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This is to certify that the

dissertation entitled

The Enhancement of Synthesis Gas Fermentations

Using Microbubble Dispersions

presented by

Marshall Dean Bredwell

has been accepted towards fulﬁllment
ofthe requirements for

Ph . D . degree in Chemical Engineering

 

 

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THE ENHANCEMENT OF SYNTHESIS GAS FERMENTATIONS
USING MICROBUBBLE DISPERSIONS

By

Marshall Dean Bredwell

A DISSERTATION

Submitted to
Michigan State University
In partial fulﬁllment of the requirements
For the degree of

DOCTOR OF PPHLOSOPHY
Department of Chemical Engineering

2000

ABSTRACT

THE ENHANCEMENT OF SYNTHESIS GAS F ERMENTATIONS
USING MICROBUBBLE DISPERSIONS

By

Marshall Dean Bredwell

Synthesis gas, a mixture of primarily carbon monoxide and hydrogen, can be used
in a variety of bioconversions. It is well suited as a carbon and electron source for
production of liquid ﬁiels and chemicals or as a source of reducing equivalents for
biological sulfur reductions. Synthesis gas ferrnentations have typically been gas-to-
liquid mass transfer limited due to the low aqueous solubility of hydrogen and carbon
monoxide, the primary components of synthesis gas. A novel technique to increase mass
transport without increased power expenditure is to use microbubbles, also known
colloidal gas aphrons. Microbubbles are small, surfactant-coated gas bubbles with
diameters on the order 60 pm that have colloidal pr0perties, such as an electric double
layer, that impart stability and useful properties such as the ability to be pumped without
collapse. Surfactants that are biocompatible with the microbial biocatalysts used in
synthesis gas fennentations and that are capable of forming stable microbubbles have
been identiﬁed. The effects of these surfactants on the metabolic activity of
Butyribacterium methylotrophicum were characterized. Non-ionic surfactants were
relatively non-toxic, while ionic surfactants were toxic at concentrations necessary to
form microbubbles. The mass transfer properties of microbubbles were determined in an
abiotic bubble column. The local mass transfer coefﬁcient, KL, and the volumetric mass

transfer coefﬁcient, KLa were determined as a function of surfactant concentration in the

surrounding bulk liquid. Synthesis-gas F ermentations were run using the biocompatible
surfactants for both the production of liquid fuels and chemicals and for the biological
reduction of sulfur. The KLa value for carbon monoxide transport in a Butyribacterium
methylotrophicum fermentation was measured with both conventional and microbubble
sparging. A six-fold increase in KLa was obtained upon switching from conventional
bubbles to microbubbles. A sulfate reducing bacteria culture was used to convert sulfur
dioxide to hydrogen sulﬁde using synthesis gas as a source of reducing equivalents. The
productivity using microbubble sparging was two-fold higher than that using
conventional sparging. Dynamic microbubble coalescence was measured using video
microscopy in a stirred vessel. Coalescence was modeled using a population balance
approach with a ﬁlm drainage model to describe the coalescence efﬁciency. The model
predicted that the reduced coalescence rate observed at higher surfactant concentrations is

due to a thickening of the liquid ﬁlm between adjacent bubbles.

 

 

 

ACKNOWLEDGMENTS

I would like to ﬁrst thank my wife for her support, love, and conﬁdence in me.
Without her, none of my work would have been successful. I wish to thank my advisor,
Dr. Mark Worden, without whom none of this work would have been done, for his
guidance and advice throughout these years. I also wish to Dr. Eric Kaufman and Dr.
Punjai Selvaraj at Oak Ridge National Laboratory for their help, guidance and support on
this project. I also wish to thank Dr. Costas Tsouris, also at ORNL, for giving me his time
and advice in the development of both the coalescence experiments and models. I would
also like to thank the other members of my graduate committee, Dr. Daina Briedis, Dr.
Estelle McGroarty, Dr. Mahendra Jain, Dr. Robert Ofoli, and Dr. Andrew Grethlein.

I would like to thank the colleagues with whom I spent most of graduate studies,
Mark Widman and Tyler Ames. I would also like to thank a number of other people with
whom I have worked with over the years. I have had the good luck in working with
skilled people such as Michael Telgenhoff at Michigan State and Mark Little and Miguel
Rodriguez at ORNL. I would also like to thank Chemical Engineering Department ofﬁce
staff of Julie Caywood, Faith Peterson, and Candy McMaster for their constant
assistance. Finally, I would like to thank my parents, Dean and Patricia, for all of their
support and love throughout the years.

The National Science Foundation, the Department of Energy at ORNL, and the

MSU Biotechnology Training Program has provided funding for this work.

iv

 

 

TABLE OF CONTENTS

LIST OF TABLES ................................................................................. ix
LIST OF FIGURES ............................................................................... x
1. INTRODUCTION .......................................................................... 1
2. OBJECTIVES AND SIGNIFICANCE .................................................. 4
2.1 Surfactant Biocompatibility ........................................................ 4
2.2 Microbubble Mass Transfer Coefﬁcients ......................................... 4
2.3 Synthesis Gas Fermentations ....................................................... 5
2.4 Microbubble Coalescence ........................................................... 6
3. LITERATURE REVIEW .................................................................. 7
3.1 Synthesis Gas ......................................................................... 7
3.1 .1 Coal Gasiﬁcation .............................................................. 7
3.1.2 Biomass Gasiﬁcation ......................................................... 8
3.2 Synthesis Gas F ermentations ....................................................... 9
3.2.1 Butyribacterium methylotrophicum ......................................... 11
3.2.2 Clostrz'dium ljungdahlii ....................................................... 14
3.2.3 Sulfate Reducers ............................................................... 17
3.2.4 Other Bacteria .................................................................. 18
3.2.5 Bioreactors for Synthesis Gas Fermentations .............................. 20
3.3 Aphrons ................................................................................ 22
3.3.1 Colloidal Gas Aphrons ........................................................ 23
3.3.2 Colloidal Liquid Aphrons .................................................... 26
3.4 Coalescence ........................................................................... 27
3.4.1 Breakage Frequency ........................................................... 28
3.4.2 Collision Frequency ........................................................... 29
3.4.3 Coalescence Efﬁciency ....................................................... 29
4. FORMATION AND STABILITY OF MICROBUBBLES ........................... 31
4.1 Introduction ........................................................................... 31
4.2 Materials and Methods ............................................................... 32
4.2.1 Microbubble Generator ....................................................... 32
4.2.2 Bubble Size Distribution ...................................................... 32
4.2.3 Formation Studies ............................................................. 32
4.2.4 Stability Studies ............................................................... 33
4.2.5 Immobilization Studies ....................................................... 33
4.3 Results and Discussion .............................................................. 33
4.3.1 Particle Size Distribution ..................................................... 33
4.3.2 Formation Studies ............................................................. 34
V

 

