Phase Behavior of Carbon Dioxide + Isobutanol and Carbon Dioxide + tert-Butanol Binary Systems

Abstract

In recent years, the dramatic increase of greenhouse gases concentration in atmosphere, especially of carbon dioxide, determined many researchers to investigate new mitigation options. Thermodynamic studies play an important role in the development of new technologies for reducing the carbon levels. In this context, our group investigated the phase behavior (vapor–liquid equilibrium (VLE), vapor–liquid–liquid equilibrium (VLLE), liquid–liquid equilibrium (LLE), upper critical endpoints (UCEPs), critical curves) of binary and ternary systems containing organic substances with different functional groups to determine their ability to dissolve carbon dioxide. This study presents our results for the phase behavior of carbon dioxide + n-butanol structural isomers binary systems at high-pressures. Liquid–vapor critical curves are measured for carbon dioxide + isobutanol and carbon dioxide + tert-butanol binary systems at pressures up to 147.3 bar, as only few scattered critical points are available in the literature. New isothermal vapor–liquid equilibrium data are also reported at 363.15 and 373.15 K. New VLE data at higher temperature are necessary, as only another group reported some data for the carbon dioxide + isobutanol system, but with high errors. Phase behavior experiments were performed in a high-pressure two opposite sapphire windows cell with variable volume, using a static-analytical method with phases sampling by rapid online sample injectors (ROLSI) coupled to a gas chromatograph (GC) for phases analysis. The measurement results of this study are compared with the literature data when available. The new and all available literature data for the carbon dioxide + isobutanol and carbon dioxide + tert-butanol binary systems are successfully modeled with three cubic equations of state, namely, General Equation of State (GEOS), Soave–Redlich–Kwong (SRK), and Peng–Robinson (PR), coupled with classical van der Waals mixing rules (two-parameter conventional mixing rules, 2PCMR), using a predictive method.

1. Introduction

The constant increase of greenhouse gases in the atmosphere and consequently climate change determined researchers to search for new mitigation options [1,2,3,4]. At the same time, the knowledge of phase behavior and thermophysical properties is a critical pre-requisite for optimal design and operation in a variety of industrial applications involving pure components and mixtures [2,4]. In this context, we focused lately on the study of phase behavior of mixtures containing carbon dioxide and organic substances with different functional groups [5,6,7,8]. For instance, we studied binary systems of carbon dioxide and three different oxygenated organic compounds with four carbon atoms, specifically ethyl acetate (ester), 1,4-dioxane (cyclic ether), and 1,2-dimethoxyethane (linear diether) [5]. While the two first compounds are structural isomers with the formula C₄H₈O₂, the last one is a linear diether with the formula C₄H₁₀O₂. Our study revealed that the CO₂ solubility increases in the order 1,4-dioxane < ethyl acetate < 1,4-dimethoxyethane which means that ethers are better solvents than esters, but oxygenated cyclic compounds have the lowest performance.

Today more than never, it is important to find alternative sources of energy, and as fossil fuels will continue to be the primary source of energy in the next years due to several factors (availability, price, ease of transportation, other), finding a suitable candidate for CO₂ capture and/or applications in the field of CCS and CCUS technologies remains one of the key topics. Research and development of highly effective CO₂ separation and capture technologies are still required to meet CO₂ reduction targets [1]. Therefore, the fundamental understanding of the phase behavior as well as the possible applications, especially new carbon mitigation ways, are the main motivations of our study. Among the organic species chosen as the second component in the study of the equilibrium between phases at high pressures in binary systems containing carbon dioxide, alcohols occupy an important place, due their multiple uses [9,10]. In addition, the carbon dioxide + n-alcohols series is one of the few for which the types of fluid phase diagram, according to the classification of van Konyneburg and Scott [11,12], are known [13,14,15]. While the global phase behavior is elucidated for carbon dioxide + n-alcohols, the carbon dioxide + branched alcohols received less attention, and for most systems, only vapor–liquid equilibria (VLE) in a limited range of temperatures and pressures are reported [2,16,17,18,19,20]. Thus, the phase behavior of both carbon dioxide + 1-butanol and + 2-butanol, its chain isomer, and binary systems are attributed to type II phase behavior. The carbon dioxide + isobutanol binary system belongs to type II phase behavior [21], while the carbon dioxide + tert-butanol system can be attributed to type I or II phase behavior [22]. Both types are characterized by a continuous liquid–vapor critical curve stretching between the critical points of pure components. The difference between type I and type II phase behavior is that the latter presents an additional liquid–liquid (LL) critical locus which intersects a three-phases liquid–liquid–vapor equilibrium (LLVE) curve in an upper critical endpoint (UCEP) (

Table 1. Literature ^a VLE experimental data for carbon dioxide + isobutanol and + tert-butanol.

P or Prange/bar	T or Trange/K	Nexp	Observations	Ref.
carbon dioxide (1) + isobutanol (2)
18.26 ÷ 81.40	313.15	10	P-x	[23]
17.30 ÷130.0	333.15 ÷ 353.15	23	P-x,y	[21]
carbon dioxide (1) + tert-butanol (2)
70.0 ÷ 115.2 103.5 ÷ 120.3	333 ÷ 368 343 ÷ 368	14 6	P-x P-y	[24]
19.5 ÷ 112.9	323.15 ÷ 353.15	30	P-x,y	[22]
10.3 ÷ 75.5	313.15	13	P-x	[25]
14.5 ÷ 79.16	313.15	10	P-x	[23]

^a Not considered in our previous studies [21,22].

