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 pointsin the binary systems carbon dioxide+ cyclobutanone

and propane+ cyclobutanone

A.R. Cruz Duartea, M.M. Mooijer-van den Heuvelb, C.M.M. Duartea, C.J. Petersb,∗a REQUIMTE/CQFB, Departemento de Qu´ımica, Faculdade de Ciˆencas e Technologia, Universidade Nova de Lisboa,

2829-516 Caparica, Portugalb 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 hasbeen determined experimentally, using Cailletet equipment. For both the systems bubble points have been determinedfor a number of isopleths covering the whole mole fraction range. Additionally, for the binary system carbondioxide+ cyclobutanone dew points and critical points could be observed for a number of overall-compositionsrich in carbon dioxide. The temperature and pressure range were, respectively, from 278 to 369 K and from 0.1 to14.0 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 poorlysoluble in water. Cyclic ketones are known for their occurrence in natural oils as the odoriferous componentand their use as solvents in industry. In that respect, cyclopentanone and cyclohexanone are the mostimportant cyclic organic ketones[1]. Cyclobutanone is smaller and more reactive than the aforementionedones. 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 partlyonly. 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

122 A.R. Cruz Duarte et al. / Fluid Phase Equilibria 214 (2003) 121–136

Research in our laboratory on the phase behaviour of clathrate hydrates in ternary systems of the kindwater+ gas+ cyclic organic components has been performed with cyclobutanone being considered asone of the cyclic organic components. If the phase diagrams are compared, it can be observed that thepressure for the three-phase equilibrium hydrate–liquid water–vapour (H–Lw–V) in the binary systemwater+ gas is reduced to lower values for the corresponding four-phase equilibrium hydrate–liquidwater–liquid cyclic organic–vapour (H–Lw–L–V) in the ternary system. For different gases the reductionvaries, i.e. 77% for methane (CH4), 80% for carbon dioxide (CO2) and 27% for propane (C3H8) [2–4].To enable proper modelling of the clathrate hydrate phase behaviour in the ternary system and to explainthe phenomena occurring in these systems, knowledge of the phase behaviour in the binary systemsgas+ cyclobutanone is a prerequisite. In this paper the experimental results for various phase transitionsin the systems CO2 + cyclobutanone and C3H8 + cyclobutanone will be presented. Additionally, theexperimental data will be correlated to determine the interaction parameter (kij), which is present in themixing 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 requireknowledge of pure component properties, typically the critical properties and vapour pressure. Of the latterproperty, two sets of experimental data are available[5,6], one set at lower temperatures, i.e. from 249.1 to298.4 K, and the other set at higher temperatures, i.e. from 317.8 to 380.2 K, respectively. Instead of usingdifferent Antoine constants for the temperature ranges of the separate data sets, the Antoine equation hasbeen fitted to the experimental data of both data sets. The Antoine equation and the objective function tobe minimised to determine the Antoine parameters are given inEqs. (1) and (2):

ln psat = A − B

C + T(1)

S =N∑

n=1

[psatcalc − psat

exp]2 (2)

wherepsat is the vapour pressure (bar);A, B andC are the Antoine constants; andT is the temperature (K).In Eq. (2), N represents the number of data points,psat

calc the calculated pressure andpsatexp 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: themethod of Ambrose[7,8] and the Joback modification of Lydersen’s method[9]. Both methods are basedon group contribution techniques, where the various groups present in the molecule contribute all withcharacteristic constants to the total value of the property. The acentric factorω is defined by the relation:

ω = −logpsat

Tr=0.7

pc− 1.000 (3)

wherepsat is the vapour pressure at a reduced temperature ofTr = 0.7 [10]. The estimated criticalproperties and acentric factor are compared to the experimental values of cyclobutane, cyclopentane, and

A.R. Cruz Duarte et al. / Fluid Phase Equilibria 214 (2003) 121–136 123

Table 1Pure component property data for cyclobutanone, cyclobutane, cyclopentanone and cyclopentane

