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PUBLICATIONS

United States Department of Commerce

National Institute of Standards and Tectinology

NIST Technical Note 1276

A Survey of Selected Topics

Relevant to Bloprocess Engineering

J. 6. Hubbard, E. J. Clark, and J. M. H. Levelt Sengers

QC

100

.U5753

//1276

1990

C.2
NATIONAL msnrUTE OF STANDARDS &

TECHNOLOGY

Reeearch Informatioii Center

GsBtheraburg, MD 20899

DATE DUE

Demco, Inc. 38-293
mo

NIST Technical Note 1276

A Survey of Selected Topics

Relevant to Bioprocess Engineering

J. B. Hubbard

E. J. Clark

J. M. H. Levelt Sengers

Thermophysics Division

Natic»ial Institute of Standards and Technology

Gaithersburg, MD 20899

May 1990

%

U.S. Department of Commerce

Robert A. Mosbacher, Secretary

National Institute of Standards and Technology

John W. Lyons, Director
National Institute of Standards U.S. Government Printing Office For sale by the Superintendent

and Technology Washington: 1 990 of Documents

Technical Note 1276 U.S. Government Printing Office

Natl. Inst. Stand. Technol. Washington, DC 20402

Tech. Note 1276

88 pages (May 1990)

CODEN: NTNOEF
ABSTRACT

The following is a collection of reports on topics considered important

and generic in biotechnology and bioprocess engineering: (1)

Isoelectric points of proteins; (2) Solubility and mass transfer of

oxygen in bioreactors; (3) Solubility and mass transfer of carbon

dioxide in bioreactors. These reports arose from a survey of the past

and current biotechnology literature with special effort given to a critique of data measurement quality. The format is as follows. The

technological importance of a topic is briefly discussed, followed by a critical review of relevant physical properties, data presentation, and

measurement techniques. A "conclusions and recommendations" section

summarizes our findings and contains specific recommendations for future

research projects. The last section consists of an annotated

bibliography and references pertaining to the survey.

iii

CONTENTS

1. Isoelectric Points of Proteins

A Survey of Compiled Data Sources 1

2. Solubility of Oxygen in Bioreactor Fluids

A Survey of Compiled Data Sources and Predictive Methods 11

3. Mass Transfer of Oxygen in Bioprocess Systems 25

4. Solubility, Reactivity and Mass Transport of Carbon

Dioxide in Bioreactor Media 63

Isoelectric Points of Proteins

A Survey of Compiled Data Sources

January 31, 1989
Contents

1

.

Relevance 3

2. Isoelectric Points of Proteins ..... 3

2.1 General 3

2 .

2

Measurement 3

2.3 Data Sources 4

3. Conclusions and Recommendations 5

4. Bibliography 6
Isoelectric Points of Proteins

A Survey of Compiled Data Sources

1. Relevance

The isoelectric point is the one characteristic of protein charge that can

be directly measured for an enormous variety of proteins. It is well

known that the surface charge of proteins is a principal factor in

determining solubility as well as aggregation properties, that

electrically induced long range interactions play a significant role in

diffusivity and that surface charge has a profound influence on certain

interfacial properties such as the adsorption of proteins onto surfaces or membranes. Professor Daniel Wang, Director of the Biotechnology Process

Engineering Center at MIT, rates isoelectric point data (electrical

mobility) as second in importance only to knowledge of the primary amino

acid sequences in proteins for separations in bioprocessing (D. Wang) in

Separations for Biotechnology, Chap. 1., Ed. M. S. Verrall and M. J.

Hudson, (Ellis Norwood L.T.D. (1987)).

2. Isoelectric Points of Proteins

2 .General

A comprehensive literature survey of compiled data sources on the

isoelectric points of proteins was performed. As such, it constitutes a first step in a systematic investigation of data needs relevant to

bioprocess engineering. The isoelectric point, pi, is the pH at which

migration in an external electric field ceases. Therefore, at this

hydrogen ion concentration the protein molecule is electrically neutral.

2 .Measurement

Isoelectric points are most conveniently measured in a gel medium

containing carrier ampholytes (buffering agents), which stabilize the pH

gradient in the gel. The system is then subjected to an electric field

and proteins are concentrated in those regions having the appropriate pH.

This technique, which is called isoelectric focusing, is one of the most

sensitive and widely used separation techniques in modern analytical

biochemistry, and accurate pi values obtained from standardized gels have

proved most useful for the practitioners of gel electrophoresis.

More generally, however, pi provides a quantitative measure of relative

protein surface charge as well as the pH of zero charge, and insofar as it

is thought that a gel more or less mimics an aqueous environment with

respect to solvation effects, pi measurements are important indicators of

absolute and relative protein solubility as well as propensity for

aggregation and stability. Thus, for proteins for which electrostatic

interactions in an aqueous, salt -containing environment play a significant

role in determining such properties as solubility, aggregation, affinity

for poljnner adsorption, biological activity, phase affinity (aqueous twophase extraction) , and adsorption affinity for various surfaces

isoelectric point data should be given high priority.
2 . 3 Data Sources

There are several substantial obstacles to be overcome in compiling highquality data for the isoelectric points of proteins obtained from gel

electrophoresis studies. First, one usually wishes to study the native

protein in a medium which resembles an aqueous solution, and so the

carrier ampholytes and solution conditions should not denature the

protein. Unfortunately, in some instances solution conditions are not

accurately described and one must either assume non- denaturing conditions

or else reject the data. Second, the temperature at which the pi

measurement is made is not always reported, and since isoelectric points

of proteins are known to be temperature dependent (pi usually decreases

with increasing temperature) , this omission can make meaningful

comparisons very difficult. Third, the number of publications in which

isoelectric point data are presented is truly enormous and the literature

is spread over a very wide range of journals. Therefore, in order to

acquire a comprehensive literature reference list, a variety of citation,

abstraction, and kejrword "data bases" must be researched. The acquisition

problem is compounded by the fact that the measurement of isoelectric

points is now so routine that words such as "isoelectric," "pi,"

"electrophoresis," etc. do not appear in the abstract or key word list of

many relevant papers. Fourth, it happens that most proteins exhibit

surface charge "microbeterogeneity" ; i.e., subtle conformational

variations and/or variable glycosylation within a single species give rise

to measurable variable surface charge densities, so that a protein is

spread over a range of isoelectric points rather than focused at a single

pi. This glycosylation and/or conformational broadening, which may have a strong temperature, pH and time dependence, is a serious impediment to

high resolution separation and identification.

Finally, the majority of proteins separated by isoelectric focusing simply

have not been identified. Not only is the primary amino acid sequence

undetermined, but the molecular weight and precise origin are unknown, so that the protein's "name" consists of, for example, a set of coordinates

obtained from two dimensional gel electrophoresis.

Despite such difficulties, there have been several attempts to collect and

evaluate extensive pi data on proteins. Because of the enormous effort

required, the number of comprehensive tabulations of isoelectric point

data on proteins is quite small; in fact, after an exhaustive search of

the literature we located only three. We then contacted the authors and

ascertained that, to the best of their knowledge, theirs are the only such

tabulations in existence. Though other extensive tabulations do exist,

they consist almost entirely of data taken from these primary

compilations. Since the last comprehensive table was published in 1981, we have elected to update by including a set of much more modest (though

not redundant) tabulations which have appeared since then.

In our literature search we used the STN International, Dialog, and

Medline/Medlars computerized "data bases," with title, abstract, and

keyword search. The citation index was used whenever key contributors

could be identified. A variety of keyword and cross referencing schemes

where employed to ensure that our literature search would be as thorough

as possible. In addition to the computerized data base search, we have

conducted extensive though rather ad-hoc "hands-on" searches in the NIST

and NIH libraries.
3. Conclusions and Reconunendatlons

Conclusions and Recommendations: Our conclusions and recommendations

concerning compiled data on the isoelectric points of proteins are as follows

(1) The 1981 tabulation by Righetti et al. represents the most recent

comprehensive publication on this topic, and an updated version would be

most welcome and useful, not only for the gel electrophoresis community,

but also for those interested in the more general aspects of biochemical

separation, measurement, and process control. This opinion is

enthusiastically supported by written and phone communication with

Professor Righetti (University of Milan) , who has offered his services and

that of an assistant in evaluating the quality of primary data sources

which would be acquired by us. Although a full update represents a Herculean task in literature acquisition, the project could be broken into

manageable pieces through several strategies; for example, an update

restricted to 3 or 4 year intervals since 1981. Professor Righetti has

stated that over 2000 reprint requests for his compilation had been

received within the first 6 months after publication, and that many of

these requests came from biotechnology industries: the practical utility

of such an undertaking is, therefore, obvious.

(2) pi measurements provide information on the relative surface charge of

proteins in a medium conducive to isoelectric focusing. However, a more

direct and complete characterization of protein charge is provided by

hydrogen ion (and certain divalent cation) titration curves. The most

recent compilation and analysis of hydrogen ion titration curves is by C.

Tanford in Advances in Protein Chemistry, 12, pp. 69-165, (1952), which is

considerably older than the Righetti tables (1981). Though the protein

titration cuirve literature seems to be very scarce relative to the pi

literature, its relevance to such interfacial properties as electrostatic

adsorption would seem to justify a modern survey.

(3) A relatively modem experimental technique called electrophoretic

light scattering (ELS) is capable of providing a rapid and accurate

determination of protein charge distributions in multicomponent solutions.

The main advantage of ELS over gel electrophoresis is that the solution

can be tailored to mimic actual physiological or bioreactor conditions

(temperature, pH, ionic strength, viscosity, etc.) so that an extrapolation from the gel environment is not necessary. Furthermore, ELS

measures diffusivity distributions in addition to surface charge, so that

aggregation processes on a microscopic scale can be accurately quantified,

and this has important implications with regard to the prediction and

recognition of good crystallization conditions and the subsequent

determination of protein structure via x-ray diffraction. ELS data exists

only for a relatively small number of proteins and there have been no attempts at a compilation of primary data sources

(4) Another relatively modem separations/analysis technique, known as capillary zone electrophoresis (CZE) has the attraction of being a "free

solution" method; i.e., a gel medium is not necessary. Instead, a very

narrow (50 /xm) long (1 m) fused silica capillary tube filled with a saltcontaining aqueous solution is "injected" with a tiny pulse of the

macromolecular mixture at one end, and a high voltage (0-36 kV) is applied

across the ends of the tube. The charged macromolecules migrate in the

external field and are swept along with the electroosmotic flow, and
detection is usually achieved with a variable wavelength UV absorption

spectrophotometer. Resolutions comparable to those obtained in

isoelectric focusing have been reported, and we therefore recommend a study of protein electrophoretic mobility and surface charge using this

comparatively simple method.

The following is a bibliography and description of compiled data sources

for the isoelectric points of proteins.

4. Bibliography

We have subdivided this bibliography into two sections, namely Primary and

Secondary Compilations. Primary refers to an original source of evaluated

compiled data, while Secondary refers to sources which contain data

extracted from a primary source, short tables or lists of isoelectric

points, very old or suspect data, or discussions of techniques and

applications of isoelectric focusing.

A. Primary Compilations

Al Pier Giorgio Righetti and Tiziana Caravaggio "Isoelectric Points and

Molecular Weights of Proteins: A Table," Journal of Chromatography 127 . pp. 1-28 (1976).

The period from about 1960 to 1976 was searched, apparently without the

aid of a computerized data base. Only the most accessible references are given for each entry and the authors plainly state that some references

might have been overlooked. The compilation contains about 800 pi values

and 345 references are cited. The following criteria were employed in

preparing the table.

1. Only named proteins are recorded.

2. Only pi's obtained by isoelectric focusing in the presence of

carrier ampholytes are tabulated.

3. The native molecular weight as well as subunit molecular weight and

stoichiometry have been recorded when this data was available.

4. For each entry, the source and, when applicable, the organ of origin

and/or subcellular location of the protein is given.

5. The pi values are listed along with the temperature at which the pH

was measured.

6. In the case of proteins displaying charge microheterogeneity (a

common occurrence) , the major pi components have been indicated.

A supplementary table of pH markers (proteins and dyes) for isoelectic

focusing is presented. Moreover, the authors discuss in some detail the

problems and pitfalls associated with (a) the measurement of pH in

isoelectric focusing (b) pH determination in the presence of electrolyte

concentration gradients (c) measuring pH after isoelectric focusing in gel

media (d) the use of pH markers.

A2 Daniel Malamud and James W. Drysdale "Isoelectric Points of Proteins:

a Table" Analytical Biochemistry 86, PP- 620-647 (1978).

The period from January 1970 - March 1976 was searched with the Medlars

data base and Biological Abstracts. No other data bases were used. There

were 3000 citations produced, 1000 of these were screened and 400 finally

selected for the table, which contains 396 entries. The following

criteria were used in preparing the table.

6
1. Only named proteins are recorded.

2. Only pi's obtained by isoelectric focusing in the presence of

carrier ampholyte are included.

3. pi's were determined under nondenaturing conditions except in the

presence of urea, and these cases are designated.

4. When only one or two charge variants of a given protein are present,

those pi values are listed. With multiple forms, the pi range is

listed, and if there is a dominant form, that value is listed first.

5. Enzyme commission numbers from the original papers are included.

6. The organism and tissue from which the protein was extracted are

listed.

The molecular weights are not listed, nor is the temperature at which the

pH was measured.

A3 Pier Giorgio Righetti and Gabriela Tudor "Isoelectric Points and

Molecular Weights of Proteins: A New Table," Journal of Chromatography

220, pp. 115-194 (1981).

The period from 1976 to 1979 was covered using the literature reference

list Acta Amphollnae, published by LKB Produkter (Bromma, Sweden). We

screened 2200 publications and 945 of these were selected for the

compilation, which consists of about 2400 pi values and 951 references.

The following criteria were employed in preparing the table

.

1. Only named proteins are recorded.

2. Only pi's obtained by isoelectric focusing in the presence of

carrier ampholyte are tabulated.

3. The native molecular weight as well as subunit molecular weight and

stoichiometry have been recorded when this data was available

.

4. For each entry, the source and, when applicable, the organ of origin

and/or subcellular location of the protein is given.

5. The pi values are listed along with the temperature at which the pH

was measured.

6. In the case of proteins displaying charge microheterogeneity (a

common occurrence), the major pi components have been indicated.

B. Secondary Compilations

Bl Felix Haurowitz The Chemistry and Function of Proteins, 2nd Edition,

Academic Press (1963)

.

This book is relatively old, by today's standards, and does not contain

isoelectric data on proteins. However, isoelectric point data for 10

monoamino acids are listed in Table VI- 1, along with ionization constants.

In addition, the isoelectric points and ionization constants for seven

amino acids are given in Table VI-2.

B2 Robert Earl Feeney and Richard Gall Allison Evolutionary

Biochemistry of Proteins^ Wiley Interscience (1969).

This book contains a number of tables of properties of homologous and

analogous proteins from avian egg whites, blood sera, milk and other

substances. The isoelectric points of 11 egg white proteins are listed in

Table 2.2, along with their molecular weight values, percent composition

of egg white, sedimentation coefficient, diffusivity and other properties.
The isoelectric points of 16 naturally occurring inhibitors of proteolytic

enzymes are presented in Table 8-1, with their molecular weight and a description of the type of enzyme inhibited is also included in the table.

B3 Gerald D. Fasman, Ed. CRC Handbook of Biochemistry and Molecular

Biology, Proteins Volume II, 3rd Edition, CRC Press, Inc. Boca Raton,

Florida (1976).

This handbook is divided into three volumes, Volume I contains data on

amino acids, peptides and polypeptides, while Volumes II and III contain

data mainly on proteins. Volume II has a number of tables of protein

properties which include isoelectric point measurements and are summarized

below.

The molecular parameters of Purified Human Plasma Proteins are given in a table on pages 242 to 253. It includes the isoelectric point data for 38

Purified Human Plasma Proteins. Other properties included are the

electrophoretic mobility at pH 8.6, sedimentation coefficient, diffusion

coefficient, partial specific volume of the protein, fractional ratio,

intrinsic viscosity, the absorption and the amount of protein in normal

plasma. References to the original research papers are also given.

The isoelectric points of Retinol- Binding Protein and Tamm-Horsfall

Mucoprotein are provided on page 304, along with many other properties

including molecular weight, sedimentation coefficient, partial specific

volume and absorption.

A series of tables lists properties of Plant Protease Inhibitors. The

tables contain isoelectric point data, molecular weights, and

specificities for a variety of substances. Separate tables are presented

for: a) Solanum Tuberosum, Potato Tubers, b) Legtunes, c) Gramlneae Cereal

Grains, and d) Other Plants. References to original research papers are given

Properties of Animal Proteinase Inhibitors are sxommarized in a series of

tables which list isoelectric point, the source of the inhibitor,

molecular weight, carbohydrate content, specificity, and reference.

Separate tables are provided for: a) Lower Animals, b) the Egg Whites of

Birds, c) Mammalian Organs and Secretions, and d) Mammalian and Chicken

Blood.

Properties of Microbial Proteinase Inhibitors are included in a table

which contains information on the isoelectric point, the inhibitor source,

the specificity, and the original reference.

B4 William W. Yotis Chapter 9 "Isoelectric Focusing of Microbial

Proteins" in Biological and Biomedical Applications of Isoelectric

Focusing, N. Catsimpoolas and J. Drysdale (Eds,), Plenum Press, pp. 265-

301, (1977).

This chapter describes the application of isoelectric focusing for the

isolation and characterization of microbial proteins. Nine tables include

isoelectric point values for various t3rpes of microbial proteins. The

isoelectric points of fungal proteins are depicted in the first three

tables, where Table 1 gives pi values for seventeen Aspergillus and

Neurospora macromolecules , Table 2 includes isoelectric points of 9

Candida and Saccharomyces proteins, and Table 3 provides pi data for 15

8

I
fungal enzymes . Tables of isoelectric point data are also included for 7

separate classes of bacterial proteins. The isoelectric points of 22

Staphylococcus Aureus proteins are listed in Table 4, while Table 5

contains.pl values for 15 Escherichia coli macromolecules . Eight

Clostridial proteins have their pi values listed in Table 6 while pi data

for 10 Streptococcal macromolecules are presented in Table 7 . The

isoelectric points for 12 proteins isolated from Gram-Positive bacteria

are given in Table 8, with Table 9 having pi data for 10 Pseudomonas and

Spirillum proteins. The last table (10) presents isoelectric data for 19

proteins isolated from various Gram-Negative Bacteria. References to all

original research papers are given.

B5 Charles R. Cantor and Paul R. Schimmell, Biophysical Chemistry Part

III The Behavior of Biological Macromolecules, W. H. Freeman and Company,

New York (1980).

This book is part of a three-book series on biophysical chemistry. The

first book covers the conformation of biological macromolecules, the

second book addresses techniques for the study of biological structure and

function, and this book discusses various aspects of the behavior of

biological macromolecules. As such, it addresses the binding of smaller

molecules to nucleic acids. The isoelectric points of five proteins known

to bind to nucleic acids are given in Table 23-8, along with their

molecular weights, binding specificity, and other properties.

B6 Jean-Claude Kader, Dominique Douady and Paul Mazliak Chapter 8

"Phospholipid Transfer Proteins" in Phospholipids, Hawthorne, Ansell

(Eds.), Elsevier Biomedical Press, pp. 279-311, (1982).

This chapter describes phospholipid transfer proteins and their role in

intermembrane exchange. The properties of 23 phospholipid transfer

proteins are presented in Table 2, including data on their isoelectric

point, molecular weight, specificity, and purification factor.

B7 Terence J. Scallen and George v. Vahouny Chapter 3 "Participation of

Sterol Carrier Proteins in Cholesterol Biosjmthesis. Utilization, and

Intracellular Transfer" in Sterols and Bile Acids, H. Danielsson and J'.

Sjovall (Eds.), Elsevier Science Piiblishers B. V., pp. 73-93, (1985).

This chapter describes sterol carrier proteins which are capable of

binding sterols and transporting them to specific enzyme sites involved in

cholesterol biosynthesis and utilization. The characteristics of two

sterol carrier proteins are given in Table 1 and include the isoelectric

points, molecular weights and substrate specificity.

B8 Bonno N. Bouma and John H. Griffin Chapter 5A "Initiation

Mechanisms: The Contact Activation System in Plasma" in Blood

Coagulation, R. F. A. Zwaal and H. C. Hemder (Eds.), Elsevier Science

Publishers B. V., pp. 103-139 (1986).

This chapter summarizes current biochemical information of selected blood

plasma proteins and presents several integrated hypotheses for the

explanation of the molecular mechanisms responsible for activation of the

contact system of blood plasma. Among the biochemical information

provided in Table 1 are isoelectric point d^ta for four blood plasma

proteins of the contact activation system. Other data in the table

include molecular weight data and concentration of the proteins in

citrated plasma.
B9 Jan L, Breslow Chapter 12 "Lipoprotein Genetics and Molecular

Biology" in Plasma Lipoproteins, A. M. Gotto, Jr. (Ed.), Elsevier Science

Publishers B. V., pp. 359-397 (1987).

This chapter reviews current knowledge of human apolipoprotein gene

structure and genetic variation. Isoelectric point values for nine

apolipoproteins are included in Table 1, along with plasma concentration,

molecular weight data and a description of the apolipoprotein function and

its association with clinical disorders. Apolipoproteins are associated

with human diseases and are important structural constituents of

lipoprotein particles. They have been shown to participate in lipoprotein

synthesis, secretion, processing and catabolism.

BIO IBI/Pustell Protein DNA Sequence Analysis Database

This computerized database has many features such as primary sequence

editing, a sequence homology search, and the location of protein coding

regions in DNA. A relatively simple feature is the Cyborg compatible

program that computes (relative) electrophoretic mobilities of biological

macromolecules from primary sequence input and solution pH. Though far

from precise, this program yields reasonable predictions of the relative

mobilities of completely denatured proteins, nucleic acids, and linear

macromolecular fragments in general.

Bll The Aarhus Hvunan Protein Database: contact: Dr. J.E. Cells, Institute

of Medical Biochemistry, Ole Worms Alle, Bldg. 170, University Parks,

Aarhus University, DK 8000 Aarhus C, Denmark.

This is typical of the most recent, and still evolving, computerized

protein databases having a strong biomedical emphasis. This database is

derived from high-resolution two-dimensional gel electrophoresis of

proteins, which means that separation is achieved in terms of both

isoelectric point and molecular weight. Under carefully controlled

conditions, protein separation is reproducible to the extent that the

position and quantity of each protein can be recorded by a computer

utilizing sensitive scanning devices. It is then possible to accurately

compare protein "patterns" of various cell types of normal and abnormal

(mutated or cancerous) origin and to establish databases of protein

information derived from these studies. In the long run, protein

databases similar to Aarhus are expected to foster a wide variety of

biological information acquisition, such as mapping of structural genes,

DNA sequence determination, protein structure, selection of antibodies,

and even purification procedures. It is clear that high quality,

extensive isoelectric point data plays a key role in the construction of

such a database.

