Page 245 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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Solution—(a) Obviously the most accurate method to esti-
Generally constants of cubic equations are determined
L
based on data for hydrocarbons up to C 8 or C 9 .Asanex-
mate V is through Eq. (5.121). From Table 2.1, M = 44.1, 5. PVT RELATIONS AND EQUATIONS OF STATE 225
◦ ample, the LK generalized correlations is based on the data
SG = 0.507, T c = 96.7 C (369.83 K), P c 42.48 bar, and ω =
0.1523. From Table 5.12, Z RA = 0.2763. T r = 0.811 so from for the reference fluid of n-C 8 . The parameter that indicates
Eq. (5.121), V sat = 89.961 cm /mol (−0.1% error). (b) Use of complexity of a compound is acentric factor. In SRK and PR
3
Eqs. (5.127)–(5.129) is not suitable for this case that Rack- EOS parameter a is related to ω in a polynomial form of at
ett equation can be directly applied. However, to show the least second order (see f ω in Table 5.1). This indicates that
application of method V sat is calculated to see their perfor- extrapolation of such equations for compounds having acen-
o
mance. From Eq. (5.127) and use of SG = 0.507 gives ρ = tric factors greater than those used in development of EOS
3
0.491 g/cm . From Eq. (5.129), m = 1492.832, B 20 = 180250.6, parameters is not accurate. And it is for this reason that most
X = 3.46356, B I = 1094.68, and B T = 6265.188 bar. Using Eq. cubic equations such as SRK and PR equations break down
(5.128), 0.491/ρ = 1 − 9.974/6265.188. This equation gives when they are applied for calculation of liquid densities for
3
density at T (300 K) and P (9.974 bar) as ρ = 0.492 g/cm . C 10 and heavier hydrocarbons. For this reason Riazi and Man-
3
V sat = M/ρ = 44.1/0.492 = 89.69 cm /mol (error of −0.4%). soori [70] attempted to improve capability of cubic equations
(c) Use of Eqs. (5.127) and (5.130) is not a suitable method for liquid density prediction, especially for heavy hydrocar-
for density of propane, but to show its performance, satu- bons.
rated liquid volume is calculated in a way similar to part Most modifications on cubic equations is on parameter a
(b): From Eq. (5.131), B = 161.5154 bar and C = 0.091395. and its functionality with temperature and ω. However, a pa-
3
o
For Eq. (5.130) we have ρ P o = 0.491 g/cm , P = 1.01325 bar, rameter that is inherent to volume is the co-volume parameter
3
P = 9.974 bar, and calculated density is ρ P = 0.4934 g/cm . b. RK EOS presented by Eq. (5.38) is the simplest and most
3
Calculated V sat is 89.4 cm /mol, which gives a deviation of widely used cubic equation that predicts reasonably well for
3
−0.8% from experimental value of 90.077 cm /mol. (d) Us- prediction of density of gases. In fact as shown in Table 5.13
ing the Chueh–Prausnitz correlation (Eq. 5.133) we have for simple fluids such as oxygen or methane (with small ω)
3
Z c = 0.276, α = 0.006497, β = 0.000381, ρ P = 0.49266 g/cm , RK EOS works better than both SRK and PR regarding liquid
3
sat
and V calc = 89.5149 cm /mol, which gives an error of −0.62% densities.
from the actual value. For liquid systems in which the free space between
molecules reduces, the role of parameter b becomes more
important than that of parameter a. For low-pressure gases,
5.9 REFRACTIVE INDEX BASED EQUATION however, the role of parameter b becomes less important than
OF STATE a because the spacing between molecules increases and as
a result the attraction energy prevails. Molar refraction was
From the various PVT relations and EOS discussed in this defined by Eq. (2.34) as
chapter, cubic equations are the most convenient equations
2
that can be used for volumetric and phase equilibrium cal- (5.134) M n − 1
culations. The main deficiency of cubic equations is their R m = VI = d 20 n + 2
2
inability to predict liquid density accurately. Use of volume
translation improves accuracy of SRK and PR equations for where R m is the molar refraction and V is the molar volume
liquid density but a fourth parameter specific of each equa- both in cm /mol. R m is nearly independent of temperature
3
tion is required. The shift parameter is not known for heavy but is normally calculated from density and refractive index
compounds and petroleum mixtures. For this reason some at 20 C(d 20 and n 20 ). R m represents the actual molar volume
◦
specific equations for liquid density calculations are used. As of molecules and since b is also proportional to molar volume
an example Alani–Kennedy EOS is specifically developed for of molecules (excluding the free space); therefore, one can
calculation of liquid density of oils and reservoir fluids and conclude that parameter b must be proportional to R m .In
is used by some reservoir engineers [19, 21]. The equation fact the polarizability is related to R m in the following form:
is in van der Waals cubic EOS form but it requires four nu-
merical constants for each pure compound, which are given 3
from C 1 to C 10 . For the C 7+ fractions the constants should be (5.135) α = 4π N A R m − μ(T)
estimated from M 7+ and SG 7+ . The method performs well for
light reservoir fluids and gas condensate samples. However, where N A is the Avogadro’s number and μ(T) is the dipole
as discussed in Chapter 4, for oils with significant amount of moment, which for light hydrocarbons is zero [7]. Values of
heavy hydrocarbons, which requires splitting of C 7+ fraction, R m calculated from Eq. (5.134) are reported by Riazi et al.
the method cannot be applied to C 7+ subfractions. In addition [70, 71] for a number of hydrocarbons and are given in Table
the method is not applicable to undefined petroleum fractions 5.14. Since the original RK EOS is satisfactory for methane we
with a limited boiling range. choose this compound as the reference substance. Parameter
TABLE 5.13—Evaluation of RK, SRK, and PR EOS for prediction of density of simple fluids.
%AAD
Compound No. of data points Temperature range, K Pressure range, bar RK SRK PR Data source
Methane 135 90–500 0.7–700 0.88 1.0 4.5 Goodwin [72]
Oxygen 120 80–1000 1–500 1.1 1.4 4.0 TRC [73]

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