Article pubs.acs.org/jced
Isothermal Vapor−Liquid Equilibrium Data for the 1,1,2,2Tetrafluoroethene + 1,1,2,2,3,3,4,4-Octafluorocyclobutane Binary System: Measurement and Modeling from (248 to 283) K Francois J. Conradie,† Philippus L. Crouse,† Xavier Courtial,‡ Izak J. van der Walt,§ and Deresh Ramjugernath*,‡ †
Fluoromaterials Science and Process Integration, Department of Chemical Engineering, University of Pretoria, Pretoria 0002, South Africa ‡ Thermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, Durban 4041, South Africa § The South African Nuclear Energy Corporation Ltd., Pretoria, South Africa ABSTRACT: High pressure vapor−liquid equilibrium data are presented for the 1,1,2,2-tetrafluoroethene + 1,1,2,2,3,3,4,4-octafluorocyclobutane binary system. The isothermal measurements were undertaken at (248.3, 263.0, and 282.9) K, with pressures ranging from (0.040 to 2.340) MPa. A static−analytical apparatus was used to carry out the measurements. The liquid and vapor phases were sampled at equilibrium using a movable rapid on-line sampler−injector (ROLSI). The uncertainties in the measurements are less than 0.1 K, 1.5 kPa, and 0.007 for the temperature, pressure, and equilibrium phase mole fractions, respectively. The experimental data were correlated with the Peng−Robinson equation of state incorporating the Mathias−Copeman alpha function, with the Wong−Sandler mixing rule utilizing the nonrandom two-liquid (NRTL) activity coefficient model. The model accurately describes the experimental data.
■
■
INTRODUCTION Due to abundant local fluorspar deposits in South Africa, the South African Department of Science and Technology is investigating several possibilities for converting fluorspar into high-end products for export. One such initiative is the production of various fluoro-polymers. Some of these fluoropolymers are produced from 1,1,2,2-tetrafluoroethene (TFE) and hexafluoropropene (HFP) monomers. These monomers can be produced by the pyrolysis of scrap polytetrafluoroethylene (PTFE). The pyrolysis process produces both TFE and HFP, along with 1,1,2,2,3,3,4,4-octafluorocyclobutane (OFCB) and some perfluoro-isobutene (PFIB). Pure TFE and pure HFP are required for the fluoro-polymers and can be recovered from the products of the pyrolysis by distillation. To optimize the separation, vapor−liquid equilibrium (VLE) data are required for the binary systems. Vapor−liquid equilibrium data for the binary system of TFE + OFCB are presented at (248.3, 263.0, and 282.9) K. A static−analytical apparatus was used to measure the VLE data. The resulting experimental data were correlated using the Peng−Robinson1 equation of state (PR-EoS) incorporating the Mathias−Copeman2 alpha function, combined with the Wong−Sandler3 mixing rule that utilizes the nonrandom two-liquid (NRTL)4 activity coefficient model. © 2012 American Chemical Society
EXPERIMENTAL SECTION Materials. TFE (C2F4) was produced in-house with a laboratory-scale distillation process at The South African Nuclear Energy Corporation (NECSA). NECSA has safety standards in place that limit the pressure in a pure TFE cylinder to 0.18 MPa. This is to prevent autopolymerization of the TFE. The OFCB (c-C4F8) was also produced in-house. The materials were used without any further purification steps. The critical temperatures (Tc) and critical pressures (Pc) from the literature5,6 for both pure components are listed in Table 1 along with the Chemical Abstracts Service (CAS) numbers, component purities, and the acentric factors. Apparatus. The experimental measurements were undertaken with a static−analytical apparatus using a rapid on-line sampler−injector (ROLSI).7 Figure 1 shows a diagram of this setup. The equilibrium cell has a volume of approximately 40 cm3 and can be operated at temperatures and pressures up to 473 K and 10 MPa. The equilibrium cell is immersed in a temperature-regulated liquid bath. The temperature of the cell is monitored by two Received: February 21, 2012 Accepted: May 30, 2012 Published: June 11, 2012 1978
dx.doi.org/10.1021/je300217x | J. Chem. Eng. Data 2012, 57, 1978−1983
Journal of Chemical & Engineering Data
Article
Table 1. Critical Properties, Other Relevant Information for the Materials, and the Mathais−Copeman Coefficients for the Experimental Vapor Pressure Data molecular weight TFE5 OFCB6
Mathias−Copeman coefficients
CAS no.
