Page 313 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

T1: IML
QC: —/—
P1: KVU/KXT
P2: KVU/KXT
20:46
June 22, 2007
AT029-Manual-v7.cls
AT029-06
AT029-Manual
6. THERMODYNAMIC RELATIONS FOR PROPERTY ESTIMATIONS 293
6.9. Show that
6.18. a. For a gas mixture that follows truncated virial EOS,
show that
2
∂ P 1
V
ig E
C V − C = T dV V = y i y j δ ij
V ∂T 2 V 2 i j
V=∞ T P
E
G = y i y j δ ij
Use this relation with truncated virial equation to derive 2 i j
Eq. (6.65). H = P y i y j δ ij − T dδ ij
E
6.10. The Joule–Thomson coefficient is defined as 2 i j dT
∂T
where δ ij is defined in Eq. (5.70) in Chapter 5.
η = b. Derive a relation for heat of mixing of a binary gas
∂P H
that obeys truncated virial EOS.
6.19. In general for mixtures, equality of mixture fugacity be-
a. Show that it can be related to PVT in the following tween two phases is not valid in VLE calculations:
form:
f V = f L
mix mix
∂V

T − V However, only under a certain condition the equality is
∂T P valid. What is that condition?
η =
C P 6.20. With the use of PR EOS and definition of solubility pa-
rameter (δ) by Eq. (6.147) one can derive the following
b. Calculate η for methane at 320 K and 10 bar from the relation for calculation of δ [17]:
SRK EOS.
⎡ L
√ ⎤
6.11. Similar to derivation of Eq. (6.38) for enthalpy departure 1 da V + 1 + 2 b
at T and V, derive the following relation for the heat δ = ⎣ √ L a − T dT ln L
√ ⎦
2 2bV
capacity departure and use it to calculate residual heat V + 1 − 2 b
capacity from RK EOS. How do you judge validity of where da/dT for PR EOS can be obtained from Table 6.1.
your result? L
With use of volume translation for V estimate values
L
of V and δ at 25 C for hydrocarbons C 5 and C 10 and
◦
2
∂P compare with values given in Table 6.10.

T
2
V
C P − C = T dV − − R
ig ∂ P ∂T V 6.21. Calculate freezing point depression of toluene when it
--`,```,`,``````,`,````,```,,-`-`,,`,,`,`,,`---
P T,V
∂T 2 ∂P is saturated with solid naphthalene at 20 C.
◦
V
V→∞ 6.22. Derive Eq. (6.240) for calculation of velocity of sound
∂V
T
from RK/SRK EOS.
6.12. Show that Eqs. (6.50) and (6.51) for calculation of resid- 6.23. Consider the dry natural gas (fluid 1) and black oil (fluid
ual entropy are equivalent. 5) samples whose compositions are given in Table 1.2.
6.13. Prove Eq. (6.81) for the Gibbs–Duhem equation. Assume there are two reservoirs, one containing the nat-
6.14. Derive Eq. (6.126) for fugacity coefficient of i in a mix- ural gas and the other containing black oil, both at 400 K
ture using SRK EOS. and 300 bar. Calculate velocity of sound in these two flu-
6.15. Derive the following relation for calculation of fugacity ids using SRK EOS.
ig
ig
ig
of pure solids at T < T tp . 6.24. Calculate (U − U ), (H − H ), and (S − S ) for steam at
500 C and 100 bar from SRK and PR EOS. How do you
◦
S sub
evaluate your results?
V P − P
S
f (T, P) = P i sub exp i i 6.25. Calculate the increase in enthalpy of n-pentane when
i
RT
its pressure increases from 600 to 2000 psia at 190.6 F
◦
using the following methods:
where P i sub is the vapor pressure of pure solid i at tem- a. SRK EOS.
perature T. b. LK method.
6.16. Derive Eq. (6.216) for the velocity of sound. c. Compare the results with the measured value of 188
6.17. A mixture of C 1 and C 5 exists at 311 K and 69.5 bar in Btu/lbmol [17].
both gas and liquid phases in equilibrium in a closed 6.26. Estimate C P , C V , and the speed of sound in liquid hexane
vessel. The mole fraction of C 1 in the mixture is z 1 = at atmospheric pressure and 269 and 300K from the
0.541. In the gas y 1 = 0.953 and in the liquid x 1 = 0.33. following methods:
Calculate K 1 and K 5 from the following methods: a. SRK EOS
a. Regular solution theory b. PR EOS
b. Standing correlation c. Compare calculated sonic velocities with reported
c. GPA/NIST graphs values of 1200 (at 269 K) and 1071 m/s (at 300 K)
d. PR EOS (Fig. 3.33, Ref. [17]).
In using PR EOS, use shift parameters of −0.2044 and 6.27. Estimate γ i ∞ for the system of n-C 4 and n-C 32 at
−0.045 for C 1 and n-C 5 , respectively. Also use BIP value 100 C from PR EOS and compare with the value from
◦
of k 1−5 = 0.054. Fig. 6.8.
Copyright ASTM International
Provided by IHS Markit under license with ASTM Licensee=International Dealers Demo/2222333001, User=Anggiansah, Erick
No reproduction or networking permitted without license from IHS Not for Resale, 08/26/2021 21:56:35 MDT