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292 CHARACTERIZATION AND PROPERTIES OF PETROLEUM FRACTIONS
process. For this reason there is no continuity in use of pa-
rameters α s and β s for use in both phases. For the same reason calculation of heat of fusion, molar volume, and solubility
parameters for paraffinic, naphthenic, and aromatic groups.
when parameters obtained from gas sonic velocity were used These relations are useful in VLE and SLE calculations for
to calculate vapor pressure errors larger than original EOS petroleum fractions through the pseudocomponent method
parameters were obtained [8]. of Chapter 3. Data on the enthalpy of fusion and freezing
Research on using the velocity of sound to obtain thermo- pointd can be used to calculate freezing point of a mixture or
dynamic properties of fluids are underway, and as more data the temperature at which first solid particles begin to form.
on the speed of sound in heavy petroleum mixtures become Application of methods presented in this chapter require in-
available usefulness of this technique of calculating proper- put parameters (critical properties, molecular weight, and
ties of undefined and heavy mixtures becomes more clear. acentric factor) that for defined mixtures should be calcu-
From the analysis shown here, one may conclude that use lated from mixing rules given in Chapter 5. For undefined
of sonic velocity is a promising method for prediction and petroleum fractions these parameters should be calculated
calculation of thermodynamic properties of fluids and fluid from methods given in Chapters 2–4. Main application of
mixtures. methods presented in this chapter will be shown in the next
chapter for calculation of thermodynamic and physical prop-
erties of hydrocarbons and undefined petroleum fractions.
6.10 SUMMARY AND RECOMMENDATIONS The main characteristic of relations shown in this chapter
is that they can be used for prediction of properties of both
In this chapter fundamental thermodynamic relations that gases and liquids through an equation of state. However, as
are needed in calculation of various physical and thermody- it will be seen in the next chapter there are some empirically
namic properties are presented. Through these relations var- developed correlations that are mainly used for liquids with
ious properties can be calculated from knowledge of a PVT higher degree of accuracy. Generally properties of liquids are
relation or an equation of state. Methods of calculation of calculated with lesser accuracy than properties of gases. --`,```,`,``````,`,````,```,,-`-`,,`,,`,`,,`---
vapor pressure, enthalpy, heat capacity, entropy, fugacity, ac- With the help of fundamental relations presented in this
tivity coefficient, and equilibrium ratios suitable for hydro- chapter a generalized cVT relation based on the velocity of
carbon systems and petroleum fractions are presented in this sound is developed. It has been shown that when EOS param-
chapter. These methods should be used in conjunction with eters are calculated through a measurable property such as
equations of states or generalized correlations presented in velocity of sound, thermophysical properties such as density,
Chapter 5. In use of cubic equations of state for phase equilib- enthalpy, heat capacity, and vapor pressure have been calcu-
rium calculations and calculation of K i values, binary interac- lated with better accuracy for both liquid and vapor phases
tion parameters recommended in Chapter 5 should be used. through the use of velocity of sound data. This technique
Cubic equations are recommended for high-pressure phase is particularly useful for mixtures of unknown composition
equilibrium calculations while activity coefficient models are and reservoir fluids and it is a promising approach for esti-
recommended for low-pressure systems. Methods of calcu- mation of thermodynamic properties of complex undefined
lation of activity coefficient and Henry’s law constants from mixtures.
a cubic EOS are presented. Recent studies show that cubic
equations are not the best type of PVT relation for prediction
of derivative properties such as enthalpy, Joule–Thomson co-
efficient, or heat capacity. For this reason noncubic equations 6.11 PROBLEMS
such as statistical associating fluid theory (SAFT) are being
investigated for prediction of such properties [38, 57]. The 6.1. Develop an equation of state in terms of parameters β
main purpose of this chapter was to demonstrate the role that and κ.
theory plays in estimation of physical properties of petroleum 6.2. In storage of hydrocarbons in cylinders always a mix-
fluids. However, among the methods presented in this chapter, tures of both vapor and liquid (but not a single phase)
the LK generalized correlations are the most suitable meth- are stored. Can you justify this?
ig
ods for calculation of enthalpy, heat capacity, and fugacity for 6.3. Derive a relation for calculation of (G − G )/RT in terms
both liquid and gas phases at elevated pressures. of PVT and then combine with Eq. (6.33) to derive
While the cubic equations (i.e., SRK or PR) are useful Eq. (6.50).
for phase behavior calculations, the LK corresponding state 6.4. Derive Edmister equation for acentric factor (Eq. 2.108)
correlations are recommended for calculation of density, from Eq. (6.101).
enthalpy, entropy, and heat capacity of hydrocarbons and 6.5. a. Derive a relation for molar enthalpy from PR EOS.
petroleum fractions. Partial molar properties and their meth- b. Use the result from part a to derive a relation for par-
ods of calculation have been presented for estimation of mix- tial molar enthalpy from PR EOS.
ture properties. Calculation of volume change due to mixing c. Repeat part a assuming parameter b is a temperature-
or heat of mixing is shown. Fundamental phase equilibria re- dependent parameter.
lations especially for vapor–liquid and solid–liquid systems 6.6. Derive a relation for partial molar volume from PR EOS
are developed. Through these relations calculation of vapor (Eq. 6.88).
pressure of pure substances, solubility of gases and solids 6.7. Derive fugacity coefficient relation from SRK EOS for
in liquids are demonstrated. Solubility parameters for pure a pure substance and compare it with results from
compounds are given for calculation of activity coefficients Eq. (6.126).
without use of any VLE data. Correlations are presented for 6.8. Derive Eq. (6.26) for the relation between C P and C V .
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