# The CO2 + 2,3,4-trimethylpentane and CO2 + 2,2,4,6,6-pentamethylheptane binary systems: high-pressure phase equilibria measurements

Stéphane Vitu, Vincent Caqueret, Jean-Luc Daridon, Jean-Patrick Bazile

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Stéphane Vitu, Vincent Caqueret, Jean-Luc Daridon, Jean-Patrick Bazile. The CO2 + 2,3,4-trimethylpentane and CO2 + 2,2,4,6,6-pentamethylheptane binary systems: high-pressure phase equilibria measurements. Fluid Phase Equilibria, 2026, 603, pp.114648. 10.1016/j.fluid.2025.114648. hal-05400364

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# The CO₂ + 2,3,4-trimethylpentane and CO₂ + 2,2,4,6,6-pentamethylheptane binary systems: high-pressure phase equilibria measurements

Stéphane Vitu<sup>a,b,*</sup> <sup>10</sup>, Vincent Caqueret<sup>a,b</sup>, Jean-Luc Daridon<sup>c</sup>, Jean-Patrick Bazile<sup>c</sup>

## ARTICLE INFO

### Keywords:

Phase equilibria

Carbon dioxide

Alkane

Binary system

Equation of state

## ABSTRACT

Two binary systems containing CO₂ and a branched alkane were newly studied in this work: CO₂ + 2,3,4-trimethylpentane and CO₂ + 2,2,4,6,6-pentamethylheptane. Their fluid phase behavior was investigated using a high-pressure variable-volume cell and a synthetic method. Saturation pressures were visually measured from (293.15 et 363.15) K and for 10 different CO₂ mole fractions for both mixtures.

Whatever the considered system, no liquid-liquid immiscibility was observed in this temperature range, suggesting a continuous vapor-liquid critical curve between the pure components critical points. A total of 160 points were acquired: 149 bubble points and 11 dew points.

These new experimental data were satisfactory modeled by using the Peng-Robinson equation of state with a temperature-dependent interaction parameter, $k_{ij}(T)$, fitted against the data.

## 1. Introduction

Despite the important quantity of experimental data available, new phase transition measurements regarding binary and ternary mixtures containing carbon dioxide are still needed nowadays. These new data can be measured in order to investigate unstudied mixtures [1–7] but also to assess the capability of thermodynamic models [8,9] or to verify and correct, if needed, previously published results [10]. Indeed, even recent studies can be affected by significant experimental errors or purity issues.

In past years, we have reported VLE data for several binary systems CO₂ + branched alkanes [5,6,11], alongside other research teams [3, 12–14]. Most of these studies concern light or common branched alkanes. In this work, two binary systems containing uncommon substituted alkanes were studied: CO₂ + 2,3,4-trimethylpentane (234m5) and CO₂ + 2,2,4,6,6-pentamethylheptane (22466m7). Liquid-vapor phase transitions were visually measured from (293.15 to 363.15) K in a high-pressure cell, using a synthetic method (SynVisVar) [15].

The experimental data obtained were plotted in isothermal diagrams and were corelated using the Peng-Robinson [16] equation of state in two ways: a purely predictive approach using the PPR78 model [17]

(estimation of the binary interaction parameter, $k_{ij}(T)$, by a group contribution method) and a corelative approach based on the adjustment of the temperature-dependent binary interaction parameter on the measured data for each studied system.

Finally, it should be noted that experimental data relating to pure 2,2,4,6,6-pentamethylheptane are scarce in the literature, this pure compound was not fully characterized. This paper thus also reports densities (under atmospheric pressure) for pure 22466m7 from (288.15 to 328.15) K for comparison with some previous works and vapor pressures data from (10 to 110) kPa since only a few experimental normal boiling points are available.

## 2. Experimental section

### 2.1. Materials

The details of the pure components used in this study are summarized in Table 1. The purities reported by the manufacturers are given in Table 1. They were confirmed by gas chromatography analyses (with a flame ionization detector) for the branched alkanes. All chemicals were thus used without further purification.

<footnote><sup>a</sup>Conservatoire National des Arts et Métiers, 2 rue Conté, 75003 Paris, France</footnote>

<footnote><sup>b</sup>Université Paris-Saclay, INRAE, AgroParisTech, UMR SayFood, 91120 Palaiseau, France</footnote>

<footnote><sup>c</sup>Université de Pau et des Pays de l'Adour, E2S UPPA, CNRS, LFCR, 64000 Pau, France</footnote>

<footnote>* Corresponding author.
E-mail address: stephane.vitu@lecnam.net (S. Vitu).</footnote>
<table><caption>**Table 1**

Pure components description.</caption><thead><tr><th>IUPAC chemical name</th><th>Abbreviation</th><th>CAS number</th><th>Source</th><th>Purity<sup>a</sup></th><th>Purification method</th></tr></thead><tbody><tr><td>carbon dioxide</td><td>CO<sub>2</sub></td><td>124–38–9</td><td>Linde</td><td>0.99995</td><td>none</td></tr><tr><td>2,3,4-trimethylpentane</td><td>234m5</td><td>565–75–3</td><td>Aldrich</td><td>0.996</td><td>none</td></tr><tr><td>2,2,4,6,6-pentamethylheptane</td><td>22466m7</td><td>13475–82–6</td><td>TCI</td><td>0.994</td><td>none</td></tr></tbody></table>

## 2.2. Characterization of the 2,2,4,6,6-pentamethylheptane

As previously mentioned, the 22466m7 has seldom been used in previous studies. Available experimental data are thus very limited for this chemical. Prior to the main study, the density and the vapor pressure of pure 22466m7 were measured.

Density measurements have been carried out for comparison with some previously published data [18–23]. A vibrating tube densimeter was used under atmospheric condition ($p = 101 \pm 2$ kPa) at temperatures ranging from (288.15 to 328.15) K. Details about the equipment, its calibration and the protocol employed can be found elsewhere [24, 25]. Taking into account the purity of the 22466m7 sample, the combined standard uncertainty is estimated to be $u(\rho) = 0.5 \text{ kg} \cdot \text{m}^{-3}$, corresponding to a relative standard uncertainty of $u_r(\rho) = 0.0007$.

Only few normal boiling temperatures measured 80 years ago can be found in the literature [26–29]. Vapor pressures were thus measured using a recirculation ebulliometer from (10 to 110) kPa with a step of 10 kPa. The apparatus and experimental protocol employed are fully described in previous works [24,25]. The equipment consists in a glass Gillespie-type recirculation still in which the pure component is brought to a boil thanks to a quartz heater. The resulting vapor and liquid phases continuously circulate through the device composed of a mixing chamber, a Cottrell pump and a separation chamber. A vacuum pump and pure nitrogen injections are used to control pressure in the apparatus.

The thermodynamic equilibrium state was considered reached after a minimum period of 30 min of temperature stability. The equilibrium temperature was recorded and a new pressure was set to measure another saturation point.

The new experimental vapor pressure data acquired for 22466m7 present combined standard uncertainties of $u(T) = 0.1$ K and $u(p) = 0.2$ kPa.

## 2.3. High-pressure experimental device and method

Fluid phase transitions were measured using a synthetic method that eliminates the need for phase sampling. The setup is built around a high-pressure PVT cell capable of operating up to 100 MPa and within a temperature range of (293 to 373) K. The cell is a horizontal stainless-steel cylinder fitted with two sapphire windows: one on the front for visual observation through a video endoscope, and another on the side for illumination via an optical fiber. Pressure is manually controlled with a piston and measured using an internal sensor that is temperature-calibrated against a primary standard (uncertainty below 0.02%). The pressure gauge is located inside the cell to minimize dead volumes.

