Page 248 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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228 CHARACTERIZATION AND PROPERTIES OF PETROLEUM FRACTIONS
Four types of cubic equations vdW, RK, SRK, and PR and
hydrocarbons and petroleum fractions. Analytical form of LK
their modifications have been reviewed. The main advantage calculation of density, enthalpy, entropy, and heat capacity of
of cubic equations is simplicity, mathematical convenience, correlation is provided for computer applications, while the
and their application for both vapor and liquid phases. The tabulated form is given for hand calculations. Simpler two-
main application of cubic equations is in VLE calculations parameter empirical correlation for calculation of Z-factor of
as will be discussed in Chapters 6 and 9. However, their abil- gases, especially for light hydrocarbons and natural gases, is
ity to predict liquid phase density is limited and this is the given in a graphical form in Fig. 5.12 and Hall–Yarborough
main weakness of cubic equations. PR and SRK equations are equation can be used for computer applications..
widely used in the petroleum industry. PR equation gives bet- For calculation of liquid densities use of Rackett equa-
ter liquid density predictions, while SRK is used in VLE calcu- tion (Eq. 5.121) is recommended. For petroleum fractions
lations. Use of volume translation improves capability of liq- in which Racket parameter is not available it should be de-
uid density prediction for both PR and SRK equations; how- termined from specific gravity through Eq. (5.123). For the
ever, the method of calculation of this parameter for heavy effect of pressure on liquid density of light pure hydrocar-
petroleum fractions is not available and generally these equa- bons, defined hydrocarbon mixtures and light petroleum frac-
tions break down at about C 10 . Values of input parameters tions, the COSTALD correlation (Eq. 5.130) may be used. For
greatly affect EOS predictions. For heavy hydrocarbons, ac- petroleum fractions effect of pressure on liquid density can
curate prediction of acentric factor is difficult and for this rea- be calculated through Eq. (5.128).
son an alternative EOS based on modified RK equation is pre- For defined mixtures the simplest approach is to use Kay’s
sented in Section 5.9. The MRK equation uses refractive index mixing rule (Eqs. 3.39 and 5.116) to calculate pseudocriti-
parameter instead of acentric factor and it is recommended cal properties and acentric factor of the mixture. However,
for density calculation of heavy hydrocarbons and undefined when molecules in a mixture are greatly different in size (i.e.,
petroleum fraction. This equation is not suitable for VLE and C 5 and C 20 ), more accurate results can be obtained by using
vapor pressure calculations. In Chapter 6, use of velocity of appropriate mixing rules given in this chapter for different
sound data to obtain EOS parameters is discussed [79]. EOS. For defined mixtures liquid density can be best calcu-
Among noncubic equations, virial equations provide more lated through Eq. (5.126) when pure component densities are
accurate PVT relations; however, prediction of fourth and known at a given temperature and pressure. For undefined
higher virial coefficients is not possible. Any EOS can be con- narrow boiling range petroleum fractions T c , P c , and ω should
verted into a virial form. For gases at moderate pressures, be estimated according to the methods described in Chapters
truncated virial equation after third term (Eq. 5.75) is recom- 2 and 3. Then the mixture may be treated as a single pseudo-
mended. Equation (5.71) is recommended for estimation of component and pure component EOS can be directly applied
the second virial coefficient and Eq. (5.78) is recommended to such systems. Some other graphical and empirical meth-
for prediction of the third virial coefficients. For specific com- ods for the effect of temperature and pressure on density and
pounds in which virial coefficients are available, these should specific gravity of hydrocarbons and petroleum fractions are
be used for more accurate prediction of PVT data at certain given in Chapter 7. Further application of methods presented
moderate conditions such as those provided by Gupta and in this chapter for calculation of density of gases and liquids
Eubank [80]. especially for wide boiling range fractions and reservoir fluids
Several other noncubic EOS such as BWRS, CS, LJ, SPHC, will be presented in Chapter 7. Theory of prediction of ther-
and SAFT are presented in this chapter. As will be discussed modynamic properties and their relation with PVT behavior
in the next chapter, recent studies show that cubic equations of a fluid are discussed in the next chapter.
are also weak in predicting derivative properties such as en-
thalpy, Joule Thomson coefficient, or heat capacity. For this
reason, noncubic equations such as simplified perturbed hard 5.11 PROBLEMS
chain (SPHC) or statistical associating fluid theory (SAFT)
are being investigated for prediction of such derived prop- 5.1. Consider three phases of water, oil, and gas are in equi-
erties [81]. For heavy hydrocarbons in which two-parameter librium. Also assume the oil is expressed in terms of
potential energy functions are not sufficient to describe the in- 10 components (excluding water) with known specifica-
termolecular forces, three- and perhaps four-parameter EOS tions. The gas contains the same compounds as the oil.
must be used. The most recent reference on the theory and Based on the phase rule determine what is the minimum
application of EOSs for pure fluids and fluid mixtures is pro- information that must be known in order to determine
vided by Sengers et al. [82]. In addition, for a limited number oil and gas properties.
of fluids there are highly accurate EOS that generally take on a 5.2. Obtain coefficients a and b for the PR EOS as given in
modified MBWR form or a Helmholtz energy representation Table 5.1. Also obtain Z c = 0.307 for this EOS.
like the IAPWS water standard [4]. Some of these equations 5.3. Show that the Dieterici EOS exhibits the correct limiting
are even available free on the webs [83]. behavior at P → 0 (finite T) and T →∞ (finite P)
The theory of corresponding state provides a good PVT rela- RT
tion between Z-factor and reduced temperature and pressure. P = V − b e −a/RTV
The LK correlation presented by Eqs. (5.107)–(5.111) is based
on BWR EOS and gives the most accurate PVT relation if ac- where a and b are constants.
curate input data on T c , P c , and ω are known. While the cubic 5.4. The Lorentz EOS is given as
equations are useful for phase behavior calculations, the a bV
LK corresponding states correlations are recommended for P + V 2 V − V + b = RT

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