Application of Supercritical Phase Equilibria to the Components of the Transesterification Reaction of rac-2-Pentanol with a Vinyl Ester

Abstract

This chapter illustrates the collection of phase equilibrium and high-pressure solubility data applied to four binary systems, (CO2 + 2-pentanol, CO2 + vinyl butyrate, CO2 + 2-pentyl butyrate and CO2 + butyric acid) at three temperatures of (313.15, 323.15, and 333.15) K and pressures up to 11 MPa. These four organic compounds were selected because they are implicated in the kinetic resolution of rac-2-pentanol, and their phase equilibria play an important role in the separation processes of the reaction compounds. Equilibrium data were obtained using a synthetic method in a high-pressure cell of variable volume. All systems were found to have type I phase behavior. Experimental high-pressure data showed a good correlation with density-based models and by the well-known Peng-Robinson (PR) and Soave-Redlich-Kwong (SRK) EoS coupled with the quadratic mixing rule in a semipredictive approach to describe the phase equilibrium topology of the four binary mixtures.

1. Introduction

The chapter presents a work based on the study of the behavior in supercritical medium of the reactants and products of the transesterification reaction of rac-2-pentanol with vinyl butyrate. A particular feature of this reaction is that rac-2-pentanol contains an asymmetrical carbon, and hence, it is formed by a racemic mixture of two enantiomers (R and S). The lipase enzyme that catalyzes this reaction is stereoselective so it favors the reaction of only one of the enantiomeric forms of the rac-2-pentanol, specifically the (R)-2-pentanol.

This reaction is of great importance from the point of view of the pharmaceutical industry because (S)-2-pentanol is obtained, and this is a basic intermediate compound in the synthesis of drugs against the Alzheimer disease. In general, the reaction of rac-2-pentanol with any vinyl ester is represented in Figure 1. This figure shows the reactants, vinyl ester (R-COO-CH=CH₂) and rac-2-pentanol, the compounds obtained by the synthesis route, (R)-2-pentyl ester and (S)-2-pentanol, and the compound that results from the hydrolysis reaction, the acid. The hydrolysis is the undesired reaction and parallelly competes with the desired reaction.

Figure 1.

Stoichiometric scheme of racemic resolution of rac-2-pentanol catalyzed by a lipase.

As can be seen, the first step consists of the formation of an enzyme-substrate complex between the vinyl ester and the lipase enzyme. As a consequence of the formation of this intermediate, vinyl alcohol is released, which by presenting a hydrogen atom attached to one of the carbon atoms adjacent to the carbonyl group is forming a keto-enolic equilibrium highly displaced toward the keto form, i.e., it is found as acetaldehyde. This fact contributes to removing vinyl alcohol from the medium and preventing that the vinyl ester will be formed again (which would be the reverse reaction to the desired reaction), being possible to achieve large final conversions, by favoring the displacement of equilibrium.

In the second reaction stage, there can be two possibilities:

• Hydrolysis: it is the reaction of the enzyme-substrate complex with water, giving rise to an acid and the regeneration of the enzyme in its initial state.

• Synthesis: the reaction of the complex with rac-2-pentanol forming the (R)-2-pentyl ester, also regenerating the enzyme.

As can be deduced from the above, the water present in the medium plays a fundamental role in the formation of (R)-2-pentyl ester, which is the product of interest. As the kinetic constant of hydrolysis is much greater than that of synthesis, for synthesis to predominate over hydrolysis, the concentration of the second substrate must be much higher than that of water, since this will achieve that:

k_H ·[H₂O] < < k_S · [rac-2-pentanol]

where [H₂O] is the concentration of water in the medium, [rac-2-pentanol] is the concentration of the second substrate, and k_H and k_S are the hydrolysis and synthesis constants, respectively. Accordingly, if the amount of water in the medium is controlled, it will be possible to minimize the speed of the hydrolysis reaction compared with that of synthesis.

Although an overview has been given here, in this particular work the vinyl ester studied will be vinyl butyrate, and the products are those corresponding to this ester: 2-pentyl butyrate and butyric acid.