Component Method pc (MPa) Tc (K) Vc (cm3 mol−1) ω TB (K)

Cyclobutanone Ambrose 4.70 587 184 0.209 372.0a

Joback 5.26 584 217 0.279 374

Cyclobutane Literature 4.99 460.0 210 0.181 285.7Cyclopentanone Literature 5.11 634.6 268 0.350 403.9Cyclopentane Literature 4.51 511.7 260 0.196 322.4

The critical property data for cyclobutanone have been determined with two estimation methods as mentioned in the table andthe data for cyclobutane, cyclopentanone and cyclopentane have been taken from literature[11].

a Available from Dechema Database Software.

cyclopentanone[11] (seeTable 1). The difference between the results of the two estimation methods isnot large, onlypc andVc estimated with the method of Ambrose are substantially lower than the valuesestimated 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 lowerpc andVc for cyclobutanoneis relatively large with the method of Ambrose. Therefore, the estimation of the critical properties withthe 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 parameterkij to be used in calculations with equations of state. The equation of state used in this study is theSoave–Redlich–Kwong (SRK) equation[12]:

p = RT

V − b− a(T )

V(V + b)(4)

where the various symbols have their usual meaning. The constantsa andb can be calculated using thecritical properties:

a(T ) = aα(T ) (5)

a = 0.42747R2T 2

c

pc(6)

α(T) =[

1 + m(ω)

(1 −

√T

Tc

)]2

(7)

m(ω) = 0.480+ 1.574ω − 0.176ω2 (8)

b = 0.08664RTc

pc(9)


When multi-component systems are considered, mixing rules have to be applied to determine themixture constantsa andb:

a =∑

i

∑j

xixj√

aiaj(1 − kij ) (10)

b =∑

i

xibi (11)

In Eq. (10), kij is the binary interaction parameter, which can be determined by minimising the objectivefunction as defined byEq. (12), using experimental bubble point data:

S =N∑

n=1

[pcalc − pexp

pexp

]2

(12)

The kij is slightly dependent on the temperature. For that purpose,kij values have been determinedfor three isotherms: one at the lowest, one at an intermediate and one at the highest temperature. Theaveraged value of the threekij values was determined, and used for calculations in the whole temperaturerange.

3. Experimental

The Cailletet equipment has been used for measuring the various phase transitions that occur in thebinary systems CO2+cyclobutanone and C3H8+cyclobutanone. Samples, consisting of both components,are confined in the top-end of a capillary glass tube and sealed by a mercury column. The compositionof the sample is determined from the injected amount of cyclobutanone and the reading of the pressureof the gas, either CO2 or C3H8, in a calibrated volume at a known temperature. The capillary tube isplaced into an autoclave, where the mercury reservoir is connected to a hydraulic oil system that canbe pressurised with a screw-type hand-pump. In this way, the mercury column is both a seal for thesample and pressure-transmitting medium. The sample can be kept at a constant temperature, within0.01 K, by circulating a heat-transferring medium around the tube with a thermostatic bath (Lauda). Thetemperature 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 measuredwith a dead-weight pressure gauge (de Wit), with a smallest weight of 0.005 MPa. For further details onthe 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 bubblepoint curve, which represents the phase transition L+ V → L. The bubble points have been determinedexperimentally for both binary systems, by increasing the pressure step-wise on the dead-weight pressuregauge at a constant temperature until the last tiny bubble of the vapour phase disappears at equilibriumconditions. 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 vapourphase, separated by a flat and hazy horizontal meniscus. The procedure for the measurement of a dewpoint is similar to that of a bubble point, i.e. the pressure is increased until the last droplet of liquiddisappears. Application of Gibbs’ phase rule to a binary system shows that there are two degrees offreedom, when phase equilibria with two phases are considered. This implies that the pressure of the


bubble and dew points, which bound the two-phase region liquid+vapour (L+V), are depending on theoverall-composition of the system for a constant temperature. Consequently, the phase transitions havebeen determined for a number of overall-compositions of the systems, covering the whole mole fractionrange.

