Page 341 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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7. APPLICATIONS: ESTIMATION OF THERMOPHYSICAL PROPERTIES 321
form for T r ≤ 0.85:
and C = 1.419 J/g · C (at 20 C). From T b and SG, K W =
P ig ◦ ◦
L
C = A 1 + A 2 T + A 3 T 2 12.264.
P
(a) To use SRK EOS use equations given in Table 6.1 and
follow similar calculations as in Example 6.2: A = 0.039685,
A 1 =−4.90383 + (0.099319 + 0.104281SG)K W
3
L
L
B = 0.003835, Z = 0.00492, V = 118.3 cm /mol, the volume
4.81407 − 0.194833 K translation is c = 13.5 cm /mol, V (corrected) = 104.8cm /
3 L 3
+ L
SG mol, and Z (correc.) = 0.00436. From Table 6.1, P 1 =
ig
6.9868, P 2 =−103.976, P 3 = 0.5445, and [C P − C ] = 21.41
0.27634 −4 L
P
A 2 = (7.53624 + 6.214610K W) × 1.12172 − × 10 J/mol · K = 21.41/68.12 = 0.3144 J/g · K. C = 0.3144 +
P
SG
1.419 = 1.733 J/g · K (error of −13%). (b) DIPPR [10] gives
0.70958 −7 the value of C = 2.138 J/g · K (error of +7%). (c) From the
L

A 3 =−(1.35652 + 1.11863K W )× 2.9027 − × 10 P
SG Lee–Kesler correlation of Eq. (6.57), T r = 0.612 and P r =
(7.43) 0.0271. From Tables 6.4 and 6.5, using interpolation (for P r )
and extrapolation (for T r , extrapolation from the liquid re-
ig
where C is in kJ/kg · K and T is in kelvin. This equation was gion) we get [(C P − C )/R] (0) = 1.291 and [(C P − C )/R] (1) =
L
ig
P
P
P
developed by Lee and Kesler of Mobile Oil Corporation in 5.558. In obtaining these values special care should be made
1975. From this relation, the following equation for estima- not to use values in the gas regions. From Eqs. (6.57) and
tion of enthalpy of liquid petroleum fractions can be obtained. (7.38) using parameters R, M, and C P ig we get C = 1.633
L
P
ig
L
(error of –18%). (d) From Eq. (7.40), [(C − C )/R] = 3.9287,
P
P
T
L
L L L A 2 2 C = 1.899 (error of −4.8%). (e) From Eq. (7.42), a = 4.2884,
H = C dT + H ref = A 1 (T − T ref ) + (T − T ref ) P
P
2 b = 0.19547, c = 0.0011, C = 2.223 J/g · K (error of +11.5%).
L
T ref P
This is the same as ASTM D 2890 test method. (f) From
L
L
3
(7.44) + A 3 (T − T ref ) + H ref Tsonopoulos correlation, Eq. (7.45), C = 2.127 J/g · K (error
P
3 of +6.6%). The generalized Lee–Kesler correlation (Eq.
L
where H ref is usually zero at the reference temperature of T ref . 6.57) gives very high error because this method is mainly
Equation (7.43) is not recommended for pure hydrocarbons. accurate for gases. For liquids, Eq. (7.40) is more accurate
The following modified form of Watson and Nelson correla- than is Eq. (6.57). Equation (7.45) although recommended
tion is recommended by Tsonopoulos et al. [18] for calcula- for coal liquids predicts liquid heat capacity of hydrocarbons
tion of liquid heat capacity of coal liquids and aromatics: relatively with relative good accuracy.
L
C = (0.28299 + 0.23605K W)
P There are some other methods developed for calculation of
L
C . In general heat capacity of a substance is proportional to
P
× 0.645 − 0.05959 SG + (2.32056 − 0.94752 SG) molar volume and can be related to the free space between
molecules. As this space increases the heat capacity decreases.
T Since parameter I (defined by Eq. 2.36) also represents mo-

× − 0.25537
1000 lar volume occupied by the molecules Riazi et al. [27] showed
L
that C varies linearly with I/(1 − I). They obtained the fol-
(7.45) P
lowing relation for heat capacity of homologous hydrocarbon
L
where C is in kJ/kg · K and T is in kelvin. This equation pre- groups:
P
dicts heat capacity of coal liquids with an average error of L
about 3.7% for about 400 data points [18]. The following ex- (7.46) C P = (a 1 M + b 1) × I + c 1 M + d 1
ample shows various methods of calculation of heat capacity R 1 − I
of liquids.
In the above relation M is molecular weight, R is the gas con-
stant, and coefficients a 1 –d 1 are specific for each hydrocarbon
L
Example 7.6—Calculate C of 1,4-pentadiene at 20 C using
◦
P family. Parameters I is calculated throughout Eqs. (2.36) and
the following methods and compare with the value of 1.994 (2.118) at the same temperature at which C L is being cal-
J/g · C reported by Reid et al. [12]. P
◦
culated. Parameters a 1 –d 1 for different hydrocarbon families
a. SRK EOS and solid phase are given in Table 7.8.
b. DIPPR correlation [10]
c. Lee–Kesler generalized corresponding states correlation 7.4.3 Heats of Phase Changes—Heat
(Eq. 6.57) of Vaporization
d. Bondi’s correlation (Eq. 7.40)
e. Kesler–Lee correlation (Eq. 7.42)—ASTM D 2890 method Generally there are three types of phase changes: solid to
f. Tsonopoulos et al. correlation (Eq. 7.45) liquid known as fusion (or melting), liquid to vapor (vapor-
ization), and solid to vapor (sublimation), which occurs at
Solution—Basic properties of 1,4-pentadiene are not given in pressures below triple point pressure as shown in Fig. 5.2a.
Table 2.1. Its properties obtained from other sources such as During phase change for a pure substance or mixtures of con-
DIPPR [10] are as follows: M = 68.1185, T b = 25.96 C, SG = stant composition, the temperature and pressure remain con-
◦
0.6633, T c = 205.85 C, P c = 37.4 bar, Z c = 0.285, ω = 0.08365, stant. According to the first law of thermodynamics, the heat
◦
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