g·mol−1
purity
Tc/K
Pc/MPa
acentric factor
c1
c2
c3
116-14-3 115-25-3
100.02 200.03
99.8 % 99.7 %
306.45 388.4
3.944 2.777
0.223 0.356
0.5939 0.8471
0.7535 0.4952
0.3769 −0.5524
Figure 1. A schematic of the apparatus (BTC, bath temperature controller; DAU, data acquisition unit; GC, gas chromatograph; MC, mechanical circulatory; PT, pressure transducer; RV, relieve valve; Vi, valve).
platinum resistance thermometer probes (Pt-100) situated at the top and bottom of the equilibrium cell. The Pt-100 probes are calibrated against a reference thermometer (CTH 6500, WIKA), calibrated by WIKA. The maximum uncertainty for the two probes is less than ± 0.1 K in the (243 to 323) K temperature range. A (0 to 10) MPa WIKA pressure transducer (model P11) is used for pressure measurements. The pressure transducer is calibrated against a reference transducer (CPT 6000, WIKA) previously calibrated by WIKA. The maximum uncertainty is less than ± 1.5 kPa. The pressure and temperature readings are recorded via a computer linked to an Agilent Data Acquisition Unit (34970A) and the Benchlink Data Logger (Agilent Technologies, version 3.0.4). Both the liquid and the vapor phases at equilibrium are sampled by the ROLSI and analyzed by a gas chromatograph (Shimadzu, GC17A) equipped with a thermal conductivity detector (TCD), using the LabSolutions software (GC Solution Analysis, v 2.30.00). A Porapak Q column (length: 3 m,
diameter: 1/8 in., 80/100 mesh) maintained at 503 K, with a helium flow rate of 25 mL·min−1, is used to separate the two components. The TCD, maintained at 523 K with a current of 50 mA, is calibrated by repeated injections of known amounts of each pure compound through a gas-tight syringe. The uncertainties for the vapor and liquid mole fractions are estimated to be less than 0.007. These uncertainties take into account the deviations due to the calibrations as well as the analysis procedures. The uncertainties were determined using methods discussed and recommended in the literature.11 Experimental Procedures. Prior to any measurements, the equilibrium cell and all associated lines are evacuated, at ambient temperature, for at least two hours to ensure that the lines are free of any contaminants. The cell is cooled down sufficiently to allow the OFCB to transfer from the OFCB container (at ambient temperature) into the equilibrium cell (at lower temperature). Approximately 15 cm3 of liquid OFCB is 1979
dx.doi.org/10.1021/je300217x | J. Chem. Eng. Data 2012, 57, 1978−1983
Journal of Chemical & Engineering Data
Article
condensed into the cell. The OFCB is then degassed to get rid of volatile impurities under rapid stirring. Thereafter the cell and its content are left at the desired temperature under efficient stirring to reach the equilibrium (achieved when the top and bottom Pt-100 probes and the pressure transducer indicated constant temperature and pressure, within the experimental uncertainty range, for at least 15 min). The vapor pressure of the heavier compound is thereby determined. Next TFE is introduced into the cell. TFE in the cylinder is stored below 0.18 MPa to prevent autopolymerization. It is introduced into a small pressure vessel (approximately 10 cm3 in volume) which is maintained in a liquid nitrogen bath, to accumulate some TFE, with a high density. The cylinder is then heated until the TFE vapor pressure is high enough to transfer the desired quantity of TFE inside the equilibrium cell. This procedure allowed for the use of TFE at a sufficient pressure for a short time and at low temperatures, avoiding any possible autopolymerization or autodecomposition. The system is then efficiently stirred at constant temperature until thermodynamic equilibrium is reached. Thereafter both liquid and vapor phases are sampled via the ROLSI sampler, and their compositions are determined by analysis through the GC. At each equilibrium point, both the liquid- and the vapor-phase composition are determined from at least five reproducible sample analyses. The same procedure is repeated stepwise to increase the quantities of TFE inside the cell and also the global composition for a full