Multiphase Bioreactor Design

optimisation routine, the optimum process conditions and corresponding minimum costs
can be found. In the next treatment, mixing is assumed not to be rate limiting.
To illustrate this method, the overall costs are calculated in (1) a batch heterogeneous
reaction crystalliser with immobilised biocatalyst and a high amount of undissolved
substrate, and (2) in a continuous heterogeneous reaction crystalliser (draft-tube baffled
or fluidised-bed) with immobilised biocatalyst and a substrate suspension as feed. In both
calculations, the volume of the suspension, the initial biocatalyst concentration, and the
biocatalyst inactivation rate are equal. For simplicity, diffusion limitation is assumed not
to occur.

Rate-limiting Bioconversion

At the optimum conditions in both systems, the bioconversion is most likely the rate-
limiting process. For control of the crystallisation process, a rate-limiting bioconversion
is advantageous, as this implies a low supersaturation and a minimal nucleation. In batch
reaction crystallisers with a large amount of undissolved substrate, the surface area of the
substrate particles will be large and the dissolution rate will exceed the bioconversion
rate. Since a substrate conversion of 100% is generally aimed at, at some point
dissolution will become rate limiting due to depletion of solid substrate (Michielsen et
al., 1999a). For that reason, use of a complete model for calculation of the amount of
product produced in a batch reaction crystalliser is to be preferred, as this gives more
accurate values. However, for gross calculation, as in this section, the assumption of one
process being rate limiting, i.e. the bioconversion, can be justified. Though in the
continuous reaction crystallisers proposed in this work (Figures 8.4 and 8.5), substrate
dissolution or the bioconversion can be rate limiting, a rate-limiting bioconversion is
favourable, as this would mean that the biocatalyst is operated at a high substrate
concentration (near saturation). If the substrate saturation concentration is high as
compared to the Michaelis constant Km, the latter results in high conversion rates. Since
the biocatalyst is often expensive in comparison with the reactants, such an efficient use
of the biocatalyst should be aimed at. If efficient use of the biocatalyst can be combined
with a high substrate conversion, the sum of the biocatalyst and substrate costs per kg of
product approaches its minimum (Michielsen et al., 1999c). In a continuous liquid-solid-
solid three-phase system with a rate-limiting bioconversion, such a combination can be
attained at low biocatalyst concentrations and long residence times (of substrate(s) and
biocatalyst).
One reason for the fact that the bioconversion often is (or becomes) rate limiting is a
high biocatalyst inactivation rate. In bioconversions, the biocatalyst inactivation rate is a
crucial parameter, as it determines the operational time and thereby the amount of
product produced per kg of biocatalyst. For that reason, the effect of biocatalyst
inactivation on the overall costs in both batch and continuous reaction crystallisers is
shown in this section.

Overall Costs Per Kg Of Product

Box 8.1 shows how the amount of product in both batch and continuous reaction
crystallisers with the bioconversion as rate-limiting process can be calculated. Thereby, it

Solid-to-solid bioconversions 251