The study of phase equilibria of mixtures involving CO₂ and other compounds at high pressure and under supercritical conditions is of crucial importance for their application in a wide range of operations related to the chemical industry such as reaction, extraction, fractionation, separation of mixtures, supercritical chromatography, synthesis, and/or fabrication of nanostructured porous materials metal support, or formation of nanocrystals, etc. [1]. It is therefore essential that experimental equilibrium data are reliable and accurate for the optimization of the involved processes [2].

Due to the high number of applications of scCO₂, many authors have studied in depth the behavior of systems (CO₂ + organic compounds) under high-pressure conditions. Isothermal data from binary systems CO₂+ different alcohols have been measured and correlations have been obtained for prediction purposes [1, 3, 4, 5, 6, 7, 8, 9, 10]. Thermodynamic knowledge of the high-pressure phase behavior of carbon dioxide + alcohol mixtures is essential for the design and optimization of many supercritical fluid extraction and supercritical fluid chromatography processes in sectors of great importance such as the oil and natural gas industry and in the food, pharmaceutical, cosmetic, and surfactant industries [1]. High-pressure equilibrium data from other organic compounds with scCO₂ can be found in the literature, such as alkanes [11], acids [12], ketones [13], amides [13], aromatic compounds such as pyrrole [14, 15], furans [16], or nitriles [17, 18]. As stated in Chapter 2, in recent decades, several reviews have been published that collect a large number of experimental data of high-pressure phase equilibrium in different systems, most of which are binary systems involving CO₂ [19, 20, 21]. These reviews classify the results based on the experimental procedure used to obtain them.

As an example, this chapter shows how to obtain phase equilibrium and high-pressure solubility data applied to four binary systems (CO₂ + organic compound). The four organic components are those involved in the kinetic resolution of rac-2-pentanol by transesterification of vinyl butyrate catalyzed by a lipase. The scheme in Figure 1 shows the stoichiometry of the reaction. The compound of interest is (S)-2-pentanol, which is a key intermediate necessary for the synthesis of several drugs for the treatment of Alzheimer’s disease that inhibit the release and/or synthesis of β-amyloid peptide [22]. The enzymatic resolution of rac-2-pentanol by Candida antarctica lipase B has been demonstrated. Commercially available C. antarctica lipase B efficiently catalyzed the enantioselective acetylation of rac-2-pentanol yielding an enantiomeric excess (ee) of 99% for (S)-2-pentanol [23].

For long, the excellent properties that scCO₂ has for the dissolution, extraction, and transport of chemical compounds are well known. This is due to its low viscosity, low surface tension, and high diffusion coefficients. The diffusivity of the substrates in scCO₂ allows an excellent mass transfer and is a clean alternative to conventional organic solvents that can contribute to the integration of reaction and separation processes in a single stage. The measurement of the high-pressure phase equilibrium data of binary mixtures (CO₂ + 2-pentanol, vinyl butyrate, 2-pentyl butyrate, or butyric acid) and the determination of the solubility between CO₂ and the organic compound would make it possible to establish the ability of CO₂ to separate reaction products and optimize the operating conditions to carry out such separation. Nevertheless, scCO₂ could have an adverse effect on the enzyme and cause deactivation due to the decrease in the pH of the enzyme microenvironment, to the covalent modification of the free amino groups on the surface of the protein forming carbamates and/or to the pressurization/depressurization cycles [24]. As discussed in Chapter 2, to solve these possible problems, the use of scCO₂/ionic liquid biphasic systems has been proposed. Ionic liquids have also been considered “green” solvents due to their negligible vapor pressure, and they can contribute to supply of a nonaqueous catalytic medium [25]. The success of these biphasic systems is based on the practical insolubility of the ionic liquid in scCO₂ and the high solubility of scCO₂ in the ionic liquid, in such a way that the extraction of organic compounds from the ionic liquid is facilitated by scCO₂ without cross-contamination of the organic compound with the ionic liquid [26, 27].

