# Phase Behavior of CO2 + 2,2-dimethylbutane and CO2 + 2-methylpentane from 293 K to 363 K and at Pressures up to 11 MPa

Jean-Patrick Bazile, Jean-Luc Daridon, Jean-Noël Jaubert, Khaled

Abou-Alfa, Stéphane Vitu

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Jean-Patrick Bazile, Jean-Luc Daridon, Jean-Noël Jaubert, Khaled Abou-Alfa, Stéphane Vitu. Phase Behavior of CO2 + 2,2-dimethylbutane and CO2 + 2-methylpentane from 293 K to 363 K and at Pressures up to 11 MPa. International Journal of Thermophysics, 2025, 46 (7), pp.107. 10.1007/s10765-025-03579-5. hal-05090439

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# Phase Behavior of CO₂ + 2,2-dimethylbutane and CO₂ + 2-methylpentane from 293 K to 363 K and at Pressures up to 11 MPa

Jean-Patrick Bazile<fnref n="1" /> Ⓓ ID · Jean-Luc Daridon<fnref n="1" /> Ⓓ ID · Jean-Noël Jaubert<fnref n="2" /> Ⓓ ID · Khaled Abou-Alfa<fnref n="3" />,<fnref n="4" /> Ⓓ ID · Stéphane Vitu<fnref n="3" />,<fnref n="4" /> Ⓓ ID

Received: 22 April 2025 / Accepted: 12 May 2025
© The Author(s) 2025

## Abstract

This study is a continuation of a series of works concerning the acquisition of new experimental data related to binary mixtures of branched alkanes with CO₂. A synthetic method was employed to measure phase transition pressures for the systems CO₂ + 2,2-dimethylbutane and CO₂ + 2-methylpentane with an adjustable-volume high-pressure cell. To our knowledge, these binary systems were investigated for the first time in this work. Bubble and dew point pressures were obtained by visual detection at constant composition with an expanded uncertainty ranging from (0.04 to 0.08) MPa. Mixtures were investigated at temperatures ranging from (293.15 to 363.15) K with pressures up to 11 MPa. The Peng-Robinson equation of state was used to correlate the experimental data. An accurate representation of the results has been obtained by using classical mixing rules with temperature-dependent binary interaction parameters regressed against experimental data. The predictive model PPR78 has also provided satisfactory results.

**Keywords** Alkane · Carbon dioxide · Equation of state · Isohexane · Neohexane · Phase equilibria

<figure><img src="image_2.png" /></figure>

<footnote>Stéphane Vitu
stephane.vitu@lecnam.net</footnote>

<footnote n="1">¹ Université de Pau et des Pays de l'Adour, E2S UPPA, CNRS, LFCR, 64000 Pau, France</footnote>

<footnote n="2">² Université de Lorraine, CNRS, LRGP, 54000 Nancy, France</footnote>

<footnote n="3">³ Université Paris-Saclay, INRAE, AgroParisTech, UMR SayFood, 91120 Palaiseau, France</footnote>

<footnote n="4">⁴ Conservatoire National des Arts et Métiers, 75003 Paris, France</footnote>
# 1 Introduction

Twenty years ago, during the development of the PPR78 model, we noted that: “very few VLE data were available for binary systems containing CO₂ and a branched alkane” [1]. The situation has changed significantly since several binary systems were studied over the past two decades. To date, the phase behaviors of ten binary systems CO₂ + a branched alkane have been investigated, as summarized in Table 1.

From Table 1, it can be seen that several “light” branched-chain alkanes (from 4 to 6 carbon atoms) where studied in mixture with CO₂ whereas only two binary systems containing a heavy branched alkane were investigated (CO₂ + heptamethyl-nonane and CO₂ + squalane). Among the ten branched alkanes listed in Table 1, only three contain a quaternary carbon (neopentane, isooctane and heptamethylnonane). It can also be noted that two hexane isomers have not yet been studied: 2,2-dimethylbutane (neohexane) and 2-methylpentane (isohexane).

In this work, new VLE measurements were thus performed for the CO₂ + 2,2-dimethylbutane and CO₂ + 2-methylpentane systems.

A high-pressure setup for phase transitions determination was employed. The binary mixtures were studied from 293.15 K to 363.15 K at different compositions approximately ranging from 0.20 CO₂ to 0.94 CO₂ mole fraction.

The experimental results were modeled using the Peng-Robinson equation of state with binary interaction parameters (BIP) predicted by the PPR78 model and also with temperature-dependent BIP regressed against the experimental data.

# 2 Experimental Section

## 2.1 Materials

The information concerning the pure components considered in this study are listed in Table 2. All chemicals were used as received, and their purities, as provided by the manufacturers, are also included in Table 2.

