Page 249 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

P2: IML/FFX
QC: IML/FFX
P1: IML/FFX
AT029-Manual
August 16, 2007
AT029-05
where a and b are the EOS constants. Is this a valid
density at 68 F and pressure of 5400 psig using the fol-
◦
lowing methods. The experimental value is 0.8838 g/cm
EOS? AT029-Manual-v7.cls T1: IML 17:42 5. PVT RELATIONS AND EQUATIONS OF STATE 229 3
5.5. A graduate student has come up with a cubic EOS in the (Ref. [59] Ch 6)
following form: a. SRK EOS
b. SRK using volume translation
aV c. MRK EOS
2
P + (V − b) = RT
(V + b)(V − b) d. Eq. (5.128)
e. COSTALD correlation (Eq. 5.130)
Is this equation a correct EOS? f. LK generalized correlation
5.6. Derive a relation for the second virial coefficient of a g. Compare errors from different methods
fluid that obeys the SWP relation. Use data on B for 5.15. Estimate liquid density of n-decane at 423 K and 506.6
methane in Table 5.4 to obtain the potential energy bar from the following methods:
parameters, σ and ε. Compare your calculated values a. PR EOS
with those obtained from LJ Potential as σ = 4.01 ˚ A and b. PR EOS with volume translation
ε/k = 142.87 K [6, 79]. c. PR EOS with Twu correlation for parameter a (Eq.
5.7. Derive Eq. (5.66) from Eq. (5.65) and discuss about your 5.54)
derivation. d. MRK EOS
5.8. Show that for the second virial coefficient, Eq. (5.70) can e. Racket equation with COSTALD correlation
be reduced to a form similar to Eq. (5.59). Also show that f. Compare the values with the experimental value of
these two forms are identical for a binary system. 0.691 g/cm 3
5.9. Derive the virial form of PR EOS and obtain the virial 5.16. Estimate compressibility factor of saturated liquid and
coefficients B, C, and D in terms of PR EOS parameters. vapor (Z and Z ) methane at 160 K (saturation pres-
L
V
5.10. With results obtained in Example 5.4 and Problem 5.9 sure of 15.9 bar) from the following methods:
for the virial coefficients derived from RK, SRK, and PR a. Z from Racket equation and Z from Standing–Katz
V
L
equations estimate the following: chart
a. The second virial coefficient for propane at temper- b. PR EOS
atures 300, 400 and 500 K and compare the results c. PR EOS with Twu correlation for parameter a (Eq.
with those given in Table 5.4. Also predict B from 5.54)
Eqs. (5.71)–(5.73). d. MRK EOS
b. The third virial coefficients for methane and ethane e. LK generalized correlation
and compare with those given in Table 5.5. f. Compare estimated values with the values from Fig.
c. Compare predicted third virial coefficients from (b) 6.12 in Chapter 6.
--`,```,`,``````,`,````,```,,-`-`,,`,,`,`,,`---
with those predicted from Eq. (5.78). 5.17. Estimate Z of saturated methane in Problem 5.16 from
V
5.11. Specific volume of steam at 250 C and 3 bar is 796.44 virial EOS and evaluate the result.
◦
cm /g [1]. The virial coefficients (B and C) are given in 5.18. A liquid mixture of C 1 and n-C 5 exists in a PVT cell at
3
Table 5.5. Estimate specific volume of this gas from the 311.1 K and 69.5 bar. The volume of liquid is 36.64 cm .
3
following methods: Mole fraction of C 1 is 0.33. Calculate mass of liquid in
a. RK, SRK, and PR equations. grams using the following methods:
b. Both virial forms by Eqs. (5.65) and (5.66). Explain a. PR EOS with and without volume translation
why the two results are not the same. b. Rackett equation and COSTALD correlation
c. Virial equation with coefficients estimated from Eqs. c. MRK EOS
(5.71), (5.72), and (5.78) 5.19. A natural gas has the following composition:
5.12. Estimate molar volume of n-decane at 373 K and 151.98
bar from LK generalized correlations. Also estimate the Component CO 2 H 2 S N 2 C 1 C 2 C 3
critical compressibility factor. The actual molar volume mol% 8 16 4 65 4 3
3
is 206.5 cm /mol.
5.13. For several compounds liquid density at one tempera- Determine the density of the gas at 70 bar and 40 Cin
◦
ture is given in the table below. g/cm using the following methods:
3
a. Standing–Katz chart
Component a N 2 H 2 O C 1 C 2 C 3 n-C 4 b. Hall–Yarborough EOS
T, K 78 293 112 183 231 293 c. LK generalized correlation
V
L
ρ, g/cm 3 0.804 0.998 0.425 0.548 0.582 0.579 5.20. Estimate Z and Z of saturated liquid and vapor ethane
a Source: Reid et al. [15]. at T r = 0.8 from MRK and virial EOSs. Compare calcu-
lated values with values obtained from Fig. 5.10.
For each compound calculate the Rackett parameter
from reference density and compare with those given
in Table 5.12. Use estimated Rackett parameter to cal- REFERENCES
culate specific gravity of C 3 and n-C 4 at 15.5 C and com-
◦
pare with values of SG given in Table 2.1. [1] Smith, J. M., Van Ness, H. C., and Abbott, M. M., Introduction
5.14. For a petroleum fraction having API gravity of 31.4 and to Chemical Engineering Thermodynamics, 5th ed.,
Watson characterization factor of 12.28 estimate liquid McGraw-Hill, New York, 1996.

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