One of the objectives of this study was to obtain experimental measurements of the high-pressure phase equilibrium of the systems (CO₂ + 2-pentanol), (CO₂ + vinyl butyrate), (CO₂ + 2-pentyl butyrate), and (CO₂ + butyric acid) in isothermal tests at temperatures of 313.15, 323.15, and 333.15 K. Another aim was to obtain the correlations of the experimental data using density-based models and by Peng-Robinson (PR) [28] and Soave-Redlich-Kwong (SRK) [29] EoS together with the quadratic mixture rule providing a semipredictive approach that describes the phase equilibria of the four binary systems. To obtain the correlations, the acentric factor (ω) was estimated using the Lee-Kessler group contribution method, and the critical temperature and critical pressure (T_c, P_c,) values of the organic compounds were obtained from the literature or were estimated using the Joback group contribution method.

2. Apparatus and experimental procedure

To obtain the experimental values of phase equilibrium of binary systems (CO₂ + 2-pentanol), (CO₂ + vinyl butyrate), (CO₂ + 2-pentyl butyrate), and (CO₂ + butyric acid), the commercial Super Phase Monitor equipment (SPM system, Thar Technologies, Inc., USA) was used, which is shown in the scheme of Figure 2. The most important elements of the device are: a high-pressure pump, a thermostated cell of variable volume, provided with two sapphire windows to locate a camera and a lighting source, a visual device, and a control software provided by the supplier. The cell has an agitator and a piston cylinder that moves by a hydraulic pump. The volume of the cell is determined by the position of the piston. The CO₂ is fed to the cell by a syringe pump (Teledyne ISCO, model 500D, USA), provided with a pressure controller. The pump has a cooling system connected to a thermostatic water bath (Frigiterm, J.P. Selecta S.A., Spain) that keeps the CO₂ in liquid phase. The measuring cell allows visual observation of its interior through the sapphire windows, and the image is collected in a video system that displays the image on the computer monitor.

Figure 2.

Scheme of the high-pressure phase equilibrium apparatus. From reference [30] with permission of Elsevier.

A synthetic method was used to carry out the measurements of phase equilibria. The procedure followed has been described elsewhere [30]. Briefly, first, the cell was purged with CO₂ at low pressure to remove the air from inside of the cell. The organic compound was then weighed with an accuracy of 0.1 mg with an analytical scale (Sartorius, model ED 1245, Germany) and loaded into the cell with a syringe. Then compressed CO₂ was introduced into the cell using the syringe pump. The molar fraction of the binary mixture within the cell was determined on the base of the CO₂ loaded mass, calculated by the volume displaced by the pump and the CO₂ density, obtained from NIST [31], at the selected pressure and temperature values. It was estimated that the mass of CO₂ when each experiment begins, after purging, was <1% and was ignored.

With the components inside the cell, the temperature was set at the selected value and the pressure was raised by moving the plunger to reduce the volume of the cell until a homogeneous phase was observed. The system was then kept in agitation for about 30 minutes to ensure that the system was in equilibrium. From this moment, the volume was increased by 80 μL in a staggered way, displacing the piston, and recording the pressure of the cell until a second phase was observed. Each experiment was repeated at least twice. Figure 3 shows, as an example, the determination of the bubble point from a graph of depressurization of a mixture (CO2 + 2-pentanol) at 313.15 K (molar fraction of CO₂: 0.541). As can be observed, the pressure displacement of the piston (correlated with cell volume) line changes slope when a new phase with a different isothermal compressibility appears. The intersection of the two lines corresponds to the equilibrium pressure, as described by Thamanavat et al. [14, 32]. This procedure was repeated at temperatures of 313.15, 323.15, and 333.15 K to obtain isothermal curves.

Figure 3.

Pressure-volume relation for the depressurization of (CO₂ + 2-pentanol) at 313.15 K; CO₂ mole fraction: 0.541.

3. Results and discussion

3.1 Experimental phase equilibrium data

Figures 4 and 5 show the comparison of the experimental values and those calculated from Peng-Robinson and Soave-Redlich-Kwong EoS and quadratic mixing rule for the systems studied in the form of isotherms (313.15, 323.15, and 333.15 K) of pressure composition (P, x). These figures also show the bubble points measured for all systems. With respect to the experimental measurements previously published [2, 9, 33, 34], the data reported by the authors agree, with deviations less than 0.3 MPa, even they are even more accurate due to the modifications made in the experimental procedure. As can be seen in Figures 5 and 6, the bubble pressure increases when the molar fraction of CO₂ is increased for all isotherms, indicating that the liquid phase, rich in organic compound, can dissolve more CO₂. However, at a constant pressure, the solubility of CO₂ in the above phase is reduced for all systems when the temperature is increased. In this work, for the temperature and molar fraction values used, three phases were not detected, but all binary mixtures exhibited critical mixture curves with a maximum pressure-temperature located in the range of critical temperatures of the organic compound and CO₂. This phase behavior corresponds in all cases to Type I according to the Scott and Konynenburg classification [35]. As explained in Chapter 2, it is represented by a critical curve that links up the critical points of pure compounds in the P-T phase diagram.

