Figure 12.9 Profile of substrate (A)
and product (B) concentration in a gel
bead particle. Uc=1.29 cm/s Ud=0.91
cm/s, εs=0.32, εo=0.0925; Xvmax=0.01
mol/m
3s, =10 mol/m
3, m=1000.
t=0:0:3, t=0:0:33, t=0:1:53,
t=0:6:40, t=0:19:0, t=19:6:0,
inside the gel bead. This maximum concentration progresses towards
the centre of the gel bead over time. Hence, after some time, product
concentration is highest in the centre. After some time a maximum
concentration profile is also reached. If at this point in time, there is still
mass transfer between the organic and medium phase, the product
concentration inside the gel bead will decrease. This transfer of product
will continue until equilibrium is reached between medium and organic
phase.Before discussing the influence of the distribution coefficient and toxic product
concentration on the time course of the substrate concentration in the medium phase, and
the time course of product concentration in the medium and organic phase, some general
remarks can be made:
● The time course profile of the substrate concentration in the water phase shows two
processes with a different time constant; the first process is completed after roughly
100 seconds, and is more or less independent of the distribution coefficient and the
toxic product concentration. It can be seen in Figure 12.9b that around that point in
time the gel bead is completely filled with substrate. The second process is the gradual
conversion of substrate to product, and is dependent on the distribution coefficient and
the toxic product concentration.
● Complete conversion of substrate can be reached with some combinations of
distribution coefficient and toxic product concentration.
● If substrate is not completely converted, then the end-product concentration inside the
gel bead and the medium phase is equal to the toxic product concentration.
Design of liquid-liquid-solid fluidised-bed bioreactors 369