22 Pore Structure and Diffusion
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N. WAKAO Department of Chemical Engineering, Yokohama National University, Minami-Ku, Yokohama, Japan
Unsteady state diffusion expenments were done to determine effective diffusivity values for inert systems. There was no difference between the diffusivity values at unsteady state and those at steady state. A two-dimensional network of macro and micro passageways was assumed as a pore model. The effective diffusivity values for inert systems were estimated on the model, and they did not depend on steady or unsteady state conditions. The effective diffusivity for a reacting system was also computed on the pore model, and the value for a reacting system was predicted to be smaller than that for an inert system if there were many macropores all the way through the pellet. If there are deadends of macropores, however, the two diffusivity values tend to be the same.
D
iffusion experiments under inert conditions either at steady state or at unsteady state have been done to determine effective diffusivity values of porous catalyst pellets for reacting systems. Steisel and Butt (I), using the computational model for pore structure of Foster and Butt (2), suggested that the effective diffusivity for inert systems ( D ) is considered to be identical with that for reacting systems ( D ) . A similar conclusion has been reached experimentally by Balder and Petersen (3) and Toei et al. (4). The purposes of this investigation are to examine, first, if D values measured from unsteady state diffusion experiments are the same as those at steady state, and, second, if there is any difference in value between D and e
D
R
e
e
D
e
Experimental Measurements of D
D
D
e
As shown in Figure 1, hydrogen is kept flowing in the two chambers to replace air in the porous solid with hydrogen; then hydrogen flowing into one chamber (pulse-side chamber) is changed to nitrogen for a certain period, and again back to hydrogen. Hydrogen is kept flowing in the hydrogen-side chamber. The gas in either chamber is at atmospheric pressure. The nitrogen concentration in the hydrogen-side chamber is measured as a function of time by intermittent sampling of the outgoing gas and determination of the concentration by gas chromatography. For the unsteady state experiments each chamber is designed to have a small volume. 281
Hulburt; Chemical Reaction Engineering—II Advances in Chemistry; American Chemical Society: Washington, DC, 1974.
282
CHEMICAL REACTION ENGINEERING
H
N
2
Π
2
PULSE-SIDE CHAMBER
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SEALED H2-SIDE CHAMBER
H
t SAMPLING FOR GAS CHROMATOGRAPH
2
Figure 1. If we assume that D nitrogen is
D
e
Experimental apparatus
is constant in each run, the material balance for
(1) with
c = 0, at £ = 0 c —
(2)
at 0 < t < to ) > ζ = 0 ) c — 0, at t > t
(3)
c = 0, at ζ = L
(4)
Co,
0
The solution in the Laplace domain is ce~ dt st
1 — e~
eto
=
where
Co ·
sinhX
(δ)
sinhX
λ = L
The rate of nitrogen diffused through the solid to the hydrogen-side chamber is
^ = -^ (l) D
(6)
t
In the Laplace domain NL =fj
N e-*
