexp − pcal /pexp)

pcal/MPa

pexp − pcal/MPa

102(pexp − pcal /pexp)

278.20 288.22 293.96 295.42 297.93 300.38 303.08 305.40 307.90 310.38 312.90 315.32 317.82 320.30 322.79 325.34 327.86 330.38 332.85 335.31 337.9 340.34 342.86 347.82

0.392 0.538 0.641 0.670 0.721 0.774 0.834 0.890 0.953 1.018 1.087 1.159 1.235 1.315 1.398 1.488 1.579 1.676 1.776 1.879 1.993 2.110 2.230 2.486

0.395 0.539 0.642 0.671 0.722 0.775 0.836 0.892 0.955 1.020 1.090 1.161 1.237 1.317 1.400 1.490 1.582 1.679 1.778 1.881 1.995 2.107 2.227 2.480

0.003 −0.001 −0.001 −0.001 −0.001 −0.001 −0.002 −0.002 −0.002 −0.002 −0.003 −0.002 −0.002 −0.002 −0.002 −0.002 −0.003 −0.003 −0.002 −0.002 −0.002 0.003 0.003 0.006

−0.50 −0.18 −0.16 −0.16 −0.15 −0.10 −0.28 −0.17 −0.20 −0.19 −0.30 −0.13 −0.19 −0.09 −0.13 −0.08 −0.23 −0.16 −0.14 −0.12 −0.08 0.14 0.11 0.24 AADP = 0.21 %

0.391 0.540 0.642 0.670 0.721 0.774 0.835 0.890 0.952 1.018 1.088 1.158 1.234 1.314 1.397 1.487 1.580 1.677 1.777 1.881 1.995 2.108 2.229 2.483

0.001 −0.002 −0.001 0.000 0.000 0.000 −0.001 0.000 0.001 0.000 0.001 0.001 0.001 0.001 0.001 0.001 −0.001 −0.001 −0.001 −0.002 −0.002 0.002 0.001 0.003

0.33 −0.38 −0.15 −0.11 −0.04 0.06 −0.07 0.06 0.05 0.08 −0.03 0.13 0.05 0.14 0.08 0.09 −0.08 −0.05 −0.07 −0.09 −0.08 0.09 0.03 0.12 AADP = 0.11 %

2

α = [1 + c1(1 − TR1/2)]2

A symmetric (Φ−Φ) approach is used for the calculation of vapor and liquid phase fugacities via the cubic Peng− Robinson (PR) equation of state (EoS): ⎞ ⎛ a ⎟(v − b) = RT ⎜P + 2 (v + 2bv − b2) ⎠ ⎝

(3)

The critical properties and acentric factors for ethane26 (Tc/K = 305.32, Pc/MPa = 4.872) and hexafluoropropylene1 (Tc/K = 358.93, Pc/MPa = 3.136) are reported in Table 1. Mathias−Copeman parameters for both components are reported in Table 1; they were fitted to experimental vapor pressure data measured in this work. The combination of the PR EoS with the nonrandom twoliquid (NRTL) local composition model (eqs 4 and 5) and the Wong−Sandler (WS) mixing rule (eq 6 and 7) contains four interaction parameters adjustable to experimental data.

(1)

The Mathias−Copeman (MC) expression is used to express the α function in the attractive term of the EoS: α = [1 + c1(1 − TR1/2) + c 2(1 − TR1/2)2 + c3(1 − TR1/2)3 ]2

if T > Tc

if T < Tc

(2) 2950

dx.doi.org/10.1021/je300431n | J. Chem. Eng. Data 2012, 57, 2947−2955

Journal of Chemical & Engineering Data

Article

Table 4. Experimental and Calculated (via the PR-MC-NRTL-WS Model) VLE Data for the System R-170 + R-1216 and Expanded Uncertainties (k = 2): U(T) = ± 0.03 K, U(p) = ± 0.007 MPa, U(x) ± 0.007, and U(y) ± 0.005 T/K = 282.93 pexp/MPa 0.689 0.825 1.109 1.309 1.612 1.941 2.225 2.509 2.686

