the substrate costs per kg of product $s equal the substrate concentration in the inflow Csi
(in kg·m−^3 ) multiplied with the substrate price ps divided by the product concentration Cp:
The biocatalyst costs per kg of product $e (in $·kg−!) equal the initial amount of active
biocatalyst Ce(0) (in kg·m−^3 ) multiplied with the biocatalyst price pe (in $·kg−^1 ) divided by
the amount of product produced (in kg·m−^3 ):
The investment and operating costs per kg of product $io (in $·kg−^1 ) equal the
investment and operating price pio (in $·m−^3 ·h−^1 ) multiplied with the operational time tb or
tc (in h) divided by the amount of product produced (in kg·m−^3 ):
In case that n reaction crystallisers are coupled to one downstream-processing plant,
the downstream-processing costs per kg of product $dp (in $·kg−^1 ) equal the downstream-
processing price p (^) dp (in $·m−3·h−^1 ) multiplied with the downstream-processing time,
which is assumed to be equal to the operational time of the reaction crystalliser tb or tc (in
h), divided by the amount of product produced (in kg·m−^3 ) in n reactors:
Since the recovery yield will probably be smaller than one, the overall costs per kg of
product $ov (in $·kg−^1 ) equal the sum of the substrate, biocatalyst, investment and
operating, and downstream-processing costs per kg of product, divided by the recovery
yield Yr:
product losses will always occur; in other words, the recovery yield (Yr) will be <1. For
that reason, the overall costs in Box 8.2 are calculated by dividing the sum of all costs by
Yr. The recovery yield is generally known to decrease with the number of unit operations
needed for downstream processing.
Costs Comparison Between Batch and Continuous Operation
Figure 8.6 shows the overall costs ($ov) in a batch reaction crystalliser and in a continuous
reaction crystalliser with a feed flow decreasing in accordance with the biocatalyst
inactivation rate, as a function of the first-order rate constant for biocatalyst inactivation
kd. The investment and operating costs (pio) and the downstream-processing costs (pdp) of
both systems are assumed to be equal.
Multiphase bioreactor design 254