).

Previously, we reported isothermal vapor–liquid equilibrium data at 333.15, 343.15, and 353.15 K for carbon dioxide + isobutanol binary system [21] and at 323.15, 333.15, 343.15, and 353.15 K for the carbon dioxide + tert-butanol system [22]. Isobutanol (2-methyl-1-propanol) and tert-butanol (2-methyl-2-propanol), as well as sec-butanol (2-butanol) are the structural (1- and 2-butanol are positional isomers, while isobutanol and tert-butanol are chain isomers) isomers of 1-butanol, the primary alcohol with four carbon atoms in molecule. Butanols are important not only as possible co-solvents for CO₂ capture but also as solvents, plasticizers, varnishes, ink component, artificial flavoring, gasoline additive, biofuels, syntheses of other chemical compounds, etc. [9,10].

We continue our study on carbon dioxide + branched alcohols reporting the vapor–liquid critical curves and new isothermal vapor–liquid equilibrium data for carbon dioxide + isobutanol and carbon dioxide + tert-butanol, respectively, at 363.15 and 373.15 K and pressures up to 147.3 bar. New data, especially the critical curves, are necessary as the analysis of the available literature data [21,22] showed that there are significant differences among both vapor–liquid equilibrium data and critical curves reported by various research groups. In addition, for both critical curves of carbon dioxide + isobutanol and + tert-butanol binary systems are reported few points in a limited range of pressures and temperatures [26,27,28,29,30]. As in our previous studies [21,22] we carefully reviewed the literature for the carbon dioxide + isobutanol and carbon dioxide + tert-butanol binary systems, Table 1 summarizes only the data reported afterwards. The available literature critical data are presented in

Table 2. Literature experimental critical data for carbon dioxide + isobutanol and + tert-butanol.

Prange/bar	Trange/K	Nexp	Observations	Reference
carbon dioxide (1) + isobutanol (2)
147.4 ÷ 122.00	373.15 ÷ 493.15	4	LV	[26]
80.30 ÷143.1	313.20 ÷ 353.20	5	LV	[27]
carbon dioxide (1) + tert-butanol (2)
101.7 ÷ 120.4	323.20 ÷ 353.20	4	LV	[28]
19.5 ÷ 112.9	341.60 ÷ 351.30	2	LV	[29]
92.3 ÷ 111.6	323.20 ÷ 343.20	2	LV	[30]

.

The new and all available literature data were modeled with the General Equation of State (GEOS) [31,32], Peng–Robinson (PR) [33], and Soave–Redlich–Kwong (SRK) [34] equations of state (EoS) coupled with classical van der Waals mixing rules (two-parameter conventional mixing rule, 2PCMR). The GEOS has four parameters and is a generalization for all cubic EoSs with two, three, and four parameters [31,32]. Instead of correlating the new data, we used one set of binary interaction parameters for each thermodynamic model determined using k₁₂–l₁₂ method [35,36,37] for the carbon dioxide + 2-butanol binary system [37], and we calculated predictively the critical curves and VLE data.

Finally, we analyzed the phase behavior of the carbon dioxide + butanols (+n-butanol, +sec-butanol, +isobutanol, and +tert-butanol) to compare their ability to dissolve carbon dioxide. The experimental and prediction results showed that the molar fraction of carbon dioxide increases in the order 1-butanol < isobutanol < 2-butanol < tert-butanol.

2. Materials and Methods

2.1. Materials

Carbon dioxide with purity of min. 0.99995 (mass fraction) was procured from Linde Gaz Romania; isobutanol (purity min. 0.995, in mass fraction) and tert-butanol (purity min. 0.995, in mass fraction) were purchased from Sigma-Aldrich, as reported in

Table 3. Description of materials.

Compound	Chemical Formula	CAS Registry Number	Source	Purification Method	Minimum Mass Fraction Purity
carbon dioxide	CO2	124-38-9	Linde Gaz Romania	None	0.99995
isobutanol	C4H10O	78-83-1	Sigma-Aldrich	None	>0.995
tert-butanol	C4H10O	75-65-0	Sigma-Aldrich	None	>0.995

. All substances were used without further purification. However, the purity of both alcohols was also tested and confirmed by gas chromatography.

2.2. Methods

The apparatus and experimental measurement procedures were described in detail in previous papers [38,39]; therefore, only short descriptions are provided.

Apparatus. The static-analytical process with phases (liquid and vapor) sampling was used for the VLE measurements. The main unit of the phase equilibrium apparatus is the high-pressure two opposite saphire windows cell with adjustable volume, connected with a sampling and analyzing system [38,39]. The sampling system contains two ROLSI^TM (rapid on-line sampler injector) valves purchased from MINES ParisTech/CEP-TEP–Centre énergétique et procédés, Fontainbleau, France [40]. These two high-pressure electromechanical sampling valves are connected to the equilibrium optical cell and to a gas chromatograph (GC) through thermally insulated capillaries. A heating resistance is used to vaporize rapidly the liquid samples from the expansion chamber of the sampler injector. The transferring lines between ROLSI and the GC are heated with a linear resistor coupled to an Armines/CEP/TEP regulator. The Perichrom gas chromatograph is fitted out with a thermal conductivity detector (TCD) and a 30 m long and 0.530 mm diameter HP-Plot/Q column. The GC carrier gas is Helium at a flow rate between 8 to 30 mL/min. The rig is completed with a syringe pump model 500D from Teledyne ISCO.

