Carbon dioxide (1) + perfluorooctane (2): 2 nd test system

7.5 Vapour-liquid equilibrium test system measurements and modelling

7.5.2 Carbon dioxide (1) + perfluorooctane (2): 2 nd test system

Results and discussion

82 | P a g e Table 7-9: Model parameters for the carbon dioxide (1) + hexane (2) system.

Isotherm [K] 𝐛_𝐢𝐣^a[K] 𝐛_𝐣𝐢^a[K] 𝐤_𝐢𝐣^b

313.12 -303.321 8395.902 0.545

aScalar NRTL model parameters, τij = bij

⁄T, αij = 0.3.

b Scalar WS mixing rule parameter (k_ij) incorporated into the Peng-Robinson EoS.

Results and discussion

83 | P a g e experimental and regressed data for the system, including expanded uncertainties for each point are tabulated in Table 7-10.

Table 7-10: Experimental and regressed VLE data for carbon dioxide (1) + perfluorooctane (2).

Experimental PR-MC-WS-NRTL Expanded

Uncertainties P[MPa] 𝐱_𝟏 𝐲_𝟏 P[MPa] 𝐲_𝟏 𝐲_{𝐜𝐚𝐥𝐜}− 𝐲_𝐞𝐱𝐩 𝐔_(𝐱𝟏) 𝐔_(𝐲𝟏)

T = 293.12 K

4.892 0.8951 0.9986 4.945 0.9983 -0.0002 0.0043 0.0001 4.163 0.7644 0.9982 4.113 0.9981 -0.0001 0.0084 0.0001

3.712 0.6899 0.9978 3.664 0.9980 0.0002 0.0097 0.0001

3.090 0.5851 0.9977 3.077 0.9979 0.0002 0.0110 0.0001

2.373 0.4536 0.9974 2.375 0.9977 0.0003 0.0113 0.0001

1.865 0.3621 0.9970 1.891 0.9975 0.0005 0.0105 0.0001

1.460 0.2821 0.9964 1.467 0.9971 0.0007 0.0092 0.0001

1.206 0.2359 0.9959 1.222 0.9967 0.0008 0.0082 0.0002

0.780 0.1503 0.9941 0.773 0.9954 0.0013 0.0058 0.0002

0.401 0.0774 0.9897 0.396 0.9919 0.0021 0.0032 0.0004

Expanded uncertainties (U) calculated with k = 2. U(T) = 0.04 K, U(P) = 0.007 MPa, U(x) = 0.0113, U(y) = 0.0004.

84 | P a g e Figure 7-11: P-xy data for the carbon dioxide (1) + perfluorooctane (2) binary system measured at 293.12 K. (▲) Exp data, this work with a static analytic apparatus.

(●) (Dias et al., 2006). (◆) Exp data, this work with a static synthetic apparatus with a variable volume cell. ( — ) PR–MC–WS-NRTL model, (---) Peng-Robinson EoS model.

0 1 2 3 4 5 6

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Pressure (MPa)

x₁, y_1,

0 1 2 3 4 5 6

0,98 0,99 1

Results and discussion

85 | P a g e The phase equilibrium data from this system was modelled using the Peng-Robinson EoS with classical mixing rules as well as the PR-MC-WS-NRTL model, in a bid to note the model which best represents the data. Figure 7-11 shows the experimental and reference data in conjunction with the two models. The reference data deviates from the PR-MC-WS-NRTL model from (x₁ >

0.5) and begins to scatter as the mole composition of the lighter component increases. The cause of the scatter in the data could have been due to the presence of air within the cell prior to the loading of the lighter component as well as leaks from the equipment. The same technique employed by Dias et al. (2006) was used in this work to measure only two points, in order to clarify the discrepancy between the experimental and reference data. The primary difference between the two techniques was in the loading procedures. The charging procedure used for the reference data commenced with loading known amounts of the liquid component via vacuum extraction but did not seem to take into account the possible presence of air within the cell before loading the liquid.

The loading procedure used in this work was discussed in Chapter 5, where careful attention is paid to ensure that no air is present within the cell prior to loading the liquid component. The two points measured with the variable volume cell in this work matched perfectly (within the uncertainty) with the data measured via the static analytic apparatus.

In Figure 7-11, it can be seen that the Peng-Robinson EoS model fails to represent the experimental data effectively and is seen to overestimate the bubble pressure curve, by a maximum magnitude of approximately 4.1% at a pressure of 3.7 MPa. The PR-MC-WS-NRTL model, on the other hand, correlates the experimental data (within uncertainty) in the liquid phase very well. The model also presents a relatively good fit in the vapour phase, with the exception of the slight deviations at pressures below 1 MPa. These deviations were possibly caused by the condensation of the heavy perfluorocarbon on the ROLSI™ capillary tip due to the low pressures. Both models converge at pressures above 5 MPa, forming a shape that closely resembles a bird’s beak as both the bubble and dew curves become horizontal as discussed by (Rainwater, 2001).

Results and discussion

86 | P a g e Figure 7-12: Relative volatility (𝛼₁₂) as a function of the liquid composition (𝑥₁), (▲) Exp data, (—) PR- MC-WS-NRTL model, (---) Peng-Robinson EoS model.

Figure 7-12 shows that the relative volatilities for the experimental data become less consistent with the model data at (x₁ < 0.3), which is similar to what was observed in the P-xy plot. The deviations at low pressure were substantially above the uncertainty for all the three points in the region. The relative deviations AARD, AAD, and Bias for the pressure and vapour composition for both models are tabulated in Table 7-11:

Table 7-11: Error analysis for the carbon dioxide (1) + perfluorooctane (2) system MODEL AAR𝐃_𝐩

(%)

𝐁𝐈𝐀𝐒_𝐩(%) 𝐀𝐀𝐃_𝐩(MPa) 𝐀𝐀𝐑𝐃_𝐲𝟏(%) 𝐁𝐈𝐀𝐒_𝐲𝟏(%) 𝐀𝐀𝐃_𝐲𝟏 PR-MC-

WS-NRTL 0.952 -0.005 0.022 0.037 0.058 0.0003

PR-EoS 2.344 0.101 0.051 0.015 -0.150 0.001

0 200 400 600 800 1000 1200 1400 1600 1800

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Relative volatility (α12)

x₁

Results and discussion

87 | P a g e The relative deviations for the PR-MC-WS-NRTL model were all substantially below 1%, while the Peng-Robinson EoS resulted in a relative deviation in pressure which was above 2%. The PR- MC-WS-NRTL model provided an excellent description of the bubble curve relative to the Peng- Robinson EoS. The generated parameters of the two models are displayed in Table 7-12.

Table 7-12: Model parameters for the carbon dioxide (1) + Perflurooctane (2) system.

Model 𝐛_𝐢𝐣^a[K] 𝐛_𝐣𝐢^a[K] 𝐤_𝐢𝐣

PR-MC-WS-NRTL 999.832 429.713 0.713^b

PR-EoS - - 0.071

aScalar NRTL model parameters, τij = bij

⁄T, αij = 0.3.

bScalar WS mixing rule parameter (k_ij) incorporated into the Peng-Robinson Eos.

The data for the two binary test systems exhibited good correlation with the PR-MC-WS-NRTL model, with the carbon dioxide (1) + hexane (2) system displaying excellent agreement with the reference data from Li et al. The experimental data for the carbon dioxide (1) + perflurooctane (2) system deviated from the reference source however the data was validated by the PR-MC-WS- NRTL model, which described the data well within the uncertainty reported for the liquid phase composition. A static synthetic technique, with a variable volume cell, was also used to further affirm the experimental data from the second test system.