213 7

Bioreactor Scale-Up
Ehsan Mahdinia, Deniz Cekmecelioglu, and Ali Demirci

7.1 Introduction – 214

7.2 Scale-Up – 214

7.2.1 Physical Properties – 218
7.2.2 Biochemical Factors – 230
7.2.3 Process Conditions – 231

7.3 Summary – 232

References – 235

The original version of this chapter was revised. The correction to this chapter can be found at
https://doi.org/10.1007/978-3-030-16230-6_11

© Springer Nature Switzerland AG 2019

A. Berenjian (ed.), Essentials in Fermentation Technology, Learning Materials in Biosciences,
https://doi.org/10.1007/978-3-030-16230-6_7
 214 E. Mahdinia et al.

What You Will Learn in This Chapter

Scale-up is the process of expanding a fermentation process from a smaller-scale fermenter,
where operational and production parameters have been studied, to a larger scale. Scale-up
is perhaps one of the hardest and most complex steps of any fermentation process for engi-
neers. Engineers must take into account all aspects that affect the integrity of the fermenta-
tion during the scale-up process. These aspects include physical (namely, heat and mass
transfer phenomena such as oxygen transfer rates and mixing time), biochemical (such as
medium compositions and rheology), and process (such as conditions of the pre-culture and
inoculum) factors. Usually, engineers focus on the most effective factor and take in one of the
common scale-up strategies. A constant height to diameter ratio for the bioreactors is per-
haps the simplest and most common strategy. A constant oxygen transfer rate coefficient is
usually the path for engineers, where oxygen is crucial for the fermentation and oxygen con-
centration limits product secretions. Also, a constant mixing time during the scale-up comes
into play, where engineers usually face a viscous sophisticated fermentation broth. Yet, there
are many other approaches that engineers can take. Often they blend these strategies and
7 improvise a new strategy that serves the fermentation in the larger scale. However, engineers’
ultimate goal is to maximize production and efficiency in plant-scale production.

7.1 Introduction

It would be a misconception to think that an ideal bench-top bioreactor in the lab could
simply be enlarged to hundreds of thousands of liters in a fermentation plant, to give the
same production performances and yields. Surely, every bioprocess engineer wishes it was
that simple! But, will a 100,000-liter bioreactor with yeast converting cornstarch to bio-
ethanol give out exactly the same outcome as the 2-liter bench-top glass bioreactor does?
In this chapter, main factors and issues surrounding bioreactor scale-up in different types
of bioreactors are discussed. Furthermore, we will review mass and heat transfer phenom-
ena with an emphasis on their role in scale-up.

7.2 Scale-Up

A fermentation process development usually starts with lab scale with bench-top
bioreactors (1–50 L) or even shake flasks (100–1000 mL) and microbial cells (few
mL). After optimization has convinced that a bioprocess is feasible, then a pilot-scale
process (50–10,000 L) is designed and implemented to establish the optimal operat-
ing conditions. It is only then, after successful lab- and pilot-scale studies, that the
bioprocess is implemented on a plant scale (> 10,000 L) for commercial productions.
Therefore, the step of setting up a bioprocess from a small to a large scale is called
scale-up. The objective of scale-up is to transfer the optimal conditions obtained in
small-scale bioreactors to the large-scale bioreactor. Scale-up studies are indispens-
able for the development of any fermentation process, so that an appropriate crite-
rion for changing the scale can be established without damaging the kinetic behavior
of microorganisms and hence the process performance. However, the kinetic behav-
ior of microorganisms is affected by local environmental conditions such as nutrient
concentration, pH, temperature, dissolved oxygen, etc. It is well known that microor-
Bioreactor Scale-Up
215 7
ganisms are more sensitive to these environmental variables in a large scale.
Therefore, small-scale trials have the tendency to overpredict the process perfor-
mance at larger scales unless inconsistencies in scale-up are eliminated. This is where
scale-up techniques become crucial. For this purpose, the environmental conditions
affecting the bioprocess must be controlled. This is done by considering the physical,
biochemical, and bioprocess factors. Physical factors include mass and heat transfer
conditions, mixing (agitation) conditions, shear stress regimes, power consumption,
pH, temperature, dissolved oxygen, etc. Biochemical factors mainly are medium com-
ponents and their concentrations along with their physiochemical properties. Finally,
process factors including pre-culture conditions, sterilization quality, and inoculation
ratio also dictate how successful scale-up is implemented [1].
The traditional method for scale-up of a fermentation process involves determining
the reactor geometry, impeller speed, and aeration rate of the large-scale bioreactor on
the basis of the experimental results of the lab-scale bioreactor. The most common
method of scale-up is based on maintaining geometric similarity of bioreactors. Once
the volume of the large-scale bioreactor has been chosen, its geometric parameters,
namely, tank height, tank diameter, and stirrer dimension, can be estimated. The typical
methods of determining impeller speed and aeration rate are dependent on empirical
correlations to keep relevant parameters constant with the change in scale. Evaluation of
impeller speed is based on keeping agitation power input per unit volume (P/V), volu-
metric oxygen mass transfer coefficient (kLa), or impeller tip velocity constant, whereas
the aeration rate is estimated by using those criteria such as keeping equal superficial
gas velocity, specific gas flow rate, or gas flow number. Engineers often keep one or
several parameter(s) constant through scale-up and build their strategy around it.
Typical fermenters are made cylindrical and have a height to diameter ratio (H/D)
between 2/1 and 3/1. This ratio can be kept constant as the simplest scale-up strategy.
However, even that would not be so simple in reality. If diameter is increased by a factor
of 5 and the ratio is kept constant, the vessel volume increases 125-fold, which would
undoubtedly make fermentation in the larger scale quite distinct. Also, there are other
parameters and ratios that can be considered besides the H/D ratio, which can be solely
considered or in combinations. . Table 7.1 presents some of these parameters and how
the rest of them are affected when each is kept constant in scaling up from an 80-L pilot-
scale fermenter to a plant-scale 10,000 L fermenter. As . Table 7.1 indicates, if the
impeller speed is maintained constant, the energy input of the impeller(s) will be 3,125
times higher in the large-scale fermenter. It is safe to presume that such a significant
increase can change markedly the performance of the larger fermenter, e.g., with oxygen
transfer rates, temperature gradient, etc.