10
Solubility of Oxygen in Bioreactor Fluids

A Survey of Compiled Data Sources and Predictive Methods

January 31, 1989

11
Contents

1. Relevance 13

2. Solubility of Oxygen 13

2.1. Solubility of Oxygen in Pure Water 17

2.2. Data on Solubility of Oxygen in Bioreactor Fluids 18

3. Conclusions and Recommendations 18

4. References 18

5. Bibliography 21

12
1

Relevance

A correct supply of oxygen to the cells that are the chemical factories

in a bioreactor is essential to the reaction process. The solubility of

oxygen is one of the determining parameters in the process of oxygen

supply. As pointed out by Schumpe et al. in their 1982 chapter on gas

solubilities in microbial culture media, in Advances in Biochemical

Engineering, Volume 24 Reaction Engineering [S1982] oxygen solubility is

of major importance. Its value is required for determining the oxygen

volume mass transfer coefficient, to establish mass balances and

calculate yield coefficients, and to design and scaleup bioreactors.

The presence of other electrolyte and nonelectrolyte solutes in

bioreactors affects significantly the solubility of oxygen. Most of the

experimental information on, and predictive models of oxygen solubility

in bioreactor media are of very recent origin and are not yet available

in the form of handbook compilations. The bibliography attached to the

present survey provides entry into the recent literature on this topic.

2, Solubility of oxygen

There are many definitions of solubility, several of which to be given

below. For the present purpose, we will define the solubility c^ as the

number of moles per kg of water at an oxygen partial pressure of 101.325

kPa.

The solubility of oxygen in water has been exhaustively measured. It is

extremely well characterized over the whole range of temperatures of

interest in bioprocessing. The lUPAC volume on Solubility of Oxygen,

published in 1981 and described in the bibliography attached, gives

complete information [B1981]

In bioreactors, however, the reaction medium is not pure water, and

therefore the operator will need to know how the oxygen solubility is

modified by the salts and organic solutes present. Traditionally, the

effect of other solutes on the solubility of a gas is called "salting

in" or "salting out," depending on the sign of the effect. The theories

for describing this effect have been reviewed by Long and McDevit

[L1952]. Hydration theories can only explain salting out, and ascribe

it to effective removal of water from the bulk by the ion. Electrostatic

theories ascribe the salting in and salting out of gases by electrolyte

solutes to the change in the dielectric constant of water caused by the

nonelectrolyte gaseous solute (oxygen in this case) . van der Waals

theories supplement the electrostatic theories by considering the

effects of dispersion forces. Internal pressure theories connect the

salt effect to the partial molar volumes of the nonelectrolyte solution

and the molar volume of the electrolyte solution [L1952, B1966] . The

activity coefficient of dissolved oxygen, 7^, is a function of the

concentration of all dissolved species. In the case that only one salt

is present, at a low concentration Cg, the simplest assumption one can make is that the species do not interact, so that;

log 71 - ki ci + kg Cg . (1)

By measuring the solubility of oxygen in pure water, c°i,sat» ^^^ ^^ ^^®

solution of salt s at the same temperature and partial pressure, cl,sat,

13
the activity coefficient of oxygen is obtained from:

log(7l/7°l) - log (c°i,sat/ci.sat) " 1^1(^1, sat " ^°l,saO + K ^s (2)

of the salt, the first term on the right in (2) can be neglected even

though k^ and kg may be of the same order.

The coefficient kg is the theoretical infinite -dilution salting out

parameter. Experimental plots of log (c°i sat/^1 sat) versus Cg show

linear behavior over concentration ranges up to a few molar. In this

range, kg is well defined. It is called the Setschenov parameter and

its value depends on the units chosen for Cg

The effects of added salt on the solubility of oxygen are tjrpically of

the order of a 30% decrease in solubility in a 1-molar NaCl solution.

It follows that the operator of the reactor does not have to worry about

this effect for salt concentrations of the order of 1 g/L or less.

Although Setchenov parameters for salting out of oxygen have been

measured for many salts, the information on most salts is limited to one source and is not substantiated. The lUPAC volume quoted [B1981] lists

data and Setchenov parameters for 50 or more solutes in water, but

cautions that most data would need confirmation.

If one prepares a list of salts present in bioreactors at concentrations

of 1 g/L and above, (see table 1) it turns out that data on oxygen

salting out are available in the lUPAC volume for only about two or three of these salts. Newer compiled data sources listed in the attached

bibliography do contain additional information.

Setschenov parameters do depend on the temperature. In the range of

interest in biological applications, temperatures from 20 to 40 °C, the

Setschenov parameter decreases only slightly [S1982] even though the

solubility of oxygen itself is strongly temperature dependent. Often,

the Setschenov parameter values are not well enough known to warrant

concern about their temperature dependence.

14
Table 1 . Solutes commonly used in bioreactors at concentrations exceeding 1 g/L

Inorganics

NaCl

KCl

MnCl2

AICI3.6H2O

C0CI2.6H2O

NH4CI

NH4H2PO4

KH2PO4

K2HPO4

NaHC03

Na2S04

(NH4)2S04

MgS04

ZnS04 . 7H2O

MnS04.H20

Setschenov par. Ref, Organics Setschenov par.Ref.

S1978,B1981,Khl984,Ll986,Z1986 methanol K1984,B1981

L1986 ethanol K1984,B1981

L1986 propanols K1984,B1981

B1981

L1986 butanols K1984,B1981

L1986 glycerol K1984,B1981

L1986 glucose B1981

sucrose B1981

casein

L1986

L1986

L1986

L1986

15
Van Krevelen and Hoftijzer [vK1948] proposed to use, Instead of the

concentration, the ionic strength I of the salt, defined as

I - (Ca Za^ + cc Zc^)/2

with z the valency, and subscripts a, c referring to anion and cation,

respectively.

Schumpe and coworkers [S1978, Q1981] generalized eq (2) to multicomponent

salt solutions. In doing so, they noticed that the use of salt- specific

Setschenov constants leads to inconsistencies. Instead, they defined

ion specific Setschenov parameters H^. Furthermore, they generalized the

log-additivity rule to multicomponent mixtures. Thus, neglecting the k]^ term

in eq 2, they obtain:

Log (c°/c) - 1/2 Cg 2 Hi Xi Zi2 (3)

i

where Xj_ is the ratio of the molality of ions of species i to the molality of

salt, Cg. Lang and Zander [L1986) list H^ values of a large number of ions.

The Setschenov parameter for any chosen salt is then obtained from:

kg - 1/2 2 Hi Xi Zi^ (4)

i

where the sum is over the contributions from the specific cation and anion.

In bioreactors, nonelectrolyte solutes such as sugars and alcohols are prevalent. The change in solubility of oxygen in sugar solutions can be

described by a relation analogous to the Setschenov equation. The solubility

of oxygen in alcohol solutions shows more complex behavior and sometimes

displays maxima and minima as a function of concentration. In such cases, one may want to substitute the experimental value of the solubility of oxygen

in the alcohol solution for the parameter c° in eqs (1-3). Both the lUPAC

volume and newer sources contain information on the solubility of oxygen in

aqueous solutions of the lower alcohols , glycerol and sugars

For small organic molecules, these empirical rules appear to offer few

problems, but erratic results have been reported if biomolecules are present

in solution [S1982]. It is not excluded that adsorption of solutes on biomass is an important effect that might affect oxygen uptake, but the

literature on this point is inconsistent [S1982]

This report falls into the following parts: (1) solubility of oxygen in pure

water; (2) availablity of "salting out" data for solutes encountered in

bioreactors; (3) recommendations for further work, and (4) brief descriptions

of relevant literature sources. The purpose of this report is not : to provide a compilation of salting out

data for oxygen in bioreactors. Rather, it is a guide to what is known and

what needs further study.

16

I
2.1 Solubility of oxygen in pure water

The Solubility Data Series of the International Union of Pure and Applied

Chemistry has published its Volume 7 on the Solubility of Oxygen and Ozone in

1981 [B1981] . It defines a number of coefficients that are used to

characterize gas solubility in liquids, such as:

Weight solubility c : the number of moles of dissolved gas per kg of solvent

when the partial pressure of the gas equals 101.325 kPa.

Bunsen Coefficient a : the volume of gas (reduced to standard conditions)

which is absorbed by unit voliome of liquid at the same temperature and at a partial gas pressure of 101.325 kPa

Ostwald coefficient L : the ratio of the volume of gas absorbed to the volume

of the absorbing liquid, all at the same temperature.

Henry ^s constant H : the proportionality constant between partial gas

pressure and the mole fraction of dissolved gas, in the limit of infinite

dilution.

Many methods of determining gas solubility are discussed in the review of

Battino and Clever [B1966] . Both in saturation methods and in extraction

methods, complete degassing is essential to success. Pumping on the solution

alone cannot achieve this goal. Spraying the preliminarily degassed liquid

through a nozzle into an evacuated flask can remove 97-98% of the dissolved

gas. Alternatively, the liquid may be stripped of the gas studied by

bubbling through another inert gas. Volumetric saturation methods proceed by

measuring by manometry, volumetry, or both, the amount of gas taken up by a known amount of degassed liquid. The contact of the gas with the liquid is

enhanced by a variety of techniques, such as vigorous shaking, or having the

gas flow over a liquid film. Many ingenious methods, developed in the course

of the past century, are described and referenced in the review by Battino

and Clever [B1966] . In modern extraction techniques, dissolved mixed gases

are removed and analyzed by mass spectrometry or by gas chromatography. It

is also possible to obtain gas solubility information by gas liquid

partitioning chromatography. Although this latter method is fast, cheap and

reasonably reproducible (~2%), a large number of assumptions have to be made

in order to extract solubility information from the data. Finally, for

oxygen, chemical methods can be used to determine its solubility, the most

popular method being one based on oxydation of manganous hydroxyde, and

introduced by Winkler in 1889. We refer to [B1966] for a discussion of this

method.

The solubility of oxygen in water at 25 °C may be considered a standard.

Seven determinations, by various methods, carried out between 1958 and 1965,

agree to 0.2%. The lUPAC volume [B1981] gives highly accurate (0.1% or better) values for the above coefficients for oxygen in water, for

temperatures from 273 to 433 K, in tabular form and in the form of

correlating equations. In addition, values of the enthalpy, entropy and

Gibbs free energy of solution are listed for this system.

17
2.2. Data on solubility of oxygen In bloreactor fluids

In table 1, solutes are listed that may be present in bioprocessing fluids at

concentrations exceeding 1 g/L. Two classes of solutes are given: inorganics

and organics . The data were obtained from articles , chapters in textbooks or conference proceedings on bioprocessing, such as the chapters by Fiechter

[F1984] and by Jaime and Blackman [J1985] papers by Ju, Ho and Baddour

[H1986, H1988, J1988] and by Linek, Benes and Holecek [L1988] . The references

to Setschenov parameter data for the salts listed are given.

3. Conclusions and Recommendations

The data on oxygen solubility in water are abundant, and the solubility is

very well characterized as a function of temperature. The data on "saltingout" effects due to a variety of inorganic and organic solutes of interest in

bioreactors are far more limited. Empirical predictive methods of the logadditive tjrpe appear satisfactory and have been generalized to pertain to

individual ionic species. The most recent and comprehensive compilation of

Lang and Zander [L1986] is limited to nitrates, chlorides and sulfates.

Schumpe et al. however, gave ion specific salting out constants for CIO4,

CO2 and P [S1978] .

It might be of interest to examine the grounds for the validity of the logadditive rule, delineate the range of validity in one and multicomponent

electrolyte solutions , explain the experimentally determined Setschenov

constants in terms of known characteristics of the ions and generalize to

weak electrolytes and to divalent ions. The Battino review [B1966] seems to

imply that each of the mechanisms that were theoretically proposed, namely

hydration, electrostatics, van der Waals forces and internal pressure

effects, explains, at best, some of the phenomena in some of the cases.

The situation in media with large amounts of biomass appears unclear [S1982]

.

Likely, the causes of the discrepancies reported are effects other than

"salting out," namely adsorption and chemical or metabolic processes at the

cell membrane or within the cell; these phenomena will have to be studied in

more depth experimentally before an understanding can be reached.

4. References

[vK1948] D. W. van Krevelen and P. J. Hoftijzer, Chemie et Industrie:

Numero Speciale du XXI '®°'® Congress International de Chim. Industrielle,

Bruxelles, p. 168 (1948).

[L1952] F. A. Long and W. F. McDevit, Chem. Rev. 51, 119, (1952).

[B1966] R. Battino and H. L. Clever, "The Solubility of Gases in Liquids,"

Chem. Rev. 66. 395-461 (1966).

[S1978] A. Schumpe, I. Adler and W. D. Deckwer, "Solubility of Oxygen in

Electrolyte Solutions," Biotech and Bioeng. 21, 145-150 (1978).

[S1979] A. Schumpe and W. D. Deckwer, "Estimation of O2 and CO2 Solubilities

in Fermentation Media," Biotech and Bioeng. 21, 1075-1078 (1979).

18
[B1981] R. Battino, Editor, "lUPAC Solubility Data Series Voltune 7, Oxygen

and Ozone," Pergamon, Oxford (1981).

[Q1981] G. Quicker, A. Schumpe, B. Koenig and W. D. Deckwer, "Comparison of

Measured and Calculated Oxygen Solubilities in Fermentation Media," Biotech

and Bioeng. 23, 635-650 (1981).

[S1982] A. Schumpe, G. Quicker and W. D. Deckwer, "Gas Solubilities in

Microbial Culture Media," Adv. Biochem. Eng. Vol. 24, Reaction Engineering,

A. Fiechter, Ed., Springer Verlag, Heidelberg (1982); pp. 2-38.

[K1984] I. Kutsche, G. Glidehaus, D. Schuller and A. Schumpe, "Oxygen

Solubilities in Aqueous Alcohol Solutions," J. Chem. Eng. Data 29, 286-287

(1984).

[Khl984] N. E. Khomutov and A. S. Groisman, "Temperature Dependence of the

Solubility of Oxygen in Aqueous Electrolytes," Russ. J. Phys. Chem. 5, 433-

434 (1984).

[L1986] W, Lang and R. Zander, "Salting-Out of Oxygen from Aqueous

Electrolyte Solutions: Prediction and Measurement," Ind. Eng. Chem. Fund.

25, 775-782 (1986).

19
References to compositions of bloreactor media

[J1985] D. W. Ja3rme and K. E. Blackman, in "Advances in Biotechnological

Processes" Vol.5, A. Mizrahi and A. L. van Wezel, Eds. Alan R. Riss, Inc.

New York 1985. p. 2-23

[F1984] A. Fiechter, in Advances in Biochemical Engineering/Biotechnology 30 : Bioprocess Parameter Control. A. Fiechter, Ed. Springer Verlag, Berlin 1984,

p. 8-60.

[H1986] C. S. Ho, L. K. Ju and C. T. Ho, Biotechnology and Bioengineering 28,

1086-1092, 1986.

[H1988] C. S. Ho and L. K. Ju, Biotechnology and Bioengineering 32, 313-325,

1988.

[J1988] L. K. Ju, C. S. Ho and R. F. Baddour, Biotechnology and

Bioengineering 31, 991-1005,1988.

[L1988] V. Linek, P. Benes and 0. Holecek, Biotechnology and Bioengineering

32, 482-490 (1988).

20
5 . Bibliography

[S1978] A. Schiunpe, I. Adler and W. D. Deckwer, "Solubility of Oxygen in

Electrolyte Solutions," Biotechnology and Bioengineering 21, 145-150 (1978).

Ion- specific salting- out parameters are presented for the solubility of

oxygen in multicomponent electrolyte solutions. The authors claim that the

parameters obtained at 25 °C can be safely used up to 40 °C.

Cations: H+, Li"^, Na+, K+, Rb"*", Cs+, NH4+, Mg2+, Ca2+, Ba2+, Mn2+.

Anions: F" , Cl", Br", I", OH", NO3", CIO4" , SOs^", P04^".

[S1979] A. Schumpe and W. D. Deckwer, "Estimation of O2 and CO2 Solubilities

in Fermentation Media," Biotechnology and Bioengineering 21, 1075-1078

(1979).

The authors postulate that the effects of individual species on the

solubility of the gas, as characterized by ion- specific Setschenov

parameters, are additive, both in water and in dilute alcohol solutions.

They determine these ion- specific Setchenov parameters for CO2 for 11 cations

and seven anions from solubility measurements and claim that they depend very

little on temperature in the range of 10-40 °C. The ion specific constants

are listed for CO2.

Setschenov plots are given for oxygen solubility in several salt solutions

that also contain alcohols, namely methanol, ethanol, propanol or glycol. If

the oxygen solubility is referred to that in the alcohol solution, rather

than to that in pure water, the same additivity rule can be applied, with

identical ion- specific constants. The validity of this rule was tested

experimentally for alcohol solutions up to 10% in weight.

Cations: H"*", Li+, Na+, K+, Rb"*", Cs"*", NH4+, Mg2+, Ca2+, Ba2+, Fe2+, Al^+.

Anions: Cl", Br", I", NO3-, SO42-, ?OiJ^-

.

Alcohols: Methanol, ethanol, propanol and glycerol.

[B1981] R. Battino, Ed. "lUPAC Solubility Data Series Volume 7, Oxygen and

Ozone," Pergamon Oxford, 1981.

This is a compilation and critical evaluation of oxygen solubility data in

pure water and in aqueous solutions. A correlation of the pure -water

solubilities in the range of °C to 100 °C is presented that is accurate to

0.1%.

There are about 125 pages of data on oxygen solubility in salt solutions.

Each page contains a critical evaluation of the oxygen solubility data in a particular publication. In general, only one source is available per salt,

and the editor cautions about reliability. A Setschenov parameter is given

wherever possible. In our table 1 of salts occurring in bioreactors, we have

indicated the ones for which solubility data and/or Setchenov parameters can

be found in the lUPAC voltune [B1981]

.

21
The lUPAC volume contains about 20 pages of information on solubility of

oygen in various aqueous alcohol solutions, from methanol through the

butanols and for glycerol (for this last system, there is only one 1912

reference)

There is a 90-page section on solubility of oxygen in biological fluids,

which in most cases are complex multicomponent media. For instance, one can

find information on oxygen solubility in fermentation media, corn steep

liquor, yeast extract, molasses and wines. There are two references for

glucose, only one of them recent [Z1976]; this latter reference also contains

data for oxygen solubility in dissacharide solutions. There are three

references for the sucrose solution, only one of them recent [H1978]

In summary, the lUPAC volume is a complete resource for oxygen solubility

data obtained prior to 1980,

[Q1981] G. Quicker, A. Schumpe, B. Koenig and W. D. Deckwer, "Comparison of

Measured and Calculated Oxygen Solubilities in Fermentation Media,"

Biotechnology and Bioengineering, 23, 635-65, (1981).

A fast volumetric method is developed for measuring solubilities of carbon

dioxide and oxygen in fermentation media. Data are reported for solubility

of both oxygen and carbon dioxide in solutions of electrolytes without and

with sugar. The log- additive rule used by Onda et al. [01970] in terms of

ionic strengths of individual salts is criticized as being inconsistent, and

is replaced by a log- additive rule in terms of individual ions and ionspecific Setschenov constants. The validity of the log-additive rule is

tested for mixed electrolyte and nonelectrolyte solutions and found to be

valid if referred to the actual solubility of oxygen in the nonelectrolyte

solution, instead of to that of oxygen in pure water. In the case of oxygen,

ion-specific Setschenov parameters are given for H2PO4" , HP04^', S203^",

HCO3' and C5H5O CH2 COG". Nonelectrolytes include lactose, sucrose, glucose,

ethanol , propanol and glycerol

[S1982] A. Schumpe, G. Quicker and W. D. Deckwer, "Gas Solubilities in

Microbial Culture Media," Advances in Biochemical Engineering, Vol. 24,

Reaction Engineering, A. Fiechter, Ed., Springer Verlag, Heidelberg 1982; p.

2-38.

This paper is a scholarly review of oxygen and carbon dioxide solubilities in

microbial media. Salting- out effects are discussed in some depth.

Estimation methods, based on the additivity rule for the Setschenov parameter

eq (3) are applied to various bioreactor media. For systems in which the

solutes are preponderantly small molecules, the predictive capability is

quite adequate.

The predictive methods may fail if the principal component (on a

g/dm-^ basis) is a macromolecular compound, such as a protein or albumen. The

authors state that the few reports on the effect of biomass on oxygen

solubility are mutually inconsistent, and that this effect needs further

experimental study and analysis.

The paper tabulates Setschenov constants for oxygen solubility in solutions

of about 30 organic compounds encountered in bioreactors. About half of

these are proteins. Over 80 literature references are cited.

22
[K1984] I. Kutsche, G, Glidehaus, D. Schuller and A, S chumpe , "Oxygen

Solubilities in Aqueous Alcohol Solutions," J. Chem. Eng. Data 286-287, 1984.

Oxygen solubilities at 25 °C are reported for alcohol solutions with mole

fractions up to 0.08. The alcohols are methanol through butanol, and

glycerol. All but the last two compounds increase the solubility of oxygen.

In several cases, the solubility is found to not be a linear function of

concentration

.

[Khl984] N. E. Khomutov and A. S. Groisman, "Temperature Dependence of the

Solubility of Oxygen in Aqueous Electrolytes," Russ. J. Phys . Chem. 58, (3),

433-434, 1984.

The effect of temperature on the solubility of oxygen is measured in four

aqueous electrolyte solutions: NaCl, LiCl, Na2S04 and Li2S04 for the range of

10 - 85 °C. The temperature dependence of the salting-out coefficient for

oxygen in these four solutions is given in graphical form. The Setschenov

parameters decrease by about 30% over this temperature range.

[L1986] W. Lang and R. Zander, "Salting-Out of Oxygen from Aqueous

Electrolyte Solutions: Prediction and Measurement," Ind. Eng. Chem. Fund.

775-782, 1986.

The solubility of oxygen in 68 electrolyte solutions was measured at

310.2 °K. These salts include 20 chlorides, 22 nitrates, 18 sulfates, three

hydrogen sulfates and five hydroxides. The concentration ranges from 0.5 to 6

molar. The ion-specific salting-out parameters are listed for all cations

and anions studied; a 1-2% precision is claimed. Extensive comparisons are made with literature data. The data generally fall into two classes: before

1920 and after 1970. Mutual agreement for a given solute is erratic. The

authors show convincingly that the log- additive Setschenov concept works for

mixed electrolyte solutions

.

23

MASS TRANSFER OF OXYGEN IN BIOPROCESS SYSTEMS

June 26, 1989

25
CONTENTS

1

.

