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Measurement and modelling of bubble and dew points in the binary systems carbon dioxide + cyclobutanone and propane + cyclobutanone
Fluid Phase Equilibria 214 (2003) 121–136
Measurement and modelling of bubble and dew points in the binary systems carbon dioxide + cyclobutanone and propane + cyclobutanone A.R. Cruz Duarte a , M.M. Mooijer-van den Heuvel b , C.M.M. Duarte a , C.J. Peters b,∗ a
REQUIMTE/CQFB, Departemento de Qu´ımica, Faculdade de Ciˆencas e Technologia, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal b Laboratory of Physical Chemistry and Molecular Thermodynamics, Faculty of Applied Sciences, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands Received 23 October 2002; accepted 14 May 2003
Abstract The fluid phase behaviour for the binary systems carbon dioxide+cyclobutanone and propane+cyclobutanone has been determined experimentally, using Cailletet equipment. For both the systems bubble points have been determined for a number of isopleths covering the whole mole fraction range. Additionally, for the binary system carbon dioxide + cyclobutanone dew points and critical points could be observed for a number of overall-compositions rich in carbon dioxide. The temperature and pressure range were, respectively, from 278 to 369 K and from 0.1 to 14.0 MPa. Correlation of the experimental data of both systems has been performed using the Soave–Redlich–Kwong (SRK) equation of state. Satisfactory results have been achieved using only one binary interaction parameter. © 2003 Elsevier B.V. All rights reserved. Keywords: Phase behaviour; Modelling; Carbon dioxide; Propane; Cyclobutanone
1. Introduction Cyclobutanone is a cyclic ketone with four carbon atoms in the cyclic structure, which is very poorly soluble in water. Cyclic ketones are known for their occurrence in natural oils as the odoriferous component and their use as solvents in industry. In that respect, cyclopentanone and cyclohexanone are the most important cyclic organic ketones [1]. Cyclobutanone is smaller and more reactive than the aforementioned ones. Furthermore, it is less readily available, which makes it less attractive for general usage in industry. Basic physical and chemical data for the pure component cyclobutanone have been determined partly only. However, critical data are deficient, as are vapour–liquid equilibrium data for binary systems. ∗
Corresponding author. Tel.: +31-15-278-2660; fax: +31-15-278-8668. E-mail address: [email protected] (C.J. Peters). 0378-3812/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0378-3812(03)00325-X
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Research in our laboratory on the phase behaviour of clathrate hydrates in ternary systems of the kind water + gas + cyclic organic components has been performed with cyclobutanone being considered as one of the cyclic organic components. If the phase diagrams are compared, it can be observed that the pressure for the three-phase equilibrium hydrate–liquid water–vapour (H–Lw –V) in the binary system water + gas is reduced to lower values for the corresponding four-phase equilibrium hydrate–liquid water–liquid cyclic organic–vapour (H–Lw –L–V) in the ternary system. For different gases the reduction varies, i.e. 77% for methane (CH4 ), 80% for carbon dioxide (CO2 ) and 27% for propane (C3 H8 ) [2–4]. To enable proper modelling of the clathrate hydrate phase behaviour in the ternary system and to explain the phenomena occurring in these systems, knowledge of the phase behaviour in the binary systems gas + cyclobutanone is a prerequisite. In this paper the experimental results for various phase transitions in the systems CO2 + cyclobutanone and C3 H8 + cyclobutanone will be presented. Additionally, the experimental data will be correlated to determine the interaction parameter (kij ), which is present in the mixing rule of the used equation of state. 2. Theory 2.1. Pure component properties of cyclobutanone Proper modelling and interpretation of experimental phase equilibrium data for binary systems require knowledge of pure component properties, typically the critical properties and vapour pressure. Of the latter property, two sets of experimental data are available [5,6], one set at lower temperatures, i.e. from 249.1 to 298.4 K, and the other set at higher temperatures, i.e. from 317.8 to 380.2 K, respectively. Instead of using different Antoine constants for the temperature ranges of the separate data sets, the Antoine equation has been fitted to the experimental data of both data sets. The Antoine equation and the objective function to be minimised to determine the Antoine parameters are given in Eqs. (1) and (2): B ln psat = A − (1) C+T S=
N
sat 2 [psat calc − pexp ]
(2)
n=1
where psat is the vapour pressure (bar); A, B and C are the Antoine constants; and T is the temperature (K). sat In Eq. (2), N represents the number of data points, psat calc the calculated pressure and pexp the experimental pressure. Since experimental data for the critical properties of cyclobutanone are not available in literature, they have been estimated. For that purpose, two different estimation methods have been applied: the method of Ambrose [7,8] and the Joback modification of Lydersen’s method [9]. Both methods are based on group contribution techniques, where the various groups present in the molecule contribute all with characteristic constants to the total value of the property. The acentric factor ω is defined by the relation: ω = −log
psat Tr =0.7 pc
− 1.000
(3)
where psat is the vapour pressure at a reduced temperature of Tr = 0.7 [10]. The estimated critical properties and acentric factor are compared to the experimental values of cyclobutane, cyclopentane, and
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Table 1 Pure component property data for cyclobutanone, cyclobutane, cyclopentanone and cyclopentane Component
Method
pc (MPa)
Tc (K)
Vc (cm3 mol−1 )
ω
TB (K)
Cyclobutanone
Ambrose Joback
4.70 5.26
587 584
184 217
0.209 0.279
372.0a 374
Cyclobutane Cyclopentanone Cyclopentane
Literature Literature Literature
4.99 5.11 4.51
460.0 634.6 511.7
210 268 260
0.181 0.350 0.196
285.7 403.9 322.4
The critical property data for cyclobutanone have been determined with two estimation methods as mentioned in the table and the data for cyclobutane, cyclopentanone and cyclopentane have been taken from literature [11]. a Available from Dechema Database Software.
cyclopentanone [11] (see Table 1). The difference between the results of the two estimation methods is not large, only pc and Vc estimated with the method of Ambrose are substantially lower than the values estimated with Joback’s method. If the deviations for the critical properties and boiling point temperature (TB ) of the other mentioned components are observed, the deviation to lower pc and Vc for cyclobutanone is relatively large with the method of Ambrose. Therefore, the estimation of the critical properties with the method of Joback is used for the modelling. 2.2. Modelling of vapour–liquid equilibrium data The availability of experimental bubble point data enables the determination of the interaction parameter kij to be used in calculations with equations of state. The equation of state used in this study is the Soave–Redlich–Kwong (SRK) equation [12]: p=
RT a(T ) − V − b V(V + b)
(4)
where the various symbols have their usual meaning. The constants a and b can be calculated using the critical properties: a(T ) = aα(T ) a = 0.42747
(5)
R2 Tc2 pc
(6)
α(T) = 1 + m(ω) 1 −
T Tc
2
m(ω) = 0.480 + 1.574ω − 0.176ω2 b = 0.08664
RTc pc
(7) (8) (9)
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When multi-component systems are considered, mixing rules have to be applied to determine the mixture constants a and b: √ xi xj ai aj (1 − kij ) a= (10) i
b=
j
xi bi
(11)
i
In Eq. (10), kij is the binary interaction parameter, which can be determined by minimising the objective function as defined by Eq. (12), using experimental bubble point data: N pcalc − pexp 2 (12) S= p exp n=1 The kij is slightly dependent on the temperature. For that purpose, kij values have been determined for three isotherms: one at the lowest, one at an intermediate and one at the highest temperature. The averaged value of the three kij values was determined, and used for calculations in the whole temperature range. 3. Experimental The Cailletet equipment has been used for measuring the various phase transitions that occur in the binary systems CO2 +cyclobutanone and C3 H8 +cyclobutanone. Samples, consisting of both components, are confined in the top-end of a capillary glass tube and sealed by a mercury column. The composition of the sample is determined from the injected amount of cyclobutanone and the reading of the pressure of the gas, either CO2 or C3 H8 , in a calibrated volume at a known temperature. The capillary tube is placed into an autoclave, where the mercury reservoir is connected to a hydraulic oil system that can be pressurised with a screw-type hand-pump. In this way, the mercury column is both a seal for the sample and pressure-transmitting medium. The sample can be kept at a constant temperature, within 0.01 K, by circulating a heat-transferring medium around the tube with a thermostatic bath (Lauda). The temperature of the fluid near the top of the tube is read by a platinum resistance thermometer (A Laboratories) with an accuracy of 0.01 K. The pressure conditions of the phase transitions are measured with a dead-weight pressure gauge (de Wit), with a smallest weight of 0.005 MPa. For further details on the Cailletet equipment and measuring procedures, one is referred to Raeissi and Peters [13]. The region where a liquid and vapour phase coexist (L + V) is bound at higher pressures by the bubble point curve, which represents the phase transition L + V → L. The bubble points have been determined experimentally for both binary systems, by increasing the pressure step-wise on the dead-weight pressure gauge at a constant temperature until the last tiny bubble of the vapour phase disappears at equilibrium conditions. If possible, dew points (L + V → V) have been determined along with critical points (L = V). Critical points are characterized by the occurrence of equal volumes of the liquid and vapour phase, separated by a flat and hazy horizontal meniscus. The procedure for the measurement of a dew point is similar to that of a bubble point, i.e. the pressure is increased until the last droplet of liquid disappears. Application of Gibbs’ phase rule to a binary system shows that there are two degrees of freedom, when phase equilibria with two phases are considered. This implies that the pressure of the
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bubble and dew points, which bound the two-phase region liquid + vapour (L + V), are depending on the overall-composition of the system for a constant temperature. Consequently, the phase transitions have been determined for a number of overall-compositions of the systems, covering the whole mole fraction range. Cyclobutanone was supplied by Fluka with a purity ≥99%. CO2 and C3 H8 were supplied by MesserGriesheim with purities of 99.995 and 99.95%, respectively. All components were used without further purification. The purity of both CO2 and C3 H8 was confirmed. Therefore, literature vapour pressure data were compared with experimental vapour pressure data that were obtained with the Cailletet facility. Similarly, the critical pressure and temperature were compared.
