Page 108 - Separation process principles 2

3.2 Diffusion Coefficients 73

Table 3.2 Experimental Binary Diffusivities of Some Gas Pairs
at 1 atrn

Gas pair, A-B Temperature, K DAB, cm2/s
-
~ir-carbon dioxide
~ir-4 than01
Air-helium
Air--n-hexane
Air-water
Argon-ammonia
Argon-hy drogen
Argon-hydrogen
Argon-methane
Reduced Pressure, P,
Carbon dioxide-nitrogen
Figure 3.3 Takahashi [4] correlation for effect of high pressure
Carbon dioxide--oxygen
Carbon dioxide-water on binary gas diffusivity.
Carbon monoxide-nitrogen
Helium-benzene
Helium-methane For binary mixtures of light gases, at pressures to about
Helium-methanol 10 atm, the pressure dependence on diffusivity is adequately
Helium-water predicted by the simple inverse relation (3-36), that is, PDAB =
Hydrogen-ammonia a constant for a given temperature and gas mixture. At higher
Hy drogen-ammonia pressures, deviations from this relation are handled in a man-
Hydrogen-cy clohexane ner somewhat similar to the modification of the ideal-gas law
Hydrogen-methane by the compressibility factor based on the theorem of corre-
Hydrogen-nitrogen sponding states. Although few reliable experimental data are
Nitrogen-benzene available at high pressure, Takahasi [4] has published a tenta-
Nitrogen-cyclohexane
tive corresponding-states correlation, shown in Figure 3.3,
Nitrogen-sulfur dioxide
patterned after an earlier correlation for self-diffusivities by
Nitrogen-water
Oxy gen-benzene Slattery [5]. In the Takahashi plot, DABP/(DABP)LP is given
Oxygen--carbon tetrachloride as a function of reduced temperature and pressure, where
is
Oxygen--cyclohexane (DABP)~p at low pressure where (3-36) applies. Mixture-
Oxy gen-water critical temperature and pressure are molar-average values.
- -
Thus, a finite effect of composition is predicted at high pres-
From Marrero, T. R., and E. A. Mason, J. Phys. Chem. Ref: Data, 1,3-118 sure. The effect of high pressure on diffusivity is important in
(1972).
supercritical extraction, discussed in Chapter 11.

Estimate the diffusion coefficient for the system oxygen (A)/
benzene (B) at 38°C and 2 atrn using the method of Fuller et al. Estimate the diffusion coefficient for a 25/75 molar mixture of argon
and xenon at 200 atrn and 378 K. At this temperature and 1 atm, the
SOLUTZON diffusion coefficient is 0.180 cm2/s. Critical constants are

From (3-37), Tc, K PC, atm
Argon 151.0 48.0
P.
Xenon 289.8 58.0
FromTable 3.1, (CV)~ 16.3 and (Cv)~ 6(15.9) +
=
=
SOLUTZON
6(2.31) - 18.3 = 90.96
From (3-36), at 2 atrn and 3 11.2 K, Calculate reduced conditions:
Tc = 0.25(151) + 0.75(289.8) = 255.1 K;
Tr = TITc = 3781255.1 = 1.48
PC = 0.25(48) + 0.75(58) = 55.5;
At 1 atm, the predicted diffusivity is 0.0990 cm2/s, which is about Pr = PI PC = 200155.5 = 3.6
2% below the experimental value of 0.101 cm2/s in Table 3.2. The
experimental value for 38°C can be extrapolated by the temperature From Figure 3.3, = 0.82
dependency of (3-36) to give the following prediction at 200°C: (DAB P)LP
200 + 273.2
( 38 + 273.2 )
DAB at 200°C and 1 atrn = 0.102