energies Review A Comparative Assessment of Biodiesel Cetane Number Predictive Correlations Based on Fatty Acid Composition Evangelos G. Giakoumis * and Christos K. Sarakatsanis Internal Combustion Engines Laboratory, School of Mechanical Engineering, National Technical University of Athens, 15780 Athens, Greece; [email protected] * Correspondence: [email protected]; Tel.: +30-210-772-1360 Received: 30 December 2018; Accepted: 24 January 2019; Published: 29 January 2019 Abstract: Sixteen biodiesel cetane number (CN) predictive models developed since the early 1980s have been gathered and compared in order to assess their predictive capability, strengths and shortcomings. All are based on the fatty acid (FA) composition and/or the various metrics derived directly from it, namely, the degree of unsaturation, molecular weight, number of double bonds and chain length. The models were evaluated against a broad set of experimental data from the literature comprising 50 series of measured CNs and FA compositions. It was found that models based purely on compositional structure manifest the best predictive capability in the form of coefficient of determination R2. On the other hand, more complex models incorporating the effects of molecular weight, degree of unsaturation and chain length, although reliable in their predictions, exhibit lower accuracy. Average and maximum errors from each model’s predictions were also computed and assessed. Keywords: biodiesel; cetane number; chain length; coefficient of determination; degree of unsaturation; fatty acid composition 1. Introduction The level of research carried out in recent decades regarding the use of biodiesel in engines has been intense. One unique aspect of biodiesels (and their parent oils/fats) is the fact that they are produced from a variety of vegetable or animal feedstock [1–5]. These possess different compositional structures in the form of fatty acids (FA), as summarized in Table1 for the most influential ones. Past research has shown that a relatively high degree of variability is observed regarding the structural form of common biodiesels depending on the originating oil [6]. Since the composition of each oil/fat in the fatty acids varies, the physical and chemical properties of biodiesel differ too. Perhaps the most prominent example here is the cetane number (cold-flow properties as well) [3,5,7]. The dimensionless cetane number is one of the most influential fuel properties. It is highly responsible for ignition delay; thus it determines, to a large extent, the proportion between premixed and diffusion combustion in a diesel engine [8]. In this regard, it affects the heat release profile and is also responsible for the emission of pollutants and combustion noise [3,5,9–13]. In light of the above, it is not surprising that the CN has been widely researched and reported in the literature, with the published values differing quite a lot. Figure1 is helpful here, illustrating the large variability in the reported CN values [6]. These values (average for each feedstock) range from lower than that of the respective automotive diesel fuel up to much higher. As discussed earlier, this variability in the measured CN values can be, at least in part, attributed to the different fatty acid methyl ester (FAME) composition, with computational and experimental errors and uncertainties playing a non-negligible Energies 2019, 12, 422; doi:10.3390/en12030422 www.mdpi.com/journal/energies Energies 2019, 12, 422 2 of 30 Energies 2019, 12, x FOR PEER REVIEW 2 of 31 non-negligible role too. To make things even worse, sometimes large variations have been reported role too. To make things even worse, sometimes large variations have been reported in the literature, in the literature, even when biodiesels from the same originating feedstock have been studied. This even when biodiesels from the same originating feedstock have been studied. This is reflected in the is reflected in the sometimes large standard deviation of the collected data, as depicted in Figure 2. sometimes large standard deviation of the collected data, as depicted in Figure2. Knothe [ 10] argued Knothe [10] argued that one major factor affecting the variability of the results is the fact that CN is that one major factor affecting the variability of the results is the fact that CN is actually a ‘lumped’ actually a ‘lumped’ quantity that expresses various phenomena such as spray formation, quantityvaporization, that expresses mixing etc. various phenomena such as spray formation, vaporization, mixing etc. FigureFigure 1. 1.Average Average cetane cetane numbers numbers ofof biodieselsbiodiesels from various feedstocks; feedstocks; the the EU EU and and US US lower lower limits limits Energiescorrespondcorrespond 2019, 12, x to toFOR automotive automotive PEER REVIEW applications applications (reprinted(reprinted fromfrom [[6]6] with permi permissionssion from from Elsevier). Elsevier). 3 of 31 Owing to its significance in engine performance and emissions, as well as to the fact that its experimental determination is time consuming, costly and scientifically challenging, it is not surprising that several CN predictive models have been developed in the past. Biodiesel CN has been correlated in these models with various other metrics or properties. Klopfenstein [14] reported one of the earliest correlations with respect to the number of carbon atoms and the number of double bonds. Similarly, Ramirez-Verduzco et al. [15] correlated CN with the molecular weight and the number of double bonds, and Pinzi et al. [16] with the degree of unsaturation and chain length. A quadratic correlation with the number of carbon atoms in the original fatty acid and the number of double bonds was statistically selected as the most suitable by Lapuerta et al. [17]. Other researchers preferred correlations of the CN directly with the fatty acid composition (without intermediate metrics such as the degree of unsaturation or the chain length). Bamgboye and Hansen [18] reported the first correlation of this kind with respect to the FA composition applyingFigureFigure multiple 2. 2.Correlation Correlation linear between between regression degree degree analysisof ofunsaturation unsaturation (MLR). Piloto-Rodriguez((aa)) andand chain length et (b) ( bal.) with with [19] biodiesel biodieselapplied average averageboth MLR andcetane artificialcetane number number neural from from networks 24 24 feedstocks feedstocks (ANN). (sub-figure (sub-figure The latter ( a(a)) approach reprinted reprinted fromfromwas [the[6]6] withwith one permissionpermfollowedission by from Ramadhas Elsevier). Elsevier). et al. [20], while the former (MLR) was chosen by Gopinath et al. 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