Cyclobutanone was supplied by Fluka with a purity≥99%. CO2 and C3H8 were supplied by Messer-Griesheim with purities of 99.995 and 99.95%, respectively. All components were used without furtherpurification. The purity of both CO2 and C3H8 was confirmed. Therefore, literature vapour pressure datawere 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 inTables 2 and 3, and visualised inFigs. 1and 2, for the systems CO2 + cyclobutanone and C3H8 + cyclobutanone, respectively. BothFigs. 1 and2 arep, T diagrams on which a number of isopleths, i.e.p, T loci at constant overall-composition, areprojected together with the vapour pressure curves of the two pure components. Besides the critical pointof pure CO2, in Fig. 1 also the critical points (L= V) for the two overall-compositionsxCO2 = 0.948and 0.899 can be observed. For the latter two overall-compositions, also the dew points are shown in

270 280 290 300 310 320 330 340 350 360 370 380

T [K]

0

3

6

9

12

15

p[M

Pa]

Fig. 1. p, T diagram with experimental data for pure component CO2 (—), literature data for cyclobutanone (- - -) [5,6] andexperimental bubble points (xCO2 = 0.105 ( ), xCO2 = 0.139 ( ), xCO2 = 0.178 ( ), xCO2 = 0.251 (�), xCO2 = 0.407 (�),xCO2 = 0.499 (�), xCO2 = 0.622 (�), xCO2 = 0.752 (�), xCO2 = 0.850 (), xCO2 = 0.899 (�) and xCO2 = 0.948 (�)), dewpoints (xCO2 = 0.899 (�), xCO2 = 0.948 (�)) and critical points ( ) of a number of isopleths for the system CO2+cyclobutanone.


270 280 290 300 310 320 330 340 350 360 370 380

T [K]

0

1

2

3

4

5

p[M

Pa]

Fig. 2. p, T diagram with experimental data for pure component C3H8 (—), literature data for cyclobutanone (- - -) [5,6] andexperimental bubble points (xC3H8 = 0.102 ( ), xC3H8 = 0.134 ( ), xC3H8 = 0.176 ( ), xC3H8 = 0.250 (�), xC3H8 = 0.404 (�),xC3H8 = 0.509 (�), xC3H8 = 0.625 (�), xC3H8 = 0.750 (�), xC3H8 = 0.847 () and xC3H8 = 0.949 (�)) of a number of isoplethsfor the system C3H8 + cyclobutanone.

this figure. Since the critical temperature of C3H8 is relatively high, compared to that of CO2, the criticalregion was not investigated for the system C3H8 + cyclobutanone. The consistency of the experimentalisopleths is examined by fitting exponential curves to the experimental data points. For the binary systemCO2+cyclobutanone the most optimal fit is represented by Eq. (13) with an average correlation coefficientof 0.999, and for the system C3H8 + cyclobutanone by Eq. (14) with an average correlation coefficientof 0.9999, respectively.

ln p = a0 + a1

T 2(13)

ln p = a0 + a1

T(14)

These fitting correlations are used to construct isothermal cross-sections, i.e. p, x cross-sections as shownin Figs. 3 and 4 for both systems at temperatures of 280, 310, 330, 350 and 365 K. The procedure to con-struct T, x cross-sections at constant pressures is similar and shown in Figs. 5 and 6 for, respectively, thesystem CO2 +cyclobutanone at pressures of 3, 6, 9 and 12 MPa, and for the system C3H8 +cyclobutanoneat 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, xand T, x cross-sections of the system CO2 + cyclobutanone, a second order polynomial equation hasbeen fitted to the experimental critical points for the overall-compositions of xCO2 = 0.899, 0.948and 1.000.


