Octane Number’s Modeling With Oxygenate/Hydrocarbon Synergy Included

Several physicochemical properties characterize a fuel that yields power, economy and low emissions: volatility, heating value, specific gravity, Sulphur content and antiknock performance. Octane Number (ON) measures the antiknock performance of a gasoline, in other words, its ability to resist knocking as it burns in the combustion chamber. An accurate ON predicting model is fundamental to enable formulation of gasoline at the maximum volumetric yield or at minimum cost [4]. Since the 1940’s technicians are trying to find better ON models [2, 3]. However, the existing models cannot yet accurately predict ON for gasoline formulations containing oxygenates, like ethanol or ether [1]. Even the trendiest models lead to gasohol formulas with either ON giveaway, or a higher than expected cost. Our work proposes an ON model including synergy parameters that capture nonlinear interactions between oxygenates and hydrocarbons. The analysis of an ON database including ethanol and hydrocarbon mixtures made it possible to find blend parameters that capture synergy, defined here as the property of a component possessing a blend ON higher than its own pure component ON. The model enables the formulation of specified gasolines with higher direct distillation naphtha and less ON booster content.


INTRODUCTION
Ghosh [2] proposed an ON model based on the contributions of 57 groups of gasoline components, which can be identified by chromatography in a fuel sample. Each group has a β coefficient, which may be viewed as the ratio of its blending ON to its pure component ON. Interactions between paraffinic, naphthenic and olefinic hydrocarbons are also quantified by the introduction of an Ip parameter, which means interaction with paraffins. The ON and β coefficients for each group were determined by regression analysis of a large database of 1471 different fuels. The method was shown to give accurate results, however the β coefficients were not published due to proprietary reasons.
Foong [1] designed a large experiment to provide the experimental octane numbers of n-heptane, isooctane, toluene and ethanol mixtures, sweeping the ethanol content from 0% to 100%.
Commercial gasolines are composed of hundreds of different hydrocarbons, their fractions varying in wide ranges [2,3]. Its composition depends primarily on the kinds of petroleum at the refinery input, and the process unit its blending streams come from.
Blending streams may come from direct distillation, fluid catalytic cracking, reforming, alkylation, and natural gasoline units. The main groups present in gasoline are paraffinic, olefinic, naphthenic, and aromatic hydrocarbons, called PONA for short. Oxygenates, as ethanol, ETBE, and MTBE are part of a different group.
Ghosh [2] defined each group as entirely paraffinic, olefinic, naphthenic or aromatic in his work, which may be good for a model based on chromatography, but is not so for a simpler model based on refinery streams, as each stream may have partial characteristics of each group. Defining the chemical characteristic of each stream as a 4-dimensional vector {p, o, n, a} where p, o, n, a, are real numbers in the range from 0 to 1 enables the application of Ghosh's model to refinery streams. Ghosh's model is defined by eq. (1) where ∑ pona means sum across all groups, and ∑ p means sum across paraffinic groups only.
If the paraffinic content of each ith group is defined as a fraction pi ranging from 0 to 1, It can be shown that then eq. (1) may be rewritten as In addition, each refinery stream can be considered as a group, largely simplifying the model and avoiding the need for a detailed chromatographic analysis of each stream for octane number evaluation purposes. Note that ONi was replaced by Ai in the right numerator term to explain interactions not proportional to octane numbers.
Interactions between ethanol and paraffinic hydrocarbons may be explained by redefining Ip as where vet is the ethanol volumetric fraction and kn, kd are parameters determined by regression.
To complete the model the coefficients Ai, βi, kn, kd still have to be determined by nonlinear regression on an experimental database while the coefficients pi of each stream may be determined by chromatography, but there are now only n-1 βi coefficients to be determined instead of 56 as in the original model. The ON coefficients must be determined by testing each stream in the CFR engine. For a gasoline containing n streams, there are 2n + 1 parameters to be determined by regression, n by chromatography. At least 2n + 1 ON tests must be performed in the CFR engine to find the ON, kn, kd, and β parameters by regression.

EXPERIMENTAL
The Table 1 shows experimental data for five refinery streams, plus ethanol. Several blends were prepared, each one tested in the CFR engine to determine its ON experimentally. The volumetric fraction of saturates for each stream was determined by chromatography. The Ai parameters were considered equal to 1 by hypothesis, to represent equal interaction strength between ethanol and any of the streams. The pi parameters were considered equal to the volumetric fraction of saturates for each stream. All other parameters eqs. (4) and (5) shown in Table 2 were obtained by regression.     were considered equal to the volumetric fraction of saturates for each stream. All other parameters eqs. (4) and (5) shown in Table 4 were obtained by regression. The Figure