Fig. 6 Comparison of shelf-life data (SLA) data obtained from extrapolation of the Model A type equations to 25 °C (298.15 K) with shelf-life data [SL(1) and SL(3)] reported in earlier studies (Dunn, 2008, 2020). Error bars for SLAdata are 95 % confidence intervals taken from Table 6. SeeFig. 1 for abbreviations
linear regression of IPR-T data and extrapolating the resulting equations to T = 25 °C. However, the SL(1) data were obtained from equations derived from experiments performed at three temperatures in the ranges T = 90-110 °C (363.15-383.15 K) for CaME, PME, SME and T = 80-100 °C (353.15-373.15 K) for MeC18:2. In the present work, SLA data were calculated from Model A type equations derived from analysis of IPR-T data measured at five or six measurement temperatures. As a consequence, variations between SLA and SL(1) data from the earlier study were observed. While SLA > SL(1) for CaME and MeC18:2, the opposite trend was noted for PME, SME and MeC18:1. In the cases where SLA > SL(1), deviations were small, 200 h for CaME and 44 h for MeC18:2. In the remaining three cases, deviations were larger with MeC18:1 demonstrating the largest deviation (9,000 h), followed by PME (1,200 h) and SME (900 h).
Ranking the calculated SLA results in descending order yielded the following:
MeC18:1 > PME > CaME > SME > MeC18:2 (15)
This order generally agrees well with what would be expected based on the degrees of unsaturation (DU) of PME, CaME, SME and MeC18:2, where DU = 0.58, 1.28, 1.53 and 2.00 (calculated from results in Table S1 in the supporting information). Predicting the shelf-life of FAME generally does not correlate well with DU (Knothe, 2002) and this is exemplified when considering that according to SLA, MeC18:1 held the highest ranking above despite having DU = 1.00, a value that was greater than the DU calculated for PME. Nevertheless, ranking the SL(1) data reported earlier (Dunn, 2020) yielded similar results with the remarkable exception that CaME [SL(1) = 2,560 h] and SME (3,130 h) were switched in the rankings. The ranking from the earlier work was curious since SME had a significantly higher total PUFAME concentration (62.09 mass%) than CaME (26.77 %). Given the aforementioned differences in the experimental method for acquiring and analyzing IPR-T data to estimate SLA for the present work and SL(1) in the earlier study, the change in the ranking of CaME and SME suggests that the methodology can significantly impact the outcomes of the analyses. Therefore, it was concluded that the method employed in the present work (five to six IPR-T data points over variable T-ranges) yielded more reliable results than the method used in the earlier study, with respect to the estimation of the shelf life of biodiesel at lower temperatures.
Two data points in Figure 6 were represented as ‘SL(3)’ results reported in an earlier study (Dunn, 2008). This study was carried out using a different instrument to measure the IP, which was generally termed as the oil stability index (OSI). The experimental data were measured taken at six temperatures in the range T = 60-80 °C (333.15-353.15 K) for SME and eight temperatures in the range T = 60-95 °C (333.15-368.15 K) for MeC18:1. The SLA values for SME and MeC18:1 were 12.9 and 5.0 times greater than their corresponding SL(3) values. The most likely explanation for these poor comparisons was the variation in instruments and experimental conditions employed to measure the respective IP data for analysis.
The SLB data obtained from extrapolation of theModel B equations are presented graphically in Figure 7 . These data are presented in a separate figure mainly for convenience