# Validation of Synthetic Method Phase Equilibria Measurements: Re-examination of CO + Methylcyclopentane, CO + 2,2-Dimethylbutane, and Benchmarking with CO + Toluene

Jean-Luc Daridon, Jean-Patrick Bazile, Jean-Noël Jaubert, Stéphane Vitu

► To cite this version:

Jean-Luc Daridon, Jean-Patrick Bazile, Jean-Noël Jaubert, Stéphane Vitu. Validation of Synthetic Method Phase Equilibria Measurements: Re-examination of CO + Methylcyclopentane, CO + 2,2-Dimethylbutane, and Benchmarking with CO + Toluene. Fluid Phase Equilibria, 2026, 605, pp.114664. 10.1016/j.fluid.2026.114664. hal-05463715

HAL Id: hal-05463715

https://hal.univ-lorraine.fr/hal-05463715v1

Submitted on 17 Jan 2026

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
<figure><img src="image_2.png" /></figure>

# Validation of synthetic method for phase equilibria measurements:
Re-examination of CO₂ + methylcyclopentane, CO₂ + 2,2-dimethylbutane,
and benchmarking with CO₂ + toluene

Jean-Luc Daridon<sup>a,*</sup> ID, Jean-Patrick Bazile<sup>a</sup>, Jean-Noël Jaubert<sup>b</sup>, Stéphane Vitu<sup>c,d</sup>

## ARTICLE INFO

Keywords:

VLE

CO₂

Methylcyclopentane

2,2 dimethylbutane

## ABSTRACT

Recent publications have reported phase equilibrium data for CO₂ + methylcyclopentane (MCP) and CO₂ + 2,2-dimethylbutane using static-analytical sampling methods that are inconsistent with previously published synthetic-method data. To verify the reliability of our earlier measurements, we have repeated vapor–liquid equilibrium (VLE) experiments for both CO₂ + MCP and CO₂ + 2,2-dimethylbutane in the range 20–90 °C using a high-pressure variable-volume PVT cell with visual observation. Our new data agree within 1–2 bar with the values previously reported by our group, confirming the reproducibility of the synthetic method. To further validate our methodology, we also investigated the CO₂ + toluene system, which has been extensively studied in the literature. Our experimental results are in agreement with reference data, thereby confirming the accuracy of the synthetic technique and of the procedures used for mixture preparation and bubble-point detection. These results support the conclusion that the discrepancies between our data and those obtained by static-analytical methods cannot be attributed to errors inherent to the synthetic technique.

## 1. Introduction

Phase equilibrium data for CO₂ + hydrocarbon mixtures are of central importance in chemical engineering and applied thermodynamics. Such data are essential for the development of accurate equations of state and predictive group-contribution models [1–4]. They also play a decisive role in industrial applications such as carbon capture, utilization and storage (CCUS), enhanced oil recovery (EOR), and supercritical fluid extraction, where solvent performance depends strongly on the solubility of the solute in supercritical CO₂.

The experimental determination of fluid phase equilibria at elevated pressures is challenging. It requires precise mixture preparation and/or chemical analysis of coexisting phases, accurate pressure–temperature control, and unambiguous detection of phase transitions or separations. Over the years, a wide range of experimental techniques have been developed, and several reviews have provided detailed classifications [5]. The choice of method depends not only on the characteristics of the mixture (binary, ternary, or multicomponent) and its complexity

(symmetric or asymmetric), but also on the type of property measured (phase equilibrium or transition) and the range of temperature–pressure conditions investigated.

As summarized by Deiters and Schneider [6], experimental methods are generally classified as analytical or synthetic, depending on the variables observed. Analytical methods establish equilibrium at a chosen pressure (P)–temperature (T) condition, followed by determination of the phase compositions through either *in situ* or *ex situ* analyses. Their main advantage is that they provide direct measurement of both vapor and liquid compositions, thereby enabling a complete phase diagram to be constructed. However, these techniques require highly accurate analytical procedures and careful sampling to avoid disturbing equilibrium. Potential sources of uncertainty include incomplete equilibration prior to sampling, phase dispersion, improper phase separation, perturbation of equilibrium upon sample withdrawal, and condensation or evaporation within the sampling line. In addition, fluctuations in temperature or pressure may shift equilibria, leading to further uncertainty.