Relevance 27

2. Introduction 27

3. Overview of Oxygen Transfer in Bioreactors 28

3.1 Resistances to Oxygen Transfer 28

3.2 Modes of Oxygen Mass Transfer 29

3.2.1 Molecular Diffusion 29

3.2.2 Convection 29

3.2.3 Gas-Liquid Interphase Mass Transfer 30

3.2.4 Intraparticle Diffusion 30

3.3 Rate of Oxygen Transfer 30

4. Factors Affecting Oxygen Mass Transfer 31

4.1 Physical Factors 31

4.1.1 Oxygen Diffusivity 31

4.1.2 Fluid Hydrodynamics and Oxygen Diffusivity 32

4.1.3 Interfacial Area (Bubbles) 32

4.1.4 Rheology 33

4.2 Chemical Factors 34

4.2.1 Electrolytes 34

4.2.2 Surfactants 34

5. Oxygen Measurement 34

5.1 Measurement of Oxygen Transfer Coefficients 34

5.2 Dissolved-Oxygen Electrodes .... 36

5.3 Linek's Critique of Dynamic Measurement of Oxygen Mass

Transfer and Diffusion 36

6. Conclusions and Recommendations 37

7. References 39

8. List of Symbols 42

9. Bibliography 44

9.1 Major Reviews of Mass Transport in Bio Applications 44

9.2 Mass Transport - Mixing and Reactor Design 46

9.3 Theory of Transfer of Gases in Liquids 47

9.4 Oxygen Measurement 47

9.5 Oxygen Diffusion 48

9.6 Measurement of the Volumetric Mass Transfer Coefficient (KLa) . . 55

9.7 Effect of Cells and Rheology on the Volumetric Mass Transfer

Coefficient 58

9.8 Correlation of Mass Transfer with Oxygen Diffusion Coefficient. . 61

26
Mass Transfer of Oxygen in Bioprocess Systems

1 . Relevance

It is widely recognized that in many aerobic fermentation systems the rate of

oxygen transport to cellular organisms is the rate- limiting factor for

biochemical conversion. Continuous oxygen supply to the growing cells is an important consideration, as even temporary depletion of dissolved oxygen can mean irreversible cell damage. Oxygen is supplied by bubbling gas through the

fermentation medium. The availability of oxygen to the growing cells is

determined by the oxygen solubility in the fermentation medium, oxygen mass transfer rate in the nutrient medium, and the metabolic uptake of dissolved

oxygen [K1985] . Due to its low solubility, oxygen must be supplied

continuously to the medium and dispersed so that the oxygen uptake rate of the

system at least equals the oxygen consumption by the cells.

The prediction and measurement of gas -liquid nutrient oxygen mass transfer

coefficients play a key role in fermentation Bioprocess Engineering. With

knowledge of the factors controlling the oxygen mass transport, bioreactor

design and operating conditions can be set to enhance this interfacial oxygen

flux and thus to maximize bioproduct formation. Oxygen transfer from the gas

to the liquid fermentation broth is influenced by hydrod3mamics , interfacial

phenomena, and chemical and physical factors. Oxygen transfer through the

gas-liquid interface becomes the rate-limiting resistance when the oxygen

consumption rate is sufficiently high, as is common with a dense suspension of

active cells.

2 . Introduction

The mass transport of oxygen in aerobic fermentation reactors is a complex

subject which depends on the type of bioprocess, reactor design, and chemical

and physical properties of the fermentation medium. Various aspects of oxygen

mass transport have been widely studied, but much of the work has narrow

application only to the process and/or reactor design studied. Considerable

effort has gone into the evaluation of various techniques to enhance bulk

mixing, with emphasis on reactor design. Much less effort has been expended

in understanding the fundamental science which affects the oxygen transfer

process

As the Contents indicates, oxygen mass transfer in a bioreactor is a multifaceted topic, ranging from molecular diffusion in simple and complex media to

the rheology of fermentation broths to gas-liquid interfacial area and bubble

djmamics, on to the actual measurement of oxygen mass transfer. It turns out

then for a well-stirred fermentation reactor, the principal resistance to

oxygen transfer is the liquid film on the liquid side of the gas -liquid

interface, which implies that the diffusivity of oxygen across this boundary

layer and the interfacial area are important quantities to be considered.

This rather lengthy report should be considered as an integrated composite of

several separate reports, each dealing with a different aspect of oxygen

transfer in aerobic fermentation processes.

27
3. Overview of Oxygen Transfer in Bioreactors

3.1. Resistances to Oxygen Transfer

Bioprocess reactors can be considered heterogeneous catalytic reactors where

physical mass transfer completely or significantly controls the overall rate

of the bioprocess. Identification of the fundamental principles involved

permits development of generalized mass transfer criteria for bioprocess

reactors for both interparticle and intraparticle pathways in solid- fluid and

fluid- fluid contacting systems. Oxygen passes through a series of transport

resistances in making its way from the gas bubble to the cell. The eight

possible resistances in the mass transfer pathways shown in figure 1 [B1986]

are:

1. Diffusion from the bulk gas through the gas film to the gas- liquid

interface

,

2. Movement through the gas- liquid interface,

3. Diffusion of the solute in the liquid film at the gas-liquid

interface, through the relatively unmixed liquid region adjacent to

the bubble to the well-mixed bulk liquid,

4. Transport of the solute through the bulk liquid to a second

relatively unmixed liquid region surrounding the cells,

5. Transport through the second unmixed liquid region associated with

the cells, which is a liquid film surrounding the solid,

6. Movement through the liquid-solid interface,

7. Diffusive transport into the solid phase containing the cells,

8. Transport across the cell envelope and to intracellular reaction

site.

Biochemical

(5) I _(7) ^ ^"f'O"

Cell

Cell membrane

'Ga&-liquid

interface Liquid-aggregate

interface Figure • 1 Schematic diagram of steps involved in transport of oxygen from a gas bubble to inside a

cell.

28
The overall oxygen transfer resistance is the suun of the individual

resistances. The relative magnitude of these resistances depends on the gasliquid interfacial phenomena, the bubble and liquid phase hydrodynamics,

temperature, cellular activity and density, the composition and rheological

properties of the fermentation medium and other factors; however, one of the

resistances is rate controlling for the process. In the case of discretely

dispersed cells, the bubble liquid film resistance (the third one above)

controls the overall oxygen transfer process. Improvement of the overall

oxygen transfer rate in bioprocess reactors will be achieved by understanding

and manipulating these factors which influence the mass transfer resistances.

3.2. Modes of Oxygen Mass Transfer

It is clear that the major mechanisms of oxygen mass transfer in bioprocess

reactors are molecular diffusion, convective mass transfer, gas- liquid

interphase mass transfer, and intraparticle diffusion.

3.2.1. Molecular Diffusion

In a quiescent liquid or gas, mass transfer takes place by molecular

diffusion, where the driving force can be concentration or chemical potential

gradient; or by migration in an external field, such as gravitation or electrostatic charge. In bioreactors, the most common tjrpe of diffusion is

due to concentration gradients, and follows Pick's law of diffusion which

states that the mass flux is proportional to the concentration gradient

[K1985] . Diffusion is reported in terms of diffusion coefficients of a component, such as oxygen, in a fluid, e.g., D^^g represents the diffusion

coefficient of A in a binary mixture of A and B and has units (m^ s"-^). Since

oxygen mass transfer involves both gas and liquid phases, diffusion

coefficients in both gas and liquid can be important.

3.2.2 Convection

One of the major goals of aerobic fermenter design is to enhance bulk fluid

mixing to obtain better gas -liquid contact and to reduce the transfer

resistances due to concentration gradients within the bulk medium. The

fermentation medium is often mixed, either mechanically, as in mechanically

stirred reactors, or pneumatically, such as in bubble columns or airlift

devices. When motion occurs in a fluid, mass transfer takes place between the

moving fluid and a boundary surface. The convective mass transfer coefficient

Kg associated with fluid flow is usually defined as

Ke = J!!i (1)

ACa

where N^^ is the molar flux of species A (mol m"^ s" ^ ) and AC^^ is the

concentration difference between two locations in the same phase; K^, therefore

has dimensions (m s" ^ ) . For explicitness and simplicity, we shall consider

only forced convection, which is the situation most often encountered when

considering oxygen mass transfer in agitated fermenters

29
3.2.3 Gas -Liquid Interphase Mass Transfer

Transfer of oxygen from a gas bubble into the nutrient mediiim involves three

steps: transfer from the gas phase to the gas-liquid interface, movement

across the interface into the liquid film, and transfer from the liquid film

to the bulk liquid. These correspond to the first three resistances in figure

1.

The overall mass transfer coefficient based on the driving force in the gas

phase, Kq , is defined as

Kg = -^ (2)

Pag - K

where P^g is the partial pressure of A in the bulk gas phase and P^ is the

partial pressure of A in equilibrium with the liquid phase concentration of A.

Likewise, Kl , the overall mass transfer coefficient based on the liquid phase

driving force, is given by

Kl = /^ (3)

^A " ^AL

where C^ is the concentration of A in equilibrium with the partial pressure of

A in the gas phase and C^l ^^ the concentration of A in the liquid phase.

For sparingly soluble gases, such as oxygen in water, the gas phase resistance

is negligible compared to the liquid phase resistance, and thus the mass transfer is controlled by the liquid phase mass transfer coefficient. When

gas solubility in the liquid phase is high, then the liquid phase resistance

is negligible compared to the gas phase resistance, and the overall mass transfer coefficient is near the gas phase transfer coefficient. If the gas

is moderately soluble in the liquid, the mass transfer coefficient is

influenced by both resistances [K1985]

.

3.2.4. Intraparticle Diffusion

In bioprocesses where the catalysts are immobilized within a porous pellet,

intraparticle diffusion is important because the reactants must diffuse

through passages inside the support particles to reach the growing organism.

The passages are usually tortuous voids, making diffusion difficult. In cases where the microorganisms grow as floes, pellets, or mycelial mass, the

intra/intercellular or clump resistance is the controlling resistance in the

overall oxygen transfer process. The diffusivity of oxygen in such pellets is

much lower than in water, and is generally the rate controlling step in mass transfer in mycelial fermentations.

3.3. Rate of (hcygen Transfer

In aerobic fermenters where oxygen mass transfer is controlled by the liquid

phase mass transfer coefficient, the rate of oxygen transfer is given by the

following equation

Ro2 = KlB (C* - CO (4)

30
where Rq2 is the rate of oxygen transfer per unit liquid volume, Kl is the

liquid oxygen transfer coefficient, a is the gas -liquid interfacial area per

unit volume of liquid, C* is the saturation oxygen concentration in the

liquid, and Cl is the dissolved oxygen concentration in the liquid. The rate

of oxygen transfer is dependent on the liquid mass transfer coefficient, the

interfacial area, and the oxygen concentration difference. Enhancements in

the rate of oxygen transfer can be achieved by increasing Kl or a, or both.

The term Kj^a is known as the volumetric oxygen transfer coefficient. KLa

varies with the gas-liquid interface area, the intensity of agitation, rate of

aeration, and the rheological properties of the fermentation medium.

4. Factors Affecting Oxygen Mass Transfer

Both physical and chemical factors influence the oxygen mass transfer and

interfacial area, thus affecting the overall oxygen mass transfer.

4.1 Physical Factors

4.1.1 Oxygen Diffusivity

The liquid phase diffusivity D^^g and the continuous phase viscosity fi^ affect

Kl . Since the fermentation medium in bioreactors is not pure water, other

components in the broth such as sugars, salts and cells, can have an important

effect on the oxygen diffusivity.

The diffusion coefficient of oxygen in water is -2.1 x 10'^ cm^ s" ^ at 25 °C

[D1970] . The diffusion coefficient increases slightly with temperature. In

general, the diffusion coefficient of oxygen in other solvents is less than in

water. The diffusion coefficient varies with ionic strength and solute

concentration which changes the solution viscosity. If solute -solvent

interactions are not altered with increased solute concentration, the

relationship given below can be used to adjust for changes in solution

viscosity from a reference solvent, such as water. If the temperature is

constant [B1986],

where Dj^ is the diffusivity in the liquid phase with increased solute, n^^ is

the viscosity of the liquid phase with increased solute, Dref ^^ ^^®

diffusivity of oxygen in water, and a*cref ^^ ^^® viscosity of water. Akita

[A1981] developed equations to predict the diffusivity of gases in aqueous

electrolyte solutions when the gas diffusivity in pure water and the densities

of the solutions are known. The results of the measurements in various

electrolyte solutions are discussed on the basis of the Eyring Theory of rate

processes, in which the activation free energy for diffusion is supposed to

consist of a sum of activation energies associated with each chemical

component in the solution. This automatically results in a log-additive

correlation between oxygen diffusivity and the concentrations of the various

species. No attempt is made to justify the assumption of additive activation

energies on the basis of physical arguments. Another log-additive correlation

of oxygen diffusion was proposed by Ju et al. [Jl985b] , who studied oxygen

transfer in glucose solutions with salts. In our opinion, however, their

findings are questionable in view of the recent work of Linek et al. [L1988a]

31
4.1.2 Fluid Hydrodynamics and Oxygen Diffvisivity

In bioprocess reactors, the complex hydrodjmamics are difficult to

characterize rigorously. Thus, empirical results and educated guesses are often an integral part of the design calculations. The convective mass transfer coefficient associated with fluid flow is defined in eq (1). It

varies with fluid properties, flow conditions, and reactor geometry.

Frequently these parameters are combined to form dimensionless groups. For

convective mass transfer, only two dimensionless groups are correlated with

the mass transfer coefficient: the Reynolds number R^ and the Schmidt nximber

Sg . These are defined by

R, = ^ ^ ^^°"' (5)

and

Se = JL- (6)

P Da

where p is the mass density of the fluid, dj, is the average or characteristic

diameter of an oxygen- containing gas bubble, V^^g is a root-mean- square fluid

velocity due to agitation, n is the kinematic viscosity of the fluid, and D^

is the diffusivity or diffusion coefficient (m^ s"^) of the solute A in the

quiescent liquid. The correlation usually takes the form

^"^

= m R,** S,<= (7)

Da

where the dimensionless group on the l.h.s. is called the Sherwood number Sh,

L is a characteristic dimension of the reactor, and where m, b, and c are empirically determined constants. For example, laminar boundary layer theory

predicts m = 0.66, b = 1/2, c = 1/3 while Calderbank's empirical oxygen

transfer correlation for turbulent aeration gives m = 0.13, b = 3/4, c = 1/3

[C1967]. Kg for gases such as oxygen in agitated fermenters is also

correlated with the power input per unit volume of the fermenter and an average gas velocity.

For a sparingly soluble gas such as oxygen in a stirred fermentation reactor

the principal mass transfer resistance is the liquid film on the liquid side

of the gas -liquid interface. This mass transfer coefficient is defined in eq.

(3) . It turns out that Kl is related to the diffusivity of A by

Kl oc (Dl)* (8)

where the exponent a depends on bubble size, distribution, and hydrodjmamic

flow conditions [W1923, L1924, H1935, F1938, D1951, D1970, M1981, M1987].

Thus, for dispersed rigid spherical bubbles, standard hydrodjmamic arguments

(see eq. (7)) predict a = 2/3, while for large, deformable bubbles with

interfacial shear, one obtains a = 1/2.

4.1.3 Interfacial Area (Bubbles)

The voliimetric mass transfer coefficient is the product of an interfacial

transfer coefficient, Kl , with the total interfacial surface area "a." The

interfacial surface area is usually obtained from photographic analysis of

32
bubble-size distributions. It is the product K^a, rather than Kl alone, which

determines the oxygen transfer efficiency of a typical aerobic bioreactor;

therefore, an accurate estimate of "a" is an important aspect of aerobic

fermentor design and operation. With a liquid in turbulent motion, bubble

break up occurs, and an equilibrium between bubble coalescence and break up

determines the inean bubble size. The interfacial area "a" depends on the

sparger design, reactor volume, gas flow rate, and bubble size. If the

sparger flow rate is F and the residence time of a tjrpical bubble in the

fermenter is t and d^, is an average bubble diameter, then for small, spherical

bubbles, "a" is given by

a =

Ft

"vT I db J

(9)

where V^ is the total liquid volume. At low Rejmolds number where laminar

flow is a good approximation to the hydrod3mamics , the terminal rise velocity

of a bubble is Vj ~ d^,^ (equate the buoyant force with Stoke 's drag). Now

(Ft/Vj) is the total bubble voltune per unit volume of reactor (holdup), and

this can also be written as (Ft/AL) where A is the reactor cross section area and L is the liquid height. Since Vj ~ L/t at low Rejmolds number, it follows

that "a" varies with dj, as a ~ dj,"^ [K1985] . A large value of "a" is usually

highly desirable, thus small bubbles play a key role in determining KLa

[K1985] . In addition, the bubble size at the outlet of a submerged sparger

orifice can be estimated by equating the buoyant force, which varies as d^,'^ and which tends to stretch the bubble to the point of instability, with the

surface tension (a) force, which tends to contract the interface, and this

leads to dj,~ a^'^. This implies that the presence of surface active agents in

a bioreactor can have a profound effect on the rate at which oxygen is

transported to the biomass. For instance, the mass transfer coefficient Kl is

usually reduced by the addition of surfactants while the volumetric transfer

coefficient KLa can either decrease or increase.

4.1,4 Kheology

The rheological properties of the materials being processed in bioreactors

influence the mass transfer rates. All types of fluid behavior can be

encountered in bioreactors. The rheological behavior of fermentation broths

[B1976, C1978] and the oxygen transfer into viscous medivim [S1981] have been

reviewed. The correlation of the "apparent" Newtonian viscosity of a fermentation reactor with KLa for oxygen is poorly understood, particularly in

the case where the medium exhibits non-Newtonian fluid behavior. It is well

known that cell morphology involving filamentous growth has a profound effect

on bulk rheological properties, leading to viscoelastic and pseudoplastic

behavior, and while this is in most cases linked to an overall decrease in

oxygen mass transfer, the effect on oxygen diffusivity is far from obvious.

Indeed, in certain polymeric solutions, marked enhancements in oxygen

diffusion have been observed along with increasing macroscopic viscosity

[P1986] . At present, there are no convincing explanations for this unusual

behavior. However, a recently received preprint from Dr. V. Linek contains

evidence that these results are in error.

33
4.2 Chemical Factors

4.2.1 Electrolytes

A most curious effect is that of dissolved electrolytes on Kj^a. In

electrolyte solutions, the rate of bubble coalescence is greatly reduced.

Robinson and coworkers [R1973] have developed an empirical correlation of the

volumetric oxygen transfer coefficient with the total ionic strength I of the

liquid medium,

I = m: Z? Ci (10)

where Z^ and C^ are the valence and concentration, respectively, of species i

and the suimnation is over all ionic species present. However, this

correlation also involves quantities such as impeller power input per unit

volume of fluid and an "ionic strength function," whose construction appears

to be devoid of any physical meaning; the question of system specificity of

this correlation has not been addressed. Nevertheless, the fact that Kj^a for

oxygen is strongly dependent on I seems to be sufficiently important as to

warrant deeper study.

4.2.2 Surfactants

The effects of surfactants may change the behavior of bubbles. Surfactants

may inhibit bubble coalescence, resulting in the formation of smaller bubbles

and increased interfacial areas. Rigid sphere behavior may be observed for

small bubbles for which the presence of adsorbed surfactants leads to

convection- induced surface concentration gradients which suppress interfacial

shear and therefore nullify internal circulation [M1983].

5. Oxygen Measurement

5 . 1 Measurement of Oxygen Transfer Coefficients

The volumetric mass transfer coefficient (K^a) is used to compare the oxygen

transfer capabilities of various aerobic fermenters. Various methods have

been developed to determine the KLa values experimentally. Two classes of

methods are used: steady state methods and dynamic methods. With steady state

methods, oxygen absorption is measured in a two-phase continuous flow system

or in a semi-batch mode. Dynamic methods involve measuring the concentration

of oxygen, usually in the liquid phase, following a step change in its

concentration in the entering gas. Each class has its advantages and

disadvantages. Several djmamic methods which rely on the use of a dissolvedoxygen probe have been developed. They are based on the djmamic oxygen

balance in a batch culture, which has the form

^ = K^aCC* - CO - Q02X (11)

dt

where Q02 is the rate of oxygen consumption per unit mass of cells, and X is

the cell concentration. This equation can be rearranged to give

34
Cl = C- .1— fOozX + ^1 . (12)

KlH [ dt J Integration of eq (11) gives

in (C* - Cl) = -KLat "•" constant, (13)

C* = C*L2 Qo2V(KLa)

In the "gassing out" djniamic method, the air supply to a culture is stopped,

and the fall in dissolved oxygen is noted. After resuming the air supply, the

increasing oxygen level in the medimn is recorded as a function of time. KLa

is obtained from a plot of In (C* - Cl) versus time which yields a straight

line with a slope of KLa. Another dynamic method involves gassing out a fermentation medium with nitrogen and then monitoring the oxygen level after

the air is restarted. Dynamic methods can also be applied to a continuous

culture where the rate of oxygen supply equals the rate of oxygen consumption

at steady state,

KLa = Qo^X

(C*L2 - Cl)

(14)

By turning the air supply off and following the linear variation of Cl with

time, the total rate of oxygen consumption (Qq2X) can be determined. Cl is

constant in a continuous culture at steady state, thus KLa can be found by

means of eq (13)

The direct oxygen balance method determines the rate of oxygen transfer into

the system by measuring the difference between the amount of oxygen in the gas

streams to and from the fermenter, their respective flow rates, and the oxygen

concentration in the liquid broth. In small scale fermenters that are well

mixed, only single measurements of the dissolved oxygen concentration in the

gas and in the liquid are necessary, but in large fermenters the fermentation

meditun may not be well mixed and a number of measurements may be needed to

determine an average oxygen concentration. Some workers [M1987] consider this

the most reliable method of measuring KLa. Nevertheless, this method does

require gaseous O2 analyzers, flow meters, and accurate measurements of

temperature and pressure.

The sulfite oxidation method is a steady-state method. It involves the

oxidation of sodium sulfite to sulfate by oxygen in the presence of a catalyst. The reaction rate is essentially independent of sodium sulfite or dissolved oxygen concentration, and the rate of reaction is very fast. This

method has been shown to depend on the equipment, pH, purity of the NagSOg and

the catalyst. A sodium sulphite solution is used to simulate a fermentation

broth, but the chemical and physical properties are different from a fermentation broth and this can lead to large differences in KLa estimates in

both systems. While not suitable for estimation of oxygen transfer

coefficients of individual fermenters, the sulfite oxidation method can be

useful in scale-up studies, by comparing the oxygen transfer characteristics

in similar but different size gas- liquid reactors.

In recent years the djmamic methods using a dissolved oxygen-electrode have

gained popularity due to their convenience and the rapid results. However,

inconsistencies are frequently observed in the data for the volumetric mass transfer coefficient for oxygen obtained by various djmamic methods [L1987].

Recently in the literature [L1987, L1988a, M1981], questions have been raised

35
about the validity of the KLa data determined by various djmamic methods and

diffusion coefficient data measured with polarographic oxygen electrodes. See

section 5.3.

5 .

2

Dissolved-Oxygen Electrodes

Dissolved-oxygen electrodes are used to measure diffusion coefficients

directly and in dynamic methods to determine K^a. Dissolved-oxygen electrodes

have a metal or glass sheath containing two electrodes and a suitable

electrolyte. The probe is covered by a membrane which separates the

electrodes and electrolyte solution from the fermentation medium. Oxygen

diffuses through the membrane and is reduced at the cathode , which is

negatively polarized with respect to the anode, producing a current which is

translated into oxygen concentration. A polarographic probe has an external

power source to establish a polarizing voltage between the electrodes. Probes

having no external power source are called galvanic probes and they rely on

the natural polarization set up between a noble cathode and a basic anode.

Dissolved-oxygen electrodes measure activity, rather than the oxygen

concentration, where activity represents the driving force for the movement of

oxygen from the bulk fluid to the cathode. Activity is related to

concentration via Henry's Law.

The electrode response is influenced by a number of factors, including the

membrane thickness and diffusivity, properties of the fluid, the presence of

bubbles at the membrane surface , and hydrod3mamic conditions near the

electrode. Thin membranes give faster response times, but interpretation of

the signal is more complex. Since the response of dissolved-oxygen electrodes

is often influenced by transient behavior of the electrode, various models

have been developed with the intent of eliminating this effect. The models

vary in their simplifying assumptions and the interpretation of probe signals.

The correct interpretation of probe signals is essential to obtain the proper

oxygen concentration.