description of the isothermal VLE. At new equilibrium conditions, the temperature, pressure, and phase compositions are determined. The vapor pressure of the compounds were measured using the same equilibrium cell as that used for the VLE experiments. The vapor pressure of the heavier compound was measured during the VLE experiments when only the heavier compound is present in the equilibrium cell. Both materials were thoroughly degassed to ensure that no impurities entered the cell during loading. For both compounds the material is loaded into the cell and degassed, and the temperature is set and allowed to stabilize under agitation. The vapor pressure of the compounds was recorded once the pressure and temperature was stable in the equilibrium cell for about 10 min. Correlations. The experimental VLE data are correlated using the PR-EoS1 with the Mathias−Copeman2 alpha function, the latter which is also used for accurate representation of the vapor pressure of each component. The three adjustable parameters (ci) of the Mathias−Copeman alpha function (presented in Table 1) are fitted to experimental vapor pressure data for both components (presented in Tables 1 and 2). The Wong−Sandler3 mixing rule is used, incorporating the NRTL4 (eq 1) activity coefficient model, using the assumption that AE(T,P → ∞,x) = gE(T,x):
E
i
NDG
F=
p/MPa
plit /MPa
|Δp|/MPa
plit10/MPa
|Δp|/MPa
248.20 253.34 263.18 273.14 283.19
0.864 1.017 1.367 1.804 2.340
0.868 1.023 1.375 1.810 2.338
0.004 0.006 0.008 0.006 0.002
0.873 1.025 1.367 1.787 2.293
0.013 0.008 0.000 0.017 0.045
∑ n=1
(
τ
∑k xk exp −αki RTki
)
τji (1)
2 ⎡⎛ ⎛ Pe, i − Pm, i ⎞2 Te, i − Tm, i ⎞ ⎢ ⎜ ⎟ ⎟⎟ Wn ∑ ⎜ ⎟ + ⎜⎜ ⎢ σT , i ⎠ ⎝ σP, i ⎠ i = 1 ⎣⎝
NC − 1
+
∑ j=1
NP
⎛ xe, i , j − xm, i , j ⎞2 ⎜⎜ ⎟⎟ + σx, i , j ⎝ ⎠
NC − 1
∑ j=1
⎛ ye, i , j − ym, i , j ⎞2 ⎤ ⎜⎜ ⎟⎟ ⎥ σ ⎝ ⎠ ⎥⎦ y,i,j (2)
where NDG is the number of data groups used in the data regression; wn is the weight of the data group; NP is the number of data points; NC is the number of components; T, P, x, and y are the temperature, pressure, liquid, and vapor mole fractions, respectively; e is the estimated data from the model; m is the experimentally measured data; i is the data for data point i; j is the fractional data for component j; σ is the standard deviation of the specific data (should the standard deviation be 0; the specific data point is not included in the objective function, and the estimated values are set equal to the measured value). The deviations from the experimental data and the regressed model are expressed by the BIAS % (eq 3) and the mean relative deviation (MRD %) (eq 4) BIAS(U )% =
MRD(U )% =
(Uexp − Ucal) 100 ·∑ n n Uexp
(3)
Uexp − Ucal 100 ·∑ n n Uexp
(4)
with n the number of data points, excluding the pure component measurements, and U = x1, y1, P, or T.
■
RESULTS AND DISCUSSION The experimental pure-component vapor-pressure data are compared to literature6,8−10 values in Tables 2 and 3. The TFE and OFCB vapor pressures are in agreement with those from literature9,10 for the entire temperature range studied. The experimental vapor pressure data for TFE and OFCB are shown in Table 4 along with the calculated vapor pressures from the PR-EoS using the Mathias−Copeman alpha function with parameters from Table 1. The vapor pressures of both pure components are very well-represented by the model chosen, with a BIAS p % very close to 0 and an MRD p % of 0.003 for the TFE and 0.09 for the OFCB. The experimental VLE data for the three isotherms are shown in Table 5. The regressed binary interaction parameters for the model chosen are shown in Table 6. The model, along with the experimental data, is graphically represented in Figure 2. The relative volatility for each isotherm is shown in Figure 3,
TFE T/K
j
)
with τii = 0 and αii = 0. AE is the excess Helmholtz free energy, and gE is the excess Gibbs free energy. τij, τji, and αij are adjustable parameters in the NRTL local composition model. kij is an adjustable binary interaction parameter for the Wong−Sandler mixing rules. Renon and Prausnitz4 suggest using αij = 0.3. The parameters are fitted to the VLE data using the maximum likelihood objective function, F, as shown here in eq 2:
Table 2. Comparison of Experimental and Literature TFE Vapor Pressures
9
∑ xi ∑
g (T , P , xi) =
τji
(
xj exp −αji RT
1980
dx.doi.org/10.1021/je300217x | J. Chem. Eng. Data 2012, 57, 1978−1983
Journal of Chemical & Engineering Data
Article
Table 5. Experimental P−x−y Data for TFE (1) + OFCB (2) System at (248.3, 263.0, and 282.9) K
Table 3. Comparison of Experimental and Literature OFCB Vapor Pressures
p/MPa
OFCB T/K
p/MPa
plit8/MPa
|Δp|/MPa
plit6/MPa
|Δp|/MPa
247.90 248.25 253.38 265.93 267.92 269.89 272.90 277.87 287.89 292.89 303.37 313.09 322.53 335.34 342.37 352.36
0.039 0.041 0.051 0.092 0.099 0.110 0.122 0.148 0.216 0.257 0.362 0.486 0.635 0.889 1.055 1.329
0.042 0.043 0.055 0.096 0.104 0.112 0.127 0.154 0.221 0.262 0.368 0.493 0.642 0.896 1.064 1.339
0.003 0.002 0.004 0.004 0.005 0.002 0.005 0.006 0.005 0.005 0.006 0.007 0.007 0.007 0.009 0.010
0.042 0.043 0.055 0.096 0.104 0.113 0.128 0.155 0.222 0.264 0.369 0.493 0.640 0.889 1.054 1.325
0.000 0.000 0.000 0.000 0.000 0.001 0.001 0.001 0.001 0.002 0.001 0.000 0.002 0.003 0.010 0.014
x1
0.040 0.256 0.307 0.349 0.380 0.427 0.477 0.525 0.569 0.615 0.866 0.081 0.254 0.366 0.450 0.535 0.607 0.699 0.798 0.897 0.994 1.357
providing an indication of the degree of separation at the different studied temperatures. Table 7 shows the MRD and BIAS % deviation from the representations of the model using the parameters from Table 1 and 6 and the experimental data for all of the different variables. The resulting MRD % have been found to be lower than (0.20, 0.88, 0.22, and 0.22) % for the liquid and vapor phase mole fractions, pressure, and temperature for all three isotherms, respectively. The relative volatility of the two components in the mixture is given by the ratio of their equilibrium constants. The relative volatility is therefore an indication of the equilibrium ratios of the two components throughout the mixture composition range. The relative volatility and consequently the equilibrium ratio indicates the ease of separating a specific mixture using a phase contacting process, for example, distillation. The larger the relative volatility or equilibrium ratio, the simpler the separation. The temperature evolution of the binary interaction parameters of the NRTL model (τ12 and τ21) and the binary
y1
T/K = 248.3 0.000 0.318 0.395 0.449 0.481 0.538 0.598 0.654 0.698 0.742 1.000 T/K = 263.0 0.000 0.155 0.268 0.344 0.417 0.472 0.534 0.617 0.688 0.763 1.000 T/K = 282.9 0.000 0.052 0.137 0.251 0.320 0.423 0.513 0.603 0.681 0.763 1.000
0.180 0.252 0.398 0.594 0.720 0.897 1.065 1.257 1.427 1.645 2.330
0.000 0.880 0.907 0.923 0.932 0.944 0.955 0.963 0.969 0.974 1.000 0.000 0.720 0.815 0.851 0.883 0.908 0.923 0.940 0.957 0.968 1.000 0.000 0.329 0.585 0.741 0.794 0.849 0.882 0.912 0.931 0.951 1.000
Table 4. Experimental Vapor Pressure Data for TFE and OFCB Compared with the Mathias−Copeman Model TFE
OFCB
T/K
p/MPa
pmod/MPa
|Δp|/MPa
T/K
p/MPa
pmod/MPa
|Δp|/MPa
248.20 253.34 263.18 273.14 283.19
0.864 1.017 1.367 1.804 2.340
0.862 1.018 1.370 1.805 2.332
0.002 0.001 0.003 0.001 0.008
247.90 248.25 253.38 265.93 267.92 269.89 272.90 277.87 287.89 292.89 303.37 313.09 322.53 335.34 342.37 352.36
0.039 0.041 0.051 0.092 0.099 0.110 0.122 0.148 0.216 0.257 0.362 0.486 0.635 0.889 1.055 1.329
0.039 0.040 0.052 0.092 0.100 0.108 0.122 0.149 0.216 0.257 0.362 0.486 0.635 0.880 1.055 1.331
0.000 0.001 0.001 0.000 0.001 0.002 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.009 0.000 0.002
1981
dx.doi.org/10.1021/je300217x | J. Chem. Eng. Data 2012, 57, 1978−1983
Journal of Chemical & Engineering Data
Article
Table 6. Adjusted Binary Parameters for the PR EoS with Mathias−Copeman Parameters, Utilizing the Wong−Sandler Mixing Rules Incorporated with the NRTL Local Composition Model for the System TFE (1) + OFCB (2) at (248.3, 263.0, and 282.9) K parameter T/K
τ12
τ21
k12
248.3 263.0 282.9
8580 5384 2333
−443 −1600 −1585
−0.5294 −0.0950 0.0805
Figure 4. Temperature evolution for the NRTL model parameters for the three studied isotherms (□, τ12; ○, τ21); , second order tendency curves.