The cell has an adjustable internal volume ranging from 8 to 30 cm³. Temperature control is achieved by circulating a heat transfer fluid through integrated flow lines connected to a thermostatic bath (temperature stability 0.1 K) while fluid temperature is monitored using a Pt100 probe with a standard uncertainty of 0.1 K. A magnetic stirrer ensures uniform mixing and thermal equilibrium during phase transition measurements.

Such a synthetic method allows to generate high-precision measurements of the mixture saturation pressure (bearing in mind that this pressure can reach several hundred bars). Yet, the precision of the method is based on a rigorous mixture preparation [15] to avoid systematic errors regarding to the composition.

<table><caption>**Table 2**

Density ($\rho$) of 2,2,4,6,6-pentamethylheptane at different temperatures ($T$) and pressure $p = 101$ kPa measured in this work<sup>a</sup> and literature values.</caption><thead><tr><th rowspan="2">T/K</th><th colspan="2">ρ/kg·m<sup>-3</sup></th></tr><tr><th>this work</th><th>literature</th></tr></thead><tbody><tr><td>288.15</td><td>748.79</td><td>748.8 [20]<br>748.80 [21]</td></tr><tr><td>293.15</td><td>745.17</td><td>745.5 [18]<br>745.21 [19]<br>745.2 [20]</td></tr><tr><td>298.15</td><td>741.53</td><td>745.16 [21]<br>741.51 [21]<br>741.84 [22]</td></tr><tr><td>303.15</td><td>737.88</td><td>738.2 [18]<br>737.93 [19]<br>737.9 [20]<br>737.86 [21]</td></tr><tr><td>308.15</td><td>734.22</td><td>730.9 [18]</td></tr><tr><td>313.15</td><td>730.57</td><td>730.61 [19]<br>730.6 [20]<br>730.55 [21]<br>731.5 [23]</td></tr><tr><td>318.15</td><td>726.90</td><td>723.5 [18]</td></tr><tr><td>323.15</td><td>723.22</td><td>723.26 [19]<br>723.2 [20]<br>723.20 [21]</td></tr><tr><td>328.15</td><td>719.54</td><td></td></tr></tbody></table>

The fluid mixture was prepared directly inside the cell. At first, the cell was connected to a vacuum pump and thoroughly evacuated. The liquid alkane was injected first using a syringe. For this purpose, the inlet valve has been modified to accommodate a septum, allowing precise injection of very small liquid quantities. This configuration is particularly effective for applications requiring accurate dosing, such as in previous work on the determination of infinite dilution partial molar volumes in CO₂ + hydrocarbon mixtures [30]. Following the liquid injection, carbon dioxide was introduced. Both the liquid alkane and CO₂ were weighed: the mass of liquid alkane was measured by double weighing of the syringe using an analytical balance, while the gaseous CO₂ was transferred from a reservoir placed on a high-capacity balance (direct weighing). To avoid disturbing the balance, gaseous CO₂ was injected through flexible PEEK tubing, and kept in liquid-vapor equilibrium in the reservoir to maintain constant pressure during transfer. The uncertainty in the injected masses was evaluated to be less than <0.005 g, enabling accurate calculation of the expanded uncertainty in the CO₂ molar fraction.

Once the mixture was prepared, phase transitions were observed by adjusting pressure at a fixed temperature. The pressure was first increased to reach a monophasic fluid state, then gradually reduced until the appearance of a second phase. Pressure was then finely adjusted in smaller increments to precisely locate the phase boundary, producing isoplethic data points ($T_i, p_i$) that describe the fluid behavior at constant composition.

After each draining, the cell was rinsed several times using toluene while maintaining a high temperature to promote the cell cleaning. After flushing, vacuum was created and maintained for hours to maximize

<footnote>a Mass fraction purity.</footnote>

<footnote>a Standard uncertainties: $u(T) = 0.01$ K, $u(p) = 1$ kPa. Relative standard uncertainty: $u_r(\rho) = 0.0007$.</footnote>
<table><caption>**Table 3**
Vapor pressure (p)ª for pure 2,2,4,6,6-pentamethylheptane as a function of temperature (T)ª measured in this work.</caption><thead><tr><th>T/K</th><th>p/kPa</th></tr></thead><tbody><tr><td>374.3</td><td>10.0</td></tr><tr><td>393.6</td><td>20.0</td></tr><tr><td>406.1</td><td>30.0</td></tr><tr><td>415.5</td><td>40.0</td></tr><tr><td>423.2</td><td>50.0</td></tr><tr><td>429.8</td><td>60.0</td></tr><tr><td>435.6</td><td>70.0</td></tr><tr><td>440.7</td><td>80.0</td></tr><tr><td>445.4</td><td>90.0</td></tr><tr><td>449.7</td><td>100.0</td></tr><tr><td>450.2</td><td>101.3</td></tr><tr><td>453.6</td><td>110.0</td></tr></tbody></table>

solvent removal and to ready a new experiment.

Standard uncertainties in observed pressure transitions were 0.02 MPa for bubble points far from the critical region, and 0.04 MPa near the critical point and for dew point detection. These were combined with uncertainties in pressure calibration, temperature control, and composition to determine the expanded uncertainty in the transition pressure, following the GUM (Guide to the Expression of Uncertainty in Measurement) [31] framework and similarly to our previous works [6,11,32].

The experimental device and the protocol employed in this work were recently controlled and validated. To do so, measurements on the CO₂ + toluene mixture (a widely investigated system) at multiple compositions were done [33]. A good agreement was found with reference data [33].

<table><caption>**Table 4**
Parameters for the modified Riedel equation (Eq. (1)) for 2,2,4,6,6-pentamethylheptane to calculate vapor pressure in units of Pa.</caption><thead><tr><th>Compound</th><th>A</th><th>B</th><th>C</th><th>D</th><th>E</th><th>T<sub>min</sub>/K</th><th>T<sub>max</sub>/K</th></tr></thead><tbody><tr><td>2,2,4,6,6-pentamethylheptane</td><td>208.671</td><td>-15052.1</td><td>-26.921</td><td>9.2388 × 10<sup>-17</sup></td><td>6</td><td>374.3</td><td>453.6</td></tr></tbody></table>

