Agitation 203
I
I
-.&.-
I
W
1. k
IF NEEDED
L-1.5WS L= 2w -4
Figure 19. Suggested bafles for square and rectangular tanks.
5.0 FLUID SHEAR RATES
Figure 20 illustrates flow pattern in the laminar flow region from a
radial flat blade turbine. By using a velocity probe, the parabolic velocity
distribution coming off the blades of the impeller is shown in Fig. 2 1. By
taking the slope of the curve at any point, the shear rate may be calculated at
that point. The maximum shear rate around the impeller periphery as well as
the average shear rate around the impeller may also be calculated.
An important concept is that one must multiply the fluid shear rate from
the impeller by the viscosity of the fluid to get the fluid shear stress that
actually carries out the process of mixing and dispersion.
Fluid shear stress = p(fluid shear rate)
Even in low viscosity fluids, by going from 1 cp to 10 cp there will be 10 times
the shear stress of the process operating from the fluid shear rate of the
impeller.
204 Fermentation and Biochemical Engineering Handbook
Figure 20. Photograph of radial flow impeller in a baffled tank in the laminar region, made
by passing a thin plane of light through the center of the tank.
f:iY
M-
~y
SHEAR RATE
~
Figure 21. Typical velocitypattem corning from the bladesofaradial flow turbine showing
calculation of the shear rate ~V/~Y.
Agitation 205
Figure 22 shows the flow pattern when there is sufficient power and low
enough viscosity for turbulence to fonn. Now a velocity probe must be used
that can pick up the high frequency response of these turbulent flow patterns,
and a chart as shown in Fig. 23 is typical. The shear rate between the small
scale velocity fluctuations is called microscale shear rate, while the shear
rates between the average velocity at this point are called the macroscale
rates. These macroscale shear rates still have the same general fonn and are
determined the same way as shown in Fig. 21.
Figure 22. Photograph of flow patterns in a mixing tank in the turbulent region, made by
passing a thin plane of light through the center of the tank.
0
..z=? 0
-u 2>- ...
~ "'
u ?0 ...
...A. I
> :::
...
-t-
o """-~~.-~-..~-0 20 40 60 80 loo 120 140
TIME. SECONDS
U = 0 + u'X x
Figure 23. Schematic, typical velocity fluctuation pattern obtained from high frequency
velocity probe placed at a point in the mixing vessel.
206 Fermentation and Biochemical Engineering Handbook
Table 2 describes four different macroscale shear rates of importance
in a mixing tank. The parameter for the microscale shear rate at a point is the
root mean square velocity fluctuation at that point, RMS.
Table 2. Average Point Velocity
Max. imp. zone shear rate
Ave. imp. zone shear rate
Ave. tank zone shear rate
Min. tank zone shear rate
5.1 Particles
The consideration of the macro- and microscale relationships in a
mixing vessel leads to several helpful concepts. Particles that are greater
1,000 microns in size are affected primarily by the shear rate between the
average velocities in the process and are an essential part of the overall flow
throughout the tank and determine the rate at which flow and velocity
distribute throughout the tank, and is a measure of the visual appearance of
the tank in terms of surface action, blending or particle suspensions.
The other situation is on the microscale particles. They are particles
less than 100 microns and they see largely the energy dissipation which
occurs through the mechanism of viscous shear rates and shear stresses and
ultimately the scale at which all energy is transformed into heat.
The macroscale environment is effected by every geometric variable
and dimension and is a key parameter for successful scaleup of any process,
whether microscale mixing is involved or not. This has some unfortunate
consequences on scaleup since geometric similarity causes many other
parameters to change in unusual ways, which may be either beneficial or
Agitation 20 7
detrimental, but are quite different than exist in a smaller pilot plant unit. On
the other hand, the microscale mixing condition is primarily a function of
power per unit volume and the result is dissipation of that energy down
through the microscale and onto the level of the smallest eddies that can be
identified as belonging to the mixing flow pattern. An analysis of the energy
dissipation can be made in obtaining the kinetic energy of turbulence by
putting the resultant velocity from the laser velocimeter through a spectrum
analyzer. Figure 24a shows the breakdown of the energy as a function of
frequency for the velocities themselves. Figure 24b shows a similar spectrum
analysis of the energy dissipation based on velocity squared and Fig. 24c
shows a spectrum analyzer result from the product of two orthogonal
velocities, V, and Vz9 which is called the Reynolds stress (a function of
momentum),
An estimation method of solving complex equations for turbulent flow
uses a method called the K-E technique which allows the solution of the
Navier-Stokes equation in the turbulent region.
5.2 Impeller Power Consumption
Figure 25 shows a typical Reynolds number-Power number curve for
different impellers. The important thing about this curve is that it holds true
whether the desired process job is being done or not. Power equations have
three independent variables along with fluid properties: power, speed and
diameter. There are only two independent choices for process considerations.
For gas-liquid operations there is another relationship called the K
factor which relates the effect ofgas rate on power level. Figure 26 illustrates
a typical K factor plot which can be used for estimation. Actual calculation
of K factor in a particular case involves very specific combinations of mixer
variables, tank variables, and fluid properties, as well as the gas rate being used.
Commonly, a physical picture of gas dispersion is used to describe the
degree of mixing required in an aerobic fermenter. This can be helpful on
occasion, but often gives a different perspective on the effect of power, speed
and diameter on mass transfer steps. To illustrate the difference between
physical dispersion and mass transfer, Fig. 27 illustrates a measurement
made in one experiment where the height of a geyser coming off the top of the
tank was measured as a function of power for various impellers. Reducing
the geyser height to zero gives a uniform visual dispersion of gas across the
surfBce ofthe tank. Figure 28 shows the actual data and indicates that the 8-inch
impeller was more effective than the 6-inch impeller in this particular tank.
208 Fermentation and Biochemical Engineering Handbook
vz
(dB)
VZ & VR SPECTRUMS
FOR 15.9 IN. A200 (PBT)
- 70 L
- 10
- 30
(dB) -50
- 70
VR
0 4 10 15 20
HZ
N - 2.0 RPS
C - 16 IN.
ZC - 12.8 IN.
RC = 5.6 IN.
