Liquid to solid phase transition detection by using a vibrating tube densimeter along with densities up to 137 MPa of beef tallow fatty acid alkyl esters

Phase behavior and thermophysical properties of biodiesel at high pressure and high temperature are limited in the literature. These are useful to develop models and to understand their behavior having in mind the use of biodiesel in engines. Liquid to solid phase transitions, by using a vibrating tube densimeter, along with densities of three beef tallow fatty acid alkyl esters were studied in this work. Measurements of the oscillating period for each biofuel were carried out in a modular array constituted by two vibrating tube densimeters coupled in series and connected to a single loading cell. The oscillating period was converted to density by the forced path mechanical calibration (FPMC) method. Experimental liquid density sets for three beef tallow biodiesel samples based on fatty acid alkyl esters (FAAEs) are reported for the first time for pressures up to 137 MPa. These biofuels, named fatty acid methyl esters (FAMEs), fatty acid ethyl esters (FAEEs) and fatty acid butyl esters (FABEs), were measured in the temperature range of 286–393 K. The detection procedure for the beginning of the high-pressure solidification was focused on the beef tallow FABEs sample based upon its lower cloud point (CP_FABEs = 281.15 K) in comparison with the reported property for the other esters (CP_FAEEs = 289.15 K, CP_FAMEs = 291 K) with the same feedstock; therefore, the conditions for the metastable liquid to solid phase transition associated to the effect of high pressure was detailed for waste beef tallow butyl ester biodiesel by performing step-by-step compressions in the interval of 286.20–298.13 K and with the help of the vibrating tube densimeters. FABEs had the lower density in contrast with FAEEs and FAMEs, this one being the denser biofuel. Modeling of liquid density data was performed by the perturbed-chain statistical associating fluid theory (PC-SAFT) Equation of State and the Tammann-Tait equation with maximum absolute average deviations of 0.15 % and 0.05 %, respectively. Both models were applied for correlating the thermodynamic derived properties of the fluid phase: isobaric thermal expansivity and isothermal compressibility.