Page 358 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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338 CHARACTERIZATION AND PROPERTIES OF PETROLEUM FRACTIONS
μ = A(μ a ) , where A and B are functions of GLR (see Prob-
B
lem 8.4). GLR were calculated from the following relation: The term (V–V 0 ) represents the free space between molecules.
As temperature increases V also increases and μ decreases.
This theory is applicable to liquids at low pressures. In Chap-
379x A
(8.24) GLR = ter 2 it was shown that parameter I (defined by Eq. 2.36) is
M B
(1 − x A ) × proportional with fraction of liquid occupied by molecules.
62.4SG B Therefore parameter I is proportional to V 0 /V and thus
where x A is the mole fraction of dissolved gas in liquid, M B
is molecular weight of liquid, and SG B is the specific grav- (8.27) μ −1 = C I −1 − 1

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ity of liquid. In this relation GLR is calculated as stm of
gas/stm of liquid (1 m /m = 1 scf/st · ft = 5.615 scf/bbl). where μ and I are evaluated at given temperature. Methods of
3
3
3
3
Units of GLR are discussed in Section 1.7.23. Prediction of calculation of I were discussed in Chapter 2 (see Eqs. (2.36)
viscosity of crude oils (gas free dead oils at 1 atm) is quite dif- and (2.118)). On this basis, one can see that 1/μ varies lin-
ficult due to complexity of mixtures. However, there are many early with 1/I for any substance. This relation has been also
empirical correlations developed for calculation of crude oils confirmed with experimental data [23]. Similar correlations
[15, 16]. For example the Glaso’s correlation for viscosity of for thermal conductivity and diffusivity were developed and
crude oils is given as the coefficients were related to hydrocarbon properties such
10
μ od = (3.141 × 10 ) × [(1.8T − 460) −3.444 ] × [log (API)] n as molecular weight [23, 24]. Equation (8.27) is applicable
10

n = 10.313 log (1.8T − 460) − 36.447 only to nonpolar and hydrocarbon liquid systems in which the
intermolecular forces can be determined by London forces.
10
(8.25) Other developments in the calculation of liquid viscosity are
reported by Chung et al. (generalized correlations for polar
where μ od is the viscosity of dead oil (gas free at 1 atm.), T is
temperature in kelvin, and API is the oil gravity. This equation and nonpolar compounds) [25] and Quinones-Cisneros et al.
should be used for crude oils with API gravity in the range of (pure hydrocarbons and their mixtures) [26].
20–48 and in the temperature range of 283–422 K (50–300 F).
◦
More advanced and accurate methods of calculation of viscos- Example 8.1—Consider a liquid mixture of 74.2 mol%
ity of crude oils is based on splitting the oil into several pseu- acetone and 25.8 mol% carbon tetrachloride (CCl 4 ) at 298.2 K
docomponents and to use methods discussed in Chapter 4 and 1 atm. Estimate its viscosity assuming the only informa-
for calculation of the mixture properties. Accurate prediction tion known for this system are T c , P c , V c , ω, M, and Z RA of each
of viscosities of heavy crude oils is a difficult task and most compound. Compare estimated value with the experimental
correlations result in large errors and errors of 50–100% are value of 0.395 mPa · s (cp) [10].
quite common in such predictions.
As seen from Eqs. (8.11) and (8.25), viscosity of liquids
and oils is mainly related to density. In general, heavier oils Solution—CCl 4 and acetone are nonhydrocarbons whose
(lower API gravity) exhibit higher viscosity. Pure hydrocar- critical properties are not given in Table 2.1 and for this rea-
bon paraffins have viscosity of about 0.35 cp (0.5 cSt.), naph- son they are obtained from other sources such as DIPPR [10]
thenes about 0.6 cp, n-alkylbenzenes (aromatics) about 0.8 cp or any chemical engineering thermodynamics text as [18,27]:
3
(1.1 cSt.), gasoline about 0.6 cp, kerosene about 2 cp, and for acetone, T c = 508.2K, P c = 47.01 bar, V c = 209 cm /mol,
residual oils’ viscosity is in the range of 10–100 000 cp [17]. ω = 0.3065, M = 58.08 g/mol, and Z RA = 0.2477; for CCl 4 ,
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The methods of measurement of viscosity of oils are given in T c = 556.4K, P c = 45.6 bar, V c = 276 cm /mol, ω = 0.1926,
ASTM D 445 and D 446. A graphical method for calculation M = 153.82 g/mol, and Z RA = 0.2722 [18]. Using the Kay’s
of viscosity of the blend is given by ASTM D 341. For light mixing rule (Eq. 7.1) with x 1 = 0.742 and x 2 = 0.258: T c =
3
oils capillary viscometers are suitable for measuring liquid 520.6K, P c = 46.6 bar, V c = 226.3cm /mol, ω = 0.2274, M =
viscosity in which viscosity is proportional to the pressure 82.8, and Z RA = 0.254. Mixture liquid density at 298 K is cal-
difference in two tubes. culated from Racket equation (Eq. 5.121): V = 80.5cm /mol
3
s
Most recently Riazi et al. [21] developed a relation for es- (ρ 25 = 1.0286 g/cm ). This gives ρ r = V c /V = 226.3/80.5 =
3
timation of viscosity of liquid petroleum fractions by using 2.8112. For calculation of residual viscosity a generalized cor-
refractive index at 20 C as one of the input parameters in addi- relation in terms of ρ r may be used. Although Eq. (8.12) is pro-
◦
tion to molecular weight and boiling point (see Problem 8.3). posed for hydrocarbons and nonpolar fluids, for liquids ρ r is
Another development on the prediction of viscosity and other quite high and the equation can be used up to ρ r of 3.0. From
transport properties for liquid hydrocarbon systems was to Eq. (8.5), ξ = 0.02428 and T r = T/T c = 0.5724 < 1.5. From
use refractive index to estimate a transport property at the Eq. (8.6), μ o = 0.00829 cp. From Eq. (8.12), μ = 0.374 cp,
same temperature in which relative index is available. The- which in comparison with experimental value of 0.395 cp
ory of Hildebrand [22] suggests that fluidity (1/μ) of a liquid gives an error of only −5.3%. This is a good prediction consid-
is proportional to the free space between the molecules. ering the fact that the mixture contains a highly polar com-
1 V − V 0 pound (acetone) and predicted density was used instead of
(8.26) = E a measured value. If actual values of ρ 25 [18] for pure com-
--`,```,`,``````,`,````,```,,-`-`,,`,,`,`,,`---
μ V 0
pounds were used (ρ 25 = 0.784 for acetone and ρ 25 = 1.584
3
where E is a constant, V is the liquid volume (i.e., molar), and g/cm for CCl 4 ) and density is calculated from Eq. (7.4) we get
3
V 0 is the value of V at zero fluidity (μ → 0). Parameters E and ρ 25 = 1.03446 g/cm (ρ r = 2.828), which predicts μ mix = 0.392
V 0 may be determined from regression of experimental data. cp (error of only −0.8%).

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