4.3.3 Stability Studies ............................................................... 38

4.3.4 Immobilization Studies ....................................................... 43
4.4 Conclusions ........................................................................... 44
5. SURFACTANT BIOCOMPATIBLITY ................................................. 46
5.1 Introduction ........................................................................... 46
5.2 Material and Methods ............................................................... 47
5.2.1 Culture Technique ............................................................. 47
5.2.2 Culture Analysis .............................................................. 50
5.2.2.1 Gas Chromatography ................................................... 50
5.2.2.2 Spectroscopy ............................................................ 51
5.2.2.3 pH Measurements ...................................................... 51
5.2.3 Surfactant Studies ............................................................. 51
5.3 Results and Discussion .............................................................. 54
5.3.1 Dry Weight Calibration Curve .............................................. 54
5.3.2 Tween Surfactants ............................................................ 54
5.3.3 Brij Surfactants ................................................................ 57
5.3.4 Products and pH ............................................................... 60
5.4 Conclusions ........................................................................... 65
6. MASS TRANSFER PROPERTIES OF MICROBUBBLES ......................... 66
6.1 Introduction ........................................................................... 66
6.2 Materials and Methods .............................................................. 68
6.2.1 Microbubble Generation ..................................................... 68
6.2.2 Axial Dispersion .............................................................. 68
6.2.3 Mass Transfer ................................................................ 70
6.2.4 Power Consumption .......................................................... 70
6.2.5 Dynamic Gassing Out ........................................................ 71
6.2.6 Mathematical Models ........................................................ 72
6.2.6.1 Axial Dispersion ....................................................... 72
6.2.6.2 Mass Transfer .......................................................... 73
6.2.6.3 Dynamic Mass Transfer .............................................. 74
6.3 Results and Discussion ............................................................. 75
6.3.1 Axial Dispersion .............................................................. 75
6.3.2 Mass Transfer ................................................................. 76
6.3.2.1 Plug Flow Model ...................................................... 76
6.3.2.2 Void Fraction and Surfactant Effects ............................... 77
6.3.3 Power Consumption ......................................................... 81
6.3.3.1 Power Consumption in F ermentations .............................. 81
6.3.3.2 Comparison of Reactor Type ......................................... 82
6.3.4 Dynamic Gassing Out ........................................................ 84
6.4 Conclusions .......................................................................... 89
6.5 Nomenclature ........................................................................ 90
6.5.1 Symbols ........................................................................ 90

vi

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6.5.2 Greek Symbols ................................................................ 93

Butyribacterium methylotrophcium FERMENTATIONS ............................ 94
7.1 Introductions ......................................................................... 94
7.2 Materials and Methods ............................................................. 94
7.2.1 Media and Cultures ........................................................... 94
7.2.2 Reactor ........................................................................ 95
7.2.3 Analytical Techniques ....................................................... 96
7.2.4 Models ......................................................................... 97
7.2.5 Carbon and Electron Balances .............................................. 97
7.3 Results and Discussion ............................................................. 98
7.3.1 Products ........................................................................ 98
7.3.2 Mass Transfer Coefﬁcients .................................................. 101
7.4 Conclusions ........................................................................... 102
7.5 Nomenclature ......................................................................... 102
7.5.1 Symbols ........................................................................ 102
7.5.2 Subscripts and Superscripts ................................................. 102
SULFATE REDUCING BACTERIA FERMENTATIONS ......................... 104
8.1 Introduction ........................................................................... 104
8.2 Materials and Methods .............................................................. 105
8.2.1 Microbubble Generation ..................................................... 105
8.2.2 Media and Cultures ........................................................... 106
8.2.3 Mass Transfer Limitation Studies .......................................... 110
8.2.4 Fermentations .................................................................. 11 1
8.2.4.1 Conventional Sparging ................................................ 111
8.2.4.2 Microbubble Sparging ................................................. 112
8.2.4.3 Mass Transfer Studies ................................................. 112
8.2.5 Analytical Techniques ........................................................ 1 13
8.2.5.1 Gas Chromatography .................................................. 113
8.2.5.2 Sulfur Chemistry ....................................................... 114
8.2.5.3 Most Probable Number (MPN) and Misc. Analytical ............ 115
8.2.6 Carbon and Electron Balances .............................................. 115
8.3 Results and Discussion .............................................................. 116
8.3.1 Conﬁrmation of Mass Transfer Limitations .............................. 116
8.3.2 Conventional Sparging ....................................................... 1 19
8.3.3 Microbubble Sparging ........................................................ 123
8.3.4 Carbon and Electron Balances .............................................. 125
8.4 Conclusions ........................................................................... 126
8.5 Nomenclature ......................................................................... 127
8.5.1 Symbols ........................................................................ 127
8.5.2 Greek Symbols ................................................................ 127
8.5.3 Subscripts and Superscripts ................................................ 127

vii

10.

11.

12.

COALESCENCE ........................................................................... 129

9.1 Introduction ........................................................................... 129
9.2 Mathematical Model ................................................................. 131
9.2.1 Population Balance Equation Model ....................................... 131
9.2.2 Collision Frequency ........................................................... 134
9.2.3 Coalescence Efﬁciency ....................................................... 136
9.2.4 Solution Techniques .......................................................... 140

9.3 Materials and Methods .............................................................. 140
9.3.1 Coalescence Measurements ................................................. 140
9.3.2 Particle Size Distributions ................................................... 141
9.3.3 Experimental Variables ...................................................... 142
9.3.4 Surface Tension ............................................................... 143

9.4 Results and Discussion .............................................................. 143
9.4.1 Data Quality .................................................................... 143
9.4.2 Deformable Drop Efﬁciency Model ........................................ 146
9.4.3 Film Drainage Efﬁciency Model for Bubbles ............................. 149
9.4.3.1 Model Results ........................................................... 149

9.4.3.2 Physical Signiﬁcance of Fitted Parameters ......................... 154

9.5 Conclusions ........................................................................... 159
9.6 Nomenclature ......................................................................... 159
9.6.1 Symbols ........................................................................ 159
9.6.2 Greek Symbols ................................................................. 161
9.6.3 Subscripts and Superscripts .................................................. 162
SUMMARY AND CONCLUSIONS .................................................... 163
APPENDICIES - FORTRAN PROGRAMS .......................................... 165
11.1 Axial Dispersion ................................................................... 166
11.2 Bubble Coalescence ............................................................... 172
BIBLIOGRAPHY ........................................................................... 178

viii

 

Table 1:

Table 2:

Table 3:

Table 4:

Table 5:

Table 6:

Table 7:

Table 8:

Table 9:

Table 10:

Table 11:

Table 12:

Table 13:

Table 14:

Table 15:

Table 16:

Table 17:

LIST OF TABLES

Effects of disk distance on bubble diameter .................................... 34
Phosphate buffered basal salts medium composition ......................... 48
Composition of trace mineral solution .......................................... 49
Composition of Vitamin solution ................................................ 50
Composition of phosphate stock solution ...................................... 50
Surfactant critical micelle concentration ....................................... 53
Carbon and electron balance results for Tween surfactants .................. 63
Mass transfer rates ................................................................. 80
Composition of the enhance PBB medium ..................................... 95
Reductance degrees ............................................................... 98
Lactic acid media .................................................................. 107
Minimal salts media ............................................................... 107
Batch vitamin solution ............................................................ 108
Heavy metal solution............................., ............................... 108
Trace elements 11 .................................................................. 109
Synthesis gas uptake from serum bottles ....................................... 119
Surface tension ..................................................................... 143

ix

Figure 1:
Figure 2:
Figure 3:
Figure 4:
Figure 5:
Figure 6:
Figure 7:
Figure 8:

Figure 9:

Figure 10:
Figure 11:
Figure 12:
Figure 13:
Figure 14:
Figure 15:
Figure 16:
Figure 17:
Figure 18:
Figure 19:
Figure 20:
Figure 21:

Figure 22:

LIST OF FIGURES

Microbubble generator ............................................................ 23
Schematic of a microbubble ...................................................... 25
Bubble size distribution using dynamic light scattering ...................... 34
Equilibrium formation time for microbubbles ................................. 35
Equilibrium formation time in the presence of salts .......................... 36
Foam and foam-liquid interface level in drainage experiments ............. 38
Initial foam gas void fractions for microbubbles .............................. 39
Microbubble stability ............................................................. 40
Drainage experiment using alginate microbubbles ........................... 44
Chemical structure of Tween and Brij surfactants ............................ 52
Dry weight calibration curve ..................................................... 54
Growth of B. methylotrophicum in batch bottles with Tween .............. 55
Speciﬁc growth rate of B. methylotrophicum with Tween .................. 56
Growth of B. methylotrophicum in batch bottles with Brij .................. 57
Speciﬁc growth rate of B. methylotrophicum with Brij ...................... 58
Acetate production ................................................................ 60
Ethanol production ................................................................ 61
Butyrate production ............................................................... 62
pH proﬁle of a Tween 80 fermentation ......................................... 64
Experimental apparatus used in axial dispersion and mass transfer. . . . . 69
Axial dispersion coefﬁcients ..................................................... 75
Optimized ﬁt for KL using a plug-flow model ................................. 77

Figure 23:
Figure 24:
Figure 25:
Figure 26:
Figure 27:
Figure 28:
Figure 29:
Figure 30:
Figure 31:
Figure 32:
Figure 33:
Figure 34:
Figure 35:
Figure 36:
Figure 37:
Figure 38:
Figure 39:
Figure 40:
Figure 41:
Figure 42:
Figure 43:
Figure 44:

Figure 45:

Mass transfer coefﬁcients from microbubbles ................................. 78

Comparative KLa values for varying reactor types ............................ 83
Experimental data from a dynamic gassing out run .......................... 84
Linear form of Equation 19 ...................................................... 85
Percent oxygen transferred to liquid phase .................................... 86
Dynamic mass transfer coefﬁcients of microbubbles ........................ 88
Flow diagram for a B. methylotrophicum fermentation ...................... 96
Fermentation product proﬁle ..................................................... 99
Mass transfer coefﬁcients from fermentation .................................. 101
802 reducing fermentation ﬂow diagram ...................................... 112
Potentiometric titration of sulﬁde ............................................... 114
CO uptake by SRB in a batch serum bottle .................................... 117
H2 uptake by SRB in a batch serum bottle ..................................... 118
Mass transfer coefﬁcient for CO ................................................ 121
Mass transfer coefﬁcient for H2 .................................................. 122
SRB reactor productivity ......................................................... 124
Captured video image of microbubbles ......................................... 144
Bubble size distribution histogram .............................................. 145
Coalescence using efﬁciency modeled with Equation 53 .................... 147
Average bubble size using efﬁciency modeled with Equation 53 ......... 148
Coalescence in 0 mg/L Tween 20 using Equation 63 ........................ 149
Coalescence in 180 mg/L Tween 20 using Equation 63 ..................... 150
Coalescence in 300 mg/L Tween 20 using Equation 63 ..................... 151

xi

Figure 46: Dynamic average bubble size .................................................... 152

Figure 47: Coalescence efﬁciency ............................................................ 153
Figure 48: Number of bubbles in vessel ..................................................... 154
Figure 49: Effect of surfactant on C1 ......................................................... 156

xii

1. INTRODUCTION

Synthesis gas, a mixture containing carbon monoxide (CO), hydrogen (H2),
carbon dioxide (CO2) and trace sulfur compounds can be readily obtained from the
gasiﬁcation of coal or biomass (Worden, 1997). Synthesis gas can be anaerobically
converted into alcohols such as ethanol (Grethlein, 1990) and butanol (Grethlein, 1991a)
which have been typically made from petroleum. The advantages of using bioprocessing
to convert synthesis gas to liquid fuels rather than typical catalytic techniques are that
coal-derived synthesis gas is a potentially less—expensive feedstock than agricultural
products such as starch, CO2 production can be limited with the addition of small
amounts of secondary electron donors (Grethlein, 1991b), and many bacteria that are
capable of converting synthesis gas (such as Butyribacterium methylotrophicum and
Clostridium ljungdahlii) have high tolerances to sulfur compounds (Grethlein, 1992b),
(Vega, 1990a). Biological processes also exhibit high substrate and product speciﬁcity,
which minimizes formation of by-products and can operate at relatively low temperatures
and pressures.

Typical problems that occur with the bioprocessing of synthesis gas are that
product concentrations are typically low and that the transport of synthesis gas
components to the liquid phase are slow due to inherently low aqueous solubilities. The
conventional method to increase gas-to-liquid mass transport in stirred tanks is to
increase the power input to enhance bubble breakup and thereby increase the effective
area for mass transport. This approach is not economically feasible in large-scale reactors

because power consumption is proportional to the impeller rate to the third power and

impeller diameter to the ﬁﬁh power (McCabe, 1985). Additionally, the high shear rates
created by the impellers can be detrimental to cellular metabolism (Bailey, 1986).

A potential way to overcome the gas-to-liquid mass transport limitations of
synthesis gas fermentations is the use of microbubble dispersions. Microbubbles (or
colloidal gas aphrons) are small, surfactant coated bubbles with a potentially a multi-
layered shell stabilized by surfactant (Sebba, 1984). Microbubbles typically have
diameters on the order of 50 pm in comparison to 2 to 5 mm for conventional bubbles
found in sparged fennenters (Kaster, 1990). The surfactant shell imparts an electrical
charge to the bubbles’ surface and helps to prevent coalescence, giving the bubbles
colloidal properties such as the ability to be pumped without collapse unlike conventional
foams (Longe, 1989). The mass transfer rate, in mass transport limited situations, is
directly proportional to the bubbles’ interfacial area per unit gas volume. Therefore
increasing the interfacial area available for mass transport without high power input
would be beneﬁcial.

Another advantage to using microbubbles with synthesis gas fermentations is that
typically synthesis gas consists of over 95% consumable substrate, and as the
components are transferred out of the bubble, the bubble will shrink. This shrinkage will
further increase the area per unit gas volume and increase the efﬁciency of mass transfer.
Additionally, the bubbles’ internal pressure increases as the bubbles shrink due to
curvature and surface tension effects (Rosen, 1989), increasing the gas component’s
liquid phase equilibrium concentration. Therefore, higher dissolved CO tensions can be

obtained without increasing the overall pressure in the system.

This research is presented in eight chapters. Chapter 2, the Objectives and
Signiﬁcance, contains the goals and requirements of this project as well as the importance
of this work. Chapter 3 contains a literature review, which gives pertinent background
information into this work. Identiﬁcation of surfactants that can form microbubbles is
given in Chapter 4, Formation and Stability of Microbubbles, and are biocompatible with
microorganisms in Chapter 5, Surfactant Biocompatibility. The mass transfer coefﬁcients
and power requirements of microbubbles are examined in Chapter 6, Mass Transfer
Properties of Microbubbles. The results of fermentations that have beneﬁted using
microbubble sparging are presented in Chapter 7, Butyrz‘bacterium methylotrophicum
Fermentations and Chapter 8, Sulfate Reducing Bacteria Fermentations. Finally, the

results of coalescence studies on microbubbles are given in Chapter 9, Coalescence.