Figure 5. Temperature evolution for the binary interaction parameter (k12); , second order tendency curves.
Figure 2. Plot of the P−x−y data for TFE (1) + OFCB (2) (△, T = 248.3 K; ○, T = 263.0 K; □, T = 282.9 K; , model).
gathered using a “static-analytical” method. The experimental results are given with the following uncertainties: ± 0.10 K, ± 1.5 kPa, and ± 0.007 for the pressure, temperature, and vapor and liquid mole fractions, respectively. The experimental data were correlated with the Peng−Robinson EoS, with the Mathias−Copeman alpha function and the Wong−Sandler mixing rules utilizing the NRTL model. The model correlated the experimental data well with a maximum mean relative deviation across all isotherms of 0.22 %, 0.22 %, 0.2 %, and 0.88 % for pressure, temperature, liquid, and vapor phases, respectively.
■
Figure 3. Plot for the relative volatility for the TFE (1) + OFCB (2) system (△, T = 248.3 K; ○, T = 263.0 K; □, T = 282.9 K; , model).
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Tel.: +27 31 2603128. Fax: +27 31 2601118.
interaction parameter of the mixing rule (kij) are presented in Figures 4 and 5, respectively. General trends of the parameters across the three isotherms have been found and could be used for interpolation in the studied temperature range, as well as for slight extrapolation outside the temperature range.
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.
■
CONCLUSIONS VLE data for the TFE and OFCB binary system at (248.3, 263.0, and 282.9) K are presented in this paper. The data are
Notes
The authors declare no competing financial interest.
Table 7. Relative Deviations, BIAS and MRD %, between the Experimental Data and the Peng−Robinson EoS with Mathias− Copeman Parameters, Utilizing the Wong−Sandler Mixing Rules Incorporated with the NRTL Local Composition Model for the System TFE + OFCB at (248.3, 263.0, and 282.9) K T/K = 248.3 BIAS % MRD %
T/K = 263.0
T/K = 282.9
T
p
x1
y1
T
p
x1
y1
T
p
x1
y1
−0.20 0.22
0.09 0.17
0.09 0.16
−0.62 0.63
−0.11 0.19
0.07 0.22
0.05 0.20
−0.57 0.88
0.02 0.09
−0.01 0.11
0.00 0.07
0.34 0.57
1982
dx.doi.org/10.1021/je300217x | J. Chem. Eng. Data 2012, 57, 1978−1983
Journal of Chemical & Engineering Data
■
Article
REFERENCES
(1) Peng, D. Y.; Robinson, D. B. A new two-constant equation of state. Ind. Eng. Chem. Fundam. 1976, 15, 59−64. (2) 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. (3) Wong, D. S. H.; Orbey, H.; Sandler, S. I. Equation of state mixing rule for nonideal mixtures using available activity coefficient model parameters and that allow extrapolation over large ranges of temperature and pressure. Ind. Eng. Chem. Res. 1992, 31, 2033−2039. (4) Renon, H.; Prausnitz, J. M. Local compositions in thermodynamic excess function for liquid mixtures. AIChE J. 1968, 14, 135− 144. (5) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill Book Company: New York, 1987. (6) Daubert, T. E.; Danner, R. P.; Sibul, H. M.; Stebbins, C. C. Physical and Thermodynamic Properties of Pure Chemicals; Taylor & Francis: London, 1998. (7) 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. (8) Kletskii, A. B.; Petric, L. E. Dependence of vapor pressure of perfluorocyclobutane. Zh. Fiz. Khim. 1967, 41, 1183−1184. (9) Yaws, C. L. Yaws Handbook of Antoine Coefficients for Vapor Pressure, 2nd electronic ed.; Knovel: New York, 2009. (10) Boublík, T.; Fried, V.; Hála, E. The Vapour Pressures of Pure Substances; Elsevier Scientific Publishing Company: New York, 1975. (11) Chirico, R. D.; Frenkel, M.; Diky, V. V.; Marsh, K. N.; Wilhoit, R. C. An XML-Based Approach for the Storage and Exchange of Experimental and Critically Evaluated Thermophysical and Thermochemical Property Data. 2. Uncertainties. J. Chem. Eng. Data 2003, 48, 1344−1359.
1983
dx.doi.org/10.1021/je300217x | J. Chem. Eng. Data 2012, 57, 1978−1983
