Page 355 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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8. APPLICATIONS: ESTIMATION OF TRANSPORT PROPERTIES 335
This equation is, in fact, a modification of Eq. (8.11) and
was originally developed for nonpolar gases in the range of nature. An approximate theory for liquid transport properties
is the Eyring rate theory [1, 4]. Effect of pressure on the liq-
0.1 <ρ r < 3. μ o is the viscosity at low pressure and at the uid viscosity is less than its effect on viscosity of gases. At low
same temperature at which μ is to be calculated. μ o may be and moderate pressure, liquid viscosity may be considered as
calculated from Eqs. (8.6)–(8.8). However, this equation is a function of temperature only. Viscosity of liquids decreases
also used by reservoir engineers for the calculation of the vis- with increase in temperature. According to the Eyring rate
cosity of reservoir fluids under reservoir conditions [9, 12]. model the following relation can be derived on a semitheo-
Later Stiel and Thodos [13] proposed similar correlations for retical basis:
the residual viscosity of polar gases: N A h 3.8T b
−4 1.111
(μ − μ o) ξ = 1.656 × 10 ρ r for ρ r ≤ 0.1 (8.16) μ = V exp T
(μ − μ o) ξ = 6.07 × 10 −6 × (9.045ρ r + 0.63) 1.739
where μ is the liquid viscosity in posie at temperature T, N A is
(8.13) for 0.1 ≤ ρ r ≤ 0.9 the Avogadro number (6.023 × 10 23 gmol ), h is the Planck’s
−1
2
4

log 10 4 − log 10 (μ − μ o) × 10 ξ
= 0.6439 − 0.1005ρ r constant (6.624 × 10 −27 g · cm /s), V is the molar volume at
3
temperature T in cm /mol, and T b is the normal boiling point.
for 0.9 ≤ ρ r ≤ 2.2
Both T b and T are in kelvin. Equation (8.16) suggests that
These equations are mainly recommended for calculation of ln μ versus 1/T is linear, which is very similar to the Clasius–
viscosity of dense polar and nonhydrocarbon gases. At higher Clapeyron equation (Eq. 7.27) for vapor pressure. More ac-
reduced densities accuracy of Eqs. (8.11)–(8.13) reduces. curate correlations for temperature dependency of liquid vis-
For undefined gas mixtures with known molecular weight cosities can be obtained based on a more accurate relation
M, the following relation can be used to estimate viscosity at for vapor pressure. In the API-TDB [5] liquid viscosity of pure
temperature T [5]: compounds is correlated according to the following relation:
g √ −5 √
μ =−0.0092696 + T 0.001383 − 5.9712 × 10 M (8.17) μ = 1000 exp A + B/T + C ln T + DT E
o
(8.14) + 1.1249 × 10 −5 M
where T is in kelvin and μ is in cp. Coefficients A–E for a
g
where T is in kelvin and μ o is the viscosity of gas at low pres- number of compounds are given in Table 8.2 [5]. Liquid vis-
sure in cp. Reliability of this equation is about 6% [5]. There cosity of some n-alkanes versus temperature calculated from
are a number of empirical correlations for calculation of vis- Eq. (8.17) is shown in Fig. 8.2. Equation (8.17) has uncer-
cosity of natural gases at any T and P; one widely used cor- tainty of better than ±5% over the entire temperature ranges
relation was proposed by Lee et al. [14]: given in Table 8.2. In most cases the errors are less than 2%
as shown in the API-TDB [5].
−4
g
C

μ = 10 A exp B × ρ
For defined liquid mixtures the following mixing rules are

A = (12.6 + 0.021M) T 1.5
/ (116 + 10.6M + T) recommended in the API-TDB and DIPPR manuals [5, 10]:
(8.15)
548
B = 3.45 + 0.01M + 3
T μ m = N x i μ 1/3 for liquid hydrocarbons
C = 2.4 − 0.2B (8.18) i=1 i
where μ is the viscosity of natural gas in cp, M is the gas ln μ m = N x i ln μ i for liquid nonhydrocarbons
g
molecular weight, T is absolute temperature in kelvin, and ρ i=1
is the gas density in g/cm at the same T and P that μ should
3
g
be calculated. This equation may be used up to 550 bar and where μ m is the mixture viscosity in cp and x i is the mole
in the temperature range of 300–450 K. For cases where M is fraction of component i with viscosity μ i . There are some
not known, it may be calculated from specific gravity of the other mixing rules that are available in the literature for liquid
gas as discussed in Chapter 3 (M = 29 SG g ). For sour natural viscosity of mixtures [18].
gases, correlations in terms of H 2 S content of natural gas are For liquid petroleum fractions (undefined mixtures), usu-
available in handbooks of reservoir engineering [15, 16]. ally kinematic viscosity ν is either available from experimen-
tal measurements or can be estimated from Eqs. (2.128)–
(2.130), at low pressures and temperatures. The following
8.1.2 Viscosity of Liquids equation developed by Singh may also be used to estimate
ν at any T as recommended in the API-TDB [5]:
Methods for the prediction of the viscosity of liquids are less
accurate than the methods for gases, especially for the estima- 311 B
tion of viscosity of undefined petroleum fractions and crude log (ν T ) = A − 0.8696
10
oils. Errors of 20–50% or even 100% in prediction of liquid T
viscosity are not unusual. Crude oil viscosity at room temper- (8.19) A = log (ν 38(100)) + 0.8696
10
ature varies from less than 10 cp (light oils) to many thou- B = 0.28008 × log (ν 38(100)) + 1.8616
10
sands of cp (very heavy oils). Usually conventional oils with
API gravities from 35 to 20 have viscosities from 10 to 100 cp where T is in kelvin and ν 38(100) is the kinematic viscosity at
and heavy crude oils with API gravities from 20 to 10 have 100 F (37.8 C or 311 K) in cSt, which is usually known from
◦
◦
viscosities from 100 to 10000 cp [17]. Most of the methods experiment. The average error for this method is about 6%.
developed for estimation of liquid viscosity are empirical in For blending of petroleum fractions the simplest method is
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