Figure 4.

Experimental data and calculated phase equilibrium behavior for carbon dioxide + organic compound at 313.15 K, 323.15 K, and 333.15 K with Peng-Robinson EoS and quadratic mixing rule. (a) 2-pentanol; (b) butyric acid; (c) vinyl butyrate; (d) 2-pentyl butyrate. From reference [30] with permission of Elsevier.

Figure 5.

Experimental data and calculated phase equilibrium behavior for carbon dioxide + organic compound at 313.15 K, 323.15 K, and 333.15 K with Soave-Redlich-Kwong EoS and the quadratic mixing rule. (a) 2-pentanol; (b) butyric acid; (c) vinyl butyrate; (d) 2-pentyl butyrate. From reference [30] with permission of Elsevier.

Figure 6.

Linear correlation between ln(x_CO2) and ln(ρ_CO2/p) for binary mixtures of CO₂ with 2-pentanol (), butyric acid (), vinyl butyrate (), and 2-pentyl butyrate () at a) 313.15 K; b) 323.15 K; c) 333.15 K. from reference [30] with permission of Elsevier.

3.2 Density-based models

The density of CO₂ was obtained by the Chrastil Equation [36], which is a linear equation that relates the solubility of the organic compound and the density of scCO₂. This equation has been used to study supercritical gaseous solutions with low solute concentration and to determine the accuracy of experimentally obtained solubility measurements.

Henry’s law is normally used to study the solubility of a gas in a liquid. It shows that the amount of gas that can be dissolved in a liquid depends linearly on its partial pressure. However, some deviations from Henry’s law are observed at high pressures and, then, it is not suitable for obtaining the solubility of supercritical fluids in organic liquids. The semiempirical Eqs. (1) and (2) were obtained, modifying Henry’s law, by Hernández et al. [37] to determine the solubility of a supercritical fluid in a liquid in terms of the molar fraction of the supercritical fluid in the liquid phase. Eq. (1) gives better solubility values when positive deviations to Henry’s law are presented for the mixture, and Eq. (2) is more suitable for mixtures with negative deviations from Henry’s law.

$$ln\left(x_{\mathit{scCO}2}\right)=Aln\left({\rho }_{\mathit{scCO}2}\right)+B\left(\mathit{constanttemperature}\right)$$E1

$$ln\left(x_{\mathit{scCO}2}\right)=A^{\prime }\frac{ln\left({\rho }_{\mathit{scCO}2}\right)}{P}+B^{\prime }\left(\mathit{constanttemperature}\right)$$E2

where $x_{\mathit{scCO}2}$ is the mole fraction of scCO₂, P is the pressure (MPa), ${\rho }_{\mathit{scCO}2}\mathit{is}$ the supercritical carbon dioxide density (kg/m³), and A, B, A’, and B’ are the fitting parameters, which are obtained from the regression of the experimental data. Table 1 shows the fitting parameters and the regression coefficients, R² and R^2’, obtained for the studied binary systems.