x1exp

0.040 0.071 0.152 0.221 0.343 0.481 0.611 0.750 0.841 T/K = 293.96

pexp/MPa 0.949 1.154 1.245 1.483 1.789 2.036 2.332 2.617 3.207 3.471 3.661

x1exp

0.050 0.091 0.110 0.172 0.262 0.340 0.443 0.543 0.761 0.860 0.931 T/K = 303.94

T/K = 303.94

PR-MC-WS-NRTL x1exp − x1cal

y1exp

x1cal

0.309 0.419 0.568 0.639 0.721 0.789 0.839 0.888 0.920

0.041 0.070 0.149 0.218 0.338 0.480 0.611 0.751 0.841

−0.001 0.312 0.001 0.424 0.003 0.573 0.003 0.643 0.005 0.722 0.001 0.789 0.000 0.839 −0.001 0.888 0.000 0.921 PR-MC-WS-NRTL x1exp − x1cal

y1exp

x1cal

0.315 0.430 0.469 0.553 0.633 0.685 0.738 0.783 0.871 0.916 0.953

0.050 0.092 0.113 0.174 0.264 0.343 0.442 0.541 0.760 0.860 0.930

y1cal

y1cal

0.000 0.310 −0.001 0.422 −0.003 0.466 −0.002 0.548 −0.002 0.629 −0.003 0.683 0.001 0.737 0.002 0.782 0.001 0.871 0.000 0.916 0.001 0.954 PR-MC-WS-NRTL

y1exp − y1cal

pexp/MPa

−0.003 −0.005 −0.005 −0.004 −0.001 0.000 0.000 0.000 −0.001

3.179 3.414 3.814 4.109 4.376 4.477 4.578

y1exp − y1cal 0.005 0.008 0.003 0.005 0.004 0.002 0.001 0.001 0.000 0.000 −0.001

pexp/MPa

x1exp

y1exp

x1cal

x1exp − x1cal

y1cal

y1exp − y1cal

1.087 1.507 1.920 2.235 2.568

0.032 0.101 0.191 0.273 0.361

0.187 0.392 0.516 0.586 0.648

0.031 0.102 0.191 0.271 0.360

0.001 −0.001 0.000 0.002 0.001

0.189 0.394 0.518 0.588 0.649

−0.002 −0.002 −0.002 −0.002 −0.001

(

a RT ij

∑i ∑j xixj b − b=

b−

⎛ ∑i xi abi 1 − ⎜ RT i + ⎝

a = RT

⎛

∑ ∑ xixj⎜⎝b − i

j

a ⎞⎟ RT ⎠ij

(4)

with

⎛ ⎛ 1 ⎡⎛ a ⎟⎞ a ⎟⎞ a ⎟⎞ ⎤⎥ = ⎢⎜ b − + ⎜b − ·(1 − kij) b− ⎝ 2 ⎢⎣⎝ RT ⎠ij RT ⎠i ⎝ RT ⎠ j ⎥⎦ (5)

∑j τj , iGj , ixj ∑j Gj , ixj

+

∑ j

⎛ ∑ G τ x ⎞ ⎜⎜τi , j − k k , j k , j k ⎟⎟ ∑k Gk , jxk ⎠ ∑k Gk , jxk ⎝

Ci , j RT

;

⎛ Cj , i ⎞ Gi , j = exp⎜ −αj , i ⎟; RT ⎠ ⎝

Ci , i = 0

0.734 0.772 0.826 0.870 0.916 0.936 0.958

0.533 0.601 0.721 0.811 0.890 0.920 0.950

y1exp

x1cal

0.234 0.353 0.444 0.519 0.599 0.653 0.694 0.713 0.735 0.738

0.056 0.112 0.169 0.242 0.368 0.489 0.594 0.630 0.691 0.701

x1exp − x1cal

y1cal

−0.004 0.740 0.000 0.772 −0.001 0.826 0.000 0.870 0.000 0.916 0.001 0.936 0.000 0.958 PR-MC-WS-NRTL x1exp − x1cal

y1cal

−0.001 0.229 −0.002 0.359 0.004 0.443 0.007 0.517 0.000 0.599 −0.011 0.656 −0.011 0.699 0.000 0.713 0.002 0.735 0.000 0.738 PR-MC-WS-NRTL

y1exp − y1cal −0.006 0.000 0.000 0.000 0.000 0.000 0.000 y1exp − y1cal 0.005 −0.006 0.001 0.002 0.000 −0.003 −0.005 0.000 0.000 0.000