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

<footnote><sup>b</sup> Université de Lorraine, CNRS, LRGP, F-54000 Nancy, France</footnote>

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

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

<footnote>* Corresponding author.
E-mail address: jean-luc.daridon@univ-pau.fr (J.-L. Daridon).</footnote>
<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Comparison of experimental vapor-liquid equilibria data for the carbon dioxide + Methylcyclopentane system at 343.15 K: ●, Vitu et al. [8]; X, Sima et al. [9].</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Comparison of experimental vapor-liquid equilibria data for the carbon dioxide + 2,2-Dimethylbutane system at 313.15 K: ●, Bazile et al. [11]; X, Sima et al. [10].</figcaption></figure>

Synthetic methods, by contrast, involve preparing a system of known overall composition and observing its phase behavior directly or indirectly. These techniques do not require compositional analysis and avoid perturbing the system during measurement. When based on direct visual observation, they allow straightforward detection of phase transitions and can be extended to multiphase equilibria involving several liquid or solid phases. Nevertheless, synthetic methods also have limitations. Detecting phase changes relies on the formation of a sufficient amount of

the new phase, which means that the technique typically identifies points slightly below the exact phase boundary [6]. Nucleation delays may also cause underestimation of transition conditions, while visual detection can involve subjective judgment, especially near critical points. Moreover, such methods are restricted to transparent systems unless specialized optical techniques (e.g., wavelength-specific imaging [7]) are employed. Uncertainties in synthetic methods arise primarily from mixture preparation, phase transition detection, and P–T measurement accuracy.

Ideally, both approaches should converge toward the same phase equilibrium data. However, for the binary systems CO₂ + methylcyclopentane significant and systematic deviations were observed between measurements carried out by two different techniques [8,9]. As shown in the pressure (P) composition (xCO₂) phase diagram in Fig. 1, Sima et al. [9], obtained results using a static-analytical approach that differ systematically by 10–15 bar from those of Vitu et al. [8] who employed a synthetic method. Such deviations are far greater than the expected uncertainties of either technique and suggest possible biases in one or both datasets. This suspicion of bias in one of the two measurement series was reinforced by the recent publication of two additional studies from these same groups on 2,2-dimethylbutane, which revealed similar magnitudes of systematic deviation of about 10–15 bar. This is illustrated in Fig. 2, which presents the analytical measurements reported by Sima et al. [10] at 313.15 K, together with the interpolated synthetic data reported by Bazile et al. [11] in the same year.

Large inconsistencies between equilibrium data obtained with analytical (composition-based) and synthetic (visual observation) techniques are unusual. When they occur, several strategies may be applied: (i) replicate measurements at critical points of discrepancy (same P–T–x) to distinguish between systematic and random deviations, (ii) assess possible metastability or nucleation delays, (iii) ensure true equilibrium was reached before sampling (analytical method) or before declaring the onset of phase separation (synthetic method), and (iv) apply thermodynamic consistency tests to evaluate the reliability of datasets. Unfortunately, such consistency tests cannot be applied to synthetic data and are generally unsuitable when one component is supercritical, which is the case here. In their publication, Sima et al. [9] attribute the significant deviations observed between synthetic and analytical methods for CO₂ + methyl cyclopentane to a lack of rigor caused by the interpolation of isoplethic VLE data in the measurements reported by Vitu et al. [8]. To assess this claim, which we consider essentially unfounded, we present in this paper a validation of synthetic measurements for the phase equilibria of CO₂–methylcyclopentane and CO₂–2,2-dimethylbutane at temperatures above the critical temperature of CO₂. As thermodynamic consistency tests could not be applied under these conditions, our analysis focused on the first two verification strategies. To this end, we carried out new measurements using a synthetic method on the binary systems CO₂–methylcyclopentane and CO₂–2,2-dimethylbutane. As a preliminary step, and to validate our measurement protocol, covering both mixture preparation and the detection of new phases, we conducted measurements on the CO₂ + toluene system at a single temperature and multiple compositions. This system was selected because it has been widely investigated in the literature [12–20]. In addition, to minimize errors associated with mixture preparation, we modified the liquid injection process in our experimental setup, as this step is critical

<table><caption>**Table 1**

Pure component description.</caption><thead><tr><th>Chemical Name</th><th>CAS</th><th>Source</th><th>MW (g.mol<sup>-1</sup>)</th><th>Purity<sup>a</sup> supplier</th><th>Purification Method</th><th>Water Content</th></tr></thead><tbody><tr><td>Carbon dioxide</td><td>124-38-9</td><td>Linde</td><td>44.0095</td><td>0.99995</td><td>None</td><td>&lt;5 ppmv</td></tr><tr><td>Toluene</td><td>108-88-3</td><td>ACROS</td><td>92.1384</td><td>0.999</td><td>None</td><td>60 ppm</td></tr><tr><td>Methylcyclopentane</td><td>96-37-7</td><td>SIGMA</td><td>84.1595</td><td>0.999</td><td>None</td><td>38.3 ppm</td></tr><tr><td>2,2-Dimethylbutane</td><td>75-83-2</td><td>TCI</td><td>86.1754</td><td>0.996</td><td>None</td><td>34.8 ppm</td></tr></tbody></table>