Example Problem 7.1

Lysozyme is an anti-bacterial and anti-fungal enzyme widely present in animals, plants, and
microorganisms. Recently, bioprocess engineers have focused on the production of human
lysozyme via genetically modified microorganisms owing to the health concerns associated
with egg lysozyme. The bioprocess parameters of the recombinant strain of Kluyveromyces
lactis were studied in a lab-scale fermenter giving 110 IU/mL of lysozyme within 43 h.
Engineers plan to produce annually 3 × 1012 IU of the enzyme. Thus, what should the main
and inoculum fermenters look like if a H/D = 3 and 20% headspace are assumed and if the
fermenters are to be operated for 11 months per year?
 216 E. Mahdinia et al.

. Table 7.1 Some common scale-up parameters and their after effects

Production fermenter: 10,000 L

Scale-up riterion Designation Pilot-scale Constant, Constant, Constant, Constant,

Fermenter P0/V N N. Di Re
80 L

Energy input P0 1.0 125 3125 25.0 0.2

Energy input/ P0/V 1.0 1.0 25 0.2 0.0016

volume

Impeller rpm N 1.0 0.34 1.0 0.2 0.4

Impeller diameter Di 1.0 5.0 5.0 5.0 5.0

Pump rate of Q 1.0 42.5 125 25.0 5.0

impeller
7 Pump rate of Q/V 1.0 0.34 1.0 0.2 0.04
impeller /volume

Max. impeller N. Di 1.0 1.7 5.0 1.0 0.2

speed (max. shear
stress)

Reynold number 1.0 8.5 25.0 5.0 1.0

NDi2 r / m

Adapted from Shuler et al. [13]

z Solution:
The complete batch period is an important parameter used to determine the number of
batches that can be processed and hence, the total production per year. This time period
includes medium preparation, sterilization time, fermentation time, product harvest, and
cleaning time, which in this case can be assumed to be 10 h. Therefore, each batch will take
roughly 53 h to complete. Thus we have:
3 ´ 1012 IU
The number of units of lysozyme produced per month = = 2.7 ´ 1011 IU / month.
11 months

Volume of the broth required to achieve the projected production per month
IU
2.7 ´ 1011
= month = 2.5 ´ 106 L / month;
110, 000 IU / L

the number of batches per month = 30 days per month × 24 hours per day/53 hours per
batch ≈ 13 batches per month ≈ 156 batches per year; and
volume per batch = 2.5 ´ 106 / 13 = 192, 307 L / batch

Since the volume is high, two bioreactors will be used to produce the projected amount
of lysozyme. Volume of each bioreactor =192,307/2 = 96,154 L
Bioreactor Scale-Up
217 7
Thus, for a working volume of 96,154 L and assuming 20% headspace, the total volume
of the bioreactor is the following:

20
total volume of bioreactor = 96,154 + 96,154 ´ = 115, 385 L or ~ 116 m3
100

Assuming that the height to diameter ratio is 3:1, the reactor dimensions are calculated as
follows:

H =3D

æ D2 ö
V = p çç ÷÷ H
è 4 ø

æ D2 ö
115.385 = p çç ÷÷ ( 3 D )
è 4 ø

D = 3.66 m and H = 11m

The width of baffles can be assumed to be 10% of the diameter of the bioreactor. There-
fore, the width is
10
W= ´ 3.66 = 37 cm
100

Impeller diameter is calculated assuming that it is 20% of the tank diameter.

20
Di = ´ 3.66 = 73 cm
100

As for the pre-fermenter, since the strain used is yeast with a relatively long lag-phase
time, the inoculation percentage is assumed as 5%. The working volume of the pre-
fermenter is thus 4808 L, and with 20% headspace and the total prefermenter volume, we
have:
total volume of bioreactor = 4808 ´ 1.2 = 5770 L or 5.77 m3

H =3D

æ D2 ö
V = p çç ÷÷ H
è 4 ø

æ D2 ö
5.77 = p çç ÷÷ ( 3D )
è 4 ø

D = 1.35 m and H = 4 m
Similarly, the baffle width will be 13.5 cm and impeller diameter will be 27 cm (. Fig. 7.1).
 218 E. Mahdinia et al.

Hh = 0.82 m

Hh = 1.86 m
Head space Head space
volume = 962 L volume =
19231 L
Hw = 3.28 m

Working
volume =
4808 L

Working

Hw = 9.14 m
volume =
7 Dp = 0.27 m 96,154 L

Dt = 1.37 m

Dp = 0.732 m

Dt = 3.66 m

. Fig. 7.1 Schematic drawing of prefermenter and main fermenter for 7 Problem 7.1

7.2.1 Physical Properties

Mass and heat transfer along with mixing conditions (or flow behavior) are the physical
properties that affect scale-up strategies. For instance, in most fermentation processes, the
heat generated by catabolism is taken into account with heat transfer rates in large-scale
bioprocesses. Also, oxygen transfer rate (OTR) that controls oxygen uptake rates (OUR),
especially in aerobic fermentations where oxygen is limiting, is another crucial factor in
scaling up. Here we will discuss the effects of these mass transfer phenomena on scale-up
strategies.

Aeration and Agitation

The oxygen uptake rate (OUR) in a fermentation process is expressed as

OUR = qO2 x = kL a CL* - CL ( ) (7.1)

Bioreactor Scale-Up
219 7

. Table 7.2 Specific oxygen uptake rates for some microorganism and human cells

Organism qO2 (mole O2 kg X−1 h−1)

Bacteria

Escherichia coli 0.9–23

Bacillus acidocaldarius 3.1–31.2

Rhodococcus erythropolis 0.2–4.3

Yeast

Candida bombicola 0.3–1.0

Saccharomyces cerevisiae 8

Hansenula anómala 0.8

Animal cells (adherent cells)

