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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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