<footnote>a Mass fraction purity.</footnote>
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Schematic diagram of the liquid injection device. (a) Needle in injection position; (b) closure of the needle valve before needle withdrawal. 1, gas inlet; 2, liquid inlet; 3, septum.</figcaption></figure>

for ensuring reliable results. Systems were then observed under saturation conditions corresponding to the feed composition $z_{CO_2}$ previously reported by analytical measurements, allowing us to visualize the system under comparable conditions. This readily allows verification of whether a system is at saturation under given $p, T$ conditions.

## 2. Experimental section

### 2.1. Materials

The sources and purities of the hydrocarbons and $CO_2$ used in preparing the investigated mixtures are provided in Table 1. Chemical purities were verified using certificates of analysis supplied by the manufacturers, and all components were employed without additional purification. In addition, the water content was checked using a Karl-Fischer analysis, and the results are reported in Table 1.

### 2.2. Apparatus and method

The synthetic-visual experiments were performed in a full-visibility cell designed with negligible dead volume. The experimental setup has been extensively described in previous publications [21–24]. The core of the system is a high-pressure volumetric cell consisting of a horizontal stainless-steel cylinder equipped with a movable piston and two sapphire windows: one on the front for direct visual observation and one on the side for illumination via an optical fiber. A video camera mounted on an endoscope provides continuous monitoring of phase transitions across the entire fluid sample. Pressure is generated by manually adjusting the position of a piston inside the high-pressure cylinder.

The PVT cell operates at pressures up to 100 MPa and within a temperature range of 293–373 K. Pressure is monitored using a gauge located inside the cell to further reduce dead volumes. Since the sensor is sensitive to temperature variations, it is calibrated as a function of temperature against a primary standard, with an uncertainty below 0.02 %. Thermal regulation is achieved by circulating a heat-transfer fluid through three integrated flow lines connected to a thermostatic bath

with a stability of ±0.02 K. Fluid temperature is measured using a Pt100 probe with a standard uncertainty of $u(T) = 0.1$ K. To ensure both thermal and chemical equilibrium during phase-change measurements, a magnetic stirrer is used to continuously homogenize the sample during experiments.

Because mixture preparation is a critical step, the procedure for determining the injected liquid mass was modified compared to previous studies. Specifically, the dual-way valve used for injecting liquid and gas was slightly redesigned to incorporate a septum positioned just before the valve needle. In this configuration, the liquid is injected under vacuum with a syringe whose needle passes through the septum and is positioned just behind the valve needle in the open position, as illustrated in Fig. 3. After injection, the needle is slightly withdrawn to allow the valve to close, then removed from the septum and weighed. Using this procedure, the injected liquid mass ($m_{L}$) is determined by double weighing the syringe. This new configuration was initially developed for preparing mixtures with small quantities of hydrocarbon solutes in excess $CO_2$, enabling the study of partial molar volumes at infinite dilution in binary $CO_2$–hydrocarbon mixtures [25]. In the present work, it has been extended to test our previous method of injection. The injected masses of $CO_2$ ($m_{CO_2}$) are determined by direct weighing using a high-capacity analytical balance. To ensure accuracy, $CO_2$ is first loaded into a small reservoir tank placed on the balance and connected to the PVT cell via lightweight, flexible high-pressure PEEK tubing (1/32" diameter). This configuration prevents disturbances to the balance during injection. In addition, $CO_2$ is maintained in liquid–vapor equilibrium within the reservoir to stabilize pressure and avoid gas mass variation in the connecting line. The uncertainties in the injected masses

<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Phase equilibrium measurements for the $CO_2$–toluene system at 323.15 K compared with literature data for benchmarking. ○, This work; ◇, Prausnitz and Benson [12]; ■, Fink and Hershey [13]; ▲, Tochigi et al. [15]; +, Laz-Zaroni et al. [16]; ×, Sanchez-Vicente et al. [20]; line, REFPROP [27].</figcaption></figure>

**Table 2**

Bubble point pressure $p_b$ ± $U(p_b)$ª measured at fixed temperature $T$ᵇ and feed composition $z_{CO_2}$ ± $U(z_{CO_2})$ᵇ (in mol%) by the synthetic method for different binary systems.

