Page 314 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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294 CHARACTERIZATION AND PROPERTIES OF PETROLEUM FRACTIONS
6.28. Using results from Problem 6.27, estimate the Henry’s
c. Clausius–Clapeyron equation
law constant for the system of n-C 4 and n-C 32 at 100 C d. Compare the results with a reported value.
◦
from PR EOS. 6.37. A natural gas is composed of 85% methane, 10% ethane,
6.29. For the mixture of benzene and toluene construct the and 5% propane. What are the mole fractions of each of
freezing/melting diagram similar to Fig. 6.32. the components in water (gas solubility) at 300 bar and
6.30. One of the advanced liquid solution theories is known as 298 K.
the quasichemical approximation, which is particularly 6.38. Ninety barrels of n-C 36 are diluted with addition of 10
useful for mixtures containing molecules quantitatively bbl of n-C 5 at 25 C. Calculate volume of the solution at
◦
different in size and shape. According to this theory the 1 bar from the following methods:
molar excess Gibbs energy for a binary system is given a. Using partial molar volume from PR EOS.
by [21]: b. Using API procedure.
6.39. Show that if Edmister equation (Eq. 2.108) is used
E
G
w 1 2w

= x 1 x 2 1 − x 1 x 2 + ··· for acentric factor, Wilson correlation for K i -values
RT kT 2 zkT
(Eq. 6.204) reduces to Hoffman type correlation (Eq.
where the higher terms are neglected. x 1 and x 2 are mole 6.202).
fractions of 1 and 2 and k is the Boltzman’s constant. W 6.40. Solubility of water in a gasoline sample at 1 atm can
and z are model parameters that must be determined for be determined approximately by Eq. (6.195). However,
each system. W/zkT is less than unity and z is called co- accurate solubility of water can be estimated through
ordination number and varies from 6 to 12 [21]. Typical a thermodynamic model with activity coefficient calcu-
value of z is 10. Use Eq. (6.137) to derive the relations lations. A gasoline from California oil has mid boiling
for γ 1 and γ 2 . point of 404 F and API gravity of 43.5 with PNA compo-
◦
6.31. Show that at constant T and P, the Gibbs–Duhem equa- sition of 30.9, 64.3, and 4.8% as reported by Lenoir and
tion in a multicomponent mixture can be written in the Hipkin [12]. Estimate solubility of water in this gasoline
following forms: sample at 100 F and 1 atm from appropriate thermody-
◦
namic model and compare the predicted value with the

x i dln γ i = 0
i value estimated from Eq. (6.195).
or
ˆ
x i dln f i = 0 REFERENCES
i
6.32. Consider a binary solution of components 1 and 2. Show [1] Smith, J. M., Van Ness, H. C., and Abbott, M. M., Introduction
that in the region that Raoult’s law is valid for compo- to Chemical Engineering Thermodynamics, 5th ed.,
nent 1, Henry’s law must be valid for component 2. McGraw-Hill, New York, 1996.
6.33. In a binary liquid, mixtures of 1 and 2, fugacity of com- [2] Elliott, J. R. and Lira, C. T., Introductory Chemical Engineering
ponent 1 at 20 C can be approximately presented by the Thermodynamics, Prentice Hall, New Jersey, 1999
◦
equation: (www.phptr.com).
[3] Daubert, T. E., Danner, R. P., Sibul, H. M., and Stebbins, C. C.,
ˆ L
f = 30x 1 − 20x 2 Physical and Thermodynamic Properties of Pure Compounds:
1 1
Data Compilation, DIPPR-AIChE, Taylor & Francis, Bristol, PA,
where f ˆL is the fugacity of 1 in the mixture in bar. At
1 1994 (extant) (www.aiche.org/dippr). Updated reference:
20 C and 30 bar determine: Rowley, R. L., Wilding, W. V., Oscarson, J. L., Zundel, N. A.,
◦
L
a. The fugacity of pure component 1, f . Marshall, T. L., Daubert, T. E., and Danner, R. P., DIPPR Data
1
b. The fugacity coefficient of pure component 1, φ 1 . Compilation of Pure Compound Properties, Design Institute for
c. The Henry’s law constant for component 1, k 1 . Physical Properties (DIPPR), Taylor & Francis, New York, 2002
(http://dippr.byu.edu).
d. Relation for the activity coefficient γ 1 in terms of x 1
(based on the standard state of Lewis rule). [4] Poling, B. E., Prausnitz, J. M., and O’Connell, J. P., Properties of
ˆL
e. Relation for f . Gases and Liquids, 5th ed., Mc-Graw Hill, New York, 2000.
2 [5] Daubert, T. E. and Danner, R. P., Eds., API Technical Data
6.34. Consider three hydrocarbon components benzene, cy- Book—Petroleum Refining, 6th ed., American Petroleum
clohexane, and n-hexane all having six carbon atoms. Institute (API), Washington, DC, 1997.
Both quantitatively and qualitatively state that solubility [6] Garvin, J., “Use the Correct Constant–Volume Specific Heat,”
of benzene in methylcylopentane is higher or benzene Chemical Engineering Progress, Vol. 98, No. 7, 2002, pp. 64–65.
in n-hexane. [7] Polt, A., Platzer, B., and Maurer, G., “Parameter der
6.35. A solution is made at the temperature of 298 K by adding thermischen Zustandsgl eichung von Bender fuer 14
5 g of naphthalene to a mixture of 50 g benzene and 50 g mehratomige reine Stoffe,” Chemische Technik (Leipzig),
n-heptane. The temperature is gradually lowered until Vol. 44, No. 6, 1982, pp. 216–224.
the particles of solid are observed. What is the temper- [8] Shabani, M. R., Riazi, M. R., and Shaban, H. I., “Use of Velocity
ature at this point? What is the temperature if 10 g of of Sound in Predicting Thermodynamic Properties from Cubic
naphthalene is added? Equations of State,” Canadian Journal of Chemical Engineering,
Vol. 76, 1998, pp. 281–289.
6.36. Estimate vapor pressure of isobutane at 50 C from the [9] Lee, B. I. and Kesler, M. G., “A Generalized Thermodynamic
◦
following methods: Correlation Based on Three-Parameter Corresponding States,”
a. SRK EOS. American Institute of Chemical Engineers Journal, Vol. 21, 1975,
b. PR EOS. pp. 510–527.
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