2. OBJECTIVES AND SIGNIFICANCE

2.1 Surfactant Biocompatibility

Surfactants increase the stability of microbubbles and decrease the average
diameter (Kaster, 1990), (Longe, 1989). The addition of external surfactant signiﬁcantly
reduces their rate of drainage (Amiri, 1990) and thereby decreases their rate of
coalescence. Most previous research on microbubbles used an ionic surfactant to supply
the microbubble surface with a signiﬁcant charge for use with applications such as
ﬂoatation or harvesting. In most cases, ionic surfactants are toxic to the cellular
metabolism due to their ability to form ionic bonds with the cellular proteins, while non-
ionic surfactants tend to form much weaker hydrogen bonds and are therefore less toxic.
Therefore, the ﬁrst objective of this study was to identify surfactants that allow formation

of microbubble dispersions while not being detrimental to cellular metabolism.
2.2 Microbubble Mass Transfer Coefﬁcients

Little information exists in the literature on the mass transfer rate from
microbubbles. The mass transfer characteristics of microbubbles, with their potentially
complex outer shell, have not been well characterized. Kaster et a1. (1990) obtained
values for the volumetric mass transfer coefﬁcient in a Saccharomyces cerevisiae
fermentation using microbubble sparging but without the addition of an external
surfactant. Walso and Gal-Or (1971) have suggested empirical equations to describe the
mass transfer coefﬁcient from swarms of small rigid bubbles, but these equations do not
account for the possible presence of a thick liquid shell. The determination of the mass

transfer properties of microbubbles enables a more accurate description of the processes

occurring during fermentations using microbubbles. Therefore, the second objective was

to study the mass transport characteristics of microbubble.
2.3 Synthesis Gas Fermentations

Continuous cell-recycle fermentations have been demonstrated for B.
methylotrophicum (Grethlein, 1990), Clostridium ljundahlii (Klasson, 1993), and for the
class of bacteria known as sulfate reducing bacteria (SRB) (van Houten, 1994). In order
to use microbubble sparging in these fermentations, modiﬁcations to handle increased
liquid ﬁltration and potential equipment difﬁculties will have to be made. Mass balances
around the reactors can be used to calculate the volumetric mass transfer coefﬁcient as
has been done in previous, conventionally sparged fermentations (Klasson, 1992).
Important parameters such as bioreactor productivity, mass transfer coefﬁcients, and
substrate conversion will be compared to conventionally sparged fermentations.
Subsequently, the third objective of this study is to show improved reactor productivity
and increased mass transfer in continuous, microbubble-sparged, synthesis-gas

fermentations.
2.4 Microbubble Coalescence

Microbubbles coalesce through drainage of the ﬁlm between two adjacent
bubbles. The rate of this coalescence could be related to the thickness of the surrounding
ﬁlm around a microbubble, the rate at which the liquid drains, and the steric hindrance
effects of the surfactant. The rate of coalescence could also be related to the conditions
that prevail in the vessel with microbubbles, i.e. turbulent ﬂows giving rise to a greater
number of collisions and thereby increasing the likelihood of coalescence. The rate of

coalescence is an important factor in understanding the phenomena occurring in a stirred

tank during fermentation. A fundamental understanding of the coalescence dynamics
occurring in a stirred vessel would allow for accurate prediction in average bubble size
during fermentations. Design criteria for microbubble—sparged fermentation processes
could also be developed using this information. Therefore, the ﬁnal objective of this work

is to conduct a fundamental study into the coalescence phenomena of microbubbles.

3. BACKGROUND AND LITERATURE REVIEW

3.1 Synthesis Gas

Synthesis gas, a mixture of carbon monoxide (CO) and hydrogen (H2) gases, is
produced by the partial oxidation of an organic feedstock at high temperature in the
presence of steam. Presently, synthesis gas for fuels and chemicals is produced primarily
by catalytic steam reformation of natural gas or by partial oxidation of heavy oil
fractions. The future of synthesis gas production lies in coal gasiﬁcation, due to its
availability and abundance, and in biomass gasiﬁcation, due to its renewability and cost.
The composition of synthesis gases can vary signiﬁcantly depending on the material
being gasiﬁed and the type of gasiﬁer used. Typically, most synthesis gases have, other
than CO and H2, methane (CH4), carbon dioxide (CO2), water (H20) and a variety of
contaminants (Simbeck, 1983). Typical contaminants also depend on the material being
gasiﬁed, but commonly are sulfur compounds such as carbonyl sulﬁde (COS) and
hydrogen sulﬁde (H28) and nitrogen compounds such as ammonia (NH3). These
contaminants are costly to remove either pre or post burn and can lead to the formation of
SOx and NOX which are causes of acid rain and ozone layer degradation.

3.1.1 Coal Gasification

Coal is a readily available, low-cost source for synthesis gas for chemicals and
fuels. The estimated coal surplus in the United States as of 1989 was 250 million tons of
coal, which corresponds to a 220-year surplus at current usage rates (Mallory, 1979).
Coal gasiﬁcation was a heavily used technology in the 1950’s until it was replaced by
lower cost raw materials such as natural gas and petroleum. Typically, synthesis gas is

produced from coal through steam gasiﬁcation, where at high temperatures and pressures,

coal, water and oxygen (02) are combined to form a mixture that is primarily CO and H2.
The direct composition of the synthesis gas is dependent on the type of gasiﬁer, the
gasiﬁcation conditions, and the source of the gasiﬁcation coal. Also, the ﬁnal
composition of the synthesis gas depends on the application for which the synthesis gas is
to be used. When used as a substitute for natural gas, the formation of CO is minimized
and emphasis is placed on CH4 and H2 compositions. When used as a source of electric
power, a high CO:H2 ratio is desired. Finally, for chemical fuels production, a speciﬁc
CO:H2 ratio is desired that is based on the product formation stoichiometry.

There are several different types of coal gasiﬁers that are currently in use and
depend primarily on different techniques for contacting the coal with O2 and H20. These
included ﬁxed or moving bed gasiﬁers, which typically operate at lower temperatures
with high solid residence times, entrained-bed gasiﬁers, which typically operate at high
temperatures, and ﬂuidized-bed gasiﬁers, which operate at moderate temperatures and
have rapid and complete gas-solids mixing. The type of gasiﬁer used strongly inﬂuences
the composition of the resulting synthesis gas. An in depth review of existing gasiﬁer
technology is given in Grethlein (1991b).

3.1.2 Biomass Gasification

Biomass gasiﬁcation offers several advantages of over conventional feedstocks
such as coal and petroleum. Most biomass has a much lower sulfur content than most
coals. Synthesis gas that was derived from wood chips at a GE gasiﬁcation plant
contained 28 ppm of H28 (Worden, 1997) compared to up to 2% in coal-derived
synthesis gas. The puriﬁcation steps to remove sulfur compounds from synthesis gas are

costly in both sorbent recycling and disposal (Kaufman, 1996a) and in energy and

equipment costs. Biomass materials are also more reactive than coal, and therefore
require lower gasiﬁcation temperatures and pressures as well as shorter residence times.
Fluidized-bed coal gasiﬁers are typically run at 1000 °C with residence times of up to 3
hours while biomass gasiﬁcation require temperatures of 850 °C with residence times
from 30 s to 5 min (Worden, 1997). Finally, the gasiﬁcation of biomass provides for the
disposal of wood and yard wastes as well as utilizing a renewable resource.