Experimental procedure. The isothermal pressure-composition data working procedure was presented in detail previously [6,7]. The procedure starts by rinsing several times with carbon dioxide the equilibrium cell as well the entire internal loop of the apparatus. The next step is to evacuate the gas from the equilibrium cell and the lines with a vacuum pump. After degassing the visual cell by using a vacuum pump and vigorously stirring, the organic compound is charged. The cell is subsequently filled with carbon dioxide using the syringe pump and the pressure is set to the chosen value. Next, the cell is heated to the desired experimental temperature. For a few hours, the mixture in the cell is stirred vigorously to enable the approach to an equilibrium state. The stirrer is then switched off for about 1 h, to ensure the complete separation of the coexisting phases. At this point, samples from both liquid and vapor phases are withdrawn by ROLSI and send to the GC to be analyzed. The repeatability is checked at the equilibrium temperature and pressure by analyzing at least six samples of the liquid phase. As the sample sizes are very small, the equilibrium state is not perturbed and the pressure in the visual cell remains constant.

The calibration of the TCD for CO₂ and butanols is done by injecting known amounts of each component using gas chromatographic syringes (250 μL for the gas, 5 and 10 μL for the liquids). Calibration data are fitted to polynomials to obtain the mole number of the component versus chromatographic area. The correlation coefficients of the GC calibration curves were 0.999 for carbon dioxide and 0.997 for both isobutanol and tert-butanol.

The uncertainties in all variables and properties were estimated as described in our previous papers [6,7]. The standard uncertainties are 0.001 and 0.005 for the liquid phase and vapor phase, respectively. The platinum temperature probe (PT-100) is connected to a digital display. It was calibrated against the calibration system Digital Precision Thermometer with PT-100 sensor at the Romanian Bureau of Legal Metrology. The uncertainty of platinum probe is estimated to be within ±0.1 K using a similar method to that explained in references [6,7]. The pressure transducer is connected to a digital multimeter. It was calibrated at 323.15 K with a precision hydraulic dead-weight tester, namely, model 580C, DH-Budenberg SA, Aubervilliers, France. The uncertainty of the pressures is estimated to be within ±0.015 MPa using the method presented previously [6,7], for pressures between (0.5 and 20) MPa.

The critical points were measured in this work using the subsequent procedure. The determination of critical points starts by analyzing the composition at constant temperature and at a sufficiently high pressure, so the system presents a homogeneous phase. Then, the pressure is very slowly modified by adjusting the volume of the cell with the manual pump in order to observe the transition from the homogeneous phase (single phase) to heterogeneous (two phases) and if a bubble or a dew point appears firstly by keeping the temperature constant. If a bubble point is obtained, the temperature is slowly increased until the first dew point is observed, then the pressure is raised to a homogeneous phase, and the composition is determined by sampling. Then, the pressure is very slowly reduced until the first drops of liquid are seen. At this point, the temperature is slowly reduced simultaneously with decreasing the volume, so the system is at the limit between homogeneous (single phase) and heterogeneous (two phases). The reducing of temperature continues until the first gas bubbles are detected. In this way, the range in which the critical points are located is reduced to 0.2 K and 0.1 bar, compared to the critical opalescence that can be observed in wider ranges of temperature (~5 K) and pressure (~10–15 bar, depending on the system analyzed). The entire procedure is then repeated by adding new quantities of CO₂ and very slowly cooling.

3. Modeling

The phase behavior of carbon dioxide + isobutanol and carbon dioxide + tert-butanol was modelled with the General Equation of State (GEOS), Soave–Redlich–Kwong (SRK), and Peng–Robinson (PR) equations of state (EoSs), coupled with classical van der Waals mixing rules (2PCMR).

The GEOS [31,32] equation of state is

$$P=\frac{RT}{V-b}-\frac{a\left(T\right)}{{\left(V-d\right)}^2+c}$$

(1)

with the classical van der Waals mixing rules

$$a={{\displaystyle \sum }}_i{{\displaystyle \sum }}_j{X}_i{X}_j{a}_{ij}b={{\displaystyle \sum }}_i{X}_i{b}_i$$

(2)

$$c={{\displaystyle \sum }}_i{{\displaystyle \sum }}_j{X}_i{X}_j{c}_{ij}d={{\displaystyle \sum }}_i{X}_i{d}_i$$

(3)

$$a_{ij}={\left(a_i{a}_j\right)}^{\frac{1}{2}}\left(1-k_{ij}\right)b_{ij}=\frac{b_i+b_j}{2}\left(1-l_{ij}\right)c_{ij}=\pm {\left(c_i{c}_j\right)}^{\frac{1}{2}}$$

(4)

with “+” for c_i, c_j > 0 and “−“ for c_i, c_j < 0. Generally, negative values are common for the c parameter of pure components.