5.3 Llnek's Critique of Dynamic Measurement of Oxygen Mass Transfer and

Diffusion.

The Working Party for Mixing of the European Federation of Chemical Engineers

recently requested Dr. Linek and his coworkers at the Institute of Chemical

Technology in Prague to test and review the reliability of the d3mamic methods

of determining KLa and the diffusion coefficient of oxygen. Linek and

coworkers tested a number of methods used in industry and reviewed the

theoretical models used in analyzing the probe response to changes in oxygen

concentration. The results of this study are published [L1987] . See also

[L1988c].

Linek et al., first of all, analyzed the problems associated with effecting a step change in oxygen concentration in the inlet gas and assuming that this

step occurs simultaneously and homogeneously throughout the reactor. After

much experimenting, they finally found a valid way of making such a change.

They claim that the methods ubiquitously used in industry ignore or neglect

important inhomogeneities and side processes in the reactor and may lead to errors of hundreds of percents in K^&.

36
Secondly, they analyzed the models that are used to describe the hydrodjmamics

near the oxygen probe in order to deduce the diffusion coefficient.

Unreliable results will be obtained if the model neglects effects that occur

in the experimental situation. Some examples given by Linek et al. are: use

of a one -dimensional diffusion model when the geometry is more complex and

side diffusion occurs, such as in the ring-shaped probe used by Ho, Ju and

coworkers [Jl985a, Jl985b, H1986, J1988]; neglect of convection when the

liquid layer is not thin; neglect of oxygen consumption by probes that are not

small.

Thus Linek et al. conclude that many of the K^a and diffusion coefficients for

oxygen in bioreactors, obtained by means of oxygen probes in djmamic

condition, are in serious doubt. In view of the fundamental and universal

importance of measurement of oxygen transport in bioreactors, the

standardization of oxygen probes and dynamic methods appear to be high

priorities.

6. Conclusions and Recommendations

Perhaps the most striking aspect of oxygen transfer in aerobic fermentation

reactors is the observed correlation between the oxygen mass transfer

coefficient Kl and the diffusivity Dl of oxygen in the liquid phase; that is,

Kl a (Dl)* (15)

where a ~ 2/3 for small, rigid bubbles whose motion is dominated by frictional

drag and o ~ 1/2 for large deformable bubbles for which form or inertial drag

predominates. In deriving eq (15) it is assumed that the major resistance to

oxygen transfer is the liquid film surrounding air bubbles, but hydrodynamic

flow conditions, bubble size distribution, and the presence of swarms or clusters of bubbles in a sparged reactor make it difficult to specify the

exponent a, and there is considerable disagreement in the literature on which

value actually holds for a given system. In view of the great economy and

simplification embodied by eq (15), it is recommended that a thorough study be

made of the dependence of a on reactor conditions. One can imagine "model"

Newtonian and non-Newtonian fermentation broths subjected to various

gas -sparging schemes in which bubble characteristics are carefully monitored

and correlated with values of a.

This brings up the question of how to obtain the total gas -liquid interface

area "a," which when multiplied by Kl , yields the volumetric oxygen transfer

coefficient KLa. Photographic analysis of bubble size distributions cannot

detect bubbles with a radius less than about 1 mm, which may mean that an important contribution to the gas- liquid interfacial area is being overlooked.

Sound velocity and attenuation are very sensitive to the specific volume of

bubbles dispersed in a liquid and we therefore recommend an acoustic study of

bubbles sizes in a reactor.

The literature on mass transport in forced convection bioreactors suggests

that local mixing may be quite inhomogeneous in a tjrpical vessel. Considering

the sensitivity of the medium to local oxygen concentration as well as to

other nutrients, we recommend a study of local hydrodynamic convection in a "model" fermentation broth, utilizing, for example, in-situ quasi-elastic

laser Doppler scattering employing fiber optics and homodyne optical mixing.

37
The most fundamental of our recommendations concerns the controversy and

ambiguity associated with the measurement of oxygen diffusion with

polarographic oxygen electrodes, which is the technique best suited for rapid

monitoring of oxygen transport in a bioreactor. The transient response method

developed by Ju and Ho [J1985a, Jl985b, H1986, J1988] has recently come under

severe criticism by Linek and coworkers [L1985, L1987, L1988a, L1989a-c] who

claim that contrary to the assumptions of Ju and Ho, side diffusion in the

liquid film on the membrane has a profound effect on transient electrical

response of the probe. The Linek analysis, in our view, casts serious doubts on the quality of much of the existing data on oxygen diffusivity in a variety

of fermentation media, and even in simple aqueous solutions.

In view of the fundamental role of oxygen in almost all bioreactors, an

optimization of probe design, and standardization of the dynamic measurement

of oxygen mass transfer and diffusion coefficients would be valid concerns of

our Institute that would yield major benefits to the bioprocessing industry.

Oxygen mass transfer in a bioreactor is a complex and multi-faceted topic. We

have therefore subdivided the Bibliography into various sections, the most

prominent being References and Major Reviews. The annotated references are included on the basis of overall relevance to our discussion and for

documentation purposes. Inasmuch as the literature on oxygen transfer in

fermentation media is enormous, we have elected to present only those

references which were useful to us in our investigations, or which we believe

will be useful to the reader, such as Major Reviews of various aspects of

oxygen mass transfer.

38
7 . References :

[A1981] K. Akita, "Diffusivities of Gases in Aqueous Electrolyte

Solutions," Ind. Eng. Chem. Fundam. 20, 89-94 (1981).

[B1976] Blanch and Bhavaraju, Biotech. Bioeng. 18, 745 (1976).

[B1986] J. E. Bailey and D. F. Ollis, Chapter 8 Transport

Phenomena in Bioprocess Systems, in Biochemical

Engineering Fundamentals, 2nd Edit., New York (1986).

[C1967] P. H. Calderbank, "Mass Transfer in Fermentation

Equipment , " in Biochemical and Biological Engineering

Science, N. Blakebrough, Ed., Academic Press, New York,

102-180 (1967).

[C1978] M. Charles, "Technical Aspects of the Rheological

Properties of Microbial Cultures , " in Advances in

Biochemical Engineering, Volume 8 - Mass Transfer in

Biotechnology, T. K. Ghose, A. Fiechter and N.

Blakebrough, Eds., Springer-Verlag, New York, 1-62 (1978).

[D1951] P. V. Danckwerts, Ind. Eng. Chem. 43, 146 (1951).

[D1970] P. V. Danckwerts, Gas-Liquid Reactors, McGraw-Hill, New

York (1970).

[F1938] N. Frossling, "Uber der Verdunstung Fallender Tropfen,"

Beitr. Geophysik, 52, 170-216 (1938).

[H1935] R. Higbie, "Rate of Absorption of a Pure Gas into a Still

Liquid During Short Period of Exposure," Trans. Am. Inst.

Chem. Eng., 31, 365-389 (1935).

[H1985J G. Hamer, Chapter 10 Chemical Engineering and

Biotechnology, in Biotechnology Principles and

Applications, I. J. Higgins , D. J. Best, and J. Jones,

Eds., Blackwell Scientific Publications, Boston, 347-414

(1985).

[HI 986] C. S. Ho, L. K. Ju, C. T. Ho, "Measuring Oxygen Diffusion

Coefficients with Polarographic Oxygen Electrodes. II.

Fermentation Media," Biotechnology and Bioengineering, 28 . 1086-1092 (1986).

[H1987] C. S. Ho, M. J. Stalker, and R. F. Baddour, "The Oxygen

Transfer Coefficient in Aerated Stirred Reactors and Its

Correlation with Oxygen Diffusion Coefficients" in

Biotechnology Processes Scale-up and Mixing, C. S. Ho and

J. Y. Oldshue, Eds., American Institute of Chemical

Engineers, New York, 85-95 (1987).

[J1985a] L. K. Ju and C. S. Ho, "Measuring Oxygen Diffusion

Coefficients with Polarographic Oxygen Electrodes: I. Electrolyte Solutions," Biotechnology and Bioengineering,

27, 1495-1499 (1985).

39
[J1985b] L. K. Ju, E. Livio, and C. S. Ho, "Measuring Oxygen

Diffusion Coefficients in Electrolyte Solutions with

Polarographic Oxygen Electrodes," Biotechnology and

Bioengineering Symp. No. 15, 347-361 (1985).

[J1988] L. K. Ju, C. S. Ho, R. F. Baddour, "Simultaneous

Measurements of Oxygen Diffusion Coefficients and

Solubilities in Fermentation Media with Polarographic

Oxygen Electrodes," Biotechnology and Bioengineering, 31 . 995-1005 (1988).

[K1985]

[L1924]

[L1985]

[L1987]

[L1988a]

F. Kargi and M. Moo-Young, Chapter 2 Transport Phenomena

in Bioprocesses, in Comprehensive Biotechnology, Volume 2

The Principles of Biotechnology: Engineering

Considerations, M. Moo -Young, C. L. Cooney, and A. E

Hxomphrey, Eds., Pergamon Press, New York, 5-56 (1985).

Lewis and W. G. Whitman, Ind. Eng. Chem. , 17, 1215 (1924),

V. Linek, J. Sinkule and V. Vacek, Dissolved Oxygen

Probes in Comprehensive Biotechnology, Volume 4, C. W.

J. A. Howell, Eds., Pergamon, New York.

Robinson and

V. Linek, V. Vacek and P. Benes, "A Critical Review and

Experimental Verification of the Correct Use of the

D)mamic Method for the Determination of Oxygen Transfer in

Aerated Agitated Vessels to Water, Electrolyte Solutions

and Viscous Liquids," The Chemical Engineering Journal,

34. 11-34 (1987).

V. Linek and V. Vacek, "Comments on Validity of Measuring

Oxygen Diffusion Coefficients with Polarographic Oxygen

Electrodes," Biotechnology and Bioengineering, 3^, 1010-

1011 (1988).

[L1988b] V. Linek, P. Benes, and 0. Holecek, "Correlation for

Volumetric Mass Transfer Coefficient in Mechanically

Agitated Aerated Vessel for Oxygen Absorption in Aqueous

Electrolyte Solutions," Biotechnology and Bioengineering,

32, 482-490 (1988).

[L1988c]

[Ll989a]

[L1989b:

V. Linek, V. Vacek, P. Benes and J

"Measurement of Oxygen by Membrane

John Wiley, Chichester, UK (1988).

Sinkule,

Covered Probes ,

V. Linek, V. Vacek, P. Benes, and J. Sinkule,

"Transient Characteristics of Oxygen Probes with

Significant Liquid Film Effects," Biotechnology and

Bioengineering, 33, 39-48 (1989).

V. Linek and V. Vacek, "Comment on the D)mamic

Measurement of Oxygen Diffusion coefficients in Viscous

Media Using Polarographic Oxygen Electrodes," Preprint,

(1989).

40
[L1989c] V. Linek, P. Benes and V. Vacek, "Measurement of Aeration

Capacity of Fermenters," In press. VCH (1989).

[M1981] M. Moo-Young and H. W. Blanch, "Design of

Biochemical Reactors Mass Transfer Criteria for

Simple and Complex Systems" in Advances in

Biochemical Engineering, Volume 19 Reactors and

Reactions, A. Fiechter, Ed. , Springer-Verlag, New

York, 1-69 (1981).

[M1983] M. Moo-Young and H. W. Blanch, Chapter 15

"Kinetics and transport Phenomena in Biological

Reactor Design," in Foundations of Biochemical

Engineering, H. W. Blanch, E. T. Papoutsakis, G.

Stephanopoulos , Eds., American Chemical Society,

Washington, D.C. , 335-354 (1983).

[Ml 987] M. Moo -Young and H. W. Blanch, Chapter 5

"Transport Phenomena and Bioreactor Design," in

Basic Biotechnology, J. Bu'Lock and B. Kristiansen,

Eds., Academic Press, New York, 133-172 (1987).

[P1986] G. Potucek and J. Stejskal, "Diffusivity of Oxygen

in Non-Newtonian Liquids , " Chemical Engineering

Science, 41, 3223-3226 (1986).

[R1973] C. W. Robinson and C. R. Wilke, "Oxygen Absorption

in Stirred Tanks: A Correlation for Ionic

Strength," Biotechnol. Bioeng. , 15, 755, (1973).

[S1981] K. Schugerl, "Oxygen Transfer into Highly Viscous

Media," in Advances in Biochemical Engineering,

Volume 19 Reactors and Reactions, A. Fiechter,

Ed., Springer-Verlag, New York, 71-173 (1981).

[W1923] W. G. Whitman, "The Two-film Theory of Gas

Absorption," Chem. Methods. Eng. , 29, 147 (1923).

41
9. List of Symbols

a gas -liquid interfacial area per unit volume of liquid

A reactor cross-section area

b empirically determined constant for eq (7)

c empirically determined constant for eq (7)

C* saturation oxygen concentration in the liquid

C^ concentration of A in equilibrium with the partial

pressure of A in the gas phase

Cy^L concentration of A in the liquid phase.

Cl dissolved oxygen concentration in the liquid

Cj concentration of species i

ACy^ concentration difference between two locations in the same phase or in different phases (mol m"^)

d], average or characteristic diameter of an oxygencontaining gas bubble

D^ diffusivity or diffusion coefficient (m^ s"^) of the

solute A in the quiescent liquid

Dj^B diffusion coefficient of solute A in a binary mixture of A and B

(m2 s'M

Dl diffusivity of oxygen in the liquid phase

Drep diffusivity of oxygen in water

Dj diffusivity in the liquid phase with increase solute

F sparger flow rate

I total ionic strength of the liquid medium

Kg convective mass transfer coefficient associated with

fluid flow (m s-i)

Kg overall mass transfer coefficient based on the driving

force in the gas phase

Kl overall mass transfer coefficient based on the liquid phase

driving force

KLa volumetric mass transfer coefficient

L characteristic length of the systems

42
m empirically determined constant for eq (7)

N^ molar flux of species A (mol m"^ s" ^

)

Py^Q partial pressure of A in the bulk gas phase

Pj partial pressure of A in equilibrium with the liquid

phase concentration of A

Qq2 rate of oxygen consumption per unit mass of cells

Rq2 rate of oxygen transfer per unit liquid volume

R^ Reynolds number

Sg Schmidt number

Sh Sherwood number

t residence time of a typical bubble

Vj total liquid volume

^rms root-mean-square fluid velocity due to agitation

Vj terminal rise velocity of a bubble

X cell concentration

Z^ valence of species i

a exponent for eq (8) which depends on bubble size,

distribution, and hydrodynamic flow conditions

p mass density of the fluid

II kinematic viscosity of the fluid

A*cREF viscosity of water

/ipj^ viscosity of the liquid phase with increased solute

a gas-liquid interfacial surface tension

43
9 . Bibliography

9.1 Major Reviews of Mass Transport in Bio Applications

M. Moo-Young and H. W. Blanch, "Design of Biochemical Reactors

Mass Transfer Criteria for Simple and Complex Systems" in Advances

in Biochemical Engineering, Volxjme 19 Reactors and Reactions, A.

Fiechter, Ed., Springer-Verlag, New York, 1-69 (1981).

The fundamental principles involved in biochemical reactors are identified. Generalized mass transfer criteria for biochemical reactors

are developed for both interparticle and intraparticle pathways in

solid- fluid and fluid- fluid contacting systems for such diverse

processes as aerobic fermentations, anaerobic fermentations, immobilized

enzjiTne reactions and insoluble substrate utilization. A wide range of

practical operating conditions is considered, ranging from rheologically

simple nonviscous materials to complex viscous non-Newtonian and

multiphase systems. Reactors of the tjrpes of geometrically simple

bubble columns, packed-bed devices, complex stirred- tank and tubularloop configurations are included. The development of correlations for mass transfer coefficients, interfacial areas and related parameters is

reviewed. Energy requirements to induce and maintain the physical mass

transfer pathways in various reactors are considered. The difficulty of

scaling-up of biochemical reactors, especially stirred reactors, is

discussed. Areas are identified where more knowledge is needed to help

establish rational design and operation procedures for biochemical

reactors.

M. Moo-Young and H. W. Blanch, Chapter 15 Kinetics and Transport

Phenomena in Biological Reactor Design, in Foundations of

Biochemical Engineering, H. W. Blanch, E, T. Papoutsakis , G.

Stephanopoulos , Eds., American Chemical Society, Washington, DC,

335-354 (1983).

Kinetic and transport factors which influence the design and operation

of bioreactors are reviewed. Rate controlling steps are identified and

the importance of aqueous phase transfer steps for mass transport is

illustrated. The effect of interfacial phenomena is discussed in terms

of bubbles with "rigid" or "mobile" surfaces. Interparticle mass

transfer rates are described for particles in stagnant environments,

moving particles with rigid surfaces, and moving particles with mobile

surfaces. The effects of non-Newtonian flow and bulk mixing patterns on oxygen transfer rates are noted. Intraparticle bioreaction rates are discussed where the limiting mass transfer step is in the interior of

the solid particles. Oxygen transfer in mold pellets is discussed, and

intraparticle diffusion involved in immobilized enzyme kinetics

described. Several types of bioreactor equipment are described, namely

bubble colxjunns, systems with stationary internals and mechanically

stirred tanks. A variety of correlations available for Kj^a. are identified. The magnitude of Kj^a is about the same whether the mixing

is done mechanically in stirred tanks or pneumatically in bubble columns

or airlift devices, but mechanically agitated systems are capable of

attaining higher values of Kj^a. None of the overall correlations for

KLa had universal applicability. Both viscous and nonviscous media are

included.

44
K. Schugerl, "Oxygen Transfer into Highly Viscous Media," in

Advances in Biochemical Engineering, Volume 19 Reactors and

Reactions, A. Fiechter, Ed. , Springer-Verlag, New York, 71-

173 (1981).

This paper considers the behavior of aerated highly viscous media

employing stirred tank reactors, sparged single and multistage tower

reactors. It reviews measuring methods for rheological properties,

interfacial properties, bubble size distribution, oxygen transfer rates, mass transfer coefficients, and power input. For three types of

reactors: stirred tank reactors, single stage tower reactors, and

multistage tower reactors, it describes the apparatus and instruments,

mathematical models, hydrodynamic properties, oxygen transfer rates and

volumetric mass transfer coefficients. Many graphs are presented

illustrating relationships between various parameters. The behavior of

single bubbles and bubble swarms are discussed. Oxygen transfer

coefficients are discussed in terms of gas flow rates, impeller speed,

power input, and fluid consistency.

B. Atkinson, F. Mavituna, Biochemical Engineering and

Biotechnology Handbook, Chapter 7 Reactors; Chapter 8 Flow

Behaviour of Fermentation Fluids; Chapter 9 Gas-Liquid Mass

Transfer; and Chapter 10 Solid and Liquid-Phase Transfer,

Stockton Press, New York, 579-835 (1983).

J. E. Bailey and D. F. Ollis, Chapter 8 Transport Phenomena in

Bioprocess Systems, and Chapter 9 Design and Analysis of

Biological Reactors, in Biochemical Engineering Fundamentals, 2nd

Edit., New York, 457-657 (1986).

P. H. Calderbank, "Mass Transfer in Fermentation Equipment," in

Biochemical and Biological Engineering Science, N. Blakebrough,

Ed., Academic Press, New York, 102-180 (1967).

M. Charles, "Technical Aspects of the Rheological Properties of

Microbial Cultures," in Advances in Biochemical Engineering,

Volume 8 Mass Transfer in Biotechnology, T. K. Ghose, A. Fiechter

and N. Blakebrough, Eds., Springer-Verlag, New York, 1-62 (1978).

E. L. Cussler, Diffusion: Mass Transfer in Fluid Systems,

Cambridge University Press, New York (1984).

F. Kargi and M. Moo -Young, Chapter 2 Transport Phenomena in

Bioprocesses, in Comprehensive Biotechnology, Volume 2 The

Principles of Biotechnology: Engineering Considerations, M. MooYoung, C. L. Cooney, and A. E. Humphrey, Eds., Pergamon Press, New

York, 5-56 (1985).

M. Moo -Young and H. W. Blanch, Chapter 5 Transport Phenomena and

Bioreactor Design, in Basic Biotechnology, J. Bu'Lock and B.

Kristiansen, Eds., Academic Press, New York, 133-172 (1987).

K. Schugerl and W. Sittig, Chapter 6 Bioreactors, in Fundamentals in

Biotechnology, P. Prave, U. Faust, W. Sittig, D. A. Sukatsch, Eds,,

VCH Publishers, Deerfield Beach, FL, 179-224 (1987).

45
9 . 2 Mass Transport - Nixing and Reactor Design

F. G. Bader, "Modelling Mass Transfer and Agitator Performance in

Multi-turbine Fermentors," Biotechnology and Bioengineering, 30 . 37-51 (1987).

H. Brauer, "Power Consumption in Aerated Stirred Tank Reactor

Systems," in Advances in Biochenical Engineering, Volume 13,

T. K. Ghose, A. Fiechter, and N. Blakebrough , Eds., SpringerVerlag, New York, 87-119 (1979)

P. H. Calderbank and M. B. Moo -Young, "The Prediction of Power

Consumption in the Agitation of non-Newtonian Fluids , " Trans

.

Instn. Chem. Engrs., 37, 26-33 (1959).

M. Charles, Chapter 3 Fermenter Design and Scale-up, in

Comprehensive Biotechnology, Volume 2 The Principles of

Biotechnology: Engineering Considerations, M. Moo-Young, C.

L. Cooney, and A. E. Hvunphrey, Eds., Pergamon Press, New York,

57-75 (1985).

M. Charles, "Fermentation Scale-up: Problems and

Possibilities," Trends in Biotechnology, 3, 134-139 (1985).

G. Hamer, Chapter 10 Chemical Engineering and Biotechnology,

in Biotechnology Principles and Applications , I.J. Higgins

,

D. J. Best, and J. Jones, Eds., Blackwell Scientific

Publications, Boston, 347-414 (1985).

R. Manfredini, V. Cavallera, L. Marini, and G. Donati, "Mixing

and Oxygen Transfer in Conventional Stirred Fermentors," in

Chemistry and Biotechnology of Biologically Active Natural

Products, C. Szantay, A. Gottsegen, and G. Kovacs, Eds.,

Elsevier, New York, 139-159 (1984).

J. Y. Oldshue, "Transport Phenomena, Reactor Design and ScaleUp," Biotech. Advs. 1, 17-30 (1983).

J. Y. Oldshue, "Transport Phenomena, Reactor Design and ScaleUp," Biotech. Advs. 3, 219-237 (1985).

J. Y. Oldshue, Chapter 4 Agitation, in Fermentation and

Biochemical Engineering Han^>ook, H. C. Vogel, Ed., Noyes

Publications, Park Ridge, NJ, 119-162 (1983).

A. Prokop, Chapter 16 Reactor Design Fundamentals - Hydrodynamics, Mass Transfer, Heat Exchange, Control, and

Scale -up, in Foundations of Biochemical Engineering, H. W.

Blanch, E. T. Papoutsakis, G. Stephanopoulos , Eds., American

Chemical Society, Washington, DC 355-376 (1983).

M. Zlokarnik, "Sorption Characteristics for Gas -Liquid

Contacting in Mixing Vessels," in Advances in Biochemical

Engineering, Volume 8 Mass Transfer in Biotechnology, T. K.

Ghose, A. Fiechter, N. Blakebrough, Eds. 133-151 (1978).

