Page 319 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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7. APPLICATIONS: ESTIMATION OF THERMOPHYSICAL PROPERTIES 299
can be considered as defined mixtures. Examples of unde-
property must be calculated for each component in the mix-
fined mixtures are petroleum fractions and reservoir fluids number of components in the mixture is large since each
whose compositions are not known. For such mixtures, some ture. In applying a mixing rule, the role of binary interaction
bulk properties are usually known. parameters (BIPs) is important when the mixture contains
Theoretically developed methods are generally more ac- components of different size and structure. For example, in a
curate for gases than for liquids. Kinetic theory provides reservoir fluid containing C 1 and a heavy component such as
sound predictive methods for physical properties of ideal C 30 the role of BIP between these two components cannot be
gases [2, 3]. For this reason, empirical correlations for calcu- ignored. Similarly when nonhydrocarbon components such
lation of physical properties of liquids have been proposed. as H 2 S, N 2 ,H 2 O, and CO 2 exist in the mixture, the BIPs of
Similarly, theoretical methods provide a more accurate es- these compounds with hydrocarbons must be considered. For
timation of physical properties of pure compounds than of some empirically developed correlations specific interaction
their mixtures. This is mainly due to the complexity of inter- parameters are recommended that should be used.
action of components in the mixtures especially in the liquid Theoretically developed thermodynamic relations of Chap-
phase. For undefined mixtures such as petroleum fractions, ters 5 and 6 give thermodynamic properties in molar quan-
properties can be calculated in three ways. One method is to tities. They should be converted into specific properties by
consider them as a single pseudocomponent and to use the using Eq. (5.3) and molecular weight. In cases that no spe-
methods developed for pure components. The second method cific mixing rule is available for a specific property the simple
is to develop empirical correlations for petroleum fractions. Kay’s mixing rule (Section 3.4.1) may be used to calculate
Such empirically developed methods usually have limited ap- mixture properties from pure component properties at the
plications and should be used with caution. They are accurate same conditions of T and P. If molar properties for all com-
for those data for which correlation coefficients have been ponents (θ mi ) are known, the mixture molar property (θ m )
obtained but may not provide reliable values for properties may be calculated as
of other fractions. These two approaches cannot be applied

to mixtures with wide boiling range, such as wide fractions, (7.1) θ m = x mi θ mi
crude oils, or reservoir fluids. The third approach is used i
for available data on the mixture to express the mixture in
terms of several pseudocomponents, such as those methods where x mi is mole fraction of component i and the summa-
discussed in Chapters 3 and 4. Then, methods available for tion is on all components present in the mixture. Subscript
--`,```,`,``````,`,````,```,,-`-`,,`,,`,`,,`---
prediction of properties of defined mixtures can be used for m indicates that the property is a molar quantity (value of
such petroleum fluids. This approach should particularly be property per unit mole). For gases especially at low pressures
used for wide boiling range fractions and reservoir fluids. (<1 bar), the volume fraction, x Vi may be used instead of mole
Fluid properties generally depend on temperature (T), pres- fraction. Similarly for specific properties this equation can be
sure (P), and composition (x i ). Temperature has a significant written as
effect on properties of both gases and liquids. Effect of pres- (7.2)
sure on properties of gases is much larger than effect of pres- θ s = i x wi θ si
sure on properties of liquids. The magnitude of this effect
decreases for fluids at higher pressures. For the liquid flu- where x wi is weight fraction of i in the mixture and subscript
ids, generally at low pressures, effect of pressure on prop- s indicates that the property is a specific quantity (per unit
erties is neglected in empirically developed correlations. As mass). In the above two equations, θ is a thermodynamic
pressure increases, properties of gases approach properties property such as volume (V), internal energy (U), enthalpy
of liquids. Effect of composition on the properties of liquid (H), heat capacity (C P ), entropy (S), Helmholtz free energy
is stronger than the effect of composition on properties of (A), or Gibbs free energy (G). Usually Eq. (7.1) is used to cal-
gases. Moreover, when components vary in size and proper- culate molar property of the mixture as well as its molecular
ties the role of composition on property estimation becomes weight and then Eq. (5.3) is used to calculate specific property
more important. For gases, the effect of composition on prop- wherever is required. In fact Eqs. (7.1) and (7.2) are equiva-
erties increases with increase in pressure. At higher pressures lent and one may combine Eqs. (5.3) and (1.15) with Eq. (7.1)
molecules are closer to each other and the effect of interac- to derive Eq. (7.2). These equations provide a good estimate
tion between dissimilar species increases. For gases at atmo- of mixture properties for ideal solutions and mixtures of sim-
spheric or lower pressures where the gas may be considered ilar compounds where the interaction between species may
ideal, composition has no role on molar density of the mixture be ignored.
as seen from Eq. (5.14). Empirically developed correlations for properties of un-
There are two approaches to calculate properties of defined defined or defined mixtures are based on a certain group of
mixtures. The first and more commonly used approach is to data on mixtures. Correlations specifically developed based
apply the mixing rules introduced in Chapter 5 for the in- on data of petroleum fractions usually cannot be used for
put parameters (T c , P c , ω) of an EOS or generalized correla- estimation of properties of pure hydrocarbons. However, if
tions and then to calculate the properties for the entire mix- in development of correlations for properties of undefined
ture. The second approach is to calculate desired property petroleum fractions pure component data are also used, then
for each component in the mixture and then to apply an ap- the resulting correlation will be more general. Such correla-
propriate mixing rule on the property. This second approach tions can be applied to both pure components and undefined
usually provides more accurate results; however, calculations mixtures and they can be used more safely to fractions
are more tedious and time-consuming, especially when the that have not been used in development of the correlation.

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