# Liquid–Liquid and Vapor–Liquid–Liquid Equilibria of the Alkyl Palmitate + Alkyl–OH + Glycerol Systems at 101.3 kPa—Measurements, Quality Test/Consistency, Thermodynamic Modeling and Molecular Dynamics Simulations

## TL;DR

This study measures and models phase behavior in biodiesel production systems to improve separation and purification processes.

## Contribution

New experimental and modeling data on LLE and VLLE for alkyl palmitate + alkyl–OH + glycerol systems at 101.3 kPa.

## Key findings

- NRTL model accurately describes phase behavior with deviations below 2.0%.
- Methanol and ethanol interact more strongly with glycerol, aiding purification.
- Phase separation is clear between palmitate-rich and glycerol-rich phases.

## Abstract

Biodiesel is a biofuel commonly produced through transesterification, also known as alcoholysis. In this process, triglycerides react with short-chain alcohols (alkyl–OH), producing a mixture of fatty acid esters and glycerol. These esters and glycerol are only partially miscible, leading to the formation of two liquid phases during product separation. Therefore, it is important to experimentally determine liquid–liquid (LLE) and/or vapor–liquid–liquid equilibrium (VLLE) data to better understand the transesterification process and to support improvements in reaction rate, selectivity, reactor and mixture simulation, optimization, and separation processes. This work aimed to experimentally measure and thermodynamically model the LLE and VLLE of alkyl palmitate + alkyl–OH + glycerol systems at 101.3 kPa. For the LLE at 318.15 K, the binodal curve was determined, and tie-line compositions were measured in a jacketed equilibrium cell. These data were subjected to quality tests and used to calculate separation factors. For the VLLE, calibration curves were constructed, and experimental data were obtained in a modified Othmer ebulliometer and subsequently tested for consistency. Thermodynamic modeling was performed using γ–γ (LLE) and γ–γ–φ (VLLE) approaches with the Non-Random Two-Liquid (NRTL) activity coefficient model. The experimental and modeling results were analyzed using phase diagrams (triangular and 3D prism representations) and showed that it is possible to clearly separate the palmitate-rich and glycerol-rich liquid phases. In the VLLE, it was observed that the alkyl–OH is essentially pure in the vapor phase. For both types of equilibria, deviations in liquid-phase compositions (LLE), bubble temperatures, and vapor-phase compositions were below 2.0%, indicating that the NRTL model is capable of accurately describing the phase behavior of these systems. The phase equilibria of the methyl/ethyl palmitate–methanol/ethanol–glycerol system were studied using molecular dynamics (MD). The analyses based on the radial distribution function (RDF), spatial distribution function (SDF) and interaction energies showed that methanol and ethanol interact more strongly with glycerol than with palmitates. As a result, the glycerol-rich phase contains more methanol or ethanol, which can significantly reduce costs in the biodiesel purification step.