<table><caption>**Table 1** List of the previous studies into the phase behavior of CO₂ + branched alkane binary mixtures</caption><thead><tr><td>Binary system CO<sub>2</sub> +</td><td>Branched alkane chemical formula</td><td>References</td></tr></thead><tbody><tr><td>2-methylpropane</td><td>C<sub>4</sub>H<sub>10</sub> (isobutane)</td><td>[2–9]</td></tr><tr><td>2,2-dimethylpropane</td><td>C<sub>5</sub>H<sub>12</sub> (neopentane)</td><td>[10–12]</td></tr><tr><td>2-methylbutane</td><td>C<sub>5</sub>H<sub>12</sub> (isopentane)</td><td>[13–18]</td></tr><tr><td>2,3-dimethylbutane</td><td>C<sub>6</sub>H<sub>14</sub></td><td>[19]</td></tr><tr><td>3-methylpentane</td><td>C<sub>6</sub>H<sub>14</sub></td><td>[1]</td></tr><tr><td>2,4-dimethylpentane</td><td>C<sub>7</sub>H<sub>16</sub></td><td>[20]</td></tr><tr><td>2,5-dimethylhexane</td><td>C<sub>8</sub>H<sub>18</sub></td><td>[1]</td></tr><tr><td>2,2,4-trimethylpentane</td><td>C<sub>8</sub>H<sub>18</sub> (isooctane)</td><td>[1, 21–24]</td></tr><tr><td>2,2,4,4,6,8,8-heptamethylnonane</td><td>C<sub>16</sub>H<sub>34</sub></td><td>[25]</td></tr><tr><td>2,6,10,15,19,23-hexamethyltetracosane</td><td>C<sub>30</sub>H<sub>62</sub> (squalane)</td><td>[26–29]</td></tr></tbody></table>
<table><caption>**Table 2** Pure components description</caption><thead><tr><th>IUPAC chemical name</th><th>Other 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></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>2,2-dimethylbutane</td><td>neohexane</td><td>22m4</td><td>75-83-2</td><td>TCI</td><td>0.996</td><td>none</td></tr><tr><td>2-methylpentane</td><td>isohexane</td><td>2m5</td><td>107-83-5</td><td>Fisher</td><td>0.999</td><td>none</td></tr></tbody></table>

## 2.2 Apparatus and Method

The technique employed to measure fluid phase transitions is a synthetic-visual method (SynVis [30]) that eliminates the need for phase sampling. The experimental setup has been extensively detailed in previous publications [19, 25, 31–33]. The core of the system is a high-pressure PVT cell, composed of a horizontal stainless-steel cylinder equipped with a sapphire window on the front and a second one on a lateral wall. The latter allows for the illumination of the cell via an optical fiber, while the front window facilitates visual observation of the phase transitions of the entire fluid sample through a video camera mounted on an endoscope. The pressure of the fluid sample is generated by manually adjusting the position of a piston in the high-pressure cylinder. The PVT cell is capable of operating at pressures up to 100 MPa within a temperature range of 293 K to 373 K. The pressure is measured using a pressure gauge installed inside the cell to minimize dead volumes. Since this pressure sensor is subject to temperature variations, it is calibrated as a function of temperature against a primary standard pressure sensor, with an uncertainty of less than 0.02 %.

The cell has been designed to minimize dead volumes and has an internal volume that can be adjusted between 8 cm³ and 30 cm³. The fluid is thermoregulated by circulating a heat transfer fluid through three flow lines directly integrated into the cell and connected to a thermostatic bath with a stability of 0.02 K. The temperature (T) of the fluid is measured with a Pt100 probe, achieving a standard uncertainty of u(T)=0.1 K. To ensure both thermal and chemical equilibrium throughout a phase change measurement, a magnetic stirrer is placed inside the cell to continuously homogenize the fluid during measurements.

The synthetic-visual method involves two main steps. First, the specific fluid mixture is prepared directly in the cell by introducing the liquid component, followed by the carbon dioxide. The amounts of both components are determined by weighing during injection. For this purpose, the mass of the liquid injected $m_L$ is measured using an analytical balance (Ohaus), while the mass of carbon dioxide introduced $m_{CO_2}$ is weighed using a high-capacity analytical balance (Mettler Toledo). To ensure accurate weighing, the carbon dioxide is first loaded into a small reservoir tank positioned on the balance and connected to the cell via a lightweight and flexible high-pressure PEEK Tubing (1/32" diameter). This configuration prevents disturbances to the balance during weighing. Additionally, $CO_2$ is maintained

<footnote><sup>a</sup>Mass fraction purity</footnote>
in liquid-vapor equilibrium within the vessel to keep the pressure constant during injection, thereby avoiding changes in gas mass within the connecting capillary line. The uncertainties in the masses loaded into the apparatus are estimated to be less than 0.005 g for both the liquid and gas loaded in the cell. From this direct weighing method, the expanded combined uncertainty with a conventional coverage factor of k=2 (providing a level of confidence ≈ 0.95) in CO₂ molar fraction, U(zCO₂), is obtained through the following expression:

$$U(z_{\text{CO}_2}) = 2u(z_{\text{CO}_2}) = 2z_{\text{CO}_2}(1 - z_{\text{CO}_2}) \sqrt{\left(\frac{u(m_{\text{CO}_2})}{m_{\text{CO}_2}}\right)^2 + \left(\frac{u(m_L)}{m_L}\right)^2} \quad (1)$$

Once both components are loaded into the cell, the second step of the method involves observing phase transitions caused by pressure changes at a given temperature to obtain isoplethic data of the form (Tᵢ, pᵢ). For this purpose, the thermo-static bath is set to a given temperature, and the pressure is increased until the fluid becomes monophasic. Under these conditions, when the temperature is stable, the pressure is gradually decreased until the appearance of a second phase. It is then increased in increments until the phase that just formed disappears. Once a monophasic state is achieved, the procedure is repeated, applying a pressure decrement Δp which is 10 times smaller than the previous one.

Using this method, the standard uncertainties in phase transition observations u(pobs) are 0.02 MPa for bubble point pressures far from critical conditions, and 0.04 MPa for bubble points in the vicinity of the critical point as well as for dew points. These uncertainties combined with the uncertainty of the pressure gauge and the influence of temperature measurement and mixture preparation uncertainties lead to the expanded uncertainty in measured transition pressure ptr:

$$U(p_{\text{tr}}) = 2 \left[ u^2(p_{\text{obs}}) + u^2(p_{\text{gauge}}) + \left[ \left( \frac{\partial p_{\text{tr}}}{\partial T} \right) u(T) \right]^2 + \left[ \left( \frac{\partial p_{\text{tr}}}{\partial z_{\text{CO}_2}} \right) u(z_{\text{CO}_2}) \right]^2 \right]^{1/2} \quad (2)$$

according to the Guide to the expression of uncertainty in measurement [34].