Table 2Experimental data of the bubble points (L + V → L), dew points (L + V → V) and critical points (L = V) for the systemCO2 + cyclobutanone

T (K) p (MPa) T (K) p (MPa) T (K) p (MPa)

xCO2 = 0.105 xCO2 = 0.139 xCO2 = 0.178277.80 0.468 277.85 0.585 278.29 0.743282.76 0.518 283.46 0.660 283.33 0.833288.25 0.574 288.34 0.730 288.35 0.923293.28 0.629 293.34 0.805 293.32 1.028298.23 0.684 298.27 0.885 298.35 1.133303.34 0.754 303.25 0.965 303.28 1.238308.25 0.819 308.33 1.055 308.26 1.348313.38 0.889 313.35 1.150 313.28 1.479318.33 0.959 318.36 1.245 318.30 1.589323.39 1.044 323.34 1.341 323.37 1.709328.51 1.119 328.45 1.450 328.41 1.859333.39 1.199 333.51 1.560 333.39 1.994338.46 1.284 338.50 1.665 338.35 2.119343.47 1.364 343.51 1.780 343.45 2.294348.58 1.459 348.45 1.891 348.47 2.414353.56 1.544 353.62 2.010 353.62 2.559358.62 1.644 358.53 2.125 358.48 2.694363.51 1.724 363.54 2.246 363.49 2.853368.64 1.829 368.58 2.366 368.55 3.018

xCO2 = 0.251 xCO2 = 0.407 xCO2 = 0.499278.05 1.062 278.25 1.838 278.23 2.090283.44 1.192 283.30 2.058 283.27 2.345288.27 1.317 288.33 2.293 288.32 2.616293.44 1.467 293.33 2.543 293.28 2.906298.26 1.607 298.29 2.803 298.34 3.216303.29 1.762 303.33 3.083 303.37 3.541308.37 1.942 308.32 3.378 308.41 3.891313.34 2.097 313.33 3.678 313.32 4.226318.32 2.277 318.32 4.003 318.27 4.586323.37 2.462 323.31 4.318 323.35 4.971328.38 2.647 328.39 4.653 328.39 5.366333.39 2.832 333.38 4.993 333.48 5.771338.43 3.027 338.35 5.343 338.34 6.166343.43 3.232 343.43 5.714 343.41 6.596348.40 3.438 348.42 6.069 348.39 7.016353.41 3.643 353.43 6.454 353.88 7.431358.46 3.858 358.48 6.819 358.49 7.881363.44 4.068 363.52 7.189 363.54 8.316368.50 4.283 368.73 7.584 368.55 8.741

xCO2 = 0.622 xCO2 = 0.752 xCO2 = 0.850278.26 2.550 277.85 3.008 278.32 3.366283.52 2.886 283.39 3.408 283.28 3.785288.49 3.221 288.46 3.818 288.23 4.241293.25 3.561 293.49 4.299 293.34 4.741


Table 2 (Continued)


298.43 3.955 298.41 4.714 298.01 5.261303.39 4.360 303.33 5.189 303.22 5.831308.30 4.771 308.34 5.704 308.91 6.406313.37 5.221 313.51 6.269 313.33 7.031318.36 5.690 318.38 6.814 318.34 7.671323.40 6.166 323.36 7.399 323.37 8.346328.40 6.666 328.36 8.004 328.38 9.021333.43 7.176 333.37 8.619 333.50 9.726338.56 7.711 338.46 9.259 338.42 10.386343.52 8.231 343.44 9.889 343.41 11.046348.64 8.781 348.51 10.534 348.42 11.681353.57 9.306 353.57 11.169 353.43 12.256358.54 9.836 358.88 11.819 358.61 12.801363.63 10.381 363.54 12.374 361.00 13.036368.56 10.901 368.53 12.944 363.69 13.281

366.07 13.491368.50 13.696

xCO2 = 0.899 xCO2 = 0.948278.21 3.539 277.93 3.713283.52 4.019 283.35 4.233288.13 4.459 288.28 4.743292.99 4.984 293.29 5.303298.24 5.559 298.29 5.913303.34 6.164 303.37 6.563308.42 6.814 308.36 7.248313.35 7.459 313.33 7.923318.31 8.129 318.29 8.608323.31 8.819 323.44 9.243328.42 9.524 325.83 9.499333.63 10.215 326.32a 9.549338.49 10.804 326.46b 9.559343.55 11.360 326.90b 9.614345.91 11.600 328.53b 9.889346.41 11.649 333.37b 10.274346.69 11.680 338.51b 10.774346.86a 11.695 343.45b 11.169346.92b 11.704 348.41b 11.390348.44b 11.855 353.42b 11.545353.48b 12.325 358.57b 11.620358.49b 12.795 363.63b 11.641363.50b 13.185 368.78b 11.671368.56b 13.516

a Critical point L = V.b Dew points L + V → V.