pexp/MPa

x1exp

y1exp

x1cal

x1exp − x1cal

y1cal

y1exp − y1cal

1.795 2.111 2.288 2.741 3.210 3.668 3.487 4.026

0.050 0.101 0.130 0.205 0.296 0.385 0.350 0.470

0.171 0.280 0.323 0.418 0.494 0.544 0.524 0.572

0.053 0.100 0.127 0.204 0.293 0.389 0.350 0.471

−0.003 0.001 0.003 0.001 0.003 −0.004 0.000 −0.001

0.183 0.285 0.330 0.421 0.490 0.542 0.523 0.574

−0.012 −0.005 −0.007 −0.003 0.004 0.002 0.001 −0.002

(8)

where N is the number of data points, xexp and xcal are the measured and calculated liquid compositions, respectively, and yexp and ycal are the measured and calculated vapor compositions, respectively. Statistical analyses are used to determine the quality of the fit of experimental data to the chosen thermodynamic model.28 The definitions of the statistics used are based on the percent deviation for any property U:

Gi , jxj

(6)

τj , i =

x1cal

2⎤ 2 ⎡N N ⎛y − ycal ⎞ ⎥ 100 ⎢ ⎛⎜ xexp − xcal ⎞⎟ exp ⎜ ⎟ F= +∑ ⎜ ∑ N ⎢⎢ 1 ⎜⎝ xexp ⎟⎠ yexp ⎟⎠ ⎥⎥ 1 ⎝ ⎦ ⎣

⎜

ln(γi) =

x1exp

0.055 0.110 0.173 0.249 0.368 0.478 0.583 0.630 0.693 0.701 T/K = 322.89

PR-MC-WS-NRTL y1exp

combination has also been used to satisfactorily correlate VLE data for binary mixtures of R-1216 and a light hydrocarbon6 and was therefore used in the present work. In addition, the number of adjustable parameters in the thermodynamic model allows a better representation of data close to the critical point. The system temperature and pressure are chosen as the independent variables, and the following flash type objective function is used for the data treatment:

)

APE=∞(T , P , x) ⎞ ⎟ CRT ⎠

0.529 0.601 0.720 0.811 0.890 0.921 0.950 T/K = 312.90

pexp/MPa 1.473 1.822 2.144 2.516 3.081 3.570 3.975 4.114 4.343 4.376

x1exp

(7)

The adjustable parameters are distributed among the mixing (α, τ12, τ21) and combining rules (k12). The nonrandomness parameter α for the NRTL model is assumed to be temperatureindependent and is fixed at 0.3 in our data treatment. The WS mixing rule with a cubic equation of state and the NRTL activity coefficient model has been shown by Shiflett and Sandler27 to accurately correlate binary fluorocarbon VLE. This model

⎡⎛ U − U ⎞⎤ exp cal ⎟⎥ %ΔU = 100·⎢⎜⎜ ⎢⎣⎝ Uexp ⎟⎠⎥⎦

(9)

Using the above definition, the absolute average deviation (AAD) and bias can be defined as: 2951

dx.doi.org/10.1021/je300431n | J. Chem. Eng. Data 2012, 57, 2947−2955

Journal of Chemical & Engineering Data

Article

Table 5. Fitted Parameters, Absolute Average Deviation (AAD), and Bias Values Corresponding to the Use of the PR-MC-NRTL-WS Model for Representing the R-170 + R-1216 System model parameters fitted to individual isotherms T/K

τ12/J·mol−1

282.93 293.96 303.94 312.90 322.89

−1356.2 −1339.1 −1218.1 2208.3 1972.2

τ21/J·mol−1 5029.3 4825.8 4949.2 1396.5 1548.8 temperature-independent

τ12/J·mol−1

T/K

τ21/J·mol−1

k12

AADx1/%

0.354 0.349 0.350 0.283 0.284 parameters fitted to k12

AADy1/%

0.94 0.80 0.64 1.12 0.50 0.28 1.13 0.53 1.53 1.66 all isotherms simultaneously AADx1/%

AADy1/%

biasx1/%

biasy1/%

0.59 −0.51 0.22 −0.16 −0.37

−0.81 1.11 −0.27 0.01 −1.41

biasx1/%

biasy1/%

−1110.3 4614.2 0.345 1.50 1.86 0.15 temperature-independent parameters fitted to isotherms in regions above and below the critical temperature of R-170

