Page 278 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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AT029-Manual
258 CHARACTERIZATION AND PROPERTIES OF PETROLEUM FRACTIONS
based on the Wohl’s model for the excess Gibbs energy [21].
E
The G relation for the van Laar model is given by 20:46 compounds two parameters, namely energy parameter and
size parameter describe the intermolecular forces. Energy of
vaporization is directly related to the energy required to over-
G E come forces between molecules in the liquid phase and molar
(6.143) = x 1 x 2 [A + B(x 1 − x 2 )] −1
RT volume is proportional to the molecular size. Therefore, when
two components have similar values of δ their molecular size
Upon application of Eq. (6.137), the activity coefficients are and forces are very similar. Molecules with similar size and
obtained as
intermolecular forces easily can dissolve in each other. The
−2
importance of solubility parameter is that when two compo-
A 12 x 1
ln γ 1 = A 12 1 + nents have δ values close to each other they can dissolve in
A 21 x 2
(6.144) each other appreciably. It is possible to use an EOS to cal-
−2

A 21 x 2 culate δ from Eq. (6.147) (see Problem 6.20). According to
ln γ 2 = A 21 1 + the theory of regular solutions, excess entropy is zero and it
A 12 x 1
can be shown that for such solutions RT lnγ i is constant at
where coefficients A 12 and A 21 are related to A and B in Eq. constant composition and does not change with temperature
L
[11]. Values of V and δ i at a reference temperature of 298
(6.143) as A − B = 1/A 12 and A + B = 1/A 21 . Coefficients A 12 i
and A 21 can be determined from the activity coefficients at K is sufficient to calculate γ i at other temperatures through
infinite dilutions (A 12 = ln γ , A 21 = ln γ ). Once for a given Eq. (145). Values of solubility parameter for single carbon
∞
∞
1 2
system VLE data are available, they can be used to calculate number components are given in Table 4.6. Values of V and
L
i
activity coefficients through Eqs. (6.179) or (6.181) and then δ i at 25 C for a number of pure substances are given in Ta-
◦
E
G /RT is calculated from Eq. (6.138). From the knowledge of ble 6.10 as provided by DIPPR [13]. In this table values of δ
E
E
3 1/2
G /RT versus (x 1 − x 2 ) the best model for G can be found. have the unit of (J/cm ) . In Table 6.10 values of freezing
Once the relation for G has been determined the activity point and heat of fusion at the freezing point are also given.
E
coefficient model will be found. These values are needed in calculation of fugacity of solids as
For regular solutions where different components have the will be seen in the next section.
E
same intermolecular forces it is generally assumed that V = Based on the data given in Table 6.10 the following rela-
S = 0. Obviously systems containing polar compounds gen- tions are developed for estimation of liquid molar volume of
E
erally do not fall into the category of regular solutions. Hy- n-alkanes (P), n-alkylcyclohexanes (N), and n-alkylbenzenes
drocarbon mixtures may be considered as regular solutions. (A) at 25 C, V 25 [23]:
◦
The activity coefficient of component i in a binary liquid solu-
tion according to the regular solution theory can be calculated 0.15
from the Scatchard–Hildebrand relation [21, 22]: ln V 25 =−0.51589 + 2.75092M
for n-alkanes (C 1 − C 36 )
2
L
V (δ 1 − δ 2) 2 2 V 25 = 10.969 + 1.1784M
1
ln γ 1 = (6.148)
RT
(6.145) for n-alkylcyclohexanes (C 6 − C 16 )
2
L
V (δ 1 − δ 2) 2 1 ln V 25 =−96.3437 + 96.54607M 0.01
2
ln γ 2 =
RT for n-alkylbenzenes (C 6 − C 24 )
L
where V is the liquid molar volume of pure components (1
or 2) at T and P and δ are the solubility parameter of pure where V 25 is in cm /mol. These correlations can reproduce
3
components 1 or 2. 1 is the volume fraction of component data in Table 6.10 with average deviations of 0.9, 0.4, and
1 and for a binary system it is given by 0.2% for n-alkanes, n-alkylcyclohexanes, and n-alkylbenzens,
respectively. Similarly the following relations are developed
x 1 V L
◦
(6.146) 1 = 1 for estimation of solubility parameter at 25 C [23]:
L
x 1 V + x 2 V L
1 2
−0.4007
where x 1 and x 2 are mole fractions of components 1 and 2. δ = 16.22609 [1 + exp (0.65263 − 0.02318M)]
The solubility parameter for component i can be calculated for n-alkanes (C 1 − C 36 )
from the following relation [21, 22]: −5
δ = 16.7538 + 7.2535 × 10 M
U H − RT
vap 1/2 vap 1/2 (6.149) for n-alkylcyclohexanes (C 6 − C 16 )
(6.147) δ i = i = i −3 2
V i L V i L δ = 26.8557 − 0.18667M + 1.36926 × 10 M
3
− 4.3464 × 10 −6 M + 4.89667 × 10 −9 M 4
where U i vap and H i vap are the molar internal energy and
heat of vaporization of component i, respectively. The tradi- for n-alkylbenzenes (C 6 − C 24 )
3 1/2
tional unit for δ is (cal/cm ) ; however, in this chapter the
3 1/2
3 1/2
unit of (J/cm ) is used and its conversion to other units is where δ is in (J/cm ) . The conversion factor from this
given in Section 1.7.22. Solubility parameter originally pro- unit to the traditional units is given in Section 1.7.22: 1
3 1/2
3 1/2
posed by Hildebrand has exact physical meaning. Two param- (cal/cm ) = 2.0455 (J/cm ) . Values predicted from these
eters that are used to define δ are energy of vaporization and equations give average deviation of 0.2% for n-alkanes, 0.5%
--`,```,`,``````,`,````,```,,-`-`,,`,,`,`,,`---
molar volume. In Chapter 5 it was discussed that for nonpolar for n-alkylcyclohexanes, and 1.4% for n-alkylbenzenes. It
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