Ignition delay time correlations for $\textrm{C}_1-\textrm{C}_4$ primary alcohols: a multivariate and automatized approach

Abstract

This paper presents modified Arrhenius expressions for normal-chain alcohols from one to four carbons, i.e., methanol, ethanol, n-propanol, and n-butanol. Multiple linear regressions (MLR) using the ordinary least squares (OLS) scheme were performed iteratively over a database of previously published experimental data. The regressions aimed to correlate the ignition delay time (IDT) to variables such as temperature, anti-knock index, pressure, and equivalence ratio. Four different MLRs were obtained, considering all or some of these variables. If a variable was not considered, the IDT was scaled to a common value accordingly (30 bar and stoichiometry). After each run, the outliers were removed and the MLRs were recalculated until a threshold error was met. The results are valid for 1000/T from 0.6 to 1.2 (833.33–1666.66 K), due to the absence of negative temperature coefficient (NTC) behavior for the regarded alcohols, at pressures from 0.9 to 50 bar, equivalence ratios from 0.3 to 2.0, and anti-knock index (AKI) from 91.5 to 107.5. The most complete correlation yielded a $R^2$ of 0.991, with a maximum overshoot of 24.4% and an average absolute error of 10.5%. Its global apparent activation energy was 116.7 kJ/mol. The AKI, pressure, and stoichiometry dependency exponents were $-$ 1.39, $-$ 0.89, and $-$ 0.49, respectively. The dependency exponents are in good agreement with the literature, although no previous correlation brought all exponents together at the same time. However, the AKI negative exponent is counter-intuitive, as a higher AKI would mean a higher knock resistance, thus leading to higher IDTs.