RUN
23 JUL 87-4
POWER SPECTRUM VZ2& VR2
FOR 15 IN. R 100 ( RUSHTON TURBINE 1
0
- 20
-40 -
-60 I I I I 1
N = 2.0 RPS
C = 16.0 IN
ZC 16.75 IN:
RC = 9.00 M.
REYNOLDS STRESS VZ xVR
FOR 15.9 IN. A200 (PBT)
I \ 8.00 HZ
-10
1
,073 FT2ISEC2
i'
-70
0 5 10 15 20
HZ
N - 2.0 RPS (4
C 8 16 IN
ZC 12.8 IN
RC - 5.6 IN
RUN
23 JUL 87-4
Figure 24. Typical spectrum analysis of the velocity as a function of (a) velocity frequency
fluctuation, (b) the frequency of the fluctuations using the square of the velocity to give the
energy dissipation, and (c) the product of two orthogonal velocities versus the frequency of
the fluctuations. The product of two orthogonal velocities is related to the momentum in
the fluid stream.
Agitation 209
- IIIII 1 Ill I IIII I I III I I Ill I 1 lj
-
-
- -
- FLAT BLADE TURBINE- -
- BAFFLED TANK 1
-
-
CURVED BLADE
-
TURBINE - BAFFLED TANK -
..
I I
-
-
-
-
- -
- BAFFLED OR OFF- CENTER
I IIIII 1111 I I Ill I I Ill I I Ill I I I
-
100
10
1 .o
0.1
DZ Np
t.'
D IMPELLER DIAMETER LlOUlD VISCOSITY
N IMPELLER ROTATIONAL SPEED
p LlOUlD DENSITY
P POWER
g GRAVITY CONSTANT
Figure 25. Power number/Reynolds number curve for the power consumption of impellers.
Figure 26. Typical curve of K factor, power drawn with gas on versus power drawn with
gas off, for various superficial gas velocities.
21 0 Fermentation and Biochemical Engineering Handbook
Figure 27. Schematic of geyser height.
3.0
2.5
2.0
a
W
ln
ln
Q
W
vj
-I
q
a
1.5
0.5
I I 1 1 I I I
0125456
GEYSER HEIGHT, INCHES
Figure 28. Plot illustrating measurement of geyser height.
Agitation 21 I
Also, the 8-inch impeller with standard blades was more effective than
the 8-inch impeller with narrow blades. These results all indicate that in this
range of impeller-size-to-tank-size ratio, pumping capacity is more impor-
tant than fluid shear rate for this particular criterion of physical dispersion.
Looking now at some actual published mass transfer rates, Fig. 29
shows the results of some experiments reported previously and Figs. 30
through 33 show some additional experiments reported which give firther
clarification to Fig. 29.
In Fig. 29, the ratio ofmixer horsepower to gas expansion horsepower
is shown with the optimum D/Trange from a mass transfer standpoint in air-
water systems. At the left of Fig. 29, it can be seen that large DIT ratios are
more effective than small D/Tratios. This is in an area where the mixer power
level is equal to or perhaps less than the gas expansion power level. Moving
to the right, in the center range it is seen that the optimum D/T ratios are on
the order of 0.1 to 0.2. This corresponds to an area where the mixer power
level is two to ten times higher than the expansion power in the gas stream.
Thus shear rate is more important than pumping capacity in this range, which
is a very practical range for many types of gas-liquid contacting operations,
including aerobic mass transfer in fermentation.
10 100 1000
RATIO, "' '' ARBITRARY UNITS
GAS RATE
Figure 29. Effect of horsepower-to-gas rate ratio at optimum DIT.
212 Fermentation and Biochemical Engineering Handbook
.04
6
I
I- .02'
5
c
y+
o= .01
008
ia'
dZ
II
d
Y
* .004
-
. T= 18" L= 18"
6FBT C=6"
CENTER INLET
I1 1 1 a,
.8 1.0 2.0 4.0 8.0 IO
.002 ' .4
HP/IOOO GALS. GASSED
Figure 30. Effect of sparge ring diameter on mass transfer performance of a flat blade
turbine, based on gassed horsepower at gas velocity F = 0.02 ft/sec.
T= 18" z= 18"
6 FBT C=6"
CENTER INLET
F=.04 FT/SEC
Figure 31. Effect ofhorsepower and impeller diameter onmass transfer coefficient at 0.04
Wsec gas velocity.
Agitation 213
J
v)
J
0
I
m
J
-
0
l-
2 .08
a
Y
h
I-
v)L
02 .04
2-
J,
h
mg
CENTER INLET
.08 -
.04
.02 -
-
A - F=.O8 FT/SEC
.O 4
.o 2 I/'
"'l'o i.0 410 8.b ;O 2b
HP/ 1000 GALS. GASSED
Figure 32. Effect ofhorsepower and impeller diameter on mass transfer coefficient at 0.08
Wsec gas velocity.,
."I
1.0 2.0 4.0 8.0 IO
HP/1000 GALS. GASSED
Figure 33. Effect ofhorsepower and impeller diameter on mass transfer coefficient for gas
velocity of 0.13 Wsec.
214 Fermentation and Biochemical Engineering Handbook
At the far right of Fig. 29 is shown high mixer power levels relative to
the gas rate, and it can be seen that DlT makes no difference to the mass
transfer. This occurs in some types of hydrogenation, carbonation, and
chlorination. In those cases, the power level is so high relative to the amount
of gas added to the tank that flow to shear ratio is of no importance.
In Figs. 30 through 33, the gas rate is successively increased in each
of the four figures. At the low gas rate, the 4-inch impeller is more effective
than the 6 or 8-inch impeller under all power levels. At the higher gas rates,
the larger impellers become more effective at the lower gas rates, while the
smaller impellers are more effective at the higher power levels, fitting
generally into the scheme shown in Fig. 29.
A sparge ring about 80% ofthe impeller diameter is more effective than
an open pipe beneath the impeller or sparge rings larger than the impeller.
Figure 34 shows this effect and indicates that the desired entry point for the
gas is where it can pass initially through the high shear zone around the
impeller.
This has led to the common practice today of using the distribution of
power in a three-impeller system, for example, 40% to the lower impeller and
30% to each of the two upper impellers, Fig. 35.
(P
0
Y
T=460mm Z=460mm
1-
0.1
I I 11 I
.2 .4 .8 1.0 2.0
KWI cu METER GASSED
Figure 34. Gas-liquid mass transfer data for 150 mm turbine in 460 mm tank at 0.07 m/
sec superficial gas velocity.