<table><thead><tr><th colspan="3">CO<sub>2</sub> + Toluene</th><th colspan="3">CO<sub>2</sub> + Methylcyclopentane</th><th colspan="3">CO<sub>2</sub> + 2,2-Dimethylbutane</th></tr><tr><th>T / K</th><th>z<sub>CO<sub>2</sub></sub></th><th>p<sub>b</sub> / bar</th><th>T / K</th><th>z<sub>CO<sub>2</sub></sub></th><th>p<sub>b</sub> / bar</th><th>T / K</th><th>z<sub>CO<sub>2</sub></sub></th><th>p<sub>b</sub> / bar</th></tr></thead><tbody><tr><td>323.15</td><td>20.11 ± 0.15</td><td>26.4 ± 0.6</td><td>323.15</td><td>45.00 ± 0.09</td><td>55.3 ± 0.6</td><td>313.15</td><td>47.84 ± 0.08</td><td>40.1 ± 0.6</td></tr><tr><td>323.15</td><td>39.99 ± 0.12</td><td>49.5 ± 0.6</td><td>363.15</td><td>62.97 ± 0.06</td><td>107.0 ± 0.6</td><td>323.15</td><td>66.01 ± 0.06</td><td>62.0 ± 0.6</td></tr><tr><td>323.15</td><td>50.00 ± 0.07</td><td>59.4 ± 0.6</td><td>343.15</td><td>67.26 ± 0.06</td><td>91.8 ± 0.6</td><td>353.15</td><td>72.84 ± 0.06</td><td>94.2 ± 0.6</td></tr><tr><td>323.15</td><td>60.01 ± 0.06</td><td>68.0 ± 0.6</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>323.15</td><td>70.01 ± 0.06</td><td>75.3 ± 0.6</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr></tbody></table>

<footnote>ª Level of confidence ≈0.95 (k = 2) for $U(p_b)$ and $U(z_{CO_2})$.</footnote>

<footnote>ᵇ Standard uncertainty $u(T) = 0.1$ K.</footnote>
<figure><img src="image_7.png" /><figcaption>Fig. 5. Comparison of new measurements with vapor-liquid equilibria data for the carbon dioxide + Methylcyclopentane system: ●, This work; ●, Vitu et al. [8]; ×, Sima et al. [9] with visualization of the cell at these conditions. a) T = 323.15 K, zCO₂ = 45.00%; b) T = 363.15 K, zCO₂ = 62.97%; c) T = 343.15 K, zCO₂ = 67.26%.</figcaption></figure>

are <0.005 g for both components. The combined standard uncertainty in the CO₂ molar fraction (zCO₂) of the synthesized mixture, is obtained from:

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

After loading the cell, the pressure is increased at constant bath

temperature to reach a monophasic state, and is subsequently decreased stepwise until the appearance of a second phase. This procedure is repeated several times, each time with a smaller pressure decrement (Δp) between steps, in order to refine the transition pressure ptrans. The standard uncertainty in observed phase transition pressures, u(pobs), is 0.02 MPa for bubble points far from critical conditions and 0.04 MPa near the critical region or for dew points. Including contributions from
<figure><img src="image_8.png" /><figcaption>Fig. 6. Visualization of the cell filled with the CO₂ + methylcyclopentane mixture with zCO₂ = 45.00 % at T = 323.15 K just below the bubble point pressure. O, This work; ●, Vitu et al. [8]; X, Sima et al. [9].</figcaption></figure>

pressure sensor, temperature control and measurement, the standard uncertainty in measurement of transition pressure uₘ(ptrans) is evaluated according to the Guide to the Expression of Uncertainty in Measurement [26] as:

$$u_m(p_{\text{trans}}) = \left( u^2(p_{\text{obs}}) + u^2(p_{\text{sensor}}) + \left[ \left( \frac{\partial p_{\text{trans}}}{\partial T} \right) u(T) \right]^2 \right)^{1/2} \quad (2)$$

In addition to the measurement uncertainty, the propagation of composition uncertainty in the transition pressure uₓ(ptrans) must be considered. This additional contribution should be evaluated by accounting for uncertainties in the weighed sample masses and the purities of both components. However, as the chemical purity of the used carbon dioxide is high only the hydrocarbon impurities were considered so that. Assuming a rectangular distribution for the sample impurities (xsp_L) for the liquid component and neglecting the contribution of impurities in the CO₂ owing to its very high purity, the additional standard uncertainty can be estimated as:

$$u_x^2(w) = \left[ \left( \frac{\partial p_{\text{trans}}}{\partial z_{\text{CO}_2}} \right) u(z_{\text{CO}_2}) \right]^2 + \left[ (1 - z_{\text{CO}_2}) \frac{1 - x_{\text{sp},L}}{\sqrt{3}} \left( \frac{\partial p_{\text{trans}}}{\partial x_{\text{sp},L}} \right) \right]^2 \quad (3)$$