## 3 Experimental Results

The experimental saturation pressures for the investigated binary systems are reported in Tables 3 and 4. For each system, 10 mixtures were prepared, ranging from zCO₂ = (0.20 to 0.94), approximatively. Phase transition pressures vary from (1.56 to 10.89) MPa. Most of these experimental data are bubble points. Some dew points were measured at the highest studied temperatures and for CO₂-rich mixtures.

Experimental data tabulated in Tables 3 and 4 were interpolated using Padé approximants to obtain isothermal (p,x or y) data and to construct standard (p,xCO₂,yCO₂) isothermal diagrams. A [p,q] Padé approximant is the ratio of two
<table><caption>**Table 3** Fluid–fluid phase transition pressures *p*<sub>tr</sub> at temperatures *T* for binary mixtures CO<sub>2</sub> + 2,2-dimethylbutane, as a function of global mole fraction *z*<sub>CO<sub>2</sub></sub> ± *U*(*z*<sub>CO<sub>2</sub></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> = 0.1999 ± 0.0012</th><th colspan="3">z<sub>CO₂</sub> = 0.4002 ± 0.0010</th><th colspan="3">z<sub>CO₂</sub> = 0.5001 ± 0.0008</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>292.96</td><td>1.56</td><td>0.04</td><td>293.26</td><td>2.79</td><td>0.04</td><td>293.06</td><td>3.30</td><td>0.04</td></tr><tr><td>303.05</td><td>1.75</td><td>0.04</td><td>303.65</td><td>3.25</td><td>0.04</td><td>303.55</td><td>3.89</td><td>0.04</td></tr><tr><td>313.45</td><td>1.97</td><td>0.04</td><td>313.45</td><td>3.68</td><td>0.04</td><td>313.05</td><td>4.44</td><td>0.04</td></tr><tr><td>323.04</td><td>2.19</td><td>0.04</td><td>322.84</td><td>4.12</td><td>0.04</td><td>323.04</td><td>5.04</td><td>0.04</td></tr><tr><td>333.04</td><td>2.41</td><td>0.04</td><td>333.34</td><td>4.64</td><td>0.04</td><td>333.24</td><td>5.69</td><td>0.04</td></tr><tr><td>343.03</td><td>2.67</td><td>0.04</td><td>343.03</td><td>5.16</td><td>0.04</td><td>343.13</td><td>6.34</td><td>0.04</td></tr><tr><td>353.23</td><td>2.99</td><td>0.04</td><td>353.13</td><td>5.70</td><td>0.04</td><td>352.93</td><td>7.00</td><td>0.04</td></tr><tr><td>363.32</td><td>3.33</td><td>0.04</td><td>363.12</td><td>6.29</td><td>0.04</td><td>363.12</td><td>7.70</td><td>0.04</td></tr></tbody><thead><tr><th colspan="3">z<sub>CO₂</sub> = 0.5998 ± 0.0006</th><th colspan="3">z<sub>CO₂</sub> = 0.7004 ± 0.0005</th><th colspan="3">z<sub>CO₂</sub> = 0.7700 ± 0.0005</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>292.96</td><td>3.67</td><td>0.04</td><td>292.86</td><td>4.05</td><td>0.04</td><td>292.96</td><td>4.40</td><td>0.04</td></tr><tr><td>302.75</td><td>4.30</td><td>0.04</td><td>302.95</td><td>4.84</td><td>0.04</td><td>303.15</td><td>5.30</td><td>0.04</td></tr><tr><td>312.95</td><td>4.98</td><td>0.04</td><td>313.25</td><td>5.69</td><td>0.04</td><td>313.25</td><td>6.24</td><td>0.04</td></tr><tr><td>323.04</td><td>5.69</td><td>0.04</td><td>323.24</td><td>6.59</td><td>0.04</td><td>323.34</td><td>7.20</td><td>0.04</td></tr><tr><td>332.64</td><td>6.39</td><td>0.04</td><td>333.14</td><td>7.43</td><td>0.04</td><td>333.04</td><td>8.17</td><td>0.04</td></tr><tr><td>342.73</td><td>7.14</td><td>0.04</td><td>343.23</td><td>8.31</td><td>0.04</td><td>343.03</td><td>9.09</td><td>0.04</td></tr><tr><td>353.23</td><td>7.93</td><td>0.04</td><td>353.03</td><td>9.14</td><td>0.04</td><td>353.03</td><td>9.92</td><td>0.08</td></tr><tr><td>363.02</td><td>8.70</td><td>0.04</td><td>363.02</td><td>9.95</td><td>0.04</td><td>363.12</td><td>10.43</td><td>0.08</td></tr></tbody><thead><tr><th colspan="3">z<sub>CO₂</sub> = 0.8200 ± 0.0005</th><th colspan="3">z<sub>CO₂</sub> = 0.8600 ± 0.0004</th><th colspan="3">z<sub>CO₂</sub> = 0.9000 ± 0.0005</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>4.56</td><td>0.04</td><td>292.96</td><td>4.79</td><td>0.04</td><td>293.16</td><td>5.05</td><td>0.05</td></tr><tr><td>303.35</td><td>5.57</td><td>0.05</td><td>303.25</td><td>5.83</td><td>0.05</td><td>303.15</td><td>6.16</td><td>0.05</td></tr><tr><td>313.35</td><td>6.59</td><td>0.05</td><td>313.35</td><td>6.92</td><td>0.05</td><td>313.05</td><td>7.32</td><td>0.05</td></tr><tr><td>323.14</td><td>7.63</td><td>0.05</td><td>323.24</td><td>8.03</td><td>0.04</td><td>323.24</td><td>8.46</td><td>0.08</td></tr><tr><td>333.14</td><td>8.66</td><td>0.04</td><td>333.14</td><td>9.02</td><td>0.08</td><td>333.34</td><td>9.09</td><td>0.08</td></tr><tr><td>343.13</td><td>9.55</td><td>0.08</td><td><strong>343.13</strong></td><td><strong>9.56</strong></td><td><strong>0.08</strong></td><td><strong>343.13</strong></td><td><strong>9.40</strong></td><td><strong>0.08</strong></td></tr><tr><td>353.03</td><td>10.08</td><td>0.08</td><td><strong>353.03</strong></td><td><strong>10.00</strong></td><td><strong>0.08</strong></td><td><strong>353.13</strong></td><td><strong>9.03</strong></td><td><strong>0.08</strong></td></tr><tr><td><strong>363.22</strong></td><td><strong>10.40</strong></td><td><strong>0.08</strong></td><td><strong>363.32</strong></td><td><strong>10.03</strong></td><td><strong>0.08</strong></td><td></td><td></td><td></td></tr></tbody><thead><tr><th colspan="3">z<sub>CO₂</sub> = 0.9400 ± 0.0005</th><th colspan="3"></th><th colspan="3"></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>293.16</td><td></td><td>5.31</td><td></td><td></td><td>0.05</td><td></td><td></td><td></td></tr><tr><td>303.35</td><td></td><td>6.55</td><td></td><td></td><td>0.05</td><td></td><td></td><td></td></tr><tr><td>313.25</td><td></td><td>7.81</td><td></td><td></td><td>0.04</td><td></td><td></td><td></td></tr><tr><td><strong>323.24</strong></td><td></td><td><strong>8.44</strong></td><td></td><td></td><td><strong>0.08</strong></td><td></td><td></td><td></td></tr><tr><td><strong>333.64</strong></td><td></td><td><strong>7.89</strong></td><td></td><td></td><td><strong>0.08</strong></td><td></td><td></td><td></td></tr></tbody></table>