Lung To (Human embryonic lung cells 0.24 mmol h−1(109cells)−1

Conjunctiva (Human eye cells) 0.28 mmol h−1(109cells)−1

Adapted from Shuler et al. [13]

where x is the biomass concentration (g/L), qO2 is the specific oxygen uptake rate
(gmol O2/g. h), CL∗ is the saturation oxygen solubility under the given conditions, and CL
is oxygen concentration at the given time. The combination of these two variables deter-
mines the total oxygen demand of the biomass. . Table 7.2 depicts typical specific oxygen
uptake rates for some common cells.
Note how the uptake rates can be different from strain to strain. Candida bombicola
and Saccharomyces cerevisiae are both yeast strains, but as you can see, Saccharomyces
cerevisiae can consume over eight times as much oxygen under aerobic conditions. Also,
it is interesting to note how bacterial strains can adapt to different conditions and how the
uptake rates differ accordingly. See how the uptake rate can be over 23- and 10-folds for
Escherichia coli and Bacillus acidocaldarius, respectively (. Table 7.2) [2].
The other side of Eq. 7.1, however, represents the oxygen supply to the fermenter,
which, like any other mass transfer phenomenon, is composed of a driving force (CL∗ − CL)
(g/L) combined with a constant value, which is the volumetric oxygen transfer coefficient
kLa (h−1). For the cases where aeration is critical, it is most common to monitor and con-
sider a constant oxygen transfer rate (OTR) throughout the scale-up. This is, for instance,
mostly the case in novel applications of biofilm reactors for value-added products, where
higher cell densities are utilized for higher production rates but at the same time oxygen
diffusion into the biofilm matrices becomes critical. Thus, in such aerobic fermentations,
kLa becomes the crucial factor in scale-up. As it is obvious from Eq. 7.2, kLa is the domi-
nant factor that reflects the effects of agitation, viscosity, impeller(s) and bubbles’ dimen-
sions and shapes, rheological properties of the liquid phase, and even the working volume.
This is due to the fact that the term in the parenthesis (CL∗ − CL) is mainly a function of
temperature and oxygen partial pressure only. Of course, nowadays it is possible and even
 220 E. Mahdinia et al.

preferable to directly measure the dissolved oxygen (DO) levels in bioreactors and simply
maintain them through the scale-up process; yet, this is not usually the option that biopro-
cessing engineers prefer. Rather, engineers follow a constant kLa coefficient, which they
can empirically estimate using Eq. 7.2 [8].
a
æ Pg ö
kL a = k ç ÷ ( vs )b ( N )g (7.2)
è Vw ø

where k, α, β,and γ are empirical constants, Pg is the gassed power output, Vw is the work-
ing volume, vs is the superficial exit gas velocity, and N is the speed of impeller(s). The
constant k in the equation for lab-scale stirred-tank bioreactors with Newtonian fluid
regimes is 0.001–0.005 for kLa expressed in mmol/L-h-atm, depending on the geometry of
the vessel and impeller(s). In common small-scale reactors, α = 0.4 and β = γ = 0.5 are
good assumptions. As it can be seen, besides the aeration rates, the agitation rates also play
a direct effect on the oxygen transfer rate and mass transfer phenomena in the process in
7 general. Again, in small-scale Newtonian regimes, the dependency on agitation rates is
negligible and therefore the (N)0.5 term is eliminated. Then the constant term varies even
Pg
more from geometry to geometry. The term can be defined as the volumetric agita-
Vw
tion power output. Sometimes, it is more convenient to use a scale-up model based on
keeping this parameter constant, since the data obtained in bench-top or pilot-scale fer-
menters are often available and can be easily used for scale-up. The other reason is that
Pg
other effective rheological properties such as viscosity are incorporated in the term .
Vw
When there is a need for a higher DO level, engineers choose either a stronger agitator
motor or a smaller working volume. Such a model simplifies the scale-up strategy; how-
ever, there is still a need to have an estimate of the required power input. It is usually easier
to determine the power input for a similar ungassed fermenter and then empirically tran-
scend it to the aerated vessel. For this purpose, an empirical equation such as the following
is used:
0.45
æ P 2 Nd 3 ö
Pg = K ç u 0.56 ÷ (7.3)
ç Q ÷
è ø

where K is a constant, Pu is the power required in the ungassed vessel, d is the impeller(s)
diameter, and Q is the volume of air supplied per minute per volume of the liquid in the
vessel for which the unit is often referred to as vvm. The constant term in this equation is
strictly dependent on the geometry of the tank and impeller(s) and the operational
conditions.
Although these empirical correlations give fair estimations on how oxygen uptake
rates are affected by scale-up, they are only estimations. For many cases of Newtonian or
non-Newtonian systems, these correlations are unable to cope with the significant effects
resulting from changes in viscosity that usually occur in fermentation processes or
medium compositions. For such effects unfortunately, it is not easy to make such estima-
tions. Also, many times when viscosity increases to high levels as the fermentation process
proceeds, engineers simply water down the composition to counter it.
Bioreactor Scale-Up
221 7
Moreover, the presence of salts and surfactant or antifoam agents in the fermentation
broth, which is very common, not only can significantly affect kLa but also affect oxygen
solubility in the broth. Yet, the driving force term in Eq. 7.1 (CL∗ − CL) is not controllable
but providing good mixing to avoid the increasing liquid film resistance around the gas
bubbles or keeping the operating temperatures as low as possible will work. The example
problems below show how kLa can be measured in real-time fermenters to help the scale-
up or design strategies.

Example Problem 7.2

Assume you have a 2-L bench-top bioreactor for production of L-asparaginase by Candida
utilis and you would like to scale it up to a pilot scale of 100 L using a conventional medium
composition. You have two different impellers. How can you determine which impeller is
better for aerobic fermentation?

z Solution:
Candida utilis is a yeast that excretes the enzyme L-asparaginase under highly aerobic
conditions. It is safe to presume that oxygen transfer rates are limiting and thus critical in
this case. Therefore, whichever impeller that provides higher kLa values with the same
power inputs is the winner. Also we must determine kLa values in both bioreactors.
There are basically three methods for determining kLa in a bioreactor: unsteady-state,
steady-state, and the sulfite method.
In the unsteady-state method, we fill fermenters with the medium (or as an easier esti-
mation with DI water) and accurately measure the CL∗ and CL using a calibrated DO
probe. By sparging the medium with nitrogen for an ample period of time, we make sure
that there is no oxygen left in it. At this time CL is zero. Then, we start sparging it with air
and measure CL values over time until we eventually reach CL∗. If mixing is sufficiently
robust, whichever impeller enables us to reach the C∗value faster is essentially better.
Nonetheless, we have

dCL
dt
= k L a CL * - CL ( ) (7.4a)

and so knowing that CL∗ is constant with constant temperature we have:

(
- d CL * - CL ) = k a dt (7.4b)
L
(C L
*
- CL )
thus

(
ln CL* - CL = - kL a t ) (7.5)

Therefore, a plot of ln(CL∗ − CL) versus time can be drawn, whose slope is the kLa term.
In other words, the steeper slope means higher kLa values.
Similarly, in the steady-state method, the fermenter is filled with the broth and oxygen
is monitored as fermentation takes place. Oxygen is uptaken by the biomass and at the
same time it is provided by aeration. Thus, from Eq. 7.1 we have

OUR
kL a = (7.6)
CL * - CL
 222 E. Mahdinia et al.

