Multiphase Bioreactor Design

(39)

ii) Zero order reaction with full substrate penetration (β>1) and no external mass transfer
limitations:

(40)

iii) Zero order reaction with partial substrate penetration (β<1) and no external mass
transfer limitations:

(41)

Transition between different reaction orders

Biofilms may be subject to different operating conditions within the same reactor,
particularly in plug flow systems. Near the reactor outlet, a substantial amount of
substrate will have been consumed and its concentration will be low, giving rise to a first
order reaction in the biofilm. Near the reactor inlet, if the concentration is large enough,
the biofilm may be completely penetrated (zero order overall process) or partially
penetrated (half order overall process). Therefore, when calculating bioreactors, it is
useful to have a way of detecting which reaction order will prevail in the biofilm system
at each zone of the reactor. The following simple criteria can be applied:

i) Transition from zero order to half order overall process:
The critical substrate concentration will be defined, by considering β=1, as:

(42)

Therefore, if S>Scrit, the overall process (apparent reaction) will be of zero order. On the
other hand, if S<Scrit, the overall process will be of half-order.

ii) Transition from half order to first order overall process:
In this case, the transition point will be defined in relation to the Monod
saturation constant. When S>2Ks, the apparent reaction will be of half-order. In
the case of S<2Ks, the process will be of first order.

Values of the diffusion-reaction parameters: illustrative examples

In spite of the limitations of the diffusion-reaction model, mainly those related to the
supposed homogeneous distribution of the active biomass in the microbial layer, many
reports have been published on its application to different substrates and different biofilm
reactors. The purpose of such studies was often to obtain values of the biofilm kinetic

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