Page 337 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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7. APPLICATIONS: ESTIMATION OF THERMOPHYSICAL PROPERTIES 317
relation based on ideal gas heat capacity, C .
Temperature, F
P ig
32 212 392 572
T 2
800 350 ig
ig
(7.33) H = C (T)dT
Jet Fuel at 1.4 bar P
(20 psia)
Gas Oil Liquid at 2.8 280 T 1
600 bar (40 psia)
where T 1 and T 2 are the same temperature points that H ig
Gas Oil Liquid at 210 must be calculated. For pure compounds C ig can be calcu-
96.5 bar (1400 psia)
Enthalpy, kJ/kg 400 140 Enthalpy, Btu/lb lated from Eq. (6.66) and combining with the above equation
P
ig
H can be calculated. For petroleum fractions, Eq. (6.72)
ig
is recommended for calculation of C
and when it is com-
P
200 bined with Eq. (7.33) the following equation is obtained for
ig
70 calculation of H from T 1 to T 2 :

3
2
H = M A 1 T − T 2 A 2 T − T 3
ig
0 0 A 0 (T 2 − T 1) + 2 2 1 + 3 2 1
0 100 200 300
B 1 2 2 B 2 3 3
2
2
Temperature, C − C B 0 (T 2 − T 1) + 2 T − T 1 + 3 T − T 1
FIG. 7.12—Enthalpy of two petroleum fractions. (7.34)
◦
Reference state: H = 0 for saturated liquid at 23.9 C
ig
◦
◦
◦
(75 F) and 1.38 bar for jet fuel, and 23.9 C (75 F) where T 1 and T 2 are in kelvin, H is in J/mol, M is the molec-
and 2.76 bar (40 psia) for gas oil. Specifications: ular weight, coefficients A, B, and C are given in Eq. (6.72)
◦
Jet fuel, M = 144, T b = 160.5 C, SG = 0.804; gas oil, in terms of Watson K W and ω. This equation should not be
M = 214, T b = 279.4 C, SG = 0.848. Gas oil is in liq- applied to light hydrocarbons (N C < 5) as stated in the appli-
◦
uid state for entire temperature range. Jet fuel has cation of Eq. (6.72). H or C ig of a petroleum fraction may
ig
P
◦
bubble point temperature of 166.8 C and dew point also be calculated from the pseudocompound approach dis-
temperature of 183.1 C at 1.4 bar (20 psia). Data cussed in Chapter 3 (Eq. 3.39). In this way H ig or C ig must
◦
source Ref. [23]. P
be calculated from Eqs. (6.68) or (6.66) for three pseudocom-
pounds from groups of n-alkane, n-alkylcyclopentane, and n-
alkylbenzene having boiling points the same as that of the
heavier than jet fuel and its enthalpy as liquid is just slightly fraction. Then H is calculated from the following equation:
ig
less than enthalpy of liquid jet fuel. However, there is a sharp
ig
ig
ig
increase in the enthalpy of jet fuel during vaporization. Pres- (7.35) H = x P H + x N H + x A H A ig
P
N
sure has little effect on liquid enthalpy of gas oil.
As it was discussed in Chapter 6, to calculate H one should where x P , x N , and x A refer to the fractions of paraffins (P),
first calculate enthalpy departure or the residual enthalpy naphthenes (N), and aromatics (A) in the mixture, which is
ig
R
from ideal gas state shown by H = H − H . General meth- known from PNA composition or may be determined from
ig
R
R
ods for calculation of H were presented in Section 6.2. H is methods given in Section 3.5. C of a petroleum fraction may
P
related to PVT relation through Eqs. (6.33) or (6.38). For gases be calculated from the same equation but Eq. (6.66) is used
ig
to calculate C of the P, N, and A compounds having boiling
that follow truncated virial equation of state (T r > 0.686 + P
R
0.439P r or V r > 2.0), Eq. (6.63) can be used to calculate H . points the same as that of the fraction.
R
Calculation of H from cubic equations of state was shown in A summary of the calculation procedure for H from an
Table 6.1. However, the most accurate method of calculation initial state at T 1 and P 1 (state 1) to a final state at T 2 and P 2
R
of H is through generalized correlation of Lee–Kesler given (state 6), for a general case that the initial state is a subcooled
R
by Eq. (6.56) in the form of dimensionless group H /RT c . (compressed) liquid and the final state is a superheated vapor,
Then H may be calculated from the following relation: is shown in Fig. 7.13. The technique involves step-by-step cal-
culation of H in a way that in each step the calculation pro-
cedure is available. The subcooled liquid is transferred to a
ig
RT c H − H ig sat sat
(7.32) H = + H saturated liquid at T 1 and P 1 where P 1 is the vapor pres-
M RT c
sure of liquid at temperature T 1 . For this step (1 to 2), H 1
represents the change in enthalpy of liquid phase at constant
where both H and H ig are in kJ/kg, T c in kelvin, R = 8.314 temperature of T 1 from pressure P 1 to pressure P 1 sat . Meth-
J/mol · K, and M is the molecular weight in g/mol. The ideal ods of estimation of P 1 sat are discussed in Section 7.3. In most
ig
gas enthalpy H is a function of only temperature and must be cases, the difference between P 1 and P 1 sat is not significant
calculated at the same temperature at which H is to be calcu- and the effect of pressure on liquid enthalpy can be neglected
ig
lated. For pure hydrocarbons H may be calculated through without serious error. This means that H 1 = 0. However, for
∼
Eq. (6.68). In this equation the constant A H depends on the cases that this difference is large it may be calculated through
choice of reference state and in calculation of H it will be a cubic EOS or generalized correlation of Lee–Kesler as
eliminated. If the reference state is known, H can be deter- discussed in Chapter 6. However, a more convenient approach
mined from H = 0, at the reference state of T and P.Asitis is to calculate T 1 sat at pressure P 1 , where T 1 sat is the saturation
ig
seen shortly, it is the H that must be calculated in calcu- temperature corresponding to pressure P 1 and it may be cal-
lation of H. This term can be calculated from the following culated from vapor pressure correlations presented in Section
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