Page 365 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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8. APPLICATIONS: ESTIMATION OF TRANSPORT PROPERTIES 345
conductivity and when no data are available it can be con-
sidered as unity [18]. June 22, 2007 14:25 recommended for practical applications in the petroleum
industry.
For calculation of thermal conductivity of liquid petroleum
fractions, if the PNA composition is available the pseudocom-
ponent method using Eq. (8.42) and Table 8.4 may be applied. 8.3 DIFFUSION COEFFICIENTS
L
The simplest method of calculation of k for petroleum frac-
T
tions when there is no information on a fraction is provided Diffusion coefficient or diffusivity is the third transport prop-
in the API-TDB [5]: erty that is required in calculations related to molecular dif-
fusion and mass transfer in processes such as mixing and
L
−4
(8.50) k = 0.164 − 1.277 × 10 T dissolution. In the petroleum and chemical processing, dif-
T
L
where T is in kelvin and k in W/m · K. In other references this fusion coefficients of gases in liquids are needed in design
equation is reported with slight difference in the coefficients. and operation of gas absorption columns and gas–gas diffu-
L
−4
For example, Wauquier [8] gives k = 0.17 − 1.418 × 10 T. sion coefficients are required to determine rate of reactions
At 298 K (25 C), this relation gives a value of 0.128 W/m · K in catalytic-gas-phase reactions, where mass transfer is a con-
◦
(near k of n-C 8 ), while Eq. (8.50) gives a value of 0.126, which trolling step. In the petroleum production, knowledge of dif-
is the same as the value of k for n-heptane. The error for this fusion coefficient of a gas in oil is needed in the study of gas
equation is high, especially for light and branched hydrocar- injection projects for improved oil recovery. If a binary sys-
bons. Average error of 10% is reported for this equation [5] tem of components A and B is considered, where there is a
and it may be used in absence of any information on a frac- gradient of concentration of A in the fluid, then it diffuses
tion. A more accurate relation uses average boiling point of in the direction of decreasing concentration (or density)—a
--`,```,`,``````,`,````,```,,-`-`,,`,,`,`,,`---
the fraction as an input parameter and was developed by the process similar to heat conduction due to temperature gradi-
API group at Penn State [5]: ent. In this case the diffusion coefficient of component A in
the system of A and B is called binary (or mutual) diffusion
L
−5

(8.51) k = T 0.2904 × 2.551 × 10 −2 − 1.982 × 10 T coefficient and is usually shown by D AB , which is defined by
T b
the Fick’s law [1]:
where both T b and T are in kelvin. This equation gives an av-
erage error of about 6%. For n-C 5 of Example 8.3, this equa- (8.54) dρ A dx wA
tion gives a value of 0.104 W/m · K with − 9% error. However, J Ay =−D AB dy =−ρD AB dy
this equation is not recommended for pure hydrocarbons. where J Ay is the mass flux of component A in the y direction
For petroleum fractions Eq. (8.46) can be used with better (i.e., g/cm · s) and dρ A /dy is the gradient of mass density in
2
accuracy with the specified ranges of boiling point and tem- the y direction. ρ is the mass density (g/cm ) of mixture and
3
perature when both T b and SG are available. For coal liquids x wA is the weight fraction of component A in the mixture. In
and heavy fractions, Tsonopoulos et al. [33] developed the the above relation, the second equality holds when ρ is con-
following relation based on the corresponding states method stant with respect to y. J A represents the rate of transport of
of Sato and Riedel:
mass in the direction of reducing density of A. It can be shown
L
(8.52) k = 0.05351 + 0.10177 (1 − T r) 2/3 that in binary systems D AB is the same as D BA [1]. From the
above equation, it can be seen that the unit of diffusivity in
L
2
2
where k is in W/m · K. This equation is not recommended for the cgs unit system is cm /s (or 1 cm /s = 10 −4 m /s). Diffu-
2
pure hydrocarbons. For some eight coal liquid samples and sion of a component within its own molecules (D AA ) is called
74 data points this equation gives an average error of about self-diffusion coefficient. From thermodynamic equilibrium
3% [33]. point of view, the driving force behind molecular diffusion is
For liquid hydrocarbons and petroleum fractions when gradient of chemical potential ∂μ A /∂y. Since chemical poten-
pressure exceeds 30–35 atm, effect of pressure on liquid ther- tial is a function of T, P, and concentration, for systems with
mal conductivity should be considered. However, this effect uniform temperature and pressure, μ a is only a function of
is not significant for pressures up to 70–100 atm. For the re- concentration (see Eq. 6.121) and Eq. (8.54) is justified. Var-
duced temperature range of 0.4–0.8 and pressures above 35 ious forms of Fick’s law can be established in the forms of
atm, the following correction factor for the effect of pressure gradients of molar concentration, mole, weight, or mass frac-
on liquid thermal conductivity is recommended in the API- tions [1]. A comparison between Eqs. (8.1), (8.28), and (8.54)
TDB [5]: shows the similarity in momentum, heat, and mass trans-
fer processes. The corresponding molecular properties (i.e.,
L
k = k L C 2 kinematic viscosity (ν), thermal diffusivity (α), and diffusion
2 1
(8.53) C 1 2 coefficient (D)) that characterize the rate of these processes
2.054T r
2
2
C = 17.77 + 0.065P r − 7.764T r − have the same unit (i.e., cm /s or ft /h). This is the reason that
exp (0.2P r)
these physical properties are called transport properties. The
L L
To calculate value of k at T 2 and P 2 , value of k at T 1 and P 1 diffusion process may also be termed mass transfer by con-
2
1
must be known. In case of lack of an experimental value, the duction. The ratio of ν/D or (μ/ρD) is a dimensionless num-
L
value of k at T 1 and P 1 can be calculated from Eqs. (8.41)– ber called Schmidt number (N Sc ) and is similar to the Prandtl
1
(8.43). There are some other generalized correlations based number (N Pr ) in heat transfer (see Eq. 8.29). Schmidt number
on the theory of corresponding states for prediction of both represents the ratio of mass transfer by convection to mass
viscosity and thermal conductivity of dense fluids [25, 34]. transfer by diffusion. Values of N Sc of methane, propane, and
However, these methods, although complex, are not widely n-octane in the air at 0 C and 1 atm are 0.69, 1.42, and 2.62,
◦
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