Page 339 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

T1: IML
QC: IML/FFX
P2: IML/FFX
P1: IML/FFX
AT029-Manual-v7.cls
June 22, 2007
17:40
AT029-Manual
AT029-07
7. APPLICATIONS: ESTIMATION OF THERMOPHYSICAL PROPERTIES 319
7.4.2 Heat Capacity
C P for gases, but for liquids more specific correlations espe-
cially at low pressures have been proposed in the literature.
Heat capacity is one of the most important thermal properties Estimation of C P and C V from equations of state was demon-
and is defined at both constant pressure (C P ) and constant vol- strated in Example 6.2.
ume (C V ) by Eqs. (6.17) and (6.18). It can be measured using For solids the effect of pressure on heat capacity is ne-
a calorimeter. For constant pressure processes, C P and in con- glected and it varies only with temperature: C = C = f (T).
S
S ∼
P
V
stant volume processes, C V is needed. C P can be obtained from At moderate and low pressures the effect of pressure on liq-
enthalpy using Eq. (6.20). uids may also be neglected as C = C = f (T). However, this
L
L ∼
V
P
Experimental data on liquid heat capacity of some pure assumption is not valid for liquids at high pressures. Some
hydrocarbons are given in Table 7.6 as reported by Poling specific correlations are given in the literature for calculation
et al. [12]. For defined mixtures where specific heat capacity of heat capacity of hydrocarbon liquids and solids at atmo-
for each compound in the mixture is known, the mixing rule spheric pressures. At low pressures a generalized expression
given by Eq. (7.2) may be used to calculate mixture heat ca- in a polynomial form of up to fourth orders is used to correlate
L
pacity of liquids C . Heat capacities of gases are lower than
Pi C P with temperature:
liquid heat capacities under the same conditions of T and P.
For example, for propane at low pressures (ideal gas state) C /R = C /R = A 1 + A 2 T + A 3 T + A 4 T + A 5 T 4
2
3
L
L
the value of C ig is 1.677 J/g · K at 298 K and 3.52 J/g · Kat P V
P (7.38) S S 2 3 4
800 K. Values of C P ig of n-heptane are 1.658 J/g · K at 298 K C /R = C /R = B 1 + B 2 T + B 3 T + B 4 T + B 5 T
P
V
and 3.403 J/g · K at 800 K. However, for liquid state and at
L
300 K, C of C 3 is 3.04 and that of n-C 5 is 2.71 J/g · K as re- where T is in kelvin. Coefficients A 1 –A 5 and B 1 –B 5 for a num-
P
ported by Reid et al. [12]. While molar heat capacity increases ber of compounds are given in Table 7.7 as given by DIPPR
with M, specific heat capacity decreases with increase in M. [10]. Some of the coefficients are zero for some compounds
3
Heat capacity increases with temperature. and for most solids the polynomial up to T is needed. In
The general approach to calculate C P is to estimate heat fact Debye’s statistical–mechanical theory of solids and exper-
ig
capacity departure from ideal gas [C P − C ] and combine it imental data show that specific heats of nonmetallic solids at
P
ig
with ideal gas heat capacity (C ) . A similar approach can be very low temperatures obey the following [22]:
P
used to calculate C V . The relation for calculation of C ig of
P S 3
petroleum fractions was given by Eq. (6.72), which requires (7.39) C = aT
P
ig
K W and ω as input parameters. C can be calculated from C ig
V
P
ig
ig
through Eq. (6.23). Both C and C are functions of only tem- where T is the absolute temperature in kelvin. In this relation
P
V
there is only one coefficient that can be determined from one
ig
perature. For petroleum fractions, C can also be calculated data point on solid heat capacity. Values of heat capacity of
P
from the pseudocompound method of Chapter 3 (Eq. 3.39) by solids at melting point given in Table 7.1 may be used as the
using Eq. (6.66) for pure hydrocarbons from different fami- reference point to find coefficient a in Eq. (7.39). Equation
lies similar to calculation of ideal gas enthalpy (Eq. 7.35). The (7.39) can be used for a very narrow temperature range near
ig
most accurate method for calculation of [C P − C ] is through the point where coefficient a is determined.
P
generalized correlation of Lee–Kesler (Eq. 6.57). Relations Cubic equations of states or the generalized correlation of
ig
ig
for calculation of [C P − C ] and [C V − C ] from cubic equa- Lee–Kesler for calculation of the residual heat capacity of
V
P
tions of state are given in Table 6.1. For gases at moderate liquids [C − C ] do not provide very accurate values espe-
ig
L
P
P
pressures the departure functions for heat capacity can be es- cially at low pressures. For this reason, attempts have been
timated through virial equation of state (Eqs. 6.64 and 6.65). made to develop separate correlations for liquid heat capac-
Once heat capacity departure and ideal gas properties are de- ity. Based on principle of corresponding states and using pure
termined, C P is calculated from the following relation:
compounds’ liquid heat capacity data, Bondi modified previ-

(7.37) C P = C P − C ig + C ig ous correlations into the following form [12]:
P P
L
ig
Relations given in Chapter 6 for the calculation of [C P − C ] C − C P ig = 1.586 + 0.49
P
P
and C ig are in molar units. If specific unit of J/g · C for heat R 1 − T r
◦
P
capacity is needed, calculated values from Eq. (7.37) should 6.3 (1 − T r) 1/3 0.4355
be divided by molecular weight of the substance. Generalized (7.40) + ω 4.2775 + +
correlation of Lee–Kesler normally provide reliable values of T r 1 − T r
L
TABLE 7.6—Some experimental values of liquid heat capacity of hydrocarbons, C [12].
P
L
Compound T,K C , J/g · K Compound T,K C , J/g · K Compound T,K C , J/g · K
L
L
P P P
Methane 100 3.372 n-Pentane 250 2.129 n-Decane 460 2.905
Methane 180 6.769 n-Pentane 350 2.583 Cyclohexane 280 1.774
Propane 100 1.932 n-Heptane 190 2.014 Cyclohexane 400 2.410
Propane 200 2.120 n-Heptane 300 2.251 Cyclohexane 500 3.220
Propane 300 2.767 n-Heptane 400 2.703 Benzene 290 1.719
i-Butane 300 2.467 n-Heptane 480 3.236 Benzene 400 2.069
n-Pentane 150 1.963 n-Decane 250 2.091 Benzene 490 2.618
--`,```,`,``````,`,````,```,,-`-`,,`,,`,`,,`---
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