4. Results 4.1. Experimental The numerical values of the experimental data are collected in Tables 2 and 3, and visualised in Figs. 1 and 2, for the systems CO2 + cyclobutanone and C3 H8 + cyclobutanone, respectively. Both Figs. 1 and 2 are p, T diagrams on which a number of isopleths, i.e. p, T loci at constant overall-composition, are projected together with the vapour pressure curves of the two pure components. Besides the critical point of pure CO2 , in Fig. 1 also the critical points (L = V) for the two overall-compositions xCO2 = 0.948 and 0.899 can be observed. For the latter two overall-compositions, also the dew points are shown in
15
p [MPa]
12
9
6
3
0 270 280 290 300 310 320 330 340 350 360 370 380
T [K] Fig. 1. p, T diagram with experimental data for pure component CO2 (—), literature data for cyclobutanone (- - -) [5,6] and experimental bubble points (xCO2 = 0.105 ( ), xCO2 = 0.139 ( ), xCO2 = 0.178 ( ), xCO2 = 0.251 (䉬), xCO2 = 0.407 (䉲), xCO2 = 0.499 (䉱), xCO2 = 0.622 (䉫), xCO2 = 0.752 (), xCO2 = 0.850 ( ), xCO2 = 0.899 (䊉) and xCO2 = 0.948 (䊏)), dew points (xCO2 = 0.899 (䊊), xCO2 = 0.948 (䊐)) and critical points ( ) of a number of isopleths for the system CO2 +cyclobutanone.
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5
p [MPa]
4
3
2
1
0 270 280 290 300 310 320 330 340 350 360 370 380
T [K] Fig. 2. p, T diagram with experimental data for pure component C3 H8 (—), literature data for cyclobutanone (- - -) [5,6] and experimental bubble points (xC3 H8 = 0.102 ( ), xC3 H8 = 0.134 ( ), xC3 H8 = 0.176 ( ), xC3 H8 = 0.250 (䉬), xC3 H8 = 0.404 (䉲), xC3 H8 = 0.509 (䉱), xC3 H8 = 0.625 (䉫), xC3 H8 = 0.750 (), xC3 H8 = 0.847 ( ) and xC3 H8 = 0.949 (䊊)) of a number of isopleths for the system C3 H8 + cyclobutanone.
this figure. Since the critical temperature of C3 H8 is relatively high, compared to that of CO2 , the critical region was not investigated for the system C3 H8 + cyclobutanone. The consistency of the experimental isopleths is examined by fitting exponential curves to the experimental data points. For the binary system CO2 +cyclobutanone the most optimal fit is represented by Eq. (13) with an average correlation coefficient of 0.999, and for the system C3 H8 + cyclobutanone by Eq. (14) with an average correlation coefficient of 0.9999, respectively. ln p = a0 +
a1 T2
(13)
ln p = a0 +
a1 T
(14)
These fitting correlations are used to construct isothermal cross-sections, i.e. p, x cross-sections as shown in Figs. 3 and 4 for both systems at temperatures of 280, 310, 330, 350 and 365 K. The procedure to construct T, x cross-sections at constant pressures is similar and shown in Figs. 5 and 6 for, respectively, the system CO2 +cyclobutanone at pressures of 3, 6, 9 and 12 MPa, and for the system C3 H8 +cyclobutanone at pressures of 0.5, 1, 2 and 3 MPa. Only interpolated values, obtained from the experimental isopleths (Figs. 1 and 2), are shown in both types of cross-sections. To estimate the critical points in the p, x and T, x cross-sections of the system CO2 + cyclobutanone, a second order polynomial equation has been fitted to the experimental critical points for the overall-compositions of xCO2 = 0.899, 0.948 and 1.000.
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Table 2 Experimental data of the bubble points (L + V → L), dew points (L + V → V) and critical points (L = V) for the system CO2 + cyclobutanone T (K)
p (MPa)
T (K)
p (MPa)
T (K)
p (MPa)
xCO2 = 0.105 277.80 282.76 288.25 293.28 298.23 303.34 308.25 313.38 318.33 323.39 328.51 333.39 338.46 343.47 348.58 353.56 358.62 363.51 368.64
0.468 0.518 0.574 0.629 0.684 0.754 0.819 0.889 0.959 1.044 1.119 1.199 1.284 1.364 1.459 1.544 1.644 1.724 1.829
xCO2 = 0.139 277.85 283.46 288.34 293.34 298.27 303.25 308.33 313.35 318.36 323.34 328.45 333.51 338.50 343.51 348.45 353.62 358.53 363.54 368.58
0.585 0.660 0.730 0.805 0.885 0.965 1.055 1.150 1.245 1.341 1.450 1.560 1.665 1.780 1.891 2.010 2.125 2.246 2.366
xCO2 = 0.178 278.29 283.33 288.35 293.32 298.35 303.28 308.26 313.28 318.30 323.37 328.41 333.39 338.35 343.45 348.47 353.62 358.48 363.49 368.55
0.743 0.833 0.923 1.028 1.133 1.238 1.348 1.479 1.589 1.709 1.859 1.994 2.119 2.294 2.414 2.559 2.694 2.853 3.018
xCO2 = 0.251 278.05 283.44 288.27 293.44 298.26 303.29 308.37 313.34 318.32 323.37 328.38 333.39 338.43 343.43 348.40 353.41 358.46 363.44 368.50
1.062 1.192 1.317 1.467 1.607 1.762 1.942 2.097 2.277 2.462 2.647 2.832 3.027 3.232 3.438 3.643 3.858 4.068 4.283
xCO2 = 0.407 278.25 283.30 288.33 293.33 298.29 303.33 308.32 313.33 318.32 323.31 328.39 333.38 338.35 343.43 348.42 353.43 358.48 363.52 368.73
1.838 2.058 2.293 2.543 2.803 3.083 3.378 3.678 4.003 4.318 4.653 4.993 5.343 5.714 6.069 6.454 6.819 7.189 7.584
xCO2 = 0.499 278.23 283.27 288.32 293.28 298.34 303.37 308.41 313.32 318.27 323.35 328.39 333.48 338.34 343.41 348.39 353.88 358.49 363.54 368.55
2.090 2.345 2.616 2.906 3.216 3.541 3.891 4.226 4.586 4.971 5.366 5.771 6.166 6.596 7.016 7.431 7.881 8.316 8.741
xCO2 = 0.622 278.26 283.52 288.49 293.25
2.550 2.886 3.221 3.561
xCO2 = 0.752 277.85 283.39 288.46 293.49
3.008 3.408 3.818 4.299
xCO2 = 0.850 278.32 283.28 288.23 293.34
3.366 3.785 4.241 4.741
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Table 2 (Continued ) T (K) 298.43 303.39 308.30 313.37 318.36 323.40 328.40 333.43 338.56 343.52 348.64 353.57 358.54 363.63 368.56
xCO2 = 0.899 278.21 283.52 288.13 292.99 298.24 303.34 308.42 313.35 318.31 323.31 328.42 333.63 338.49 343.55 345.91 346.41 346.69 346.86a 346.92b 348.44b 353.48b 358.49b 363.50b 368.56b a b
p (MPa) 3.955 4.360 4.771 5.221 5.690 6.166 6.666 7.176 7.711 8.231 8.781 9.306 9.836 10.381 10.901
3.539 4.019 4.459 4.984 5.559 6.164 6.814 7.459 8.129 8.819 9.524 10.215 10.804 11.360 11.600 11.649 11.680 11.695 11.704 11.855 12.325 12.795 13.185 13.516
Critical point L = V. Dew points L + V → V.