<table><caption>**Table 5**
Fluid-fluid phase transition pressures p<sub>tr</sub> at temperatures T for binary mixtures CO₂ + 2,3,4-trimethylpentane, as a function of global mole fraction z<sub>CO₂</sub> ± U(z<sub>CO₂</sub>) with its expanded uncertainty U(p<sub>tr</sub>)<sup>a,b,c</sup>.</caption><thead><tr><th colspan="3">z<sub>CO₂</sub> = 0.2017 ± 0.0015</th><th colspan="3">z<sub>CO₂</sub> = 0.3998 ± 0.0012</th><th colspan="3">z<sub>CO₂</sub> = 0.4999 ± 0.0010</th></tr><tr><th>T/K</th><th>p<sub>tr</sub>/MPa</th><th>U(p<sub>tr</sub>)/MPa</th><th>T/K</th><th>p<sub>tr</sub>/MPa</th><th>U(p<sub>tr</sub>)/MPa</th><th>T/K</th><th>p<sub>tr</sub>/MPa</th><th>U(p<sub>tr</sub>)/MPa</th></tr></thead><tbody><tr><td>292.86</td><td>1.83</td><td>0.04</td><td>293.16</td><td>3.06</td><td>0.04</td><td>292.66</td><td>3.57</td><td>0.04</td></tr><tr><td>302.65</td><td>2.02</td><td>0.04</td><td>302.75</td><td>3.49</td><td>0.04</td><td>302.65</td><td>4.15</td><td>0.04</td></tr><tr><td>312.65</td><td>2.22</td><td>0.04</td><td>312.85</td><td>3.97</td><td>0.04</td><td>312.95</td><td>4.78</td><td>0.04</td></tr><tr><td>323.24</td><td>2.43</td><td>0.04</td><td>322.74</td><td>4.42</td><td>0.04</td><td>322.84</td><td>5.40</td><td>0.04</td></tr><tr><td>333.14</td><td>2.63</td><td>0.04</td><td>332.64</td><td>4.91</td><td>0.04</td><td>332.74</td><td>6.06</td><td>0.04</td></tr><tr><td>343.13</td><td>2.89</td><td>0.04</td><td>342.83</td><td>5.42</td><td>0.04</td><td>342.93</td><td>6.74</td><td>0.04</td></tr><tr><td>353.23</td><td>3.15</td><td>0.05</td><td>353.63</td><td>6.01</td><td>0.05</td><td>353.63</td><td>7.48</td><td>0.05</td></tr><tr><td>363.62</td><td>3.47</td><td>0.05</td><td>363.52</td><td>6.56</td><td>0.05</td><td>364.02</td><td>8.21</td><td>0.05</td></tr><tr><td colspan="3">z<sub>CO₂</sub> = 0.6000 ± 0.0006</td><td colspan="3">z<sub>CO₂</sub> = 0.7000 ± 0.0005</td><td colspan="3">z<sub>CO₂</sub> = 0.7700 ± 0.0005</td></tr><tr><td>T/K</td><td>p<sub>tr</sub>/MPa</td><td>U(p<sub>tr</sub>)/MPa</td><td>T/K</td><td>p<sub>tr</sub>/MPa</td><td>U(p<sub>tr</sub>)/MPa</td><td>T/K</td><td>p<sub>tr</sub>/MPa</td><td>U(p<sub>tr</sub>)/MPa</td></tr><tr><td>292.96</td><td>4.15</td><td>0.04</td><td>293.16</td><td>4.49</td><td>0.04</td><td>292.96</td><td>4.70</td><td>0.04</td></tr><tr><td>303.45</td><td>4.91</td><td>0.04</td><td>302.65</td><td>5.31</td><td>0.04</td><td>302.55</td><td>5.61</td><td>0.04</td></tr><tr><td>313.45</td><td>5.67</td><td>0.04</td><td>312.95</td><td>6.26</td><td>0.04</td><td>312.95</td><td>6.67</td><td>0.05</td></tr><tr><td>323.34</td><td>6.45</td><td>0.04</td><td>322.94</td><td>7.23</td><td>0.05</td><td>322.94</td><td>7.76</td><td>0.05</td></tr><tr><td>333.64</td><td>7.29</td><td>0.04</td><td>332.64</td><td>8.22</td><td>0.05</td><td>332.84</td><td>8.89</td><td>0.05</td></tr><tr><td>343.93</td><td>8.16</td><td>0.04</td><td>343.03</td><td>9.28</td><td>0.05</td><td>343.03</td><td>10.07</td><td>0.05</td></tr><tr><td>354.13</td><td>9.02</td><td>0.04</td><td>353.13</td><td>10.33</td><td>0.05</td><td>352.83</td><td>11.17</td><td>0.05</td></tr><tr><td>363.92</td><td>9.88</td><td>0.04</td><td>363.92</td><td>11.43</td><td>0.05</td><td>364.02</td><td>12.40</td><td>0.05</td></tr><tr><td colspan="3">z<sub>CO₂</sub> = 0.8201 ± 0.0004</td><td colspan="3">z<sub>CO₂</sub> = 0.8600 ± 0.0003</td><td colspan="3">z<sub>CO₂</sub> = 0.9000 ± 0.0004</td></tr><tr><td>T/K</td><td>p<sub>tr</sub>/MPa</td><td>U(p<sub>tr</sub>)/MPa</td><td>T/K</td><td>p<sub>tr</sub>/MPa</td><td>U(p<sub>tr</sub>)/MPa</td><td>T/K</td><td>p<sub>tr</sub>/MPa</td><td>U(p<sub>tr</sub>)/MPa</td></tr><tr><td>292.96</td><td>4.82</td><td>0.04</td><td>292.96</td><td>4.96</td><td>0.05</td><td>292.96</td><td>5.14</td><td>0.05</td></tr><tr><td>302.65</td><td>5.81</td><td>0.05</td><td>303.45</td><td>6.09</td><td>0.05</td><td>303.35</td><td>6.32</td><td>0.05</td></tr><tr><td>313.05</td><td>6.98</td><td>0.05</td><td>312.85</td><td>7.18</td><td>0.05</td><td>312.95</td><td>7.51</td><td>0.05</td></tr><tr><td>322.84</td><td>8.12</td><td>0.05</td><td>323.14</td><td>8.47</td><td>0.05</td><td>322.74</td><td>8.77</td><td>0.05</td></tr><tr><td>332.64</td><td>9.32</td><td>0.05</td><td>333.14</td><td>9.73</td><td>0.05</td><td>332.64</td><td>10.05</td><td>0.05</td></tr><tr><td>343.13</td><td>10.58</td><td>0.05</td><td>343.13</td><td>10.98</td><td>0.08</td><td>343.03</td><td>11.24</td><td>0.08</td></tr><tr><td>353.23</td><td>11.78</td><td>0.08</td><td>353.63</td><td>12.16</td><td>0.08</td><td>353.63</td><td>12.21</td><td>0.08</td></tr><tr><td>363.62</td><td>12.90</td><td>0.08</td><td>363.62</td><td>13.11</td><td>0.08</td><td>364.22</td><td>13.11</td><td>0.08</td></tr><tr><td colspan="3">z<sub>CO₂</sub> = 0.9400 ± 0.0004</td><td colspan="3"></td><td colspan="3"></td></tr><tr><td>T/K</td><td>p<sub>tr</sub>/MPa</td><td>U(p<sub>tr</sub>)/MPa</td><td>T/K</td><td>p<sub>tr</sub>/MPa</td><td>U(p<sub>tr</sub>)/MPa</td><td>T/K</td><td>p<sub>tr</sub>/MPa</td><td>U(p<sub>tr</sub>)/MPa</td></tr><tr><td>293.06</td><td>5.32</td><td>0.05</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>303.25</td><td>6.57</td><td>0.05</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>313.55</td><td>7.93</td><td>0.05</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>323.44</td><td>9.19</td><td>0.08</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>332.84</td><td>10.18</td><td>0.08</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>343.43</td><td>11.14</td><td>0.08</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>353.03</td><td>11.89</td><td>0.08</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>363.92</td><td>12.42</td><td>0.08</td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

<footnote>ª Standard uncertainties u are u(T) = 0.1 K, u(p) = 0.2 kPa.</footnote>

<footnote>ª Bold data are dew points; the rest are bubble points.</footnote>

<footnote>ᵇ Standard uncertainty u(T) = 0.1 K.</footnote>

<footnote>ᶜ Level of confidence ≈ 0.95 (k = 2) for U(p<sub>tr</sub>).</footnote>
<caption>**Table 6**</caption>

Fluid-fluid phase transition pressures $p_{tr}$ at temperatures $T$ for binary mixtures $CO_2 + 2,2,4,6,6-pentamethylheptane$, as a function of global mole fraction $z_{CO_2}$ ± $U(z_{CO_2})$ with its expanded uncertainty $U(p_{tr})^{a,b,c}$.