The economics favor the gasiﬁcation of biomass over the burning of biomass
because the basic conversion efﬁciency of gasiﬁcation is about 32% compared with 15%-
20% for the combustion route (Parkinson, 1996). The ﬁnal composition of the gas
obtained from biomass gasiﬁcation is dependent on the operating conditions, gasiﬁer
temperature, and whether it is air-blown or oxygen-blown. An investigation of the how
gasiﬁer conditions effect the ﬁnal gas composition are given in Maschio (1994) and in
Kinoshita (1991).

The ﬁrst biomass gasiﬁcation facility came on line in Fall of 1995 in Vamamo,
Sweden that uses a pressurized, air-blown gasiﬁer. This plant is in the 30 to 60 MW
range. Other ventures, using a variety of feedstocks, are being brought online. In Hawaii,
the Paciﬁc Center for High Technology is using IGT’s Renugas process to generate a low
BTU gas from sugar cane bagasse and in Minnesota, the Renugas process is being used to

produce gas from alfalfa stems (Parkinson, 1996).
3.2 Synthesis Gas Fermentations
Synthesis gas can be catalytically converted into chemical products such as

methanol in reactors operated at high temperatures and pressures (Kinoshita, 1991) which

can then be used as a fuel additive or as a precursor to other chemicals. A major catalytic

route for synthesis gas is through Fischer-Tropsch synthesis. Fischer-Tropsch is a
catalytic approach to convert CO and H2 to a variety of parafﬁnic, oleﬁnic, and
oxygenated compounds, which can then be used as either fuel additives or desirable
chemicals. A key disadvantage to the use of Fischer-Tropsch synthesis is the lack of
catalyst speciﬁcity, generating a wide range of fractions with a low molecular weight
fraction, a gasoline fraction, and a diesel oil fraction (Grethlein, 1991b). The only
products that can be formed with 100% selectivity are the Cl compounds. This creates
difﬁculty in generating higher molecular weight alcohols and acids (e.g. butanol and
butyrate) because the existing catalysts give a wide range of products. The existing
catalysts are also easily poisoned by sulfur compounds, which must be removed prior to
undergoing Fischer-Tropsch synthesis. Finally, conventional catalytic techniques usually
require a strict ratio of CO to H2, which is typically adjusted prior to the catalytic reaction
through separate gas-shifting reactors to modify the synthesis gas composition through
the water-gas shift reaction.

The biological conversion of synthesis gas has many advantages of conventional
catalytic techniques. First, the reaction speciﬁcity is high with fermentation conditions
able to be optimized to produce speciﬁc products (e.g. ethanol or acetate) (Phillips,
1993), (Grethlein, 1991b). Second, biological conversion happens at temperatures and
pressures around room temperature and atmospheric pressure. Third, most biological
catalysts used are highly tolerant to sulfur species (Grethlein, 1992b), (Reis, 1992) and
can in many cases be used without prior removal. It has been estimated that the operating

costs for the production of clean synthesis gas can amount to over half of the total

10

operating costs for coal processes such as SASOL (Grethlein, 1991b). Finally, biological
conversion does not have a set CO/I-I2 ratio in respect to the metabolic reactions.

Some of the key disadvantages to biological processing result in low reactor
productivies. Work has been done on this issue in attempts to increase the productivies
from fermentations. With some high productivity bacteria, such as Clostridium
ljungdahlii, under development this issue is becoming no longer as signiﬁcant as it was.
Development in the separations of dilute aqueous fermentation products has lead to the
use of extractive distillations to remove ethanol. A company in Fayetteville, AR
(Bioengineering Resources, Inc.) have made signiﬁcant process developments in the
production of ethanol from synthesis gas and have given cost estimates that are
competitive with the costs of producing ethanol from fermentation of agricultural
materials. A key drawback in the fermentation of synthesis gas components is the low
aqueous solubilities of CO and H2, being 60% and 4% by mass as soluble as oxygen, a
sparingly soluble gas (Worden, 1997). This results in synthesis gas fermentations being
gas-to-liquid mass transport limited (Worden, 1989), (Klasson, 1992).

3.2.1 Butyribacterium methylotrophicum

B. methylotrophicum is an obligate anaerobe that is capable of growth on a variety
of substrates including glucose (Moench, 1983), forrnate and methanol (Kerby, 1987), H2
and CO2 (Lynd, 1982), and CO (Lynd, 1982). When grown on methanol in the presence
of acetate and CO2, a nine-hour doubling time was observed (Lynd, 1983) while the CO
adapted strain was able to grow on 100% CO gas with a doubling time of 12 hours (Lynd,
1982). The CO adapted strain has been shown to produce a variety of substrates that is

linked to the fermentation pH (Grethlein, 1990). At pH 6.8, the primary fermentation

11

product is acetate with a molar ratio of acetate:butyrate of 32:1 (Grethlein, 1990). At pH
6.0, acetate and butyrate are produced in nearly equimolar amounts. Ethanol and butanol
are minor products with butanol concentrations up to 2.7 g/L being produced at low pH
(Grethlein, 1991a).

The acetogenic metabolism of B. methylotrophicum has been elucidated for CO
and CO2 utilization for the formation of acetyl-CoA and butyryl—CoA , the formation of
ethanol and butanol, and the formation of acetate and butyrate (Shen, 1996). A detailed
description of the enzymatic pathways involved in the product formation from B.
methylotrophicum can be found in Grethlein et a1. (Grethlein, 1992a). The primary steps
involved in the CO metabolism involve the reaction of CO and H20 with CO
dehydrogenase to yield CO2, the production of formate from CO2 via formate
dehydrogenase, tetrahydrofolate-linked transformations resulting in a methyl-corrinoid
complex, the reaction of CO with CO dehydrogenase to form an enzyme-bound carbonyl
moiety, and the synthesis of acetyl-CoA from both the methyl and carbonyl groups bound
to the CO dehydrogenase complex. The consumption of H2 and CO2 occur via the same
mechanism with H2 being used to reduce CO2 to bound CO (Grethlein, 1992a).

Continuous fermentations have been developed to exploit the CO metabolism of
B. methylotrophicum to produce products such as acetate, butyrate, ethanol, and butanol
(Grethlein, 1990). The stoichiometry of the unicarbonotrophic metabolism of CO is given

in Equation 1 below (Grethlein, 1991b).
4C0 —> 2.17C02 + 0.74CH3C00H + 0.45Cell (1)

Similarly, the carbon-balanced reaction for growth on H2 and CO2 is given in Equation 2

below (Grethlein, 1991b).

12

2H, +1.03C0, —> 0.43CH,C00H + 0.13Cell (2)

The products of these fermentations have been found to be linked to the pH as mentioned
previously, with more than half of the incoming carbon was converted to CO2 and acetate
the primary liquid-phase product, accounting for 67% of the reduced-product carbon.

