Chemical Reactions on Solid Surfaces - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 444

Figs. E9-4.6 A and B show the change of bulk phase concentrations with reaction time. One
can observe that LHHWapproximation agrees with the full rate description reasonably well
at the shape of curves. In this case, the adsorption of A and desorption of B are one tenth of
the rate of surface reaction, the effects of adsorption and desorption are still observable, but
the simplification is reasonable. Wider differences in rates would make the approximation
less obvious.
The fractional coverages on the catalyst surface are computed via Eqns (E9-4.23) and
(E9-4.24) after the bulk phase concentrations were obtained. Figs. E9-4.6C and E9-4.6D
show the variations of surface coverage as a function of reaction time. One can observe
that the fractional surface coverage as predicted by the LHHWapproximation is quite similar
to the full rate descriptions. LHHW approximation becomes suitable once the fraction of
vacant sites becomes steady (nearly constant).
One can observe from Fig. E9-4.6 A that while the variation of bulk concentrations for
LHHW approximation looks similar to the full solutions, there is a shift log t (to the right)
that could make the agreement closer. This is due to the fact that the finite rates of adsorption
of A and desorption of B contributes to the decline of overall rate as used by LHHWapprox-
imation. As a result, the LHHW approximations over-predicted the reaction rate and thus
leading to a quicker change in the bulk phase concentrations. Overall, the shape of the curve
(or how the concentrations change with time) is remarkably similar. Therefore, if one were to
correlate the experimental data, the difference between the quality of full solutions and the
quality of fit from LHHW approximations would not be noticeable as different rate param-
eters would be used. In data analysis/parametric estimation, the prediction curves are
shifted left or right to creating a better match.

c) Pseudosteady State Hypothesis (PSSH)

We next examine the approximation by PSSH based on the same set of parameters. The
PSSH assumes that the rate of change of intermediates be zero. In this case,

0 ¼ r s$A ¼ r 1 r 2 ¼ k A ðqC A q A =K A ÞC s k S ðq A q B K A =K B =K C ÞC s (E9-4.30)

0 ¼ r s$B ¼ r 2 r 3 ¼ k S ðq A q B K A =K B =K C ÞC s k B ðq B =K B qC B ÞC s (E9-4.31)

which yield

q A ðk A =K A þ k S Þþq B k S K A =K B =K C þ qk A C A ¼ 0 (E9-4.32)

q A k S q B ðk S K A =K B =K C þ k B =K B Þþqk B C B ¼ 0 (E9-4.33)

Eqns (E9-4.32) and (E9-4.33) can be solved to give

q A ¼ ðK C k 1

þ K A k 1 ÞC A þ K C k A C B

B S

K A q (E9-4.34)

K C k 1 þ K A k 1 þ k 1

A

B S

q B ¼ ðk A þ K A k 1

ÞC B þ k B C A

S

K B q (E9-4.35)

K C k 1 þ K A k 1 þ k 1

A B S