The estimation of the uncertainty component attributable to impurities in hydrocarbons remains a central challenge, as the identities of the impurities are often unknown. To obtain an approximate estimate of the contribution of sample impurities to the uncertainty in Eq. (1), we assumed that the impurities belong to the same chemical family as the hydrocarbon of interest, with a molecular weight differing by 20 %. Based on this assumption, the derivative was evaluated using a finite-difference approach, by calculating phase equilibria with the PPR78 [1–4] model for both the pure hydrocarbon and a binary system contaminated with 1 % impurity.

## 3. Results

### 3.1. CO₂ + toluene: validation system

To assess the reliability of the synthetic technique employed, measurements were first carried out on the CO₂ + toluene binary system at 323.15 K, a reference system extensively documented in the literature. The results are reported in Table 2 and illustrated in Fig. 4, which compares the new experimental data with literature values at the same temperature [13,15], thereby displaying the complete phase diagram for this system. Table 2 also includes new experimental data for the two controversial binary systems, CO₂ + methylcyclopentane and CO₂ + 2, 2-dimethylbutane, together with their expanded uncertainties.

A close inspection of Fig. 4 demonstrates consistency between the present measurements and literature data. In particular, comparison with the data of Fink and Hershey [13] yields a mean absolute deviation of approximately 1.2 bar, whereas comparison with the data of Tochigi et al. [15] shows a mean deviation of 2.5 bar, with maximum deviations of 1.4 and 3.5 bar, respectively. An average absolute deviation of 2.6 bar

is observed between our data and those reported by Lazzaroni et al. [16], with a maximum deviation of 3.4 bar, representing the largest discrepancy among the data sets considered. In contrast, the comparison with the Sanchez-Vicente et al. [20] data set shows very good agreement with our measurements, with an average deviation of 0.5 bar and a maximum deviation of 1 bar. It should also be noted that the data sets from the cited studies differ substantially from one another, with a maximum deviation of up to 6.5 bar observed from the data of Tochigi et al. [15] and Lazzaroni et al. [16], which further highlights the reliability and quality of our results. The values provided by REFPROP, the NIST Standard Reference Database [27], were also included in Fig. 4. A very good agreement can be observed between the measurements and the values calculated with REFPROP, except for composition between 60 and 80 % where REFPROP calculations underestimate the bubble point pressure. The average deviation is on the order of 0.6 bar relative to the REFPROP predictions.

The literature data used for comparison were obtained using four distinct techniques: two analytical and two synthetic methods in order to avoid bias when comparing them with our measurements, which were obtained using a visual synthetic method. Fink and Hershey [13] employed a dynamic analytical method, in which both phases are continuously recirculated until equilibrium is reached, after which samples are taken for composition analysis. Tochigi et al. [15] used a static analytical approach, in which the system is agitated in a closed cell to ensure liquid-vapor equilibrium before sampling both phases. In contrast, Lazzaroni et al. [16] and Sanchez-Vicente et al. [20] applied visual synthetic techniques with different objectives. Lazzaroni et al. [16] brought the system to equilibrium and visually monitored the liquid-vapor interface to quantify the phase volumes and deduce equilibrium compositions. Sanchez-Vicente et al. [20], on the other hand, determined phase transition conditions by observing the first appearance of a gas bubble or liquid drop in a single-phase system, thereby identifying the bubble or dew points respectively.

This new series of measurements on the CO₂ + toluene binary system confirms that the synthetic method employed in our laboratory does not introduce systematic biases, neither pressure deviations of roughly 15 bar in bubble-point determination nor compositional errors of approximately 10 % in mole fraction, such as those observed between our data [8,11] and the analytic measurements of Sima et al. [9,10] for the CO₂ + methylcyclopentane and CO₂ + 2,2-dimethylbutane binary systems. These significant discrepancies are most likely due to specific, transient issues, such as incorrect calibration of pressure or temperature probes, which inevitably induce systematic measurement variations.

Having validated our experimental protocol and equipment on the CO₂ + toluene system, we then applied the same methodology to the systems of interest, namely CO₂ + methylcyclopentane and CO₂ + 2,2-dimethylbutane, using the same methodology.

