Page 171 - Adsorption Technology & Design, Elsevier (1998)

Design procedures 159

+ u----- + -- + = 0 (6.42)
Ot Oz cf Ot cf Ot

~ = k(q*- gl) (6.43)
cot

OT~ AH Oq
----- = ha (T f- Ts) (6.44)
Ot cs cot

bcqm
q* - (6.45)
(1 +be)
-AH)
(6.46)
b = b0exp RgT

Because of the number of assumptions made, this model is perhaps one of
the simplest non-isothermal examples which has been solved by finite
difference numerical approximations. There are many examples in the
research literature of models which contain fewer simplifications. One
example is described by Sowerby and Crittenden (1991). In this example a
significant proportion of the feed is adsorbed, i.e. u is not constant, the
equilibrium is more complex, the rate equation contains two film re-
sistances, the film coefficients are temperature dependent and heat loss from
the column is allowed for. Further guidance on the subject of multi-
component, non-isothermal adsorption can be obtained by reference to
Ruthven (1984), Yang (1987) and Tien (1994).

6.5.4 Cyclic fixed bed process design

The a priori design of cyclic PSA and TSA processes is not absolutely
reliable because fundamental mathematical models of all the component
steps are not yet sufficiently developed and tested. Much of the necessary
input data is probably still of questionable accuracy. Mathematical models
are therefore of most use in predicting the location of optimum operating
conditions but are less accurate in predicting exact product compositions.
Consequently the modelling of both PSA and TSA is a fertile ground for
fundamental research, as manifested by the growth in the number of
publications on the subject (Sircar 1991). Sophisticated numerical analysis
techniques which require substantial computing resources are often used to
solve the model equations. Most are tested only on small-scale laboratory
apparatus and hence few models could be applied to industrial-scale plant