Calculations

Before we compare a three-phase fluidised-bed bioreactor with its two-phase analogue,
we will first show some typical results of the model. For these simulations we took a
batch operation strategy for both liquids, with both liquids flowing co-currently, see also
Figure 12.2. Figure 12.1 gives a short overview of the different simulations done. First
we show a typical time course of substrate and product concentration inside the gel bead.
Next the influence of the distribution coefficient and toxic product concentration is
shown. These parameters are system dependent; a toxic product concentration depends on
the micro-organism used, and can hardly be influenced; the distribution coefficient
depends on the two liquids used, but can be influenced by adding specific compounds to
the organic solvent for enlarging the distribution coefficient. The influence of the
dodecane flux is discussed at the end of this section. The parameters that were used
throughout the simulations are summarised in Table 12.3.
In Figure 12.9 a typical time course of substrate and product concentration inside the
gel bead is shown. The maximum substrate conversion rate was 0.01 mol/(m^3 s), the toxic
product concentration was 10 mol/m^3 , and the distribution coefficient was 1000. We took
a medium flux of 1.29×10−^2 m/s and a dodecane flux of 0.91×10−^2 m/s, which resulted in
gel bead hold-up of 0.32 and a dodecane hold-up of 0.093.

Figure 12.9a:

Substrate diffuses into the gel bead and gradually penetrates towards the

centre of the gel bead. As time progresses the concentration increases, the

profile flattens, and a maximum concentration is reached. As time period

increases the concentration decreases as a result of consumption, until all

substrate is converted into product. With the set of parameters used for

calculating the profiles in Figure 12.9a, total conversion

Table 12.3 Overview of parameters used in

simulations

Reactor Constants

nozzles 209

diameter nozzle 0.001 m

reactor height 1 m

reactor diameter 0.06 m

Physical parameters

density medium 998 kg/m^3

density dodecane 742.7 kg/m^3

density gel bead 1065.1 kg/m^3

viscosity medium 0.0009325 Nm/s

viscosity dodecane 0.00135 Nm/s

Design of liquid-liquid-solid fluidised-bed bioreactors 367