### 3.2. CO₂ + methylcyclopentane

New synthetic measurements were performed under three selected conditions, covering temperatures between 293 K and 373 K and varying mixture compositions. The number of experimental points was deliberately limited to three, as the aim was not to reconstruct the full phase diagram but rather to assess the reproducibility of the results. The corresponding data are reported in Table 2, and the experimental points are plotted in Fig. 5a-c. For comparison, each figure also includes the data reported by Sima et al. [9], which correspond to liquid-phase compositions at saturation determined analytically after equilibration, sampling, and analysis.

Their experiments were performed using a high-pressure phase equilibrium apparatus with a variable-volume sapphire cell and an integrated sampling system. Using this apparatus, a static-analytical method was employed, allowing sampling of both liquid and vapor phases for analysis by gas chromatography. In addition, their setup included a liquid circulation loop that allowed the measurement of
<figure><img src="image_9.png" /><figcaption>**Fig. 7.** Comparison of new measurements with vapor-liquid equilibria data for the carbon dioxide + 2,2-Dimethylbutane system: ○, This work; ●, Bazile et al. [11]; X, Sima et al. [10] with visualization of the cell at these conditions. a) T = 313.15 K, zCO₂ = 47.84%; b) T = 323.15 K, zCO₂ = 66.01%; c) T = 353.15 K, zCO₂ = 72.84%.</figcaption></figure>

liquid-phase density using a vibrating-tube densimeter.

The new measurements show very good agreement with our previous results [8] obtained using the synthetic method. This confirms the reproducibility of the technique and eliminates the possibility that the deviations with data reported by Sima et al. [9] were due to calibration issues. In this work, particular care was taken to verify all instrument calibrations prior to experimentation, and the procedure was validated using the reference CO₂ + toluene system as shown in the previous paragraph.

These additional measurements confirm that a substantial deviation exists between our data and those reported by Sima et al. [9]: approximately 12–15 bar in pressure, corresponding to about 10–15 % in composition. A major advantage of the synthetic method using a full visibility cell is the ability to directly observing the system under controlled pressure–temperature conditions. Therefore, we reproduced their reported conditions in our apparatus and allowed the system to reach equilibrium. Under these conditions, clear phase separation was observed, with the vapor phase occupying a substantial fraction of the
cell volume, confirming that the compositions given by Sima et al. were far from the bubble-point condition. For each condition studied here, a photo was taken and added to the graphs in Fig. 5. From these figures, one can obtain a rough estimate of the vapor volume fraction, which in all the tested cases is greater than 50 %. Accordingly, the observed deviations cannot be ascribed to errors in detecting vapor onset in our experiments.

In order to compare the images shown in Fig. 5 with the measurement conditions of the bubble point in the full-visibility PVT cell, an image (for a single composition) of the fluid inside the cell taken at the bubble point is provided in Fig. 6. In this figure, very small gas bubbles can be observed; they appear as tiny streaks because the fluid is in motion due to the agitation from the magnetic stir bar, which is kept continuously in operation throughout the experiment. To visualize this more clearly, a short video corresponding to a depletion just below the bubble point has been included in the supplementary material.

### 3.3. CO₂ + 2,2-dimethylbutane

Because deviations comparable to those observed for the CO₂ + methylcyclopentane system were also identified when comparing our data with those of Sima et al. [10] for the CO₂ + 2,2-dimethylbutane mixture, we repeated the same test procedure for this system. To this end, three mixtures of CO₂ + 2,2-dimethylbutane were prepared and investigated at different temperatures, with compositions selected to match the saturation conditions reported by Sima et al. [10] in their analytical measurements. The resulting bubble-point pressures are listed in Table 2 and shown in Fig. 6a-c.

In addition, a visual inspection of the cell was carried out at the saturation conditions reported by Sima et al. [10], and a photograph of the system was included in each graph of Fig. 7. The results, supported by these images, lead to the same conclusion as for the previous mixtures: the deviation between the synthetic and analytical techniques cannot be attributed to an onset-detection error in the synthetic method. The amount of gas released is far too significant. Indeed, in almost all cases, the gas volume fraction is on the order of 50 % or higher. Under such conditions, it is not possible, even with minimal rigor, to overlook the bubble onset point.

## 4. Conclusions

Although the synthetic technique, and in particular our implementation of it, has been established for many years and validated through numerous measurements on various systems, we were surprised to see that in recent publications, newly reported data, considered by their authors to be more rigorous, deviated significantly from our values. This prompted us to carry out a series of tests, which led us to the following conclusions.

* Our measurements on the CO₂ + toluene system show excellent consistency with literature data, thereby validating both our experimental methodology and the mixture preparation procedure.

* Replicated measurements for the CO₂ + Methylcyclopentane and CO₂ + 2,2-Dimethylbutane systems confirm the validity of our previously reported data [8,11].