<footnote><sup>a</sup>Bold italicized datum is a critical point, bold data are dew points; the rest are bubble points</footnote>

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

<footnote><sup>c</sup>Level of confidence ≈ 0.95 (k = 2) for *U*(*p*<sub>tr</sub>)</footnote>
polynomials, with degree p in the numerator and degree q in the denominator. It often gives better performance than a Taylor series approximation of order p+q, providing smoother data fitting. In this work, two second-degree polynomials (p=q=2) were sufficient to achieve a good fit of the data while remaining within the expanded uncertainty bounds.

The interpolated data are reported in Tables 5 and 6 for eight temperatures ranging from (293.15 to 363.15) K.

The (p, x, y) diagrams with the interpolated experimental data are plotted in Figs. 1 and 2. From these figures, it clearly appears that the studied binary systems behave classically, with a continuous vapor-liquid critical locus connecting the critical points of the pure compounds involved in the mixture. This corresponds to a type I phase behavior according to the classification of van Konynenburg and Scott [35].

# 4 Modeling and Discussion

## 4.1 The Peng-Robinson Equation of State with Temperature-Dependent Binary Interaction Parameters

The phase behavior data obtained in this study were modeled using the Peng-Robinson equation of state (PR EOS) [36]. The expression of the PR EOS, as applied to a mixture, is given by

$$p = \frac{RT}{v_m - b_m} - \frac{a_m}{v_m(v_m + b_m) + b_m(v_m - b_m)} \quad (3)$$

where p corresponds to the pressure, R the gas constant, T the temperature, $v_m$ the molar volume, $a_m$ and $b_m$ the mixture parameters. Classical (van der Waals) mixing rules were used in this study:

$$a_m = \sum_i \sum_j z_i z_j (1 - k_{ij}(T)) \sqrt{a_i a_j} \quad (4)$$

$$b_m = \sum_i z_i b_i \quad (5)$$

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

Two strategies were used to evaluate the binary interaction parameters:

* The PPR78 group contribution method [37, 38] was employed to predict $k_{ij}(T)$. This model has proven (over a wide range of temperatures, pressures, and compositions) its accuracy and reliability for predicting phase-equilibrium (VLE, LLE, VLLE), enthalpy, heat-capacity changes on mixing and critical points [39] in systems containing hydrocarbons, permanent gases, sulfur compounds, water,
<table><caption>**Table 4** Fluid–fluid phase transition pressures $p_{tr}$ at temperatures $T$ for binary mixtures $CO_2 + 2$-methyl-pentane, as a function of global mole fraction $z_{CO_2} \pm U(z_{CO_2})$ with its expanded uncertainty $U(p_{tr})^{a,b}$</caption><thead><tr><th colspan="3">z<sub>CO₂</sub> = 0.2058 ± 0.0011</th><th colspan="3">z<sub>CO₂</sub> = 0.3993 ± 0.0009</th><th colspan="3">z<sub>CO₂</sub> = 0.5020 ± 0.0008</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>293.36</td><td>1.78</td><td>0.04</td><td>293.16</td><td>2.90</td><td>0.04</td><td>293.46</td><td>3.46</td><td>0.04</td></tr><tr><td>303.05</td><td>1.96</td><td>0.04</td><td>303.15</td><td>3.36</td><td>0.04</td><td>303.05</td><td>3.97</td><td>0.04</td></tr><tr><td>313.45</td><td>2.16</td><td>0.04</td><td>313.35</td><td>3.80</td><td>0.04</td><td>313.75</td><td>4.59</td><td>0.04</td></tr><tr><td>323.74</td><td>2.37</td><td>0.04</td><td>323.14</td><td>4.26</td><td>0.04</td><td>323.04</td><td>5.15</td><td>0.04</td></tr><tr><td>334.04</td><td>2.61</td><td>0.04</td><td>333.04</td><td>4.71</td><td>0.04</td><td>333.54</td><td>5.82</td><td>0.04</td></tr><tr><td>343.73</td><td>2.86</td><td>0.04</td><td>342.83</td><td>5.20</td><td>0.04</td><td>343.93</td><td>6.47</td><td>0.04</td></tr><tr><td>352.73</td><td>3.12</td><td>0.04</td><td>353.13</td><td>5.75</td><td>0.04</td><td>353.53</td><td>7.12</td><td>0.04</td></tr><tr><td>363.32</td><td>3.47</td><td>0.04</td><td>363.32</td><td>6.29</td><td>0.04</td><td>363.32</td><td>7.76</td><td>0.04</td></tr></tbody><thead><tr><th colspan="3">z<sub>CO₂</sub> = 0.6000 ± 0.0005</th><th colspan="3">z<sub>CO₂</sub> = 0.7005 ± 0.0009</th><th colspan="3">z<sub>CO₂</sub> = 0.7697 ± 0.0004</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>293.46</td><td>3.80</td><td>0.04</td><td>293.66</td><td>4.20</td><td>0.04</td><td>293.16</td><td>4.43</td><td>0.04</td></tr><tr><td>303.05</td><td>4.42</td><td>0.04</td><td>303.15</td><td>4.97</td><td>0.04</td><td>302.95</td><td>5.28</td><td>0.04</td></tr><tr><td>313.75</td><td>5.15</td><td>0.04</td><td>313.05</td><td>5.77</td><td>0.04</td><td>312.65</td><td>6.23</td><td>0.04</td></tr><tr><td>323.24</td><td>5.86</td><td>0.04</td><td>323.54</td><td>6.67</td><td>0.04</td><td>323.14</td><td>7.27</td><td>0.04</td></tr><tr><td>333.14</td><td>6.64</td><td>0.04</td><td>333.34</td><td>7.58</td><td>0.05</td><td>333.04</td><td>8.25</td><td>0.04</td></tr><tr><td>342.83</td><td>7.33</td><td>0.04</td><td>342.83</td><td>8.46</td><td>0.04</td><td>343.33</td><td>9.25</td><td>0.04</td></tr><tr><td>352.93</td><td>8.12</td><td>0.04</td><td>352.83</td><td>9.30</td><td>0.04</td><td>352.93</td><td>10.14</td><td>0.04</td></tr><tr><td>363.02</td><td>8.87</td><td>0.04</td><td>363.22</td><td>10.18</td><td>0.04</td><td>363.82</td><td>10.89</td><td>0.08</td></tr></tbody><thead><tr><th colspan="3">z<sub>CO₂</sub> = 0.8210 ± 0.0004</th><th colspan="3">z<sub>CO₂</sub> = 0.8602 ± 0.0003</th><th colspan="3">z<sub>CO₂</sub> = 0.9000 ± 0.0005</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>293.56</td><td>4.68</td><td>0.04</td><td>293.06</td><td>4.82</td><td>0.05</td><td>293.06</td><td>5.05</td><td>0.05</td></tr><tr><td>302.95</td><td>5.59</td><td>0.04</td><td>303.15</td><td>5.87</td><td>0.05</td><td>302.95</td><td>6.15</td><td>0.05</td></tr><tr><td>313.35</td><td>6.64</td><td>0.05</td><td>312.95</td><td>6.92</td><td>0.05</td><td>313.25</td><td>7.37</td><td>0.05</td></tr><tr><td>323.24</td><td>7.69</td><td>0.05</td><td>323.04</td><td>8.01</td><td>0.05</td><td>323.14</td><td>8.53</td><td>0.08</td></tr><tr><td>333.54</td><td>8.74</td><td>0.05</td><td>332.64</td><td>9.07</td><td>0.08</td><td>333.14</td><td>9.28</td><td>0.08</td></tr><tr><td>343.33</td><td>9.76</td><td>0.08</td><td>343.13</td><td>10.06</td><td>0.08</td><td><strong>342.93</strong></td><td><strong>9.75</strong></td><td><strong>0.08</strong></td></tr><tr><td>352.93</td><td>10.47</td><td>0.08</td><td><strong>353.53</strong></td><td><strong>10.54</strong></td><td><strong>0.08</strong></td><td><strong>353.03</strong></td><td><strong>9.90</strong></td><td><strong>0.08</strong></td></tr><tr><td><strong>363.02</strong></td><td><strong>10.88</strong></td><td><strong>0.08</strong></td><td><strong>362.82</strong></td><td><strong>10.67</strong></td><td><strong>0.08</strong></td><td><strong>363.02</strong></td><td><strong>9.37</strong></td><td><strong>0.08</strong></td></tr></tbody><tfoot><tr><td colspan="3">z<sub>CO₂</sub> = 0.9400 ± 0.0005</td><td colspan="3"></td><td colspan="3"></td></tr></tfoot></table><table><thead><tr><th>T/K</th><th>p<sub>tr</sub>/MPa</th><th>U(p<sub>tr</sub>)/MPa</th></tr></thead><tbody><tr><td>293.06</td><td>5.30</td><td>0.05</td></tr><tr><td>302.95</td><td>6.50</td><td>0.05</td></tr><tr><td>313.05</td><td>7.77</td><td>0.04</td></tr><tr><td><strong>322.74</strong></td><td><strong>8.57</strong></td><td><strong>0.08</strong></td></tr><tr><td><strong>333.44</strong></td><td><strong>8.76</strong></td><td><strong>0.08</strong></td></tr><tr><td><strong>343.13</strong></td><td><strong>8.26</strong></td><td><strong>0.08</strong></td></tr></tbody></table>