<table><thead><tr><th colspan="3">z<sub>CO₂</sub> = 0.1998 ± 0.0024</th><th colspan="3">z<sub>CO₂</sub> = 0.4009 ± 0.0019</th><th colspan="3">z<sub>CO₂</sub> = 0.4998 ± 0.0016</th></tr><tr><th>T/K</th><th>p<sub>tr</sub>/MPa</th><th>U(p<sub>tr</sub>)/MPa</th><th>T/K</th><th>p<sub>tr</sub>/MPa</th><th>U(p<sub>tr</sub>)/MPa</th><th>T/K</th><th>p<sub>tr</sub>/MPa</th><th>U(p<sub>tr</sub>)/MPa</th></tr></thead><tbody><tr><td>293.26</td><td>1.53</td><td>0.04</td><td>292.96</td><td>2.88</td><td>0.04</td><td>292.76</td><td>3.45</td><td>0.04</td></tr><tr><td>303.35</td><td>1.73</td><td>0.04</td><td>302.75</td><td>3.27</td><td>0.04</td><td>303.55</td><td>4.06</td><td>0.04</td></tr><tr><td>313.15</td><td>1.86</td><td>0.05</td><td>313.25</td><td>3.70</td><td>0.04</td><td>313.25</td><td>4.59</td><td>0.04</td></tr><tr><td>322.54</td><td>1.99</td><td>0.05</td><td>323.04</td><td>4.11</td><td>0.05</td><td>322.74</td><td>5.14</td><td>0.05</td></tr><tr><td>332.64</td><td>2.16</td><td>0.05</td><td>332.94</td><td>4.56</td><td>0.05</td><td>332.64</td><td>5.75</td><td>0.05</td></tr><tr><td>342.53</td><td>2.35</td><td>0.05</td><td>343.33</td><td>5.03</td><td>0.05</td><td>342.53</td><td>6.38</td><td>0.05</td></tr><tr><td>352.83</td><td>2.57</td><td>0.05</td><td>353.53</td><td>5.54</td><td>0.05</td><td>352.93</td><td>7.05</td><td>0.05</td></tr><tr><td>363.92</td><td>2.86</td><td>0.05</td><td>363.02</td><td>6.04</td><td>0.05</td><td>363.92</td><td>7.82</td><td>0.05</td></tr><tr><td colspan="3">z<sub>CO₂</sub> = 0.6000 ± 0.0012</td><td colspan="3">z<sub>CO₂</sub> = 0.7002 ± 0.0005</td><td colspan="3">z<sub>CO₂</sub> = 0.7699 ± 0.0004</td></tr><tr><td>T/K</td><td>p<sub>tr</sub>/MPa</td><td>U(p<sub>tr</sub>)/MPa</td><td>T/K</td><td>p<sub>tr</sub>/MPa</td><td>U(p<sub>tr</sub>)/MPa</td><td>T/K</td><td>p<sub>tr</sub>/MPa</td><td>U(p<sub>tr</sub>)/MPa</td></tr><tr><td>292.96</td><td>4.03</td><td>0.04</td><td>293.06</td><td>4.49</td><td>0.04</td><td>293.16</td><td>4.76</td><td>0.04</td></tr><tr><td>303.55</td><td>4.78</td><td>0.04</td><td>303.15</td><td>5.37</td><td>0.04</td><td>303.05</td><td>5.74</td><td>0.05</td></tr><tr><td>313.25</td><td>5.51</td><td>0.04</td><td>313.25</td><td>6.30</td><td>0.04</td><td>313.35</td><td>6.83</td><td>0.05</td></tr><tr><td>322.74</td><td>6.26</td><td>0.04</td><td>323.04</td><td>7.24</td><td>0.05</td><td>323.14</td><td>7.96</td><td>0.05</td></tr><tr><td>333.04</td><td>7.09</td><td>0.05</td><td>333.04</td><td>8.27</td><td>0.05</td><td>333.04</td><td>9.17</td><td>0.05</td></tr><tr><td>342.53</td><td>7.90</td><td>0.05</td><td>343.33</td><td>9.32</td><td>0.05</td><td>343.33</td><td>10.44</td><td>0.05</td></tr><tr><td>353.13</td><td>8.80</td><td>0.05</td><td>353.73</td><td>10.45</td><td>0.05</td><td>353.93</td><td>11.75</td><td>0.05</td></tr><tr><td>363.42</td><td>9.71</td><td>0.05</td><td>364.32</td><td>11.57</td><td>0.05</td><td>364.42</td><td>13.03</td><td>0.05</td></tr><tr><td colspan="3">z<sub>CO₂</sub> = 0.8501 ± 0.0003</td><td colspan="3">z<sub>CO₂</sub> = 0.9000 ± 0.0002</td><td colspan="3">z<sub>CO₂</sub> = 0.9450 ± 0.0003</td></tr><tr><td>T/K</td><td>p<sub>tr</sub>/MPa</td><td>U(p<sub>tr</sub>)/MPa</td><td>T/K</td><td>p<sub>tr</sub>/MPa</td><td>U(p<sub>tr</sub>)/MPa</td><td>T/K</td><td>p<sub>tr</sub>/MPa</td><td>U(p<sub>tr</sub>)/MPa</td></tr><tr><td>293.46</td><td>5.07</td><td>0.05</td><td>292.16</td><td>5.09</td><td>0.05</td><td>293.06</td><td>5.42</td><td>0.05</td></tr><tr><td>302.95</td><td>6.13</td><td>0.05</td><td>303.15</td><td>6.39</td><td>0.05</td><td>303.25</td><td>6.71</td><td>0.05</td></tr><tr><td>313.25</td><td>7.38</td><td>0.05</td><td>313.25</td><td>7.71</td><td>0.09</td><td>313.05</td><td>8.07</td><td>0.05</td></tr><tr><td>323.04</td><td>8.70</td><td>0.05</td><td>323.24</td><td>9.15</td><td>0.09</td><td>323.04</td><td>9.57</td><td>0.09</td></tr><tr><td>333.04</td><td>10.14</td><td>0.05</td><td>332.94</td><td>10.64</td><td>0.09</td><td>333.14</td><td>11.07</td><td>0.08</td></tr><tr><td>343.33</td><td>11.61</td><td>0.05</td><td>343.33</td><td>12.22</td><td>0.08</td><td>343.33</td><td>12.49</td><td>0.08</td></tr><tr><td>353.33</td><td>13.02</td><td>0.08</td><td>353.53</td><td>13.68</td><td>0.08</td><td>353.53</td><td>13.75</td><td>0.08</td></tr><tr><td>363.92</td><td>14.42</td><td>0.08</td><td>363.42</td><td>14.90</td><td>0.08</td><td>363.32</td><td>14.86</td><td>0.08</td></tr><tr><td colspan="3">z<sub>CO₂</sub> = 0.9736 ± 0.0002</td><td colspan="3"></td><td colspan="3"></td></tr><tr><td>T/K</td><td>p<sub>tr</sub>/MPa</td><td>U(p<sub>tr</sub>)/MPa</td><td>T/K</td><td>p<sub>tr</sub>/MPa</td><td>U(p<sub>tr</sub>)/MPa</td><td>T/K</td><td>p<sub>tr</sub>/MPa</td><td>U(p<sub>tr</sub>)/MPa</td></tr><tr><td>292.56</td><td>5.47</td><td>0.05</td><td>292.56</td><td>5.47</td><td>0.05</td><td>292.56</td><td>5.47</td><td>0.05</td></tr><tr><td>303.25</td><td>6.86</td><td>0.05</td><td>303.25</td><td>6.86</td><td>0.05</td><td>303.25</td><td>6.86</td><td>0.05</td></tr><tr><td>313.15</td><td>8.28</td><td>0.08</td><td>313.25</td><td>8.28</td><td>0.08</td><td>313.25</td><td>8.28</td><td>0.08</td></tr><tr><td>323.24</td><td>9.65</td><td>0.08</td><td>323.24</td><td>9.65</td><td>0.08</td><td>323.24</td><td>9.65</td><td>0.08</td></tr><tr><td>333.04</td><td>10.94</td><td>0.08</td><td>333.04</td><td>10.94</td><td>0.08</td><td>333.04</td><td>10.94</td><td>0.08</td></tr><tr><td>343.03</td><td>12.10</td><td>0.08</td><td>343.03</td><td>12.10</td><td>0.08</td><td>343.03</td><td>12.10</td><td>0.08</td></tr><tr><td>353.43</td><td>13.07</td><td>0.08</td><td>353.43</td><td>13.07</td><td>0.08</td><td>353.43</td><td>13.07</td><td>0.08</td></tr><tr><td>363.92</td><td>13.83</td><td>0.08</td><td>363.92</td><td>13.83</td><td>0.08</td><td>363.92</td><td>13.83</td><td>0.08</td></tr></tbody></table>

