Page 95 - Characterization and Properties of Petroleum Fractions

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2. CHARACTERIZATION AND PROPERTIES OF PURE HYDROCARBONS 75
accurately. However, Part b in this case is also accurate. Es-
timation of the CH value is less accurate than prediction of of compounds selected, the source of data, number of data
points, and the basis for the evaluation all affect evaluation
boiling point and gives errors higher than K W . outcome. The number of numerical constants in a correla-
tion and number of input parameters also affect the accu-
racy. Usually older methods are based on a fewer and less
2.9 ANALYSIS AND COMPARISON OF accurate data than newer methods. It would be always useful
VARIOUS CHARACTERIZATION METHODS to test different methods on a set of data that have not been
used in obtaining the correlation coefficients. The most ap-
Generally there are a large number of pure hydrocarbons propriate procedure would be to compare various methods
and their properties can be used for evaluation purposes. with an independent data set not used in the development of
However, hydrocarbons from certain groups (i.e., paraffins, any methods considered in the evaluation process. Another
naphthenes, and aromatics) are more abundant in petroleum fair comparison of two different correlation would be to use
fractions and can be used as a database for evaluation pur- the same database and reobtain the numerical constants in
poses. Molecular weight, critical properties, and acentric fac- each correlation from a single database. This was done when
tor are important properties and their predictive methods Eqs. (2.52) and (2.53) were compared, as discussed in Sec-
are presented in this chapter. Errors in any of these proper- tion 2.4.1. These are the bases that have been used to compare
ties greatly influence the accuracy of the estimated physical some of the correlations presented in this chapter.
property. Methods of estimation of these properties from bulk Basically there are two parameters for the evaluation of
properties such as boiling point and specific gravity that are a correlation. One parameter is the percent average absolute
presented in this chapter have been in use in the petroleum deviation (%AAD). Average errors reported in this chapter and
industry for many years. In some process simulators a user throughout the book are based on percent relative deviation
should select a characterization method out of more than a (%D). These errors are defined as following:
dozen methods included in the simulator [56]. In each ap-
plication, the choice of characterization method by the user (2.134) estimated value − actual value × 100
strongly influences the simulation results. Although there has %D = actual value
not been a general and comprehensive evaluation of various
characterization methods, a conclusion can be made from 1 --`,```,`,``````,`,````,```,,-`-`,,`,,`,`,,`---
individual’s experiences reported in the literature. In this sec- (2.135) %AAD = N |%D|
tion first we discuss criteria for evaluation of various methods
and then different predictive methods for molecular weight, where N is the total number of data points and summation is
critical constants and acentric factor are compared and eval- made on all the points. |%D| is called percent absolute devi-
uated. ation and it is shown by %AD. The maximum value of |%D|
in a data set is referred as %MAD. The second parameter is
2
2.9.1 Criteria for Evaluation called Rsquared (R ) that is considered as an index of the cor-
of a Characterization Method relation when parameters of a correlation are obtained from
a data set. A value of 1 means perfect fit while values above
Methods of characterization and correlations presented in 0.99 generally give good correlation. For a set of data with
this chapter are mainly based on properties of pure hydrocar- X column (independent variable) and Y column (dependent
bons. However, some of these correlations such as Eq. (2.52) variable) the parameter is defined as
for estimation of the molecular weight of heavy fractions or
the correlations presented for prediction of the kinematic vis- 2 [N ( XY ) − ( X )( Y )] 2
cosity are based mainly on the properties of fractions rather (2.136) R = [N X − ( X ) ] × [N Y − ( Y ) ]
2
2
2
2
than pure compounds. The main application of these correla-
tions is for basic properties of undefined petroleum fractions where X and Y are values of the independent and correspond-
in which bulk properties of a fraction are used to estimate ing dependent variables and N is the number of data points.
2
2
a desired parameter. Therefore, the true evaluation of these The is the summation over all N values of X, X , Y, Y , and
2
characterization methods should be made through properties XY as indicated in the above equation. The R value can be
of petroleum fractions as will be discussed in upcoming chap- interpreted as the proportion of the variance in y attributable
ters. However, evaluation of these methods with properties of to the variance in x and it varies from 0 to maximum value
pure hydrocarbons can be used as a preliminary criteria to of 1.
judge the accuracy of various correlations. A method, which For most of the correlations presented in this chapter such
is more accurate than other methods for pure hydrocarbons, as Eqs. (2.40), (2.42), or (2.46a) the %AAD for various prop-
is not necessarily the best method for petroleum mixtures. A erties is usually given in the corresponding tables where the
database for pure hydrocarbons consists of many compounds constants are shown. Most of these properties have been cor-
2
from different families. However, evaluations made by some related with an R value of minimum 0.99. Some of these
researchers are based primarily on properties of limited pure properties such as kinematic viscosity or CH weight ratio
2
hydrocarbons (e.g., n-alkanes). The conclusions through such showed lower values for R . Evaluation of some of the other
evaluations cannot be generalized to all hydrocarbons and correlations is made through various examples presented in
petroleum fractions. Perhaps it is not a fair comparison if this chapter.
a data set used to develop a method is also used to evalu- Nowadays with access to sophisticated mathematical tools,
ate the other methods that have used other databases. Type it is possible to obtain a very accurate correlation from any

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