The four parameters a, b, c, and d for a pure component are expressed by

$$a\left(T\right)=\frac{R^2{T}_c^2}{P_c}\beta \left(T_r\right){\Omega }_{a}b=\frac{R{T}_c}{P_c}{\Omega }_b$$

(5)

$$c=\frac{R^2{T}_c^2}{P_c^2}{\Omega }_{c}d=\frac{R{T}_c}{P_c}{\Omega }_d$$

(6)

Setting four critical conditions, with ${\alpha }_c$ as the Riedel criterion:

$$P_r=1{\left(\frac{\partial P_r}{\partial V_r}\right)}_{T_r}=0{\left(\frac{{\partial }^2{P}_r}{\partial V_r^2}\right)}_{T_r}=0{\alpha }_c={\left(\frac{\partial P_r}{\partial T_r}\right)}_{V_r}$$

(7)

at $T_r=1$ and $V_r=1$, the expressions of the parameters Ω_a, Ω_b, Ω_c, Ω_d are obtained

$${\Omega }_a={\left(1-B\right)}^3{\Omega }_b=Z_c-B{\Omega }_c={\left(1-B\right)}^2\left(B-0.25\right)$$

(8)

$${\Omega }_d=Z_c-\frac{\left(1-B\right)}{2}B=\frac{1+m}{{\alpha }_c+m}$$

(9)

where $P_r$, $T_r$, $\mathrm{and}{V}_r$. are the reduced variables, and $Z_c$ is the critical compressibility factor.

The temperature function used is

$$\beta \left(T_r\right)=T_r^{-m}$$

(10)

GEOS parameters, m and α_c, were calculated by constraining the EoS to reproduce the experimental vapour pressure and liquid volume on the saturation curve between the triple point and the critical point [6,7].

The SRK [34] EoS is

$$P=\frac{RT}{V-b}-\frac{a\left(T\right)}{V\cdot \left(V+b\right)}$$

(11)

where the two parameters, a and b, are

$$a=0.42748\frac{R^2{T}_c^2}{P_c}\alpha \left(T\right)$$

(12)

$$b=0.08664\frac{R{T}_c}{P_c}$$

(13)

$$\alpha \left(T_R,\omega \right)={\left[1+m_{SRK}\left(1-T_R^{0.5}\right)\right]}^2$$

(14)

$$m_{SRK}=0.480-1.574\omega -0.176{\omega }^2$$

(15)

The Peng–Robinson [33] equation of state is

$$P=\frac{RT}{V-b}-\frac{a\left(T\right)}{V\left(V+b\right)+b\left(V-b\right)}$$

(16)

where the two constants, a and b, are

$$a=0.45724\frac{R^2{T}_c^2}{P_c}\alpha \left(T\right)$$

(17)

$$b=0.077796\frac{R{T}_c}{P_c}$$

(18)

$$\alpha \left(T_R,\omega \right)={\left[1+m_{PR}\left(1-T_R^{0.5}\right)\right]}^2$$

(19)

$$m_{PR}=0.37464-1.54226\omega -0.26992{\omega }^2$$

(20)

As Equations (8) and (9) are general forms for all the cubic equations of state with two, three, and four parameters, to obtain the parameters of the SRK EoS, we set the following restrictions: ${\Omega }_c=-{\left(\frac{{\Omega }_b}{2}\right)}^2$ and ${\Omega }_d=-\frac{{\Omega }_b}{2}$. From this, it follows:

$${\Omega }_c={\left(1-B\right)}^2\left(B-0.25\right)=-\frac{{\left(Z_c-B\right)}^2}{4}$$

(21)

$${\Omega }_d=Z_c-0.5\left(1-B\right)=-\frac{\left(Z_c-B\right)}{2}$$

(22)

It results in $Z_c\left(SRK\right)=\frac{1}{3}$, and the relation for B (SRK) is

$$B=0.25-\frac{1}{36}{\left(\frac{1-3B}{1-B}\right)}^2$$

(23)

This equation is solved iteratively, and it results $B\left(SRK\right)=0.246$. Correspondingly, for the other parameters we obtained ${\Omega }_a\left(SRK\right)={\left(1-B\right)}^3=0.42748$ and ${\Omega }_b\left(SRK\right)=Z_c-B=0.08664$.

Similarly, for PR EoS we set the restrictions: ${\Omega }_c=-2{\left({\Omega }_b\right)}^2$ and ${\Omega }_d=-{\Omega }_b$. It results in

$$B=0.25-\frac{1}{8}{\left(\frac{1-3B}{1-B}\right)}^2$$

(24)

$$Z_c=\frac{1+B}{4}$$

(25)

giving $B\left(PR\right)=0.2296$ and $Z_c\left(PR\right)=0.3074$.

The calculations were made using the software package PHEQ, developed in our laboratory [41] and GPEC (Global Phase Equilibrium Calculations) [42,43,44]. The method proposed by Heidemann and Khalil [45] with numerical derivatives proposed by Stockfleth and Dohrn [46] is implemented in our software to calculate the critical curves.

4. Results and Discussion

4.1. Experimental Results

Vapor–liquid equilibrium compositions for the carbon dioxide + isobutanol and carbon dioxide + tert-butanol binary systems were measured at 363.15 and 373.15 K and pressures up to 147.30 and 121.8 bar, respectively.

