is assumed that the bioconversion obeys zero-order kinetics, and that the biocatalyst
inactivates according to first-order kinetics. In the continuous reaction crystalliser,
biocatalyst losses due to wash-out are assumed to be negligible. This means that the
bioconversion rate, and consequently the product supersaturation, can be kept constant by
decreasing the feed flow in accordance with the biocatalyst inactivation rate; in this
manner, the system is operated at pseudo steady-state. The densities of the substrate and
the product are assumed to be equal, so that the volume of the initial substrate suspension
equals the volume of the resulting product suspension.
Box 8.2 shows the calculation of the overall costs per kg of product produced in these
batch and continuous reaction crystallisers with bioconversion as the rate-limiting
process. Although the investment and operating costs are composed of a multitude of
components like depreciation, labour, energy, cooling water, etc., the costs of these
components were all lumped in the hourly price for handling 1 m^3 of suspension in the
crystalliser (pio). According to Van ‘t Riet (1986), pio is in the order of 10–100 $·m−^3 ·h−^1
for small-scale fermenters (1–3 m^3 ), whereas for large-scale fermenters (100–300 m^3 ) pio
is in the order of 1 $·m−^3 ·h−^1. Above 100–300 m^3 the sensitivity decreases and therewith
the need to increase the fermenter volume (Van ’t Riet, 1986). For a reaction crystalliser,
pio is assumed to be of the same order of magnitude. The two downstream-processing
operations, centrifugation and drying, are “volume-dependent” processes; the scale and
related costs are, to a great extent, determined by the volume of the flow to be processed;
and the concentration of the product is less relevant. For that reason, the downstream-
processing price (pdp) is defined on the basis of the hourly costs to process 1 m^3 of
product suspension from the crystalliser. In order to reduce the downstream—processing
costs per kg of product ($dp), probably more than one crystalliser (n) will be coupled to
one centrifugation and drying unit (see Box 8.2). Finally, during downstream processing,
some
Box 8.1 The amount of product in batch and continuous heterogeneous
reaction crystallisers with the bioconversion as rate-limiting process; in
the continuous reaction crystalliser, biocatalyst losses due to wash-out are
assumed to be negligible, and the volume is assumed to be constant and
well-mixed, with equal inflow and outflow rates.In case of first-order biocatalyst inactivation, the active biocatalyst concentration Ce (in
kg·m−^3 ) decreases with time t (in h) and can be expressed as a function of the initial
biocatalyst concentration Ce(0), the first-order rate constant for biocatalyst inactivation kd
(h−^1 ), and time t:
Assume that production is stopped when 1% of the initial active biocatalyst
concentration is left (Ce(t)0=0.01·Ce(0)). For the stop moments tb and tc (in the batch and
the continuous system, respectively) can now be derived:
Multiphase bioreactor design 252