Page 167 - Principles of Catalyst Development

CATALYST CHARACTERIZATION 155
is the "ink-bottIe" pore shown in Fig. 7.l8c, in which narrow openings
access larger volumes. Condensation in the adsorption branch occurs in
the large volume. With desorption, lower pressures are ne:cessary to empty
the neck, giving the hysteresis curve (c) in Fig. 7.17. This branch is more
indicative of aperture sizes.
Usually, intermediate curves, such as (b) in Fig. 7.17, are found. Possibly
some type of constricted pore system prevails or perhaps shapes as in (b),
Fig. 7.18. This adds some uncertainty to which branch to use. Some discrimi-
nation is possible by comparing surface areas from the: adsorption and
desorption branches, Sads and Sdeso respectively, and applying the following
criteria:
1. If Sads < SBET = Sdeso pores are cylindrical and the desorption
branch describes the pore size distribution.
2. If Sads < SBET« Sdes severe pore neck constrictions exist and each
branch may be used.
3. If Sads < Sdes« SSET, considerable micropore volume is present so
that neither is accurate.

7.3.6. Diffusivity

Measurement of diffusivity is not normally practiced in characterizing
particle properties. This is a pity, since valuable information is available
with simple techniques. It is true that the value of measured diffusivities in
calculations of effectiveness factors is doubtful. Exact conditions of pressure,
temperature, and concentration profiles in the pellet are impossible to
duplicate. Diffusion coefficients estimated from rate-particle size curves
generally do not agree with direct measurements. However, by comparing
calculated to measured diffusivities in simple mixtures, it is possible to
estimate the tortuosity factor

(7.14)

which is not only transferable to more severe conditions but is also an index
of texture.
The classical method for measuring diffusivity is the Wicke-Kallenbach
technique shown in Fig. 7.19.(21) The catalyst in the form of a cylinder is
constrained in a cell which may be as simple as a piece of tygon tubing.
More elaborate temperature-pressure cells have been dt~vised. Hydrogen
on one side of the cylinder diffuses into nitrogen on th(~ other, and vice
versa. This flux is measured and gives Dell' A steady-state technique, this
method does not detect diffusion into closed-end pores. Although simple
to use, the biggest objection is the need for cylindrical samples. Pellets are