T (K) 298.41 303.33 308.34 313.51 318.38 323.36 328.36 333.37 338.46 343.44 348.51 353.57 358.88 363.54 368.53
xCO2 = 0.948 277.93 283.35 288.28 293.29 298.29 303.37 308.36 313.33 318.29 323.44 325.83 326.32a 326.46b 326.90b 328.53b 333.37b 338.51b 343.45b 348.41b 353.42b 358.57b 363.63b 368.78b
p (MPa) 4.714 5.189 5.704 6.269 6.814 7.399 8.004 8.619 9.259 9.889 10.534 11.169 11.819 12.374 12.944
3.713 4.233 4.743 5.303 5.913 6.563 7.248 7.923 8.608 9.243 9.499 9.549 9.559 9.614 9.889 10.274 10.774 11.169 11.390 11.545 11.620 11.641 11.671
T (K) 298.01 303.22 308.91 313.33 318.34 323.37 328.38 333.50 338.42 343.41 348.42 353.43 358.61 361.00 363.69 366.07 368.50
p (MPa) 5.261 5.831 6.406 7.031 7.671 8.346 9.021 9.726 10.386 11.046 11.681 12.256 12.801 13.036 13.281 13.491 13.696
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Table 3 Experimental data of the bubble points (L + V → L) for the system C3 H8 + cyclobutanone T (K)
p (MPa)
T (K)
p (MPa)
T (K)
p (MPa)
xCO2 = 0.102 308.36 313.34 318.28 323.33 328.39 333.48 338.38 343.38 348.39 353.39 358.52 363.58 368.64
0.418 0.459 0.493 0.538 0.578 0.619 0.664 0.709 0.764 0.804 0.864 0.919 0.969
xCO2 = 0.134 298.31 303.42 308.29 313.31 318.32 323.37 328.40 333.34 338.52 343.63 348.48 353.49 358.52 363.49 368.64
0.431 0.482 0.521 0.562 0.612 0.657 0.717 0.756 0.822 0.882 0.942 1.006 1.066 1.132 1.202
xCO2 = 0.176 288.36 293.31 298.35 303.23 308.29 313.37 318.27 323.40 328.48 333.48 338.57 343.48 348.58 353.45 358.51 363.54 368.67
0.401 0.446 0.491 0.541 0.591 0.646 0.706 0.766 0.832 0.896 0.972 1.042 1.112 1.182 1.266 1.346 1.426
xCO2 = 0.250 278.32 284.14 288.33 293.30 298.40 303.47 308.46 313.36 318.39 323.48 328.46 333.36 338.42 343.57 348.57 353.44 358.56 363.67 368.61
0.411 0.476 0.521 0.586 0.646 0.706 0.801 0.852 0.927 1.006 1.092 1.176 1.272 1.377 1.462 1.562 1.672 1.782 1.892
xCO2 = 0.404 277.68 283.20 288.22 293.32 298.35 303.39 308.44 313.31 318.41 323.35 328.30 333.41 338.41 343.46 348.46 353.44 358.52 363.61 368.50
0.455 0.520 0.590 0.660 0.740 0.826 0.916 1.006 1.106 1.216 1.322 1.422 1.572 1.702 1.842 1.977 2.127 2.287 2.437
xCO2 = 0.509 278.24 283.26 288.44 293.41 298.48 303.55 308.30 313.28 318.40 323.32 328.43 333.46 338.40 343.37 348.49 353.40 358.53 363.46 368.53
0.487 0.552 0.627 0.707 0.792 0.887 0.982 1.087 1.202 1.317 1.452 1.587 1.727 1.882 2.038 2.203 2.378 2.558 2.743
xCO2 = 0.625 278.45 283.27 288.23 293.28 298.26 303.34 308.17
0.504 0.569 0.649 0.734 0.824 0.924 1.029
xCO2 = 0.750 278.17 283.25 288.25 293.33 298.39 303.37 308.26
0.463 0.578 0.663 0.753 0.858 0.963 1.078
xCO2 = 0.847 278.02 283.43 288.44 293.54 298.35 303.37 308.36
0.520 0.600 0.685 0.780 0.886 0.996 1.110
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Table 3 (Continued ) T (K) 313.28 318.49 323.26 328.27 333.33 338.37 343.42 348.31 353.44 358.45 363.50 368.49 xCO2 = 0.949 277.84 283.37 288.39 293.54 298.49 303.27 308.33 313.44 318.27 323.43 328.46 333.43 338.36 343.41 348.46 353.49 358.38 363.55 368.52
p (MPa) 1.144 1.279 1.404 1.549 1.699 1.859 2.034 2.205 2.395 2.595 2.800 3.009
T (K) 313.36 318.34 323.30 328.37 333.40 338.40 343.43 348.50 353.42 358.48 363.43 368.51
p (MPa) 1.203 1.338 1.478 1.638 1.803 1.978 2.168 2.388 2.573 2.793 3.028 3.268
T (K) 313.41 318.36 323.34 328.40 333.48 338.46 343.44 348.46 353.48 358.46 363.55 368.50
p (MPa) 1.240 1.386 1.541 1.706 1.891 2.076 2.276 2.491 2.716 2.961 3.217 3.486
0.541 0.631 0.721 0.826 0.936 1.052 1.181 1.331 1.482 1.657 1.837 2.032 2.237 2.492 2.707 2.967 3.227 3.527 3.827
4.2. Modelling Antoine parameters for cyclobutanone have been obtained from fitting Eq. (1) to the experimental data points for cyclobutanone given in literature [5,6]. If in Eq. (1) pressure is taken in bar and temperature in Kelvin, their numerical values are A = 10.79, B = 3794 and C = −20.03. Besides, the pure component parameters of the various components, for both binary systems isothermal bubble point data at 280, 330 and 365 K have been used as input for the Eoskij-programme of Tassios [14]. The objective function given in Eq. (12) is minimised and an averaged value for kij over the three temperatures is obtained (see Table 4). Fig. 7 compares experimental and modelling results for the binary system CO2 + cyclobutanone. In this figure, also two isotherms, respectively, at 310 and 350 K, are included which were not used to evaluate the binary interaction parameter kij . For completeness, in Fig. 7 also the calculated isothermal dew point curves have been included.