a Bold data are dew points; the rest are bubble points.

b Standard uncertainty $u(T) = 0.1$ K.

c Level of confidence $\approx 0.95$ ($k = 2$) for $U(p_{tr})$.

<caption>**Table 7**</caption>

Isothermal ($p,x$ or $y$) data for the $CO_2 + 2,3,4-trimethylpentane$ binary system at eight different temperatures $T$ interpolated from the original measurements in Table 5.

<table><thead><tr><th colspan="3">T/K = 293.15</th><th colspan="3">T/K = 303.15</th><th colspan="3">T/K = 313.15</th><th colspan="3">T/K = 323.15</th></tr><tr><th>p/MPa</th><th>x<sub>CO₂</sub></th><th>y<sub>CO₂</sub></th><th>p/MPa</th><th>x<sub>CO₂</sub></th><th>y<sub>CO₂</sub></th><th>p/MPa</th><th>x<sub>CO₂</sub></th><th>y<sub>CO₂</sub></th><th>p/MPa</th><th>x<sub>CO₂</sub></th><th>y<sub>CO₂</sub></th></tr></thead><tbody><tr><td>1.84</td><td>0.2017</td><td>—</td><td>2.03</td><td>0.2017</td><td>—</td><td>2.23</td><td>0.2017</td><td>—</td><td>2.43</td><td>0.2017</td><td>—</td></tr><tr><td>3.06</td><td>0.3998</td><td>—</td><td>3.51</td><td>0.3998</td><td>—</td><td>3.98</td><td>0.3998</td><td>—</td><td>4.45</td><td>0.3998</td><td>—</td></tr><tr><td>3.60</td><td>0.4999</td><td>—</td><td>4.18</td><td>0.4999</td><td>—</td><td>4.79</td><td>0.4999</td><td>—</td><td>5.43</td><td>0.4999</td><td>—</td></tr><tr><td>4.16</td><td>0.6000</td><td>—</td><td>4.89</td><td>0.6000</td><td>—</td><td>5.64</td><td>0.6000</td><td>—</td><td>6.44</td><td>0.6000</td><td>—</td></tr><tr><td>4.49</td><td>0.7000</td><td>—</td><td>5.35</td><td>0.7000</td><td>—</td><td>6.28</td><td>0.7000</td><td>—</td><td>7.26</td><td>0.7000</td><td>—</td></tr><tr><td>4.71</td><td>0.7700</td><td>—</td><td>5.67</td><td>0.7700</td><td>—</td><td>6.69</td><td>0.7700</td><td>—</td><td>7.79</td><td>0.7700</td><td>—</td></tr><tr><td>4.83</td><td>0.8201</td><td>—</td><td>5.86</td><td>0.8201</td><td>—</td><td>6.99</td><td>0.8201</td><td>—</td><td>8.16</td><td>0.8201</td><td>—</td></tr><tr><td>4.98</td><td>0.8600</td><td>—</td><td>6.06</td><td>0.8600</td><td>—</td><td>7.22</td><td>0.8600</td><td>—</td><td>8.46</td><td>0.8600</td><td>—</td></tr><tr><td>5.16</td><td>0.9000</td><td>—</td><td>6.31</td><td>0.9000</td><td>—</td><td>7.52</td><td>0.9000</td><td>—</td><td>8.84</td><td>0.9000</td><td>—</td></tr><tr><td>5.33</td><td>0.9400</td><td>—</td><td>6.54</td><td>0.9400</td><td>—</td><td>7.90</td><td>0.9400</td><td>—</td><td>9.13</td><td>0.9400</td><td>—</td></tr><tr><th colspan="3">T/K = 333.15</th><th colspan="3">T/K = 343.15</th><th colspan="3">T/K = 353.15</th><th colspan="3">T/K = 363.15</th></tr><tr><th>p/MPa</th><th>x<sub>CO₂</sub></th><th>y<sub>CO₂</sub></th><th>p/MPa</th><th>x<sub>CO₂</sub></th><th>y<sub>CO₂</sub></th><th>p/MPa</th><th>x<sub>CO₂</sub></th><th>y<sub>CO₂</sub></th><th>p/MPa</th><th>x<sub>CO₂</sub></th><th>y<sub>CO₂</sub></th></tr><tr><td>2.64</td><td>0.2017</td><td>—</td><td>2.88</td><td>0.2017</td><td>—</td><td>3.15</td><td>0.2017</td><td>—</td><td>3.46</td><td>0.2017</td><td>—</td></tr><tr><td>4.93</td><td>0.3998</td><td>—</td><td>5.44</td><td>0.3998</td><td>—</td><td>5.98</td><td>0.3998</td><td>—</td><td>6.54</td><td>0.3998</td><td>—</td></tr><tr><td>6.08</td><td>0.4999</td><td>—</td><td>6.76</td><td>0.4999</td><td>—</td><td>7.45</td><td>0.4999</td><td>—</td><td>8.15</td><td>0.4999</td><td>—</td></tr><tr><td>7.26</td><td>0.6000</td><td>—</td><td>8.09</td><td>0.6000</td><td>—</td><td>8.94</td><td>0.6000</td><td>—</td><td>9.81</td><td>0.6000</td><td>—</td></tr><tr><td>8.26</td><td>0.7000</td><td>—</td><td>9.29</td><td>0.7000</td><td>—</td><td>10.33</td><td>0.7000</td><td>—</td><td>11.35</td><td>0.7000</td><td>—</td></tr><tr><td>8.93</td><td>0.7700</td><td>—</td><td>10.08</td><td>0.7700</td><td>—</td><td>11.21</td><td>0.7700</td><td>—</td><td>12.31</td><td>0.7700</td><td>—</td></tr><tr><td>9.37</td><td>0.8201</td><td>—</td><td>10.59</td><td>0.8201</td><td>—</td><td>11.77</td><td>0.8201</td><td>—</td><td>12.86</td><td>0.8201</td><td>—</td></tr><tr><td>9.74</td><td>0.8600</td><td>—</td><td>10.98</td><td>0.8600</td><td>—</td><td>12.11</td><td>0.8600</td><td>—</td><td>13.07</td><td>0.8600</td><td>—</td></tr><tr><td>10.12</td><td>0.9000</td><td>—</td><td>11.23</td><td>0.9000</td><td>—</td><td>12.18</td><td>0.9000</td><td>—</td><td>13.02</td><td>—</td><td>0.9000</td></tr><tr><td>10.21</td><td>0.9400</td><td>—</td><td>11.14</td><td>—</td><td>0.9400</td><td>11.88</td><td>—</td><td>0.9400</td><td>12.40</td><td>—</td><td>0.9400</td></tr></tbody></table>
<caption>**Table 8**</caption>