46
9 . 3 Theory of Transfer of Gases in Liquids

P. H. Calderbank, D. S. L. Johnson, and J. Loudon, "Mechanics

and Mass Transfer of Single Bubbles in Free Rise Through Some

Newtonian and non-Newtonian Liquids," Chem. Eng. Sci., 25 . 235-256 (1970).

P. H. Calderbank, "Physical Rate Processes in Industrial

Fermentation Part I: The Interfacial Area in Gas-Liquid

Contacting with Mechanical Agitation," Trans. Instn. Chem.

Engrs, 36. 443-463 (1958).

P. D. Coppock, "The Behaviour of Gas Bubbles in Relation to

Mass Transfer," Trans. Instn. Chem. Engrs., 29, 75-86 (1951).

P. V. Danckwerts, Ind. Eng. Chem. 43, 146 (1951).

P. V. Danckwerts, Gas-Liquid Reactors, McGraw-Hill, New York

(1970).

D. Hammerton and F. H. Garner, "Gas Absorption from Single

Bubbles," Trans Instn. Chem. Engrs., 32, S18-S24 (1954).

R. Higbie, "Rate of Absorption of a Pure Gas into a Still

Liquid During Short Period of Exposure," Trans. Am. Inst.

Chem. Eng., 31, 365-389 (1935).

N. Frossling, "Uber der Verdunstung Fallender Tropfen," Beitr.

Geophysik, 52, 170-216 (1938).

Lewis and W. G. Whitman, Ind. Eng. Chem., 17, 1215 (1924).

W. G. Whitman, "The Two-film Theory of Gas Absorption," Chem.

Methods. Eng., 29, 147 (1923).

9 . 4 Oxygen Measurement

W. B. Arminger, Chapter 7 Instrumentation for Monitoring and

Controlling Bioreactors, in Comprehensive Biotechnology,

Volume 2 The Principles of Biotechnology: Engineering

Considerations, M. Moo -Young, C. L. Cooney and A. E. Humphrey,

Eds., Pergamon Press, New York, 133-148 (1985).

J. E. Bailey and D. F. Ollis, Chapter 10 Instrumentation and

Control, in Biochemical Engineering Fundanentals , 2nd Edit.,

New York, 658-725 (1986).

A. Fiechter, M. Meiners, D. A. Sukatsch, Chapter 7 Biological

Regulation and Process Control, in Fundamentals in

Biotechnology, P. Prave, U. Faust, W. Sittig, D. A. Sukatsch,

Eds., VCH Publishers, Deerfield Beach, FL (1987).

47
B, Kristiansen, Chapter 9 Instrvunentation, in Basic Biotechnology,

J, Bu'Lock and B. Kristiansen, Eds., Academic Press, New York, 252-

281 (1987).

D. K. McMillan, Chapter 4 Dissolved Oxygen and Carbon Dioxide

Measurements , in Biochemical Measurement and Control , Instrioment Society of America, Research Triangle, NC, 65-76

(1987).

9 . 5 Oxygen Diffusion

K. Akita, "Diffusivities of Gases in Aqueous Electrolyte

Solutions," Ind. Eng, Chem. Fundam. 20, 89-94 (1981).

Diffusivities of oxygen in aqueous electrolyte solutions were measured

for 18 species of cations, 13 species of anions, and combinations

thereof. A polarographic oxygen electrode and a dissolved-oxygen

analyzer were used in the diffusion cell. Air was used as the oxygen

source. Measurements were made at 10, 20, and 40 "C, and electrolyte

concentrations were varied to near saturation. The solubility of oxygen

in liquid was also measured. Correlations were made between the oxygen

diffusivity and the solution viscosity.

The results of the measurements of oxygen diffusivities in various

aqueous electrolyte solutions were discussed on the basis of the Eyring

theory of rate processes . The free energy of activation of oxygen in a solution is assumed to consist of the sum of contributions due to

various chemical species in the solution. The variations of the free

energy with temperature for different diffusing solutes are discussed.

The paper states that the prediction of diffusivities of gases in

aqueous electrolyte solutions is possible if gas diffusivities in pure

water and the densities of the solutions are available. Equations are

given.

T. Goldstick and I. Fatt, "Diffusion of Oxygen in Solutions of

Blood Proteins," Fundamental Processes in Fluidized Beds,

Amer. Inst. Chem. Eng., New York, pp. 101-113 (1970).

The diffusion coefficient of dissolved oxygen was determined in aqueous

solutions of potassium chloride, bovine serum albumin, and human

oxyhemoglobin over the complete concentration range. A modified Clark

type of polarographic oxygen electrode monitored the oxygen partial

pressure at the bottom of a layer of liquid after the partial pressure

was changed at the top. Mathematical analysis of the resulting

transient data gave the oxygen diffusion coefficient directly, without

requiring a value for the oxygen solubility or any empirical constant.

All solutions of electrolytes were made with reagent grade chemicals and

fresh distilled water. The blood protein solutions were made from

outdated human whole blood. The albumin solutions were made from stock

solutions of 5, 30, and 35% bovine serum albumin. Auxiliary

polarographic techniques were developed to measure the oxygen

consumption rate and combining capacity. The experimental data indicate

that the diffusion coefficient of oxygen decreases slowly and regularly

with solute concentration.

48
Results Indicate the oxygen diffusion coefficient for oxygen In pure

water at 25 "C Is 2.13 x 10"* cm^ s"^. A table of data compares

published values for the diffusion coefficient of oxygen In water at

25 "C, values from 18 other papers are presented. The data scatter

about a mean of 2.2 x 10'* cm^ s"^. The diffusion coefficient of oxygen

In Isotonic saline (0.150 M NaCl/L) at 25 "C was found to be 2.07 x 10"*

cm^ s"^. Oxygen diffusion coefficient measurements were made In KCl

solutions with concentrations ranging from 1 x 10"* to 5 mol/L. The

diffusion coefficient holds approximately constant to about 0.1 mol/L,

but above 1 Mole/L of KCL It drops rapidly. In bovine serinn albumin

solutions whose concentration is the same as the total protein

concentration In the plasma, the oxygen diffusion coefficient at 25 "C

Is 1.80 X 10"* cm^ s"l. The ratio of this coefficient to that of water

Is 0.85.

The oxygen diffusion coefficient In human hemoglobin solution of 33.5

g/100 ml, the normal red blood cell concentration, Is 0.76 x 10"* cm^

s"^ at 25 "C. The ratio of this coefficient to that In pure water is

0.36. Diffusion coefficient measurements of dissolved oxygen in

isotonic bovine serum albumin and hioman oxyhemoglobin solutions at 25 °C were made at protein concentrations up to 55 g/100 ml. The diffusion

coefficients show a steady decrease with Increasing protein

concentration, with the coefficients for the hemoglobin solutions being

slightly lower than the albiamin solutions.

C. S. Ho, R. F. Baddour, and D. I. C. Wang, "Effective

Dlffusivity of Oxygen in Microbial Pellets," Biotech. Advs. 2,

21-33 (1984).

A state-of-the-art review of the dlffusivity of oxygen in microbial

pellets is presented. The development and evolution of the means for

quantitative characterization of the effective oxygen dlffusivity in

microbial pellets is emphasized. Twenty-one values of the effective

oxygen dlffusivity in microbial pellets taken from the literature are listed in a table. The paper concludes that effective dlffusivity of

oxygen in microbial pellets is a most important physical parameter

affecting the submerged fermentation with microbial pellets.

C. S. Ho, L. K. Ju, C. T. Ho, "Measuring Oxygen Diffusion

Coefficients with Polarographic Oxygen Electrodes. II.

Fermentation Media," Biotechnology and Bioengineering, 28 . 1086-1092 (1986).

Oxygen diffusion coefficients in fermentation media were measured and

correlations were developed. The authors conclude that in s3mthetic

fermentation media, the amount of salts and of other substances present,

such as sugars, dramatically affects the oxygen diffusion coefficient.

Experiments were carried out in pure glucose solutions, aqueous

solutions of glucose with one salt added, s)mthetic media, and aqueous

solutions of commercial nutrient broth in varying concentrations.

Oxygen diffusion coefficients were measured at 22 "C and 1 atm.

Relative oxygen diffusion coefficients, i.e., the ratio of the diffusion

constant in the test meditim to the diffusion constant in pure water, were reported. The relative oxygen diffusion coefficients in aqueous

glucose solutions decreased to 0.78 at 10% in weight. The data were

49
analyzed for a correlation with viscosity and the Stokes -Einstein

equation was found to satisfactorily describe the functional relation

between the oxygen diffusion coefficient and the solvent viscosity. For

aqueous solutions of glucose-NaCl and glucose- (NH^ ) 2 SO^ , the relative

oxygen diffusion coefficients decreased as the salt concentration

increased with constant glucose concentration. It was concluded that

oxygen diffusion coefficients in glucose solutions plus salts follow a log-additive relationship. Measurements of oxygen diffusion

coefficients in aqueous solutions of nutrient broth were analyzed and a linear correlation of the relative diffusion coefficient as a function

of nutrient broth concentration was found.

C. S. Ho and L. K. Ju, "Effects of Microorganisms on Effective

Oxygen Diffusion Coefficients and Solubilities in Fermentation

Media," Biotechnology and Bioengineering 32, 313-325 (1988).

The effects of microorganisms on effective oxygen diffusion coefficients

and solubilities in fermentation media were studied. Effective oxygen

diffusion coefficients and solubilities in fermentation media containing

microorganisms of different sizes and shapes were measured with a polarographic oxygen electrode by applying coupled steady- state and

unsteady- state analyses for oxygen diffusion through a liquid layer on

the membrane surface of the electrode. Effective oxygen diffusion

coefficients and solubilities were measured for submerged cultures of

Saccharomyces cerevisiae, Escherichia coli, and Penicillium chrysogenum.

The effective oxygen diffusion coefficients were correlated with cell

volume fractions in fermentation media, and further compared with values

predicted from theoretical models in the literature. Both effective

oxygen diffusion coefficients and solubilities decreased with increasing

cell concentrations in the fermentation media. The experimental results

showed the effective oxygen diffusion coefficients in fermentation media

were larger than those predicted when it was assumed the microbial cells were impenetrable. The authors conclude that this indicates that oxygen

molecules diffuse through the cells during the diffusion process.

Within the cell concentration range of typical submerged fermentations,

the effective oxygen diffusion coefficient of the fermentation medium is

described as 0^/0^ = 1 + A^f + A2f, where f is the cell volume fraction

and both A^ and A2 are functions of the shape of the cells and the ratio

of effective oxygen diffusion coefficient in microbial cells to that in

the medium.

C. S. Ho, L. K. Ju, and R. F. Baddour, "The Anomaly of Oxygen

Diffusion in Aqueous Xanthan Solutions," Biotechnology and

Bioengineering, 32, 8-17 (1988).

A membrane -covered polarographic oxygen electrode was used to measure

oxygen diffusion coefficients in aqueous polyelectrolyte solutions of

xanthan gum, sodium alginate, and sodium carboxymethylcellulose (CMC).

The oxygen diffusion coefficient and solubility in test solutions were

determined by applying the coupled steady-state and unsteady- state

analyses for oxygen transfer through a thin layer on the electrode

surface. Oxygen solubilities were found to decrease with increasing

polymer concentration. In sodium alginate solutions, dilute xanthan gum

solutions and CMC solutions with CMC concentrations higher than 0,4

wt%, oxygen diffusion coefficients decrease with an increase in polymer

50
concentration. The authors interpret this using Wang's obstruction

theory and Kulkarni and Mashelkar's modified free-volume theory.

However, in dilute CMC solutions and xanthan solutions, when xanthan gum

concentrations exceed 0.5 wt%, oxygen diffusion coefficients increase

with increasing polymer concentration and values higher than in pure

water are observed.

L. K. Ju, E. Livio, and C. S. Ho, "Measuring Oxygen Diffusion

Coefficients in Electrolyte Solutions with Polarographic

Oxygen Electrodes," Biotechnology and Bioengineering Symp. No.

15, 347-361 (1985).

This paper reports oxygen diffusion coefficients in various single and

mixed electrolyte solutions. Diffusion coefficients were measured using

a membrane -covered dissolved-oxygen electrode and analyzed using a steady-state analysis. The salts used were sodium chloride, potassium

chloride, sodium sulphate, ammonium sulphate, magnesium sulphate, and

mixtures of ammonium sulphate -sodium chloride and of magnesium sulphate

potassium chloride. Oxygen diffusion coefficient measurements were

conducted in pure water and in various solutions of electrolytes at 21

°C and 1 atm pressure. Relative oxygen diffusion coefficients, which

are the ratio of the diffusion coefficient in the test solution to the

diffusion coefficient in pure water, are reported. Results show that

oxygen diffusion coefficients for both single and mixed electrolyte

solutions can be correlated by the square root of total ionic strength

of electrolyte solutions as: D = Dq(1 - f(I^)) where D is the diffusion

coefficient in the test solution, D^ is the diffusion coefficient in

pure water, I is the ionic strength and f is a factor characteristic of

the salts present.

L. K. Ju and C. S. Ho, "Measuring Oxygen Diffusion

Coefficients with Polarographic Oxygen Electrodes: I. Electrolyte Solutions," Biotechnology and Bioengineering, 27 . 1495-1499 (1985).

This paper describes a rapid method of measuring oxygen diffusion

coefficients in electrolytes solutions with a commercially available

membrane -covered oxygen electrode and reports results for electrolyte

solutions. Measurements of the oxygen diffusion coefficient were

conducted in water and in aqueous solutions of four salts at 22 °C and 1 atm pressure. The salts were sodium chloride, potassium chloride,

sodium sulphate and magnesium sulphate and solutions were prepared over

a range of molar concentrations. Absolute values of the oxygen

diffusion coefficients as a function of the electrolyte concentrations

in the aqueous solutions are reported, as well as the ratio of the

oxygen diffusion coefficient in the electrolyte to the oxygen diffusion

coefficient of water at infinite dilution of salts. The presence of

ions results in a decrease in the diffusion coefficient, and the

marginal effect of the electrolyte concentration on the diffusion

coefficient decreases rapidly as the concentration increases.

Experimental results show that the oxygen diffusion coefficients in

electrolyte solutions vary approximately linearly with the square root

of the electrolyte ionic strength. The authors interpret this with

Eyring's significant liquid structure theory and indicate that by

combining the effects of the ionic strength on the viscosity and the

51
distance between the diffusing molecule and its neighboring molecules,

it is expected that the diffusion coefficient varies linearly with the

square root of the ionic strength of the solution.

L. K. Ju, C, S, Ho, R. F. Baddour, "Simultaneous Measurements

of Oxygen Diffusion Coefficients and Solubilities in

Fermentation Media with Polarographic Oxygen Electrodes ,

Biotechnology and Bioengineering, 31, 995-1005 (1988).

This paper describes an experimental method capable of measuring

simultaneously oxygen diffusion coefficients and solubilities in aqueous

solutions by applying coupled steady-state and unsteady-state analyses

for oxygen diffusion through a thin layer of test solution on the

surface of a membrane covered oxygen electrode. The principles of the

electrode and the methods of analysis are described. Oxygen diffusion

coefficients and solubilities were reported for glucose solutions and

various fermentation media at 22 "C and 1 atm pressure. The

fermentation media studied were a commercial tryptic soy broth, and

media of Penicillium chrysogenum, Saccharomyces cerevisiae y-30, and

Micrococcus glutamicus. The diffusion coefficients of glucose solutions

over a range of concentrations correlated with solution viscosities on a logarithmic plot of the relative oxygen diffusion coefficients as a function of the relative viscosities. The equation Di/D^ =

(/ii/;io)"° • ^25 f£^. ^^Q ^j^t^ where D^/D^ is the relative diffusion

constant and a*i/a*o ^^ ^^® relative viscosity. The oxygen solubility

data fit the model logCk^/ki) = 5.93 x 10"* c^ , where k^/kj^ is the ratio

of solubility in water to that in the media, and c^ is the sugar

concentration. For fermentation media, log additive models were applied

to both oxygen diffusion coefficients and solubilities. Straight lines

were obtained in the semilogarithmic plots of experimental results of

Dj^/Dq and k^/k^ with the fractional composition of the media.

T. Koyama, T. Araiso, and M. Mochizuki, "Oxygen Diffusion

Coefficient of Cell Membranes," Advances in Experimental

Medicine and Biology, 200, 99-106, (1986).

A nanosecond fluorescence depolarization technique was used to measure

microviscosity in erythrocyte membranes of various animal species and in

lung cells and myocytes of bull frogs. The diffusion coefficient of

oxygen molecules (Dq2) was estimated from the microviscosity and an

equation for the relation between the viscosity and diffusion

coefficient. Oxygen diffusion coefficients are reported for several

animal species and for various organs of the frog. D02 values were

found to be significantly different among species, and among the various

organs in a single species. A comparison between sizes of moving area

of phospholipid molecules in membrane and in the ideal fluid state

suggested that actual Dq2 values in cell membranes may be 10 times

larger than the estimated values.

V. Linek and V. Vacek, "Comments on Validity of Measuring

Oxygen Diffusion Coefficients with Polarographic Oxygen

Electrodes," Biotechnology and Bioengineering, 31, 1010-1011

(1988).

52
This paper challenges the validity of the method developed by Ju and Ho

for measuring oxygen diffusion coefficients with polarographic oxygen

electrodes. The authors state that Ju and Ho's analysis is in error

because in development of their equations, they have mistakenly

dismissed the ratio of oxygen solubility in the test liquid to that in

water, causing the permeability ratio to be taken for the diffusivity

ratio. The authors suggest Ju and Ho's data can be converted to the

diffusivity ratio by multiplying by the ratio of oxygen solubility in

water to that in the test solution. Figures are presented showing that

by multiplying Ju and Ho's original data by the ratio of oxygen

solubilities, the data agree better with data derived from the Akita

correlation. This paper also objects to Ju and Ho's analysis because it

does not consider the oxygen side diffusion which may occur with the

electrode.

V. Linek, V. Vacek, P. Benes, and J. Sinkule, "Transient

Characteristics of Oxygen Probes with Significant Liquid Film

Effects," Biotechnology and Bioengineering, 33, 39-48 (1989).

The effect of the liquid film on the dynamics of membrane -covered probes

was studied mainly with respect to the measurement of the volumetric

oxygen mass transfer coefficient, KLa, in viscous broths. The effect of

the liquid film on the oxygen probe transient characteristics is much

more pronounced than its effect on the probe sensitivity. Six

experimental procedures for the determination of transient

characteristics with significant liquid film effects were tested. A

comparison between transient characteristics obtained experimentally and

those calculated from rational models indicated that only one procedure

gave consistent results. Recalculation of transient characteristics

with no liquid film (as measured in the gas phase) to that with liquid

film (occurring in viscous liquids) is recommended, as well as the

selected experimental procedure which yields consistent results in the

situations where the steady-state probe reading is decreased up to one- half due to the liquid film.

P. Luhring and A. Schumpe, "Diffusionskoeffizienten und

Loslichkeiten von Sauerstoff in Organischen Flussigkeiten,

Chem. Ing. Tech., 58, 976-977 (1986). (in German)

M. Onuma, T. Omura, T. Umita, J. Aizawa, "Diffusion

Coefficient and Its Dependency on Some Biochemical Factors,"

Biotechnology and Bioengineering, 22, 1533-1539 (1985).

Diffusion coefficients for glucose and oxygen through a microbial

aggregate were measured, and their dependence on biochemical factors was investigated. The dependency of diffusion coefficients on the

carbon/nitrogen ratio and the bacteria concentration of the microbial

aggregate and the water temperature was studied. The kinetic and

diffusion studies used synthetic sewage as the test media. Diffusion

coefficient data for oxygen and glucose are presented. The diffusion

coefficients were found to be dependent on bacteria concentration,

carbon/nitrogen concentration, and temperature. Diffusion coefficients

of oxygen and glucose were measured in water over the temperature range

of 5 - 30 °C, and expressions for the diffusion coefficients, as a function of temperature, were obtained. The diffusion coefficients for

53
glucose and oxygen were estimated to be 86 - 95% of the corresponding

values in water at the high bacteria concentration, while they were

estimated almost as 100% of the corresponding values in water at the low

bacteria concentration.

G. Potucek and J. Stejskal, "Diffusivity of Oxygen in non- Newtonian Liquids," Chemical Engineering Science, 41, 3223-

3226 (1986).

The diffusion coefficient for oxygen was measured in solutions of two

types of polyacrylamide in water. Three concentration levels of each

polyacrylamide were studied, all showed pseudoplastic behavior. The

values of oxygen concentration at saturation were determined by means of

a Clark electrode modified by Cerkasov, Oxygen diffusion coefficients

are reported. The effect of poljnner tjrpe and its concentration on the

oxygen diffusivity was determined. The diffusion coefficient of oxygen

in a poljnner solution is of the same order of magnitude as the diffusion

coefficient in a pure solvent. The data indicate that the addition of a small quantity of long chain polymer can result in both increasing and

decreasing the diffusivity of oxygen in solutions, depending on the

concentration and length of the chain of the macromolecules. In

contrast to Newtonian liquids where the diffusivity decreases with

increasing viscosity of liquid, the diffusivities in non-Newtonian

solutions are often higher than in water at the same temperature. Other

studies confirming these findings are cited. A table of data lists

diffusion coefficients of oxygen in water taken from ten other studies.

G. A. Ratcliff and J. G, Holdcroft, "Diffusivities of Gases in

Aqueous Electrolyte Solutions," Trans. Inst. Chem. Engrs . 41,

315-319 (1963).

This paper first reviews theories of diffusivities of gases in fluids.

Using Eyring's lattice model of a liquid, the diffusivity of a solute in an aqueous electrolyte is shown to vary approximately linearly with the

concentration of the electrolyte. A model was developed for predicting

diffusivities in electrolyte solutions. Experimental measurements were

reported of the diffusivity of carbon dioxide in water and in aqueous

solutions of six salts at 25 "C and 1 atm pressure. The diffusivities

were obtained by measuring the rate of absorption of carbon dioxide into

the deaerated electrolyte solutions flowing over a sphere. Correlations

of diffusivity and viscosity are studied and tentative relationships

proposed for predicting diffusivities in electrolyte solutions.

T. Sridhar and 0. E. Potter, "Diffusion Coefficient of Oxygen

in Liquids," Chem. Eng. Commun. 21, 47-54 (1983).

This paper describes the measurement of the diffusion coefficient of

oxygen in water and cyclohexane. A laminar dispersion of the solute in

a solvent, in Poiseuille flow, in a long capillary tube is used to

measure the coefficients. A polarographic t3npe of oxygen detector was used to measure dissolved oxygen. The measured diffusion coefficient of

oxygen in distilled water at about 293 and 303 K were shown on a graph

and appear to be about 2.2 m^ s"^ x 10"^ and 2.9 m^ s'^ x 10"^. Other

literature values of the oxygen diffusion coefficient in water in the

temperature range of about 280 to 328 K are also shown on the graph.

54
An equation is given for the theoretical prediction of the diffusion

coefficient of oxygen in water at various temperatures. An equation to

predict the diffusion coefficient of any other gas in the same liquid is

presented to use when the measured diffusion coefficient of oxygen in

the liquid is known.

9.6 Measurement of the Voliniietrlc Mass Transfer Coefficient (I^a)

Y. Kawase and M. Moo-Young, "Influence of Very Small Bubbles

on KLa Measurement in Viscous Microbiological Cultures,"

Biotechnological and Bioengineering, 30, 345-347 (1987).