268.22−322.96

0.11

T/K

τ12/J·mol−1

τ21/J·mol−1

k12

AADx1/%

AADy1/%

biasx1/%

biasy1/%

T < 305.32 T > 305.32

−1310.5 2233.8

4892.4 1345.6

0.354 0.283

0.93 1.42

0.87 1.13

0.21 −0.14

−0.14 −0.63

AADU =

biasU =

1 N 1 N

Table 1. Pressure deviations observed after fitting of the α function parameters are reported in the respective tables. The experimental data are well-correlated by the PR EoS with absolute average deviations on pressure (AADP) of 0.04 % and 0.11 % for R-170 and R-1216, respectively. The experimental data for R-170 are compared to saturated vapor pressures calculated from the high accuracy reference EoS for R-17031 from REFPROP,26 as in Table 2. The experimental data are found to be consistent with the literature correlation (AADP = 0.06 %). A reference EoS for R-1216 is not available in the open literature. Coquelet et al.1 have reported saturated vapor pressures and Wagner equation32 parameters for R-1216 valid from 253 K up to the pure component critical point. The R-1216 vapor pressures determined in this work are compared to those calculated by the Wagner equation with the literature parameters.1 The pressure deviations for this comparison are reported in Table 3. The experimental data for R-1216 are consistent with the literature correlation (AADP = 0.21 %). Experimental VLE data for the system R-170 + R-1216 are reported in Table 4 for two isotherms above the critical

N

∑ |%Ui| i=1

(10)

N

∑ (%Ui) i=1

(11)

High AADU values are indicative of either a systematic or large random difference between the experimental data and the correlating model. The biasU value is the average deviation of the data set, and large positive or negative values indicate systematic differences between the data and the chosen model. Experimental data sets are accurately represented by a correlating model when these statistical parameters are near zero. The extended scaling laws20 can be used to approximate the near-critical phase behavior and critical loci for binary mixtures using experimental VLE data. For this method, the near critical region of the pressure−composition diagram is represented by complementing the near-critical scaling law with a linear term. Using the proposed equations: y − x = γ1(Pc − P) + μ(Pc − P)β

(12)

(y + x ) − xc = γ2(Pc − P) 2

(13)

where β is a constant (β = 0.325), the adjustable coefficients γ1, γ2, and μ, and the critical coordinates Pc and xc are regressed from a set of experimental coexistence points (P,x,y) below the critical point of a mixture. Mixture critical points can also be calculated from experimental data using an EoS. Such procedures were initially proposed by Heidemann and Khalil29 and Michelsen and Heidemann30 and later improved by Stockfleth and Dohrn21 with a more generalized algorithm. The latter method has been used in this work to calculate the critical loci for the binary mixtures via the “PR-MC-NRTL-WS” model using binary interaction parameters correlated from experimental VLE data in the ethane supercritical domain.

■

RESULTS AND DISCUSSION Experimental saturated vapor pressures for R-170 and R-1216 are reported in Tables 2 and 3. The measured vapor pressure data cover the temperature range of the VLE measurements and were used to fit MC parameters for the PR EoS, as in

Figure 2. Experimental VLE data and modeling results for the system R-170 + R-1216: ○, 282.93 K; ●, 293.96 K; ◊, 303.94 K; ⧫, 312.90 K; □, 322.89 K; , PR-MC-NRTL-WS model; ×, critical points calculated by the extended scaling laws; ···, critical points calculated by the PR-MC-NRTL-WS model. 2952

dx.doi.org/10.1021/je300431n | J. Chem. Eng. Data 2012, 57, 2947−2955

Journal of Chemical & Engineering Data

Article

Figure 3. Interaction parameter plots for the PR-MC-NRTL-WS model for the system R-170 (1) + R-1216 (2). Primary axis: ●, τ12; ○, τ21; Secondary axis: +, k12. ···, R-170 critical temperature.

correlated model parameters is observed at the critical temperature of R-170 (305.32 K), with the parameters changing either sign or magnitude; see Figure 3. Similar observations have been previously reported5,33,34 and is thought to result from the difference in absorption of a subcritical gas and supercritical gas in a liquid.33 It is advisible to use the model parameters fitted for isotherms in the regions above and below the critical point of R-170 for industrial application or process simulators. The experimental VLE data and representation through the “PR-MC-NRTL-WS” model combination with parameters fitted to individual isotherms are plotted in Figure 2. The studied system does not exhibit azeotropy nor liquid−liquid immiscibility over the range of experimental temperatures investigated in this work. Deviations between the experimental and the calculated (PR-MC-NRTL-WS) liquid and vapor compositions are reported in Table 4, and scatter diagrams are plotted in Figure 4. In general, the VLE data are well-correlated by the “PR-MC-NRTL-WS” model over the entire composition range for both vapor and liquid phases.