One trend with continuous fermentation using slow-growing anaerobes such as B.
methylotrophicum is that the biomass concentration in the reactor is low and subsequently
product concentrations are lower. The average biomass concentration in previous
fermentations was approximately 0.28 g/L (Grethlein, 1990). The low speciﬁc growth
rate of the organism, a 12 hour doubling time, requires very low dilution rates in order to
prevent cell washout. The low dilution rates limit the reactor’s volumetric productivity,
which was approximately 0.001 g/L*h for alcohols and 0.015 g/L*h for acids (Grethlein,
1990). A total cell-recycle can be used to increase the biomass and product
concentrations and therefore increase volumetric productivities. In the case of B.
methylotrophicum, increases of 830% for acetate, 850% for butyrate, 820% for ethanol,
1481% for butanol, and 2440% for cell mass have been obtained using a total cell recycle
over a continuous fermentation without cell recycle (Grethlein, 1991b). This represents
an 8-9-fold increase in acid production and an 8-14 fold increase in alcohol production.

The inhibitory effects of a number of products and potential synthesis gas
components have been investigated. The effect of the product alcohols, ethanol and
butanol, have been investigated up to approximately 12 g/L (Grethlein, 1991b). It was
shown that for ethanol, signiﬁcant inhibitory effects start to occur at concentrations above
5 g/L and for butanol these effects started at concentrations of 2.8 g/L. This indicates that

butanol is the more toxic product (Grethlein, 1991b). The effect of the alcohols on the

13

bacteria is through damage to the cellular membrane, where the alcohol can increase
ﬂuidity of the membrane, causing a number of detrimental effects such as the disruption
of the nutrient transport and energy generation systems. The effect of the produced acids,
acetate and butyrate, were also studied in concentrations up to 12 g/L. There did not seem
to be signiﬁcant inhibition due to these acids, but the fermentations did give evidence for
co-metabolism of CO gas and either acetate or butyrate (Grethlein, 1991b).

The effect of sulﬁde on the metabolism was examined through the addition of
sodium sulﬁde (Na2S) and hydrogen sulﬁde gas (H2S) (Grethlein, 1992b). The addition
of H28 gas to the headspace severely inhibited the both cell growth and acetate
production in concentrations higher than 3.2%. With the addition of Na2S to the liquid
phase, inhibition was seen to occur in the growth rate at concentrations between 1.4% and
3.3%, but the speciﬁc and molar yields of acetate and butyrate were not signiﬁcantly
effected. The results from this data indicate that below 2% H28 in the headspace, there
was little inhibition from sulﬁde and therefore should not affect the metabolism of B.
methylotrophicum during coal-derived synthesis gas conversion (Grethlein, 1992b).

3.2.2 Clostridium ljungdahlii

Clostridz'um ljungdahlz'z', a gram-positive, motile, rod-shaped anaerobic bacteria
was isolated in 1987 from chicken waste at the University of Arkansas. It was shown to
be capable of converting CO, H2, and CO2 to a mixture of acetate and ethanol (Barik,
1988). In addition to synthesis gas components, C. ljungdahlii is also capable of growth
on xylose, arabinose, and fructose (Klasson, 1992). It is expected that the ethanol and

acetate are formed through an acetyl—CoA intermediate. It has been shown to produce

14

ethanol in concentrations up to 48 g/L in a CSTR with cell recycle (Klasson, 1993). The

production of ethanol and acetate from C0 and H2 is shown stoichiometrically below.

6C0 +3H, —2 C, H5011 +4C0, (3)
2C0, +611, —> CZHSOH +3H,0 (4)
4C0 +2H, 0 —> CH,C00H +2C02 (5)
2C0, +4H, —> CH,CO0H +2H,0 (6)

The ‘wild’ type strain of C. ljungdahlii showed an ethanol/acetate ratio of only
0.05 with a maximum production of ethanol of 0.1 g/L (Vega, 1989a). Work with the
fermentation parameters, such as lowering the pH to 4.0, has brought about a signiﬁcant
increase in the ethanol/acetate ratio up to 3 (Gaddy, 1995). The development of a
designed medium, without yeast extract, has been able to virtually invert the ethanol and
acetate production (Phillips, 1993) and nearly eliminate acetate as a product. These
studies also found that both the product concentration and cell concentration, which
ranged from 1 to 2 g/L using a total cell recycle, were independent of inlet gas ﬂow rate
(Phillips, 1993). Using the designed medium, after 25 days, the ethanol concentration was
as high as 48 g/L (Phillips, 1993).

Research with C. ljungdahlii has shown that the presence of reducing agents in
liquid media has brought about an increase in solvent formation (Klasson, 1991a). The
reducing agents cause altered electron ﬂow which directs the ﬂow of carbon to acid and
alcohol production. The reducing equivalents are transferred in the form of NADH,
which results in increased alcohol formation. The addition of small quantities of reducing
agents such as methyl and benzyl viologen, sodium thioglycollate, and ascorbic acid,

have been able to double and quadrupole the ethanol/acetate ratio (Klasson, 1992). Other

15

research investigating the connection between sporulation and increased solventogenesis
has identiﬁed that a shift of the bacteria into a sporulation state is accompanied by
morphological changes and increased solventogensis (Klasson, 1992). Studies with C.
ljungdahlz'i have been done using complex nutrients such as cellobiose, rhamnose, and
galactose, which were found to promote sporulation in other Clostrz’dium species
(Klasson, 1992). The increase in ethanol concentration was the‘highest in the presence of
cellobiose and galactose, where ethanol concentrations were four times the concentration
obtained in the presence of yeast extract and cell concentrations were 20% higher
(Klasson, 1992).

Since ethanol production seems to be linked to a phase of the bacteria that is on
the edge of sporulation, studies using two continuous reactors in series have been done
(Klasson, 1992). The scheme uses the ﬁrst reactor to promote cell growth, while the
second reactor is used for the production of ethanol. The conditions and media
constituents in the ﬁrst reactor are optimized for cell growth, while in the second reactor,
the pH is dropped from 4.5 to 4.0, the dilution rate is shifted to control the growth rate,
and media additions such as cellobiose are added. This two-reactor scheme was capable
of a 30-fold improvement in speciﬁc productivies over a single reactor (Klasson, 1992).

Reactor development using C. ljungdahlii that is currently under investigation
include the use of increased pressure in fermentations in order to overcome gas-to-liquid
mass transport limitations that are prevalent in synthesis gas fermentations. High-pressure
fermentations can be useful in minimizing reactor volume requirements. Pressure
fermentations have been successful for some synthesis gas bacteria, such as

Peptostreptococcus productus, to a point where the liquid phase carbon monoxide

16

concentration has become high enough to cause inhibition of metabolism (Vega, 1990b).
Therefore, it has become necessary to develop conditions were the carbon monoxide
tension remains low despite increased pressure. This has been done through high cell
concentrations, obtained through feeding alternative substrates and gradual stepwise
increasing of the cell concentration (Vega, 1990b). Pressure fermentations using C.
ljungdahlii have been done at pressures up to 2.5 atm (Vega, 1989a) and work is
underway to obtain a pressure adapted strain for higher pressures.

Another technique to enhance gas-to-liquid mass transfer using C. ljungdahliz' is
the use of solvents. Synthesis gas components are more soluble in a munber of organic
compounds such as toluene and heptane (Halling, 1994), and their introduction into the
fermentation media may result in an increase in gas-to-liquid mass transfer rates. An
increase of 2.2 fold was seen for oxygen gas in a 15% by volume media with the
preﬂuorocarbon, FC40, in waste gas treatment (Cesario, 1997). Recently, work by
Rodriguez (M. Rodriguez, unpublished results) have seen a 4-fold increase in the mass
transfer coefﬁcient in serum bottle fermentations of C. ljungdahlii using a 20% by
volume media with hexadecane.

