# Inside VMG | July 2014

## Estimation of Octane Numbers in VMGSim

*By Herbert Loria - VMG Calgary*

### Introduction

Octane number is an important characteristic of spark engine fuels, such as gasoline, jet fuel or fractions used to produce these fuels, that represents the antiknock characteristic of a fuel. The octane number scale is based on the blending of iso-octane and n-heptane. A fuel’s octane number is measured on a scale that ranges from pure iso-octane (octane number = 100) to pure n-heptane (octane number = 0). Estimation of octane numbers is a challenging task, since they very much depend on the chemical structure of the components in a mixture.

There are two types of octane numbers: the *Research Octane Number* (RON), which is measured under city conditions and the *Motor Octane Number* (MON) that is measured under
road conditions.

The objective of this communication is to introduce new octane number estimation methods for pure hydrocarbons and their mixtures, which have been applied to VMGSim. In the case of pure hydrocarbons, VMGSim includes now an octane number estimation method based on the hydrocarbon chemical structure.

In practice, octane numbers of mixtures may be greater than, equal to or less than the calculated from the volumetric average of the octane numbers of mixture components, indicating non-linear blending. For this reason, a new estimation method for octane numbers of hydrocarbon mixtures was added to VMGSim, this technique is based on a generalized interaction parameter method based on the contribution of chemical structure groups.

### Pure Hydrocarbon Octane Numbers

In order to predict accurate octane numbers for mixtures involving hydrocarbons their pure component octane numbers must be correctly estimated. Octane numbers of some pure hydrocarbons generally found in fuels are given in American Petroleum Institute (API) publications. This information can be used to correlate octane numbers of PIONA (n-Paraffins, Iso-Paraffins, Olefins, Naphthenes and Aromatics) chemical families to polynomials based on normal boiling points. RON experimental data from the API Technical Handbook were correlated for each PIONA group. The correlated RON for each PIONA group follows this relationship:

where *RONi* is the RON of each PIONA group, *i* represents each PIONA group, *Tb* is the normal boiling point, and *a*, *b*, *c*, *d*,
*e*, *f* are the constants for each PIONA group.

These RON values can be used to obtain the RON of hydrocarbons based on the amount of each PIONA group present on them:

where *xwi* is the weight fraction of each PIONA group present in the fraction and *RONi* is the RON from on equation 1. Once the RON of the hydrocarbon is known, its MON
can be estimated using the following correlation proposed by Riazi:

where *SG* is the specific gravity of the pure compound at 60 F.

### Mixture Octane Numbers

When fuel components are blended, the blend octane number may be quite different from that of either component, even when two components have the same octane number. Blending would be linear if a blend octane number was equal to the one predicted by summing the components octane numbers in proportion to their concentrations. In practice, discrepancies between blends octane numbers and linearly predicted values are correlated by specific empirical equations and these have been used to correct the linear predictions.

Twu and Coon (5) proposed a methodology based on generalized interaction parameters to predict RON and MON of blends. The component-oriented interaction parameter approach is general and predicts, without performing additional blending studies, the blending behavior of fuels.

Twu and Coon’s correlation is in a simple form and a universal set of binary interaction parameters can be generalized. The only inputs to the correlation are the RON and MON of each component of the mixture and volume fractions of the components in the mixture.

The new VMGSim implementation for mixture octane numbers calculation is based on the Twu and Coon method and considers that the components can be subdivided in PIONA chemical groups to define a universal set of binary interaction parameters.

### Interaction Parameter Correlation

The RON or MON of a mixture can be calculated by blending the octane numbers of its components, each component can be subdivided in 5 other components each one representing a PIONA chemical structure. The octane numbers are calculated according to:

where *i* is the pure component in the mixture, *n* is the number of pure components in the mixture, *ONi* is the RON or MON of a pure component in the mixture,
*zi* is the volume fraction of component *i* in the mixture and, *Kij* is the binary interaction parameter between mixture pure component *i* and *j*.

The binary interaction parameter between mixture components (*Kij*) is related to the binary interaction parameter between chemical structures (*klm*) and the octane numbers of
those chemical structures (*ONlm*) by:

The only parameters that are necessary to know to solve the previous equations are the chemical group interaction parameters (*klm*). Assuming symmetric interaction parameters
(*klm* = *kml*) and that interaction parameters between same chemical groups are equal to zero (*kll* = 0), the total of binary parameters for blending mixture components
formed by PIONA groups is only ten.

### Regression of Universal Binary Interaction Parameters

The extensive mixture data used to regress the ten universal interaction parameters were taken from Healy et al. (6) and Morgan et al. (7) The compiled data covered a wide range of commercial mixtures and gasoline blends. A total of 189 blends and 157 components were used in this study.

The blending components used were typical refinery gasoline stocks consisting of straight run, catalytically cracked, thermal cracked, catalytically reformed and thermally reformed gasoline, isomers, polymers, alkylates, iso-pentane, n-pentane, n-butane, toluene, iso-octane and well as n-heptane. Data required for each component were RON, MON, PIONA content, and volume fractions.

The overall average absolute error (AAE%) for all 189 blends was only 1.00% for RON and 1.43% for MON. Dispersion plots are shown in Figures 1 and 2.

**Figure 1** Dispersion plot between calculated and estimated RON values

**Figure 2** Dispersion plot between calculated and estimated MON values

These results indicate that the proposed methodology enables the proposed octane number correlation to accurately predict octane number of many different mixtures using only ten universal binary interaction parameters.

### Validation

An ASTM publication based on the API Research Project 45 was used to test the octane number interaction parameters method. This publication provides RON and MON for blends of 20 vol% of hydrocarbons with 80 vol% of an octane primary reference mixture (60 vol% iso-octane + 40 vol% n-heptane). Table 3 shows the experimental and calculated RON and MON for 26 hydrocarbons.

**Table 3** Experimental and calculated RON/MON for mixtures of 20 vol% of the compound and 80 vol% of a mixture of 60 vol% iso-octane + 40 vol% n-heptane

As it can be seen the AAE% for the 26 evaluated mixtures was 2.23% and 5.01% for RON and MON
respectively, which confirms the accuracy of the proposed methodology for the calculation of octane numbers.

### References

**1**. American Petroleum Institute. Technical Data Book - Petroleum Refining, 5th Ed. Washington, D.C. American Petroleum Institute, 1992.

**2**. American Petroleum Institute. Knocking Characteristics of Pure Hydrocarbons. Philadelphia, Pa: American Society for Testing Materials, 1958.

**3**. Riazi, M. R. Characterization and Properties of Petroleum Fractions. West Conshohocken, PA: ASTM International, 2005.

**4**. Octane Number and Aniline Point of Petroleum Fuels. Albahri, T. A., Riazi, M.R. and Alqattan, A.A. 2002, Fuel Chemistry Division Preprints, Vol. 47, pp. 710-711.

**5**. Predict Octane Numbers Using a Generalized Interaction Method. Twu, C.H and Coon, J.E. 1996, Hydrocarbon Processing, pp. 51-56.

**6**. A New Approach to Blending Octanes. Healy, W.C., Maasen, C.W. and Peterson, R.T. 1959, API Division of R, 24th Midyear Meeting, pp. 132-191.

**7**. Mapping Surrogate gasoline Compositions into RON/MON Space. Morgan, et al., et al. 2010, Combustion and Flame, Vol. 157, pp. 1122-1131.

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