temperature of R-170 [(312.90 and 322.89) K] and three isotherms below this temperature [(282.93, 293.96, and 303.94) K]. The binary mixture data are used to fit interaction parameters (k12, τ12, τ21) for the “PR-MC-NRTL-WS” model, as in Table 5. Parameters are fitted for three cases, that is, for individual isotherms, for isotherms in the regions above and below the critical point of R-170, and simultaneously over all experimental data. The calculated AAD and bias on equilibrium compositions are also reported in Table 5. In general the data are well-correlated for all three fitting procedures with AADx1,y1 < 2 % for all instances. However for the first case, that is, parameters fitted to individual isotherms, a discontinuity of the

Figure 4. Deviation plots for liquid and vapor compositions in the R-170 (1) + R-1216 (2) system related to the PR-MC-NRTL-WS model: ○, 282.93 K; ●, 293.96 K; △, 303.94 K; ▲, 312.90 K; +, 322.89 K.

Table 6. Extended Scaling Law Parameters and Predicted Mixture Critical Points for the R-170 + R-1216 System T/K

μ·10

λ1·10

λ2·10

Pc/MPa

x1c

312.90 322.89

34.55 66.50

1284.3 1282.7

−1828.3 −1592.6

4.520 4.433

0.746 0.586

3

4

4

Figure 5. Composition dependence of relative volatility (α12) for the R-170 (1) + R-1216 (2) system: ○, 282.93 K; ●, 293.96 K; △, 303.94 K; ▲, 312.90 K; +, 322.89 K; , PR-MC-NRTL-WS model; ···, line of constant relative volatility (α12 = 1). Error bands: ± 4 % for experimental results. 2953

dx.doi.org/10.1021/je300431n | J. Chem. Eng. Data 2012, 57, 2947−2955

Journal of Chemical & Engineering Data

Article

pressures for R-1216 and R-170 and literature pure component critical points are also plotted in Figure 6. The predicted critical points are in good agreement with the isothermal phase envelopes, in Figure 2. The system exhibits a continuous mixture critical line and can be classified as a Type I system according to the classification of Van Konynenburg and Scott.35

An accurate description of the relative volatility (αij) of mixtures is essential for process design purposes. Relative volatilities were calculated from the experimental data and compared to values calculated from the PR-MC-NRTL-WS model. The composition dependence of αij is plotted in Figure 5. A good agreement between the experimental and the calculated values is observed over the entire composition range for all studied temperatures. The mixture critical points for the two isotherms above the critical temperature of R170 were estimated by the extended scaling laws,20 as in Table 6. The accuracy of this prediction is dependent on the number of data points measured in the near critical region; however, it provides a useful qualitative estimate of the location of mixture critical points. The critical locus for the mixture was also estimated via an EoS method using the algorithm of Stockfleth and Dohrn.21 The PR-MC-NRTL-WS model with parameters fitted from the experimental VLE in the R-170 supercritical domain were used to predict a series of mixture critical points, as in Table 7. The critical points predicted by both methods are plotted on the VLE diagram, in Figure 2, and a PT diagram, in Figure 6. Experimental and calculated vapor

■

CONCLUSIONS VLE data are presented at five temperatures for the system R-170 + R-1216. The experimental data were measured on a “static-analytic” type apparatus taking advantage of two electromagnetic capillary samplers. The experimental results are given with the following maximum expanded uncertainties (k = 2): U(T) = ± 0.03 K, U(p) = ± 0.007 MPa, U(x) = ± 0.007, and U(y) = ± 0.005. Measured VLE data are well-correlated with in-house thermodynamic software based on the Peng− Robinson equation of state, that is, the PR-MC-NRTL-WS model. The studied system does not exhibit azeotropy nor liquid−liquid immiscibility over the range of investigated temperatures (282.93 to 322.89) K. Mixture critical points were estimated by the use of extended scaling laws and an equation of state method; they are in good agreement with the isothermal phase envelopes.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +27 31 2603128. Fax: +27 31 2601118. 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. Pelchem is acknowledged for the supply of hexafluoropropylene. Notes

The authors declare no competing financial interest.