Assuming that the fermentation process is slow enough that the OUR values at the
time of measurements are constant, it is possible then to measure the OUR value in the
bioreactor or externally in a respirometer, and then CL∗ and CL must be accurately mea-
sured at the same time to calculate the respective kLa value. However, this requires exact
measurement of OUR and oxygen concentrations. Moreover, if later on we decide to
scale up the process to industrial-scale fermenters with tens or hundreds of thousands
of liter volumes, turning the huge fermenter into a real-time respirometer is easier said
than done! In such large volumes, even oxygen concentration measurements become a
challenge when the mixing is never ideal anymore and the liquid depth and hydrostatic
pressure are significant at the sparger level at the bottom making the CL∗values signifi-
cantly different at the bottom compared to the headspace zones.
As a result of such complications, the more common sulfite method comes into play,
where the fermenter is filled with the medium along with sulfite anions ( SO32- ) . Sulfite
anions irreversibly and readily react with dissolved oxygen and are converted to sulfate
( SO 2-
4 ) until CL reaches zero.
7 Cu 2+
2SO32 - + O 2 ® 2 SO 42 -

Then, we start aerating the mixture and as oxygen is dissolved, it is instantly con-
sumed. As the stoichiometry of the above reaction dictates, the rate of sulfate formation
doubles the rate of oxygen consumption and considering Eq. 7.4a we have

dCSO4
= 2 kL a C * (7.7a)
dt

and

dCSO4 / dt
kL a = (7.7b)
2 C*

Thus, by monitoring the sulfate concentration in the mixture over a short period of time
and calculating the rate of change we can calculate the kLa value. Note that determining
sulfate concentration in the mixture is essentially easier than monitoring dissolved oxygen
concentrations or finding OUR values, but, obviously the sulfite method cannot be applied
to a real-time fermentation process unlike the steady-state method [5].

Example Problem 7.3

In order to scale up a prototype fermenter design for citric acid fermentation using Yarrowia
lipolytica from bench-top to pilot scale, we wish to use a constant kLa approach. To obtain
information about the coefficient, the bench-top bioreactor was filled with DI water at
30°C. Nitrogen was sparged into the vessel with 500 rpm agitation to take out all the dis-
solved oxygen. Then, air was introduced instead of nitrogen and agitation was set at
200 rpm and another time at 400 rpm. Percentage of DO saturation was recorded versus
time as shown in . Table 7.3. Using these findings and oxygen solubility, determine the kLa
values for each agitation regime.
From the oxygen solubility table, we can see that CL∗ = 7.559 mg/L. Therefore, the data
for 200 and 400 rpm can be processed to prepare . Tables 7.4, 7.5, and 7.6, respectively.
Bioreactor Scale-Up
223 7

. Table 7.3 Diffused oxygen measurements within

10 minutes of aeration with 200 rpm and 400 rpm agitation

Time (min) %DO (200 rpm) %DO (400 rpm)

0 0.0 0

0.5 21.1 34.6

1 37.5 57.3

1.5 47.9 71.6

2 56.5 82.5

2.5 63.7 89.3

3 69.7 92.9

3.5 74.7 94.7

4 78.5 96.1

4.5 82.1 97.3

5 85.3 97.8

5.5 87.8 98.2

6 89.8 98.6

6.5 91.5 99.0

7 92.9 99.2

7.5 94.1 99.5

8 95.0 100.0

8.5 95.9 100.0

9 96.8 100.0

9.5 97.3 100.0

10 97.8 100.0

Then, plotting CL and ln(CL∗ − CL) changes versus time at 200 and 400 rpm we have:

8
7
6
CL (mg O2/L)

5
4
400 rpm
3 200 rpm
2
1
0
0 1 2 3 4 5 6 7 8 9 10
Time (min)
 224 E. Mahdinia et al.

3
2
1
ln (C*-CL)

0
0 1 2 3 4 5 6 7 8 9 10
-1
-2
-3 400 rpm
-4 200 rpm

Time (min)

and from Eq. 7.4b, for 200 rpm, we have:

7 kL a = 0.3714 min -1 or 22.28 h -1

And for 400 rpm we have

kL a = 0.6828 min -1 or 40.96 h -1

As it can be seen, by doubling the agitation rate from 200 to 400 rpm, the kLa coefficient and
thus OUR is almost doubled as well. This is the simplest example of a bench-top bioreactor
with DI water. Things can be much more complex as size increases and complex broth com-
positions are used. Still, this example clearly shows how complicated operational physical
properties can be formed in a bioreactor, and all without exception must be taken into
account carefully while designing or scaling up a fermentation process. See how nicely the
200 rpm points in the second plot fall into a straight line and 400 rpm ones don’t… why??

. Table 7.4 Solubility of oxygen in water exposed to water-saturated air at atmospheric

pressure (101.3 kPa)

Temperature (°C) Oxygen Solubility mg/L

Chlorinity: 0 5.0 10.0 15.0 20.0 25.0

0.0 14.621 13.728 12.888 12.097 11.355 10.657

1.0 14.216 13.356 12.545 11.783 11.066 10.392

2.0 13.829 13.000 12.218 11.483 10.790 10.139

3.0 13.460 12.66 11.906 11.195 10.526 9.897

4.0 13.107 12.335 11.607 10.920 10.273 9.664

5.0 12.770 12.024 11.320 10.656 10.031 9.441

6.0 12.447 11.727 11.046 10.404 9.779 9.228

7.0 12.139 11.442 10.783 10.162 9.576 9.023

8.0 11.843 11.169 10.531 9.930 9.362 8.826

9.0 11.559 10.907 10.290 9.707 9.156 8.636

Bioreactor Scale-Up
225 7

. Table 7.4 (continued)