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131
15
p [MPa]
12
9
6
3
0 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
xCO2 [-] Fig. 3. p, x Cross-section with interpolated data points for the system CO2 + cyclobutanone at temperatures of 280 K (䉬), 310 K (䉱), 330 K (bubble points (䉲), dew points ()), 350 K (bubble points (䊏), dew points (䊐)) and 365 K (bubble points (䊉), dew points (䊊)). The critical points ( ) represented are estimated from the fitting curve of the experimental critical points.
5
p [MPa]
4
3
2
1
0 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
xC3H8 [-] Fig. 4. p, x Cross-section with interpolated data points for the system C3 H8 + cyclobutanone at temperatures of 280 K (䉬), 310 K (䉱), 330 K (䉲), 350 K (䊏) and 365 K (䊉).
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550 500
T [K]
450 400 350 300 250 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
xCO2 [-] Fig. 5. T, x cross-section with interpolated data points for the system CO2 + cyclobutanone at pressures of 3 MPa (䉬), 6 MPa (䉱), 9 MPa (䉲), and 12 MPa (bubble points (䊉), dew points (䊊)). The critical points ( ) represented are estimated from the fitting curve of the experimental critical points.
550 500
T [K]
450 400 350 300 250 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
xC3H8 [-] Fig. 6. T, x cross-section with interpolated data points for the system C3 H8 + cyclobutanone at pressures of 0.5 MPa (䉬), 1 MPa (䉱), 2 MPa (䉲) and 3 MPa (䊉).
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15
12
p [MPa]
9
6
3
0 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
xCO2 [-] Fig. 7. p, x Cross-section with experimental data for the system CO2 + cyclobutanone at temperatures of 280 K (䉬), 310 K (䉱), 330 K (bubble points (䉲), dew points ()), 350 K (bubble points (䊏) dew points (䊐), 365 K (bubble points (䊉), dew points (䊊)), critical points ( ), results of calculation of the bubble point (—) and dew point (- - -) curves with the SRK equation of state.
4
p [MPa]
3
2
1
0 0.00 0.10
0.20 0.30
0.40
0.50
0.60 0.70
0.80 0.90
1.00
xC3H8 [-] Fig. 8. p, x Cross-section with experimental data for the system C3 H8 + cyclobutanone at temperatures of 280 K (䉬), 310 K (䉱), 330 K (䉲), 350 K (䊏), 365 K (䊉), results of calculation of the bubble point (—) and dew point (- - -) curves with the SRK equation of state.
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Table 4 Optimised kij values for the SRK equation of state with the Tassios programme Eoskij [14] System
kij
p (%)
x range
CO2 + cyclobutanone C3 H8 + cyclobutanone
0.020 ± 0.001 0.081 ± 0.001
2.96 2.01
0.000–0.899 0.000–1.000
For the system C3 H8 +cyclobutanone a similar comparison between experimental and modelling results is shown in Fig. 8. Also in this case two isotherms, respectively, at 310 and 350 K, are included which were not used to evaluate the binary interaction parameter kij . As can be seen from Fig. 8, the modelling results follow the trend of the experimental results.
5. Discussion The bubble point pressure, at constant temperatures, increases with increasing content of CO2 in the overall-composition. In Fig. 3, it can be observed that this increase of the bubble-point pressure with overall-composition xCO2 is gradual. In Fig. 5, the temperature decreases gradually with increasing overall-composition xCO2 . In the p, x cross-section of Fig. 3 critical points for various temperatures and dew points for the higher temperatures, 330, 350 and 365 K, can be observed. From Figs. 3 and 5, which are derived p, x and T, x cross-sections, respectively, it can be seen that the various isopleths, as depicted in Fig. 1, show mutual consistency. Correlation of the experimental data at 280, 330 and 365 K with the SRK equation of state gives a value of the binary interaction parameter kij of 0.020 (see Table 4). The relatively small value of this parameter suggests a minor deviation from ideal behaviour in the liquid phase, which is also confirmed by the occurrence of an almost linear dependence of the various bubble point curves with the CO2 mole fraction (see Fig. 3). The course of the bubble and dew point curves can be predicted satisfactorily. From Fig. 7 it can be seen that the deviations between the experimental and calculated pressures increase for the isotherms at higher temperatures, especially at near-critical conditions and at larger values of xCO2 as well (see Fig. 7). The SRK equation of state calculations predict higher pressures in this region than have been found experimentally, i.e. with AAD = 8–10% for that particular region. The general course of the curves in the p, x and T, x cross-sections of Figs. 4 and 6, for the system C3 H8 + cyclobutanone, is similar to those observed in Figs. 3 and 5, respectively. For the considered overall-compositions of the binary system C3 H8 + cyclobutanone no critical points, and dew points have been observed. However, an inflection point seems to be present in the range 0.6 ≤ xC3 H8 ≤ 0.9. This suggests that the system is close to a liquid–liquid two-phase split. Correlation of the experimental data with the SRK equation of state gives a kij of 0.081. This value for kij suggests the occurrence of larger deviations from ideality in the liquid phase than was established for the system CO2 + cyclobutanone, which is confirmed by the course and shape of the bubble point curves shown in Fig. 8. The prediction with the SRK equation of state shows that the point of inflection in the bubble point curve at higher temperatures is located at approximately xC3 H8 = 0.75. The curvature is stronger for the correlated line than for a fitting curve through the experimental data. Most likely, the liquid–liquid immiscibility occurs at higher temperatures, because there is more curvature for the p, x cross-sections at higher temperatures.
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6. Conclusions The vapour–liquid phase behaviour of the binary systems CO2 + cyclobutanone and C3 H8 + cyclobutanone has been investigated experimentally with Cailletet equipment and, in addition, has been modelled with the Soave–Redlich–Kwong equation of state. For the binary system CO2 +cyclobutanone the conditions for bubble points have been determined for a number of isopleths in the range from 0.000 ≤ xCO2 ≤ 1.000, and dew points and critical points at overallcompositions of xCO2 = 0.899 and 0.948. With an optimised value of kij = 0.020 for the SRK equation of state the experimental data can be correlated satisfactorily (p = 2.96%). In the region close to the critical point the deviation in pressure is larger (p = 8–10%), however, the general course is predicted well. In the system C3 H8 + cyclobutanone only bubble point conditions could be measured. The bubble point curve in the constructed p, x and T, x cross-sections show a point of inflection, which is confirmed by the calculations with the SRK equation of state. The kij parameter has been optimised to a value of 0.081 for this system in the considered temperature and pressure region. The point of inflection suggests a tendency to liquid–liquid immiscibility, which has not been observed at the conditions experimentally investigated. List of symbols a constant SRK equation of state b constant SRK equation of state H, L, V hydrate, liquid, vapour phases kij interaction parameter N number of data points p pressure (MPa or bar) pc critical pressure (MPa) R gas constant (8.314) (J mol−1 K−1 ) S objective function T temperature (K) TB normal boiling point temperature (K) Tc critical temperature (K) Tr reduced temperature V molar volume (cm3 mol−1 ) Vc critical molar volume (cm3 mol−1 ) x liquid phase composition Greek letters α temperature correction factor for the constant a in the mixing rule used ω acentric factor Subscripts C3 H8 propane CO2 carbon dioxide w water
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References [1] J. Braithwaite, Ketones, in: D.F. Othmer, R.E. Kirk, M. Howe-Grant, J.I. Kroschwitz (Eds.), Kirk-Othmer Encyclopedia of Chemical Technology, vol. 14, fourth ed., Wiley, New York, 1995, pp. 978–1021. [2] M.M. Mooijer-van den Heuvel, C.J. Peters, J. de Swaan Arons, Fluid Phase Equilib. 172 (2000) 73–91. [3] M.M. Mooijer-van den Heuvel, R. Witteman, C.J. Peters, Fluid Phase Equilib. 182 (2001) 97–110. [4] M.M. Mooijer-van den Heuvel, C.J. Peters, J. de Swaan Arons, Fluid Phase Equilib. 193 (2002) 245–259. [5] S.W. Benson, G.B. Kistiakowski, J. Am. Chem. Soc. 64 (1942) 80–86. [6] E.F. Meyer, C.A. Hotz, J. Chem. Eng. Data 21 (1976) 274–279. [7] D. Ambrose, NPL Rep. Chem. 98, National Physical Laboratory, Teddington, USA, 1979. [8] D. Ambrose, NPL Rep. Chem. 92, National Physical Laboratory, Teddington, USA, 1978 (corrected 1980). [9] K.G. Joback, M.Sc. thesis in chemical engineering, Massachusetts Institute of Technology, Cambridge, MA, USA, 1984. [10] K.S. Pitzer, D.Z. Lippmann, R.F. Curl, C.M. Huggins, D.E. Petersen, J. Am. Chem. Soc. 77 (1955) 3433. [11] R.C. Reid, J.M. Prausnitz, B.E. Poling, The properties of gases and liquids, fourth ed., McGraw-Hill, New York, 1987. [12] G. Soave, Chem. Eng. Sci. 27 (1972) 1197–1203. [13] S. Raeissi, C.J. Peters, J. Supercrit. Fluids 20 (2001) 221–228. [14] D.P. Tassios, Applied Chemical Engineering Thermodynamics, Springer-Verlag, Berlin, Germany, 1993.