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

<sup>b</sup>Standard uncertainty $u(T) = 0.1$ K

<sup>c</sup>Level of confidence ≈ 0.95 ($k=2$) for $U(p_{tr})$
<table><caption>**Table 5** Isothermal (p,x or y) data for the CO₂ + 2,2-dimethylbutane binary system at eight different temperatures T interpolated from the original measurements in Table 3</caption><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>1.56</td><td>0.1999</td><td>-</td><td>1.75</td><td>0.1999</td><td>-</td><td>1.97</td><td>0.1999</td><td>-</td><td>2.19</td><td>0.1999</td><td>-</td></tr><tr><td>2.79</td><td>0.4002</td><td>-</td><td>3.22</td><td>0.4002</td><td>-</td><td>3.67</td><td>0.4002</td><td>-</td><td>4.13</td><td>0.4002</td><td>-</td></tr><tr><td>3.31</td><td>0.5001</td><td>-</td><td>3.87</td><td>0.5001</td><td>-</td><td>4.44</td><td>0.5001</td><td>-</td><td>5.05</td><td>0.5001</td><td>-</td></tr><tr><td>3.68</td><td>0.5998</td><td>-</td><td>4.33</td><td>0.5998</td><td>-</td><td>4.99</td><td>0.5998</td><td>-</td><td>5.70</td><td>0.5998</td><td>-</td></tr><tr><td>4.07</td><td>0.7004</td><td>-</td><td>4.85</td><td>0.7004</td><td>-</td><td>5.69</td><td>0.7004</td><td>-</td><td>6.57</td><td>0.7004</td><td>-</td></tr><tr><td>4.41</td><td>0.7700</td><td>-</td><td>5.30</td><td>0.7700</td><td>-</td><td>6.22</td><td>0.7700</td><td>-</td><td>7.19</td><td>0.7700</td><td>-</td></tr><tr><td>4.58</td><td>0.8200</td><td>-</td><td>5.54</td><td>0.8200</td><td>-</td><td>6.58</td><td>0.8200</td><td>-</td><td>7.63</td><td>0.8200</td><td>-</td></tr><tr><td>4.81</td><td>0.8600</td><td>-</td><td>5.79</td><td>0.8600</td><td>-</td><td>6.92</td><td>0.8600</td><td>-</td><td>8.04</td><td>0.8600</td><td>-</td></tr><tr><td>5.05</td><td>0.9000</td><td>-</td><td>6.15</td><td>0.9000</td><td>-</td><td>7.35</td><td>0.9000</td><td>-</td><td>8.41</td><td>0.9000</td><td>-</td></tr><tr><td>5.31</td><td>0.9400</td><td>-</td><td>6.53</td><td>0.9400</td><td>-</td><td>7.80</td><td>0.9400</td><td>-</td><td>8.44</td><td>-</td><td>0.9400</td></tr></tbody><thead><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></thead><tbody><tr><td>2.41</td><td>0.1999</td><td>-</td><td>2.67</td><td>0.1999</td><td>-</td><td>2.99</td><td>0.1999</td><td>-</td><td>3.33</td><td>0.1999</td><td>-</td></tr><tr><td>4.64</td><td>0.4002</td><td>-</td><td>5.17</td><td>0.4002</td><td>-</td><td>5.71</td><td>0.4002</td><td>-</td><td>6.29</td><td>0.4002</td><td>-</td></tr><tr><td>5.69</td><td>0.5001</td><td>-</td><td>6.34</td><td>0.5001</td><td>-</td><td>7.01</td><td>0.5001</td><td>-</td><td>7.70</td><td>0.5001</td><td>-</td></tr><tr><td>6.43</td><td>0.5998</td><td>-</td><td>7.17</td><td>0.5998</td><td>-</td><td>7.92</td><td>0.5998</td><td>-</td><td>8.71</td><td>0.5998</td><td>-</td></tr><tr><td>7.44</td><td>0.7004</td><td>-</td><td>8.30</td><td>0.7004</td><td>-</td><td>9.16</td><td>0.7004</td><td>-</td><td>9.96</td><td>0.7004</td><td>-</td></tr><tr><td>8.18</td><td>0.7700</td><td>-</td><td>9.10</td><td>0.7700</td><td>-</td><td>9.93</td><td>0.7700</td><td>-</td><td>10.43</td><td>0.7700</td><td>-</td></tr><tr><td>8.66</td><td>0.8200</td><td>-</td><td>9.55</td><td>0.8200</td><td>-</td><td>10.09</td><td>0.8200</td><td>-</td><td>10.40</td><td>-</td><td>0.8200</td></tr><tr><td>8.97</td><td>0.8600</td><td>-</td><td>9.61<sup>a</sup></td><td>0.8600<sup>a</sup></td><td>0.8600<sup>a</sup></td><td>9.98</td><td>-</td><td>0.8600</td><td>10.04</td><td>-</td><td>0.8600</td></tr><tr><td>9.13</td><td>0.9000</td><td>-</td><td>9.38</td><td>-</td><td>0.9000</td><td>9.04</td><td>-</td><td>0.9000</td><td></td><td></td><td></td></tr><tr><td>7.95</td><td>-</td><td>0.9400</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