Temperature (°C) Oxygen Solubility mg/L

10.0 11.288 10.656 10.058 9.493 8.959 8.454

11.0 11.027 10.415 9.835 9.287 8.769 8.279

12.0 10.777 10.183 6.621 9.089 8.586 8.111

13.0 10.537 9.961 9.416 8.899 8.411 7.949

14.0 10.306 9.747 9.218 8.716 8.242 7.792

15.0 10.084 9.541 9.027 8.540 8.079 7.642

16.0 9.870 9.344 8.844 8.370 7.922 7.496

17.0 9.665 9.153 8.667 8.207 7.770 7.356

18.0 9.467 8.969 8.497 8.049 7.624 7.221

19.0 9.276 8.792 8.333 7.896 7.483 7.090

20.0 9.092 8.621 8.174 7.749 7.346 6.964

21.0 8.915 8.456 8.021 7.607 7.214 6.842

22.0 8.743 8.297 7.873 7.470 7.087 6.723

23.0 8.578 8.143 7.730 7.337 6.963 6.609

24.0 8.418 7.994 7.591 7.208 6.844 6.498

25.0 8.263 7.850 7.457 7.083 6.728 6.390

26.0 8.113 7.711 7.327 6.962 6.615 6.285

27.0 7.968 7.575 7.201 6.845 6.506 6.184

28.0 7.827 7.444 7.079 6.731 6.400 6.085

29.0 8.691 7.317 6.961 6.621 6.297 5.990

30.0 7.559 7.194 6.845 6.513 6.197 5.896

31.0 7.430 7.073 6.733 6.409 6.100 5.806

32.0 7.305 6.957 6.624 6.307 6.005 5.717

33.0 7.183 6.843 6.518 6.208 5.912 5.631

34.0 7.065 6.732 6.415 6.111 5.822 5.546

35.0 6.950 6.624 6.314 6.017 5.734 5.464

36.0 6.837 6.519 6.215 5.925 5.648 5.384

37.0 6.727 6.416 6.119 5.835 5.564 5.305

38.0 6.620 6.316 6.025 5.747 5.481 5.228

39.0 6.515 6.217 5.932 5.660 5.400 5.152

40.0 6.412 6.121 5.842 5.576 5.321 5.078

41.0 6.312 6.026 5.753 5.493 5.243 5.005

(continued)
 226 E. Mahdinia et al.

. Table 7.4 (continued)

Temperature (°C) Oxygen Solubility mg/L

42.0 6.213 5.934 5.667 5.411 5.167 4.933

43.0 6.116 5.843 5.581 5.331 5.091 4.862

44.0 6.021 5.753 5.497 5.252 5.017 4.793

45.0 5.927 5.665 5.414 5.174 4.944 4.724

46.0 5.835 5.578 5.333 5.097 4.872 4.656

47.0 5.744 5.493 5.252 5.021 4.801 4.589

48.0 5.654 5.408 5.172 4.947 4.730 4.523

49.0 5.565 5.324 5.094 4.872 4.660 4.457

7 50.0 5.477 5.242 5.016 4.799 4.591 4.392

© Copyright 1999 by American Public Health Association, American Water Works Association,
Water Environment Federation

. Table 7.5 Oxygen transfer rate terms for 200 rpm

Time %DO CL C L∗ − C L ln(CL∗ − CL)

0.0 0.0 0.000 7.559 2.023

0.5 21.1 1.593 5.966 1.786

1 37.5 2.838 4.721 1.552

1.5 47.9 3.618 3.941 1.371

2 56.5 4.269 3.290 1.191

2.5 63.7 4.813 2.746 1.010

3 69.7 5.267 2.292 0.830

3.5 74.7 5.645 1.914 0.649

4 78.5 5.935 1.624 0.485

4.5 82.1 6.203 1.356 0.304

5 85.3 6.451 1.108 0.103

5.5 87.8 6.634 0.925 −0.078

6 89.8 6.787 0.772 −0.258

6.5 91.5 6.914 0.645 −0.439

7 92.9 7.021 0.538 −0.619

7.5 94.1 7.110 0.449 −0.800

Bioreactor Scale-Up
227 7

. Table 7.5 (continued)

Time %DO CL C L∗ − C L ln(CL∗ − CL)

8 95.0 7.184 0.375 −0.981

8.5 95.9 7.246 0.313 −1.161

9 96.8 7.317 0.242 −1.418

9.5 97.3 7.357 0.202 −1.599

10 97.8 7.390 0.169 −1.779

. Table 7.6 Oxygen transfer rate terms for 400 rpm

Time %DO CL C L∗ − C L ln(CL∗ − CL)

0.0 0 0.000 7.559 2.023

0.5 34.6 2.612 4.947 1.599

1 57.3 4.331 3.228 1.172

1.5 71.6 5.412 2.147 0.764

2 82.5 6.236 1.323 0.280

2.5 89.3 6.750 0.809 −0.212

3 92.9 7.022 0.537 −0.622

3.5 94.7 7.158 0.401 −0.915

4 96.1 7.264 0.295 −1.221

4.5 97.3 7.355 0.204 −1.589

5 97.8 7.393 0.166 −1.794

5.5 98.2 7.423 0.136 −1.995

6 98.6 7.453 0.106 −2.246

6.5 99.0 7.483 0.076 −2.582

7 99.2 7.499 0.060 −2.806

7.5 99.5 7.521 0.038 −3.276

8 100.0 7.559 0.000 –

8.5 100.0 7.559 0.000 –

9 100.0 7.559 0.000 –

9.5 100.0 7.559 0.000 –

10 100.0 7.559 0.000 –

 228 E. Mahdinia et al.

Another common parameter for scale-up is the impeller power consumption per volume
P/V. This strategy is perhaps the oldest scale-up strategy that has been used ever since
penicillin production revolutionized the early twentieth century. Usually a ratio of 1.0:2.0
KW/m3 is simply maintained. However, such simplification in massive scale-up opera-
tions leads to significant energy inefficiency, which is certainly unacceptable. Therefore,
more complex alterations emerge. For instance, instead of a constant P/V ratio, impeller
power number (Np) is defined, measured, and held constant.