Measurement and modelling of bubble and dew points in the binary systems carbon dioxide + cyclobutanone and propane + cyclobutanone A.R. Cruz Duarte a , M.M. Mooijer-van den Heuvel b , C.M.M. Duarte a , C.J. Peters b,∗ a
REQUIMTE/CQFB, Departemento de Qu´ımica, Faculdade de Ciˆencas e Technologia, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal b Laboratory of Physical Chemistry and Molecular Thermodynamics, Faculty of Applied Sciences, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands Received 23 October 2002; accepted 14 May 2003
Abstract The fluid phase behaviour for the binary systems carbon dioxide+cyclobutanone and propane+cyclobutanone has been determined experimentally, using Cailletet equipment. For both the systems bubble points have been determined for a number of isopleths covering the whole mole fraction range. Additionally, for the binary system carbon dioxide + cyclobutanone dew points and critical points could be observed for a number of overall-compositions rich in carbon dioxide. The temperature and pressure range were, respectively, from 278 to 369 K and from 0.1 to 14.0 MPa. Correlation of the experimental data of both systems has been performed using the Soave–Redlich–Kwong (SRK) equation of state. Satisfactory results have been achieved using only one binary interaction parameter. © 2003 Elsevier B.V. All rights reserved. Keywords: Phase behaviour; Modelling; Carbon dioxide; Propane; Cyclobutanone
1. Introduction Cyclobutanone is a cyclic ketone with four carbon atoms in the cyclic structure, which is very poorly soluble in water. Cyclic ketones are known for their occurrence in natural oils as the odoriferous component and their use as solvents in industry. In that respect, cyclopentanone and cyclohexanone are the most important cyclic organic ketones [1]. Cyclobutanone is smaller and more reactive than the aforementioned ones. Furthermore, it is less readily available, which makes it less attractive for general usage in industry. Basic physical and chemical data for the pure component cyclobutanone have been determined partly only. However, critical data are deficient, as are vapour–liquid equilibrium data for binary systems. ∗
Corresponding author. Tel.: +31-15-278-2660; fax: +31-15-278-8668. E-mail address: [email protected] (C.J. Peters). 0378-3812/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0378-3812(03)00325-X
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Research in our laboratory on the phase behaviour of clathrate hydrates in ternary systems of the kind water + gas + cyclic organic components has been performed with cyclobutanone being considered as one of the cyclic organic components. If the phase diagrams are compared, it can be observed that the pressure for the three-phase equilibrium hydrate–liquid water–vapour (H–Lw –V) in the binary system water + gas is reduced to lower values for the corresponding four-phase equilibrium hydrate–liquid water–liquid cyclic organic–vapour (H–Lw –L–V) in the ternary system. For different gases the reduction varies, i.e. 77% for methane (CH4 ), 80% for carbon dioxide (CO2 ) and 27% for propane (C3 H8 ) [2–4]. To enable proper modelling of the clathrate hydrate phase behaviour in the ternary system and to explain the phenomena occurring in these systems, knowledge of the phase behaviour in the binary systems gas + cyclobutanone is a prerequisite. In this paper the experimental results for various phase transitions in the systems CO2 + cyclobutanone and C3 H8 + cyclobutanone will be presented. Additionally, the experimental data will be correlated to determine the interaction parameter (kij ), which is present in the mixing rule of the used equation of state. 2. Theory 2.1. Pure component properties of cyclobutanone Proper modelling and interpretation of experimental phase equilibrium data for binary systems require knowledge of pure component properties, typically the critical properties and vapour pressure. Of the latter property, two sets of experimental data are available [5,6], one set at lower temperatures, i.e. from 249.1 to 298.4 K, and the other set at higher temperatures, i.e. from 317.8 to 380.2 K, respectively. Instead of using different Antoine constants for the temperature ranges of the separate data sets, the Antoine equation has been fitted to the experimental data of both data sets. The Antoine equation and the objective function to be minimised to determine the Antoine parameters are given in Eqs. (1) and (2): B ln psat = A − (1) C+T S=
N
sat 2 [psat calc − pexp ]
(2)
n=1
where psat is the vapour pressure (bar); A, B and C are the Antoine constants; and T is the temperature (K). sat In Eq. (2), N represents the number of data points, psat calc the calculated pressure and pexp the experimental pressure. Since experimental data for the critical properties of cyclobutanone are not available in literature, they have been estimated. For that purpose, two different estimation methods have been applied: the method of Ambrose [7,8] and the Joback modification of Lydersen’s method [9]. Both methods are based on group contribution techniques, where the various groups present in the molecule contribute all with characteristic constants to the total value of the property. The acentric factor ω is defined by the relation: ω = −log
psat Tr =0.7 pc
− 1.000
(3)
where psat is the vapour pressure at a reduced temperature of Tr = 0.7 [10]. The estimated critical properties and acentric factor are compared to the experimental values of cyclobutane, cyclopentane, and
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Table 1 Pure component property data for cyclobutanone, cyclobutane, cyclopentanone and cyclopentane Component
Method
pc (MPa)
Tc (K)
Vc (cm3 mol−1 )
ω
TB (K)
Cyclobutanone
Ambrose Joback
4.70 5.26
587 584
184 217
0.209 0.279
372.0a 374
Cyclobutane Cyclopentanone Cyclopentane
Literature Literature Literature
4.99 5.11 4.51
460.0 634.6 511.7
210 268 260
0.181 0.350 0.196
285.7 403.9 322.4
The critical property data for cyclobutanone have been determined with two estimation methods as mentioned in the table and the data for cyclobutane, cyclopentanone and cyclopentane have been taken from literature [11]. a Available from Dechema Database Software.
