Page 258 - gas transport in porous media

Chapter 14: Experimental Determination of Transport Parameters
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5

3

4
Figure 14.5. Chromatographic set-up in SPSC arrangement; 1 carrier gas; 2 tracer sampling valve;
3 column with pellets; 4 tracer detector + A/D conversion + data logger; 5 detail of the packed column

with the high carrier-gas velocity. The use of inert tracers prevents their adsorption
and the possible surface diffusion, which obscures the effective diffusion coefficients
(Schneider and Smith, 1968a) and transport characteristics. Another advantage of
the SPSC arrangement is the averaging of obtained transport characteristics over
many pellets present in the column. In addition: SPSC guarantees low carrier gas
consumption.
The analysis of outlet peaks is based on the model of processes in the column.
Today the Kubín-Kuˇcera model (Kubín, 1965; Kuˇcera, 1965), which accounts for all
the above-mentioned processes, as long as they can be described by linear (differ-
ential) equations, is used nearly exclusively. Several possibilities exist for obtaining
rate parameters of intracolumn processes (axial dispersion coefficient, external mass
transfer coefficient, effective diffusion coefficient, adsorption/desorption rate or equi-
librium constants) from the column response peaks. The moment approach in which
moments of the outlet peaks are matched to theoretical expressions developed for the
system of model (partial) differential equations is widespread because of its simplicity
(Schneider and Smith, 1968b).
The today’s availability of computers makes matching of column response peaks to
model equations the preferred analysis method. Such matching can be performed in
the Laplace- (Kamiyanagi and Furusaki, 1983) or Fourier-domain (Zygourakis and
Moudgalya, 1987), or, preferably in the time-domain (Wakao et al., 1979; Fahim and
Wakao, 1982).
ForaT → C system the impulse response (i.e., response to a tracer Dirac pulse)
of a column packed with porous spherical particles of radius, R, in which tracer equi-
librium adsorption is in the Henry region of the adsorption isotherm (characterized
by the adsorption equilibrium constant, K T ) and intraparticle diffusion character-
ized by an effective diffusion coefficient D TC takes place is given by (Schneider,
1984).
∞

2
Pe 2γλ t
h(t) = Q exp − f 1 cos − f 2 λdλ (14.26)
2 δ o t dif
0