PHASE BEHAVIOR DATA AND THERMODYNAMIC MODELING OF THE BINARY SYSTEM {CO₂ + COUMARIN} AT HIGH PRESSURES

Abstract

In this work, vapor - liquid (VLE) equilibrium for the binary system carbon dioxide (1) + coumarin (2) at high pressures was measured by a static synthetic method using a variable-volume view cell. Experimental data were obtained in the temperature range of 318 - 338 K and pressures up to 20 MPa. Coumarin molar fraction ranged from 3.0x10^-3 to 6.0x10^-3. Coumarin melting point reduction at high pressures was observed. The experimental results were modeled using the Peng-Robinson (PR) equation of state with van der Waals quadratic mixing rules (vdW - QMRs), providing a good representation of the experimental phase equilibrium data. Critical properties and the acentric factor were estimated using the Constantinou and Gani method, which showed to be satisfactory on the quality of data correlation. Results indicate coumarin solubility increases with increasing phase transition pressure at a given temperature.

Keywords:
Coumarin; CO₂; Phase transition; Experimental data; Peng-Robinson Cubic Equation

INTRODUCTION

Coumarin and its derivatives belong to a large class of compounds that naturally contain benzo-α-pyrone. They are widely used as fragrance ingredients, fixing agents in cosmetics, dyes and aromatic compounds (Fylaktakidou et al, 2004; Matos et al, 2015; Symeonidis et al, 2009). Coumarin has various biological activities such as anti-inflammatory, antitumor, anti-allergic, anti-HIV, antiviral, antioxidant, antimicrobial, and anti-asthmatic (Borges et al, 2005; Matos et al, 2011; Matos et al, 2015; Tabart et al, 2009). Coumarin can be found in a wide variety of fungi, bacteria, plants, and essential oils (Hamdi et al, 2008; Matos et al, 2015; Panteleon et al, 2008).

Previous studies using supercritical carbon dioxide (scCO₂) and co-solvents to extract coumarin from natural sources are available (Lanças et al, 1997; Oliveira et al, 2013; Rodrigues et al, 2008; Vilegas et al, 1997). The use of scCO₂ for the extraction of coumarin and other bioactive compounds is an interesting technique because this fluid has unique characteristics that enable the extraction free of organic solvents.

Interaction between solvent and solute is important to develop the extraction of bioactive compounds, and other applications such as nanoencapsulation (Dohrn et al, 2010; Reverchon and De Marco, 2006). Solubility measurements of the system carbon dioxide and coumarin can contribute to optimize supercritical extraction, since the transfer mass coefficient has implicit dependence (Dohrn et al, 2010). The study of phase behavior provides important information about a system. Adjustment of mathematical models to experimental data allows the construction of a phase diagram.

Coumarin solubility investigations by analytical or semi-continuous flow methods are available in the literature (Rodrigues et al, 2008; Yoo et al, 1997). In these methods, the composition varies throughout the experiment. However, data obtained by the static synthetic method with a view cell are unpublished. The main differential of this technique is the possibility to visualize and identify phase transition types. Phase transition measurements using the proposed static method are adequate to avoid supersaturation regions in opposition to the dynamic method. Thus, this work focused on measuring and modeling phase equilibrium data of the binary system CO₂ (1) + coumarin (2) at high pressures and temperature range of 318 K-338 K. The static synthetic method with a variable-volume cell was used to determine phase transitions. Experimental data of phase equilibria were modeled by the Peng-Robinson cubic equation with van der Waals quadratic mixing rules. The coumarin mole fractions investigated varied from 3.0 x 10^-3 to 6.0 x 10^-3. Vapor - liquid (VLE) phase transition type was observed.

MATERIALS AND METHODS

Materials

Carbon dioxide (CO₂) was purchased from White Martins S.A (Osasco-SP, Brazil) with purity of 99.9 wt% (liquid phase). Coumarin with 98% purity degree was acquired from Aldrich (São Paulo-SP, Brazil). All substances were used without any pre-treatment.

Apparatus and Experimental Procedure

The apparatus used in this work consisted of a high-pressure variable-volume cell, following the static synthetic method. Methodology and apparatus were described in previous works (Ferreira et al, 2013; Giufrida et al, 2014; Giufrida et al, 2016; Pinto et al, 2013; Zanette et al, 2014). Maximum internal volume of the equilibrium cell was 25 cm³, internal cell diameter was 1.8 cm and contained a movable piston. It also had two sapphire windows, one for visual observations, 2.5 cm inner diameter (i.d.), and a lateral one for light entrance, 1.5 cm i.d. Maximum operating temperature and pressure were, respectively, 423 K and 35.0 MPa.