cyclopentanone [11] (see Table 1). The difference between the results of the two estimation methods is not large, only pc and Vc estimated with the method of Ambrose are substantially lower than the values estimated with Joback’s method. If the deviations for the critical properties and boiling point temperature (TB ) of the other mentioned components are observed, the deviation to lower pc and Vc for cyclobutanone is relatively large with the method of Ambrose. Therefore, the estimation of the critical properties with the method of Joback is used for the modelling. 2.2. Modelling of vapour–liquid equilibrium data The availability of experimental bubble point data enables the determination of the interaction parameter kij to be used in calculations with equations of state. The equation of state used in this study is the Soave–Redlich–Kwong (SRK) equation [12]: p=
RT a(T ) − V − b V(V + b)
(4)
where the various symbols have their usual meaning. The constants a and b can be calculated using the critical properties: a(T ) = aα(T ) a = 0.42747
(5)
R2 Tc2 pc
(6)
α(T) = 1 + m(ω) 1 −
T Tc
2
m(ω) = 0.480 + 1.574ω − 0.176ω2 b = 0.08664
RTc pc
(7) (8) (9)
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When multi-component systems are considered, mixing rules have to be applied to determine the mixture constants a and b: √ xi xj ai aj (1 − kij ) a= (10) i
b=
j
xi bi
(11)
i
In Eq. (10), kij is the binary interaction parameter, which can be determined by minimising the objective function as defined by Eq. (12), using experimental bubble point data: N pcalc − pexp 2 (12) S= p exp n=1 The kij is slightly dependent on the temperature. For that purpose, kij values have been determined for three isotherms: one at the lowest, one at an intermediate and one at the highest temperature. The averaged value of the three kij values was determined, and used for calculations in the whole temperature range. 3. Experimental The Cailletet equipment has been used for measuring the various phase transitions that occur in the binary systems CO2 +cyclobutanone and C3 H8 +cyclobutanone. Samples, consisting of both components, are confined in the top-end of a capillary glass tube and sealed by a mercury column. The composition of the sample is determined from the injected amount of cyclobutanone and the reading of the pressure of the gas, either CO2 or C3 H8 , in a calibrated volume at a known temperature. The capillary tube is placed into an autoclave, where the mercury reservoir is connected to a hydraulic oil system that can be pressurised with a screw-type hand-pump. In this way, the mercury column is both a seal for the sample and pressure-transmitting medium. The sample can be kept at a constant temperature, within 0.01 K, by circulating a heat-transferring medium around the tube with a thermostatic bath (Lauda). The temperature of the fluid near the top of the tube is read by a platinum resistance thermometer (A Laboratories) with an accuracy of 0.01 K. The pressure conditions of the phase transitions are measured with a dead-weight pressure gauge (de Wit), with a smallest weight of 0.005 MPa. For further details on the Cailletet equipment and measuring procedures, one is referred to Raeissi and Peters [13]. The region where a liquid and vapour phase coexist (L + V) is bound at higher pressures by the bubble point curve, which represents the phase transition L + V → L. The bubble points have been determined experimentally for both binary systems, by increasing the pressure step-wise on the dead-weight pressure gauge at a constant temperature until the last tiny bubble of the vapour phase disappears at equilibrium conditions. If possible, dew points (L + V → V) have been determined along with critical points (L = V). Critical points are characterized by the occurrence of equal volumes of the liquid and vapour phase, separated by a flat and hazy horizontal meniscus. The procedure for the measurement of a dew point is similar to that of a bubble point, i.e. the pressure is increased until the last droplet of liquid disappears. Application of Gibbs’ phase rule to a binary system shows that there are two degrees of freedom, when phase equilibria with two phases are considered. This implies that the pressure of the
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bubble and dew points, which bound the two-phase region liquid + vapour (L + V), are depending on the overall-composition of the system for a constant temperature. Consequently, the phase transitions have been determined for a number of overall-compositions of the systems, covering the whole mole fraction range. Cyclobutanone was supplied by Fluka with a purity ≥99%. CO2 and C3 H8 were supplied by MesserGriesheim with purities of 99.995 and 99.95%, respectively. All components were used without further purification. The purity of both CO2 and C3 H8 was confirmed. Therefore, literature vapour pressure data were compared with experimental vapour pressure data that were obtained with the Cailletet facility. Similarly, the critical pressure and temperature were compared.
4. Results 4.1. Experimental The numerical values of the experimental data are collected in Tables 2 and 3, and visualised in Figs. 1 and 2, for the systems CO2 + cyclobutanone and C3 H8 + cyclobutanone, respectively. Both Figs. 1 and 2 are p, T diagrams on which a number of isopleths, i.e. p, T loci at constant overall-composition, are projected together with the vapour pressure curves of the two pure components. Besides the critical point of pure CO2 , in Fig. 1 also the critical points (L = V) for the two overall-compositions xCO2 = 0.948 and 0.899 can be observed. For the latter two overall-compositions, also the dew points are shown in
15
p [MPa]
12
9
6
3
0 270 280 290 300 310 320 330 340 350 360 370 380
T [K] Fig. 1. p, T diagram with experimental data for pure component CO2 (—), literature data for cyclobutanone (- - -) [5,6] and experimental bubble points (xCO2 = 0.105 ( ), xCO2 = 0.139 ( ), xCO2 = 0.178 ( ), xCO2 = 0.251 (䉬), xCO2 = 0.407 (䉲), xCO2 = 0.499 (䉱), xCO2 = 0.622 (䉫), xCO2 = 0.752 (), xCO2 = 0.850 ( ), xCO2 = 0.899 (䊉) and xCO2 = 0.948 (䊏)), dew points (xCO2 = 0.899 (䊊), xCO2 = 0.948 (䊐)) and critical points ( ) of a number of isopleths for the system CO2 +cyclobutanone.
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5
p [MPa]
4
3
2
1
0 270 280 290 300 310 320 330 340 350 360 370 380
T [K] Fig. 2. p, T diagram with experimental data for pure component C3 H8 (—), literature data for cyclobutanone (- - -) [5,6] and experimental bubble points (xC3 H8 = 0.102 ( ), xC3 H8 = 0.134 ( ), xC3 H8 = 0.176 ( ), xC3 H8 = 0.250 (䉬), xC3 H8 = 0.404 (䉲), xC3 H8 = 0.509 (䉱), xC3 H8 = 0.625 (䉫), xC3 H8 = 0.750 (), xC3 H8 = 0.847 ( ) and xC3 H8 = 0.949 (䊊)) of a number of isopleths for the system C3 H8 + cyclobutanone.
this figure. Since the critical temperature of C3 H8 is relatively high, compared to that of CO2 , the critical region was not investigated for the system C3 H8 + cyclobutanone. The consistency of the experimental isopleths is examined by fitting exponential curves to the experimental data points. For the binary system CO2 +cyclobutanone the most optimal fit is represented by Eq. (13) with an average correlation coefficient of 0.999, and for the system C3 H8 + cyclobutanone by Eq. (14) with an average correlation coefficient of 0.9999, respectively. ln p = a0 +
a1 T2
(13)
ln p = a0 +
a1 T
(14)
These fitting correlations are used to construct isothermal cross-sections, i.e. p, x cross-sections as shown in Figs. 3 and 4 for both systems at temperatures of 280, 310, 330, 350 and 365 K. The procedure to construct T, x cross-sections at constant pressures is similar and shown in Figs. 5 and 6 for, respectively, the system CO2 +cyclobutanone at pressures of 3, 6, 9 and 12 MPa, and for the system C3 H8 +cyclobutanone at pressures of 0.5, 1, 2 and 3 MPa. Only interpolated values, obtained from the experimental isopleths (Figs. 1 and 2), are shown in both types of cross-sections. To estimate the critical points in the p, x and T, x cross-sections of the system CO2 + cyclobutanone, a second order polynomial equation has been fitted to the experimental critical points for the overall-compositions of xCO2 = 0.899, 0.948 and 1.000.