2p ( M - M d )
Np = (7.4)
r N 2d 5

In the above equation, M is torque (with full working volume of DI water) (N·m), Md is torque
(empty vessel) (N·m), ρ is broth density, N is agitation speed (rpm), and d is impeller diameter.
Note that as the impeller gets larger, the power number decreases drastically. The only perqui-
site to this strategy is that the torque must be carefully measured and it is important to measure
7 the net impeller torque without bearing resistance. A constant power number scale-up strat-
egy in some cases may prove more energy efficient than the constant P/V ratio strategy.
Nevertheless, the power number can be obtained alternatively to calculate the P/V ratio as:

Np r N 3d 5
P /V = (7.5)
V

As the flow regimes change with the Reynolds number, the power number also changes
empirically for different impeller geometries. . Figure 7.2 shows the dependency of power

100
60
40 1
2,3
20
4
10 5
P 6 1
Np = 4 2
N3d5r
2 3

1 4
06
04 5
02
01
2 4 6 10 2 4 6 102 2 4 6 103 2 4 6 104 2 4 6 105
Nd2r
1-Curve blade turbine Re =
2-Straight blade turbine m
3-Pithed blade turnbine
4-High pitch propeller
5- Low pitch propeller

. Fig. 7.2 Power number versus Reynolds number in a model bioreactor. (Adapted from Bates et al. [3])
Bioreactor Scale-Up
229 7
number in model bioreactors with some most common impellers. Such a graph is handy
for engineers to estimate the power input needed in the large-scale fermenter based on the
Reynolds number.

Case Study 7.1

Xanthan gum is a natural polysaccharide heavily used in food and cosmetic industries for a
number of important reasons, including emulsion stabilization, temperature stability, compatibil-
ity with food ingredients, and its pseudoplastic rheological properties [6]. Xanthan gum is
produced by the bacterium Xanthomonas campestris through aerobic fermentation. Shortly after
the fermentation starts, the gum production excels and the broth viscosity increases dramatically.
Although, the produced gum needs to be dewatered and dried in the downstream processing,
engineers have no choice other than adding water to the broth to dilute it so that the heat and
oxygen transfer and even agitation are not impaired by the viscosity jump. It is possible to defeat
viscosity to some extent, by heating the beer up in the downstream steps, but it is not feasible
during the fermentation since the temperatures for optimum production are around 30°C. Now
can you imagine how such a viscosity jump that deeply affects production itself may affect your
scale up strategy? Which strategy would be the best?

Shear Rate
Shear stress in a fermenter depends on the rheological properties of broth, which are
defined for broth viscosity during the fermentation process and shear rate, which is a
function of impeller geometry and impeller rotational speed. For Newtonian fluids they
are defined as
t ave = mn ave (7.6)

n ave = k N (7.7)

where τave is the average shear stress between impeller blades and fermenter inner wall
(N. m−2), μ is dynamic viscosity (N. s. m−2), νave is the average shear rate between impeller
blades and fermenter inner wall (s−1), κ is a constant that depends on the system geometry
only for Newtonian fluids, and N is the impeller rotational speed (rps). These equations
can now estimate the shear rates in agitated systems with viscosities similar to water and
with perfect Newtonian behaviors. With deviations from these conditions, which is usu-
ally the case in most fermentation broths, complex equations must be used. Most mold
strains due to filamentous growth and mammalian cells are very sensitive to shear rates for
which there is a threshold. Higher shear rates are simply fatal or reduce product yields.
Thus, in these cases, the highest feasible shear rate is calculated and kept constant, which
depends on the impeller tip speed and thus on the agitator speed. Since agitation is critical
in fermentation, especially in aerobic and/or viscous conditions, increasing the impeller
diameter or the number of impellers may provide robust agitation without creating over-
stress. The case study below shows that overstress may not always be a conspicuous matter
of life and death and yet very problematic [14].

Case Study 7.2

Bacillus subtilis natto is a highly aerobic Gram-positive bacteria that excretes menaquinone-7, a
potent form of vitamin K, under aerobic conditions [10]. This form of vitamin K2 is the most
expensive vitamin. Thus, this bacterium has been used to produce supplementary vitamin K2 for
decades. Scientists have discovered that this strain has a high potency to form biofilm matrices
 230 E. Mahdinia et al.

that have a positive effect on vitamin secretion. Furthermore, engineers are working to perform
the fermentation in agitated and aerated liquid states, since conventional static solid states are
not easy to scale up. Although robust agitation and aeration do not affect growth or metabolism
in B. subtilis but actually improve them, the shear stress caused by them decimates the biofilm
formations and therefore knocks out vitamin secretion. To overcome this dilemma, engineers are
working on biofilm reactors where mature biofilm formations are allowed to form on suitable
support surfaces, which would be resilient enough to tolerate robust agitation and aeration up to
feasible extents. The downside to biofilm reactors, however, is that oxygen molecules need to
diffuse all the way into the biofilm to reach the production sites [4]. Would optimization methods
be helpful to find optimum conditions for maximum vitamin secretion and solve such trade-off
equations? How do these considerations come into play when optimum conditions in lab-scale
studies are supposed to be scaled up?

Mixing Time
For highly viscous, non-Newtonian broths, the conventional equations are not valid. In
7 these cases, robust agitation becomes the ultimate goal. For instance, when acid or base
solutions, antifoam agents, or fed-batch ingredients are to be added to the broth periodi-
cally, it is essential to have robust mixing. Providing robustness with a larger impeller or
higher numbers of impellers is easier and yet much less energy efficient. Alternatively, we
can opt for a taller fermenter where the impeller diameter does not need to increase for
robustness; however, a deep stack of broth can definitely be more troublesome. For exam-
ple, oxygen solubility at the bottom of the deep fermenter near the sparger will be signifi-
cantly higher than the surface. This inevitably not only creates an undesirable oxygen
gradient, but also significantly increases the gas power input (P/Vα d3) and thus power
requirements become prohibitive in large-scale fermenters. Thus, there is a trade-off. In
this case, engineers may choose to scale up based on equal mixing or blending time.
Mixing time can be defined as

V
tm = (7.8)
Nd 3

where V is the working volume (m3), N is the impeller rotational speed (rpm), and d is the
impeller diameter (m).

