(12)
where Keq is the equilibrium constant for reversible Michaelis-Menten kinetics.
Substituting (12) and (8) in (11) and considering v=1, the dimensionless balance for
reaction and diffusion of substrate becomes
(13)
where α0, α 1 and α 2 are kinetic constants, the expressions of which are given in Table 4.2.
The condition S>Seq in dimensionless form is β>α 1 /α 0. Thus, the expression for the
overall rate of reaction, robs, for reversible Michaelis-Menten kinetics is
(14)
An adequate method to describe the influence of diffusional resistance on the observed
reaction rate is to use the concept of effectiveness factors. The external mass transfer
effects on the activity of an immobilized biocatalyst can be quantitatively expressed by
the effectiveness factor ηext, defined as the ratio of the observed reaction rate robs to the
kinetic rate calculated with bulk concentrations rkin=r(SB, PB)
(15)
Figure 4.5 shows the dependence of the effectiveness factor ηext on βB and μ for
Michaelis-Menten kinetics. For inhibition-type kinetics, the increase in rate caused by the
decreasing substrate inhibition towards the center of the catalyst particle can be greater
than the decrease in rate caused by the drop in concentration. This can cause the
effectiveness factor to exceed unity, as shown by Figure 4.6.
Design and modelling of immobilised biocatalytic reactors 101