Reprinted from
PHARMACEUTICAL ENGINEERING
facilities and euipment
The Official Technical Magazine of ISPE
January/February 2013, Vol 33, No 1
Mass Transfer Correlation Studies
©Copyright ISPE 2013
www.PharmaceuticalEngineering.org
Why Conduct Pilot Studies
for Agitated Gas-Liquid Mass
Transfer?
by Gregory T. Benz
This article presents the rationale for conducting detailed mass transfer
correlation studies in aerobic fermenters, in order to minimize power
consumption in full scale design and maximize the chance of having
correctly designed equipment.
I Introduction
n an agitated, aerated bioreactor, one of the significant
costs is electrical power. Several years ago,2 a study described that the power used for agitated, gas-liquid mass
transfer consisted mainly of two sources: agitator power
and compressor power. For the specific case of an aerated bioreactor, it was shown that the sum of these two
power sources goes through a minimum, as a function
of airflow, bounded by stoichiometry at the low end of
airflow and by excessive liquid entrainment at the high
end of airflow. This concept is illustrated in Figure 1.
Such a curve depends on having an accurate relationship for calculating the mass transfer coefficient and there
are sources that explain how to design a pilot program to
empirically create such a relationship. The purpose of this
article is to illustrate vividly the possible error in published
correlations compared to real broth data, and thereby
emphasize the importance of experimental work to develop
process-specific correlations.
Background
We will use an aerobic bioreactor as an illustration of concept for this article. For such a reactor, mass transfer may
conceptually be written in the form:
(1)
OTR = kLa* (driving force)
Figure 1. Power minimization curves.
In the above correlation, kL is the liquid film coefficient, and
has units of length/time, e.g., M/s. “a” is interfacial area/volume, and has units of 1/length, e.g., 1/M. Thus, kLa has units
of 1/time, e.g., s-1. Driving force has units of mass or moles/
volume, e.g., mmol/l or mg/l.
For a small vessel (< 1000l, for example), the driving
force is simply the difference between the actual mean Dissolved Oxygen (DO) concentration and the mean saturation
value, or (Csat – C). (The value of Csat depends on the partial
pressure of gas at the location in question, as well as the
temperature.) For a larger vessel, it is best to use a log mean
driving force:
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facilities and equipment
Mass Transfer Correlation Studies
(Csat – C)in – (Csat – C)out
log mean
= _____________________
driving force
ln ((Csat – C)in / (Csat – C)out)
(2)
Thus, if driving force and kLa are known, the mass transfer
rate is easily determined. But how is this kLa calculated?
Though many different forms of correlation have been used
in the literature, the most common form is:
kLa = A(P/V)b(Us)c
(3)
The constants, A, B and C, must be experimentally determined for the specific gas-liquid system in question. They
may depend on the actual magnitudes of P/V and Us, and
possibly on impeller type and scale of equipment, as well as
the chemical composition and physical properties of the gas
and liquid. For these reasons, it is important to try not to
extrapolate the correlation beyond the range over which it
was developed. The dimensions of “A” depend on the units
used; it is not a dimensionless number.
Several such correlations have been published in the
literature. The works of many others were summarized4 by
dividing their data into coalescing systems (essentially tap
or distilled water) and non-coalescing systems (essentially
water with high ionic strength, as would be expected of
fermenters with a nutrient solution as the broth.) Later, an
“average” correlation for an air-water system was published.1
These authors note that such correlations are generally no
more than ± 30% accurate.
This author has worked with various clients over the
years to design experimental programs and interpret the results for specific broths. A couple of these will be used in this
article, called simply broth 1 and broth 2. These two broths
differ markedly from the published correlations, as can be
seen in Table A.
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Tank diameter : 5 M
Liquid volume: 229000 l
Ungassed liquid level: 12 M
Temperature: 37°C
Feed gas: air, at 21% oxygen
Csat at 21% oxygen, 1 atmosphere: 7.2 mg/l
DO at bottom of vessel: 2 mg/l
DO at top of vessel: 1 mg/l
Backpressure: 0.3 bar
Barometric pressure: 1 atm or 760 torr
Moles of CO2 respired per mole of oxygen consumed:
0.95
Liquid density: 1000 g/l
Total gas line pressure losses: 1.5 bar
Compressor efficiency: 70%
Agitator mechanical efficiency: 95%
Design OTR: 150 mmol-l-h
The total power (agitator plus compressor) has been plotted
in Figure 2 as a function of airflow in a series of curves representing each of the kLa correlations in Table A.
