In case of zero-order bioconversion kinetics and assuming that in the batch reaction
crystalliser the maximum attainable product concentration Cp(tb) (see below) has not been
reached, the amount of product produced (in kg·m−^3 ) in the batch reaction crystalliser and
in the continuous reaction crystalliser without biocatalyst losses due to wash-out and with
a feed flow decreasing in accordance with the biocatalyst inactivation rate, can now be
expressed as (with qp is the specific production rate, in kg·kg−^1 ·h−^1 ):
Note that the product concentration in the continuous reaction crystalliser Cp (in
kg·m−^3 ) is constant and can be calculated from the pseudo steady-state mass balance; in
case of no product seeding, Cp can be expressed as a function of qp, Ce(0), the volume of
the suspension in the reactor V (in m^3 ), and the initial flow F(0) (in m3·h−^1 ):
In a batch reaction crystalliser, the maximum attainable product volume at t=tb, VP(tb)
(in m^3 ), is restricted by the volume of the liquid phase V 1 (in m^3 ), the volume occupied by
the biocatalyst Ve (in m^3 ), and the volume of the substrate left at t=tb, Vs(tb) (in m^3 ),
according to (with is the overall yield of product on substrate (in m^3 .m^3 ), xmax is the
maximum attainable conversion (−), and assuming that the densities (in kg·m−^3 ) of the
substrate σs and the product σp are equal):
The amount of product produced in a batch reaction crystalliser Cp(tb) (in kg·m−^3 ) can
now be expressed as:
Box 8.2 The overall costs per kg 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 a batch reaction crystalliser, the substrate costs per kg of product $s (in $·kg−^1 ) equal
the initial substrate concentration Cs(0) (in kg·m−^3 ) multiplied with the substrate price ps
(in $·kg−^1 ) divided by the amount of product produced (in kg·m−^3 ). In a continuous
reaction crystalliser without biocatalyst losses due to wash-out and with a feed flow
decreasing in accordance with the biocatalyst inactivation rate, the bioconversion rate,
and consequently the product concentration in the reactorC (in kg·m−^3 ) is constant and
Solid-to-solid bioconversions 253