Multiphase Bioreactor Design

(49 )

(50)

Determination of the single-pass conversion in the MBR

The conversion per pass, Xn, is expressed by:

(51)

If R=10,000; Xl=0.9999Xf and then Xn=0.0001Xf
This clearly shows that the conversion per pass of the reaction mixture in the
membrane module, where enzyme is confined, is very small. As an example when the
conversion is 60%, the single pass conversion is only 0.006%. Since it is usually accepted
that less than 1 % conversion is typical of differential reactors, this confirms the
classification of MBR as a differential (mixed) reactor.
The number of cycles, N, with partial recirculation is defined as follows:

(52)

which is given by:

(53)

From Equations 33, 52 and 53 it can be verified that N=R.
The hydraulic residence time corresponds in practice to the time needed for the total
removed of the recirculating liquid. The fact that steady-state conditions can be reached
within one reaction volume permeated through the system indicates a well mixed reactor
type with no hindrance to the passage of products from the reactor to the permeate
(Deeslie and Cheryan, 1981) in agreement with transmission experiments previously
reported (Carvalho et al., 2000b,2001b).

Modelling of the continuous MBR

The comparison of the MBR with general types of reactors leads to similarities with a
plug flow reactor (PFR) since no agitation device was employed. However, if the
recirculation velocity becomes high enough that the conversion degree could be
considered independent of the position in the reactor, then the reactor will assume a
continuous stirred tank reactor (CSTR) behaviour.

CSTR

Multiphase bioreactor design 220