7.2.2 Biochemical Factors

So far, we have discussed how fermentation at a large scale can be distinct from a lab scale,
backing it up through physical and design point of views. But that is not all of it. The
media compositions used for plant production scarcely include any pure or lab-grade
components. Rather, economy is engineers’ first priority and therefore low-grade abun-
dant and natural resources are used. For instance, if scientists find out that glucose is the
key nutrient to producing an enzyme, they should undertake a series of lab-scale experi-
ments to figure out how glucose affects enzyme production and what the optimum condi-
tions are and perhaps use pure glucose only for clarity purposes of the results. Yet, it is
quite impractical to use pure glucose for plant-scale production, because it would be too
expensive. It is replaced with either unrefined molasses or unrefined dextrose extracts
from inexpensive sources. Now, the best way to tackle such a situation is to carry out some
Bioreactor Scale-Up
231 7
lab experiments using the exact plant-scale composition and thus reiterate the conditions.
But, even this may not be sufficient as the composition, purity, and physical properties of
these natural resources may change from batch to batch or over time. The emergence of a
trace toxic or inhibitory component in the resources may halt the process or result in
changes in purity, and amounts of the nutrients may take the metabolic paths sideways.
Therefore, engineers do keep lab-scale fermentation studies on the side even after the
plant starts its work specifically to monitor and tackle such unprecedented changes. The
incoming nutrient purity and composition are monitored using analytical chemistry tech-
niques such as high performance liquid chromatography (HPLC) or gas chromatography
(GC), and changes in the composition of the working medium are implemented accord-
ingly to keep the fermentation process smooth [7, 11].

7.2.3 Process Conditions

Processes that are undertaken prior to inoculation of a plant-scale fermenter and officially
starting the production may affect how well the fermentation continues. Basically, these
processes are sterilization of the working medium and pre-culture fermentation to pro-
duce the inoculum. Sterilizing the working medium for a large fermenter is quite different
from the lab-scale counterpart. For the large-scale medium, a longer sterilization time is
required to ensure a complete sterilization, as heat transfer rate into the large fermenter is
always lower. Also, as mentioned earlier, the industrial medium may contain complex
components. As sterilization temperatures reach 121.1 °C (250 °F), many spontaneous
chemical reactions take place between these components (i.e., reducing sugar and amino
groups end up with Maillard reactions). These unwanted reactions not only degrade
valuable nutrients in the medium, but also may create substances which are harmful to
microorganisms and biosynthesis of the product. Thus, efficiency of the fermentation
process is lowered. Engineers often sterilize different medium components such as carbon
sources, nitrogen sources, and minerals separately to minimize these undesirable side
reactions. Usually growth rates (which are very important) in the media that are sterilized
as a whole are significantly lower than those that are sterilized separately. However, before
deciding to sterilize components separately, studies on the lab scale must prove it to be
practical [16].
Another factor that affects the growth and condition of the main fermentation process
is the condition of the inoculum. Engineers always keep a keen eye for the integrity and
condition of the inoculum. Cell concentration, age, and phase of the inoculum cells even
by an hour, morphology of the cells, and the metabolic trait from which the inoculum
comes are imperative parameters that can determine the success or failure of a fermenta-
tion process [12].
Therefore, it’s good to remember the following tips:
5 If there are not enough cells in the inoculum despite a constant inoculation volumet-
ric ratio, lag phase of the main fermentation will be prolonged. This not only imposes
higher operational costs but also may decrease the product yields drastically as the
optimum window for harvest is lost.
5 Usually, the inoculum cells are best when they are in their late exponential phases of
the growth (e.g., for enzyme production). This is true for all scales of production, and
that is when they should be harvested from the pre-cultures.
 232 E. Mahdinia et al.

5 The number of pre-cultures may have significant effects on how fast and robust the
inoculum is. This is a sensitive effect because the number of pre-cultures needed for a
large fermentation process may be several more than a lab-scale one.
5 For fermentation of filamentous microorganisms like fungi, in addition to all of the
above parameters, it is also important whether the inoculum is in pellet or filamen-
tous form as metabolism in these forms is quite distinct especially for biosynthesis of
complex materials such as enzymes and other secondary metabolites. The case study
below investigates these effects in an important industrial application of filamentous
strains [17].

Case Study 7.3

Citric acid is a weak organic acid that naturally occurs in citrus fruits and gives them the special
taste. It has a very vast and diverse range of industrial applications in food and drink, detergent,
cosmetic, pharmaceutical, dietary supplement, and even steel industries. For over a century,
7 bioprocess engineers have produced citric acid using filamentous bacterial and fungal strains
such as Aspergillus niger. They have learned by experience that broth pelleting and morphology
in the seed stages strongly influence the outcomes. For instance, it was found that broth
morphology influences broth thickness, which affects not only mixing but also aeration
resistance and coating of instrument sensors, which can be a huge problem, especially in
large-scale fermenters. Thus, they learned that identification and consideration of this phenom-
enon, which has close correlations to shear in the pre-cultures and the main fermenter, in
developing scale-up conditions and interpreting scale-up behavior can be extremely beneficial
for better production [9, 15].

7.3 Summary

The ultimate goal in fermentation process development is the large-scale commercial

implementation. Plant-scale fermenters give us the opportunity to produce numerous
valuable products through microbial fermentation. Before plant-scale fermenters are
designed and put to work, bioprocess engineers must closely study and optimize the
process in lab-scale and pilot-scale fermenters. An optimized lab-scale process can
then be transferred to pilot scale following the established scale-up strategies. In doing
so, engineers must consider all factors that make the fermentation process distinct in
larger scales. These factors primarily include physical properties of the broth and the
fermenter itself such as heat and mass transfer (especially oxygen transfer in aerobic
fermentations) that are affected by agitation, aeration, broth rheology and fermenter
geometry and design. Secondly, the broth or medium biochemical properties such as
deviations from ideal and pure compositions in small-scale fermentations followed by
the physical factors are also an aspect to consider. Finally yet importantly are process
conditions that include sterilization step(s) and inoculum conditions. Considering
these factors, the scale-up strategies can simply be based on a constant height to diam-
eter ratio (H/D) up to constant impeller power input to working volume ratio (P0/V),
power number (Np), or in most aerobic fermentations a constant volumetric oxygen
transfer coefficient (kLa). As process conditions get more complicated and the rheo-
logical properties of the medium deviate from ideal Newtonian fluids, a combination
of these strategies may be considered. A constant H/D ratio is perhaps the simplest
Bioreactor Scale-Up
233 7
scale-up strategy and can easily miss some special cases. On the other hand, keeping a
constant P0/V ratio is perhaps the most common scale-up strategy due to good flexibil-
ity and simplicity and yet is usually not energy efficient and so following a constant Np
may prove a better option. In aerobic fermentation, where oxygen mass transfer rates
prove to be limiting, engineers try to provide the best aeration efficiency by implement-
ing a constant kLa strategy. In some more exclusive cases, where shear rate is crucial,
such as fermentation with filamentous microorganisms, engineers focus on agitation
rates and impeller designs to carry out a successful scale-up. Of course, there may be
more specific combinations and conditions that can be applied to pre-defined cases;
yet, in this chapter, the most common and basic scale-up strategies that have been
implemented by bioprocessing engineers are covered.

