Send Orders of Reprints at Reprints@benthamscience.net Thermodynamic Modeling of High-pressure Equilibrium Data for the Systems L-lactic Acid + (propane + Ethanol) and L-lactic Acid + (carbon Dioxide + Ethanol)

This short communication reports the thermodynamic modeling of high-pressure equilibrium data (cloud points) for the systems L-lactic acid + (propane + ethanol) and L-lactic acid + (carbon dioxide + ethanol) from 323.15 K to 353.15 K and at pressures up to 25 MPa.The experimental data were modeled using the Peng-Robinson equation of state with the classical van der Waals quadratic mixing rule (PR-vdW2) and with the Wong-Sandler mixing rule (PR-WS). It is shown that the PR-vdW2 and PR-WS models were both able to satisfactorily represent the phase behavior of the system L-lactic acid + (carbon dioxide + ethanol). However, for the system L-lactic acid + (propane + ethanol), the PR-vdW2 model was not able to appropriately describe its phase behavior. The production of high-purity biodegradable polymers is an important issue for their potential applications in medicine and food industry.Biodegradable lactic-acid based polymers have highly promising properties and are easily synthesized from components available from renewable sources [1]. Lactic acid is one of the simplest chiral molecules and is usually found as a mixture of two stereoisomers (Land D-lactic acid).It is used as a raw material in the synthesis of poly (L-lactic acid) (PLA)[2, 3]. In particular, PLA is important forits biocompatibility and resorbability [4]. Knowledge of the phase equilibriaof the reaction system, which consists of the monomer, the biodegradable polymer and the supercritical/compressed solvent along with the possible presence of a cosolvent, plays a crucial role in the development and optimization of the reaction because the location of the phase boundary of the system is important for establishing appropriate reaction conditions [5, 6]. The phase behavior of L-lactide was studied in supercritical carbon dioxide at high pressures. The L-lactide + carbon dioxide system exhibited the solid – fluid and the liquid – vapor equilibria, which were determined in the temperature range 275 – 355 K and in the pressure range 10 – 80 MPa. This system shows the type of phase behavior where the two branches of the solid L-lactide + liquid + vapor curve end with the first and second critical endpoints [7]. Another study showed the phase behavior of L-lactic acid based polymers of low molecular weight in supercritical carbon dioxide at high pressures. This system also exhibited the solid – fluid and the liquid – vapor equilibria. Supercritical carbon dioxide was a poor solvent for low molecular weight L-lactic acid based polymers. The liquid-vapor equilibrium in this …