fatty acids and freons. The PPR78 model has also been successfully applied to phase envelope prediction of petroleum fluids. Structurally speaking, the PPR78 model combines the well-established PR EOS and a group-contribution method to estimate the temperature-dependent binary interaction parameters, $k_{ij}(T)$, which are key-parameters of the model, accounting for molecular interactions between molecules i and j. Using the group-contribution formalism, each molecule is seen as an aggregate of elementary molecular groups interacting each other. According to the group-contribution concept, the expression of the $k_{ij}(T)$ quantity involves group-interaction parameters revealing the nature and the strengths of the physico-chemical interactions between elementary groups. For the readers familiar with advanced EOS/g$^E$ mixing rules, it can be stated that the PPR78 model is based on the UHVM (Unified Huron-Vidal Michelsen) [40] mixing rules, in which a linear mixing rule was used for $b_m$ and a Van Laar type activity coefficient model was selected.

<figure><img src="image_3.png" /></figure>

<footnote><sup>a</sup>Critical point</footnote>
<table><caption>**Table 6** Isothermal (p,x or y) data for the CO₂ + 2-methylpentane binary system at eight different temperatures T interpolated from the original measurements in Table 4</caption><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>1.78</td><td>0.2058</td><td>—</td><td>1.96</td><td>0.2058</td><td>—</td><td>2.15</td><td>0.2058</td><td>—</td><td>2.36</td><td>0.2058</td><td>—</td></tr><tr><td>2.90</td><td>0.3993</td><td>—</td><td>3.35</td><td>0.3993</td><td>—</td><td>3.79</td><td>0.3993</td><td>—</td><td>4.25</td><td>0.3993</td><td>—</td></tr><tr><td>3.44</td><td>0.5020</td><td>—</td><td>3.97</td><td>0.5020</td><td>—</td><td>4.55</td><td>0.5020</td><td>—</td><td>5.17</td><td>0.5020</td><td>—</td></tr><tr><td>3.77</td><td>0.6000</td><td>—</td><td>4.43</td><td>0.6000</td><td>—</td><td>5.11</td><td>0.6000</td><td>—</td><td>5.86</td><td>0.6000</td><td>—</td></tr><tr><td>4.16</td><td>0.7005</td><td>—</td><td>4.97</td><td>0.7005</td><td>—</td><td>5.78</td><td>0.7005</td><td>—</td><td>6.64</td><td>0.7005</td><td>—</td></tr><tr><td>4.43</td><td>0.7697</td><td>—</td><td>5.30</td><td>0.7697</td><td>—</td><td>6.28</td><td>0.7697</td><td>—</td><td>7.27</td><td>0.7697</td><td>—</td></tr><tr><td>4.65</td><td>0.8210</td><td>—</td><td>5.60</td><td>0.8210</td><td>—</td><td>6.64</td><td>0.8210</td><td>—</td><td>7.67</td><td>0.8210</td><td>—</td></tr><tr><td>4.83</td><td>0.8602</td><td>—</td><td>5.87</td><td>0.8602</td><td>—</td><td>6.94</td><td>0.8602</td><td>—</td><td>8.03</td><td>0.8602</td><td>—</td></tr><tr><td>5.07</td><td>0.9000</td><td>—</td><td>6.17</td><td>0.9000</td><td>—</td><td>7.37</td><td>0.9000</td><td>—</td><td>8.51</td><td>0.9000</td><td>—</td></tr><tr><td>5.31</td><td>0.9400</td><td>—</td><td>6.53</td><td>0.9400</td><td>—</td><td>7.78</td><td>0.9400</td><td>—</td><td>8.60</td><td>—</td><td>0.9400</td></tr></tbody><thead><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></thead><tbody><tr><td>2.59</td><td>0.2058</td><td>—</td><td>2.85</td><td>0.2058</td><td>—</td><td>3.13</td><td>0.2058</td><td>—</td><td>3.47</td><td>0.2058</td><td>—</td></tr><tr><td>4.72</td><td>0.3993</td><td>—</td><td>5.21</td><td>0.3993</td><td>—</td><td>5.76</td><td>0.3993</td><td>—</td><td>6.28</td><td>0.3993</td><td>—</td></tr><tr><td>5.79</td><td>0.5020</td><td>—</td><td>6.42</td><td>0.5020</td><td>—</td><td>7.09</td><td>0.5020</td><td>—</td><td>7.75</td><td>0.5020</td><td>—</td></tr><tr><td>6.63</td><td>0.6000</td><td>—</td><td>7.37</td><td>0.6000</td><td>—</td><td>8.11</td><td>0.6000</td><td>—</td><td>8.89</td><td>0.6000</td><td>—</td></tr><tr><td>7.56</td><td>0.7005</td><td>—</td><td>8.48</td><td>0.7005</td><td>—</td><td>9.33</td><td>0.7005</td><td>—</td><td>10.17</td><td>0.7005</td><td>—</td></tr><tr><td>8.26</td><td>0.7697</td><td>—</td><td>9.24</td><td>0.7697</td><td>—</td><td>10.16</td><td>0.7697</td><td>—</td><td>10.86</td><td>0.7697</td><td>—</td></tr><tr><td>8.70</td><td>0.8210</td><td>—</td><td>9.74</td><td>0.8210</td><td>—</td><td>10.48</td><td>0.8210</td><td>—</td><td>10.88</td><td>—</td><td>0.8210</td></tr><tr><td>9.13</td><td>0.8602</td><td>—</td><td>10.06</td><td>0.8602</td><td>—</td><td>10.53</td><td>—</td><td>0.8602</td><td>10.67</td><td>—</td><td>0.8602</td></tr><tr><td>9.30</td><td>0.9000</td><td>—</td><td>9.75</td><td>—</td><td>0.9000</td><td>9.91</td><td>—</td><td>0.9000</td><td>9.35</td><td>—</td><td>0.9000</td></tr><tr><td>8.77</td><td>—</td><td>0.9400</td><td>8.26</td><td>—</td><td>0.9400</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr></tbody></table>

