(259a) Modelling of Multiphasic Behavior of Biodiesel Transesterification Operating Below Critical Conditions Using CO2 as a Co-solvent with PC-SAFT EoS

Biodiesel is composed of fatty acid esters generated via methanolysis or ethanolysis of triglycerides. The preferred method for biodiesel production is transesterification of triglycerides with methanol or ethanol. Phase behavior plays a critical role in biodiesel transesterification. The reaction is generally carried out at high temperatures, pressures and high short alcohols to oil ratios, in order to increase the solubility of non-polar and polar phases.

The process can be performed uncatalyzed using supercritical conditions: temperatures of 250 - 400 °C and pressures of 19- 24 MPa with high methanol/ethanol to oil ratios of 40:1 molar. The severity of these conditions guarantees good reaction kinetics and the formation of a singular phase in the reactor. This process has recently received much attention in literature however it still presents challenges regarding the intensive energy requirements for the process and downstream separation of products from excess reactants.^1–6

The catalyzed process has different approaches including acid and basic homogeneous catalysts and is the current commercial path to produce biodiesel.⁷ however ongoing challenges regarding the presence of water, free fatty acid impurities, and extra cost associated with the separation of the biodiesel from glycerol are still present.^7,8

Heterogeneous catalysts have also been investigated showing economical profitability, and provide a solution for the final catalyst separation.⁹ They vary in nature from alkaline earth, titanium silicates, anion exchange resins and polymers,^10–14

Carbon dioxide has been suggested as co-solvent with beneficial properties for biodiesel transesterification at supercritical conditions because: it is abundant in nature, it has been widely used in vegetable oil extraction, it has a rather mild critical value (31.1 °C and 7.39 MPa), and increases the solubility between alcohols and triglycerides favoring conversion^15,16.

Findings from Soh et al¹⁷ showed triglycerides transesterification does not need to be done at supercritical conditions and can be coupled with heterogeneously catalyzed reactions. Carbon dioxide works as a co-solvent for both the polar and oleic phase. Expanding the two phases with CO₂ increases the solubilized triglycerides on the alcohol phase, which consequently encourages the transesterification reaction. Almost complete conversion was obtained in moderate reaction times (< 2 Hr). Also, temperatures around 95 °C and pressures of 9.5 MPa were enough to achieve 98% methyl oleate yield in a tri-phasic catalyzed reaction process. Benefitial transport properties

Despite the system's simplicity, some species present on the biodiesel reaction, namely methanol/ethanol and glycerol have a high degree of molecular interaction as hydrogen bonding, and relevant polar forces. Understanding the systems phase behavior development from a modelling perspective requires models that can capture the complexity of this interactions.

Perturbed Chain Statistically Association Fluid Theory (PC-SAFT) by Gross and Sadowski,^18,19 has become a widely used engineering resource due to its accurate prediction capabilities and has been successfully applied to many associative mixtures. Additionally PC-SAFT has been extended to polar compounds.^20–24 In particular Nguyen et al.^25,26 and Corazza et al.²⁷ looked into biodiesel related phase equilibria, parametrizing pure methyl- and ethyl-esters at different conditions and obtaining promising results for methanol, ethanol, glycerol, and biodiesel binary and ternary systems.

Up to seven molecular parameters describe each pure component phase and are fitted to saturation data. The equation of states is written as an expansion of the Helmholtz free energy segregated into a reference fluid and the main interaction forces- i.e. dispersion, hydrogen bonding, and polar forces. Binary interaction coefficients are then calculated using binary data to mitigate accumulated errors that result from averaging approximations on mixtures.

Modelling of the biodiesel reaction in the presence of carbon dioxide has focused on supercritical conditions and most of the work done has been performed with cubic equations of state. Modelling this reaction at milder conditions of pressure and temperature where multiple phases are present using SAFT like equations has not been done before.

Modelling results achieved accurate phase behavior representation for pure, binary and ternary systems including carbon dioxide using a polar version of PC-SAFT. Group contribution methods allowed generalization for methyl-esters and ethyl-esters modelling simplifying the required components basis and minimizing the number of parameters. Small errors were obtained using very low values of binary interaction coefficients (below 7%) for binary systems. Successful modelling for liquid-liquid and vapor-liquid-liquid regimes suggest the possibility to determine optimal conditions for transesterification performed in multiphasic reactors in presence of CO₂

The global aim of this study is to fully characterize biodiesel-related compounds with carbon dioxide as a co-solvent with the PC-SAFT, predict supercritical, and sub-critical phase behavior generating binary and ternary diagrams to describe interactions amongst species. These calculations could potentially suggest a new process design by estimating favorable thermodynamic conditions as pressure, temperature and reactants ratios for biodiesel production using carbon dioxide as a co-solvent in subcritical conditions based on their phase behavior equilibria.

Keywords: Biodiesel, PC-SAFT, Phase-Behavior, Carbon-Dioxide, Co-solvent

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