The production of high-purity biodegradable polymers is an important issue for their potential applications in medicine and food industry.Biodegradable lactic-acid based polymers have highly promising properties and are easily synthesized from components available from renewable sources [1].Lactic acid is one of the simplest chiral molecules and is usually found as a mixture of two stereoisomers (L-and D-lactic acid).It is used as a raw material in the synthesis of poly (L-lactic acid) (PLA) [2,3].In particular, PLA is important forits biocompatibility and resorbability [4].
Knowledge of the phase equilibriaof the reaction system, which consists of the monomer, the biodegradable polymer and the supercritical/compressed solvent along with the possible presence of a cosolvent, plays a crucial role in the development and optimization of the reaction because the location of the phase boundary of the system is important for establishing appropriate reaction conditions [5,6].
The phase behavior of L-lactide was studied in supercritical carbon dioxide at high pressures.The L-lactide + carbon dioxide system exhibited the solidfluid and the liquidvapor equilibria, which were determined in the temperature range 275 -355 K and in the pressure range 10 -80 MPa.This system shows the type of phase behavior where the two branches of the solid L-lactide + liquid + vapor curve end with the first and second critical endpoints [7].
Another study showed the phase behavior of L-lactic acid based polymers of low molecular weight in supercritical carbon dioxide at high pressures.This system also exhibited the solidfluid and the liquidvapor equilibria.Supercritical carbon dioxide was a poor solvent for low molecular weight L-lactic acid based polymers.The liquidvapor equilibrium in this system depended to a great extent on the structure of the end groups, while for the solidfluid equilibrium, the effect of the molecular weight was more pronounced [1].
A previous study [8]reported the phase equilibrium data (cloud points) of L-lactic acid +(propane + ethanol) and Llacticacid + (carbon dioxide+ethanol).The phase equilibrium experiments were conducted in a variable-volume view cell employing the static synthetic method from 323.15 K to 353.15 K and at pressures up to 25MPa; the mass ratio of ethanol to carbon dioxide orpropane was maintained at 1:9.The L-lactic acid + (propane + ethanol) exhibited vaporliquid, liquid-liquid and vapor-liquid-liquid transitions, whereas the L-lactic acid +(carbon dioxide+ ethanol) exhibited only liquid-liquid type transitions [8].
In addition to experimental data measurements, the development and application of thermodynamics models to represent the phase behavior of multicomponent mixtures plays a crucial role in elucidating the phenomena involved in the fractionation/separation step in the process design and optimization of, for instance, polymerization reactions performed at high pressures.The use of thermodynamics modelsis also relevant to establishing the process flow sheet of a chemical plant.For this purpose, cubic equations of state may be advantageously used to represent experimental phase equilibrium data, allowing process simulation to select appropriate operational conditions [9].
The thermodynamic modeling of the systems L-lactic acid + (propane + ethanol) and L-lactic acid + (carbon dioxide + ethanol) in this work used the previously reported phase equilibrium data [8].Based on the description of these systems at high pressures, the Peng-Robinson equation of state [10]was employed with the classical van der Waals quadratic mixing rule (PR-vdW2) and with the Wong-Sandler mixing rule (PR-WS) [11,12] to represent the experimental values found.The calculation procedure for modeling the experimental data of the systems investigated in this work followed the same procedure described previously by Araújo et al. [13] and Pinto et al. [14].
As briefly presented in our previous works [9,[13][14][15][16] the mixture parameter for vdW2 can be summarized as ( where a i and b i are the parameters of the pure compounds [10], and l ij and k ij are adjustable parameters. The mixture parameters a and b for the WS mixing rule are given by [11,12] (5) (6) where (7) and (8) For PR-EoS, the constant C is given by √ ( √ ).
The combination rule was used considering the reformulated Wong-Sandler mixing rule, by rewriting the cross second virial coefficient in the following form, as presented by Orbey and Sandler [12]: The Non-random two-liquid model (NRTL) [17] was used for the molar excess Gibbs free energy ( ( calculation.Thus, the binary interaction parameters fitted for PR-WS model were α ij , g ij , g ji and K ij . The binary interaction parameters for both models (PR-vdW2 and PR-WS) were estimated by minimizing the least square objective function (Equation 10) using the stochastic Simulated Annealing method, and the optimization procedure was refined using the Simplex method.The saturation pressure (bubble or dew point) was calculated by implementing an algorithm presented by Ferrari et al. [18] and Bender et al. [5], which is based on Michelsen's work [19].The pure component properties of carbon dioxide, propane, ethanol and L-lactic acid are presented in Table 1, including the purity, supplier, critical properties and acentric factor of all components.
The objective function used in this work was Where and are the calculated and experimental saturation pressure values, respectively, and is the number of experimental observations.The binary interaction parameters were estimated by minimizing the least square objective function of the experimental and calculated pressures using the stochastic particle swarm optimization method [18], and the procedure was refined using the Modified Simplex method [22].For the binary system {CO 2 (1) + Ethanol (2)}, the interaction parameters were taken from the literature [13].The binary interaction parameters of PR-vdW2 and PR-WS fitted to the experimental values for the systems investigated are shown in Table 2 and Table 3, respectively.For the system {Propane (1) + Ethanol (2) + L-lactic acid (3)}, when using the PR-WS model, the NRTL model was adopted to compute the molar excess Gibbs energy [14].error (abs error) and the Root Mean Square Deviation (RMSD), hence showing the good agreement between the experimental and calculated pressure transition values [23].
Figs. (3 and 4) present the pressure-temperature diagram obtained for the {Propane (1) + Ethanol (2) + L-lactic acid (3)} system for all overall mass fractions.These figures show that the PR-WS model (continuous line)was able to fit both the liquid-liquid (LLE) (Fig. 3) and the vapor-liquid bubble point (VLE-BP) (Fig. 4)transition data.These diagrams show the good performance of the PR-WS model (continuous line) and the adequate strategy adopted for all phase equilibrium data modeling.Fig. (5) presents the pressure-temperature diagram obtained for the system {CO 2 (1) + Ethanol (2) + L-lactic acid (3)}.Like the PR-vdW2 model, the PR-WS model (continuous line) showed good performance and demonstrated that the strategy adopted was adequate for the phase equilibrium data modeling.This determination can be verified by inspectingthe absolute error (abs error) and Root  This work reported the thermodynamic modeling of highpressure phase equilibrium data for the systems L-lactic acid + (propane + ethanol) and L-lactic acid + (carbon dioxide + ethanol) in the temperature range of 323.15K to 353.15 K and at pressures up to 25 MPa.In general, both systems investigated were modeled using the Peng-Robinson equation ofstate coupled with the Wong-Sandler mixing rule.However, the Peng-Robinson equation of state with the classical van der Waals quadratic mixing rule was unable to represent the system L-lactic acid + (propane + ethanol), possiblydue to the high asymmetry exhibited by this systemin terms of the molecular size and intermolecular forces.The thermodynamic modeling performed in this work may be of great value for conducting polymerization reactions of such lactones in compressed carbon dioxide and propane.

Fig. ( 1 )
Fig. (1) presents the pressure-temperature diagram obtained for the {Propane (1) + Ethanol (2) + L-lactic acid (3)} system, where it can be observed that the PR-vdW2 model (continuous line) only fitted the vapor-liquid bubble point (VLE-BP) transition data.Fig. (2) presents the pressure-temperature diagram obtained for the {CO 2 (1) + Ethanol (2) + L-lactic acid (3)} system.This diagram shows the good performance of the PR-vdW2 model (continuous line) and the adequate strategy adopted for phase equilibrium data modeling, as corroborated in Table 2 by the low values of the absolute
[23] Square Deviation (RMSD) in Table3, which are low for both systems, attesting the good agreement between the experimental and calculated (PR-WS model) pressure transition values[23].