Bioreactor Design and Operation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 947

To combat evaporation problems, air sparged into fermentors may be pre-humidified by
bubbling through columns of water outside the fermentor; humid air entering the fermentor
has less capacity for evaporation than dry air.
Fermentors are also equipped with water-cooled condensers to return to the broth any
vapors carried by the exit gas. Evaporation can be a particular problem when products or
substrates are more volatile than water. For example, Acetobacter species are used to produce
acetic acid from ethanol in a highly aerobic process requiring large quantities of air. It has been
reported for stirred-tank reactors operated at air flow rates between 0.5 and 1.0 L-air/min/L-
broth 1 that from a starting alcohol concentration of 5%, 30 e 50% of the substrate is lost within
48 h due to evaporation (Akiba T. and Fukimbara, 1973 Fermentation of volatile substrate in
a tower-type fermentor with a gas entrainment process. J. Ferment. Technol. 51. 134 e 141.).

18.9. EFFECT OF IMPERFECT MIXING

So far, we have been based on our analysis on ideal reactors: well mixed in batch and CSTR
for example. This perfect mixing can never be achieved in reality, but it does give us a conve-
nient tool in reactor analysis and design. When scaling reactor up or down, the degree of mix-
ing can have a significant effect, especially for microbes.
One method of examining non-ideal contacting in reactors is through residence time
distribution. While residence time distribution is a useful tool in detecting possible mixing
behaviors, it is of little use in terms of reactor performance analysis. Different contacting
schemes, for example a PFR followed by a well-mixed flow reactor, have the combined resi-
dence time distribution as that if the order of the two reactors is reversed. However, the efflu-
ents out of the last reactor can be different if the reaction kinetics is not of first order.
Ideally, one would solve the Navier e Stokes equation (momentum balance and overall
mass balance), together with mass balance equations, and the reaction kinetics, for a real
reactor. This has the potential of correctly predicting the behavior in a reactor. While we
are in the reach of computational capabilities, still the computational effort is significant.
Traditionally, empirical methods are used at least for fast estimation.
There are two classic approaches to model the non-ideality of mixing in mixed flow
reactors: 1) surface adhesion of cells and 2) compartments of different flow conditions,
including dead zones. Fig. 18.13 shows a schematic of natural compartmentalization of
culture in a chemostat. The mixing flow pattern of stirrers can generate semi segregation
of regions of cultures, in turn the reactor behaviors are affected by the semi-separated region
formation.

18.9.1. Compartment Model
Compartmentalization can occur due to non-ideal mixing. Different parts of the reactor
may behave as if they are isolated from the other parts. Refer to Fig. 18.13 , mass balances
in the top compartment with Monod growth model lead to

m max S 1

K S þS 1 k d

d X 1

d t ¼ k LX aðX 2 X 1 Þð1þa 1 ÞDX 1 þ

X 1 (18.60)