Table 4. Mole fraction of component 1 in the liquid phase, X₁, and mole fraction of component 1 in the vapor phase, Y₁, at various temperatures, T, and pressures, P, for the binary system carbon dioxide (1) + isobutanol (2) and carbon dioxide (1) + tert-butanol (2).

P/bar	X1	Y1	P/bar	X1	Y1
carbon dioxide (1) + isobutanol (2)			carbon dioxide (1) + tert-butanol (2)
T/K = 363.15 ± 0.1
20.90	0.1139	0.9770	19.30	0.1129	0.9612
31.00	0.1454	0.9901	31.10	0.1926	0.9706
45.60	0.2115	0.9872	45.10	0.2822	0.9779
60.90	0.2838	0.9953	60.60	0.3790	0.9879
76.70	0.3683	0.9887	76.10	0.4919	0.9846
90.90	0.4439	0.9834	90.40	0.5819	0.9638
106.35	0.5232	0.9726	105.80	0.6834	0.9389
120.30	0.5947	0.9578	119.00	0.8303	0.8812
131.50	0.6867	0.9377	118.90a	0.8980	0.8980
142.10 a	0.8781	0.8781
T/K = 373.15 ± 0.1
33.50	0.1634	0.9724	15.30	0.0838	0.8922
56.10	0.2521	0.9782	30.40	0.1786	0.9591
79.90	0.3590	0.9819	45.60	0.2703	0.9434
95.50	0.4320	0.9800	60.20	0.3586	0.9729
110.10	0.5054	0.9646	75.60	0.4566	0.9817
125.10	0.5832	0.9508	91.30	0.5510	0.9602
140.50	0.7062	0.9194	105.50	0.6287	0.9466
147.30 a	0.8564	0.8564	118.60	0.7344	0.9067
			121.80 a	0.8798	0.8798

Standard uncertainties: u(T) = 0.1 K, u(P) = 0.1 bar, u(X₁) = 0.001, u(Y₁) = 0.005. ^a Critical points.

presents the new isothermal experimental data together with the corresponding estimated uncertainties for all quantities. To the best of our knowledge, the two isotherms for the carbon dioxide + tert-butanol system are for the first time measured, while for carbon dioxide + isobutanol system only the 363.15 K is not reported. The available literature data [26] at 373.15 K for the carbon dioxide + isobutanol binary system are plotted together with our data in Figure 1. Some differences can be observed between our data and those measured by reference [26] for the liquid phase. It should be mentioned that the reported uncertainty of their phase compositions is ±1.0% [20]. However, the new data are in good agreement with our previous measurements [21,22].

In Figure 2, we compare experimental data of carbon dioxide + 1-butanol binary system [47], as well as for all C₄H₁₀O isomers, i.e., carbon dioxide + 2-butanol [47], carbon dioxide + isobutanol, and carbon dioxide + tert-butanol systems at the same temperature, 363.15 K.

It can be observed that our experimental data for carbon dioxide + isobutanol and + tert-butanol are in good agreement with those reported by Galicia-Luna et al. [47] for carbon dioxide + 1-butanol and + 2-butanol, respectively. At higher pressures, the solubility of carbon dioxide increases in the order 1-butanol < isobutanol < 2-butanol < tert-butanol, as observed by other researchers [23]. Although the differences in compositions are small, especially between 2-butanol and isobutanol, this correlation opens new perspectives for applications, such as isomers separation based on pressure difference [23].

Furthermore, the new isothermal data for both systems are also shown in Figure 3. Thus, Figure 3a compares the data measured at 363.15 K for both carbon dioxide + isobutanol and carbon dioxide + tert-butanol, while Figure 3b shows data determined at 373.15 K. At both temperatures, carbon dioxide is more soluble in tert-butanol in the liquid phase, and its solubility increases with an increase in the pressure.

We also measured the vapor–liquid critical curves starting from the critical point of carbon dioxide up to 373.15 and 147.3 bar for carbon dioxide + isobutanol binary system and up to 405.15 K and 121.4 bar for carbon dioxide + tert-butanol binary system, values which are near or over the critical pressure maximum (CPM). The new critical data are presented in Table 5 and plotted in Figure 4. In the same figure we drew the critical temperatures and pressures for both systems available from literature. Thus, Semenova et al. [26] reported four critical points at high temperatures and Wang et al. [27] estimated five critical points at temperatures closer to the critical point of carbon dioxide for the carbon dioxide + isobutanol system. Wang et al. [28] estimated four points, while Chen et al. [29] and Kim et al. [30] estimated only two points each for the carbon dioxide + tert-butanol system.

In Figure 5, we compare the LV critical curves for carbon dioxide + all butanol isomers. The miscibility gap increases in the order tert-butanol < 2-butanol < isobutanol < 1-butanol. The critical data reported for the carbon dioxide + isobutanol and carbon dioxide + tert-butanol binary systems agree very well with the data measured for carbon dioxide + 1-butanol and carbon dioxide + 2-butanol binary systems. Experimental data, including critical compositions, are reported for the entire temperature range for the carbon dioxide + 2-butanol system [48,49], while for the carbon dioxide + 1-butanol binary system critical pressures and temperatures are available almost in the entire temperature range from Ziegler et al. [50] and Yeo et al. [51]. Gurdial et al. [52] measured several critical data for the carbon dioxide + 1-butanol system at temperatures closer to the critical point of carbon dioxide.