Table 3Experimental data of the bubble points (L + V → L) for the system C3H8 + cyclobutanone


xCO2 = 0.102 xCO2 = 0.134 xCO2 = 0.176308.36 0.418 298.31 0.431 288.36 0.401313.34 0.459 303.42 0.482 293.31 0.446318.28 0.493 308.29 0.521 298.35 0.491323.33 0.538 313.31 0.562 303.23 0.541328.39 0.578 318.32 0.612 308.29 0.591333.48 0.619 323.37 0.657 313.37 0.646338.38 0.664 328.40 0.717 318.27 0.706343.38 0.709 333.34 0.756 323.40 0.766348.39 0.764 338.52 0.822 328.48 0.832353.39 0.804 343.63 0.882 333.48 0.896358.52 0.864 348.48 0.942 338.57 0.972363.58 0.919 353.49 1.006 343.48 1.042368.64 0.969 358.52 1.066 348.58 1.112

363.49 1.132 353.45 1.182368.64 1.202 358.51 1.266

363.54 1.346368.67 1.426

xCO2 = 0.250 xCO2 = 0.404 xCO2 = 0.509278.32 0.411 277.68 0.455 278.24 0.487284.14 0.476 283.20 0.520 283.26 0.552288.33 0.521 288.22 0.590 288.44 0.627293.30 0.586 293.32 0.660 293.41 0.707298.40 0.646 298.35 0.740 298.48 0.792303.47 0.706 303.39 0.826 303.55 0.887308.46 0.801 308.44 0.916 308.30 0.982313.36 0.852 313.31 1.006 313.28 1.087318.39 0.927 318.41 1.106 318.40 1.202323.48 1.006 323.35 1.216 323.32 1.317328.46 1.092 328.30 1.322 328.43 1.452333.36 1.176 333.41 1.422 333.46 1.587338.42 1.272 338.41 1.572 338.40 1.727343.57 1.377 343.46 1.702 343.37 1.882348.57 1.462 348.46 1.842 348.49 2.038353.44 1.562 353.44 1.977 353.40 2.203358.56 1.672 358.52 2.127 358.53 2.378363.67 1.782 363.61 2.287 363.46 2.558368.61 1.892 368.50 2.437 368.53 2.743

xCO2 = 0.625 xCO2 = 0.750 xCO2 = 0.847278.45 0.504 278.17 0.463 278.02 0.520283.27 0.569 283.25 0.578 283.43 0.600288.23 0.649 288.25 0.663 288.44 0.685293.28 0.734 293.33 0.753 293.54 0.780298.26 0.824 298.39 0.858 298.35 0.886303.34 0.924 303.37 0.963 303.37 0.996308.17 1.029 308.26 1.078 308.36 1.110


Table 3 (Continued)


313.28 1.144 313.36 1.203 313.41 1.240318.49 1.279 318.34 1.338 318.36 1.386323.26 1.404 323.30 1.478 323.34 1.541328.27 1.549 328.37 1.638 328.40 1.706333.33 1.699 333.40 1.803 333.48 1.891338.37 1.859 338.40 1.978 338.46 2.076343.42 2.034 343.43 2.168 343.44 2.276348.31 2.205 348.50 2.388 348.46 2.491353.44 2.395 353.42 2.573 353.48 2.716358.45 2.595 358.48 2.793 358.46 2.961363.50 2.800 363.43 3.028 363.55 3.217368.49 3.009 368.51 3.268 368.50 3.486

xCO2 = 0.949277.84 0.541283.37 0.631288.39 0.721293.54 0.826298.49 0.936303.27 1.052308.33 1.181313.44 1.331318.27 1.482323.43 1.657328.46 1.837333.43 2.032338.36 2.237343.41 2.492348.46 2.707353.49 2.967358.38 3.227363.55 3.527368.52 3.827

