Page 244 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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224 CHARACTERIZATION AND PROPERTIES OF PETROLEUM FRACTIONS
the following form [68]:
set of equations:

B T = mX + B I sat B + P/P ce
V = V 1 − C ln
B + P sat /P ce
m = 1492.1 + 0.0734P + 2.0983 × 10 −6 P 2
1 ∂V C
5
X = B 20 − 10 /23170 κ =− V sat ∂ P = (BP ce + P)

(5.129) T
−3
log B 20 =−1.098 × 10 T + 5.2351 + 0.7133ρ o 1/3 2/3
(5.132) B =−1 − 9.070217τ + 62.45326τ
3
B I = 1.0478 × 10 + 4.704 P − 3.744 × 10 −4 P 2 4/3
− 135.1102τ + eτ
+ 2.2331 × 10 −8 P 3
C = 0.0861488 + 0.0344483ω
where B T is in bar and ρ is the liquid density at atmospheric 2
o
3
pressure in g/cm . In the above equation T is absolute tem- e = exp 4.79594 + 0.250047ω + 1.14188ω
perature in kelvin and P is the pressure in bar. The average
τ = 1 − T/T c
error from this method is about 1.7% except near the critical
point where error increases to 5% [59]. This method is not where V sat is the saturation molar volume and P sat is the sat-
o
recommended for liquids at T r > 0.95. In cases that ρ is not uration pressure at T. V is liquid molar volume at T and P
available it may be estimated from Eq. (5.121) or (5.127). Al- and κ is the isothermal bulk compressibility defined in the
though this method is recommended for petroleum fractions above equation (also see Eq. 6.24). T c is the critical temper-
but it gives reasonable results for pure hydrocarbons (≥C 5 ) ature and ω is the acentric factor. P ce is equivalent critical
as well. pressure, which for all alcohols was near the mean value of
For light and medium hydrocarbons as well as light 27.0 bar. This value for diols is about 8.4 bar. For other series
petroleum fractions the Tait-COSTALD (corresponding state of compounds P ce would be different. Garvin found that use of
liquid density) correlation originally proposed by Hankinson P ce significantly improves prediction of V and κ for alcohols.
and Thomson may be used for the effect of pressure on liquid For example, for estimation of κ of methanol at 1000 bar and
density [66]: −7 −1
100 C, Eq. (5.132) predicts κ value of 7.1 × 10 bar , which
◦
−1 gives an error of 4.7% versus experimental value of 6.8 × 10 −7
B + P −1

(5.130) ρ P = ρ P o 1 − C ln bar , while using P c the error increases to 36.6%. However,
B + P o one should note that the numerical coefficients for B, C, and e
in Eq. (5.132) may vary for other types of polar liquids such
where ρ P is density at pressure P and ρ P o is liquid density at
o as coal liquids.
reference pressure of P at which density is known. When ρ P o Another correlation for calculation of effect of pressure on
is calculated from the Rackett equation, P = P sat where P sat
o
is the saturation (vapor) pressure, which may be estimated liquid density was proposed by Chueh and Prausnitz [69] and
from methods of Chapter 7. Parameter C is a dimensionless is based on the estimation of isothermal compressibility:
constant and B is a parameter that has the same unit as pres- ρ P = ρ P o[1 + 9β(P − P )] 1/9
o
sure. These constants can be calculated from the following
equations: β = α 1 − 0.89 ω exp 6.9547 − 76.2853T r + 191.306T r 2

√
B 1/3 2/3 3 4
=−1 − 9.0702 (1 − T r) + 62.45326 (1 − T r) − 203.5472T + 82.7631T r
r
P c
− 135.1102 (1 − T r) + e (1 − T r) 4/3 V c Z c
(5.131) α = =
RT c P c
2
e = exp 4.79594 + 0.250047ω + 1.14188ω
(5.133)
C = 0.0861488 + 0.0344483ω
The parameters are defined the same as were defined in Eqs.
(5.131) and (5.132). V c is the molar critical volume and the
where T r is the reduced temperature and ω is the acentric
factor. All the above relations are in dimensionless forms. units of P, V c , R, and T c must be consistent in a way that
Obviously Eq. (5.130) gives very accurate result when P is PV c /RT c becomes dimensionless. This equation is applicable
close to P ; however, it should not be used at T r > 0.95. The for T r ranging from 0.4 to 0.98 and accuracy of Eq. (5.134) is
o
COSTALD correlation has been recommended for industrial just marginally less accurate than the COSTALD correlation
applications [59, 67]. However, in the API-TDB [59] it is rec- [67].
ommended that special values of acentric factor obtained
from vapor pressure data should be used for ω. These val- Example 5.8—Propane has vapor pressure of 9.974 bar at 300
L
ues for some hydrocarbons are given by the API-TDB [59]. K. Saturated liquid and vapor volumes are V = 90.077 and
V
3
Application of these methods is demonstrated in Example V = 2036.5cm /mol [Ref. 8, p. 4.24]. Calculate saturated liq-
5.8. The most recent modification of the Thomson method uid molar volume using (a) Rackett equation, (b) Eqs. (5.127)–
for polar and associating fluids was proposed by Garvin in (5.129), (c) Eqs. (5.127) and (5.130), and (d) Eq. (5.133).
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