Agitation 21 5
f
30%
30%
40%
Figure 35. Typical power consumption relations for triple impeller installation, giving
higher horsepower in proportion to the lower impeller.
In regard to tank shape, it has turned out over the years that about the
biggest tank that can be shop-fabricated and shipped to the plant site over the
highways is about 14 ft (4.3 m) in diameter. As fermentation volumes have
gone from 10,000 gallons (38 m3) to 50 or 60 thousand gallons, tank shapes
have tended to get very tall and narrow, resulting in Z/Tratios of 2: 1,3 : 1,4: 1,
or even higher on occasion. This tall tank shape has some advantages and
disadvantages, but tank shape is normally a design variable to be looked at
in terms of optimizing the overall plant process design.
This leads to the concept of mass transfer calculation techniques in
scaleup. Figure 36 shows the concept of mass transfer from the gas-liquid
step as well as the mass transfer step to liquid-solid andor a chemical
reaction. Inherent in all these mass transfer calculations is the concept of
dissolved oxygen level and the driving force between the phases. In aerobic
fermentation, it is normally the case that the gas-liquid mass transfer step
from gas to liquid is the most important. Usually the gas-liquid mass transfer
rate is measured, adriving force between the gas and the liquid calculated, and
the mass transfer coefficient, &a or &a obtained. Correlation techniques
use the data shown in Fig. 37 as typical in which &a is correlated versus
power level and gas rate for the particular system studied.
216 Fermentation and Biochemical Engineering Handbook
LIQUID
C
I
I
I
I
I
I
I
I
adc/de=k(c)a(c,)b
Figure 36. Schematic showing gas-liquid mass transfer step related to the other steps of
liquid-solid mass transfer and chemical reaction.
20
1
1 10 100
POWER/ VOL., RELATIVE
Figure 37. Typical &a versus horsepower and gas velocity correlation; box on right
indicates typical pilot plant experiments; box on left indicates typical full-scale range.
Agitation 21 7
If the data are obtained on small scale, then translation to larger scale
equipment means an increase in superficial gas velocity, F, because of the
change in liquid level in the large scale system. This normally pushes the data
toward the left and would possibly result in a lower power level being required
full-scale for the same mass transfer rate.
This has to be examined with great care, because any change in the
power level will change the liquid-solid mass transfer rate; change the blend
time, the shear rate and, therefore, the viscosity of non-Newtonian broth, and
could necessitate many other process considerations.
5.3 Mass Transfer Characteristics of Fluidfoil Impellers
Experiments made with the sulfite oxidation technique evaluate the
overall &a relationship for radial flow turbines and a very typical curve,
shown in Fig. 38a gives the value of&a versus power and various gas rates.
One will notice that there is a break in the curve which occurs about at the
point where the power of the mixer is approximately two or three times higher
than the power in the gas stream. A curve taken on similar conditions for the
A3 15 impeller does not show the break point (Fig. 38b), and matching of the
two curves shows that at the low end of the power levels the A3 15 results in
a higher mass transfer relationship, while at higher power levels, the R100 is
somewhat better. However, with &20%, which is with reasonable accuracy
for these kind of measurement comparisons, the mass transfer performance
is quite similar. The difference of performance on a given fermentation
application should thus be higher or lower in terms of the mass transfer
coefficient and needs to be studied in detail when a retrofit is desired.
One large difference between A3 15 and R100 impellers in fermentation is
the blend time. Every RlOO impeller sets up two flow pattern zones. Thus,
in a large fermentation tank with three or four RlOO impellers there are six
to eight separate mixing zones/cells in the vessel. If the A3 15 impeller is used
for the one or more different impeller positions, it sets up one overall flow
pattern which gives one complete mixing zone and results in a blend time on
a batch basis of approximately one-half to one-third the time it takes on the
RlOO configuration. It is quite typical in current practice to use a radial flow
turbine at the bottom while using a series of A3 15 impellers (either one, two
or three, on the top positions). This has the overall tendency to reduce the macro-
and microscale shear rates and also can either increase productivity at the
same power level or retain the original productivity at a reduced power level.
This, in a fermentation process, is of very great importance economically.
218 Fermentation and Biochemical Engineering Handbook
- F
1.0 1
.045 m/s
.034 m/s
.018 m/s
.012 m/s
DUAL R100s
D/T - 0.33
Z/T - 1.56
-
I I II I I 111
1c
kGa
pmol 02
bar m3s
0.1
1
P/V( kW/m3)
1 .o
ki;a
gmol 0~
bar m3s
0.1
-
F
.045 m/s
.034 m/s
.018 m/s
.012 m/s
DUAL A315s
Dl/T - 0.44
D2/T - 0.37
Z/T - 1.56
1 II 1 I II
-
1 10
P/V( kW/m3)
Figure 38. Typical curves of &a versus power and various gas rates for radial flow
turbines, (a) R100; (b) A-3 15.
Agitation 219
However, before retrofitting a large fermentation tank it should be
realized unless there is some process data arising from understanding the
relationship between the mass transfer and the biological oxidation require-
ment, retrofitting existing radial flow turbine installations withA3 15 impeller
types does not always give an improvement in process result. The average
is normally about two or three times as frequent for a plus result as for neutral
or negative results.
It is very difficult to study the effect of fluidfoil impellers in the pilot
plant since the pilot plant in general has much shorter blend time and a much
more uniform blending composition than appears in the full scale tank. Thus,
putting fluidfoil impellers in the pilot plant improves the blending under a
situation where the blending is already much improved over full scale
performance.
6.0 FULL-SCALE PLANT DESIGN
There are four ways in which mixers are often specified when
considering installation of more productive units in a fermentation plant. This
can involve either a larger tank with a suitable mixer or improvement of the
productivity of a given tank by a different combination of mixer horsepower
and gas rate. These are listed below:
a. Change in productivity requirements based on production
data with a particular size fermenter in the plant.
b. New production capacity based on pilot plant studies.
c. Specification of agitator based on the sulfite absorption
d. Specification of the oxidation uptake rate in the actual
rate in aqueous sodium sulfite solution.
broth for the new system.