4.2. Modelling

Antoine parameters for cyclobutanone have been obtained from fitting Eq. (1) to the experimental datapoints for cyclobutanone given in literature [5,6]. If in Eq. (1) pressure is taken in bar and temperature inKelvin, 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 isothermalbubble 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 threetemperatures is obtained (see Table 4). Fig. 7 compares experimental and modelling results for the binarysystem CO2 + cyclobutanone. In this figure, also two isotherms, respectively, at 310 and 350 K, areincluded which were not used to evaluate the binary interaction parameter kij. For completeness, in Fig. 7also the calculated isothermal dew point curves have been included.


0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

xCO2 [-]

0

3

6

9

12

15

p[M

Pa]

Fig. 3. p, x Cross-section with interpolated data points for the system CO2 + cyclobutanone at temperatures of 280 K (�), 310 K(�), 330 K (bubble points (�), dew points (�)), 350 K (bubble points (�), dew points (�)) and 365 K (bubble points (�), dewpoints (�)). The critical points ( ) represented are estimated from the fitting curve of the experimental critical points.

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

xC3H8

[-]

0

1

2

3

4

5

p[M

Pa]

Fig. 4. p, x Cross-section with interpolated data points for the system C3H8 +cyclobutanone at temperatures of 280 K (�), 310 K(�), 330 K (�), 350 K (�) and 365 K (�).


0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

xCO2

[-]

250

300

350

400

450

500

550

T[K

]

Fig. 5. T, x cross-section with interpolated data points for the system CO2 + cyclobutanone at pressures of 3 MPa (�), 6 MPa(�), 9 MPa (�), and 12 MPa (bubble points (�), dew points (�)). The critical points ( ) represented are estimated from thefitting curve of the experimental critical points.

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

xC3H8 [-]

250

300

350

400

450

500

550

T[K

]

Fig. 6. T, x cross-section with interpolated data points for the system C3H8 + cyclobutanone at pressures of 0.5 MPa (�), 1 MPa(�), 2 MPa (�) and 3 MPa (�).


0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

xCO2 [-]

0

3

6

9

12

15

p[M

Pa]

Fig. 7. p, x Cross-section with experimental data for the system CO2 + cyclobutanone at temperatures of 280 K (�), 310 K (�),330 K (bubble points (�), dew points (�)), 350 K (bubble points (�) dew points (�), 365 K (bubble points (�), dew points (�)),critical points ( ), results of calculation of the bubble point (—) and dew point (- - -) curves with the SRK equation of state.

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

xC3H8 [-]

0

1

2

3

4

p[M

Pa]

Fig. 8. p, x Cross-section with experimental data for the system C3H8 + cyclobutanone at temperatures of 280 K (�), 310 K(�), 330 K (�), 350 K (�), 365 K (�), results of calculation of the bubble point (—) and dew point (- - -) curves with the SRKequation of state.


Table 4Optimised kij values for the SRK equation of state with the Tassios programme Eoskij [14]

System kij �p (%) x range

CO2 + cyclobutanone 0.020 ± 0.001 2.96 0.000–0.899C3H8 + cyclobutanone 0.081 ± 0.001 2.01 0.000–1.000

For the system C3H8+cyclobutanone a similar comparison between experimental and modelling resultsis shown in Fig. 8. Also in this case two isotherms, respectively, at 310 and 350 K, are included whichwere not used to evaluate the binary interaction parameter kij. As can be seen from Fig. 8, the modellingresults follow the trend of the experimental results.