* The synthetic method, when properly applied, is reliable for determining high-pressure phase equilibria.

* The discrepancies reported in the literature are unlikely to originate from our methodology and may instead stem from other reasons.

### CRediT authorship contribution statement

**Jean-Luc Daridon:** Writing – review & editing, Writing – original draft, Methodology, Data curation, Conceptualization.
**Jean-Patrick Bazile:** Writing – review & editing, Writing – original draft, Data curation, Conceptualization.
**Jean-Noël Jaubert:** Writing – review & editing, Writing – original draft, Data curation, Conceptualization.

**Stephane Vitu:** Writing – review & editing, Writing – original draft, Data curation, Conceptualization.

### 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.

### Supplementary materials

Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.fluid.2026.114664. Visual observation of the onset of bubble formation in the PVT cell during a controlled pressure drop.

### Data availability

Data will be made available on request.

### References

[1] J.-N. Jaubert, F. Mutelet, VLE predictions with the Peng-Robinson equation of state and temperature dependent kij calculated through a group contribution method, Fluid Phase Equilib. 224 (2004) 285–304, https://doi.org/10.1016/j.fluid.2004.06.059.

[2] S. Vitu, R. Privat, J.-N. Jaubert, F. Mutelet, Predicting the phase equilibria of CO₂+ hydrocarbon systems with the PPR78 model (PR EOS and kij calculated through a group contribution method), J. Supercrit. Fluids 45 (2008) 1–26, https://doi.org/10.1016/j.supflu.2007.11.015.

[3] R. Privat, J.-N. Jaubert, G.M. Kontogeorgis, Let us rethink advanced mixing rules for cubic equations of state, Fluid Ph. Equilib. 596 (2025) 114455, https://doi.org/10.1016/j.fluid.2025.114455.

[4] J.-N. Jaubert, Y. Le Guennec, A. Piña-Martinez, N. Ramirez-Velez, S. Lasala, B. Schmid, I.K. Nikolaidis, I.G. Economou, R. Privat, Benchmark database containing binary-system-high-quality-certified data for cross-comparing thermodynamic models and assessing their accuracy, Ind. Eng. Chem. Res. 59 (2020) 14981–15027, https://doi.org/10.1021/acs.iecr.0c01734.

[5] S. Peper, J.M.S. Fonseca, R. Dohm, High-pressure fluid-phase equilibria: trends, recent developments, and systems investigated (2009–2012), Fluid Ph. Equilib. 484 (2019) 126–224, https://doi.org/10.1016/j.fluid.2018.10.007.

[6] U.K. Deiters, G.M. Schneider, High pressure phase equilibria: experimental methods, Fluid Ph. Equilib. 29 (1986) 145–160, https://doi.org/10.1016/0378-3812(86)85018-X.

[7] J.-L. Daridon, C.-W. Lin, H. Carrier, J. Pauly, F.P. Fleming, Combined investigations of fluid phase equilibria and fluid-Solid phase equilibria in complex CO₂–crude oil systems under high pressure, J. Chem. Eng. Data 65 (2020) 3357–3372, https://doi.org/10.1021/acs.jedc.0c00144.

[8] S. Vitu, J.-N. Jaubert, J. Pauly, J.-L. Daridon, D. Barth, Phase equilibria measurements of CO₂+methyl cyclopentane and CO₂+isopropyl cyclohexane binary mixtures at elevated pressures, J. Supercrit. Fluids 44 (2008) 155–163, https://doi.org/10.1016/j.supflu.2007.10.003.

[9] S. Sima, C. Secuianu, J. Heringer, D.V. Nichita, High-pressure phase behaviour of carbon dioxide + methylcyclopentane binary system, Fluid Ph. Equilib. 598 (2025) 114497, https://doi.org/10.1016/j.fluid.2025.114497.

[10] S. Sima, C. Secuianu, D.V. Nichita, High-pressure phase equilibrium in the carbon dioxide + branched alkane binary systems: 1. Carbon dioxide + 2,2-dimethylbutane, Mol. Phys. (2025) e2530644, https://doi.org/10.1080/00268976.2025.2530644.

[11] J.-P. Bazile, J.-L. Daridon, J.-N. Jaubert, K. Abou-Alfa, S. 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, Int. J. Thermophys. 46 (2025) 107, https://doi.org/10.1007/s10765-025-03579-5.

[12] J.M. Prausnitz, P.R. Benson, Solubility of liquids in compressed hydrogen, nitrogen, and carbon dioxide, AIChE J. 5 (1959) 161–164, https://doi.org/10.1002/aic.690050208.