6.1 Some General Relationships in Large Scale Mixers Compared
to Small Scale Mixers
In general, a large scale mixing tank will have a lower pumping
capacity per unit volume than a small tank. This means that its blend time
and circulation time will be much larger than in a pilot tank.
There is also a tendency for the maximum impeller shear rate to go up
while the average impeller zone shear rate will go down on scaleup. In
220 Fermentation and Biochemical Engineering Handbook
addition, the average tank zone shear rate will go down as will the minimum
tank zone shear rate.
This means that there is a much greater variety of shear rates in the
larger tank, and in dealing with pseudoplastic sluny it will have a quite
different viscosity relationship around the tank in the big system compared to
the smaller system.
Microscale shear rates operate in the range of 300 microns or less, and
are governed largely by the power input.
The power input from the gas per unit volume will increase on scaleup.
This is because there is a greater head pressure on the system, and there is also
an increasing gas velocity.
It may be that the power level for the mixer may be reduced since the
energy from the gas going through the tank is higher in order to maintain a
particular mass transfer coefficient, &a; however, this changes the relative
power level compared to the gas and other mass transfer rates, such as the
liquid-solid mass transfer rate. The capacity for the blending type flow
pattern is not affected in the same way with changes in the mixer power level
as is the gas-liquid mass transfer coefficient.
6.2 Scale-up Based on Data from Existing Production Plant
If data are available on a fermentation in a production-size tank,
scaleup may be made by increasing, in a relative proportion, the various mass
transfer, blending and shear rate requirements for the fill-scale system. For
example, it may be determined that the new production system is to have a new
mass transfer rate of x% of the existing mass transfer rates, and there may be
specifications put on maximum or average shear rates, and there may be a
desire to look at changes in blend time and circulation time. In addition, there
may be a desire to look at the relative change in C02 stripping efficiency in
the revised system.
At this point, there is no reason not to consider any size or shape of tank.
Past tradition for tall, thin tanks, or short, squat tanks, or elongated
horizontal, cylindrical tanks does not mean that those traditions must be
followed in the future. To illustrate the principle involved in the gas-liquid
mass transfer, look at Fig. 36 which gives the three different mass transfer
steps commonly present in fermentation. The mass transfer rate must be
divided by a suitable driving force, which gives us the mass transfer
coefficient required. The mass transfer coefficient is then scaled to the larger
Agitution 221
tank size and is normally related to superficial gas velocity to an exponent,
power per unit volume to an exponent, and to other geometric variables such
as the D/T ratio of the impeller.
A thorough analysis takes a look at every proposed tank shape, looks
at the gas rate range required, calculates the gas phase mass transfer driving
force, and then calculates the required &a to meet that. Reference is made
to data on the mixer under the condition specified and to various DIT ratios
to obtain the right mixer horsepower level for each gas rate.
Atthis point, the role ofviscosity must be considered. Figure 39 shows
the effect ofviscosity on mass transfer coefficient. It is necessary to measure
viscosity with a viscosimeter which mixes while it measures viscosity. Figure
40 illustrates the Stormer viscosimeter which is one device that can be used
to establish viscosity under mixing conditions with shear rates that can be
established.
In looking at the new size tank, estimates should be made of the shear
rate profile around the system, and then using the relationship that viscosity
is a function of shear rate, and the fact that it is shear stress
Shear stress = p (shear rate)
that actually cames out the process, one can then estimate the viscosity
throughout the tank, and the product of viscosity and shear rate to give
the shear stress. Estimates can then be made of how different the proposed
new tank may be compared to the existing known performance of the
production tank.
n
r
I
L
Y
r
5
3
RYU gta
(PENICILLIN-TANK @
DEINDOERFER AND GADEN -\
(PENICILLIN-FLASK CUM CULTURE)
.002 0.01 0.1 0.5
APPARENT VISCOSITY, Pa*s
Figure 39. Illustration of the decrease in K,a with increase in apparent viscosity.
222 Fermentation and Biochemical Engineering Handbook
Figure 40. Schematic illustrating Stormer viscosimeter.
One relationship that cannot be changed simply going from a small to
large scale is the fact that the Reynolds number normally increases in the large
tank over what it was in the small tank. The Reynolds number is typically
anywhere from 10 to 50 times higher in the large vessel than in the small. This
means that the fluid in the pilot scale will appear much more viscous in terms
of flow pattern and many other parameters than it will in the full scale tank.
It is usually not practical where conducting a process to change viscosity
between pilot plant and full scale, but if one is interested in getting an idea of
the flow pattern and some of the macroscale effects, then a synthetic fluid of
a lower viscosity than the actual could be substituted in the full scale work
to give a better picture of the expected flow pattern.
Agitation 223
At this point discussion of the quantitative and qualitative nature of
available data is desirable. The user, production, research and engineering,
and purchasing department should have discussions with the suppliers and
technical personnel to arrive at satisfactory combinations of proposals.
6.3 Data Based on Pilot Plant Work
To keep ratios of impellers, gas bubbles and solid clumps in the
fermentation related to full scale, the impeller size and blade width in the small
scale must always have a physical dimension two or three times bigger than
the particle size of concern.
It is possible to model the fermentation biological process from a fluid
mechanics standpoint, even though the impeller is not related properly
geometrically to the gas-liquid mass transfer step. Thus, one scale of pilot
plant might be usable for one or two of the fermentation mass transfer steps,
and/or chemical reaction steps, but might not be suitable for analysis of other
mass transfer steps. The decision, then, is basedon how suitable existing data
are for any steps which are not modeled properly in the pilot plant.
Ideally, data should be taken during the course of the fermentation
about gas rate, gas absorption, dissolved oxygen level, dissolved carbon
dioxide level, yield of desired product, and other parameters which might
influence the decision on the overall process. Figure 4 1 shows a typical set
of data for this situation.
A TYPICAL FERMENTATION
G57
v)
I I I
TIME
Figure 41. Schematic of typical data from fermentation showing the change in oxygen
content of gas, CO, content in liquid and fermentation yield.
224 Fermentation and Biochemical Engineering Handbook
If the pilot plant is to duplicate certain properties of fluid mixing, then
it may be necessary to use non-geometric impellers and tank geometries to
duplicate mixing performance and not geometric similarity. As a general
rule, geometric similarity does not control any mixing scaleup property
whatsoever.
