Page 304 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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284 CHARACTERIZATION AND PROPERTIES OF PETROLEUM FRACTIONS
TABLE 6.13—Values of b and T B for use in
computing K i values from Eq. (6.202) [Ref. 41]. 20:46 6.9 USE OF VELOCITY OF SOUND IN
PREDICTION OF FLUID PROPERTIES
Compound b,K T B ,K
N 2 261.1 60.6 One application of fundamental relations discussed in this
CO 2 362.2 107.8
H 2 S 631.1 183.9 chapter is to develop an equation of state based on the ve-
C 1 166.7 52.2 locity of sound. The importance of PVT relations and equa-
C 2 636.1 168.3 tions of state in estimation of physical and thermodynamic
C 3 999.4 231.1 properties and phase equilibrium were shown in Chapter 5
i-C 4 1131.7 261.7
n-C 4 1196.1 272.8 as well as in this chapter. Cubic equations of state and gen-
i-C 5 1315.6 301.1 eralized corresponding states correlations are powerful tools
n-C 5 1377.8 309.4 for predicting thermodynamic properties and phase equilib-
i-C 6 (all) 1497.8 335.0 ria calculations. In general most of these correlations pro-
n-C 6 1544.4 342.2 vide reliable data if accurate input parameters are used (see
n-C 7 1704.4 371.7
n-C 8 1852.8 398.9 Figs. 1.4 and 1.5). Accuracy of thermodynamic PVT mod-
n-C 9 1994.4 423.9 els largely depends on the accuracy of their input parame-
n-C 10 2126.7 447.2 ters (T c , P c , and ω) particularly for mixtures where no mea-
C 6 (lumped) 1521.1 338.9 sured data are available on the pseudocritical properties and
Use Eq. (6.203)
C 7+
acentric factor. While values of these parameters are avail-
able for pure and light hydrocarbons or they may be esti-
where H 2 vap is the molar heat of vaporization for the solvent mated accurately for light petroleum fractions (Chapter 2),
and T b2 is the increase in boiling point when mole fraction for heavy fractions and heavy compounds found in reservoir
of solute in the solution is x 1 . Methods of estimation of H 2 vap fluids such data are not available. Various methods of predict-
are discussed in the next chapter. ing these parameters give significantly different values espe-
cially for high-molecular-weight compounds (see Figs. 2.18
and 2.20).
Example 6.13—Calculate the freezing point depression of One way to tackle this difficulty is to use a measured prop-
benzene when 5 g of benzoic acid is dissolved in 100 g of erty such as density or vapor pressure to calculate critical
benzene at 20 C. properties. It is impractical to do this for reservoir fluids un-
◦
der reservoir conditions, as it requires sampling and labora-
Solution—For this system the solute is benzoic acid (compo- tory measurements. Since any thermodynamic property can
nent 1) and the solvent is benzene (component 2). From Ta- be related to PVT relations, if accurately measured values of a
ble 6.10 for benzoic acid, M 1 = 122.1 and T M1 = 395.5K,and thermodynamic property exist, they can be used to extract pa-
f
for benzene, M 2 = 78.1, T M2 = 278.6 K, and H /RT M2 = 4.26. rameters in a PVT relation. In this way there is no need to use
2
For 5 g benzoic acid and 100 g benzene from a reverse form various mixing rules or predictive methods for calculation of
of Eq. (1.15) we get x 1 = 0.031. To calculate freezing point T c , P c , and ω of mixtures and EOS parameters can be directly
depression we can use Eq. (6.213): calculated from a set of thermodynamic data. One thermody-
namic property that can be used to estimate EOS parameter is
x 1 RT 2 velocity of sound that may be measured directly in a reservoir
∼ M2
T M2 = f fluid under reservoir conditions without sampling. Such data
H
2 can be used to obtain an accurate PVT relation for the reser-
voir fluids. For this reason Riazi and Mansoori [44] used ther-
f
where x 1 = 0.031, T M2 = 278.6 K, and RT M2 / H = 1/4.26 =
2 modynamic relations to develop an equation of state based
0.2347. Thus T M2 = 0.031 × 278.6 × 0.2347 = 2 K. A more on velocity of sound and then sonic velocity data have been
accurate result can be obtained by use of Eq. (6.211) for non- used to obtain thermodynamic properties [8, 44, 45]. Colgate
ideal systems as
et al. [45, 46] used velocity of sound data to determine critical
properties of substances. Most recently, Ball et al. [48] have
f
1 H f T M2 H T M2
ln =− 2 1 − ≈ 2 2 constructed an ultrasonic apparatus for measuring the speed
γ 2 x 2 RT M2 T RT M2 of sound in liquids and compressed gases. They also reported
speed of sound data for an oil sample up to pressure of 700
For this system since x 2 is near unity, γ 2 = 1.0 and same value bars (see Fig. 6.34) and discussed prospects for use of velocity
for T M2 is obtained; however, for cases that x 2 is substantially of sound in determining bubble point, density, and viscosity
lower than unity this equation gives different result. of oils.
TABLE 6.14—Recommended methods for VLE calculations.
Pressure Mixtures of similar substances Mixtures of dissimilar substances
<3.45 bar (50 psia) Raoult’s law (Eq. 6.180) Modified Raoult’s law (Eq. 6.181)
<13.8 bar (200 psia) Lewis rule (Eq. 6.198) Activity coefficients (Eq. 6.179)
P < 5–10 bar, Henry’s law (Eq. 6.184) for dilute liquid systems (x i < ∼0.03)
Any P, 255 < T < 645 K Chao–Seader (Eq. 6.200) for nonpolar systems and outside critical region
> 13.8 bar (200 psia) Eq. (6.197) with SRK or PR EOS using appropriate BIPs
P < 69 bar (1000 psia) Standing correlation (Eq. 6.202) for natural gases, gas condensate reservoir
fluids and light hydrocarbon systems with little C 7+

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