Page 270 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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250 CHARACTERIZATION AND PROPERTIES OF PETROLEUM FRACTIONS

V 1 Example 6.4—For the mixture of Example 6.3 calculate the
heat of mixing at 25 C.
◦
Molar Volume, V V 2 Solution—Heat of mixing is calculated from Eq. (6.85) using
real
values of ¯ H 1 and ¯ H 2 calculated in Example 6.3 as −292.8 and
−294.2 kJ/kg, respectively. Pure components H 1 and H 2 are
ideal V 1 calculated from the correlation given for H in Example 6.3 at
V 2 x 1 = 1 (for H 1 ) and x 1 = 0 (for H 2 )as H 1 =−5.7 kg/kJ and H 2 =
x 1 123.7 kJ/kg. From Eq. (6.85), H mix = (0.667) × [(−292.8) −

0 1 (−5.7)] + (1 − 0.667) × [(−294.2) − (123.7)] =−330.7 kJ/kg.
Mole Fraction, x 1
This means that to make 1 kg of solution of 66.7 wt% sul-
(a) Systems with increase in volume due to mixing furic acid at 25 C, 330.7 kJ heat will be released.
◦
For the ideal solutions, H, V, G, and S of the mixture may
V 1 be calculated from pure component properties through the
following relations [1, 21]:
ideal
V 2
Molar Volume V (6.89) H id = x i H i
id

i
(6.90)
V
=
x i V i
i
real V 1 (6.91) G id = x i G i + RT x i ln x i
V 2 i i
x 1
(6.92) S id = x i S i − R x i ln x i
0 Mole Fraction, x 1 1 i i

id
id
ig
ig
(b) Systems with decrease in volume due to mixing where H , V , G , and S can be either molar or specific
enthalpy, volume, Gibbs energy, and entropy of mixture. In
FIG. 6.6—Variation of molar volume of a binary mixture with case of specific property, x i is weight fraction. For example, if
composition.
V is specific volume (= 1/ρ), Eq. (6.90) can be written in the
following form for density:
the following relation [17]:
1 x wi
¯
¯

V t = n i,after V i (T, P, n i,after ) − n i,before V i (T, P, n i,before ) (6.93) =
mixing ρ ρ i
i i i
(6.87) where x wi is the weight fraction of i and ρ i is the density of
where n i,before is the moles of i before mixing and n i,after rep- pure i. This equation was previously introduced in Chapter 3
resents moles of i in the solution after the mixing. Obviously (Eq. 3.46). Although all hydrocarbon mixtures do not really
since the mixture composition before and after the mixing are behave like ideal solutions, mixtures that do not contain non-
not the same, ¯ V i for i in the solution before the mixing and its hydrocarbons or very heavy hydrocarbons, may be assumed
value for i in the solution after the mixing are not the same. as ideal solutions. For simplicity, application of Eqs. (6.89)
The same equation may be applied to enthalpy by replacing and (6.90) is extended to many thermodynamic properties as
V with H to calculate heat of mixing when two solutions are it was shown in Chapters 3 and 4. Mixture heat capacity, for
mixed at constant T and P. Partial molar volume and enthalpy example, is calculated similar to enthalpy as:
may be calculated from their definition, Eq. (6.78) through an (6.94)
EOS. For example in deriving the relation for ¯ V i , derivative C P = x i C Pi
i
[∂(nV)/∂n i ] T,P,nj =i should be determined from the EOS. For
the PR EOS the partial molar volume is given as [20] where x i is either mole or mass fraction depending on the unit
of C P .If C P is the specific heat (i.e., J/g · C), weight fraction
◦
(6.88) ¯ V i = X 1 + X 2 should be used for x i . Obviously the main application of these
X 3 + X 4 equations is when values of properties of pure components
where are available. For cases that these properties are predicted
from equations of state or other correlations, the mixing rules
2
X 1 = (RT + b i P) × V + 2bV − b 2 are usually applied to critical properties and the input param-

X 2 = 2b i RT − 2 x j a ij − 2b i P (V − b) × (V − b) + b i a eters of an EOS rather than to calculated values of a thermo-
j
2
X 3 = P V + 2bV − b 2 + 2P (V − b)(V + b) dynamic property in order to reduce the time and complexity

X 4 =−2RT (V + b) + a of calculations. For hydrocarbon mixtures that contain very
light and very heavy hydrocarbons the assumption of ideal so-
where V is the mixture molar volume calculated from PR lution and application of Eqs. (6.89)–(6.93) will not give accu-
EOS. For more accurate calculation of ¯ V i , corrected V rate results. For such mixtures some correction terms to con-
through use of volume translation concept (Eq. 5.50) may sider the effects of nonideality of the system and the change in --`,```,`,``````,`,````,```,,-`-`,,`,,`,`,,`---
be used. Similar relation for ¯ H i can be obtained (see Prob- molecular behavior in presence of unlike molecules should be
lem 6.5). added to the RHS of such equations. The following empirical
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