It may also not be possible to duplicate all of the desired variables in
each run, so a series of runs may be required changing various relationships
systematically and then a synthesis made of the overall results.
One variable in particular is important. The linear superficial gas
velocity should be run in a few cases at the levels expected in the full-scale
plant. This means that foaming conditions are more typical of what is going
to happen in the plant and the fermenter should always be provided with
enough head space to make sure the foam levels can be adequately controlled
in the pilot plant. As a general rule, foam level is related to the square root
of the tank diameter on scaleup or scale-down.
In duplicating maximum impeller zone shear rates on a small scale,
there may be a very severe design problem in the mechanics of the mixer, or
the shaft speed, mechanical seals and other things. This means that careful
consideration must be given to the type of runs to be made and whether the
pilot plant or the semi-work-scale equipment must be available at all times to
duplicate the maximum impeller zone shear rates in the plant or whether this
sort of data will be obtained on a different type of unit dedicated to that
particular variable.
Figure 37 shows what often happens in the pilot plant in terms of
correlatingmass transfer coefficient, &a, with power andgas rate in the pilot
plant. This curve is then translated to a suitable relationship for full scale.
It is possible to consider that with the higher superficial gas velocity, the
power level may be reduced in the full scale to keep the same mass transfer
coefficient. The box on the right in Fig. 37 shifts to the box on the left. This
should be considered, but it should be borne in mind that this changes the ratio
of the mixer power to gas power level in the system; changes the blend time;
changes the flow pattern in the system; the foaming characteristics and also
can markedly affect the liquid-solid mass transfer rate if that is important in
the process.
In all cases, a suitable mass transfer driving force must be used. Figure
42 illustrates a typical case for fermentation processes and illustrates that
there is a marked difference between the average driving force, the log-mean
driving force, and the exit gas driving force. In a large fermenter, it is this
author’s experience that gas concentrations are essentially step-wise stage
functions and a log-mean average driving force has been the most fruitful.
Agitation 225
Figure 43 illustrates a small laboratory fermenter with a Z/T ratio of 1, and
in this case, depending on the power level, an estimate must be made of the
gas mixing characteristics and an evaluation made ofthe suitability of the exit
gas concentration for the driving force compared to the log-mean driving
force. This is one area which needs to be explored in the pilot program and
the calculation procedures.
Xz.15 Ap= .025
pp = .225
P= 2
Xz.21 Ap =.22
I pp=.42
Figure 42. Typical driving force for larger fermenter.
Ap=0.025
I----
I
Ap =0.22
AIR
Figure 43. Driving force for small laboratory fermenter.
226 Fermentation and Biochemical Engineering Handbook
Just to indicate another peculiarity in the waste-treating industry, it is
quite common to run an unsteady state reaeration test in which the tank is
stripped of oxygen; air is started with the mixer running and the dissolved
oxygen level increase is monitored until the tank is saturated and no further
mass transfer occurs. At that point, the DO level is usually between the
saturation value at the top and the saturation value at the bottom condition,
Fig. 44. This means that for steady state there must be enough absorption in
the bottom and enough stripping at the top; a very peculiar mass transfer
situation results compared to what is happening on any waste treatment
production or fermentation mixer. Running experimental tests and basing a
lot of calculations on that particular driving force would give markedly
different results from those obtained with the mixer operating normally.
- P=1.5
Xz.21 Ap= -.09
pp = .31
- DO=30
p"= 0.4
P= 2.5
X=.21 Ap = 0.13
I- pp=.53
STEADY STATE SATURATED
Figure 44. Driving force for unsteady state saturation run carried to equilibrium.
6.4 Sulfite Oxidation Data
There are data using excess sodium sulfite with suitable catalysts
which keep the dissolved oxygen level at zero, and the data have been obtained
on small and large size fermentation tanks on this basis. One caution is that
the data should have been taken when the tank was completely clean of
antifoams which may be residual from the fermentation process. This
antifoam can cause marked differences in the mass transfer coefficient.
Agitation 22 7
If someone has a relationship between the sulfite oxidation number and
the performance required in the fermenter, this is a perfectly valid way to
specify equipment and tests can be run to give an indication of the overall
mass transfer rate ensuing.
6.5 Oxygen Uptake Rate in the Broth
If it is desired to relate fermenter performance to oxygen uptake rate in
the broth, this number can be specified along with suitable desired gas rates,
and the mixer estimated, based on this performance. Again, someone must
have the link between this particular mass transfer specification and the
actual performance of the fermenter.
Ifthis number is based on pilot plant data, then the effect ofthe different
shear rates and different blend times on the mass transfer relationship,
viscosity and the resulting fermentation must be considered.
6.6 Some General Concepts
Table 3 gives some typical power levels used in various gas-liquid
mixing operations, including waste-treating and fermentation, to give some
idea of the range of variables. Obviously, the tremendous variety of units
used precludes an attempt to guess at a mixer based on general overall
approximations.
The lower impeller does the major part of the work on dispersing gas
in the system and it is typical practice today to put a high proportion of the
power into the lower impeller, somewhat similar to what is shown in Fig. 35.
Multiple impellers do have zoning action in terms of blending, which is not
a great factor in a fermentation which takes seven days, but there are
instantaneous differences in the mass transfer, blending and concentration
profiles in a tank with multiple impellers.
Table 3. Some Gas-Liquid Applications
Agitator Power Fermenter Size . . . . .Power Levels.. . . .
(hP) (gal) (hp/gal) (kW/m3)
100 2,000 50/1,000 9.9
900 40,000 23/1,000 4.5
3,500 100,000 35/1000 6.9
100 10,000,000 0.01/1,000 0.002
228 Fermentation and Biochemical Engineering Handbook
In addition, the role of the lower impeller in both mass transfer and
mixing must be considered and the desirability of having multiple impellers
in the tank can be considered.
If it is desired to consider axial flow impellers in a gas-liquid system
for any reason, it should be remembered that the upward flow of gas tends to
negate the downward action ofthe pumping capacity ofthe axial flow turbine.
A radial flow turbine must have three times more power than the power in the
gas stream for the mixer power level to be hlly effective. On the other hand,
the axial flow impeller must have eight to ten times more power than in the
gas stream for it to establish the axial flow pattern.