4.2. Modelling Results

The new and literature data for carbon dioxide + isobutanol and carbon dioxide + tert-butanol were predictively modeled with three thermodynamic models, namely, GEOS, PR, and SRK EoSs coupled with classical van der Waals mixing rules.

Recently, we showed that the binary interaction parameters (k₁₂ and l₁₂) determined by the k₁₂-l₁₂ method [35,36,37] for the carbon dioxide + 2-butanol binary system can be successfully used to model either carbon dioxide + different organic substances containing four C atoms without and with one or two oxygen atoms (n-butane, 1-butanol, 1,2-dimethoxyethane, ethyl acetate, dioxane [5,6,7,8]), either carbon dioxide + a lower member of the same homologous series, i.e., 2-propanol [53].

The carbon dioxide + 2-butanol binary system can be used as a model system as critical data are available in the entire range, including the UCEP and LLV [48].

Here, we use the same modeling procedure, and we calculated the critical curves and VLE data for the two systems containing carbon dioxide and the chain isomers, isobutanol and tert-butanol, using the binary interaction parameters determined for the carbon dioxide + 2-butanol binary system [37] for each thermodynamic model. These parameters are presented in Table 6.

It should be noted that the parameters from Table 6 were determined using the values of pure components (CO₂, 2-butanol) critical data and acentric factors from Reid et al. [54]. Therefore, we recalculated the critical curve using the binary interaction parameters (BIPs) from Table 6 for the carbon dioxide + 2-butanol system using the pure components critical data and acentric factors from both Poling et al. [55] and DIPPR [56] database.

Table 5. Critical points data carbon dioxide (1) + isobutanol (2) and carbon dioxide (1) + tert-butanol (2) binary systems ^a.

T/K	P/bar	X1	T/K	P/bar	X1
carbon dioxide + isobutanol			cabon dioxide + tert-butanol
304.21 b	73.83	1.0000	304.21 b	73.83	1.0000
316.65	87.20		320.45	87.40	0.9715
317.05	87.50		323.15 c	89.90	0.9687
318.15	89.00		326.25	92.90	0.9630
320.15	91.60		330.75	96.80	0.9570
327.60	101.60		333.15 c	99.20	0.9528
332.95	109.60		337.85	102.30	0.9477
335.25	112.30		341.85	105.40	0.9420
339.25	117.30		343.15 c	106.80	0.9408
348.50	128.65		346.75	109.20	0.9332
353.35	133.80		352.35	112.50	0.9218
353.50	134.05		353.15 c	112.90	0.9215
356.85	137.00		362.65	118.20	0.8994
359.05	138.40		363.15	118.90	0.8980
363.15	142.10	0.8781	373.15	121.80	0.8798
364.15	142.40		375.95	122.90	0.8738
367.65	144.70		381.35	124.00	0.8563
369.35	145.70		387.65	124.60	0.8371
371.65	146.90		395.55	124.70	0.8047
373.15	147.30	0.8564	399.75	124.50	0.7821
547.80 b	42.95	0.0000	405.15	121.40	0.7417
			506.20 b	39.72	0.0000

^a u(T) = 0.1 K, u(P) = 0.1 bar, u(X₁) = 0.001.^b DIPPR [56] values. ^c Measured in our group [21,22].

Table 5. Critical points data carbon dioxide (1) + isobutanol (2) and carbon dioxide (1) + tert-butanol (2) binary systems ^a.

T/K	P/bar	X1	T/K	P/bar	X1
carbon dioxide + isobutanol			cabon dioxide + tert-butanol
304.21 b	73.83	1.0000	304.21 b	73.83	1.0000
316.65	87.20		320.45	87.40	0.9715
317.05	87.50		323.15 c	89.90	0.9687
318.15	89.00		326.25	92.90	0.9630
320.15	91.60		330.75	96.80	0.9570
327.60	101.60		333.15 c	99.20	0.9528
332.95	109.60		337.85	102.30	0.9477
335.25	112.30		341.85	105.40	0.9420
339.25	117.30		343.15 c	106.80	0.9408
348.50	128.65		346.75	109.20	0.9332
353.35	133.80		352.35	112.50	0.9218
353.50	134.05		353.15 c	112.90	0.9215
356.85	137.00		362.65	118.20	0.8994
359.05	138.40		363.15	118.90	0.8980
363.15	142.10	0.8781	373.15	121.80	0.8798
364.15	142.40		375.95	122.90	0.8738
367.65	144.70		381.35	124.00	0.8563
369.35	145.70		387.65	124.60	0.8371
371.65	146.90		395.55	124.70	0.8047
373.15	147.30	0.8564	399.75	124.50	0.7821
547.80 b	42.95	0.0000	405.15	121.40	0.7417
			506.20 b	39.72	0.0000

^a u(T) = 0.1 K, u(P) = 0.1 bar, u(X₁) = 0.001.^b DIPPR [56] values. ^c Measured in our group [21,22].

Table 6. Binary interaction parameters used in calculations [37].

