Optimal octane number correlations for mixtures of toluene reference fuels (TRFs) and ethanol

Abstract

This paper presents a method for correlating the octane numbers of fuel mixtures, and applies this to the study of toluene reference fuels (TRFs) blended with ethanol. This method combines linear regression and exhaustive (or brute-force) searching for optimal Scheffé polynomials, where optimality is defined as the shortest polynomial that meets a reasonable estimate of the reproducibility limits in the standard, octane number test procedures.

Two correlations for the RON and MON are found to be optimal. These achieve maximum absolute errors (MAE) of less than 2 octane numbers across TRF/ethanol mixtures with a RON between 80 and 120. These two correlations use mole fractions as the correlating variables, are consistent with previously published, linear TRF correlations, and show that binary (non-linear) interactions between iso-octane/ethanol, n-heptane/ethanol and toluene/ethanol are all significant. The use of liquid volume fractions is also shown to lead to poor correlation performance, thereby demonstrating the superiority of mole fractions as the correlating variables.

Introduction

A fuel’s susceptibility to knock in spark ignition engines (SI) is characterized by its octane number (ON). Knock is the result of autoignition of the end-gas and, in general, is affected by the engine design, engine operating condition and the fuel’s reactivity. Standard test procedures in Cooperative Fuel Research (CFR) engines are used to determine the Research Octane Number (RON) [1] and Motor Octane Number (MON) [2].

The octane numbers of pure compounds were extensively measured in the 1950s by the American Petroleum Institute [3]. Some have since been updated. Measurement of the octane numbers of mixtures are less common, however, and the octane blending of mixtures can be quite involved [4], [5]. This is particularly the case for oxygenated hydrocarbons, such as ethanol/gasoline mixtures, the use of which has received significant attention in recent years [4], [6], [7], [8], [9], [10].

Ethanol is commonly blended with gasoline in part because of its low autoignition reactivity and high heat of vaporization, which together result in ethanol’s relatively high octane number. Octane number measurements have been conducted for ethanol blended with different commercial gasolines [9], [10], primary reference fuels (PRFs) (mixtures of n-heptane and isooctane) [4], [11], [12], [13], and toluene reference fuels (TRFs) (mixtures of PRF and toluene) [4], [11], [12], [13]. Significant non-linear blending has been reported in some cases.

ON correlations for TRFs [14], [15], [16], TRF/ethanol mixtures [13], [17] and gasoline distillate blends [18], [19], [20], [21] have also been proposed. It is generally agreed that octane numbers of mixtures are better correlated with the fuel components’ mole fractions than volume fractions [9], [10], [14], [15]. However, whilst these studies of TRF/ethanol mixtures reported good agreement between measured and correlated octane numbers, the presented correlations did not return the octane numbers of the pure TRF/ethanol components and are relatively complex. These functions are therefore likely to have limited accuracy, particularly when the mixture approaches one of the pure components.

This paper therefore proposes an alternative method for ON correlation. Whilst this method can be generalized to any mixture, we only apply it to the study of TRF/ethanol fuels in this work. This method makes use of Scheffé polynomials [22], which provide a composition-based model for mixture properties. It involves use of linear regression and exhaustive (or brute-force) searching for Scheffe polynomials that result in the best correlation with a given number of polynomial terms. Particular correlations for the RON and MON of TRF/ethanol mixtures are identified as being consistent with existing TRF-only correlations [15], sufficiently accurate to be useful and sufficiently simple to provide insight into the most significant component interactions.