6.7 Reverse Rotation Dual Power Impellers
In gas-liquid systems, one of the reasons that the power of the impeller
is lower with the gas on than with the gas off is that the gas bubbles collect
behind the impeller blade. This streamlines the blade, reducing power.
Looking at Fig. 45, speculation can be made on what would happen if one
were to fill up and streamline the back of the impeller with solid material.
What happens is that with no gas rate, Fig. 46, the impeller draws less
horsepower with the back of the blade streamlined than with the back of the
blade flat.
Figure 45. Typical dual power number impeller with streamlined back of blade.
Agitation 229
AIR - WATER
1 .o
.9
.a
.4
.3
.2
.1
0
Y
0.001 0.01 0.1
SUPERFICIAL GAS VELOCITY, METERS/SEC.
Figure 46. Power characteristics of dual power number impellers.
When the gas is turned on, the flat impeller blade has a K factor, which
is the ratio of impeller power with gas on to power with gas off, and changes
markedly with gas rate, typical of impellers of that type, while the impeller
with the streamlined back of the blade has much less change in power with
gas rate.
The schematic relationship shown in Fig. 46 gives a wide variety of
power consumption availabilities without gas and with gas by having the
mixer and motor capable of being reversed electrically, and opens up a wide
variety of process options.
7.0 FULL SCALE PROCESS EXAMPLE
There is no way that a mixer can transfer oxygen from gas to liquid any
faster than the solid microorganisms can utilize the oxygen in their growth
process. If the mixer is capable of supplying the oxygen faster than the
organisms can use it, the main effect will be to increase the dissolved oxygen
level, C, to balance out the mass transfer equation
230 Fermentation and Biochemical Engineering Handbook
and the dissolved oxygen level may or may not have an effect on the growth
process.
On the other hand, if the organism can utilize oxygen faster than the
aerator can provide it, the dissolved oxygen will tend toward zero, although
this may affect the resulting oxygen demand ofthe organism and bring the two
demands even more closely into balance.
It is normally helpfil to break the fermentation process down into
several distinct steps and examine the role that mixing plays in these various
steps. Then, the total effect on the process result from the combination of
these different steps can be examined.
One of the first requirements is to get a measure of the effectiveness of
the existing mixer in the process. This section takes the perspective that there
is an existing fill scale fermenter that is carrying out a certain process. The
basic questions covered here are: (i) what is the role of mixing in this
particular process? (ii) what are the possible advantages and disadvantages
of increasing the mass transfer ability of the agitator to take advantage of the
maximum potential ofthe present strain of microorganism in the process? and
(iii) what is the potential advantage of providing a mixer that will provide
adequate mass transfer for both an increased productive strain at the same cell
concentration, or will provide proper oxygen mass transfer at an increased
cell concentration?
In looking at the performance of a mixer in a tank with a particular
starting concentration of microorganisms, it is possible to determine the
kinetics of the antibiotic production which produces the growth of the
microorganisms throughout the process. Typical data is shown in Fig. 41
previously.
One factor that can add considerable codusion to the analysis is the
observation that understimulation or overstimulation of the growth rates of
microorganisms in their initial and log growth phase can change their ability
to produce antibiotic at the maximum yield point in the cycle and affect the
ultimate total yield obtained at the end. It is entirely possible that increasing
the mass transfer rate available to the fermentation can have a detrimental
effect on total yield because it changes the metabolic situation in the
organisms during the first few hours of fermentation, which affects their
ultimate potential for total yield.
This effect must be carefully distinguished in analyzing the use of a
higher mass transfer ability agitator, which can take advantage of increased
Agitation 23 I
respiration requirements of new improved strains or higher cell concentra-
tions during the total cycle.
It is also common that fermentations made in different parts of the
world, although supposedly somewhat similar, because of inherently differ-
ent conditions of processing can give different results in equipment that is
quite similar.
The use of higher mixer mass transfer abilities can be examined in two
ways:
a. The effect it has on a given type and concentration of
starting seed, which includes biomass growth rates and
total yield.
b. The effect it has on production from a new, more produc-
tive strain or an increased initial seed concentration.
8.0 THE ROLE OF CELL CONCENTRATION ON MASS
TRANSFER RATE
Within a given batch run, the cell concentration changes as a function
of time. In addition, the viscosity goes up with cell concentration at a given
point on the time curve of a fermenter. Figures 47 and 48 give typical data
showing the change in viscosity as a function of the number of days of
fermentation for different kinds of systems.
On the other hand, Fig. 49 shows the change in mass transfer rate with
viscosity, which is caused largely by a change in cell concentration of the total
process. It is true that the rate of oxygen transferred per MJ goes down as the
cell concentration goes up. However, this cost must be balanced against the
increasing productivity of a given dollar investment in fermentation tank,
piping and total plant cost. Analysis needs to be made of the role that mixer
cost, including both capital and power, plays in the total productivity cost in
order to evaluate desirability of going in this direction.
A previous paper by Ryu and Oldshue treated an example where the
final cell concentration was changed from 10 to 12 to 20 gll, and the oxygen
mass transfer dropped from 10 to 8.3 to 6.4 mols oxygenh4J.
Looking at Table 4, the cost of electrical power and other essentials
listed a capital cost of $900/kW (1982 cost about $2000/kW) if installed
mixer capacity is used, including the associated blower and air supply, and
including the installation of the equipment, with the electrical hookup. This
is for a D/T ratio of 0.37.
232 Fermentation and Biochemical Engineering Handbook
SHEAR RATE
Figure 47. Viscosity at various shear rates for various days in the fermentation cycle.
I
I 2 3 4 5 6
FERMENTATION TIME (DAYS)
Figure 48. Viscosity at constant shear rates for various days in the fermentation cycle.
Agitation 233
CONSTANT HPt GAS
I I
I 10 100
RELATIVE VISCOSITY
Figure 49. Decrease in mass transfer rate with viscosity for a given mixer and air rate.
Table 4. Cost of Mixing for Production of Antibiotics
(Based on Oxygen Transfer Rate)
Cost of electrical power
Equipment Cost (expressed as power cost)
Efficiency of oxygen mass transfer
Dilute system, lOg/l*
More concentrated, 20gll*
Power and Equipment cost
Cost of dissolved oxygen
10 glr
20 gll
Production cost of antibiotics
Fractional cost for mixing
(antibiotics production)
Production Yield
10 mols O,/MJ
6.4. mols O,/MJ
l.St/MJ
0.15$/mol 0,
0.23#/mol 0,
46#fl<g
0.6-1.6%**
1 kgl200 mols 0,
*Cell concentration.