Full Scale Example
To illustrate the consequences of different kLa correlations,
the total power as a function of airflow was calculated using
the methods2 for the following specific production bioreactor
data and assumptions:
Mass Transfer
Correlation Constants
A
B
C
Bakker (1)
0.946
0.6
0.6
Coalescing (4)
0.41
0.4
0.5
Non-coalescing (4)
0.25
0.7
0.2
Broth 1
0.67
0.55
0.6
Broth 2
3.73
0.542
0.741
Table A. Typical constants used in mass transfer correlations.
2
January/February 2013
PHARMACEUTICAL ENGINEERING
Figure 2. The total power (agitator plus compressor).
facilities and euipment
Mass Transfer Correlation Studies
Discussion of Results
As can be seen, even the published correlations can differ
from each other by a factor of 3 or more. Actual broths can
deviate significantly from each other as well as published
correlations. One could easily be seriously in error if the
wrong correlation is used for design. In one direction, the
wrong correlation can waste money by installing massively
oversized equipment and using excessive power. An error in
the other direction may result in lower product yield, lower
product concentration, or even lower production capacity
than the plant design calls for.
“
Actual broths can deviate
significantly from each other as
well as published correlations.
Looking Forward
Maybe someday there will be a universal kLa correlation
which takes account all chemical and physical properties
and is valid for all impeller types, covers all possible ranges
of variables and includes all effects of scale. Until then, it is
highly advisable to do the “wet” testing necessary to develop
broth-specific correlations that lead to accurate design while
minimizing total power costs. The present worth of electrical
power costs can be $1,000 to $3,000 per kilowatt. Thus, the
difference in power costs for a typical production fermenter
can be hundreds of thousands of dollars depending on the
correlation used. The exception of course, is for processes
that produce such valuable products that massively oversizing equipment is a reasonable option.
Nomenclature
A
Correlation constant; units depend on correlation
units.
a
Gas-liquid interfacial area/volume, 1/M
b
correlation exponent (dimensionless)
C
Dissolved oxygen concentration, mass or moles/
volume (e.g., mg/l)
Csat
Dissolved oxygen concentration at saturation
(mg/l)
c
Correlation exponent (dimensionless)
DO
Dissolved oxygen concentration, general term
(mg/l)
kLa
Overall mass transfer coefficient, 1/time (1/s)
kL
Liquid film coefficient, M/s
OTR
Oxygen Transfer Rate, mass or moles per volumetime), e.g. mg/l-hr.
P
Agitator power, W
P/V
Specific Power: agitator invested power/(mass or
volume) of liquid (e.g., W/l)
Us
Superficial Gas Velocity, distance/time (M/s)
V
Liquid volume, l
VVM Volume of gas/volume of liquid/minute at standard
conditions (min-1)
Z
Liquid level within tank, M
References
1. Bakker, A., Smith, J. ,Myers, K.,“How to Disperse Gases
in Liquids,” Chemical Engineering Magazine, 12, (1), pp.
98-114, 1994.
2. Benz, G., “Optimize Power Consumption in Aerobic Fermenters,” Chemical Engineering Progress, May 2003,
pp. 100-103.
3. Benz, G., “Piloting Bioreactors for Agitation Scale-Up,”
Chemical Engineering Progress, February 2008, pp.3234.
4. van’t Riet, K., Tramper, J., Basic Bioreactor Design,
Marcel Dekker Inc., p.251, 1991.
About the Author
Gregory T. Benz is President of Benz
Technology International, Inc. He received
his BSChE from the University of Cincinnati in 1976, and has taken a course on fermentation biotechnology from the Center
for Professional Advancement. A registered
Professional Engineer in Ohio, he has more than 35 years of
experience in the design of agitation systems. Currently, his
company does general mixing consultation, including pilot
plant protocol, equipment specification, and bid evaluation.
Current activity includes several cellulosic ethanol, singlecell protein, and biomass projects. Benz also teaches courses
on agitation with CEU/PDH credits. He is a member of
AIChE, ISPE, SIM, and the American Chamber of Commerce
in Shanghai. He is a Course Director for Aurora Analytics
(www.aurora-analytics.com), currently teaching two courses
on fluid agitation: one for bio/pharmaceutical, the other for
biofuels. He is a registered expert with Intota (www.Intota.
com). He can be contacted by telephone: +1-937-289-4504
or email: benztech@mindspring.com.
Benz Technology International, Inc., 2305 Clarksville
Road, Clarksville, Ohio 45113.
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