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Table 2 Experimental data of the bubble points (L + V → L), dew points (L + V → V) and critical points (L = V) for the system CO2 + cyclobutanone T (K)
p (MPa)
T (K)
p (MPa)
T (K)
p (MPa)
xCO2 = 0.105 277.80 282.76 288.25 293.28 298.23 303.34 308.25 313.38 318.33 323.39 328.51 333.39 338.46 343.47 348.58 353.56 358.62 363.51 368.64
0.468 0.518 0.574 0.629 0.684 0.754 0.819 0.889 0.959 1.044 1.119 1.199 1.284 1.364 1.459 1.544 1.644 1.724 1.829
xCO2 = 0.139 277.85 283.46 288.34 293.34 298.27 303.25 308.33 313.35 318.36 323.34 328.45 333.51 338.50 343.51 348.45 353.62 358.53 363.54 368.58
0.585 0.660 0.730 0.805 0.885 0.965 1.055 1.150 1.245 1.341 1.450 1.560 1.665 1.780 1.891 2.010 2.125 2.246 2.366
xCO2 = 0.178 278.29 283.33 288.35 293.32 298.35 303.28 308.26 313.28 318.30 323.37 328.41 333.39 338.35 343.45 348.47 353.62 358.48 363.49 368.55
0.743 0.833 0.923 1.028 1.133 1.238 1.348 1.479 1.589 1.709 1.859 1.994 2.119 2.294 2.414 2.559 2.694 2.853 3.018
xCO2 = 0.251 278.05 283.44 288.27 293.44 298.26 303.29 308.37 313.34 318.32 323.37 328.38 333.39 338.43 343.43 348.40 353.41 358.46 363.44 368.50
1.062 1.192 1.317 1.467 1.607 1.762 1.942 2.097 2.277 2.462 2.647 2.832 3.027 3.232 3.438 3.643 3.858 4.068 4.283
xCO2 = 0.407 278.25 283.30 288.33 293.33 298.29 303.33 308.32 313.33 318.32 323.31 328.39 333.38 338.35 343.43 348.42 353.43 358.48 363.52 368.73
1.838 2.058 2.293 2.543 2.803 3.083 3.378 3.678 4.003 4.318 4.653 4.993 5.343 5.714 6.069 6.454 6.819 7.189 7.584
xCO2 = 0.499 278.23 283.27 288.32 293.28 298.34 303.37 308.41 313.32 318.27 323.35 328.39 333.48 338.34 343.41 348.39 353.88 358.49 363.54 368.55
2.090 2.345 2.616 2.906 3.216 3.541 3.891 4.226 4.586 4.971 5.366 5.771 6.166 6.596 7.016 7.431 7.881 8.316 8.741
xCO2 = 0.622 278.26 283.52 288.49 293.25
2.550 2.886 3.221 3.561
xCO2 = 0.752 277.85 283.39 288.46 293.49
3.008 3.408 3.818 4.299
xCO2 = 0.850 278.32 283.28 288.23 293.34
3.366 3.785 4.241 4.741
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Table 2 (Continued ) T (K) 298.43 303.39 308.30 313.37 318.36 323.40 328.40 333.43 338.56 343.52 348.64 353.57 358.54 363.63 368.56
xCO2 = 0.899 278.21 283.52 288.13 292.99 298.24 303.34 308.42 313.35 318.31 323.31 328.42 333.63 338.49 343.55 345.91 346.41 346.69 346.86a 346.92b 348.44b 353.48b 358.49b 363.50b 368.56b a b
p (MPa) 3.955 4.360 4.771 5.221 5.690 6.166 6.666 7.176 7.711 8.231 8.781 9.306 9.836 10.381 10.901
3.539 4.019 4.459 4.984 5.559 6.164 6.814 7.459 8.129 8.819 9.524 10.215 10.804 11.360 11.600 11.649 11.680 11.695 11.704 11.855 12.325 12.795 13.185 13.516
Critical point L = V. Dew points L + V → V.
T (K) 298.41 303.33 308.34 313.51 318.38 323.36 328.36 333.37 338.46 343.44 348.51 353.57 358.88 363.54 368.53
xCO2 = 0.948 277.93 283.35 288.28 293.29 298.29 303.37 308.36 313.33 318.29 323.44 325.83 326.32a 326.46b 326.90b 328.53b 333.37b 338.51b 343.45b 348.41b 353.42b 358.57b 363.63b 368.78b
p (MPa) 4.714 5.189 5.704 6.269 6.814 7.399 8.004 8.619 9.259 9.889 10.534 11.169 11.819 12.374 12.944
3.713 4.233 4.743 5.303 5.913 6.563 7.248 7.923 8.608 9.243 9.499 9.549 9.559 9.614 9.889 10.274 10.774 11.169 11.390 11.545 11.620 11.641 11.671
T (K) 298.01 303.22 308.91 313.33 318.34 323.37 328.38 333.50 338.42 343.41 348.42 353.43 358.61 361.00 363.69 366.07 368.50
p (MPa) 5.261 5.831 6.406 7.031 7.671 8.346 9.021 9.726 10.386 11.046 11.681 12.256 12.801 13.036 13.281 13.491 13.696
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Table 3 Experimental data of the bubble points (L + V → L) for the system C3 H8 + cyclobutanone T (K)
p (MPa)
T (K)
p (MPa)
T (K)
p (MPa)
xCO2 = 0.102 308.36 313.34 318.28 323.33 328.39 333.48 338.38 343.38 348.39 353.39 358.52 363.58 368.64
0.418 0.459 0.493 0.538 0.578 0.619 0.664 0.709 0.764 0.804 0.864 0.919 0.969
xCO2 = 0.134 298.31 303.42 308.29 313.31 318.32 323.37 328.40 333.34 338.52 343.63 348.48 353.49 358.52 363.49 368.64
0.431 0.482 0.521 0.562 0.612 0.657 0.717 0.756 0.822 0.882 0.942 1.006 1.066 1.132 1.202
xCO2 = 0.176 288.36 293.31 298.35 303.23 308.29 313.37 318.27 323.40 328.48 333.48 338.57 343.48 348.58 353.45 358.51 363.54 368.67
0.401 0.446 0.491 0.541 0.591 0.646 0.706 0.766 0.832 0.896 0.972 1.042 1.112 1.182 1.266 1.346 1.426
xCO2 = 0.250 278.32 284.14 288.33 293.30 298.40 303.47 308.46 313.36 318.39 323.48 328.46 333.36 338.42 343.57 348.57 353.44 358.56 363.67 368.61
0.411 0.476 0.521 0.586 0.646 0.706 0.801 0.852 0.927 1.006 1.092 1.176 1.272 1.377 1.462 1.562 1.672 1.782 1.892
xCO2 = 0.404 277.68 283.20 288.22 293.32 298.35 303.39 308.44 313.31 318.41 323.35 328.30 333.41 338.41 343.46 348.46 353.44 358.52 363.61 368.50
0.455 0.520 0.590 0.660 0.740 0.826 0.916 1.006 1.106 1.216 1.322 1.422 1.572 1.702 1.842 1.977 2.127 2.287 2.437
xCO2 = 0.509 278.24 283.26 288.44 293.41 298.48 303.55 308.30 313.28 318.40 323.32 328.43 333.46 338.40 343.37 348.49 353.40 358.53 363.46 368.53
0.487 0.552 0.627 0.707 0.792 0.887 0.982 1.087 1.202 1.317 1.452 1.587 1.727 1.882 2.038 2.203 2.378 2.558 2.743
xCO2 = 0.625 278.45 283.27 288.23 293.28 298.26 303.34 308.17
0.504 0.569 0.649 0.734 0.824 0.924 1.029
xCO2 = 0.750 278.17 283.25 288.25 293.33 298.39 303.37 308.26
0.463 0.578 0.663 0.753 0.858 0.963 1.078
xCO2 = 0.847 278.02 283.43 288.44 293.54 298.35 303.37 308.36
0.520 0.600 0.685 0.780 0.886 0.996 1.110
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Table 3 (Continued ) T (K) 313.28 318.49 323.26 328.27 333.33 338.37 343.42 348.31 353.44 358.45 363.50 368.49 xCO2 = 0.949 277.84 283.37 288.39 293.54 298.49 303.27 308.33 313.44 318.27 323.43 328.46 333.43 338.36 343.41 348.46 353.49 358.38 363.55 368.52
p (MPa) 1.144 1.279 1.404 1.549 1.699 1.859 2.034 2.205 2.395 2.595 2.800 3.009
T (K) 313.36 318.34 323.30 328.37 333.40 338.40 343.43 348.50 353.42 358.48 363.43 368.51
p (MPa) 1.203 1.338 1.478 1.638 1.803 1.978 2.168 2.388 2.573 2.793 3.028 3.268
T (K) 313.41 318.36 323.34 328.40 333.48 338.46 343.44 348.46 353.48 358.46 363.55 368.50
p (MPa) 1.240 1.386 1.541 1.706 1.891 2.076 2.276 2.491 2.716 2.961 3.217 3.486
0.541 0.631 0.721 0.826 0.936 1.052 1.181 1.331 1.482 1.657 1.837 2.032 2.237 2.492 2.707 2.967 3.227 3.527 3.827
4.2. Modelling Antoine parameters for cyclobutanone have been obtained from fitting Eq. (1) to the experimental data points for cyclobutanone given in literature [5,6]. If in Eq. (1) pressure is taken in bar and temperature in Kelvin, their numerical values are A = 10.79, B = 3794 and C = −20.03. Besides, the pure component parameters of the various components, for both binary systems isothermal bubble point data at 280, 330 and 365 K have been used as input for the Eoskij-programme of Tassios [14]. The objective function given in Eq. (12) is minimised and an averaged value for kij over the three temperatures is obtained (see Table 4). Fig. 7 compares experimental and modelling results for the binary system CO2 + cyclobutanone. In this figure, also two isotherms, respectively, at 310 and 350 K, are included which were not used to evaluate the binary interaction parameter kij . For completeness, in Fig. 7 also the calculated isothermal dew point curves have been included.