[13] S.D. Fink, H.C. Hershey, Modeling the vapor-liquid equilibria of 1,1,1-trichloro-ethane + carbon dioxide and toluene + carbon dioxide at 308, 323, and 353 K, Ind. Eng. Chem. Res. 29 (1990) 295–306, https://doi.org/10.1021/ie00098a022.

[14] A.L. Muhlbauer, J.D. Raal, Measurement and thermodynamic interpretation of high-pressure vapour–Liquid equilibria in the toluene+CO₂ system, Fluid Ph. Equilib. 64 (1991) 213–236, https://doi.org/10.1016/0378-3812(91)90015-Y.

[15] K. Tochigi, K. Hasegawa, N. Asano, K. Kojima, Vapor–liquid equilibria for the carbon dioxide + pentane and carbon dioxide + toluene systems, J. Chem. Eng. Data 43 (1998) 954–956, https://doi.org/10.1021/je980052s.

[16] M.J. Lazzaroni, D. Bush, J.S. Brown, C.A. Eckert, High-pressure vapor–liquid equilibria of some carbon dioxide + organic binary systems, J. Chem. Eng. Data 50 (2005) 60–65, https://doi.org/10.1021/je0498560.
[17] E.N. Lay, V. Taghikhani, C. Ghotbi, Measurement and correlation of CO₂ solubility in the systems of CO₂ + toluene, CO₂ + benzene, and CO₂ + *n*-hexane at near-critical and supercritical conditions, J. Chem. Eng. Data 51 (2006) 2197–2200, https://doi.org/10.1021/je0602972.

[18] W. Wu, J. Ke, M. Poliakoff, Phase boundaries of CO₂ + toluene, CO₂ + acetone, and CO₂ + ethanol at high temperatures and high pressures, J. Chem. Eng. Data 51 (2006) 1398–1403, https://doi.org/10.1021/je060099a.

[19] E.N. Lay, Measurement and correlation of bubble point pressure in (CO₂ + C₆ H₆), (CO₂ + CH₃ C₆ H₅), (CO₂ + C₆ H₁₄), and (CO₂ + C₇ H₁₆) at temperatures from (293.15 to 313.15) K, J. Chem. Eng. Data 55 (2010) 223–227, https://doi.org/10.1021/je900312z.

[20] Y. Sanchez-Vicente, W.J. Tay, S.Z. Al Ghafri, E.C. Efika, J.P.M. Trusler, Density and phase behavior of the CO₂ + methylbenzene system in wide ranges of temperatures and pressures, Ind. Eng. Chem. Res. 59 (2020) 7224–7237, https://doi.org/10.1021/acs.iecr.9b05377.

[21] J. Pauly, J. Coutinho, J.-L. Daridon, High pressure phase equilibria in methane+ waxy systems, Fluid Ph. Equilib. 255 (2007) 193–199, https://doi.org/10.1016/j.fluid.2007.04.014.

[22] S. Vitu, J.-N. Jaubert, J. Pauly, J.-L. Daridon, D. Barth, Bubble and dew points of carbon dioxide + a five-component synthetic mixture: experimental data and modeling with the PPR78 model, J. Chem. Eng. Data 52 (2007) 1851–1855, https://doi.org/10.1021/je7001978.

[23] J.F.R. Yanes, F. Montel, J.L. Daridon, Fluid phase equilibria in asymmetric model systems. Part I: CO₂+ diphenylmethane, J. Supercrit. Fluids 186 (2022) 105585, https://doi.org/10.1016/j.supflu.2022.105585.

[24] J.-L. Daridon, F. Montel, D.V. Nichita, J. Pauly, Fluid-fluid and fluid-solid phase equilibria in carbon dioxide + waxy systems 1. CO + *n*-C, Fluid Ph. Equilib. 538 (2021) 113023, https://doi.org/10.1016/j.fluid.2021.113023.

[25] A.A. Acuña, M. Artal, G. Galliero, J.-L. Daridon, Exploring cluster formation in CO₂ + hydrocarbon mixtures: from binary to ternary systems, J. Supercrit. Fluids 228 (2026) 106778, https://doi.org/10.1016/j.supflu.2025.106778.

[26] ISO/IEC Guide 98-3, Uncertainty of Measurement – Part 3: Guide to the Expression of Uncertainty in Measurement (GUM:1995), 2008, International Organization for Standardization, Geneva, 2008. n.d.

[27] E.W. Lemmon, M.L. Huber, M.O. McLinden, Reference fluid Thermodynamic and Transport properties-REFPROP, Gaithersburg, MD, 2007.