Figure 1 shows a schematic view of the experimental apparatus employed.

Figure 1
Schematic diagram of the experimental apparatus: (C) CO₂ cylinder; (V1, V2, V3, V4, V5, and V6) valves; (TD) pressure transducer; (PI) pressure indicator; (TI) temperature indicator; (OW) observation window; (LW) lighting window; (EC) equilibrium cell, stainless steel 25 cm³ maximum capacity; (P) piston; (MS) magnetic stirrer; (PP) pressure control pump, and (TB) thermostatic bath.

The experimental procedure is summarized as follows: a known amount of coumarin, determined on a precision scale balance (Marte, model AM220, Santa Rita do Sapucaí, MG, Brazil), was loaded into the equilibrium cell, with an uncertainty of ± 0.0001 g. The cell was then flushed with low pressure CO₂ to remove any residual air. The amount of CO₂ remaining in the equilibrium cell was negligible ( ̴10^-5 mol) when compared to the total amount of CO₂ used to determine experimental data. A given amount of CO₂ was loaded using a syringe pump (ISCO, model 500D, Lincoln, USA), resulting in an uncertainty of ±0.005 g in CO₂ loadings. The mixture was conducted under constant stirring using a magnetic bar inside the cell while obtaining experimental data.

The cell was equipped with an aluminum jacket for temperature control. A PID controller (DIGI MEC, SHM 112, Sertãozinho, SP, Brazil) was connected to a thermocouple (T type, uncertainty of ±1.0 K), which was fixed in direct contact with the mixture inside the cell.

CO₂ was used as an auxiliary fluid at the back of the cell to pressurize the system slowly until it reached a single phase. The system remained at this point for at least 30 min to guarantee stabilization in a homogeneous state. The pump was used in pressure gradient mode, with gradual decrease of pressure at 0.1 MPa.min^-1, until the phase transition was observed (Pinto et al, 2013).

The experiments were carried out in the temperature range of 318 K - 338 K. Phase transitions were determined visually, as described by McHugh and Krukonis (1994). Experiments were obtained in triplicate for all temperatures studied.

THERMODYNAMIC MODELING

The experimental data obtained in the present work were correlated using the Peng- Robinson equation of state. All transitions were considered vapor-liquid equilibria. The isofugacity criterion for each component i in the system was used in the calculations as follows:

$$y_i^{f1}{\widehat{\phi }}_i^{f1}=y_i^{f2}{\widehat{\phi }}_i^{f2}$$ (1)

where y_i ^f1 and y_i ^f2 are the mole fractions of component i in the fluid phases f¹ and f², respectively, ϕ_i ^f1 and ϕ_i ^f2 are the fugacity coefficients of component i in the same fluid phases. The van der Waals (vdW) quadratic mixing rules (QMRs) for a and b parameters were used in all calculations.

$$a={\displaystyle \sum _{i=1}^c{\displaystyle \sum _{j=1}^c{y}_i{y}_j\sqrt{a_i{a}_j}(1-k_{ij})}}$$ (2)

$$b={\displaystyle \sum _{i=1}^c{\displaystyle \sum _{j=1}^c{y}_i{y}_j\frac{b_i+b_j}{2}(1-l_{ij})}}$$ (3)

where y_i is the mole fraction of component i, a_i and b_i are the Peng-Robinson parameters for the pure component i, c is the number of components, and k_ij and l_ij are the binary interaction parameters.

Binary interaction parameters were fitted for each temperature (318, 328 and 338 K) using the experimental data of Table 1 and the objective function (Equation 4).

$$OF\left(P\right)={\displaystyle \sum _{o=1}^{no}{\left(P_{\exp }-P_{calc}\right)}^2}$$ (4)

where no is the number of data points and P_exp and P_calc are, respectively, experimental and calculated pressure at the bubble point.

Table 1
Experimental solubility. Phase equilibrium data for temperature (T), pressure (P) with standard deviation, and molar fraction x for the CO₂ (1) + coumarin (2) system.

