Page 175 - Adsorption Technology & Design, Elsevier (1998)

Design procedures 163

shape of the isotherm causes the MTZ to take on an asymptotic or constant
pattern form at some distance from the bed inlet. The MTZ then becomes
stable and does not change its shape. Cooney and Lightfoot (1965) provide a
mathematical proof of the constant pattern MTZ and Coulson et al. (1991)
provide a simplified analysis. For many practical systems the distance
required to develop a constant pattern MTZ is small, but it does depend on
the degree of non-linearity of the isotherm and on the kinetics. The constant
pattern condition may be described as follows:

c q
-- = -- (6.47)
co qo

For a single component under constant pattern conditions an expression for
the asymptotic form of breakthrough curve can be obtained by integrating
the appropriate rate expression, subject to the constant pattern condition.
Consider the case of plug flow and constant velocity, a linear rate of
adsorption based on solid phase conditions (equation (6.48)), a Langmuir
isotherm, a simple substitution (equation (6.49)) and the constant pattern
condition (equation (6.47)):

Ogl = k(q* - q) (6.48)
Ot

fl = 1- qo (6.49)
qs
The solution is given by equations (6.50) to (6.52)"

'02(1-01)] (Or)
1
k(t2 - tl) = In (6.50)
1-fl
Cl
i 1 = -- (6.51)
co
C2
i 2 = -- (6.52)
co

Table 6.4 provides a summary of solutions for single-component constant
pattern behaviour with a Langmuir isotherm and plug flow. Several kinetic
models are listed but it is important to note that for highly non-linear systems
the use of an incorrect kinetic model can lead to large errors in the prediction
of dynamic capacity.