Adaptation of the Peng-Robison equation of state for use with biodiesel

Abstract

Biodiesel is well known nowadays as an alternative fuel to help mitigate the scarcity of fossil oils and, address more strict environmental requirements. The major advantage of biodiesel is that it is derived from renewable resources. It is also believed to assist in reducing the emissions of green house gases to the atmosphere, while providing similar engines efficiencies as conventional diesel with no retrofitting of existing diesel engines. The design and optimization of biodiesel production as industrial process demand the developing of thermodynamic modelling able to accurately predict phase and chemical equilibrium of mixtures that are important in the production of biodiesel. Traditionally, the thermodynamic behaviour of biodiesel, and its precursors, are considered to be a highly non-ideal mixtures due to associative effects related with hydrogen bonded interactions, and the presence of size asymmetric compounds. The most important limitation of biodiesel representation refers to the scarcity of experimental data available in the literature which is restricted to a small amount of relevant mixtures and within conditions where low pressures and low temperatures prevail. According to the above limitations, it is not surprising that only few attempts have been reported in the literature to represent phase equilibriums and only one was reported for chemical equilibriums. In addition, even when in some cases a successful implementation was reported by using a Cubic Plus Association (CPA) equation of state, those implementations only refer to a simple representation of biodiesel systems, where not all important components are considered in the mixture. Thus, rather than deriving a completely new equation of state that is tailored to specifically biodiesel, the approach in this research was to extend the Peng-Robinson Equation of State, with Huron-Vidal mixing Rules, for use with biodiesel systems. The Peng-Robinson Equation of State was chosen because it is familiar to Chemical Engineers and because it is available in most commercial process simulators. Thus, Chemical Engineers will be able to immediately implement the results of this study into process design scenarios. Six major vegetable oils and methanol were considered as part of feedstock composition for the selection of the most important components within transesterification reactions. Upon undertaking the study it was found that the binary phase equilibrium data for biodiesel and its precursors, which are needed for regressing equation of state parameters, were not available for all of them. Thus, as a first approximation, the KT­UNIFAC activity coefficient model, which estimates activity coefficients based only upon the structure of a molecule, was used to compute activity coefficients that were subsequently used to regress equation of state parameters. In computing the activity coefficients, it was found that there were three binary functional groups for which KT­UNIF AC parameters were not available. In order to obtain these parameters, molecular simulation was used to estimate activity coefficients for compounds that contained the missing functional groups. Once the molecular simulations were completed, and activity coefficients were generated for compounds that contained missing KT-UNIFAC group parameters, the group parameters were subsequently regressed. A database of activity coefficients was subsequently generated from KT-UNIF AC, from which the equation of state parameters were finally regressed. The equation of state parameters were tested, for their predictive capabilities, by computing Vapour-Liquid Equilibrium (VLE) conditions, Liquid-Liquid Equilibrium (LLE) conditions and, finally, chemical equilibrium conditions. The computations were then compared to the very small amount of relevant experimental data that is available. It was found that while the computations almost always yielded qualitatively correct trends, the predictions were seldom quantitatively correct. Thus, the author concludes that subsequent attempts at creating an equation of state for use with biodiesel should be preceded by obtaining the requisite experimental VLE and LLE data. Otherwise, the representation of biodiesel mixtures using predictive models, independent of experimental data, will be limited to only few cases as: vapour-liquid equilibrium of glycerol-methanol, glycerol-water, and liquid-liquid equilibrium of fatty acid methyl esters - methanol glycerol. It was observed that the worse predictions corresponded to those mixtures where the bigger molecules were included, such as: triglycerides (TG's), and monoglerides (MG's).