Compound	T (K)	CO2 density range (kg·m^−3)	A	-B	R^2	-A’	B′	R^2’
2-Pentanol	313.15	93.4–250.7	1.0647	5.9939	0.9949	3.2701	2.1380	0.9750
	323.15	142.0–327.7	0.8269	4.8724	0.9965	3.5596	2.0295	0.9864
	333.15	140.3–339.6	0.9068	5.3782	0.9929	3.7674	1.9017	0.9940
Butyric acid	313.15	59.1–238.7	0.8498	4.6715	0.9895	1.9381	1.2714	0.9876
	323.15	65.5–312.4	1.1091	6.1856	0.9334	2.9343	1.7907	0.9958
	333.15	118.8–349.0	0.7498	4.4433	0.9751	2.8796	1.4424	0.9989
Vinyl butyrate	313.15	45.7–185.1	0.7676	3.9554	0.9393	1.3095	0.9444	0.9944
	323.15	36.5–232.2	0.6835	3.6511	0.9504	1.2351	0.7730	0.9991
	333.15	39.9–233.1	0.6537	3.5833	0.9651	1.1726	0.5646	0.9976
2-Pentyl butyrate	313.15	50.1–172.4	0.6571	3.4738	0.9746	1.1812	0.7841	0.9945
	323.15	48.2–197.7	0.9353	4.8913	0.9328	1.8270	1.2287	0.9953
	333.15	65.8–227.8	0.8914	4.7735	0.9474	2.0089	1.2002	0.9934

Table 1.

Fitting parameters of Eqs. (1) and (2) for (CO₂ + 2-pentanol, butyric acid, vinyl butyrate, or 2-pentyl butyrate) binary systems at 313.15, 323.15, and 333.15 K. from reference [30] with permission of Elsevier.

Figure 6 shows the results of the fittings at 313.15, 323.15, and 333.15 K. The following order was found for the solubility of CO₂ in the organic compounds for all temperatures: 2-pentanol > butyric acid > esters. From these results, it can be induced that the relative polarity of CO₂ and the organic compounds has an important contribution to the CO₂ solubility [38]. From these results, it can be concluded that the unreacted (S)-2-pentanol could be recovered from a biphasic system liquid ionic/CO₂, since the solubility of CO₂ in 2-pentanol is higher than that in the other compounds involved in the transesterification reaction and would allow the successful separation of the racemic mixture.

3.3 Thermodynamic modeling

As was reported on Chapter 2, the available literature shows a vast compilation of EoS to predict phase behavior of binary systems. Among them, Peng-Robinson [28] and Soave-Redlich-Kwong [29] EoS, which are cubic equations, are widely used because of their simplicity and accuracy. The experimental data obtained in this study were fitted using the two EoS mentioned above, which were combined with quadratic (Q) mixing rules with two binary interaction parameters (BIP) designated as k_ij, l_ij.

To correlate the data, the Phase Equilibria 2000 (PE2000) software, developed by Brunner et al. [39], was used. This software employs the Simplex-Nelder-Mead algorithm [40] to optimize binary interaction parameters. Critical parameters were estimated by the contribution method of the Joback group [41] or taken from the literature [42, 43, 44, 45], and acentric factors were estimated by the Lee-Kessler group contribution method [46]. Table 2 collects the values of the critical parameters used.

Compound	Mw (g/mol)	pc (MPa)	Tc (K)	ω
Carbon Dioxide	44.10	7.38a	304.2a	0.225a
Acetone	58.08	4.70b	508.1b	0.306**
2-Pentanol	88.20	3.68c	560.3c	0.557**
Butyric Acid	88.11	4.06d	615.2d	0.690**
Vinyl Butyrate	114.14	3.56*	539.9*	0.394**
2-Pentyl Butyrate	158.24	2.34*	618.7*	0.565**

Table 2.

Acentric factor (ω) and critical parameters (p_c,T_c) of the pure compounds used for thermodynamic modeling. From reference [30] with permission of Elsevier.

^a

Retrieved from DIPPR database [42].

^b

Retrieved from Ambrose et al. [43].

^c

Retrieved from Gude and Teja [44].

^d

Retrieved from Andereya and Chase [45].

^*

Estimated with Joback method.

^**

Estimated with Lee-Kessler method.

Figures 4 and 5 show the experimental and calculated data obtained with EoS. A great agreement was found between the experimental and calculated data for all mixtures with Peng-Robinson and Soave-Redlich-Kwong EoS.

Table 3 shows the BIP used with the Peng-Robinson and Soave-Redlich-Kwong EoS for each system and temperature. The suitability of using the modeling approach to correlate the experimental bubble point data with the points calculated by Peng-Robinson and Soave-Redlich-Kwong EoS was assessed from the relative mean square deviation (RMSD). The found values are collected in Table 4.