Isothermal (p,x or y) data for the CO₂ + 2,2,4,6,6-pentamethylheptane binary system at eight different temperatures T interpolated from the original measurements in Table 6.

<table><thead><tr><th colspan="3">T/K = 293.15</th><th colspan="3">T/K = 303.15</th><th colspan="3">T/K = 313.15</th><th colspan="3">T/K = 323.15</th></tr><tr><th>p/MPa</th><th>x<sub>CO₂</sub></th><th>y<sub>CO₂</sub></th><th>p/MPa</th><th>x<sub>CO₂</sub></th><th>y<sub>CO₂</sub></th><th>p/MPa</th><th>x<sub>CO₂</sub></th><th>y<sub>CO₂</sub></th><th>p/MPa</th><th>x<sub>CO₂</sub></th><th>y<sub>CO₂</sub></th></tr></thead><tbody><tr><td>1.53</td><td>0.1998</td><td>—</td><td>1.72</td><td>0.1998</td><td>—</td><td>1.86</td><td>0.1998</td><td>—</td><td>2.01</td><td>0.1998</td><td>—</td></tr><tr><td>2.89</td><td>0.4009</td><td>—</td><td>3.28</td><td>0.4009</td><td>—</td><td>3.69</td><td>0.4009</td><td>—</td><td>4.12</td><td>0.4009</td><td>—</td></tr><tr><td>3.48</td><td>0.4998</td><td>—</td><td>4.02</td><td>0.4998</td><td>—</td><td>4.58</td><td>0.4998</td><td>—</td><td>5.17</td><td>0.4998</td><td>—</td></tr><tr><td>4.04</td><td>0.6000</td><td>—</td><td>4.76</td><td>0.6000</td><td>—</td><td>5.51</td><td>0.6000</td><td>—</td><td>6.29</td><td>0.6000</td><td>—</td></tr><tr><td>4.51</td><td>0.7002</td><td>—</td><td>5.37</td><td>0.7002</td><td>—</td><td>6.28</td><td>0.7002</td><td>—</td><td>7.26</td><td>0.7002</td><td>—</td></tr><tr><td>4.76</td><td>0.7699</td><td>—</td><td>5.75</td><td>0.7699</td><td>—</td><td>6.82</td><td>0.7699</td><td>—</td><td>7.96</td><td>0.7699</td><td>—</td></tr><tr><td>5.04</td><td>0.8501</td><td>—</td><td>6.15</td><td>0.8501</td><td>—</td><td>7.38</td><td>0.8501</td><td>—</td><td>8.72</td><td>0.8501</td><td>—</td></tr><tr><td>5.20</td><td>0.9000</td><td>—</td><td>6.38</td><td>0.9000</td><td>—</td><td>7.70</td><td>0.9000</td><td>—</td><td>9.15</td><td>0.9000</td><td>—</td></tr><tr><td>5.43</td><td>0.9450</td><td>—</td><td>6.71</td><td>0.9450</td><td>—</td><td>8.10</td><td>0.9450</td><td>—</td><td>9.57</td><td>0.9450</td><td>—</td></tr><tr><td>5.54</td><td>0.9736</td><td>—</td><td>6.87</td><td>0.9736</td><td>—</td><td>8.26</td><td>0.9736</td><td>—</td><td>9.64</td><td>0.9736</td><td>—</td></tr><tr><td>T/K = 333.15</td><td></td><td></td><td>T/K = 343.15</td><td></td><td></td><td>T/K = 353.15</td><td></td><td></td><td>T/K = 363.15</td><td></td><td></td></tr><tr><td>p/MPa</td><td>x<sub>CO₂</sub></td><td>y<sub>CO₂</sub></td><td>p/MPa</td><td>x<sub>CO₂</sub></td><td>y<sub>CO₂</sub></td><td>p/MPa</td><td>x<sub>CO₂</sub></td><td>y<sub>CO₂</sub></td><td>p/MPa</td><td>x<sub>CO₂</sub></td><td>y<sub>CO₂</sub></td></tr><tr><td>2.17</td><td>0.1998</td><td>—</td><td>2.36</td><td>0.1998</td><td>—</td><td>2.58</td><td>0.1998</td><td>—</td><td>2.84</td><td>0.1998</td><td>—</td></tr><tr><td>4.56</td><td>0.4009</td><td>—</td><td>5.03</td><td>0.4009</td><td>—</td><td>5.52</td><td>0.4009</td><td>—</td><td>6.04</td><td>0.4009</td><td>—</td></tr><tr><td>5.78</td><td>0.4998</td><td>—</td><td>6.41</td><td>0.4998</td><td>—</td><td>7.07</td><td>0.4998</td><td>—</td><td>7.76</td><td>0.4998</td><td>—</td></tr><tr><td>7.10</td><td>0.6000</td><td>—</td><td>7.94</td><td>0.6000</td><td>—</td><td>8.81</td><td>0.6000</td><td>—</td><td>9.69</td><td>0.6000</td><td>—</td></tr><tr><td>8.27</td><td>0.7002</td><td>—</td><td>9.32</td><td>0.7002</td><td>—</td><td>10.38</td><td>0.7002</td><td>—</td><td>11.45</td><td>0.7002</td><td>—</td></tr><tr><td>9.17</td><td>0.7699</td><td>—</td><td>10.41</td><td>0.7699</td><td>—</td><td>11.66</td><td>0.7699</td><td>—</td><td>12.88</td><td>0.7699</td><td>—</td></tr><tr><td>10.14</td><td>0.8501</td><td>—</td><td>11.58</td><td>0.8501</td><td>—</td><td>13.00</td><td>0.8501</td><td>—</td><td>14.32</td><td>0.8501</td><td>—</td></tr><tr><td>10.67</td><td>0.9000</td><td>—</td><td>12.19</td><td>0.9000</td><td>—</td><td>13.63</td><td>0.9000</td><td>—</td><td>14.87</td><td>0.9000</td><td>—</td></tr><tr><td>11.05</td><td>0.9450</td><td>—</td><td>12.47</td><td>—</td><td>0.9450</td><td>13.75</td><td>—</td><td>0.9450</td><td>14.82</td><td>—</td><td>0.9450</td></tr><tr><td>10.95</td><td>—</td><td>0.9736</td><td>12.11</td><td>—</td><td>0.9736</td><td>13.07</td><td>—</td><td>0.9736</td><td>13.78</td><td>—</td><td>0.9736</td></tr></tbody></table>

# 3. Experimental results

## 3.1. Pure 2,2,4,6,6-pentamethylheptane density and vapor pressure

Table 2 reports the density of 22466m7 measured in this work and provides previously published data for comparison.