3.2.3 Sulfur Reducers

The class of bacteria known as sulfate reducing bacteria (SRB), is capable of
using a variety of sources for reducing equivalents in the reduction of sulfur compounds.
Microbial processes utilizing sulfate-reducing bacteria (SRB) have found potential
application in treatment processes of sulfur laden wastes. In particular, processes for ﬂue
gas desulfurization (Selvaraj, 1995), gypsum recovery (Kauﬁnan, 1996b), sulfur recovery

from sulﬁte/sulfate wastewater from pulp and paper, chemical and mining industries

17

(Hammack, 1994), and degrading explosive material. The cost of feedstock and
bioreactor productivity are critical parameters in the economic viability of the microbial
processes (Selvaraj, 1996b). Lactic acid, ethanol, hydrogen, synthesis gas, and sewage
digest have all been proposed as electron donors for SRB. Lactic acid and ethanol are
most likely too expensive of a feedstock for the process. In speciﬁc locations, sewage
digest could be available at low or negative cost (Selvaraj, 1996b).

Synthesis gas is an attractive feedstock for the SRB process due to its wide
availability from coal or biomass gasiﬁcation, its zero COD discharge, and it possible
availability on site. Various groups have demonstrated that SRB could be supported by
carbon dioxide (CO2) and/or CO as their sole carbon source and hydrogen as their energy
source (van Houten, 1994), (du Preez, 1992). Recently, van Houten et al. (1994) operated
a gas-lift, sulfate-reducing reactor with a feedstock of CO/I-I2 with CO concentrations up
to 20% that was capable of a maximum sulfate conversion rate of 10 g SO42'/(d*L) and
du Preez et al. (1994) operated a pilot-scale packed bed reactor with a feedstock of CO
that was capable of a maximum rate of 2.4 g SO42'/(d*L).

3.2.4 Other Synthesis Gas Bacteria

A number of other bacteria have been shown to be capable of using synthesis gas
components for the production of a variety of compounds, in most cases acetate. None of
the other bacteria have been to shown to produce ethanol at the same level as C.
ljungdahlii or as many different products as B. methylotrohicum. A strain of
Peptostreptococcus productus that was capable of utilizing CO as the energy source at

mesophillic temperatures was isolated from an anaerobic sewage digester in 1984. This

18

bacteria grew quickly, td = 1.5 h, with up to 50% CO in the headspace with acetate and

CO2 as the major products. The reaction stoichiometry is presented below (Vega, 1989b).
4C0+2H20—>2C02 +CH3C00H (7)

It was also seen that P. productus was able to grow at higher concentrations of CO (up to
90%), but an increase in the concentration of yeast extraction was required.

Signiﬁcant work has been done with P. productus. Through batch culture, key
kinetic parameters, such as speciﬁc uptake rate and yield coefﬁcients that are usable in
the prediction of reactor performance (Vega, 1989d) have been determined. A model has
been developed using the parameters estimated from batch culture to evaluate the
conversion and levels of CO as a function of inlet gas ﬂow rate under mass transfer-
limited conditions (Vega, 1989c). Since the primary product from P. productus is acetate
rather than ethanol, work has drifted from P. productus to higher ethanol producers such
as C. ljungdahlii.

Methane (CH4) gas can also be generated from synthesis gas through
fermentation. A mixed culture of Rhodospirillum rubrum, a photosynthetic bacterium,
and two methanogens, Methanosarcina barkerz', and Methanobacterium formicum has
been used to convert synthesis gas to CH4 (Klasson, 1990). The triculture carries out the
same reactions as the water gas-shift reaction and methanation. These reactions are given

below.
C0+H,0—>H,+C02 (8)
4H2+C0,—>CH4+2H20 (9)
In the triculture, R. rubrum carries out reaction 8 while M. barkeri and M. formicum carry

out reaction 9. The reason that two different organisms were used to convert H2 to CH4

19

was that while M. formicum has a high rate of H2 uptake, it is inhibited in the presence of
CO, and while M. barkeri has a tolerance to CO, it has a lower rate of H2 uptake
(Klasson, 1990).

This triculture has been used in many different reactor conﬁgurations, continuous
stirred tank reactors (CSTR), bubble column reactors, and trickle-bed reactors (TBR)
(Vega, 1990b) to convert synthesis gas into methane. The yield of methane from H2 were
estimated to be 83% of theoretical and 100% CO conversion was obtained in these
reactors (Vega, 1990b).

3.2.5 Bioreactors for Synthesis Gas Fermentations

Due to the mass transfer limitations that occur in synthesis gas fermentations, the
design of such reactors and fermentation systems centers around increasing the mass
transfer coefﬁcient (Klasson, 1991b). The mass transfer capabilities of the reactor must
be sufﬁcient enough to generate high cell densities and supply enough substrate to the
liquid phase. Many different types of reactors have been examined for possible use in
synthesis gas fermentations: CSTR, packed—bed, bubble column, gas-lift and trickle-bed.

Free-cell reactors such as the CSTR have used a variety of techniques to increase
both biocatalyst density and to help overcome mass transfer limitations. Two stage
reactor schemes for C. ljungdahlii have been used where one reactor vessel is used to
promote growth and a second reactor in series has environmental conditions, such as low
pH and a shift in the dilution rate, optimized for product formation (Klasson, 1991b). The
Michigan Biotechnology Institute (MBI) has used two stage reactor schemes for the
conversion of synthesis gas components to butanol using one reactor to convert synthesis

gas to butyrate using B. methylotrophz'cum and the second reactor to convert butyrate to

20

butanol using Clostridium acetobutylicum (Grethlein, 1992a). Grethlein et al. (1991b)
used headspace and cell recycling in tandem to ensure mass transfer limitation operation
and maintain high cell density for the production of n-butanol with B. methylotrophcium.
Stirred-tank reactors are capable of achieving high mass transfer rates but require
substantial energy input for agitation. An increase in impeller speed from 300 rpm to 450
rpm increased the volumetric mass transfer coefﬁcient from 28.1 h’1 to 101.1 h'1 using a
mixed triculture fermentation (Klasson, 1992). This approach, while effective, results in
dramatic increases in power consumption. This increase is especially dramatic for large-
scale systems because power consumption is proportional to the impeller rate to the third
power and impeller diameter to the ﬁfth power (McCabe, 1985).

Immobilized cell reactors such as a trickle-bed reactor have been used as a
possible alternative to the free-cell reactors. Immobilized cell reactors eliminate the need
for mechanical agitation and expensive cell-recycle systems and usually give high
interfacial area and high mass transfer coefﬁcients (Charpentier, 1981). Klasson et. a1.
(Klasson, 1992) found for a triculture fermentation that CO conversion for a given gas
loading rate was two-fold greater in a trickle-bed reactor with the cells immobilized on
ceramic saddles than in a CSTR. Selvaraj et a1. (Selvaraj, 1997a) found an eight-fold
increase in productivity for the reduction of 802 to S?" by SRB in a trickle-bed reactor
with the cells immobilized on BIO-Sep beads over a CSTR on a sewage digest media.
Similar results were also obtained using coal synthesis gas as a feedstock (Selvaraj,
1996a). A packed-bed reactor was used in a pilot plant for the reduction of sulfate and
nitrate waste using SRB and synthesis gas as a feedstock (du Preez, 1994). Similarly, air-

lift reactors have been used with SRB fed a synthesis gas substrate (van Houten, 1994).

