Chemical Reactions on Solid Surfaces - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 437

which recovers the Langmuir isotherm includes species A, although the adsorption of A is
not in equilibrium. The nonequilibrium of A in the isotherm is accommodated by the replace-
ment of C A with the virtual concentration of A that is in equilibrium with other species in the
system. Therefore, the virtual concentration may be applied to simplify the derivation for
adsorption controlled processes or provide a check on the final expression.

Example 9-4 The reaction network of isomerization on a solid catalyst follows the following
scheme:

A þ s % A $s (E9-4.1)

A $s % B $s

(E9-4.2)

B $s %

þ s (E9-4.3)

B

þÞ ¼ (E9-4.4)

overall A % B

Discuss the relevance of LHHW kinetics based on the detailed kinetics as the reaction being
performed in a batch reactor. Treat the reaction network via a) microkinetics (i.e. full solu-
tions), b) using LHHW approximations, i.e. rate-limiting step assumptions; and c) PSSH
on intermediates.
Solution. This is the simplest case of surface catalyzed reaction shown in Table 9.3 .Aswe
have discussed in detail the derivation of LHHW kinetic expressions, we now go back to
the detailed reaction network analysis before turning to the LHHW simplifications
(assumptions).

a) Microkinetics (Full Solutions)

As the reaction rate expression follows stoichiometry for elementary steps, reactions
(E9-4.1) through (E9-4.3) :

r 1 ¼ k A C A qCs k A q A Cs (E9-4.5)

r 2 ¼ k S q A Cs k S q B Cs (E9-4.6)

r 3 ¼ k B q B Cs k B C B qCs (E9-4.7)

Mole balances of all the species in the batch reactor lead to

d C A

d t ¼k A ðC A q q A =K A ÞC s

(E9-4.8)

d C B

d t ¼ k B ðq B =K B qC B ÞC s

(E9-4.9)

d q A

d t ¼ k A ðqC A q A =K A Þk S ðq A q B K A =K B =K C Þ

(E9-4.10)

d q B
d t ¼ k S ðq A q B K A =K B =K C Þk B ðq B =K B qC B Þ

(E9-4.11)

q ¼ 1 q A q B (E9-4.12)