EoS	k12	l12
GEOS	0.050	−0.040
PR	0.025	−0.108
SRK	0.020	−0.111

Table 6. Binary interaction parameters used in calculations [37].

EoS	k12	l12
GEOS	0.050	−0.040
PR	0.025	−0.108
SRK	0.020	−0.111

Figure 4. P–T fluid phase diagram of the carbon dioxide (1) + isobutanol (2) and carbon dioxide (1) + tert-butanol (2) systems. Critical points (CP) of pure components: ●, CP CO₂ [56]; ●, CP isobutanol [56]; ●, CP tert-butanol [56]. CP CO₂ + isobutanol: ○, this work; □, [26]; ◊, [27]. CP CO₂ + tert-butanol: ○, this work; □, [28]; ◊, [29]; ∆, [30].

Figure 4. P–T fluid phase diagram of the carbon dioxide (1) + isobutanol (2) and carbon dioxide (1) + tert-butanol (2) systems. Critical points (CP) of pure components: ●, CP CO₂ [56]; ●, CP isobutanol [56]; ●, CP tert-butanol [56]. CP CO₂ + isobutanol: ○, this work; □, [26]; ◊, [27]. CP CO₂ + tert-butanol: ○, this work; □, [28]; ◊, [29]; ∆, [30].

Figure 5. P–T fluid phase diagram of the carbon dioxide (1) + tert-butanol (2), carbon dioxide (1) + 2-butanol (2), carbon dioxide (1) + isobutanol (2), and carbon dioxide (1) + 1-butanol (2) binary systems. The symbols represent the binary systems as follows: CO₂ + tert-butanol (●, this work; ■, [28]; ▲, [29]; ◆, [30]); CO₂ + 2-butanol (✱, [48]; ×, [49]); CO₂ + isobutanol (●, this work; ▲, [27]; ◆, [26]); CO₂ + 1-butanol (∆, [52]; □, [50]; ◊, [51]).

Figure 5. P–T fluid phase diagram of the carbon dioxide (1) + tert-butanol (2), carbon dioxide (1) + 2-butanol (2), carbon dioxide (1) + isobutanol (2), and carbon dioxide (1) + 1-butanol (2) binary systems. The symbols represent the binary systems as follows: CO₂ + tert-butanol (●, this work; ■, [28]; ▲, [29]; ◆, [30]); CO₂ + 2-butanol (✱, [48]; ×, [49]); CO₂ + isobutanol (●, this work; ▲, [27]; ◆, [26]); CO₂ + 1-butanol (∆, [52]; □, [50]; ◊, [51]).

In

Table 7. Critical parameters (T_c, P_c, V_c) and acentric factor (ω) for pure components.

Database	Reid et al. [54]				Poling et al. [55]				DIPPR [56]
Substance	Tc/K	Pc/bar	Vc/cm3/mol	ω	Tc/K	Pc/bar	Vc/cm3/mol	ω	Tc/K	Pc/bar	Vc/cm3/mol	ω
carbon dioxide	304.10	73.80	93.9	0.239	304.12	73.74	94.07	0.225	304.21	73.83	94	0.223621
1-butanol	563.10	44.20	275	0.593	563.05	44.23	275	0.590	563.1	44.14	273	0.588280
2-butanol	536.10	41.80	269	0.577	536.05	41.79	269	0.574	535.9	42.02	270	0.580832
isobutanol	547.80	43.00	273	0.592	547.78	43.00	273	0.590	547.8	42.95	274	0.585710
tert-butanol	506.20	39.70	275	0.612	506.21	39.73	275	0.613	506.2	39.72	275	0.615203

, we compiled the critical data and acentric factors for all butanol isomers and carbon dioxide from the three sources mentioned, while in

Table 8. GEOS parameters (α_c, m) for pure components.

Substance	m	αc
carbon dioxide	0.3146	7.0517
1-butanol	0.6437	9.0580
2-butanol	0.6533	9.0298
isobutanol	0.6005	9.9243
tert-butanol	0.6814	9.1161

and

Table 9. The critical compressibility factor (Z_c), and GEOS parameters (Ω_a, Ω_b, Ω_c, Ω_d, B).

EoS	GEOS					PR	SRK
Substance	CO2	1-butanol	2-butanol	isobutanol	tert-butanol	all	all
B	0.1785	1.3342	1.3396	0.1521	0.1716	0.2467	0.2296
Zc	0.2746	0.2576	0.2540	0.2586	0.2597	0.3333	0.3074
Ωa	0.5545	−0.0373	−0.0392	0.6097	0.5685	0.4275	0.4572
Ωb	0.0961	−1.0766	−1.0857	0.1065	0.0881	0.0866	0.0778
Ωc	−0.0483	0.1211	0.1257	−0.0704	−0.0538	−0.0187	−0.0121
Ωd	−0.1362	0.4247	0.4238	−0.1654	−0.1545	−0.0434	−0.0778

we provided all GEOS parameters (m, α_c, Ω_a, Ω_b, Ω_c, and Ω_d).

The differences in critical maximum pressures are very small for all three EoSs, and hence, we decided to use the BIPs from Table 6 in combination with the critical data and acentric factors from DIPPR [56], presented in Table 7, as recommended by other researchers [57].

