Characterization of Heavy Undefined Fractions
Authors: Magoulas K.G. 
Published: December 2007

Abstract
New correlations are presented for the critical properties and the acentric factor as functions of the parameters (data) typically available for heavy undefined fractions: the Molecular Weight (MW) and the Specific Gravity (SG) at 60/60°F.
The validation of the proposed method, in comparison with those of Kesler-Lee and Twu, is performed on:Vapor pressures (Ps) and saturated liquid densities (dls) of petroleum and coal liquid fractions.Solubilities and liquid densities for binary systems of CO2 with petroleum and coal liquid fractions and with bitumens.Constant Volume Depletion (CVD) for gas condensates.Differential Liberation (DLE) for crude oils.
The proposed correlations perform generally better than the other two, especially for high MW fractions, resulting in satisfactory predictions of the VLE and PVT behavior even for reservoir fluids with only one adjustable parameter at the saturation point.

Introduction
One of the main problems in the thermodynamic modelling of fossil fuels with cubic Equations of State (EoS) is the lack of accurate estimates of the critical temperature, critical pressure and acentric factor for the distillation residues or their subfractions. The same problem appears in describing heavy fractions found in hydrocarbon reservoir fluids. Few data may be available for such fractions, usually the molecular weight (MW) and the specific gravity (SG).
There are several methods and correlations for characterizing heavy compounds and undefined fractions. Whitson (1983) presented an extensive comparison of various critical property prediction correlations and their influence on equation of state predictions of the PVT data for six reservoir fluids. The results indicated that relatively small differences in Tc, Pc and ? values provide significant differences in EoS prediction, a statement which is in agreement with that of Voulgaris et al. (1991). The author suggested the Kesler-Lee (K-L, 1976) method for the Tc, Pc and ? prediction but concluded that no single characterization scheme can be assumed significantly more accurate than the others.
In one of his more recent publications Witson (1995) suggested that the Twu (1984) correlations for Tc, Pc are attractive because of their generality and supposed ability to predict reasonable critical properties even for very heavy fractions.
Our preliminary calculations, however, indicated that the two methods yield rather poor predictions of vapor pressures when applied to heavy fractions. It is the objective of this work, therefore, to provide correlations for the critical properties and the acentric factor as functions of the parameters (data) typically available for heavy undefined fractions: the Molecular Weight (MW) and the Specific Gravity (SG) at 60/60°F.
An extensive comparison of the proposed method with the other two, i.e. those of K-L and Twu, is then performed. These methods use the normal boiling point (Tb) and the specific gravity (SG at 60/60°F) as input parameters. They also provide correlations of MW as function of Tb, since for heavy petroleum cuts and coal liquids, Tb values cannot be experimentally measured. The comparison is based on given MW and SG and concerns the:Prediction of vapor pressures (Ps) and saturated liquid densities (dls) of petroleum and coal liquid fractions.Prediction of solubilities and liquid densities for binary systems of CO 2 with petroleum and coal liquid fractions and with bitumens.Simulation of Constant Volume Depletion (CVD) Experiment for gas condensates.Simulation of Differential Liberation Experiment (DLE) for crude oils.
For the methods of K-L and Twu, the MW is used to obtain the required Tb values, while the acentric factor is always calculated through the K-L correlations.