Bioreactor Design and Operation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 924

DH c ; S
YF X = S ¼ DH c ;X þYF H =X

(18.12)

Where D H S is the heat of combustion of the substrate, YF X/S is the substrate yield factor,
D H c,X is the heat of combustion of the cells, and YF H/X is the metabolic heat evolved per
gram of cells produced. The equation can be rearranged to yield:

DH c ; S
YF X = S YF X = S DH c ; S

YF H = X ¼ (18.13)

The bioreactor heat transfer surface area required can then be calculated given the heat
transfer fluid temperature and design flow rates.

18.4. SCALE-UP

The preceding sections have discussed the complexities of design parameters for biore-
actors. This section will consider how the complexities impact scaling for bioreactors. If
the height to diameter ratio remains constant, surface to volume ratio dramatically
decreases during scale-up. This changes the contribution of surface aeration and dissolved
carbon dioxide removal in comparison to the contribution from sparging. Physical condi-
tions in a large fermentor cannot exactly duplicate those in a small fermentor if geometric
similarity is maintained. When changes alter the distribution of chemical species in
a reactor or destroy or injure cells, the metabolic response of the culture will differ
from one scale to another. Tabl e 18. 5 demonstrates the interdependence of scale-up param-
eters. In this example, a stirred-tank diameter has been scale-up by a factor of 5. The
height to diameter ratio remained constant. Comparison of four common scale-up
approaches is shown: constant power-to-volume ratios (P 0 /V), constant K L a, constant
tip speed (

u D i , or impeller rotation rate u times impeller diameter D i ), and constant Rey-

nolds Number (Re).
Different scale-up rules can give very different results. Scale-up problems are all related
to transport processes. Relative timescales for mixing and reaction are important in deter-
mining degree of heterogeneity. Scale-up may move from a system where microkinetics
control the system at small scale to one where transport limitations control the system
response at large scale. When a change in the controlling regime takes place, the results
for the small-scale experiments become unreliable in predicting large-scale performance.
One approach to predicting reactor limitations is the use of characteristic time constants
for conversion and transport processes. Typical time constants are: the residence time
or V/Q for flow system, diffusion time scale L 2 /D e , mixing time 4V=ð

R

: uD Þ

for stirred
vessel, conversion time C A /r, etc. Processes with time constants that are small compared
to the main processes appear

1 5

to be essentially at equilibrium. For example, if

ðK L aÞ 1 t O 2 conversion, then the broth would be saturated with O 2 because O 2 supply

is much more rapid than the conversion. Conversely, if the O 2 consumption is of the same
order of magnitude as O 2 supply ½ðK L aÞ 1

, the dissolved O 2 concentra-
tion may be very low. Experimental measurements of DO have shown great variability
in O 2 concentration with some values at zero. This means that cells pass periodically

z t O 2

conversion