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15
p [MPa]
12
9
6
3
0 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
xCO2 [-] Fig. 3. p, x Cross-section with interpolated data points for the system CO2 + cyclobutanone at temperatures of 280 K (䉬), 310 K (䉱), 330 K (bubble points (䉲), dew points ()), 350 K (bubble points (䊏), dew points (䊐)) and 365 K (bubble points (䊉), dew points (䊊)). The critical points ( ) represented are estimated from the fitting curve of the experimental critical points.
5
p [MPa]
4
3
2
1
0 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
xC3H8 [-] Fig. 4. p, x Cross-section with interpolated data points for the system C3 H8 + cyclobutanone at temperatures of 280 K (䉬), 310 K (䉱), 330 K (䉲), 350 K (䊏) and 365 K (䊉).
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550 500
T [K]
450 400 350 300 250 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
xCO2 [-] Fig. 5. T, x cross-section with interpolated data points for the system CO2 + cyclobutanone at pressures of 3 MPa (䉬), 6 MPa (䉱), 9 MPa (䉲), and 12 MPa (bubble points (䊉), dew points (䊊)). The critical points ( ) represented are estimated from the fitting curve of the experimental critical points.
550 500
T [K]
450 400 350 300 250 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
xC3H8 [-] Fig. 6. T, x cross-section with interpolated data points for the system C3 H8 + cyclobutanone at pressures of 0.5 MPa (䉬), 1 MPa (䉱), 2 MPa (䉲) and 3 MPa (䊉).
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15
12
p [MPa]
9
6
3
0 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
xCO2 [-] Fig. 7. p, x Cross-section with experimental data for the system CO2 + cyclobutanone at temperatures of 280 K (䉬), 310 K (䉱), 330 K (bubble points (䉲), dew points ()), 350 K (bubble points (䊏) dew points (䊐), 365 K (bubble points (䊉), dew points (䊊)), critical points ( ), results of calculation of the bubble point (—) and dew point (- - -) curves with the SRK equation of state.
4
p [MPa]
3
2
1
0 0.00 0.10
0.20 0.30
0.40
0.50
0.60 0.70
0.80 0.90
1.00
xC3H8 [-] Fig. 8. p, x Cross-section with experimental data for the system C3 H8 + cyclobutanone at temperatures of 280 K (䉬), 310 K (䉱), 330 K (䉲), 350 K (䊏), 365 K (䊉), results of calculation of the bubble point (—) and dew point (- - -) curves with the SRK equation of state.
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Table 4 Optimised kij values for the SRK equation of state with the Tassios programme Eoskij [14] System
kij
p (%)
x range
CO2 + cyclobutanone C3 H8 + cyclobutanone
0.020 ± 0.001 0.081 ± 0.001
2.96 2.01
0.000–0.899 0.000–1.000
For the system C3 H8 +cyclobutanone a similar comparison between experimental and modelling results is shown in Fig. 8. Also in this case two isotherms, respectively, at 310 and 350 K, are included which were not used to evaluate the binary interaction parameter kij . As can be seen from Fig. 8, the modelling results follow the trend of the experimental results.
5. Discussion The bubble point pressure, at constant temperatures, increases with increasing content of CO2 in the overall-composition. In Fig. 3, it can be observed that this increase of the bubble-point pressure with overall-composition xCO2 is gradual. In Fig. 5, the temperature decreases gradually with increasing overall-composition xCO2 . In the p, x cross-section of Fig. 3 critical points for various temperatures and dew points for the higher temperatures, 330, 350 and 365 K, can be observed. From Figs. 3 and 5, which are derived p, x and T, x cross-sections, respectively, it can be seen that the various isopleths, as depicted in Fig. 1, show mutual consistency. Correlation of the experimental data at 280, 330 and 365 K with the SRK equation of state gives a value of the binary interaction parameter kij of 0.020 (see Table 4). The relatively small value of this parameter suggests a minor deviation from ideal behaviour in the liquid phase, which is also confirmed by the occurrence of an almost linear dependence of the various bubble point curves with the CO2 mole fraction (see Fig. 3). The course of the bubble and dew point curves can be predicted satisfactorily. From Fig. 7 it can be seen that the deviations between the experimental and calculated pressures increase for the isotherms at higher temperatures, especially at near-critical conditions and at larger values of xCO2 as well (see Fig. 7). The SRK equation of state calculations predict higher pressures in this region than have been found experimentally, i.e. with AAD = 8–10% for that particular region. The general course of the curves in the p, x and T, x cross-sections of Figs. 4 and 6, for the system C3 H8 + cyclobutanone, is similar to those observed in Figs. 3 and 5, respectively. For the considered overall-compositions of the binary system C3 H8 + cyclobutanone no critical points, and dew points have been observed. However, an inflection point seems to be present in the range 0.6 ≤ xC3 H8 ≤ 0.9. This suggests that the system is close to a liquid–liquid two-phase split. Correlation of the experimental data with the SRK equation of state gives a kij of 0.081. This value for kij suggests the occurrence of larger deviations from ideality in the liquid phase than was established for the system CO2 + cyclobutanone, which is confirmed by the course and shape of the bubble point curves shown in Fig. 8. The prediction with the SRK equation of state shows that the point of inflection in the bubble point curve at higher temperatures is located at approximately xC3 H8 = 0.75. The curvature is stronger for the correlated line than for a fitting curve through the experimental data. Most likely, the liquid–liquid immiscibility occurs at higher temperatures, because there is more curvature for the p, x cross-sections at higher temperatures.
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6. Conclusions The vapour–liquid phase behaviour of the binary systems CO2 + cyclobutanone and C3 H8 + cyclobutanone has been investigated experimentally with Cailletet equipment and, in addition, has been modelled with the Soave–Redlich–Kwong equation of state. For the binary system CO2 +cyclobutanone the conditions for bubble points have been determined for a number of isopleths in the range from 0.000 ≤ xCO2 ≤ 1.000, and dew points and critical points at overallcompositions of xCO2 = 0.899 and 0.948. With an optimised value of kij = 0.020 for the SRK equation of state the experimental data can be correlated satisfactorily (p = 2.96%). In the region close to the critical point the deviation in pressure is larger (p = 8–10%), however, the general course is predicted well. In the system C3 H8 + cyclobutanone only bubble point conditions could be measured. The bubble point curve in the constructed p, x and T, x cross-sections show a point of inflection, which is confirmed by the calculations with the SRK equation of state. The kij parameter has been optimised to a value of 0.081 for this system in the considered temperature and pressure region. The point of inflection suggests a tendency to liquid–liquid immiscibility, which has not been observed at the conditions experimentally investigated. List of symbols a constant SRK equation of state b constant SRK equation of state H, L, V hydrate, liquid, vapour phases kij interaction parameter N number of data points p pressure (MPa or bar) pc critical pressure (MPa) R gas constant (8.314) (J mol−1 K−1 ) S objective function T temperature (K) TB normal boiling point temperature (K) Tc critical temperature (K) Tr reduced temperature V molar volume (cm3 mol−1 ) Vc critical molar volume (cm3 mol−1 ) x liquid phase composition Greek letters α temperature correction factor for the constant a in the mixing rule used ω acentric factor Subscripts C3 H8 propane CO2 carbon dioxide w water
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