**Of production cost.
234 Fermentation and Biochemical Engineering Handbook
Electrical power is assumed at 0.7$/MJ (to obtain $/kW-hour multiply
by 3.6). The equipment is amortized, using present worth, over a 5-year
period, which results in a figure of 0.8$/MJ. Total cost of the equipment and
operation is therefore 1.5$/MJ. The cost of dissolving oxygen is 0.15$/mol
0, dissolved at 10 g/Z. At 20 g/Z, it is 0.23$/mol 0,.
Assuming that it takes 200 mols of oxygen to produce 1 kg of product
and that there is a production cost of $60 total per kg of product, the percent
cost of oxygen in the dilute system is approximately 0.7% of the total
production cost. There is also assumed in this example that there is a fixed
cost of $3Okg which does not change with the agitator, and that the variable
fermentation cost goes down as the productivity of the particular tank in the
process increased.
This is listed in Column A of Table 5, Column D gives the results from
the paper by Ryu and Oldshue, which described the use of a 500 hp mixer
operating at 20g/Z. While the percent of cost due to the mixer has increased,
the total production cost per kg of product has gone down 25% to a value of
approximately $45.2/kg.
Table 5. Comparison of New Mixer to Original Mixer
Original
Low Power Mixer ..New High Power Mixer..
(A) (D) (E) (F) (GI
Agitation Power, kW 150
Aeration Power, kW 37
Relative product yield (arbitrary units) 100
Cell concentration, gA 10
Oxygen uptake rate, g 0,h 0.5
transfer rate, g 0,llh 0.7
Maximum available oxygen
Fixed fermentation cost, $/kg 30
Variable ferm. cost, $/kg 30
Total production cost,
$/kg of product 60
Cost of oxygen transfer operation
(mixing equipment, power), $/kg 0.42
380
95
200
20
1 .o
1.1
30
15.2
45.2
0.52
380 380 380
95 95 95
180 200 200
20 20 20
0.9 1.0 1.0
1.1 1.1 1.1
30 30 30
16.67 15.16 15.34
46.7 45.16 45.34
0.57 0.58 0.72
Present cost of oxygen
transfer operation 0.7 1.1 1.2 1.3 1.6
Present cost savings - 25 22 25 24.5
Maximum impeller zone shear rate
(relative) 1 .oo 1.30 1.30 1.15 1.00
Agitation 235
Assume that this higher power mixer, having a maximum impeller zone
shear rate 30% higher than Case A, decreased the growth ability of the
microorganisms due to increased shear on these particles, changing the floc
structure, etc. Further assume that this cut the production ofpenicillin to 90%
of the value it could have had based on cell concentration only. This means
that the mixer is producing less product than Column D would indicate, and
the production costs have gone up to $46.7/kg (Case E), because all the
additional capacity of the larger aerator cannot be used. It can be seen that
the aerator has given the ability to transfer 1.1 g 02/l/hr, in contrast to the 200
hp unit value of 0.7 g O,/l/hr.
Assume that studies in the laboratory indicate that if the shear rate is
cutdown towhereitis only 15%higherthan CaseA,thentheorganismretains
its growth potential. This mixer in Case F has a D/T ratio 40% higher and
therefore, instead of $9OO/kW, costs $1200/kW, including the associated
blower. Putting this into the cost example, even though it changes drastically
the initial cost of the equipment, the productivity is improved to the point that
the actual production cost is approximately $45.2/kg as it was in Case D.
If studies indicate that the shear rate has to be cut back to the same as
it was in Case A, this means the mixer cost is now $1575/kW because of the
increased torque and D/T, and it does raise the production cost up to $45.3
(Case G), but is still a very small percentage of the total production cost, and
is a very small percentage in terms of mixer cost of the total production.
The main point here is that in this particular example, mixer horse-
power and capital cost can effect tremendous changes in productivity because
of their low cost in terms of the total cost.
9.0 SOME OTHER MASS TRANSFER CONSIDERATIONS
The desorption of CO, is an essential part of effective fermentation.
The pressure and liquid depth that enhances absorption of oxygen discour-
ages the desorption of CO,. Tall, thin tanks with the same volume of air,
yielding a higher superficial velocity, normally give more pounds of oxygen
transfer per total horsepower of mixer in air than do short, squat tanks. There
also is less absorption of CO, under the same conditions. Therefore, some
idea ofthe role of CO, desorption rates, back pressure of CO, and other things
must be obtained in order to evaluate this particular phenomenon. In addition,
the fluid mixing pattern in the fermenter must be considered. As broth
becomes more viscous, and tanks become taller, more impellers are used and
236 Fermentation and Biochemical Engineering Handbook
there is a possibility of much longer top to bottom blending times being
involved which do affect the dissolved C02-oxygen level throughout the
system. In general, the dissolved C0,-oxygen level will assume some value
intermediate between the values that would be predicted based on concentra-
tion driving forces at the bottom and the top due to the gas stream.
10.0 DESIGN PROBLEMS IN BIOCHEMICAL ENGINEERING
1. A mixer applying 150 kW to the mixer shaft is operating in a batch
fermentation at a cell concentration of 20g/l. Associated with the mixer is
a blower, which is providing air at a total expansion horsepower of 37 kW
leaving the sparge ring. The cost of power is 0.5$/MJ. Use an overall energy
efficiency for the equipment of 0.9.
The cost of the mixer plus the associated blower required, plus
installation of both is $900/kW with an impeller diameter to tank diameter
ratio of 0.35.
By using large diameter impellers at slower speeds, the maximum
impeller zone fluid shear rate can be changed, and the cost of the mixerkW
must be changed accordingly. The cost of the mixer can be approximated
to change inversely proportional to the maximum impeller zone fluid shear
rate to the 2.3 exponent
Cost cc (MIZSR)-2,3
The particular antibiotic requires 200 mols of oxygen for each kg of
product produced. The total production cost ofthe antibiotic is estimated as
$60/kg, of which $30 is a fixed cost, independent of productivity of the
fermenter, and $30 is the cost associated with the actual fermentation tank
itself.