Moreover, in a recent paper [6], we studied the effect of critical parameters and acentric factors of pure components from different database for carbon dioxide + dioxane (C₄H₈O₂) binary mixture, and we showed that the differences are small for the VLE calculations.

In Figure 6, we compare the model results with the critical experimental data for all butanol binary systems. PR and SRK EoSs behave similarly for all systems, and the CPMs are slightly shifted to the right compared with the experimental ones, while the GEOS reproduces better the CPMs, except for carbon dioxide + isobutanol system. As the figure is busy, we compare the new data with the chosen reference model, carbon dioxide + 2-butanol system, and the predictions by the GEOS and PR in Figure 7. The predictions for the carbon dioxide + tert-butanol binary system are very good for all three models (Figure 7b), while for the carbon dioxide + isobutanol system (Figure 7a) GEOS seems to overpredict the CPM, but the corresponding temperature is closer to the experimental one. Both PR and SRK also overpredict the CPM, but at a lower pressure and at higher temperature than the GEOS for the carbon dioxide + isobutanol binary system.

The LV critical curve of the carbon dioxide + 1-butanol system is very well reproduced by all three thermodynamic models (Figure 7c), only the temperature corresponding to the CPM is slightly higher than the experimental one for PR and SRK equations of state.

It must be noted that both PR and SRK predict type II phase behavior for all four systems. However, clear experimental evidence exists only for the carbon dioxide + 2-butanol system [48], while for the carbon dioxide + 1-butanol and carbon dioxide + isobutanol Büchner [58] reported in 1906 few liquid–liquid equilibrium points (temperature and the composition of liquid 1) at very low temperature (251.15 K for carbon dioxide + isobutanol and 253.15 to 256.15 K for carbon dioxide + 1-butanol system) [20]. On the other hand, tert-butanol has a very high freezing point of about 25.5 °C which can mask any observation of an LLV equilibrium for its binary mixture with carbon dioxide. Therefore, it can be assumed that all carbon dioxide + butanol systems belong to type II phase behavior. However, without knowing the UCEP’s temperature, the k₁₂-l₁₂ method cannot be applied directly to the carbon dioxide + isobutanol and carbon dioxide + tert-butanol binary systems.

The BIPs from Table 6 were also used to predict the new and available VLE data for the carbon dioxide + isobutanol and carbon dioxide + tert-butanol binary systems with the GEOS, PR, and SRK models. Considering that the predictions were made with the binary interaction parameters tailored for the carbon dioxide + 2-butanol system and from the P-T global diagrams, it is expected that they will be primarily qualitative for the structural isomers, carbon dioxide + isobutanol and carbon dioxide + tert-butanol binary systems. Still, the predictions by GEOS, PR, and SRK EoSs are remarkably good, especially for the carbon dioxide + tert-butanol system. As an example, we illustrated the prediction results at 363.15 and 373.15 K for carbon dioxide + isobutanol (Figure 8a) and carbon dioxide + tert-butanol (Figure 8b), comparing the new data and all three thermodynamic models used, in Figure 8.

The three models present similar trends for both systems, except for the GEOS equation which shows a lower solubility than the experimental one in the liquid phase for the carbon dioxide + isobutanol system. This behavior is consistent with the inflection observed on the first part of the liquid–vapor critical curve, starting from the critical point of carbon dioxide towards the CPM. It should be also noted that the composition of the vapor phase is underestimated by all models, but it is significantly smaller compared with the experimental values for the carbon dioxide + tert-butanol system.

The prediction results are satisfactory for the carbon dioxide + 1-butanol binary system. In Figure 9, we exemplified at 363.15 the calculations by PR EoS for carbon dioxide + 1-butanol, carbon dioxide + 2-butanol, carbon dioxide + isobutanol, and carbon dioxide + tert-butanol binary systems. Although the composition of the liquid phase is systematically underpredicted at higher pressures for all systems, the solubility increases in the same order 1-butanol < isobutanol < 2-butanol < tert-butanol. The prediction results are encouraging and open the path to obtain at least qualitative information when experimental data are not available.

5. Conclusions

New isothermal vapor–liquid equilibrium data for the carbon dioxide + isobutanol and carbon dioxide + tert-butanol system were measured with a visual high-pressure static-analytic setup at 363.15 and 373.15 K. The vapor–liquid critical curves were also measured at pressures up to 147.3 bar and 373.15 K for the carbon dioxide + isobutanol system and up to 121.4 bar and 405.15 K for the carbon dioxide + tert-butanol system. The new data are consistent with our previous measurements for the same systems. The General Equation of State, Soave–Redlich–Kwong, and Peng–Robinson equations of state coupled with classical van der Waals mixing rules were used to model the phase behavior of these systems in a predictive manner. Unique sets of binary interaction parameters obtained by the k₁₂-l₁₂ method for the carbon dioxide + 2-butanol system were used to model the carbon dioxide + isobutanol and carbon dioxide + tert-butanol systems. 2-Butanol, isobutanol, and tert-butanol are the structural isomers for 1-butanol, and their binaries with carbon dioxide could be attributed to type II phase behavior. All models predict reasonably well the phase behavior of carbon dioxide + butanols.

The experimental data and the thermodynamic models suggest that the solubility increases in the order 1-butanol < isobutanol < 2-butanol < tert-butanol.