of biocatalyst) increases with increasing kd, as the amount of biocatalyst, not being used
up as soon as x=100%, decreases. At kd>4·10− 4 h−1, both the substrate and biocatalyst
costs increase with increasing kd. This is caused by the decrease in the amount of product
produced due to the fact that (almost) complete biocatalyst inactivation is reached earlier
with increasing kd. The latter implicates that at kd>4·10−^4 h−^1 , Pr=Prmax, and that the
conversion x decreases with increasing kd. The investment and operating costs ($io) and
the downstream-processing costs ($dp) are generally not affected by an increase in kd, as
the decrease in tb is balanced by the decrease in the amount of product produced (see Box
8.2). However, at kd≤4·10−^4 h−^1 these costs decrease with increasing kd, as despite the
decrease in tb, the maximum attainable product concentration still can be reached.
The continuous system described in this work only differs from the batch system in
that the substrate availability is not limited. As expected (see Box 8.2), Figure 8.6b shows
that in such a continuous system the substrate, investment and operating, and
downstream-processing costs per kg of product produced ($s, $io and $dp, respectively) are
unaffected by kd. However, the overall costs ($ov) increase with increasing kd due to the
increase of the biocatalyst costs ($e) with increasing kd (Figure 8.6b). The latter is caused
by the fact that the amount of product produced decreases with increasing kd, whereas
the initial active biocatalyst concentration is a constant (see Box 8.2). Note that in such a
continuous system, the productivity of the biocatalyst is maximal at any biocatalyst
inactivation rate, and the conversion x (=Cp/Csi) depends on F(0) (assuming qp, Ce(0), and
V to be constant; see Box 8.1). By setting F(0) at 50 m^3 ·h−^1 , a conversion of 100% is also
obtained in the continuous system, so that a proper comparison of both systems is
possible. Figure 8.6b also shows that only at kd=4·10−^4 h−1, the batch system can compete
with the continuous system; at kd=4·10−^4 h−^1 , both the substrate conversion x is 100% and
the biocatalyst productivity Pr is maximal (see Figure 8.6a).
In practice however, the biocatalyst inactivation rate is often a given constant at
certain conditions, and the initial biocatalyst and substrate concentrations are variables.
The optimum initial biocatalyst and substrate concentrations for batch operation can be
determined by plotting the overall costs ($ov) versus Ce(0)/Cs(0) (see Figure 8.7). With
e.g. kd=1·10−^3 h−^1 , the minimum overall costs ($ov,batch) were found at Ce(0)/Cs(0) = 0.10
(Figure 8.7). Since at this ratio x=100% and Pr=Prmax (Figure 8.7), these minimum
overall costs correspond to the costs that would be obtained in the continuous system
descibed in this section.
In this section it is shown that by introducing a number of assumptions, batch
operation at high concentrations of undissolved substrate can compete with continuous
operation, if both the conversion is 100% and the productivity of the biocatalyst is
maximal, unless mixing becomes rate limiting in batch reaction crystallisers.
CONCLUSIONS
Solid-to-solid bioconversions appear to offer interesting possibilities for biocatalysis at
high substrate concentrations and at low costs in different application areas. Based on the
preparation, the solid-to-solid bioconversions reported in the literature were classified
into four types. To select the most appropriate type for a specific bioconversion, rules of
thumb
Multiphase bioreactor design 256