Page 167 - Adsorption Technology & Design, Elsevier (1998)

Design procedures 155

Table 6.2 Summary of available analytical solutions for breakthrough curves in
isothermal, trace component systems with plug flow and a rectangular isotherm
i , ,,,, i .. ii , i i , i i i
Rate expression Plug flow model
, in|, i i i
Quasi-chemical Bohart and Adams (1920)
Linear rate-solid film Cooper (1965)
Linear rate-fluid film Cooper (1965)
Solid diffusion Cooper (1965)
Pore diffusion
Cooper and Liberman (1970)
Film + pore diffusion Weber and Chakravorti (1974)
Fluid film + solid diffusion Yoshida et al. (1984)
llll i , i ii ,, i i iii i i i

known. The rate expression is somewhat unrealistic in this model, but the
differences between breakthrough curves calculated from the model and
from a more realistic diffusion equation are relatively small.
Beyond these relatively simple systems and for all other non-linear
isotherms, it is necessary to obtain solutions for the breakthrough curves by
applying numerical approximation techniques to the model equations.
Standard finite difference or collocation methods are commonly used. Table
6.3 provides a brief source list to solutions for plug flow and axially dispersed
models with Langmuir, Freundlich or more general isotherms.

6.5.3 Non-isothermal and multicomponent systems

So far it has been assumed that operation has been isothermal and that, for
the most part, the system has comprised a single adsorbate present at low
concentration in an inert carrier gas or solvent. In such systems there will be
only a single transition or mass transfer zone. For many systems of practical
significance however, the situation will in reality be much more complex
because the adsorption column is more likely to be operated adiabatically
and there will often be more than one adsorbable component in the
feedstock. The concentration profile will show more than one mass transfer
zone in such cases.
A simplification arises if the concentrations of all adsorbable species in a
non-adsorbing carrier gas or solvent are very low. In this case the equilibria
remain within the Henry's law region, i.e. equation (6.26) applies, and
thereby each component's equilibrium can safely be considered to be
unaffected by the presence of the other components. Extension of the
analyses provided above for single components then becomes relatively