Our density data are in very good agreement with those recently reported by Luning Prak et al. [20,21] who have used 22466m7 with a purity comparable to our sample.

22466m7 vapor pressures were measured between 10 and 110 kPa. These data are reported in Table 3 and were used to regress the parameters of a modified version of the Riedel equation

$$ \ln p = A + B/T + C\ln T + D T^E \quad (1) $$

with p the pure compound vapor pressure in Pa and T the temperature in K.

A normal boiling temperature of 450.2 K was measured in this work whereas old literature values [26–29] ranged from (450.4 to 451.5) K but the purity of the 22466m7 used in these past works was not really provided.

The parameters of Eq. (1) were fitted against the experimental data (Table 3), they are reported in Table 4.

## 3.2. Saturation pressures for the studied CO₂ + branched alkanes binary systems

Ten mixtures were prepared for both studied binary systems: from z<sub>CO₂</sub> = (0.20 to 0.94) for CO₂ + 234m5 and from z<sub>CO₂</sub> = (0.20 to 0.97), approximately, for CO₂ + 22466m7. Experimental data were mainly bubble points with a maximum bubble pressure reaching 14.9 MPa.

The experimental saturation pressures for the investigated binaries are reported in Tables 5 and Table 6.

From the raw experimental data tabulated in Tables 5 and 6, Padé approximants were employed to obtain isothermal data (p,x) or (p,y), enabling to plot isothermal phase diagrams.

The interpolated isothermal data are reported in Tables 7 and Table 8 for eight temperatures ranging from (293.15 to 363.15) K.

The interpolated data are presented graphically in Figs. 1 and Fig. 2 with calculated bubble and dew curves. Taking into account that no liquid-liquid immiscibility was detected during the experiments and the

general shape of the data, it can be concluded that the studied systems present a continuous vapor-liquid critical curve, corresponding to type I or II binary mixtures [34].

Fig. 3 compares the experimental data obtained for both studied systems at 293.15 K and 363.15 K.

Despite the size difference between 234m5 and 22466m7, the binary systems present very close saturation pressures in a large part of the phase diagram. In the CO₂ rich-part of the domain, when the temperature increases, the CO₂ + 22466m7 binary obviously exhibits a pressure maximum notably higher than the CO₂ + 234m5 system. The gap reaches approximately 18 bar at 363.15 K and this gap is likely to become more pronounced at higher temperatures.

# 4. Modeling and discussion

## 4.1. The Peng-Robinson equation of state with temperature-dependent binary interaction parameters

The well-known Peng-Robinson equation of state (PR EOS) [16] was used to correlate the experimental data. For a mixture, this equation can be written as follow

$$ p = \frac{R T}{v_m - b_m} - \frac{a_m}{v_m(v_m + b_m) + b_m(v_m - b_m)} \quad (2) $$

in which p is the pressure, R the gas constant, T the temperature, v_m the molar volume, a_m and b_m the mixture parameters. Van der Waals mixing rules were employed in this work:

$$ a_m = \sum_i \sum_j z_i z_j (1 - k_{ij}(T)) \sqrt{a_i a_j} \quad (3) $$

$$ b_m = \sum_i z_i b_i \quad (4) $$

with z_i and z_j the mole fractions of components i and j, respectively, a_i and a_j the pure components PR EOS parameters and k_{ij}(T) the binary interaction parameter.

Several strategies can be envisaged to evaluate or predict this interaction parameter. Simple mixtures without pronounced interactions between molecules can be correctly described using a constant, and generally very small, k_{ij} fitted against the available
<figure><img src="image_3.png" /><figcaption>**Fig. 1.** (p, x<sub>CO₂</sub>, y<sub>CO₂</sub>) isothermal diagrams for CO₂ + 2,3,4-trimethylpentane. ○: bubble points, ●: dew points. Dashed curves: PPR78 model. Solid curves: PR EOS with k<sub>ij</sub>(T) fitted against interpolated experimental data.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Fig. 2. (p, x<sub>CO2</sub>, y<sub>CO2</sub>) isothermal diagrams for CO<sub>2</sub> + 2,2,4,6,6-pentamethylheptane. ○: bubble points, ●: dew points. Dashed curves: PPR78 model. Solid curves: PR EOS with k<sub>ij</sub>(T) fitted against interpolated experimental data.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Comparison of the measured data for the studied systems at 293.15 K (left diagram) and 363.15 K (right diagram). ○: CO₂ + 22466m7, ●: CO₂ + 234m5. Smoothed curves drawn for eye-guide.</figcaption></figure>

<table><caption>**Table 9**

Critical temperature (T_c), critical pressure (p_c) and acentric factor (ω) of the pure components involved in this study.</caption><thead><tr><th>Component</th><th>T<sub>c</sub>/K</th><th>p<sub>c</sub>/MPa</th><th>ω</th></tr></thead><tbody><tr><td>Carbon dioxide<sup>a</sup></td><td>304.21</td><td>7.383</td><td>0.2236</td></tr><tr><td>2,3,4-trimethylpentane<sup>a</sup></td><td>566.40</td><td>2.730</td><td>0.3153</td></tr><tr><td>2,2,4,6,6-pentamethylheptane<sup>b</sup></td><td>624.89</td><td>1.817</td><td>0.3943</td></tr></tbody></table>

a DIPPR database.

b Estimated by a group contribution method [35].

experimental data. For more complex mixtures, a temperature-dependent (and eventually composition-dependent) k<sub>ij</sub> may be mandatory. Group contribution approaches were also developed to predict the binary interaction parameters. Such methods are particularly useful in the absence of experimental data.

In this work, the fully predictive PPR78 model [17] was tested first. Then, a temperature-dependent k<sub>ij</sub> was regressed against the interpolated experimental data so as to obtain a better description of the fluid phase equilibria of the studied systems. An expression coming from the PPR78 model was used for this purpose. Consequently, in this approach, the only difference is whether the interaction coefficients are predicted via group contributions or fitted to the experimental data, while still considering a temperature dependence. This allows a direct comparison of the impact of group contributions on prediction accuracy. The expression derived from the PPR78 model is

$$k_{ij}(T) = k_{12}(T) = \frac{A_{12} \left( \frac{298.15}{T} \right)^{(B_{12}/A_{12}-1)} - \left( \frac{\sqrt{a_1}}{b_1} - \frac{\sqrt{a_2}}{b_2} \right)^2}{2 \frac{\sqrt{a_1} \sqrt{a_2}}{b_1 b_2}} \quad (5)$$

in which each component of a binary mixture 1 + 2 is considered as a single group.

The parameters A<sub>12</sub> and B<sub>12</sub> were regressed to minimize the deviations between calculated and experimental liquid phase and gas phase mole fractions.