■

Figure 6. PT diagram for the R-170 (1) + R-1216 (2) system: ⧫, R-170 experimental saturated vapor pressures; ●, R-1216 experimental saturated vapor pressures; △, R-170 pure component critical point;26 □, R-1216 pure component critical point;1 , R-170 vapor pressures calculated with the PR EoS with MC parameters fitted in this work; − − −, R-1216 vapor pressures calculated with the PR EoS with MC parameters fitted in this work; ×, critical points calculated with the extended scaling laws; ···, critical points calculated with the PR-MC-NRTL-WS model.

Table 7. Predicted Mixture Critical Points for the R-170 + R-1216 System Calculated via the PR-MC-NRTL-WS Model T/K

Pc/MPa

x1c

358.93 353.41 347.57 341.32 334.76 328.04 321.40 315.17 309.92 306.43 305.32

3.136 3.433 3.711 3.953 4.149 4.295 4.394 4.461 4.532 4.658 4.872

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

REFERENCES

(1) Coquelet, C.; Ramjugernath, D.; Madani, H.; Valtz, A.; Naidoo, P.; Meniai, A. H. Experimental Measurement of Vapor Pressures and Densities of Pure Hexafluoropropylene. J. Chem. Eng. Data 2010, 55, 2093−2099. (2) Dicko, M.; Belaribi-Boukais, G.; Coquelet, C.; Valtz, A.; Brahim Belaribi, F.; Naidoo, P.; Ramjugernath, D. Experimental Measurement of Vapor Pressures and Densities at Saturation of Pure Hexafluoropropylene Oxide: Modeling Using a Crossover Equation of State. Ind. Eng. Chem. Res. 2011, 50, 4761−4768. (3) El Ahmar, E.; Valtz, A.; Naidoo, P.; Coquelet, C.; Ramjugernath, D. Isothermal Vapor-Liquid Equilibrium Data for the Perfluorobutane (R610) + Ethane System at Temperatures from (263 to 353) K. J. Chem. Eng. Data 2011, 56, 1918−1924. (4) Valtz, A.; Courtial, X.; Johansson, E.; Coquelet, C.; Ramjugernath, D. Isothermal vapor-liquid equilibrium data for the carbon dioxide (R744) + decafluorobutane (R610) system at temperatures from 263 to 353 K. Fluid Phase Equilib. 2010, 304, 44−51. (5) 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. (6) Coquelet, C.; Valtz, A.; Naidoo, P.; Ramjugernath, D.; Richon, D. Isothermal Vapor-Liquid Equilibrium Data for the Hexafluoropropylene (R1216) + Propylene System at Temperatures from (263.17 to 353.14) K. J. Chem. Eng. Data 2009, 55, 1636−1639.

