Page 325 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

T1: IML
P2: IML/FFX
P1: IML/FFX
QC: IML/FFX
AT029-Manual-v7.cls
AT029-Manual
17:40
AT029-07
June 22, 2007
7. APPLICATIONS: ESTIMATION OF THERMOPHYSICAL PROPERTIES 305
point temperature and pressure (T tp , P tp ) are also needed in
SLE calculations. Values of density and heat capacity of liquid 7.3.1 Pure Components
and solid phases for some compounds at their melting points Experimental data for vapor pressure of pure hydrocarbons
are given in Table 7.1, as obtained from DIPPR [10]. The triple are given in the TRC Thermodynamic Tables [11]. Figures 7.4
point temperature (T tp ) is exactly the same as the melting or and 7.5 show vapor pressure of some pure hydrocarbons from
freezing point temperature (T M ). As seen from Fig. 5.2a and praffinic and aromatic groups as given in the API-TDB [9].
◦
from calculations in Example 6.5, the effect of pressure on the Further data on vapor pressure of pure compounds at 37.8 C
◦
melting point of a substance is very small and for a pressure (100 F) were given earlier in Table 2.2. For pure compounds
change of a few bars no change in T M is observed. Normal the following dimensionless equation can be used to estimate
freezing point T M represents melting point at pressure of 1 vapor pressure [9]:
atm. P tp for a pure substance is very small and the maximum (7.8) ln P r vap = T r −1 × aτ + bτ 1.5 + cτ 2.6 + dτ 5

difference between atmospheric pressure and P tp is less than vap
where τ = 1 − T r and P r is the reduced vapor pressure
1 atm. For this reason as it is seen in Table 7.1 values of T M vap
and T tp are identical (except for water). (P /P c ), and T r is the reduced temperature. Coefficients a–
--`,```,`,``````,`,````,```,,-`-`,,`,,`,`,,`---
Effect of temperature on solid density in a limited temper- d with corresponding temperature ranges are given in Ta-
ature range can be expressed in the following linear form: ble 7.2 for a number of pure compounds. Equation (7.8) is
a linearized form of Wagner equation. In the original Wagner
S

(7.7) ρ = A − 10 −6 × B T equation, exponents 3 and 6 are used instead of 2.6 and 5 [12].
m
The primary correlation recommended in the API-TDB [9]
3
S
where ρ m is the solid molar density at T in mol/cm . A and for vapor pressure of pure compounds is given as
B are constants specific for each compound, and T is the B E
2
absolute temperature in kelvin. Values of B for some com- (7.9) ln P vap = A + T + C ln T + DT + T 2
pounds as given by DIPPR [10] are n-C 5 : 6.0608; n-C 10 : 2.46; n-
C 20 : 2.663; benzene: 0.3571; naphthalene: 2.276; benzoic acid: where coefficients A–E are given in the API-TDB for some 300
2.32; and water (ice): 7.841. These values with Eq. (7.7) and compounds (hydrocarbons and nonhydrocarbons) with spec-
values of solid density at the melting point given in Table 7.1 ified temperature range. This equation is a modified version
can be used to obtain density at any temperature as shown in of correlation originally developed by Abrams and Prausnitz
the following example. based on the kinetic theory of gases. Note that performance
of these correlations outside the temperature ranges specified
is quite weak. In DIPPR [10], vapor pressure of pure hydro-
Example 7.2—Estimate density of ice at –50 C. carbons is correlated by the following equation:
◦
B E
vap
Solution—From Table 7.1 the values for water are obtained (7.10) ln P = A + T + C ln T + DT
3
S
as M = 18.02, T M = 273.15 K, ρ = 0.9168 g/cm (at T M ).
In Eq. (7.7) for water (ice) B = 7.841 and ρ S m is the molar where coefficients A–E are given for various compounds in
S
3
density. At 273.15 K, ρ = 0.050877 mol/cm . Substituting Ref. [10]. In this equation, when E = 6, it reduces to the Riedel
m equation [12]. Another simple and commonly used relation
in Eq. (7.7) we get A = 0.053019. With use of A and B in
S
Eq. (7.7) at 223.15 K (−50 C) we get ρ = 0.051269 mol/cm 3 to estimate vapor pressure of pure compounds is the Antoine
◦
m
S
3
or ρ = 0.051269 × 18.02 = 0.9238 g/cm . equation given by Eq. (6.102). Antoine parameters for some
700 pure compounds are given by Yaws and Yang [13]. An-
toine equation can be written as
7.3 VAPOR PRESSURE (7.11) ln P vap (bar) = A − B
T + C
As shown in Chapters 2, 3, and 6, vapor pressure is required where T is in kelvin. Antoine proposed this simple modifi-
in many calculations related to safety as well as design and cation of the Clasius–Clapeyron equation in 1888. The lower
operation of various units. In Chapter 3, vapor pressure rela- temperature range gives the higher accuracy. For some com-
tions were introduced to convert distillation data at reduced pounds, coefficients of Eq. (7.11) are given in Table 7.3. Equa-
pressures to normal boiling point at atmospheric pressure. In tion (7.11) is convenient for hand calculations. Coefficients
Chapter 2, vapor pressure was used for calculation of flamma- may vary from one source to another depending on the tem-
bility potential of a fuel. Major applications of vapor pres- perature range at which data have been used in the regres-
sure were shown in Chapter 6 for VLE and calculation of sion process. Antoine equation is reliable from about 10 to
equilibrium ratios. As it was shown in Fig. 1.5, prediction 1500 mm Hg (0.013–2 bars); however, the accuracy deteri-
of vapor pressure is very sensitive to the input data, partic- orates rapidly beyond this range. It usually underpredicts
ularly the critical temperature. Also it was shown in Fig. 1.7 vapor pressure at high pressures and overpredicts vapor pres-
that small errors in calculation of vapor pressure (or relative sures at low pressures. One of the convenient features of this
volatility) could lead to large errors in calculation of the height equation is that either vapor pressure or the temperature can
of absorption/distillation columns. Methods of calculation of be directly calculated without iterative calculations. No gener-
vapor pressure of pure compounds and estimation methods alized correlation has been reported on the Antoine constants
using generalized correlations and calculation of vapor pres- and they should be determined from regression of experimen-
sure of petroleum fractions are presented hereafter. tal data.

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