Thermodynamic Modeling and Simulation of Biodiesel Systems at Supercritical Conditions

Abstract

Biodiesel is becoming a promising fuel in many markets in the world for being a renewable energy source and for not requiring significant adaptation in existing diesel engines. It is biodegradable and its polluting gas emissions are less harmful to the environment. Transesterification is used for the biodiesel synthesis at supercritical conditions using triacylglycerols and solvents in a heterogeneous reaction. The Peng−Robinson (PR), the volume-translated Peng−Robinson (VT-PR), and the perturbed chain statistical associating fluid theory (PC-SAFT) equations of state were using to predict the fluid phase behavior of systems containing solvents and components present in the synthesis of biodiesel at supercritical conditions. Two pure component parameters for the VT-PR equation, N and k 3 , and the five pure component parameters for the PC-SAFT equation, m, σ, and ε as well as the associating parameters κ A i B j and ε A i B j , were predicted based on the vapor pressures and the saturated liquid volumes. Results were compared with experimental data presented in the literature, considered thermodynamically consistent, and it was confirmed that noncubic equations of state are more accurate than cubic equations of state. Thermodynamic modeling was also compared with the thermodynamic simulation using artificial neural networks (ANN) and molecular descriptors at different architectures. Results, in terms of deviations of bubble pressures of and vapor phase composition, predicted by the optimum ANN model are slightly more efficient than the ones obtained by the thermodynamic models, mainly the PC-SAFT equation of state.

Surface Tension of Liquid Organic Acids: An Artificial Neural Network Model

“…This may be due to the very different behaviours of the acids considered [ 23 ] and the large amount of available data. It is clear that more complex methods are needed for obtaining significantly better results, and the ANN models presently seem to be an excellent alternative [ 16 , 21 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 ].…”

“…The procedure followed takes into account the recent recommendations by Faúndez et al [38], and is very similar to that followed in other papers [21,[33][34][35]. It is even implemented in an accessible and easy-to-use computer program, such as EASYANN (http://easyann.gvilella.me/), accessed on 16 February 2021 [32].…”

“…As an alternative to the previous methods, some authors have used artificial neural networks (ANNs) for the study of the surface tension and other thermophysical properties [ 16 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 ]. ANNs take their inspiration from biological neural networks, with the mathematical model of a single neuron and the way in which neurons are interconnected (i.e., the “architecture”), leading to a framework for different machine learning algorithms.…”

“…It is possible to find that the model is over-fitted leading to large unacceptable errors. This can be avoided by dividing the dataset into three subsets: Training, test, and prediction [ 32 , 33 , 38 ]. While the training set is used to establish the main parameters of the model (bias, weights, etc.…”

Generating a Machine-Learned Equation of State for Fluid Properties

“…This contribution aims at taking a step in this direction, exploring the question of whether current ML approaches can be employed to substitute analytical EoS. In a seminal contribution, Arce et al 37 compared the quality of fit of common EoS for binary systems involving solvents and biodiesel components at supercritical conditions to that of an ANN, finding a good agreement between both the EoS, the ANN and experimental data. The work of Arce et al suggests that an ANN could be built to substitute an analytical EoS.…”