Page 230 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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210 CHARACTERIZATION AND PROPERTIES OF PETROLEUM FRACTIONS
TABLE 5.3—Recommended BIPs for SRK and PR EOS [19].
PR EOS 17:42 SRK EOS
Comp. N 2 CO 2 H 2 S N 2 CO 2 H 2 S
N 2 0.000 0.000 0.130 0.000 0.000 0.120
CO 2 0.000 0.000 0.135 0.000 0.000 0.135
H 2 S 0.130 0.135 0.000 0.120 0.120 0.000
C 1 0.025 0.105 0.070 0.020 0.120 0.080
C 2 0.010 0.130 0.085 0.060 0.150 0.070
C 3 0.090 0.125 0.080 0.080 0.150 0.070
iC 4 0.095 0.120 0.075 0.080 0.150 0.060
nC 4 0.090 0.115 0.075 0.800 0.150 0.060
iC 5 0.100 0.115 0.070 0.800 0.150 0.060
nC 5 0.110 0.115 0.070 0.800 0.150 0.060
C 6 0.110 0.115 0.055 0.800 0.150 0.050
0.110 0.115 0.050 0.800 0.150 0.030
C 7+
Values recommended for PR EOS by Ref. [6] are as follows: N 2 /CO 2 : −0.013; N 2 /C 1 : 0.038; C 1 /CO 2 : 0.095; N 2 /C 2 :
0.08; C 1 /C 2 : 0.021.
hydrocarbon systems, k ij = 0; however, for the key hydrocar- of Eq. (5.59) for a ternary gas mixture (N = 3) becomes
bon compounds in a mixture where they differ in size value 2 2 2
of k ij is nonzero. For example, for a reservoir fluid that con- a mix = y a 11 + y a 22 + y a 33 + 2y 1 y 2 a 12 + 2y 1 x 3 a 13 + 2y 2 y 3 a 23
3
2
1
tains a considerable amount of methane and C 7+ the BIP for (5.64)
C 1 and C 7 fractions cannot be ignored. For nonhydrocarbon–
hydrocarbon pairs k ij values are nonzero and have a signif- where a 11 = a 1 , a 22 = a 2 , and a 33 = a 3 . Interaction coefficients
icant impact on VLE calculations [20, 35]. Values of k ij for such as a 12 can be found from Eq. (5.61): a 12 = √ a 1 a 2 (1 − k 12 )
a particular pair may be determined from matching exper- where k 12 may be taken from Table 5.3 or estimated from Eq.
imental data with predicted data on a property such as va- (5.63). a 13 and a 23 can be calculated in a similar way.
por pressure. Values of k ij are specific to the particular EOS
being used. Some researchers have determined k ij for SRK
or PR equations. Values of BIP for N 2 ,CO 2 , and methane 5.6 NONCUBIC EQUATIONS OF STATE
with components in reservoir fluids from C 1 to C 6 and three
subfractions of C 7+ for PR and SRK are tabulated by Whit- The main reason for wide range application of cubic EOS is
son [19]. Values that he has recommended for use with SRK their application to both phases of liquids and vapors, math-
and PR equations are given in Table 5.3. There are some gen- ematical simplicity and convenience, as well as possibility
eral correlations to estimate BIPs for any equation [36, 37]. of calculation of their parameters through critical constants
The most commonly used correlation for estimating BIPs and acentric factor. However, these equations are mainly use-
of hydrocarbon–hydrocarbon (HC–HC) systems is given by ful for density and phase equilibrium calculations. For other
Chueh and Prausnitz [37]: thermodynamic properties such as heat capacity and en-
⎧ ⎫
B thalpy, noncubic equations such as those based on statistical

⎨ 2(V ci V c j ) 1/6 ⎬
(5.63) k ij = A 1 − 1/3 associating fluid theory (SAFT) or perturbed hard chain the-
(V ci ) 1/3 + V
⎩ c j ⎭ ory (PHCT) may be used. Some of these equations have been
particularly developed for special mixtures, polar molecules,
where V ci and V c j are critical molar volume of components hard sphere molecules, and near critical regions. Summary
3
i and j in cm /mol. Originally A = 1 and B = 3; however, in of these equations is given by Poling et al. [8]. In this sec-
practical cases B is set equal to 6 and A is adjusted to match tion three important types of noncubic EOS are presented:
saturation pressure and other variable VLE data [20, 38]. For (1) virial, (2) Carnahan–Starling, and (3) modified Benedict–
most reservoir fluids, A is within 0.2–0.25; however, as is seen Webb–Rubin. --`,```,`,``````,`,````,```,,-`-`,,`,,`,`,,`---
in Chapter 9 for a Kuwaiti oil value of A was found as 0.18.
As discussed by Poling et al. [8], Tsonopoulos recommends
the original Chueh–Prausnitz relation (A = 1 and B = 3) for 5.6.1 Virial Equation of State
nonpolar compounds. Pedersen et al. [39] proposed another
relation for calculation of BIPs for HC–HC systems. Their cor- The most widely used noncubic EOS is the virial equation or
relation is based on data obtained from North Sea reservoir its modifications. The original virial equation was proposed
fluids and it is related to molecular weights of components in 1901 by Kammerlingh–Onnes and it may be written either
i and j as k ij = 0.001M i /M j where M i > M j . Another corre- in the form of polynomial series in inverse volume (pressure
∼
lation was proposed by Whitson [40] for estimation of BIPs explicit) or pressure expanded (volume explicit) as follows:
of methane and C 7+ fraction components based on the data B C D
presented by Katz and Firoozabadi [36] for use with PR EOS. (5.65) Z = 1 + V + V 2 + V 3 + ···
His correlation is as: k 1 j = 0.14 SG j – 0.0688, where 1 refers 2
to methane and j refers to the C 7+ ( j) fraction, respectively. Z = 1 + B P + C − B 2 P 2
2
Equations (5.59)–(5.62) can be applied to either liquid or RT R T
vapor mixtures. However, for the case of vapor mixtures with D − 3BC + 2B 3 3
N components, mole fraction y i should be used. Expansion (5.66) + R T 3 P + ···
3

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