Temperature/Ka	y2 (coumarin)	Pressure/MPa	Transition
318	3.0x10-3	10.85±0.032	VLE
318	4.0x10-3	13.65±0.153	VLE
318	4.5x10-3	14.80±0.007	VLE
318	5.0x10-3	15.46±0.118	VLE
318	5.5x10-3	16.22±0.013	VLE
318	6.0x10-3	17.00±0.071	VLE
328	3.0x10-3	13.93±0.190	VLE
328	4.0x10-3	15.22±0.035	VLE
328	4.5x10-3	15.92±0.175	VLE
328	5.0x10-3	16.72±0.038	VLE
328	5.5x10-3	17.36±0.205	VLE
328	6.0x10-3	17.91±0.034	VLE
338	3.0x10-3	15.54±0.105	VLE
338	4.0x10-3	18.00±0.274	VLE
338	4.5x10-3	18.39±0.170	VLE
338	5.0x10-3	18.86±0.010	VLE
338	5.5x10-3	19.46±0.210	VLE
338	6.0x10-3	19.86±0.057	VLE

• ^au(T) = 1.0 K

Previous work (Ferreira et al, 2013) conducted by our research group described the procedure to minimize the objective function. According to the authors, the “Solver” tool available in the Microsoft Excel (2016 version) spreadsheet for Windows and the XSEOS (Castier et al, 2008) Excel add-in were used to minimize the objective function and fit Peng-Robinson interaction parameters.

Critical temperature (T_c = 794.77 K), critical pressure (P_c = 4.347 MPa), and acentric factor (ω = 0.3945) of coumarin used in the PR-EoS were obtained using the Constantinou and Gani method (Poling et al, 2000). Similar values were found by Yoo et al. (1997) using the Lyderson-Forman-Thodos method. The values of same properties for CO₂ were obtained from Poling et al. (2000).

Absolute average deviations (AAD%) between calculated and experimental data were calculated according to equation (5)

$$AAD=\frac{1}{N}\left(\frac{\left|P_{cal}-P_{\exp }\right|}{P_{\exp }}\right)100$$ (5)

where N is the number of experimental data points in an isothermal, P _cal (MPa) is the theoretically calculated transition pressure, and P _exp (MPa) is the experimental transition pressure.

RESULTS AND DISCUSSIONS

Experimental Results

Table 1 shows experimental data of phase transitions for the binary system CO₂(1) + coumarin (2). The measured experimental data are presented in terms of mole fraction of coumarin (2) and the transition pressure value.

Standard deviation for the pressure transition was calculated for triplicate values of the phase transition (MPa) in the range of 0.01 - 0.05 MPa based on three repetitions for each experimental point. Experimental conditions of pressure, temperature, and mole fraction of coumarin were 10 to 20 MPa, 318 to 338 K, and 3.0x10^-3 to 6.0x10^-3, respectively.

The phenomenon of coumarin melting point reduction at high pressures has been discussed in a previous study (Rodrigues et al., 2008). This hypothesis was confirmed by visual method since the experimental apparatus used in the present work provided a clear view of phase transitions. Solubility of supercritical CO₂ inside the solid particle caused the melting point depression (Lian et al, 2010). Figure 2 shows the liquid coumarin formed at 318 K and in mole fraction of 6x10^-3, due to melting point depression at high pressure.

Figure 2
Equilibrium cell during experiments. a) Solid coumarin before pressurization. b) First moment of liquid coumarin precipitation. c) Coumarin accumulates as pressure decreases.

The experimental data of phase transition pressures reached values up to 20 MPa with 6x10^-3 coumarin mole fraction. To reach a homogeneous phase, pressure higher than 30 MPa is required if the coumarin molar fraction is higher than 6x10^-3, which is over the apparatus operational limit of pressure. On the other hand, compositions lower than 2x10^-3 were difficult to visualize. Therefore, the composition range between 3x10^-3 and 6x10^-3 was chosen. Binary system CO₂ (1) + coumarin (2) data are given in Figure 3 with pressure error bars.

Figure 3
Pressure-composition diagram for the system CO₂ (1) + Coumarin (2); () 318 K, () 328 K, () 338 K.

The extractive method applied by Rodrigues et al. (2008) resulted in higher values of solubility, which may have occurred owing to the fact that it was in a supersaturation zone. This effect can be avoided using the static synthetic method. In addition, it is not possible to visualize both a homogeneous phase and phase transition through the extractive method.

Yoo et al. (1997) determined solubility values of coumarin in supercritical CO₂ using a microscale apparatus through the analytical method. The authors observed lower values than those found in the present work. Despite the difference, solubility data obtained in this study were intermediate and similar to those reported in the literature. Figure 4 shows coumarin in supercritical CO₂ studied in past works using different methods.