Volumetric mass transfer coefficients obtained using an unsteady-state

method involving transient dissolved oxygen absorption or desorption are compared with those obtained with a proposed djmamic CO2 gas analysis

method that consists of continuous monitoring of the response of the

outlet gas composition to a step input change of CO2 in the inlet stream

of a gas- liquid contactor. Measurements were made in solutions of

polyacrylamide and solutions of carboxjrme thy1- cellulose, which are non- Newtonian fluids. The influences of very small bubbles on volumetric

mass transfer measurements made by two methods are discussed. Their

effect on the CO2 measuring technique was found to be insignificant

compared to that when using the conventional dissolved- oxygen technique

where significant underestimations of KLa occur.

V. Linek, V. Vacek and P. Benes, "A Critical Review and

Experimental Verification of the Correct Use of the Dynamic

Method for the Determination of Oxygen Transfer in Aerated

Agitated Vessels to Water, Electrolyte Solutions and Viscous

Liquids," The Chemical Engineering Journal, 34, 11-34 (1987).

This paper discusses inconsistencies in data reported in the literature

for the volumetric mass transfer coefficient for oxygen, Kj^a, obtained

by various djmamic methods. Methods of mass transfer coefficient

measurement are described and models used to evaluate mass balance in

the gas and liquid phases are analyzed critically. Methods of measuring

oxygen concentration and factors which influence oxygen probe signals

are described, and errors in interpretation of oxygen probe data leading

to errors in KLa estimates are also discussed. Experimental

measurements are reported for KLa for basic tjrpes of systems as a function of the stirring rate, and are compared with data for similar

systems reported in the literature. The liquids used were distilled

water and aqueous solutions of electrolytes, glycine and carbox3niiethylcellulose (CMC) . The oxygen concentration was measured by two oxygen

probes with pol3rpropylene membranes and platinum cathodes. Data were

analyzed using both the correct and incorrect variants of the djrnamic

method, and the results are compared separately for coalescing systems

(water and dilute solutions of structure -breaking electrolytes), non- coalescing systems (aqueous solutions of structure -making electrolytes)

and viscous batches (solutions of glycerine and CMC) . Data were compared on the basis of a correlation of KLa as a function of power

dissipated per unit of liquid phase volume, and superficial gas flow.

Results indicate only one dynamic method gives correct results which

agree with the steady state sulphite method, and conform to a simple

relationship. It is concluded that inconsistencies in KLa data reported

55
in the literature are the result of incorrect techniques used by various

researchers for K^a measurement.

V. Linek, P. Benes, and 0. Holecek, "Correlation for

Volumetric Mass Transfer Coefficient in Mechanically Agitated

Aerated Vessel for Oxygen Absorption in Aqueous Electrolyte

Solutions," Biotechnology and Bioengineering, 32, 482-490

(1988).

The purpose of this paper was to find an equation to express the

dependence of Kj^a of oxygen absorption in aqueous inorganic electrolyte

solutions on the physical properties of the liquid phase. Empirical

equations used in computing K^^a in mechanically agitated aerated vessels

agree well with the measured dependence of K^a on the power input of the

stirrer and the superficial gas velocity. They do not fit the

dependence of KLa on the physical properties of the liquid batch. It was deduced from published data that suitable equations to describe the

dependence of KLa on the liquid physical properties must include an independent variable to characterize the rate of bubble coalescence.

Experimental values of KLa were compared with those calculated from

different relations and the rate of coalescence for aqueous electrolyte

solutions was found to be described on the basis of the Gibbs theory of

adsorption of the solute in the surface layer of the solution. The

authors state that the majority of dissolved oxygen concentrations

reported in the literature are incorrect due to errors in assuming ideal

mixing of the gas in the vessel when it is not justified, and incorrect

interpretation of the oxygen probe data.

M. Moresi and M. Patete, "Prediction of KLa in Conventional Stirred

Fermenters," J. Chem. Tech. Biotechnol., 42, 197-210 (1988).

A series of oxygen absorption rates in sodium sulphite solutions

homogeneously measured in a series of stirred fermenters are presented

and a single correlation suitable for further scaling-up exercises is

developed. Values of the volumetric oxygen transfer coefficients, KLa,

were determined over a wide range of superficial air velocities and

impeller rotational speeds. Despite the great scale-up ratios, very

different operating conditions and geometric dissimilarity of the

fermentors, a data correlation was developed using the gassed power

consiunption and aeration rate per unit volume as key parameters. It

appears the correlation is an acceptable prediction of KLa values in

multiple- impeller fermenters even when geometric similarity between

bench- and pilot-scale fermenters is not maintained.

N. M. G. Oosterhuis, A. P. J. Sweere, and N. W. D. Kossen,

"Determination of the Liquid Side Oxygen Transfer Coefficient

in a Biological Medium," Chem. Eng. Res. Des. 63, 203-205

(1985).

A simple method is presented to analyze the effect of the bubble

diameter on the liquid side oxygen transfer coefficient. The oxygen

transfer rate, Kl , was determined in a bubble column. From these

measurements, the volumetric oxygen transfer rate, KLa, was obtained as

a function of gas bubble diameter. The experiments were carried out in

water as well as in a biological medium. The oxygen concentration was

56
measured by means of a polarographlc oxygen probe. Results are presented showing the liquid side oxygen transfer coefficient as a function of bubble size, and are compared with data from the literature.

The oxygen transfer coefficient was found to be lower in the biological

medium than in pure water. This effect was suggested to be caused by

changes in the boundary layer of the medium. An increase of Kl occurred

with bubble diameters between 1 and 2 mm, with the highest K^ values

reported at bubble diameters -2.5 mm. For larger bubbles, a decrease of

the Kl was observed.

A. Schumpe, "Determination of Mass Transfer Coefficients on

the Basis of Dissolved Oxygen Measurements - Design of Gassing

Equipment," Chem. Ing. Tech. 52, 501-505 (1985). (In German)

Sources of error in the dynamic and static method for determination of mass transfer coefficients are discussed on the basis of experimental

results obtained in bubble columns. Experimental errors due to the

polarographlc electrode arise from delayed electrode response, the

resistance in the liquid film, and bubbles in contact with the

electrode. The influence of very small bubbles in viscous media tends

to result in too small an estimation for K^a.

C. G. Sinclair, "Formulation of the Equations for Oxygen

Transfer in Fermenters," Biotechnology Letters, 6, 65-70

(1984).

This paper discusses the equations used for oxygen transfer in

gas/liquid systems and suggests that the common expression for oxygen

transfer in gas/liquid systems is incorrect because it assumes the

oxygen transfer coefficient does not depend on the oxygen concentrations

C* and C. It argues that KLa, as normally defined, is a function of

oxygen concentration and that below about 20% saturation in the liquid

phase, the error rapidly increases and the normal method of computing

KLa seriously overestimates the value. It is suggested that this is the

reason KLa values measured with the sulphite oxidation technique are always greater than the values of KLa obtained by the outgassing

techniques. An expression of the driving forces for oxygen transfer as chemical potential differences is proposed as a means to lead to a more

correct formulation of the oxygen transfer equation.

0. Stenberg and B. Andersson, "Gas-Liquid Mass Transfer in

Agitated Vessels I. Evaluation of the Gas-Liquid Mass

Transfer Coefficient from Transient-Response Measurements,"

Chem. Eng. Sci., 43, 719-724 (1988).

This paper tests the influence from gas -phase dispersion and liquidphase mixing and suggests an experimental method for evaluating the gasliquid mass transfer coefficient, KLa, in agitated vessels from

trans lent- response measurements. The method is based on measuring the

average concentration in the liquid phase by multiple electrodes and

using a calculated gas -phase dispersion. Results are presented showing

the differences between different methods of evaluating. The method

gives an average KLa value, and the data indicate that the KLa is much

higher in the impeller stream and much lower than average below the

impeller.

57
0. Stenberg and B. Andersson, "Gas -Liquid Mass Transfer in

Agitated Vessels II. Modelling of Gas-Liquid Mass Transfer,"

Chemical Engineering Science, 43, 725-730 (1988).

A study of the effects of the size, impeller speed, power input and gas

superficial velocity upon KLa are reported. The mass transfer

coefficient was determined by a new and improved method using unsteadystate measurements of oxygen dissolution rate in water in three

geometrically similar agitated vessels. The oxygen content was monitored with four oxygen membrane electrodes. The data were fit to 10

scaling models based on the hold-up and bubble diameter. It was concluded that hold-up has the major effect on KLa. Bubble diameter is

more difficult to measure, but its variation with reactor size, power

input and gas flow rate is smaller.

C. R. Thomas, "On the Formulation of Oxygen Transfer

Equations," Biotechnology Letters, 7, 165-166 (1985).

This paper disagrees with Sinclair's recent paper [S1984] which claimed

that the commonly used oxygen transfer equation is incorrectly

formulated and the "oxygen transfer coefficient," KLa, is dependent on

C* and C. This paper agrees that the driving force for diffusion is a difference in chemical potential (rather than concentration difference)

,

but asserts that Sinclair's subsequent analysis was faulty, and that the

commonly used equation for oxygen transfer is correct,

X. M. Yang, Z. X. Mao, S. Z. Yang and W. Y. Mao, "An Improved

Method for Determination of the Volumetric Oxygen Transfer

Coefficient in Fermentation Processes," Biotechnology and

Bioengineering, 31, 1006-1009 (1988).

This paper presents a quick, convenient method for determination of KLa

values in fermentation processes, using a membrane covered galvanic

electrode to measure oxygen. The method combines the steady- state

method with the dynamic method to measure the volumetric oxygen transfer

coefficient. Fermentation media for E. coli was used as the test

solution. Both theoretical considerations and experimental results are provided.

9.7 Effect of Cells and Rheology on the Volumetric Mass Traxisfer

Coefficient

G. F. Andrews, J. P. Fonta, E. Marrotta, and P. Stroeve, "The

Effects of Cells on Oxygen Transfer Coefficients I: Cell

Accumulation Around Bubbles", The Chemical Engineering

Journal, 29, B39-46 (1984).

A study was conducted to determine whether cells have any enhancement

effect on the transfer of oxygen in an aerobic fermentation. The number

of cells on or near the Interface of a bubble in a fermentation broth

was considered. The gas- liquid interface was discussed, considering

both stationary and mobile Interfaces. Experiments were conducted to

measure the cell capture efficiency of bubbles of about 0.5 - 1.1 mm

rising through a fermentation medium having Escherichia coli cells. The

58
capture efficiency data are explained by a mobile interface. The drag

on adsorbed cells may force the interface to move, thus increasing the

capture efficiency, the nxjunber of adsorbed cells and the drag in a "snowball" effect. Adsorbed cells move around the bubble into the wake

where some form a packed mass near the rear stagnation point. Contact

between cells in this mass may initiate cell flocculation. Also, oxygen

demand may exceed supply in the mass, leading to locally anoxic

conditions

G. F. Andrews, J. P. Fonta, E. Marrotta, and P. Stroeve, "The

Effects of Cells on Oxygen Transfer Coefficients II: Analysis

of Enhancement Mechanisms," The Chemical Engineering Journal,

29, B47-B55 (1984).

Explanations were sought for the higher oxygen transfer coefficients,

Kl , occasionally observed in fermentation broths than in cell-free

liquids of the same rheology and concentration of surface -active

material. This paper considers whether the presence of microorganisms

caused changes in Kl in bubble aerated systems and in surface aerated

systems. Chemical enhancement and physical factors involving interface

blockage and hydrodjmamic enhancement were considered. In bubble

aerated systems, the hydrodjmamic effect was considered most important.

The hydrodynamic effect is described as a consequence of drag on cells

adsorbed at a bubble interface which forces the interface to move,

increasing both the cell capture efficiency and the mass transfer

coefficient. An enhancement factor of about three was predicted and has

been observed. This effect is dominant in bubble aerated systems.

Chemical enhancement and direct uptake by cells of oxygen from the gas

phase are considered negligible because few cells adsorb on the upper

half of the bubble, from where most of the oxygen is transferred. The

cells accumulate near the rear stagnation point but are considered to

have little effect on the total oxygen transfer rate. The interface

blockage effect in bubble -aerated systems is limited to a 10% reduction

in Kl because most of the oxygen is transferred through the boundary

layer region on the top of the bubble, however cells do not accumulate

on the interface in this region. The effects may be greater in surface

aerated devices. In surface -aerated systems, Kl is lower, cell

accumulation at the interface is greater and chemical enhancement is

significant, especially when high cell concentrations occur at the

interface.

M. Y. Chisti, K. Fujimoto and M. Moo-Young, "Hydrodynamic and

Oxygen Mass Transfer Studies in Bubble Columns and Airlift

Bioreactors" in Biotechnology Processes Scale-up and Mixing,

C. S. Ho and J. Y. Oldshue, Eds., American Institute of

Chemical Engineers, New York, 72-81 (1987).

The hydrodjmamic and oxygen mass transfer properties of dispersions are discussed for three reactor configurations: a rectangular bubble

column, a similar internal loop airlift, and a cylindrical external loop

airlift device. Three-phase systems are used in which fungal

fermentation media are simulated using cellulose fiber for microbial

biomass. Experimental results are presented on gas holdup and gasliquid mass transfer carried out in pneumatic devices with simulated

fluid systems for yeast, bacterial and fungal cultures. The overall

59
volumetric mass transfer coefficient, Kj^aL, and gas holdup are shown to

correlate with superficial gas velocity, reactor geometry, and fluid

properties. Correlation equations, having a theoretical basis, were

developed. Both Kj^aL and the gas holdup were found to decrease by up to

80% relative to the values in solid- free aqueous solutions when solids

were used to simulate basic fungal fermentation media.

M. Y. Chisti and M. Moo-Young, "Hydrodynamics and Oxygen

Transfer in Pneumatic Bioreactor Devices," Biotechnology and

Bioengineering, 31, 487-494 (1988).

The hydrodjmamic and mass transfer properties of pneumatic reactors are studied for application to mould fermentations. Gas holdup and oxygen

transfer studies in non-Newtonian suspensions of cellulose fibres were

conducted in two types of reactors , a bubble column and an internal loop

airlift tower, both having rectangular cross sections. The overall

volumetric oxygen transfer coefficient was determined by the dynamic

gassing- in method using a fast response dissolved oxygen electrode

connected to a dissolved oxygen meter. Cellulose fiber solutions in

hard tap water and in sodium chloride solutions were studied. Results

indicated the ratio of mass transfer coefficient to bubble size, KLa/dg, was essentially independent both of the reactor tjrpe and of the gas

velocity, but KL/dg depended strongly on the solid content of the fluids

and declined with increasing solid concentration. The conclusion was

that the mass transfer coefficient, Kl , declined with increasing amounts

of solids, with the implication that Kl was directly proportional to the

bubble size. The behavior of Kl with changes in bubble size was also

discussed.

M. Donde Castro, G. Goma and G. Durand, "Transfer Oxygen

Potential of an Air-Pulsed Continuous Fermentor" in

Biotechnology Processes Scale-Up and Nixing, C. S. Ho and J.

Y. Oldshue, Eds., American Institute of Chemical Engineers,

New York, 135-141 (1987).

A new type of air-pulsed continuous reactor is presented. Measurements

were made of the dissolved oxygen concentration in the liquid, the

oxygen pressure, and the COg concentration in the gas output. The

medium was K. fragilis grown in a glucose solution. The oxygen transfer

potential and the gas hold-up values were measured to determine the

effect of pulsation. KLa was measured using the sulfite oxidation

method and values are given for various aeration rates. Results are compared with those of other agitation techniques and compare favorably.

A. Schumpe and W. D. Deckwer, "Viscous Media in Tower

Bioreactors: Hydrodynamic Characteristics and Mass transfer

Properties," Bioprocess Engineering, 2, 79-94 (1987).

The purpose of this paper was to provide information needed for design

and scale-up of conventional tower reactors with respect to oxygen

transfer into viscous Newtonian and non-Newtonian media. It considers

flow regimes, liquid phase backmixing, phase holdups, and the volumetric

mass transfer coefficient. Other studies of tower reactors with viscous

liquids were reviewed relating to flow regime, effective shear rate,

liquid mixing, gas holdup and gas/liquid mass transfer. New data are

60
reported for solutions of glycerol, soditun carboxymethyl cellulose

(CMC) , polyacrylamide (PAA) and xanthan in bubble columns with three

different diameters. The volumetric mass transfer coefficients were

measured by the dynamic method. Based on the wide variation of the flow

behavior index, the effective shear rate is concluded to be smaller than

predicted. New dimensionless correlations were developed, applied to

predict KLa in fermentation broths, and compared to other reactor tjrpes.

The relation is successfully applied to predict Kj^a in mycelial

fermentation broths.

H. N. Chang and M. Mob -Young, Analysis of Oxygen Transport in

Immobilized Whole Cells, in Bloreactor Immobilized Enzymes and

Cells Fundamentals and Applications, M. Moo -Young, Ed.

,

Elsevier Applied Science, New York, 33-51 (1988)

D. D. Drury, B. E. Dale, and R. J. Gillies, "Oxygen Transfer

Properties of a Bloreactor for Use Within A Nuclear Magnetic

Resonance Spectrometer," Biotechnology and Bioengineerlng, 32 . 966-974 (1988).

K. Gbewonyo, D. Dimasi, and B. C. Buckland, "Characterization

of Oxygen Transfer and Power Absorption of Hydrofoil Impellers

in Viscous Mycelial Fermentations" in Biotechnology Processes

Scale-Up and Mixing, C. S. Ho., J. Y. Oldshue, Eds., American

Institute of Chemical Engineers, New York, 128-134 (1987).

M. Lavery and A. W. Nienow, "Oxygen Transfer in Animal Cell

Culture Medium," Biotechnology and Bioengineerlng, 30, 368-373

(1987).

9.8 Correlation of Mass Transfer (I^a) with Oxygen Diffusion

Coefficient (Dj,)

C. S. Ho, M. J. Stalker, and R. F. Baddour, "The Oxygen

Transfer Coefficient in Aerated Stirred Reactors and Its

Correlation with Oxygen Diffusion Coefficients" in

Biotechnology Processes Scale-up and Mixing, C. S. Ho and J.

Y. Oldshue, Eds., American Institute of Chemical Engineers,

New York, 85-95 (1987).

The oxygen transfer coefficient in aqueous electrolyte solutions was studied in an aerated, stirred reactor. Oxygen transfer coefficient

were measured and correlated with oxygen diffusion coefficients and

pertinent physical parameters for various single and mixed electrolyte

solutions. The oxygen transfer coefficient correlated with the

diffusion coefficient as Kl « Dl°"^^ where Kl is the oxygen transfer

coefficient and Dl is the oxygen diffusion coefficient in the media.

This was theorized for oxygen transfer from rigid spheres to bulk

solutions by the boundary layer theory. It appears that the small gas

bubbles produced in electrolyte solutions behave as rigid spheres. The

resulting correlation allows for the prediction of oxygen transfer

behavior by knowing the oxygen diffusion coefficients of aqueous

solutions in aerated stirred reactors. Bubble diameters were measured

and it was found that the bubble diameter decreased with increased ionic

strength. The diameter decrease leveled off at the ionic strength of

61
0.42 mol/L. Interfacial area was measured and determined to increase

with increased ionic strength up to 0.42 mol/L. The study showed that

small gas bubbles were produced in aqueous electrolyte solution

dispersions and these bubbles can be treated as rigid spheres for mass transfer purposes.

62
Solubility, Reactivity and Mass Transport of Carbon

Dioxide in Bioreactor Media

March 31, 1989

63
Contents

1

.

Relevance 65

2. Solubility of Carbon Dioxide 65

2.1 General 65

2.2 Solubility Measurement ..... 66

3

.

Reactivity 66

4. Buffers 68

5. Total Carbon Dioxide Content 70

6. Mass Transport of Carbon Dioxide 70

7. Facilitated Transport 71

8

.

Carbon Dioxide Measurement 72

8.1 Dissolved Carbon Dioxide 72

8.2 Carbon Dioxide in Gas 72

8.3 Interpretation of CO2 Measurements 73

9. Conclusions and Recommendations 74

10. References 75

11. Literature Relating to Facilitated Transport 78

12. Bibliography 80

64
Solubility, Reactivity, and Mass Transport

of Carbon Dioxide in Bioreactor Media

1 . Relevance

Carbon dioxide in bioreactors is not only a waste product of living

cells that needs to be removed in order for the cells to keep on

thriving. It is also an active participant in chemical reactions that

are crucial to the well-being of the cells in the reactor, because these

reactions maintain the proper pH and facilitate the transport of carbon

dioxide and ionic species across barriers to diffusion. Furthermore,

CO2 reacts with amino acids and proteins. This chapter therefore

addresses not only the topics of solubility, sensing, and diffusion of

carbon dioxide, but also deals with the reactivity of carbon dioxide,

and the role it plays in buffering and in facilitated transport.

2. Solubility of Carbon Dioxide

2 . 1 General

The solubility of carbon dioxide in bioreactor media is a complex

process due to the reactivity of CO2 , which will be described below. The

least interesting aspect is the ordinary solubility of CO2 in water, and

the salting out by the presence of other solutes. This part of the

problem is treated in much the same way as we described it for oxygen

solubility. For the definition of the many coefficients that are used

to characterize the solubility of gases, we therefore refer to our report on the solubility of oxygen.

The solubility of carbon dioxide in water has not been as well

characterized as that of oxygen, which has been exhaustively treated in

a recent lUPAC volume. A recent review on solubility of gases by

Wilhelm and coworkers [W1977] lists mole fraction and Ostwald

coefficient data for CO2 in the temperature range from 273 to 343 K,

which result from only two data sources [M1952] and [M1971] all other

data being restricted to temperatures near 298 K.

As is the case for oxygen, carbon dioxide will be "salted out" by the

other solutes present in the bioreactor, and this effect is again

described by means of empirical ion-specific Setschenov parameters, as defined in our oxygen solubility report. The principal source of such

ion-specific Setschenov parameters for carbon dioxide is the review by

Schumpe et al. [S1982] where values are listed for 11 cations and seven

anions. Schumpe et al. state that these parameters have little

temperature dependence in the range of 10-40 "C.

The section on reactivity of CO2 will describe the effects on its

solubility due to the presence of buffers and to variation of pH.

65
2.2. Soliiblllty Measurement

In this section, we refer to laboratory measurement of the solubility of

carbon dioxide. The sensing of dissolved carbon dioxide in bioreactors

and their off-gas will be discussed separately.

The solubility of carbon dioxide in water can be measured by any of the

many methods that have been developed for gas solubility measurement in

the past 2 centuries . Appropriate references are given in our oxygen

solubility report. Quicker et al. [Q1981] have recently developed a reasonably accurate method suitable for solubility measurement in

bioreactor fluids. They measure the decrease in pressure that results

when a large area of a stirred deaerated fluid is exposed to a volume of

the gas of interest. The method is claimed to be accurate to 1% in

solubility. Complications result when the biofluid contains respiring

organisms; if toxic substances are added in order to stop the breathing,

however, they will also affect the solubility. The work of Quicker et

al. nevertheless, is the principal source of information on carbon

dioxide solubility in fermentation media.

3 . Reactivity

The principal difference between the behavior of oxygen and carbon

dioxide in bioreactors is that carbon dioxide reacts with water and

amines while oxygen is inert. In table 1, we summarize the reactions and

reaction products involving carbon dioxide. This information was obtained from [H1986] , [H1987] , [M1987] and [E1955] Equilibrium

constants for these reactions over a wide range of temperature can be

calculated from tabulated thermodynamic data [B1982]

.