* For a binary system 1+2, each pure component was considered as a single elementary group and the following expression, derived from the PPR78 model, was used:

$$k_{ij}(T) = k_{12}(T) = \frac{A_{12} \left(\frac{298.15}{T}\right)^{(B_{12}/A_{12})-1} - \left(\frac{\sqrt{a_1}}{b_1} - \frac{\sqrt{a_2}}{b_2}\right)^2}{2 \frac{\sqrt{a_1 a_2}}{b_1 b_2}} \quad (6)$$

Whereas the first approach is purely predictive, this second approach involves regressing the parameters $A_{12}$ and $B_{12}$ against the experimental data to improve the description of the investigated systems. This strategy thus led to the best possible performance of the PR EOS with classical mixing rules.
<figure><img src="image_4.png" /><figcaption>Fig. 1 (p, x<sub>CO₂</sub>, y<sub>CO₂</sub>) isothermal diagrams for CO₂+2,2-dimethylbutane with interpolated experimental phase transition points measured in this work. ○: bubble points, ●: dew points, ▲: critical point. 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" /></figure>
<figure><img src="image_6.png" /><figcaption>Fig. 2 (p, x<sub>CO₂</sub>, y<sub>CO₂</sub>) isothermal diagrams for CO₂ + 2-methylpentane with interpolated experimental phase transition points measured in this work. ○: 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>
<table><caption>**Table 7** Mean absolute deviations in liquid and gas phase mole fractions obtained from two modelling methods: PPR78 model (purely predictive approach) and PR EOS with $k_{ij}(T)$ regressed against measured data through Eq. 6</caption><thead><tr><th rowspan="2">Binary system</th><th colspan="2">PPR78 (prediction)</th><th colspan="4">PR + kij(T) (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>CO<sub>2</sub>(1) + 22m4(2)</td><td>0.018</td><td>0.014</td><td>132.1</td><td>123.2</td><td>0.013</td><td>0.012</td></tr><tr><td>CO<sub>2</sub>(1) + 2m5(2)</td><td>0.036</td><td>0.004</td><td>131.6</td><td>135.1</td><td>0.015</td><td>0.008</td></tr></tbody></table>

$$ ^{a}|\Delta x| = |x_{1,\text{exp}} - x_{1,\text{cal}}| = |x_{2,\text{exp}} - x_{2,\text{cal}}| $$

$$ ^{b}|\Delta y| = |y_{1,\text{exp}} - y_{1,\text{cal}}| = |y_{2,\text{exp}} - y_{2,\text{cal}}| $$

## 4.2 Analysis and Discussion

The parameters $A_{12}$ and $B_{12}$ were regressed against the smoothed experimental data to minimize the average absolute deviations between experimental and calculated liquid phase and gas phase compositions. The modelling results are summarized in Table 7 with the deviations obtained by the two modelling methods and the optimal values found for parameters $A_{12}$ and $B_{12}$.

The calculated isothermal bubble and dew curves are plotted in Fig. 1 and 2. The results obtained via the purely predictive PPR78 approach are very satisfactory. Slightly better descriptions of the phase behavior of the studied mixtures can be reached by considering each molecule as a single group. The fitted parameters $A_{12}$ and $B_{12}$ are provided in Table 7. Using these parameters, the value of $k_{ij}(T)$ increases more or less linearly from 0.111 (293.15 K) to 0.143 (363.15 K) for the binary system CO₂ + 22m4 whereas it varies linearly from 0.112 (293.15 K) to 0.140 (363.15 K) for the system CO₂ + 2m5. Such values are comparable to $k_{ij}$ reported in the literature [19, 41] for similar systems modeled with the PR EOS.

## 5 Conclusion

The binary systems CO₂ + 2,2-dimethylbutane and CO₂ + 2-methylpentane were investigated using a high-pressure cell and a synthetic method. Saturation pressures were visually detected between 293.15 K and 363.15 K.

The main conclusion is that both systems behave classically, presenting continuous vapor–liquid critical locus without liquid–liquid phase splitting in the investigated temperature range.

The PR EOS with classical mixing rules is perfectly able to describe the phase equilibria of the studied systems provided that a temperature-dependent binary interaction parameter ($k_{ij}$) is used.

This study completes previous works regarding to the phase behavior of CO₂ + branched alkane systems. With the data generated in this work, all existing
branched alkanes composed of 4, 5 and 6 carbon atoms were studied in mixture with CO₂. Further investigations remain to be carried out with heavier branched alkanes.

**Author Contributions** Material preparation and measurements were performed by J.P.B. and J.L.D. J.N.J., S.V. and K.A.A. performed model implementation and optimisation. J.L.D. and S.V. supervised the work. The first draft of the manuscript was written by S.V. and J.L.D. and all authors commented on previous versions of the manuscript. All authors read and approved the final version.

**Funding** Open access funding provided by Université Paris-Saclay. No funds, grants, or other support were received for this study.

**Data Availability** The data measured in this work are tabulated in the paper.

**Declarations**

**Conflict of interest** The authors declare no competing interests.

**Open Access** This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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