Figure 4
Solubility data for coumarin in supercritical CO₂ from this study at 318 K (●), 328 K (▲) and 338 K (), from Rodrigues et al. (2008) at 308 K (□), 318 K (○) and 328 K (), and from Yoo et al. (1997) at 308 K (), 313 K () and 323 K ().

Coumarin solubility increased with increasing phase transition pressure at a given temperature. Contrary to this study, both methods found in the literature describe a crossover temperature in solubility. This can be mainly related to the different methods used. Another point to observe is the temperature range. In this work the temperature range was 318-338 K, whilst for Rodrigues et al (2008) it was 308-328 K, and for Yoo et al. (1997) the temperature range was 308-323 K.

In this study, the composition ranged between 3.0x10^-3 and 6.0x10^-3. As for the other works, the composition range resulted in 0.91x10^-2 - 3.01x10^-2 (Rodrigues et al, 2008), and 1.0x10^-3 - 2.66x10^-3 (Yoo et al, 1997). Then, although crossover was not observed in experimental data in the present study, it could occur with different composition values that were not analysed.

Modeling Results

Table 2 presents the parameter values of k_ij and l_ij calculated for this study.

Table 2
Fitted parameters for each temperature using the experimental data obtained in this work.

T (K)	Parameters
	k12	l12
318	0.1674	0.0045
328	0.1691	0.0026
338	0.1836	0.0126

Figure 5 shows the correlation of all experimental data obtained using the PR-EoS. These data express the predicted values of solubility. The thermodynamic modeling used here can correlate the experimental data satisfactorily.

Figure 5
Experimental and calculated pressure transitions for the binary system CO₂ (1) + coumarin (2) at T = 318 K (); 328 K (); 338 K (). Calculations with the Peng-Robinson equation of state (----) and parameters from Table 2.

The model used in this work agrees with the experimental data. Absolute pressure average deviations (AAD%) were 4.6%, 1.6% and 2.5% for 318, 328 and 338 K isothermal, respectively.

Although there was no crossover in the experimental data, this phenomenon tended to occur at higher compositions, first with the isotherms 318 and 328 K, and then with isotherms 318 and 338 K, according to the calculated pressure transitions shown in Figure 5. The difference in pressure may be related to the distinct methodology and different temperature, pressure and solubility used in other works available in the literature (Rodrigues et al, 2008; Yoo et al, 1997).

CONCLUSIONS

This phase equilibrium study reported new VLE equilibrium data for the binary system CO₂ (1) + coumarin (2). The analyzed system has characteristics of a type II transition. The static synthetic method was used with temperatures ranging from 318 K to 338 K. Maximum pressure obtained was close to 20 MPa. The Peng-Robinson equation of state calculated satisfactorily the phase equilibrium of CO₂ (1) + coumarin (2) system. Data reported in the present study are similar to experimental data found in the literature. Differences in concentrations as compared to the literature may be attributed to the experimental methodologies used. Moreover, the temperature range studied should also be observed.

The visual identification of the phase transition type for the measured system was not trivial due to the melting point depression phenomenon and the high asymmetry between the CO₂ molecule and coumarin. Near the phase transition point, the depressurization rate was decreased to avoid supersaturation. Although measured experimental data did not show crossover such as those in literature, it was possible to predict crossover using the PR-EoS with the binary parameters. These results show the robustness of the model applied and the experimental data consistency.

ACKNOWLEDGEMENTS

This research work was supported by CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior and CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico - Brazil.

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LIST OF SYMBOLS

• y₂  Mole fraction of coumarin
• φ₂ ^∞  Fugacity coefficient of coumarin at infinite dilution
• a  van der Waals mixing rules parameter
• b  van der Waals mixing rules parameter
• k_ij  Binary interaction parameters
• l_ij  Binary interaction parameters
• T_c  Critical temperature
• P_c  Critical Pressure
• ω  Acentric factor
• PR-EoS  Peng-Robinson - Equation of State
• P_calc  Calculated Pressure
• P_exp  Experimental Pressure
• AAD  Absolute average deviations

Publication Dates

• Publication in this collection
  30 Sept 2019
• Date of issue
  Apr-Jun 2019

History

• Received
  23 July 2018
• Reviewed
  14 Jan 2019
• Accepted
  16 Jan 2019