5. Discussion

The bubble point pressure, at constant temperatures, increases with increasing content of CO2 inthe overall-composition. In Fig. 3, it can be observed that this increase of the bubble-point pressurewith overall-composition xCO2 is gradual. In Fig. 5, the temperature decreases gradually with increasingoverall-composition xCO2 . In the p, x cross-section of Fig. 3 critical points for various temperatures anddew points for the higher temperatures, 330, 350 and 365 K, can be observed. From Figs. 3 and 5, whichare derived p, xand T, xcross-sections, respectively, it can be seen that the various isopleths, as depicted inFig. 1, show mutual consistency. Correlation of the experimental data at 280, 330 and 365 K with the SRKequation of state gives a value of the binary interaction parameter kij of 0.020 (see Table 4). The relativelysmall value of this parameter suggests a minor deviation from ideal behaviour in the liquid phase, whichis also confirmed by the occurrence of an almost linear dependence of the various bubble point curveswith the CO2 mole fraction (see Fig. 3). The course of the bubble and dew point curves can be predictedsatisfactorily. From Fig. 7 it can be seen that the deviations between the experimental and calculatedpressures increase for the isotherms at higher temperatures, especially at near-critical conditions and atlarger values of xCO2 as well (see Fig. 7). The SRK equation of state calculations predict higher pressuresin 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 systemC3H8 + cyclobutanone, is similar to those observed in Figs. 3 and 5, respectively. For the consideredoverall-compositions of the binary system C3H8 + cyclobutanone no critical points, and dew points havebeen observed. However, an inflection point seems to be present in the range 0.6 ≤ xC3H8 ≤ 0.9. Thissuggests that the system is close to a liquid–liquid two-phase split. Correlation of the experimental datawith the SRK equation of state gives a kij of 0.081. This value for kij suggests the occurrence of largerdeviations 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 predictionwith the SRK equation of state shows that the point of inflection in the bubble point curve at highertemperatures is located at approximately xC3H8 = 0.75. The curvature is stronger for the correlated linethan for a fitting curve through the experimental data. Most likely, the liquid–liquid immiscibility occursat higher temperatures, because there is more curvature for the p, x cross-sections at higher temperatures.


6. Conclusions

The vapour–liquid phase behaviour of the binary systems CO2 +cyclobutanone and C3H8 +cyclobuta-none has been investigated experimentally with Cailletet equipment and, in addition, has been modelledwith the Soave–Redlich–Kwong equation of state.

For the binary system CO2 +cyclobutanone the conditions for bubble points have been determined for anumber of isopleths in the range from 0.000 ≤ xCO2 ≤ 1.000, and dew points and critical points at overall-compositions of xCO2 = 0.899 and 0.948. With an optimised value of kij = 0.020 for the SRK equationof state the experimental data can be correlated satisfactorily (�p = 2.96%). In the region close to thecritical point the deviation in pressure is larger (�p = 8–10%), however, the general course is predictedwell.

In the system C3H8 + cyclobutanone only bubble point conditions could be measured. The bubblepoint curve in the constructed p, x and T, x cross-sections show a point of inflection, which is confirmedby the calculations with the SRK equation of state. The kij parameter has been optimised to a value of0.081 for this system in the considered temperature and pressure region. The point of inflection suggestsa tendency to liquid–liquid immiscibility, which has not been observed at the conditions experimentallyinvestigated.

List of symbolsa constant SRK equation of stateb constant SRK equation of stateH, L, V hydrate, liquid, vapour phaseskij interaction parameterN number of data pointsp pressure (MPa or bar)pc critical pressure (MPa)R gas constant (8.314) (J mol−1 K−1)S objective functionT temperature (K)TB normal boiling point temperature (K)Tc critical temperature (K)Tr reduced temperatureV molar volume (cm3 mol−1)Vc critical molar volume (cm3 mol−1)x liquid phase composition

Greek lettersα temperature correction factor for the constant a in the mixing rule usedω acentric factor

SubscriptsC3H8 propaneCO2 carbon dioxidew water


References

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[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.

Documents

Measurement and modelling of bubble and dew points in the binary systems carbon dioxide + cyclobutanone and propane + cyclobutanone