Chemical Reactions on Solid Surfaces - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 442

which can be rearranged to give

k A

q A ¼

k A C A q ¼ K A C A q

(E9-4.19)

and

k B
k B C B q ¼ K B C B q

q B ¼ (E9-4.20)

Total active site balance:

1 ¼ q þ q A þ q B ¼ q þ K A C A q þ K B C B q (E9-4.21)

Thus,

1

q ¼ (E9-4.22)

1 þ K A C A þ K B C B

Substituting (E9-4.22) into (E9-4.19), (E9-4.20) and then (E9-4.16) , we obtain

K A C A

q A ¼ (E9-4.23)

1 þ K A C A þ K B C B

K B C B

q B ¼ (E9-4.24)

1 þ K A C A þ K B C B

C A C B =K C

r ¼ k S C s K A (E9-4.25)

1 þ K A C A þ K B C B

At time t 0 in the batch reactor, the reaction is not started yet. However, LHHWexpression

(E9-4.25) requires that the adsorption and desorption are already in equilibrium. While this
requirement is not of issue for reactions carried out in flow reactors (after the transient
period) or when the amount of catalyst is negligible, it becomes important when noticeable
amount of catalysts is employed in a batch reactor. For example, the concentration of A can be
obtained via mole balance,

¼

K A C A0

C AT0 ¼ C A0 þ q A0 C s ¼ C A0 þ

þ K A C A0 þ K B C B0 C s

(E9-4.26)

1

The concentrations of A and B in the bulk fluid phase charged into the batch reactor are C AT0
and C BT0 ¼

0, assuming only reactant Awas loaded. Since there is no B present in the initial
reaction mixture, C B0 ¼ 0. From Eqn (E9-4.26) , we can solved for the effective concentration of

A in the batch reactor as

q

ðC AT0 C s K A Þ

2

C AT0 C s K A þ 4K A C AT0 þ

C A0 ¼ (E9-4.27)

2

That is to say that the concentration of A in the bulk fluid phase at t 0 is smaller than that in

the original bulk fluid phase before contacting with the solid catalyst.

¼