Page 43 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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1. INTRODUCTION 23
1.7.18 Units of Viscosity and Kinematic Viscosity
simplified to the following form at the temperatures of 311
(100 F) and 372 K, (210 F) respectively [1].
◦
◦
Viscosity (absolute viscosity) shown by μ is a property that
characterizes the fluidity of fluids and it has the dimension (1.19) SUS 100F = 4.632ν 100F ν 100F ≥ 75 cSt
of mass per length per time (M/L · t). If the relation between
dimensions of force (F) and mass (M) is used (F = M·L·t ),
−2
then absolute viscosity finds the dimension of F·t·L −2 which (1.20) SUS 210F = 4.664ν 210F ν 210F ≥ 75 cSt
is the same as dimension for the product of pressure and where ν 100F is the kinematic viscosity at 100 F (311 K) in cSt.
◦
time. Therefore, in the SI system the unit of viscosity is Pa · s As an example, a petroleum fraction with kinematic viscosity
(N · m ·s). In the cgs system the unit of viscosity is in g/cm · s of 5 cSt at 311 K has an equivalent Saybolt Universal Viscosity
−2
that is called poise (p) and its hundredth is called centipoise of 42.4 SUS as calculated from Eq. (1.17).
(cp), which is equivalent to milli-Pa · s (mPa · s). The conver- Another unit for the viscosity is SFS (Saybolt foural sec-
sion factors in various units are given below. onds) expressed for Saybolt foural viscosity, which is mea-
2
1cp = 1.02 × 10 −4 kg · s/m = 1 × 10 −3 Pa · s = 1 mPa · s sured in a way similar to Saybolt universal viscosity but
f measured by a larger orifice (ASTM D 88). The conversion
2
= 10 −2 p = 2.089 × 10 −5 lb f · s/ft = 2.419 lb/h · ft
= 3.6 kg/h · m from cSt to SFS is expressed through the following equations
at two reference temperatures of 122 F (323 K) and 210 F
◦
◦
1Pa·s = 1 kg/m · s = 1000 cp = 0.67194 lb/ft · s (372 K) [47].
2
1 lb/h·ft = 8.634 ×10 −6 lb f · s/ft = 0.4134 cp =1.488 kg/h · m 13924
2
3
1kg · s/m = 9.804 ×10 cp = 9.804 Pa·s = 0.20476 lb f · s/ft 2 (1.21) SFS 122F = 0.4717ν 122F +
2
f ν 122F − 72.59ν 122F + 6816
2
4
1lb f ·s/ft = 4.788 × 10 cp = 4.884 kg ·s/m 2
f
5610
The ratio of viscosity to density is known as kinematic vis- (1.22) SFS 210F = 0.4792ν 210F + ν 2 + 2130
2
cosity (ν) and has the dimension of L/t . In the cgs system, 210F
the unit of kinematic vsicosity is cm /s also called stoke (St)
2
and its hundredth is centistoke (cSt). The conversion factors For conversion of Saybolt foural viscosity (SFS) to kinematic
are given below. viscosity (cSt.), the above equations should be used in reverse
or to use tabulated values given by API-TDB [47]. As an exam-
2
2
2
1ft /h = 2.778 × 10 −4 ft /s = 0.0929 m /h = 25.81 cSt ple, an oil with Saybolt foural viscosity of 450 SFS at 210 F
◦
2
2
4
1ft /s = 9.29 × 10 cSt = 334.5m /h has a kinematic viscosity of 940 cSt. Generally, viscosity of
2
2
2
1 cSt = 10 −2 St = 10 −6 m /s = 1mm /s = 3.875 × 10 −2 ft /h highly viscous oils is presented by SUS or SFS units.
2
= 1.076 × 10 −5 ft /s
2
4
4
2
6
1m /s = 10 St = 10 cSt = 3.875 × 10 ft /h 1.7.19 Units of Thermal Conductivity
Thermal conductivity (k) as discussed in Chapter 8 represents
Another unit to express kinematic viscosity of liquids is amount of heat passing through a unit area of a medium for
Saybolt universal seconds (SUS), which is the unit for the one unit of temperature gradient (temperature difference per
Saybolt universal viscosity (ASTM D 88). Definition of viscos- unit length). Therefore, it has the dimension of energy per
ity gravity constant (VGC) is based on SUS unit for the viscos- time per area per temperature gradient. In the SI units it is
ity at two reference temperatures of 100 and 210 F (37.8 and expressed in J/s · m · K. Since thermal conductivity is defined
◦
98.9 C). The VGC is used in Chapter 3 to estimate the com- based on a temperature difference ( T), the unit of C may
◦
◦
position of heavy petroleum fractions. The relation between also be used instead of K. Because J/s is defined as watt (W),
SUS and cSt is a function of temperature and it is given in the the unit of thermal conductivity in the SI system is usually
API TDB [47]. The analytical relations to convert cSt to SUS written as W/m · K. In the English system, the unit of ther-
are given below [47]. Btu
mal conductivity is ft · h· ◦ F and in some references is written
Btu
SUS eq = 4.6324ν T as h·ft · ◦ F/ft , which is the ratio of heat flux to the temperature
2
[1.0 + 0.03264ν T ] gradient. The conversion factors between various units are
given below.
+ 2 3 −5
3930.2 + 262.7ν T + 23.97ν + 1.646ν × 10
T T
(1.17) 1 W/m · K (J/s · m· C) = 0.5778 Btu/ft · h· F
◦
◦
= 1.605 × 10 −4 Btu/ft · s· F
◦
where ν T is the kinematic viscosity at temperature T in cSt. = 0.8593 kcal/h · m· C
◦
The SUS eq calculated from this relation is converted to the
◦
SUS T at the desired temperature of T through the following 1 Btu/ft · h· F = 1.7307 W/m · K
relation. 1 cal/cm · s· C = 242.07 Btu/ft · h· F = 418.95 W/m · K
◦
◦
−4
(1.18) SUS T = [1 + 1.098 × 10 (T − 311)]SUS eq
1.7.20 Units of Diffusion Coefficients
where T is the temperature in kelvin (K). For conversion of
cST to SUS at the reference temperature of 311 K (100 F), Diffusion coefficient or diffusivity represents the amount of
◦
only Eq. (1.17) is needed. Equation (1.18) is the correction mass diffused in a medium per unit area per unit time per
term for temperatures other than 100 F. For kinematic vis- unit concentration gradient. As shown in Chapter 8, it has
◦
cosities greater than 70 cSt, Eqs. (1.17) and (1.18) can be the same dimension as the kinematic viscosity, which is
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