z Problems
1. Which of the H/D ratios of a fermenter is better for oxygen transfer efficiency, a
tall-narrow or short-squat fermenter? Briefly explain.
2. A stirred tank reactor is to be scaled up from 0.1 m3 to 10 m3. The dimensions of the
small tank are Dt = 0.64 m, Dimpeller = 0.106 m, and N = 470 rpm. Thus:
(a) Determine the dimensions of the large tank (DL, Dimpeller, HL) by using geometric
similarity.
(b) What would be the required rotational speed (N) of the impeller in the large tank
for a constant impeller speed taken as N × Dimpeller = constant?
3. A strain of Azotobacter vinelandii is cultured in a 15-m3-stirred fermenter for the
production of alginate. Under current conditions, the mass transfer coefficient, kLa, is
0.18 s−1. Oxygen solubility in the fermentation broth is 8 × 10−3 kg/m3. The specific
oxygen uptake rate is 12.5 mmol/g. h. What is the maximum cell density in the
broth?
4. A value of kLa = 30 h−1 has been determined for a fermenter at its maximum practi-
cal agitator rotational speed with air being sparged at 0.5 L gas/L reactor volume/
min. E. coli with qO2 of 10 mmol O2/g dry wt./h are to be cultured. The critical
dissolved oxygen concentration is 0.2 mg/L. The solubility of oxygen from air in the
fermentation broth is 7.3 mg/L at 30°C. Thus:
(a) What maximum concentration of E. coli can be sustained in this fermenter under
aerobic conditions?
(b) What concentration could be maintained if pure oxygen was used to sparge the
reactor?
5. E. coli has a maximum respiration rate, qO2max, of about 240 mg O2/g dry wt./h. It is
desired to achieve a cell mass of 20 g dry wt./L. The kLa is 120 h−1 in a 1000 L reactor
(800 L of working volume). A gas stream enriched in oxygen is used (i.e., 80%
oxygen) which gives a value of CL∗ = 28 mg/L. If oxygen becomes limiting, growth
and respiration become slow. For these conditions it is safe to presume:
qO 2 max CL
qO 2 =
mg
0.2 + CL
L

where CL is the dissolved oxygen concentration in the fermenter. What is CL when the
cell mass is at 20 g/L?
 234 E. Mahdinia et al.

6. Calculate the oxygen transfer rate and kLa of an air-water system in a fermenter, in
which the experimental work was carried out with a working volume of 20 L of water
at 30°C. The pressure inside the fermenter was kept constant at 5 psig while two
agitation rates of 100 and 300 rpm were employed. The results for the two runs are
presented in the table below.
Time %DO Time % DO

100 rpm 300 rpm 100 rpm 300 rpm

0 3.2 0 5.5 79.2 99.2

0.5 6.2 25.7 6 82.2 99.4

1 16.8 65.3 6.5 85 100

1.5 27.1 83.9 7 87.3 100

2 37 91.8 7.5 89.2 100

7 2.5 45.5 95 8 90.9 100

3 52.9 96.7 9 93.7 100

3.5 59.3 97.6 10 95.6 100

4 64.8 98.2 11 97.1 100

4.5 71.3 98.6 12 98.2 100

5 75.6 98.9 13 99.1 100

7. Bacterial fermentation was carried out in a bioreactor containing broth with average
density of 1200 kg/m3 and viscosity of 0.02 N.s/m2. The broth was agitated at 90 rpm
and air was introduced through the sparger at a flow rate of 0.4 vvm. The fermenter
was equipped with two sets of flat-blade turbine impellers and four baffles. Tank
diameter is Dt = 4 m, impeller diameter is Di = 2 m, baffle width is Wb = 0.4 m, and
the liquid depth is H = 6.5 m. Therefore, determine:
(a) Ungassed power, P
(b) Gassed power, Pg
(c) KLa
8. A medium containing 105 spores per liter needs to be sterilized before starting the
fermentation. By assuming that the death rate for spores (kd) at 121 °C is 0.903 min−1,
determine the sterilization time for 10 L and 10,000 L fermenters for 10−3 probability
of failure. Ignore effects of heat-up and cool-down periods.
9. Suppose we want to produce vitamin K from Bacillus subtilis natto in a fed-batch
biofilm reactor using glycerol as a limiting nutrient. The biofilms are placed on
straight-blade Rushton turbine rings. Since the vitamin is produced in the biofilm
matrices; in order to preserve the biofilm formations from overstress, we need to
hold Reynold numbers below 10,000. Since the glycerol medium is quite viscous,
engineers have suggested a constant mixing time strategy to scale up from a 2-L
bioreactor to a 10,000-L pilot-scale one. If the mixer for the pilot-scale fermenter is
1000 times stronger than the one in the model fermenter, what should be the
impeller rotational speed and diameter for maximum mixing robustness?
Bioreactor Scale-Up
235 7
Take Home Messages
5 Every value-added product that comes from fermentation in bioreactors starts
with studying the process in small-scale flask fermentations and bench-top bio-
reactors in labs. Once they know enough about the bioprocess, biological engi-
neers need to expand the process from those lab-scale modules to pilot-scale
fermenters and finally plant-scale ones. This is called scale-up.
5 The bioprocess behavior in small-scale bench-top bioreactors in labs that can be
only a few liters in volume are mostly distinct from the ones in plant-scale fer-
menters that can be up to hundreds of thousand liters of volume.
5 To address complexities during the scale-up process, engineers often follow
certain and well-examined scale-up strategies while fully considering physical,
biochemical, and process factors that dictate such complexities in the process.
5 Some of the most commonly used scale-up strategies include maintaining a
key parameter fixed throughout the scale-up process. These key parameters are
selected considering the nature of the bioprocess and to minimize distinctions in
behavior to keep optimum conditions as much as possible.
5 Most common parameters are volumetric oxygen transfer coefficient kLa (in aero-
bic fermentations of course), volumetric power consumption of the impeller(s)
P/V, impeller power number (Np), shear stress τ, and mixing time tm.
5 Sometimes engineers are not content with these conventional strategies and
end up blending them together or crafting a process-specific strategy, all to
ensure best of production conditions on the final scale.

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