At 20 g/1 cell concentration, the mixer is capable of transferring 6.4
mols of oxygen per MJ.
It is proposed to increase the solids concentration in the system to 40
g/l, which will effectively double the productivity of the fermentation tank
itself. The oxygen transfer activity of the mixer is lowered, due to the
increased viscosity, to 4 mol of oxygen per MJ.
Assuming that the mixer is operated for 250 days per year, and using
a 5-year evaluation period, calculate the cost of mixing, capital and
operating, in this process, and the percentage cost ofmixing under the present
operation.
Agitation 23 7
At 40 gl1 of cells, the process horsepower required may be estimated
as being proportional to the cell concentration to the 1.4 exponent
(Process mixer hp) oc (cell c~ncentration)'.~
This takes into account the transfer rate due to the change in viscosity
and the additional transfer rate needed because ofthe increase in total biomass
in the system.
Calculate the cost of mixing in the new revised system at 40 gll, the total
mixer horsepower (air horsepower is in the same proportion as at 20 glZ), and
reduction in antibiotic production cost.
2. The new larger mixer has a higher maximum impeller zone shear
rate, which is estimated at 1.4 times as high as a small unit at the same D/T
ratio. Assume that this higher shear rate has cut the productivity of the
increased cell concentration to 90% of its normal value. In this case,
assuming that the mixer is not changed, calculate the cost of mixing and the
percent mixing cost/total product cost, and the savings compared to the
original 15 0 kW mixer.
3. A new mixer has been designed at the same total horsepower, but
Calculate the new capital cost of mixing and calculate the total mixing
with a shear rate 1.2 times as high as the previous 150 kW unit.
cost and increase in productivity over the original smaller unit.
4. A large diameter impeller at a slower speed would require a larger
mixer drive, to reduce the shear rate to the same as it was in the original 150
kW unit. Again calculate the cost of the mixer, mixing cost per MJ and
calculate the percent mixing cost/total product cost, as well as the percent
savings over the original 150 kW mixer.
238 Fermentation and Biochemical Engineering Handbook
11.0 SOLUTION-FERMENTATION PROBLEMS
I'roblcin I
187 1
160 0.9
o.~C/MJ x - x
900 x 100
3.6 x 6 x 260 x 24
Total
= 0.76/MJ
= O.~(/MJ
= ld$/MJ
200
_= 31.3 MJ/kg 01 product
6.4
This yields 47(/kg
0.47
- = 0.8% cost of mixing
60
150 x 2.6 = 390 kW mixet
37.0 x 2.6 = 96.2 kW air
200
- = 50 MJ/kg product
4
= 75$/kg
$15.00 t (0.76 - 0.47) - $15.28 kg - Operating cost
+E - Fixed cost
$45.28 - Total cost
0.75
45.28
Mixing cos3 - 1.6%
60-4528 = 25%
Cost savings 7
Problem 2
-= 75t 83Clkg
0.9
$30/kg
- + (0.83 - 0.47) = $17.02 - Operating cost
1.0
+3o.oo - Fixed cost
$47.02 kg - Total cost
-si 0.83
1.8% Cost of mixing
47.02
$GO - $47.02
= 22% Cost saving
$60
Agitation 239
I’roblcm 3
0.8BIMJ x 1.4 = 1.12
t-0.7
-
1.82 &/MJ
200 -- - 50 MJ/kg
4
50 x 1 .82 = 91 $/kg
$15.00 + 10.91 - 0.47) = $15.44
+3o.oo
$45.44
0.91
45.44
__- -
2% Cost of mixing
60 - 45.44
= 24% cost saving
60
Problem 4
Cost = (1.4)t2.3 = 2.17
2.17 x 0.8 = 1.744IMJ
+0.7
2.44$/MJ
2.44 x 50 = $1.22/kg
$15 + (1.22 - 0.47) = $15.75
+3o.oo
$45.75
-= 2.7% Cost of mixing
45.75
60 - 45.75
-= 24% Cost saving
60
240 Fermentation and Biochemical Engineering Handbook
LIST OF ABBREVIATIONS
D
KLa
&a
MJ
N
P
P
P*
Q
S.R.
S.S.
P
W
F
K8
c'
c
DO
H
K factor
z
T
O.U.R.
MIZSR
d1
kwh
kW
CI
kg
Impeller diameter
Gas-liquid mass transfer coefficient based on
partial pressures
Gas-liquid mass transfer coefficient based on liquid
concentrations
Megajoule
Impeller
Power
Pressure
Equilibrium partial pressure
Impeller pumping capacity
Shear Rate
Shear Stress
Viscosity
Width of square or rectangular tank
total air
Superficial gas velocity,
cross-section area of tank
Liquid solid coefficient
Equilibrium oxygen concentration corresponding to
partial pressure in air stream
Liquid oxygen concentration
Dissolved oxygen concentration
Impeller head
Ratio of horsepower with gas to power with gas off at
Liquid level
Tank diameter
Oxygen Uptake Rate
Maximum impeller zone shear rate
Grams per liter
Kilowatt-hour
Kilowatt
Center Inlet gas introduction
Kilogram
constant speed
Agitation 241
REFERENCES
1.
2.
3.
4.
5.
6.
7.
Deindoerfer, F. H. and Gaden, E. L., Appl. Microbiol., 3:253 (1955)
Oldshue, J. Y., FermentationMixing Scale-UpTechniques, Biotech, Bioeng.,
Oldshue, J. Y., Suspending Solids and Dispersing Gases inMixing Vessels,
Ind. Eng. Chem., 61:79-89 (1969)
Oldshue, J. Y., Spectrum of Fluid Shear Rates in Mixing Vessel, Chemeca
'70 Australia, Butterworth (1970)
Oldshue, J. Y., Coyle, C. K., and Connelly, G. L., Gas-Liquid Contacting
with Impeller Mixers, Chem. Eng. Prog., 85-89 (March, 1977)
Oldshue, J. Y., Coyle, C. K., et al., Fluid Mixing in the optimization of
fermentation Production, Process Biochem., 13(1 l), England 1978)
Ryu, D. Y. and Oldshue, J. Y., A Reassessment of Mixing Costs in
Fermentation Processes, Biotech. Bioeng., XX621-629 (1977)
VIII:3-24 (1966)