Fig. 7 Comparison of shelf-life data (SLB) data obtained from extrapolation of the Model B type equations to 25 °C (298.15 K) with shelf-life data [SL(2)] reported in an earlier study (Dunn, 2020). Error bars for SLB data are 95 % confidence intervals taken from Table 7. See Fig. 1for abbreviations
and to avoid overcrowding the results presented in Figure 6 . Presented alongside the SLB data are shelf-life data obtained from analysis of pressurized-differential scanning calorimetry (P-DSC) data reported in an earlier study (Dunn, 2020), which are denoted as ‘SL(2)’. The mathematical procedures for estimating the SL(2) data are explained in more detail in the earlier work.
The SLA and SL(2) data were most comparable for SME, MeC18:1 and MeC18:2, where the deviations were −1,400, 2,400 and 37 h, respectively. On the other hand, deviations for CaME and PME were much larger (−31,100 and −12,200 h). Similar comparison of SLB and SL(2) data suggested that the values may be comparable for MeC18:2 (deviation = 78 h). Otherwise, the deviations for CaME, PME, SME and MeC18:1 were larger (−20,500, 18,200, 5,500 and 99,700 h). Analogous results were observed from comparison of SLB and SL(1) results, where deviations for MeC18:2 were lowest (85 h), while those for CaME, PME, SME and MeC18:1 were larger (10,800, 29,200, 5,950 and 88,300 h).
Ranking the SLB values in Table 7 in descending order yielded the following results:
MeC18:1 > PME > CaME > SME > MeC18:2 (16)
This ranking was identical to the ranking shown noted in Eq. 15 for SLA. The calculated SLB of MeC18:1 was between one and two orders in magnitude greater than the SLB values for CaME, PME and SME, and three orders in magnitude greater than the SLB of MeC18:2. Compared with the SLA and SLB rankings in the present work, the SL(2) data reported in (Dunn, 2020) exhibited some variations, where CaME had the highest value, followed by PME, MeC18:1, SME and MeC18:2. This ranking did not agree well with those shown in Eqs. 15 and 16 for SLA and SLB. It is possible that thermal degradation occurred in the non-isothermal P-DSC scans conducted for the earlier study (Dunn, 2020). These effects may have altered the reaction kinetics as the P-DSC cell temperature was ramped to higher temperatures.
Earlier, it was noted that SLB was consistently greater than SLA for all five FAME studied in the present work. For CaME, PME and MeC18:1, deviations between these two values were more than one order in magnitude. There may be some question on the reliability of SLA and/or SLB data as estimates for the shelf-life of biodiesel at low temperatures. For example, SLA = 2,760 h and SLB = 13,400 h were estimated for CaME (see Tables 6 and 7 ). These data convert to 115 d (16.4 wk) and 558 d (79.8 wk). Between the two time periods, the latter appears to be more realistic for CaME, which has a low total PUFAME concentration (26.77 mass%), if it is stored in a dark space absent from moisture. Similar arguments apply to SLB results for PME (1,430 d [205 wk]; total PUFAME = 9.7 %), SME (378 d [54.0 wk]; total PUFAME = 62.09 %) and MeC18:1 (4,500 d [643 wk]; no PUFAME). Both sets of results could be realistic for MeC18:2 (SLA: 3.12 d [0.45 wk]; SLB: 4.83 d [0.69 wk]; 99.0 % PUFAME). Given these considerations, it is concluded that the extrapolation of Model B type equations to lower temperatures yielded more realistic shelf-life results (SLB) than similar processing ofModel A type equations (SLA).