	2-Pentanol		Butyric Acid		Vinyl Butyrate		2-Pentyl Butyrate
T (K)	kij	lij	kij	lij	kij	lij	kij	lij
Peng-Robinson - Quadratic
313.15	0.0821	−0.0328	−0.0618	−0.1007	−0.0499	−0.0998	−0.0212	−0.0425
323.15	0.0747	−0.0371	−0.0650	−0.1178	−0.0683	−0.0706	−0.0613	−0.1196
333.15	0.0688	−0.0348	−0.0402	−0.1007	−0.0627	−0.0557	−0.0636	−0.1237
Soave-Redlich-Kwong - Quadratic
313.15	0.0898	−0.0351	−0.0723	−0.1028	−0.0505	−0.0858	−0.0300	−0.0700
323.15	0.0873	−0.0255	−0.0743	−0.1205	−0.0631	−0.0728	−0.0501	−0.1001
333.15	0.0814	−0.0290	−0.0467	−0.1012	−0.0644	−0.0562	−0.0501	−0.1003

Table 3.

Binary interaction parameters (BIP) (k_ij, l_ji) used for the thermodynamic modeling of the (CO₂ + 2-pentanol), (CO₂ + vinyl butyrate), (CO₂ + 2-pentyl butyrate), and (CO₂ + butyric acid) binary systems at 313.15, 323.15, and 333.15 K. from reference [30] with permission of Elsevier.

	2-Pentanol	Vinyl Butyrate	2-Pentyl butyrate	Butyric Acid
T (K)	Peng-Robinson - Quadratic
313.15	3.91	3.95	4.02	5.88
323.15	1.16	6.51	5.62	3.71
333.15	3.91	2.08	4.78	2.52
T (K)	Soave-Redlich-Kwong - Quadratic
313.15	4.01	3.78	3.90	6.18
323.15	1.99	6.46	5.12	4.25
333.15	4.37	2.19	4.79	2.51

Table 4.

RMSD values (%) obtained for the thermodynamic modeling using Peng-Robinson and Soave-Redlich-Kwong EoS combined with quadratic mixing rules for the studied systems at 313.15, 323.15 K, and 333.15 K.

As a consequence of the analysis of the results, it can be observed that, for pressures close to the critical point of the system, the molar fraction of the organic component in the vapor phase increased for all the mixtures studied as the temperature increased at constant pressure. This means that the solvation capacity of the vapor phase (rich in CO₂) increases when its density increased to reach the critical point of the mixture. In addition, when the temperature increases, the chemical potential of the organic compound also increases.

The experimental results and the results obtained from the density-based and thermodynamic models allow us to infer that the different solubility of organic compounds in CO₂ could be useful to carry out the kinetic resolution of the racemic mixture of (R, S)-2-pentanol at different temperature values. In the racemic resolution of rac-2-pentanol, the (S)-2-pentanol does not react with the vinyl ester and can be dissolved in scCO₂. However, (R)-2-pentanol reacts with vinyl butyrate when an ionic liquid is used as a reaction medium to obtain (R)-2-pentylbutyrate. However, these conclusions have been inferred from binary mixtures, so further studies with mixtures of CO₂ with all components of the reaction would be required to corroborate the results.

4. Conclusions

Using a synthetic method in a cell of variable volume at high pressure, the phase equilibria of binary systems of (CO₂ + butyric acid), (CO₂ + 2-pentanol), (CO₂ + 2-pentyl butyrate), and (CO₂ + vinyl butyrate) at three temperatures (313.15 K, 323.15 K, and 333.15 K) have been obtained. A type I behavior was observed and three coexisting phases were not appreciated for the experimental conditions used.

A Chrastil-type correlation has been employed to correlate the scCO₂ solubility in organic compounds as a function of CO₂ density obtaining an equivalent accuracy to EoS-based models. The CO₂ solubility in organic compounds can be established as follows: 2-pentanol > butyric acid > esters, under the studied operating conditions. Differences in the relative polarity of the compound and CO₂ produce differences in the mutual solubility of the components.

The experimental and calculated data provided good agreement with EoS correlation of Peng-Robinson and Soave-Redlich-Kwong applied with quadratic mixing rules and two BIPs.