Estimation of high-pressure speed of sound for biodiesel using the QSPR-Gibbs energy additivity method

Abstract

The speed of sound (SoS), influenced by the chemical composition of biodiesel feedstock, temperature, and pressure, is of significant importance in various applications. This study aims to propose estimative models for high-pressure speed of sound using the Qualitative Structure-Property Relationship (QSPR) approach with the Gibbs Energy Additivity (GEA) method. High-pressure speed of sound data for pure fatty acid methyl esters and biodiesels were collected from previous literature for numerical determination and model validation. Two approaches were employed to enhance estimative ability: dividing pressure into shorter ranges and utilizing polynomial correlations. Consequently, the long pressure range was divided into three segments for linear correlation: Pressure Range I (PR I, 0.1 – 50 MPa), Pressure Range II (PR II, 50 – 100 MPa), and Pressure Range III (PR III, 100 – 210 MPa). Additionally, for polynomial correlation, the pressure range was segmented into Polynomial Function I (PRP I, 0.1 – 100 MPa) and Polynomial Function II (PRP II, 100 – 210 MPa). Results demonstrated excellent agreement between estimated and literature sound speed values for both methods, with a lower Average Absolute Deviation (AAD) than previous methods. However, the second-order polynomial correlation model demonstrated superior capability in estimating sound speed, with AADs of 0.24 % and 0.06 % for biodiesel under PRP I and PRP II, respectively, and an overall AAD of 0.22 % for pure FAME and biodiesel under PRP I. Furthermore, the proposed model was used to extrapolate untested sound speed data for pure FAME across a temperature range of 293.15 K to 373.15 K and pressures up to 200 MPa.