The mass transfer rate between the different phases can be described with the equations
given in Table 12.2; the rates are a combination of mass transfer per gel bead or droplet,
and the number of gel beads or droplets present, respectively. The resulting rates are
given per volume reactor.
The mass transfer coefficient for the transfer of product from medium to organic phase
(K) is a combination of the transfer coefficient from bulk to interface at both sides of the
interface:
The mass transfer coefficients kbead,s, kbead,p, and are calculated with the equation of
Ranz and Marshall (1952); the mass transfer coefficient is calculated with the
equation of Newman (1931); see appendix A for equations. As contact time in the latter
equation, we used the residence time of a droplet (t=Hbed εo/Ud).
Table 12.2 Substrate and product transfer rates
between the different phases
(^) Medium/gel bead Medium/droplet
substrate
no transfer to the droplet
product
(^)
Kinetics
Let us consider bioconversions carried out by either non-growing cells or enzymes
immobilized in -carrageenan gel beads. It is further assumed that there is only one
limiting substrate, which dissolves well in medium and not in the organic solvent.
Medium is water containing all other essential nutrients. Straightforward Michaelis-
Menten kinetics with first order product inhibition are considered:
When the product concentration reaches the toxic concentration ( ) the substrate
consumption rate is zero. More complicated kinetics can be used, but this is the most
simple model to demonstrate the benefits for in situ extraction.
Mass balances
Multiphase bioreactor design 364