Page 320 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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300 CHARACTERIZATION AND PROPERTIES OF PETROLEUM FRACTIONS
However, one important limitation in use of such correlations
is boiling point range, carbon number, or molecular weight book. Equation (7.3) is valid for both liquids and gases once
their Z values are calculated from an equation of state or a
of fractions and compounds used in the development of generalized correlation. If Z is known for all components in
the correlations. For example, correlations that are based a mixture, then Z m can be calculated from Eq. (7.1) and ρ m
on properties of petroleum fractions and pure components from Eq. (7.3). Specific methods and recommendations for
with carbon number range of C 5 –C 20 cannot be used for calculation of density of gases and liquids are given in the
estimation of properties of light gases (natural gases or LPG), following sections.
heavy residues, or crude oils. Another limitation of empir-
ically developed correlations is the method of calculation 7.2.1 Density of Gases
of input parameters. For example, a generalized correlation
developed for properties of heavy fractions requires critical Generally both equations of state and the Lee–Kesler gener-
properties as input parameter. For such correlations the same alized correlation (Section 5.7) provide reliable prediction of
method of estimation of input parameters as the one used gaseous densities. For high-pressure gases, cubic EOS such
in the development of correlation should be used. The most as PR or SRK EOS give acceptable values of density for both
reliable correlations are those that have some theoretical pure and mixtures and no volume translation (Section 5.5.3)
background, but the coefficients have been determined is needed. For practical calculations, properties of gases can
empirically from data on petroleum fractions as well as pure be calculated from simple equations of state. For example,
compounds. One technique that is often used in recent years Press [7] has shown that the original simple two-parameter
to develop correlations for physical properties of both pure Redlich–Kowng equation of state (RK EOS) gives reasonably
compounds and complex mixtures is the artificial neural acceptable results for predicting gas compressibility factors
network method [4–6]. These methods are called neural net- needed for calculation of valve sizes. For moderate pressures
works methods because artificial neural networks mimic the truncated virial equation (Eq. 5.76) can be used with coeffi-
behavior of biological neurons. Although neural nets can be cients (B and C) calculated from Eqs. (5.71) and (5.78). For
used to correlate data accurately and to identify correlative low-pressure gases (<5 bar), virial equation truncated after
patterns between input and target values and the impact of the second term (Eq. 5.75) with predicted second virial coef-
each input parameter on the correlation, they lack necessary ficient from Tsonopoulos correlation (Eq. 5.71) is sufficient
theoretical basis needed in physical property predictions. to predict gas densities. For light hydrocarbons and natural
The resulting correlations from neural nets are complex and gases, the Hall–Yarborough correlation (Eq. 5.102) gives a
involve a large number of coefficients. For this reason corre- good estimate of density. For defined gas mixtures the mixing
lations are inconvenient for practical applications and they rule may be applied to the input parameters (T c , P c , and ω) and
have very limited power of extrapolation outside the ranges the mixture Z value can be directly calculated from an EOS.
of data used in their developments. However, the neural For undefined natural gases, the input parameters may be
net model can be used to identify correlating parameters in calculated from gas-specific gravity using correlations given
order to simplify theoretically developed correlations. in Chapter 4 (see Section 4.2).

7.2.2 Density of Liquids
7.2 DENSITY
For high-pressure liquids, density may be estimated from cu-
Density is perhaps one of the most important physical proper- bic EOS such as PR or SRK equations. However, these equa-
ties of a fluid, since in addition to its direct use in size calcula- tions break at carbon number of about C 10 for liquid density
tions it is needed to predict other thermodynamic properties calculations. They provide reasonable values of liquid density
as shown in Chapter 6. As seen in Section 7.5, methods to when appropriate volume translation introduced in Section
estimate transport properties of dense fluids also require re- 5.5.3 is used. The error of liquid density calculations from
duced density. Therefore once an accurate value of density cubic equations of states increases at low and atmospheric
is used as an input parameter for a correlation to estimate pressures. For saturated liquids, special care should be taken
a physical property, a more reliable value of that property to take the right Z value (the lowest root of a cubic equation).
can be calculated. Methods of calculation of density of fluids Once a cubic equation is used to calculate various thermody-
have been discussed in Chapter 5. Density may be expressed namic properties (i.e., fugacity coefficient) at high pressures,
3
in the form of absolute density (ρ, g/cm ), molar density it is appropriate to use a cubic equation such as SRK or PR
3
3
(ρ m , mol/cm ), specific volume (V,cm /g), molar volume (V m , with volume translation for both liquid and gases. However,
3
cm /mol), reduced density (ρ r = ρ/ρ c = V c /V, dimensionless), when density of a liquid alone is required, PR or SRK are not
ig
or compressibility factor (Z = PV/RT = V/V , dimensionless). the most appropriate method for calculation of liquid density.
Equations of states or generalized correlations discussed in For heavy hydrocarbons and petroleum fractions, the modi-
Chapter 5 predict V m or Z at a given T and P. Once Z is known, fied RK equation of state based on refractive index proposed
the absolute density can be calculated from in Section 5.9 is appropriate for calculation of liquid densi-
ties. The refractive index of heavy petroleum fractions can be
MP
(7.3) ρ = estimated accurately with methods outlined in Chapter 2. One
ZRT should be careful that this method is not applicable to non- --`,```,`,``````,`,````,```,,-`-`,,`,,`,`,,`---
where M is the molecular weight, R is the gas constant, and hydrocarbons (i.e., water, alcohols, or acids) or highly polar
T is the absolute temperature. If M is in g/mol, P in bars, aromatic compounds.
3
T in kelvin, and R = 83.14 bar · cm /mol · K, then ρ is calcu- For the range that Lee–Kesler generalized correlation (Eq.
3
lated in g/cm , which is the standard unit for density in this (5.107) and Table 5.9) can be used for liquids, it gives density

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