The critical parameters (T_c and p_c) and the acentric factor (ω) of the

<figure><img src="image_6.png" /><figcaption>**Table 10**

Mean absolute deviations in liquid and gas phase mole fractions obtained from two modelling approaches: PPR78 model and PR EOS with k<sub>ij</sub>(T) regressed against measured data.</figcaption></figure>

<table><thead><tr><th rowspan="2"></th><th colspan="3">PPR78<br>(prediction)</th><th colspan="3">PR + k<sub>ij</sub>(T)<br>(regression)</th></tr><tr><th>|Δx|<sup>a</sup></th><th>|Δy|<sup>b</sup></th><th>A<sub>12</sub>/MPa</th><th>B<sub>12</sub>/MPa</th><th>|Δx|</th><th>|Δy|</th></tr></thead><tbody><tr><td>Binary system</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>CO<sub>2</sub> + 234m5</td><td>0.065</td><td>0.020</td><td>129.83</td><td>254.94</td><td>0.017</td><td>0.006</td></tr><tr><td>CO<sub>2</sub> + 22466m7</td><td>0.057</td><td>0.049</td><td>145.97</td><td>201.85</td><td>0.020</td><td>0.015</td></tr></tbody></table>

a |Δx| = |x<sub>1,exp</sub> - x<sub>1,cal</sub>| = |x<sub>2,exp</sub> - x<sub>2,cal</sub>|.

b |Δy| = |y<sub>1,exp</sub> - y<sub>1,cal</sub>| = |y<sub>2,exp</sub> - y<sub>2,cal</sub>|.

c Dew points located just above the calculated phase diagrams, the deviation thus cannot be calculated.

pure compounds are obviously required to perform VLE calculations using the PR EOS. When available, the parameters provided in the DIPPR database were used. However, the 22466m7 critical parameters are unknown. For this component, T_c and p_c were thus estimated using the group contribution method established by Constantinou and Gani [35]. Combining the estimated 22466m7 critical temperature (0.7 × T_c, estimated = 437.42 K) and the parameters of the Riedel equation (Table 4) obtained from our vapor pressures measurements, the 22466m7 saturation pressure at 0.7 × T_c was calculated and a value of 0.3943 was finally obtained for its acentric factor. Table 9 summarizes the critical parameters used to model our data.

## 4.2. Modelling results

A<sub>12</sub> and B<sub>12</sub> parameters regressed against the measured data are provided in Table 10 along with the pertinent deviations between experimental and calculated liquid phase and gas phase compositions.

The different calculated bubble and dew curves are represented in Figs. 1 and Fig. 2 for comparison with experimental data. Despite a qualitatively fair representation of the systems fluid phase behavior, the PPR78 model slightly underestimates the saturation pressures of the mixtures. The use of a regressed temperature-dependent k<sub>ij</sub> allows a very
<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Comparison of the data measured in this work for the binary system CO₂ + 2,3,4-trimethylpentane with literature data [36–40] for mixtures CO₂ + isomers of 2,3,4-trimethylpentane at 333.15 K (left) and 353.15 K (right). ◦,●: CO₂ + 2,3,4-trimethylpentane (this work). ■: CO₂ + 2,2,4-trimethylpentane [36,37]. ▲: CO₂ + 2,5-dimethylhexane [36]. ×: CO₂ + n-octane [38–40]. Solid curves: PR EOS with kᵢⱼ(T) fitted against data measured in this work for CO₂ + 2,3,4-trimethylpentane.</figcaption></figure>

good correlation of the experimental data for both binary systems with average deviations not exceeding 0.02 mol fraction regarding the bubble curves.

For the system CO₂ + 234m5, the binary interaction parameter was found to be practically independent of the temperature since it slightly decreases from 0.110 at 293 K to 0.107 at 363 K. In this temperature range, a constant kᵢⱼ = 0.11 could be sufficient to correctly describe the mixture's phase behavior. For the CO₂ + 22466m7 system, the temperature dependance was found to be more pronounced with a kᵢⱼ increasing from 0.097 (at 293 K) to 0.119 (at 363 K).

Such kᵢⱼ values are consistent with kᵢⱼ reported in the literature for comparable binary systems. For example, Romero Yanes et al. [5] used an interaction parameter of roughly 0.09 to describe the binary system CO₂ + heptamethylnonane whereas Mutelet et al. [36] found a value of approximately 0.10 for the CO₂ + 2,2,4-trimethylpentane mixture.

### 4.3. Comparison with previously studied CO₂ + branched alkane binary systems

To our knowledge, the binary systems CO₂ + 234m5 and CO₂ + 22466m7 are investigated for the first time in this work. It is though possible to compare our experimental data with previously published data related to binary systems containing CO₂ + an isomer of 234m5. Indeed, we found literature data for three relevant binaries: CO₂ + 2,2,4-trimethylpentane [36,37], CO₂ + 2,5-dimethylhexane [36] and CO₂ + n-octane [38–40]. Fig. 4 provides a comparison between these systems at 333.15 K and 353.15 K.

Fig. 4 highlights that the saturation pressures of the systems CO₂ + 234m5 and CO₂ + n-octane are practically superimposed while, for a given CO₂ mole fraction, CO₂ + 2,5-dimethylhexane system displays the lowest saturation pressures and CO₂ + 2,2,4-trimethylpentane lies between 2,3,4-trimethylpentane and 2,5-dimethylhexane.

Such a trend was also observed between binary systems CO₂ + n-hexane and isomers of n-hexane. At 323 K, the saturations pressures of the CO₂ + n-hexane and CO₂ + 2,3-dimethylbutane systems are more less identical whereas CO₂ + 2,2-dimethylbutane presents slightly lower bubble pressures [3,6].

## 5. Conclusion

Saturations pressures were measured for two unconventional binary systems containing carbon dioxide and a branched alkane: CO₂ + 2,3,4-trimethylpentane and CO₂ + 2,2,4,6,6-pentamethylheptane, both studied for the first time in this work. Binary mixtures were investigated at 8 temperatures, from 293 K to 363 K, using a high-pressure visual cell and a synthetic method employed and mastered for decades by our group.

Bubble points constituted the vast majority of the acquired experimental data. These data were used to construct isothermal phase diagrams, revealing that both binary systems present a continuous vapor-liquid critical locus. Their phase behavior thus corresponds to type I or type II according to van Konynenburg and Scott.

The Peng-Robinson equation of state with classical mixing rules provided a reliable description of the phase behavior of the studied CO₂ + branched alkane systems. Excellent agreement with the experimental data was achieved when using regressed temperature-dependent kᵢⱼ. Moreover, the model remained reasonably accurate even when using kᵢⱼ predicted by the fully predictive PPR78 approach, although small deviations were noted.

## Funding

No funds, grants, or other support were received for this study.

## CRediT authorship contribution statement

**Stéphane Vitu:** Writing – review & editing, Writing – original draft, Visualization, Validation, Methodology, Investigation, Data curation.

**Vincent Caqueret:** Methodology, Investigation. **Jean-Luc Daridon:** Writing – review & editing, Writing – original draft, Supervision, Resources, Investigation, Funding acquisition, Data curation, Conceptualization. **Jean-Patrick Bazile:** Methodology, Investigation, Data curation.
# Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

# Data availability

The data measured in this work are tabulated in the paper

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