Rate of reactions

Reaction 2, hydration of CO2 , proceeds very slowly for pH below 8 since

it has an activation energy of 16-20 kcal/mole.

Reaction 3, production of bicarbonate, is instantaneous.

Reaction 4, production of the carbonate ion, is very slow and often

ignored.

Reaction 7 is rate -determining in the chain of reactions with NH3

.

Reaction 8 is very fast.

66
Table 1. Reactions Involving CO^ In aqueous media

Reaction

A. Hydration reactions

pK (25 "6) Name of Product A.

1 C02(g) ^ C02(d)

2 COzCd) + H2O ^ H2CO3

H2CO3 HCO," + H+

HCO3" -» H+ + 003"

2.59

3.77

10.33

carbonic acid

bicarbonate

carbonate Ion

B. Reactions Involving caustic

5 CO,2 + OH'" -» HCO,

HCO3" + OH" CO,

C. Reactions Involving ammonia and amino groups

7 NH3 + CO2 -> NH2COOH

8 NH2COOH + NH3 ;l NH/ + NH2COO"

9 NH2C00' + H2O -^ NH^COg"

10

carbamic acid

Ionized ammonium carbamate

ammonium bicarbonate Ion

NH^C03" - NH/ + CO3'

11 Ri R2 (C00H)CNH2 + CO2 -^ Ri R2 (COOH)CNHCOOH a carbamate

formed with free amino group protein

67
Role of nH

Reaction 1, dissolution of CO2 , does not depend on pH.

Reaction 3, production of HCO3", shifts to the right as pH increases.

Reaction 4, production of the carbonate ion, shifts completely to the

left for between 5.5 and 6.5.

Reaction 11 occurs at pH values above the isoelectric point of the

protein. It competes successfully with reaction 2.

4 . Buffers

The bicarbonate ion fulfills an important buffering function in

bioreactors. A buffer is a solution which is resistant to changes in

hydrogen ion concentration. Its use is obviously the stabilization of

acidity or basicity levels in solutions, so that small or moderate

additions of either acids or bases will have negligible effect on the pH

of the system. In their chemical action, then, buffers are working

examples of Le Chatelier's principle, which states that for a system in

equilibrium, any stress placed on the system will tend to initiate a response which compensates for that stress. Buffers generally consist of

a weak acid together with its salt, or, less commonly, a weak base and

its salt. Consider the equilibrium system

HA -^ H"^ + A" (1)

where HA is any weak acid and A" is the anion from the dissociated acid

and from salts of this acid. Two important chemical stresses can be

placed on the system. First, an acid can be added, which places a stress on the equilibrium by adding excess H* on the right hand side.

As a consequence, a reaction takes place between A and the added H"*" to

form undissociated molecules of HA; this reaction proceeds until

ionization equilibrium has been restored, with the net effect of

removing most of the additional H"*" ions and thereby minimizing the pH

change that naturally results from added acid. Second, a stress may be

placed on the system through the addition of some base, in which case

free H"*" ions will be removed through neutralization, which causes a deficiency of H"*" on the right hand side. The response in this case is

the further dissociation of HA molecules so as to restore chemical

equilibrium. The net effect of the added base is therefore minimized by

the subsequent dissociation of additional acid.

As an example of the dramatic effect of a buffer on pH, consider the law

of mass action that applies to the ionization of a weak acid, eq. (1):

K =

[H^] [A-] ^ [HM C,

^2)

[HA] Ca

where C, stands for the salt concentration, and C^^ for the concentration

of the weak acid, both in moles/liter, and HA is the ionization constant

for the acid. Upon adding to the system x moles/liter of a strong acid,

such as HCl or HNO3 , we obtain

68
„ = [H'l (C. - X)

<i ^3j

(Ca + X)

and so the pH Is given by

pH = Ka ^ logio

c,

[ Ca

- X

+ X

(4)

Choose a symmetric buffer for which salt and weak acid concentrations

are identical (C^ = C^^ = C) and eq (4) becomes

pH = pK^ - 0.87 arctanh (x/C) (5)

where the hjrperbolic arctangent function is indicated. For the

physically relevant values of x/C < 1, this function can be expanded to

yield

pH = pKa - 0.87 [x/C + (x/C)V8 +...]. (6)

This equation shows that for small x/C, the value of pH will be pinned

to that of pK^

.

As a concrete example of buffering, consider the first ionization of

carbonic acid

H2CO3 ^ H"^ + HCO3" (7)

which has a pKj^ of about 6.5. For the buffer, take a solution of 0.1 M

H2CO3 along with 0.1 M NaHCOg , and for the strong acid choose 0.01 M

HCl. From eq. (6) we readily see that the pH undergoes only a slight

change upon the addition of HCl, from pH 6.5 to pH 6.4, whereas

acidifying the solution in the absence of a buffer would cause the pH to

drop down to 2

.

Note that even if a large quantity of strong acid is added, 0.05 M HCl

for instance, the pH of the buffered solution decreases by only 0.48

units. In addition, a bit of numerical analysis of eq (4) suggests

that, for small values of x relative to C^ or C^^ , the pH is far more

sensitive to the ratio C^/C^^ than to either absolute value. This

implies that buffering efficiency is determined primarily by the

ionization constant of the weak acid used and the ratio of acid to salt,

rather than the absolute concentration of acid or salt. A buffer may

therefore be diluted without adversely affecting its efficiency.

Buffers commonly found in fermentation media include phosphates,

sulfates and an assortment of buffers consisting of amino acids and

their conjugate salts.

69
5. Total Carbon Dioxide Content

At this point it is convenient to introduce the notion of "total carbon

dioxide content" of the liquid phase (T) , which, in the absence of

carbamate formation, may be expressed as

T [CO2] = [CO2] + [H2CO3] + [HCO3-] + [C03=] . (8)

As a simple consequence of the law of mass action, T (CO2) has a wide

range of behavior as a function of the partial pressure of CO2 in the

gas phase, p(C02). In fact, T(C02) vs p(C02) curves have shapes which

depend strongly on the pH range considered, as well as on the ionization

constant K^ of any weak acid HA, with A the conjugate base, that is used

as a buffer. As explained in the section on buffering, the combination

of HA and A tends to stabilize the pH in a narrow range around pK^ . The

total carbon dioxide content is not simply linearly related to the

partial pressure of CO2 when buffers are present. This is evident from

the following examples taken from [E1955] . For instance, in a solution

of 0.02 M of sodium bicarbonate, if buffered at a pH of 7.1, at a partial pressure of CO2 of 63 mm Hg, T equals 22 mM/L. At a pH of 9.1,

however, which is attained by dropping the partial pressure of CO2 all

the way down to 0,45 mm Hg, T decreases only marginally, to 17 mM/L, On

the other hand, if the buffer is 4 -methyl imidazole (Im) at 0.025 M, the same drop in p(C02) causes a smaller pH rise, from 7.2 to 8.2, while

T(C02) decreases precipitously, from 28 to about 2 mM/L, Im has a pK^^

of about 7.4 and is therefore a crude mimic of hemoglobin (considered as a buffer) . The point is that the measurement of the partial pressure of

CO2 in the off- gas alone cannot be used as an indicator of the total

amount of CO2 present in the solution if certain details of the various

chemical reactions are ignored.

Furthermore, if amino acids and proteins are present, the uptake of CO2 as carbamate can make a significant contribution to T(C02) and must be

included in any predictive correlation scheme.

6. Mass Transport of Carbon Dioxide

The mass transport of carbon dioxide in bioreactors is similar in many

ways to the mass transport of oxygen in bioprocess systems which is

described in our report on the mass transport of oxygen. The major

differences between the mass transport of oxygen and carbon dioxide

relate to the reactivity of carbon dioxide with the fermentation media

and the enhanced diffusivity of carbon dioxide by facilitated transport.

For a detailed discussion of mass transport in bioreactors, the reader

is referred to our report on mass transport of oxygen. Carbon dioxide

encounters basically the same resistances to mass transport as oxygen,

although in reverse order, since CO2 is produced in the reactor and is

transported out. The modes of mass transport are similar, although the

facilitated transport of carbon dioxide may play a key role in transport

of CO2 through the liquid film surrounding a gas bubble. Unlike oxygen,

the rate limiting step in the mass transport of COg may not be the

transport through the liquid film at the bubble. Rather, in the absence

70

I
of the enzjnme carbonic anhydrase, the limiting mechanism is the

transformation of dissolved CO2 to H2CO3 (see table 1).

The diffusion coefficient of CO2 in water is -1.95 x 10'^ cm^ s"^ at

25 °C and increases somewhat with temperature [H1986, H1987]. Ho et al.

reviewed the diffusion of COg in bioreactors [H1986, H1987]. In aqeuous

media, CO2 reacts with water, producing carbonic acid and carbonate ions

(see sec. 3, Reactivity), thus producing an electrolyte solution. Other

salts are also present in fermentation media. The diffusivity of CO2

may be affected by the ionic strength of the media [A1981, R1963] . More

importantly, the diffusion of carbon dioxide is influenced by

facilitated transport.

7. Facilitated Transport

This term is frequently used to describe the selectively enhanced

diffusive flux of a solute through a membrane or some other barrier,

such as a layer of fluid. The fluxes are much larger than expected on

the basis of the solubility, molecular diffusion coefficient and the

concentration gradient, because small amounts of mobile "carrier"

solubilize the diffusing solute. Selectivity usually arises from a highly specific carrier-solute reversible reaction. The flux tends to

saturate at high solute concentrations, since the number of carrier

molecules required for the transport is limited; also fluxes can be

strongly coupled when two (or more) diffusing solutes react

competitively or cooperatively with the mobile carrier.

The following simple "mobile carrier" scheme can explain why facilitated

diffusion is surprisingly fast, quite selective, and nonlinear in the

concentration difference across the membrane. First, a carrier molecule

reacts (reversibly) with a solute molecule to form a complex in the

vicinity of the bulk medium-membrane interface. The carrier complex

then diffuses to the other side of the membrane where, because the

adjacent medium contains very little solute, the complex spontaneously

dissociates according to the law of mass action. The free carrier then

diffuses back across the membrane, where it facilitates the transport of

another solute molecule, and so on. Here we implicitly assume that the

uncomplexed solute cannot effectively enter the membrane because of its

low solubility, and that the mobile carrier has a much greater affinity

for the membrane than for the bulk medium. The transmembrane fltax is

not simply proportional to the concentration difference across the

membrane because of the solubilizing effect of the mobile carrier.

In the case of carbon dioxide, transport through a liquid film around

the gas bubble is facilitated through the formation of bicarbonate. It

is estimated that this reaction, with an overall pK of 6.4 at 25 "C,

involves only a very small fraction of the dissolved COg . It

nevertheless speeds up the transport of CO2 through a membrane by

several orders of magnitude. This is the reason that, unlike the case

of oxygen, the transport through the liquid film is not the ratelimiting step in the mass transport of carbon dioxide.

71
For further reading on Facilitated Transport, the reader is referred to

the list of recent literature relating to Facilitated Transport listed

in section 11.

8. Carbon Dioxide Measurement

The measurement of carbon dioxide evolution in bioreactors is important

to estimate cell respiration and growth and to control the bioprocess.

The CO2 content can be measured in the liquid broth or in the exhaust

gas [A1985, G1983].

8 .

Dissolved Carbon Dioxide

Two methods are available for measuring CO2 in the liquid. The first

involves measuring the dissolved CO2 with an electrode probe inserted

directly into the broth. The electrode is, in essence, a pH electrode

immersed in a buffered bicarbonate solution enclosed in a membrane

permeable to CO2 [P1980, S1981 , M1987] . The sensor is described in

greater detail in section 8.3, Interpretation of Measurements.

The second method for CO2 in liquids involves measuring the CO2 gas

desorbed from the liquid through a coiled tube inserted into the broth

[D1979, Yl981a, Y1981b] . The tube is made of a material highly

permeable to CO2 which diffuses from the broth into the tube where it is

picked up by an inert gas flowing at a controlled rate. The CO2 content

of the gas can be analyzed using gas chromatography, infrared detectors,

or thermal conductivity.

8.2 Carbon Dioxide In Gas

Mass spectrometry is based on the separation of ionized molecules under

vacuum. The separation is based on the mass to charge ratio. Several

volatile components may be analyzed simultaneously. Mass spectrometry

has been used for COg both with direct gas analysis and with liquid

analysis. With liquid analysis, a probe having a strong, permeable

membrane is inserted into the fermentation broth, then a vacuum is

applied to draw the dissolved volatile substances out of the broth. The

membrane must be structurally strong enough to withstand vacuiom, yet

sufficiently thin to permit rapid diffusion of the volatile substances.

It is also difficult to find the proper conditions for analysis of

individual components of a mixture. The advantages of mass spectrometry

over other conventional analysis are speed of response (10-40 s),

greater accuracy, and a number of channels, allowing many fermenters to

be hooked to one instrument. However, a mass spectrometer is generally

more expensive than other instruments [G1983, K1987].

Gas Chromatography is an important off-line analytical technique used

for CO2 analysis. Chromatography columns separate gas mixtures so that

the components emerge from the column at different times. Various

detectors are used to detect and measure them. The gas sampling

technique is complex and each analysis may take 10-20 min. However,

only gas chromatography and mass spectrometry can measure multiple gas

components simultaneously with one instrument [W1985]

72
Infrared detectors are useful since carbon dioxide absorbs at a characteristic wavelength. The gas from the fermentor is passed in a path between a detector and a light source emitting the characteristic

wavelength. Some of the radiation is absorbed, and an energy change is

detected and related to the partial pressure of the COg in the gas,

which is translated into COg concentration [K1987]

.

Thermal conductivity is less specific to COg because other gas

components, such as HgO and H2 , affect its measurement. It is cheaper

and less specific, but not suitable if the measurement has to be

accurate to within 5-10% [V1985].

8.3 Interpretation of COj Measurements

The accumulation of COg in the fermentation medium is a complex and

dynamic process dependent upon a number of factors . Removal of CO2 is

accomplished by aeration and agitation of the solution. Many

researchers monitor the CO2 concentration in the vent gas and infer the

CO2 concentration in the broth. Until recently, researchers assumed

that the dissolved CO2 concentration in the solution was in equilibrium

with the partial pressure of the CO2 in the gas stream leaving the

fermenter [N1968, 11971a, 11971b, 11971c, Y1977, B1979, E1980] . However

this assumption is in error because of the reactivity of the CO2 with

the media. Smith and Ho [S1985] studied CO2 in penicillin fermentations

and clearly demonstrated that no such equilibrium existed when the

fermentation reached its maximum growth phase. The pH of the medium has

a significant effect on the CO2 concentration [L1985, M1985] . It should

be clearly understood what information the measurement of carbon dioxide

provides

.

Carbon dioxide sensors

What is measured is a quantity indicative of the concentration of CO2

molecules in the solution, or its direct counterpart, its partial

pressure in the gas phase. This is a perfectly acceptable procedure, as long as the concentration thus measured is not considered equivalent

with the "total amount of carbon dioxide", T, which was defined earlier,

eq (8). T may differ from the concentration measured by the sensor by a large factor, depending on the pH and the pK^ of other buffers present.

To illustrate this latter point, it is instructive to consider the

carbon dioxide electrode in some detail.

Carbon dioxide electrode

The principle of the carbon dioxide electrode is to translate a pH,

measured by means of the potential of a pH electrode, into a partial

pressure. This is achieved by immersing the pH electrode in a bicarbonate solution enveloped by a membrane permeable to CO2 molecules

in the off-gas. Solution and electrode cavity are therefore in free

exchange, and have the same fugacity, which is equal to the partial

pressure of CO2 under the well-founded assumption that the gas phase

behaves as an ideal gas. By combining the hydration reactions A2 and

A3, and setting the H2O activity equal to 1, one obtains, [M1987]

:

73
^ ^

[a(H^)] [a(HC03-)]

^^^ [a(C02)]

with a referring to the activity of the species in question, and pK^

equal to 6.36 at 25 "C if units of concentration are moles/liter. Since

the electrode solution is immersed in a solution of bicarbonate, the

HCO3 " activity cannot change , and it follows that the carbon dioxide

activity is proportional to that of H* . Relating the pH, and the CO2

concentrations in the various phases to the measured voltage and to the

partial pressure of CO2 in the vapor is tedious but straightforward; it

requires knowledge of the activity and fugacity reference states, which

can be expressed by means of Henry's constant. In practice, a carbon

dioxide electrode is set up in such a way [M1987] [P1980] that it can be

calibrated by replacing the bicarbonate solution by buffered solutions

of known pH.

As stressed before, the carbon dioxide sensor indicates the presence of

CO2 , and therefore its reading correlates perfectly with the partial

pressure in the vapor; what the sensor cannot do is indicate how much

CO2 is "hidden" in the solution in the form of bicarbonate or other

species. At pH levels above 6.3, the amount thus hidden can be very

high.

9 . Conclusions and Recommendations

It appears as though the bioprocess engineering community regards the

solubility of CO2 as a relatively straightforward problem, which can be

modeled, just as for inert gases, for aqueous solutions of simple salts

and acids, by means of Setschenov parameters, provided that carbamate

formation by the amino groups on proteins is properly taken into

account

As we have seen, however, the biophysical chemistry community has long

been aware of the profound effect of protein buffers and certain small

molecules on the total amount T of carbon dioxide present in the liquid

phase. T is not simply a linear function of the partial pressure of CO2

it also depends on the pH and on the ionization constant of the buffer

used. In certain regions of parameter space, T can vary dramatically

with very small changes in p, pK^ or pH, even if carbamate formation is

not possible; in other regions, T remains virtually constant while the

partial pressure undergoes major changes.

We recommend that a systematic study be made of the total amount of COg

present in a well-characterized aqueous solution of proteins and amino

acids with various buffers. The most obvious choice of a protein would

be hemoglobin. Rapid equilibration of COg between vapor and liquid phase

can be achieved through facilitated transport, in conjunction with the

enzyme carbonic anhydrase.

74
The result of such a study would enable the bloprocess engineer to

reliably estimate the total amount of carbon dioxide as a function of

process parameters other than the off- gas composition or sensed amount

alone, and therefore permit control of the total amount of carbon

dioxide in solution by appropriate choice of buffer and pH.

10. References

[A1981] K. Akita, "Diffusivities of Gases in Aqueous Electrolyte

Solutions," Ind. Eng. Chem. Fundam. 20, 89-94 (1981).

[A1985] W. B. Armiger, Chapter 7 Instr\imentation for Monitoring and

Controlling Bioreactors, in Comprehensive Biotechnology - The

Principles, Applications and Regulations of Biotechnology in Industry,

Agriculture and Medicine; Volume 2 The Principles of Biotechnology:

Engineering Considerations, C. L. Cooney and A. E. Humphrey, Eds.

Pergamon Press; New York, 133-148 (1985).

[B1979] J. P. Barford and R. J. Hall, "Investigation of the Significance

of a Carbon and Redox Balance to the Measurement of Gaseous Metabolism

of Saccharomyces cerevisiae," Biotechnol. Bioeng. 21, 609-626 (1979).

[B1982] L. Brewer, "Thermodynamic values for Desulfurization

Processes," in Flue Gas Desulfurization. Hudson, J.L., Rochelle, G.T.,

Ed.; ACS Symposium Series No. 188, American Chemical Society,

Washington, DC, pp. 1-39, (1982).

[D1979] K. Dairaku and T. Yamane, "Use of the Porous Teflon Tubing

Method to Measure Gaseous or Volatile Substances Dissolved in

Fermentation Liquids," Biotechnol. Bioeng. 21, 1671-1676 (1979).

[E1980] A, A, Esener, N. W. F. Kossen and J. A. Roels, "Carbon Dioxide

Hold-Up as a Source of Error in Batch-Culture Calculations," Biotechnol.

Bioeng. 22, 1979-1983 (1980).

[G1983] J. R. Getchell, Chapter 15 Instrumentation and Control Systems,

in Fermentation and Biochemical Engineering Handbook - Principles,

Process Design, and Equipment, H. C. Vogel, Ed., Noyes Publications,

Park Ridge, NJ , 400-429 (1983).

[H1986] C. S. Ho and J. F. Shanahan, "Carbon Dioxide Transfer in

Bioreactors," CRC Critical Reviews in Biotech. 4, 185-252 (1986).

[H1987] C. S. Ho, M. D. Smith and J. F. Shanahan, "Carbon Dioxide

Transfer in Biochemical Reactors," Adv. Biochem. Eng. 35, 83-125 (1987).

[11971a] A. Ishizake, H. Shibai, Y. Hirose and Y. Shiro, Agr. Biol.

Chem. 35, 1733, (1971).

[11971b] A. Ishizake, Y. Hirose and T. Shiro, Agr. Biol. Chem. 35,

1852, (1971).

[11971c] A. Ishizake, Y. Hirose and T. Shiro, Agr. Biol. Chem. 35,

1860, (1971).

75
[H1987] B. Kristiansen, Chapter 9 Instrumentation, in Basic

Biotechnology, J. Bu'Lock and B. Kristiansen, Eds. Academic Press, New

York, 133-172 (1987).

[L1985] H. Livansky, "Kinetics of pH Equilibration in Solutions of

Hydrogen Carbonate During Bubbling with a Gas Containing Carbon

Dioxide," Coll. Czech. Chem. Commun. 50, 553-558 (1985).

[M1952] T. J. Morrison and F. Billett, J. Chem. Soc. 3819 (1952).

[M1971] C. N. Murray and J. P. Riley, Deep-Sea Res. 18 533 (1972).

[M1985] I. G. Minkevich and M. Neubert, "Influence of Carbon Dioxide

Solubility on the Accuracy of Measurements of Carbon Dioxide Production

Rate by Gas Balance Technique," Acta Biotechnol. 5, 137-143 (1985).

[M1987] G. K. McMillan, Chapter 4 Dissolved Oxygen and Carbon Dioxide

Measurements, in Biochemical Measurement and Control, Instrument Society

of America, Research Triangle Park, NC, 65-76 (1987).

[N1968] L. Nyiri and Z. L. Lengyel, "Studies on Ventilation of Culture

Broths. I. Behavior of 602 Model Systems," Biotechnol. Bioeng. 10,

133-150 (1968).

[P1980] E. Puhar, A. Einsele, H. Buhler and W. Ingold, "SteamSterilizable pCOg Electrode," Biotechnol. Bioeng. 22, 2411-2416 (1980).

[Q1981] G. Quicker, A. Schumpe, B. Koenig and W. D. Deckwer,

"Comparison of Measured and Calculated Oxygen Solubilities in

Fermentation Media," Biotechnol. and Bioeng. , 23, 635-65 (1981).

[R1963] G. A. Ratcliff and J. G. Holdcroft, "Diffusivities of Gases in

Aqueous Electrolyte Solutions," Trans. Instn. Chem. Engrs. 41, 315-319

(1963).

[S1981] M. Shoda and Y. Isikawa, "Carbon Dioxide Sensor for

Fermentation Systems," Biotechnol. Bioeng. 23, 461-466 (1981).

[S1982] A. Schumpe, G. Quicker and W. D. Deckwer, "Gas Solubilities in

Microbial Culture Media," Adv. Biochem, Eng. Vol. 24, Reaction

Engineering, A. Fiechter, Ed., Springer-Verlag; New York, 2-38 (1982).