2954

dx.doi.org/10.1021/je300431n | J. Chem. Eng. Data 2012, 57, 2947−2955

Journal of Chemical & Engineering Data

Article

(7) Richon, D. Experimental techniques for the determination of thermophysical properties to enhance chemical processes. Pure Appl. Chem. 2009, 81, 1769−1782. (8) McLinden, M. O.; Lemmon, E. W.; Jacobsen, R. T. Thermodynamic properties for the alternative refrigerants. Int. J. Refrig. 1998, 21, 322−338. (9) Holderbaum, T.; Gmehling, J. PSRK: A Group Contribution Equation of State Based on UNIFAC. Fluid Phase Equilib. 1991, 70, 251−265. (10) Granryd, E. Hydrocarbons as refrigerants-an overview. Int. J. Refrig. 2001, 24, 15−24. (11) Sievert, A. C.; Tong, W. R.; Nappa, J. Synthesis of perfluorinated ethers by an improved solution phase direct fluorination process. J. Fluorine Chem. 1991, 53, 397−417. (12) Millauer, H.; Schwertfeger, W.; Siegemund, G. Hexafluoropropylene Oxide - A Key Compound in Organofluorine Chemistry. Angew. Chem., Int. Ed. Engl. 1985, 24, 161−179. (13) Turner, D. E. Alternative refrigerant including hexafluoropropylene. U.S Patent 6258292, Crown Colony Ct., 2001. (14) Turner, D. E. A non-flammable refrigerant fluid containing hexafluoropropene and hydrocarbons. U.S. Patent 5714083, 750 Lakeside Dr., 1998. (15) 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. Analusis 2000, 28, 426−431. (16) Mathias, P. M.; Copeman, T. W. Extension of the PengRobinson equation of state to complex mixtures: Evaluation of the various forms of the local composition concept. Fluid Phase Equilib. 1983, 13, 91−108. (17) Renon, H.; Prausnitz, J. M. Local compositions in thermodynamic excess functions for liquid mixtures. AIChE J. 1968, 14, 135−144. (18) Wong, D. S. H.; Sandler, S. I. A theoretically correct mixing rule for cubic equations of state. AIChE J. 1992, 38, 671−680. (19) Peng, D. Y.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 1976, 15, 59−64. (20) Ungerer, P.; Tavitian, B.; Boutin, A. Applications of molecular simulation in the oil and gas industry - Monte Carlo methods; Edition Technip: Paris, 2005. (21) Stockfleth, R.; Dohrn, R. An algorithm for calculating critical points in multicomponent mixtures which can easily be implemented in existing progams to calculate phase equilibria. Fluid Phase Equilib. 1998, 145, 43−52. (22) Laugier, S.; Richon, D. New apparatus to perform fast determinations of mixture vapor-liquid equilibria up to 10 MPa and 423 K. Rev. Sci. Instrum. 1986, 57, 469−472. (23) Valtz, A.; Coquelet, C.; Baba-Ahmed, A.; Richon, D. Vaporliquid equilibrium data for the propane + 1,1,1,2,3,3,3-heptafluoropropane (R227ea) system at temperatures from 293.16 to 353.18 K and pressures up to 3.4 MPa. Fluid Phase Equilib. 2002, 202, 29−47. (24) Taylor, B. N.; Kuyatt, C. E. Guidelines for evaluating and expressing the uncertainty of NIST measurement results. In NIST Technical Note 1297; Physics Laboratory, National Institute of Standards and Technology: Gaithersburg, MD, 1994. (25) Soo, C. B. Experimental thermodynamic measurements of biofuel related associating compounds and modeling using the PC-SAFT equation of state. Doctoral thesis, MINES ParisTech, Paris, France, 2011. (26) Lemmon, E. W.; Huber, M. L.; McLinden, M. O. Reference Fluid Thermodynamic and Transport Properties (REFPROP), NIST Standard Reference Database 23, Version 8.0; Physical and Chemical Properties Division, National Institute of Standards and Technology: Gaithersburg, MD, 2007. (27) Shiflett, M. B.; Sandler, S. I. Modeling fluorocarbon vapor-liquid equilibria using the Wong-Sandler model. Fluid Phase Equilib. 1998, 147, 145−162. (28) Lemmon, E. W. A generalized model for the prediction of the thermodynamic properties of mixtures including vapor-liquid equilibrium. Doctoral thesis, University of Idaho, Moscow, ID, 1996.

(29) Heidemann, R. A.; Khalil, A. M. The calculation of critical points. AIChE J. 1980, 26, 769−779. (30) Michelsen, M. L.; Heidemann, R. A. Calculation of critical points from cubic 2 constant equations of state. AIChE J. 1981, 27, 521−523. (31) Buecker, D.; Wagner, W. A reference equation of state for the thermodynamic properties of ethane for temperatures from the melting line to 675 K and pressures up to 900 MPa. J. Phys. Chem. Ref. Data 2006, 35, 205−266. (32) Wagner, W. New vapor pressure measurements for argon and nitrogen and a new method for establishing rational vapor pressure. Cryogenics 1973, 13, 470−482. (33) Valtz, A.; Coquelet, C.; Baba-Ahmed, A.; Richon, D. Vaporliquid equilibrium data for the CO2 + 1,1,1,2,3,3,3-heptafluoropropane (R227ea) system at temperatures from 276.01 to 367.30 K and pressures up to 7.4 MPa. Fluid Phase Equilib. 2003, 207, 53−67. (34) Valtz, A.; Coquelet, C.; Richon, D. Vapor-liquid equilibrium data for the sulphur dioxide (SO2) + 1,1,1,2,3,3,3-heptafluoropropane (R227ea) system at temperatures from 288.07 to 403.19 K and pressures up to 5.38 MPa. Representation of the critical point and azeotrope temperature dependence. Fluid Phase Equilib. 2004, 220, 77−83. (35) Van Konynenburg, P. H.; Scott, R. L. Critical lines and phase equilibria in binary van der Waals mixtures. Philos. Trans. R. Soc. London 1980, 298, 495−540.

2955

dx.doi.org/10.1021/je300431n | J. Chem. Eng. Data 2012, 57, 2947−2955