[S1985] M. D. Smith and C. S. Ho, "On Dissolved Carbon Dioxide in

Penicillin Fermentations," Chem. Eng. Commun. 37, 21-27 (1985).

[W1977] E. Wilheim, R. Battino and R. J. Wilcox, "Low- Pressure

Solubility of Gases." Chemical Reviews, 21 219-262 (1977).

[W1985] H. Y. Wang,* Chapter 21 Analysis of Fermentation Gases, in

Comprehensive Biotechnology - The Principles Applications and

Regulations of Biotechnology in Industry, Agriculture and Medicine.

Volume 4 The Practice of Biotechnology: Specialty Products and Service

Activities, C. W. Robinson J. A. Howell and M. Moo-Young, Eds. 423-431

(1985).

76
[Y1977] H. Yagi and F. Yoshida, "Desorptlon of Carbon Dioxide from

Fermentation Broth," Biotechnol. Bioeng. 19, 801-809 (1977).

[Y1981a] T. Yamane, M. Matsuda and E. Sada, "Application of Porous

Teflon Tubing Method to Automatic Fed-Batch Culture of Microorganisms.

I. Mass Transfer through Porous Teflon Tubing," Biotechnol. Bioeng. 23,

2493-2507 (1981).

[Y1981b] T, Yamane, M. Matsuda and E. Sada, "Application of Porous

Teflon Tubing Method to Automatic Fed-Batch Culture of Microorganisms.

II. Automatic Constant-Value Control of Fed Substrate (Ethanol)

Concentration in Semibatch Culture of Yeast," Biotechol. Bioeng. 23,

2509-2524 (1981).

77
11. Llteratiire Relating to Facilitated Transport

T. L. Donaldson and Y. N. Nguyen, "Carbon Dioxide Reaction Kinetics and

Transport in Aqueous Amine Membranes," Ind. Eng. Chem. Fundam. 19, 260-

266 (1980).

T. L. Donaldson and J. A. Quinn, "Kinetic Constants Determined from

Membrane Transport Measurements : Carbonic Anhydrase Activity at High

Concentrations," Proc. Nat. Acad. Sci. USA 71, 4995-4999 (1974).

T. L. Donaldson and J. A. Quinn, "Carbon Dioxide Transport through

Enzymatically Active S3nithetic Membranes," Chem. Eng. Sci. 30, 103-115

(1975).

P. M. Gallagher, A. L. Athayde, and C. F. Ivory, "The Combined Flux

Technique for Diffusion-Reaction Problems in Partial Equilibrium:

Application to the Facilitated Transport of Carbon Dioxide in Aqueous

Bicarbonate Solutions," Chem. Eng. Sci., 41, 567-578 (1986).

J. D. Goddard, J. S. Schultz and S. R. Suchdeo, "Facilitated Transport

via Carrier-Mediated Diffusion in Membranes: Part II. Mathematical

Aspects and Analyses , " AIChE J. 20, 625-645 (1974).

L. J. C. Hoofd, R. R. Tong and P. Stroeve, "Nonequilibrium Facilitated

Transport of Carbon Dioxide in Bicarbonate and Bovine Albumin

Solutions," Ann. Biomed. Eng. 14, 493-511 (1986).

I. L. Hunter, Chapter 9 Nutrient Uptake, in Comprehensive BiotechnologyThe Principles, Applications and Regulations of Biotechnology in

Industry, Agriculture and Medicine; Vol. I The Principles of

Biotechnology: Scientific Fundamentals, A. T. Bull, H. Dalton and M.

Moo-Young, Eds. Pergamon Press; New York, 141-158 (1985).

S. L. Matson, J. Lopez and J. A. Quinn, "Separation of Gases with

Synthetic Membranes," Chem. Eng. Sci. 38, 503-524 (1983).

J. H. Meldon, H. A. Smith and C. K. Colton, "The Effect of Weak Acids

Upon the Transport of Carbon Dioxide in Alkaline Solutions," Chem. Eng.

Sci. 32, 939-950 (1977).

J. H. Meldon, P. Stroeve and C. E. Gregoire, "Facilitated Transport of

Carbon Dioxide: A Review," Chem. Eng. Commun. 16, 263-300 (1982).

J. H. Meldon, "Facilitated Gas Transport in Liquids," NATO ASI Series E,

72, Mass Transfer in Chemically Reacting Multiphase Systems, Vol.1: Two

Phase Systems, E. Alper, Ed., 369-380 (1983).

J. H. Meldon and J. E. Roberts, "Theory of Membrane CO2 Transport with

Equilibrium Reaction," NATO ASI Series E, 72, Mass Transfer with

Chemically Reacting Multiphase Systems Vol 1: Two-Phase Systems, E. Alper, Ed., 381-389 (1983).

78
J. H. Meldon and Y. S. Hang, "The Transport of Carbon Dioxide in

Purified Protein Solutions," AIChE Symp. Series 79, 36-42 (1983).

J. H. Meldon, A. Paboojian and G. Rajangam, "Selective 60 Permeation in

Immobilized Liquid Membranes," AIChE J. 82, 114-120 (1986).

N. C, Otto and J. A. Quinn, "The Facilitated Transport of Carbon Dioxide

through Bicarbonate Solutions," Chem. Eng. Sci. 949-961 (1971).

E. Ruckenstein and V. Sasidhar, "Transient Behaviour of Facilitated

Transport through Liquid Membranes," J. Memb. Sci. 12, 27-50 (1982).

J. S. Schultz, J. D. Goddard and S. R. Suchdeo, "Facilitated Transport

via Carrier-Mediated Diffusion in Membranes Part I. Mechanistic Aspects,

Experimental Systems and Characteristic Regimes," AIChE J. 20, 417-445

(1974).

P. Stroeve and E. Ziegler, "The Transport of Carbon Dioxide in High

Molecular Weight Buffer Solutions," Chem. Eng. Commun. 6, 81-103 (1980).

P. Stroeve, L. J. C. Hoofd and F. Kreuzer, "Facilitated Carbon Dioxide

Transport in Bovine Albumin Solutions," Ann. Biomed. Eng. 13, 551-571

(1985).

P. Stroeve, "Diffusion with Chemical Reaction in Biological Systems,"

Adv. Exp. Med. Biol. 191, Oxygen Transport to Tissue VII, F. Kreuzer,

S. M. Cain, Z. Turek and T. K. Goldstick, Eds. Plenum Press, New York,

45-61 (1985).

S. R. Suchdeo and J. S. Schultz, "The Permeability of Gases through

Reacting Solutions: The Carbon Dioxide -Biocarbonate Membrane System,"

Chem. Eng. Sci. 29, 13-23 (1974).

S. R. Suchdeo and J. S. Schultz, "Mass Transfer of CO2 Across Membranes:

Facilitation in the Presence of Bicarbonate Ion and the Enzyme Carbonic

Anhydrase," Biochim. Biophys. Acta, 352, 412-440 (1974).

K. Tanishita, I. Tanasawa, T. Yamaguchi, and M. Sugawara, "Facilitated

Diffusion of Carbon Dioxide in Whole Blood and Hemoglobin Solutions,"

Pflug. Arch. 405, 83-90 (1985).

J. D. Way, R. D. Noble, T. M. Flynn and E. D. Sloan, "Liquid Membrane

Transport: A Survey," J. Memb. Sci. 12, 239-259 (1982).

J. K. Way, R. D. Noble, D. L. Reed and G. M. Ginley, "Facilitated

Transport of CO^ in Ion Exchange Membranes," AIChE J. 33, 480-487

(1987).

Biology and Chemistry of the Carbonic Anhydrases, R. E. Tashian and D.

Hewett-Emmett, Eds., Annals of the New York Academy of Sciences, 249,

(1984).

79
12 . Bibliography

[A1981] K. Akita, "Diffusivities of Gases in Aqueous Electrolyte

Solutions," Ind. Eng. Chem. Fundam. 20^ 89-94 (1981).

Diffusivities of oxygen in aqueous electrolyte solutions were

measured for 18 species of cations, 13 species of anions, and

combinations thereof using a polarographic oxygen electrode and a dissolved- oxygen analyzer in a diffusion cell. Correlations were made

between the oxygen diffusivity and the solution viscosity. The results

were discussed on the basis of the Eyring theory of rate processes. The

paper states that the prediction of diffusivities of gases in aqueous

electrolyte solutions is possible if gas diffusivities in pure water and

the densities of the solutions are available. Equations are given.

[A1985] W. B. Armiger, Chapter 7 Instrxomentation for Monitoring and

Controlling Bioreactors, in Comprehensive Biotechnology - The

Principles, Applications and Regulations of Biotechnology in Industry,

Agriculture and Medicine; Volume 2 The Principles of Biotechnology:

Engineering Considerations, C. L. Cooney and A. E. Humphrey, Eds.

Pergamon Press; New York, 133-148 (1985).

This chapter addresses instrumentation systems for monitoring and

controlling bioreactors. In-line, on-line and off-line systems are discussed. Analysis of the chemical environment includes descriptions of

probes for pH, oxygen, carbon dioxide and specific ion probes. Off-gas

analysis and measurement of volatile components are also discussed.

[D1979] K. Dairaku and T. Yamane, "Use of the Porous Teflon Tubing

Method to Measure Gaseous or Volatile Substances Dissolved in

Fermentation Liquids," Biotechnol. Bioeng. 21, 1671-1676 (1979).

This paper describes results obtained using the Tubing Method to

measure volatile substances dissolved in fermentation liquids.

Experiments were performed to compare different tubing materials in the

analysis of ethanol dissolved in water. A porous Teflon tubing was shown to have excellent mass transfer and dynamic response

characteristics

[E1958] J. T. Edsall and J. Wjrman "Biophysical Chemistry," Academic

Press, New York, 1958. Chapter 10, Carbon Dioxide and Carbonic Acid.

This chapter presents a scholarly, detailed and exhaustive treatment

of the reactivity of carbon dioxide, and the consequences for

biochemistry. Solubility and hydration of carbon dioxide, and their

dependence on the partial pressure, the pH and on the pK^ of buffers

present are carefully and quantitatively discussed. The biologically

important conversion of carbon dioxide to carbamates in solutions of

compounds containing amino groups is described in detail.

[E1980] A. A. Esener, N. W. F. Kossen and J. A. Roels, "Carbon Dioxide

Hold-Up as a Source of Error in Batch-Culture Calculations," Biotechnol.

Bioeng. 22, 1979-1983 (1980).

80
The authors suspected that the dissolved COg was a much higher value

than was previously expected while using equilibrium relationships.

Their method of justifying the statement came after a total carbon

balance was performed over a batch fermentation vessel, when some of the

carbon seemed to be missing. This was attributed to a supersaturatlon

of CO2 or bicarbonate Ions In the liquid media.

[G1983] J. R. Getchell, Chapter 15 Instrumentation and Control Systems,

In Fermentation and Biochemical Engineering Handbook - Principles,

Process Design, and Equipment, H. C. Vogel, Ed., Noyes Publications,

Park Ridge, NJ , 400-429 (1983).

This chapter discusses fermentation control systems and the

Instruments used. It Includes a description of the principles of

operation for many tjrpes of sensors. Including pH, C02 , and 02 sensors. Mass spectrometers are also described.

[H1986] C. S. Ho and J. F. Shanahan, "Carbon Dioxide Transfer In

Bloreactors," CRC Critical Reviews In Biotechnology 4, 185-252 (1986).

The first five pages of this review contain information on CO2

solubility in biological media. The ion-specific Setschenov parameters

for 14 cations and 8 anions are all from Ref. [S1982] The plots of CO2

solubility in salt solutions containing sucrose was taken from [Q1981]

.

As factors that complicate the question of CO2 solubility in

bloreactors, the authors mention the effects of alcohols that are not

well known for COg absorptive processes due to the presence of

macromolecules , the effects of pH control and antifoamlng agents, and,

last but not least, the respiratory action of microorganisms.

[H1987] C. S. Ho, M. D. Smith and J. F. Shananan, "Carbon Dioxide

Transfer in Biochemical Reactors," Adv. Biochem. Eng. 35 83-125 (1987).

The first four pages of this review contain virtually the same Information as those of [H1986] . Although the bulk of the review deals

with CO2 mass transfer, there are also sections on reactions involving

CO2 , desorption of CO2 and effects of CO2 on microbial processes.

[M1987] G. K. McMillan, "Biochemical Measurement and Control,"

Instrximent Society of America, 1987. Chapter 10: Dissolved Oxygen and

Carbon Dioxide Measurements.

This chapter gives a rather detailed description of the workings of

dissolved-oxygen and carbon dioxide electrodes, including response lag

times and membrane contamination. Special attention is given to the

effects of pH on the partial pressure of the off-gas, and therefore on

the reading of the carbon dioxide electrode. The author states that the

dramatic effect of basic pH values on total carbon dioxide in solution

is usually (but unjustifiably) Ignored when carbon dioxide production

rate, or the respiratory quotient, is calculated from the amount of

carbon dioxide In the off- gas or (equlvalently) from the reading of the sensor. This, in turn, will lead to errors in the estimation of the

rate of cell metabolism, which negatively affects the optimization of

control parameters.

81
[N1968] L. Nyiri and Z. L. Lengyel, "Studies on Ventilation of Culture

Broths.. I. Behavior of CO2 Model Systems," Biotechnol. Bioeng. 10, 133-

150 (1968).

The effects of temperature, agitation, aeration, viscosity, and the

presence of protein and buffers on the dissolution, hydration and

chemical reactions of COg were studied. It was concluded that the rate

of CO2 hydration increased with increasing temperatures from to 40 "C.

Similar results were found when the rate of agitation was increased. The

bicarbonate ion was influenced by the buffer components, the buffer

capacity and the viscosity of the culture medium.

[01970] K. Onda, E. Sada, T. Kobayashi, S. Kito and K. Ito, "Salting-Out

Parameters of Gas Solubility in Aqueous Salt Solutions," J. Chem. Eng.

Japan, 3, 18-24 (1970).

The solubility of COg in ten aqueous electrolyte solutions is

measured at 25 "C, by determining the amount of gas absorbed by

solutions of various molatities from 0.5 to 5 molar at standard pressure

conditions. The Bunsen coefficient is reported and found to vary

linearly with the ionic strength. The data, augmented by literature

data in International Critical Tables and in Landolt-Bornstein Tables

from to 40 "C, are represented by means of the log-additive rule, with

salt-specific Setschenov parameters defined in terms of ionic strengths.

See, however, the criticism of this method in [Q1981] . The values of

the Setschenov parameters used in the fit of the solubility data,

however, are not given.

[P1980] E. Puhar, A. Einsele, H. Buehler and W. Ingold, "Steamsterizable pCOg Electrode." Biotechnol. and Bioeng., Vol. XXII, pp.

2411-2416 (1980).

[Q1981] S. Quicker, A. Schumpe, B. Koenig and W. D. Deckwer, "Comparison

of Measured and Calculated Oxygen Solubilities in Fermentation Media,"

Biotechnol. and Bioeng. , 23, 635-65 (1981).

A fast volumetric method is developed for measuring solubilities of

carbon dioxide and oxygen in fermentation media. Data are reported for

both oxygen and carbon dioxide in solutions of electrolytes without and

with sugar. The log-additive rule used by Onda et al. [01970] in terms

of ionic strengths of individual salts is criticized as being

inconsistent, and is replaced by a log-additive rule in terms of

individual ions and ion-specific Setschenov constants. The validity of

the log-additive rule is tested for mixed electrolyte and nonelectrolyte

solutions and found to be valid if referred to the actual solubility of

the gas in the nonelectrolyte solution, instead of to that of oxygen in

pure water. In the case of carbon dioxide, ion- specific Setschenov

parameters are given for Mn^* , Cu^* and SaOg^" . Nonelectrolytes

Include lactose, sucrose, and glucose.

[R1963] G.A. Ratcliff and J.G. Holdcroft, "Diffusivities of Gases in

Aqueous Electrolyte Solutions," Trans. Inst. Chem. Engrs. 41, 315-319

(1963).

82
Theories of diffusivities of gases in fluids are reviewed. Using

Eyring's lattice model of a liquid, the diffusivity of a solute in an aqueous electrolyte is shown to vary linearly with the electrolyte

concentration. A model was developed to predict diffusivity in

electrolyte solutions. Experimental data of the CO2 diffusivity in water

and in aqueous solutions of six salts were reported. Diffusivities were obtained by measuring the rate of COg absorption into the deaerated

electrolyte solutions flowing over a sphere. Correlations of

diffusivity and viscosity are studied and relationships proposed for

predicting diffusivities in electrolyte solutions.

[S1979] A. Schiimpe and W. D. Deckwer, "Estimation of Og and CO2

Solubilities in Fermentation Media," Biotechnol. and Bioeng. , 2i, 1075-

1078 (1979).

The authors postulate that the effects of individual species on the

solubility of the gas, as characterized by ion- specific Setschenov

parameters, are additive, both in water and in dilute alcohol solutions.

They determine these ion-specific Setchenov parameters for CO2 for 11

cations and seven anions from solubility measurements and claim that

they depend very little on temperature in the range of 10-40 °C. The

ion- specific constants are listed for COg

.

Setschenov plots are given for oxygen solubility in several salt

solutions that also contain alcohols, namely methanol, ethanol, propanol

or glycol. If the oxygen solubility is referred to that in the alcohol

solution, rather than to that in pure water, the same additivity rule can be applied, with identical ion-specific constants. The validity of

this rule was tested experimentally for alcohol solutions up to 10% in

weight.

Cations: H+ , Li+ , Na+ , K"^ , Rb+ , Cs+ , NH/ , Mg2+ , Ca^* , Ba^^, Fe^^ , A13+.

Anions: CI", Br", I", NO3", SOg^-, SO^^" , P0^3-

Alcohols: Methanol, ethanol, propanol and glycerol.

[S1985] M, D. Smith and C. S. Ho, "On Dissolved Carbon Dioxide in

Penicillin Fermentations," Chem. Eng. Commun. 37, 21-27 (1985).

The behavior of dissolved carbon dioxide in penicillin fermentations was

studied. Results indicate that the partial pressure of carbon dioxide

in the off gas and that dissolved in the fermentation medium were not in

equilibrium. During fermentation, excessive dissolution of 602 occurs,

and can be attributed to a slower rate of CO2 desorption from the

feimientation medium compared to the rate of CO2 absorption from the

respiring cells,

[W1977] E, Wilhelm, R. Battino and R, J. Wilcox, "Low-Pressure

Solubility of Gases," Chemical Reviews , 219-262 (1977).

This is an exhaustive review of solubility data for numerous gases

in water in the temperature range of 273-373 K. For CO2 , there are many

data sources at 25 "C, but two [M1952] [M1971] were found useful at

higher temperatures. Mole fraction and Ostwald coefficient data for CO2

at 1.01325 atm partial pressure are listed on pp. 226 and 227 for the

83
temperature range of 273-343 K. They were calculated from an empirical

4- term representation of the solubility of gases in water in this range,

as given on p. 223, eq (35). The coefficients for CO2 are listed in

Table I, p, 224. From eq (35), representations of all thermodjniamic

properties of solution are derived. Although these properties are listed

for many gases, CO2 is not of them, for reasons not explained.

[W1985] H. Y. Wang, Chapter 21 Analysis of Fermentation Gases, in

Comprehensive Biotechnology - The Principles Applications and

Regulations of Biotechnology in Industry, Agriculture and Medicine.

Volxome 4 The Practice of Biotechnology: Specialty Products and Service

Activities, C. W. Robinson, J. A. Howell and M. Moo-Young, Eds. 423-431

(1985).

Various methods of analysis for gases from fermentors are discussed, with particular emphasis on oxygen and carbon dioxide. The

methods covered include manometric methods and gas electrodes,

continuous flow oxygen and carbon dioxide analyzers, process gas

chromatography, mass spectrometer-based analyzers, and a gas sampling

system.

[Y1977] H. Yagi and F. Yoshida, "Desorption of Carbon Dioxide from

Fermentation Broth," Biotechnol. Bioeng. 19, 801-809 (1977).

The behavior and removal of COg from the culture media was studied.

They assumed a distribution of bicarbonate ions throughout the vessel,

which varied with the rate of the hydration reactions. Other

simplifying assumptions were also made. The effect of pH on the HLa was investigated. While maintaining the same operating conditions, data

from other aqueous media, all having different pH values were compared

to the experimental data. No trend of pH dependence of the for COg

desorption was found. It was concluded that COg desorption took place

almost as a purely physical process.

[Y1981a] T. Yamane, M. Matsuda and E. Sada, "Application of Porous

Teflon Tubing Method to Automatic Fed-Batch Culture of Microorganisms.

I. Mass Transfer through Porous Teflon Tubing," Biotechnol. Bioeng. 23,

2493-2507 (1981).

This paper describes a theoretical treatment of radial mass transfer through the tubing and also the experimental results using

ethanol or oxygen as the diffusive solute. Experimental data of djmamic

response of the porous Teflon tubing experimental system for stepwise

additions of ethanol to water are presented.

84
NIST-114A

(REV. 3-89) U.S. DEPARTMENT OF COMMERCE

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

BIBLIOGRAPHIC DATA SHEET

1. PUBUCATION OR REPORT NUMBER

NIST/TN-1276

2. PERFORMING ORGANIZATION REPORT NUMBER

3. PUBUCATION DATE May 1990

4. TITLE AND SUBTITLE A Survey of Selected Topics Relevant to Bioprocess Engineering

5. AUTHOR(S)

J.B. Hubbard, E.J. Clark and J.M.H. Levelt Sengers

6. PERFORMING ORGANIZATION (IF JOINT OR OTHER THAN NIST, SEE INSTRUCTIONS)

U.S. DEPARTMENT OF COMMERCE

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

GAITHERSBURQ, MD 20899

7. CONTRACT/GRANT NUMBER

8. TYPE OF REPORT AND PERIOD COVERED

Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (STREET, CITY, STATE, ZIP)

Same as item #6

10. SUPPLEMENTARY NOTES

DOCUMENT DESCRIBES A COMPUTER PROGRAM; SF-185, FIPS SOFTWARE SUMMARY, IS ATTACHED.

11. ABSTRACT (A 200-WORD OR LESS FACTUAL SUMMARY OF MOST SIGNIFICANT INFORMATION. IF DOCUMENT INCLUDES A SIGNIFICANT BIBUOGRAPHY OR

LITERATURE SURVEY, MENTION IT HERE.)

The following is a collection of reports on topics considered important and generic in

biotechnology and bioprocess engineering: (1) Isoelectric points of proteins; (2) Solubility

and mass transfer of oxygen in bioreactors; (3) Solubility and mass transfer of carbon

dioxide in bioreactors. These reports arose from a survey of the past and current biotechnology

literature with special effort given to a critique of data measurement quality. The format

is as follows. The technological importance of a topic is briefly discussed, followed by a critical review of relevant physical properties, data presentation, and measurement techniques

A "conclusions and recommendations" section summarizes our findings and contains specific

recommendations for future research projects. The last section consists of an annotated

bibliography and references pertaining to the survey.

12. KEY WORDS (6 TO 12 ENTRIES; ALPHABETICAL ORDER; CAPITALIZE ONLY PROPER NAMES; AND SEPARATE KEY WORDS BY SEMICOLONS)

Bioprocess engineering, bioreactor electrophoresis, carbon dioxide, isoelectric point, oxygen, protein

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