21

Multiple groups have increased pressure in reactor schemes to increase the
carbon monoxide and hydrogen tensions (du Preez, 1994), (Klasson, 1992). Recently,
Soni et al. (1998) have tried increased pressure on methanogens. The idea is that higher
pressure will allow for higher levels of dissolved CO and H2 which will lead to higher
concentrations of biomass (du Preez, 1994). Theoretical results using fermentation
parameters for P. productus indicate that for a 10 fold increase in total pressure, a 16 fold
increase in the CO uptake by the bacteria could be obtained (Klasson, 1991b). One
drawback to the use of increased pressure is the inhibitory effects of higher levels of
dissolved CO tension. Thus, maintaining low dissolved CO tensions in high pressure
fermentations is of great importance and can be achieved by having high reactor cell
densities (Vega, 1990b). High reactor cell densities in high-pressure reactors for P.
productus have been obtained by stepwise increases in pressure (Vega, 1990b). This
approach allows the cells to gradually acclimate to the increased pressure. Work is

ongoing to develop a high-pressure adapted strain of C. ljungdahlii (Klasson, 1992).
3.3 Aphrons

The term aphron comes from the Greek word aphros, which means foam. The
existence of aphrons was ﬁrst reported by Sebba (1987). They typically are below 100
pm in diameter and are encapsulated by a surrounding liquid ﬁlm and encased in
surfactant, which acts to stabilize them. There are two different types of aphrons,
colloidal gas aphrons (CGA) where the dispersed phase consists of a gas, and colloidal
liquid aphrons (CLA) where the dispersed phase consists of an organic liquid or oil with
a soluble surfactant dissolved within. While being similar in structure, CLA and CGA

have signiﬁcantly different properties and generation techniques.

22

3.3.1 Colloidal Gas Aphrons

Collodial gas aphrons, also known as microbubbles are made by creating a high-
shear zone at a gas-liquid interface. Devices such as a venturi throat (Sebba, 1987) and a
spinning disk apparatus (Sebba, 1985) (Figure 1) have previously been used to generate
dispersions. When a gas bubble becomes trapped in the liquid, it can be pulled into the
high-shear zone and further broken down into smaller and smaller bubbles. The
surfactant present in the liquid is absorbed at the interface stabilizing the smaller bubbles
and reducing the rate of coalescence in the system. Microbubbles also exhibit colloidal

properties that allow them to be pumped, unlike conventional foams (Longe, 1989).

  

Stirring Motor

  

 

5 Liter
Fermenter

 

 

 

 

 

Spinning Disk

Figure 1: Microbubble generator
It has been suggested that microbubbles have a complex outer shell arrangement,

having both a surfactant bilayer at the liquid shell-bulk liquid interface and a surfactant

23

monolayer at the gas-liquid shell interface as shown in Figure 2 (Sebba, 1987). This
liquid shell has been likened to the liquid ﬁlm that surrounds a soap bubble blown into air
(Sebba, 1987). The surfactant molecules in the outer bilayer impart an electrical double
layer that reduces bubble coalescence through electrical repulsion (Sebba, 1987). The
electric double layer of bubbles created in aqueous solutions of surfactant has been
shown to be quite signiﬁcant, ranging from —250 mV with a strong, ionic surfactant
(Usui, 1981), to 60 mV with a weak, non-ionic surfactant (Laskowski, 1989), (Collins,
1978). The zeta potential, a measurement of the surface charge on a bubble or particle,
has also been shown to decrease with increasing bubble size (Usui, 1981). The
signiﬁcance of the zeta potential in microbubble dispersions is the stability provided to
the microbubbles through the electric charge, and the shorter range van der Waals forces.
It can be shown that the repulsive forces between colloids is proportional to the surface

potential (Schramm, 1992).

24

Figure 2: Schematic of a microbubble

Microbubbles have been used in aerobic fermentations of S. cerevisiae that were
generated with only the natural surfactants produced by the bacteria. The mass transfer
coefﬁcients obtained from this microbubble-sparged fermentation were found to be
independent of impeller rate and 4 times that of conventional sparging at low impeller
rates (Kaster, 1990). The independence of power input on the mass transfer is an added
beneﬁt of microbubbles in that a minimal impeller rate is needed to only maintain
adequate mixing and high power input is not necessary to promote bubble breakup.
Microbubbles have also been used for the bioremediation of soil to increase the amount
of oxygen retained in the soil and to promote increased mass transfer to ﬂowing
groundwater (Michelsen, 1991). Jenkins et al. (1993) found increased oxygen utilization
using microbubbles over conventional oxygenation methods during in situ biodegradation

of xylene in soil columns.

25

Another major use for microbubbles has been in ﬂoatation. Microbubbles have
been used to harvest S. cerevisiae from a suspension (Save, 1995). CGA offers a rapid
and efﬁcient method for the recovery of microorganisms, greater than that obtained
through conventional foam fractionation. It was also found that surfactant type played a
signiﬁcant role in developing attractive forces between the cell and CGA. Anionic
surfactants, such as sodium dodecyl sulfate (SDS), did not promote good attachment to
cells while hydrophobic cationic surfactants, such as cetyl pyridinium chloride (CPC)
gave high separation factors (Save, 1995). Models have been developed to describe the
separation of microorganisms by CGA (Save, 1994). CGA have also been proposed to be
used for the recovery of proteins through interaction between the aphron and the protein
due to electrostatic and hydrophobic forces. The aphron phase would then rise due to
buoyancy and thereby separate proteins (J auregi, 1996).

The ﬂoatation process has also been used extensively in clariﬁcation and washing.
A review of microbubble ﬂoatation processes has been written by Solari et a1. (1992).
CGA have been used to clarify pahn oil mill efﬂuent, suspensions of algae, and
suspensions of inorganic minerals, primarily through electrostatic or hydrophobic
interactions (Subramaniam, 1990). CGA have extensively been used for the washing of
soils to remove oily wastes (Roy, 1992a); (Roy, 1994), the separation of heavy metals
(Cabezon, 1994), the separation of organic dyes (Roy, 1992b), and solvent sublation
(Caballero, 1989).

3.3.2 Colloidal Liquid Aphrons
A similar type of dispersion is a colloidal liquid aphron (CLA). CLAs have an

organic or oil phase in an aqueous environment. CLAs have the same structure as

26

microbubbles (Sebba, 1984), and their size ranges from submicron to 50 um in diameter
(Zhang, 1996a). In order to produce CLA, the oil (or internal) phase has to be brought to
a small size, and these dr0plets must be surrounded by the soapy ﬁlm. This can be
accomplished by spreading the oil phase on a dilute surfactant solution. For the oil to
spread on the surfactant solution, the oil must have an oil soluble surfactant present at a
concentration that is just sufﬁcient to produce a spreading coefﬁcient greater than the
surface pressure produced by the surfactant dissolved in the aqueous phase.

CLA have been found to be extremely stabile. Zhang et al. (1996a) found that
after 230 days of storage, the maximum in the peak size shifted from 11 pm to 18 pm for
kerosene in water CLAs. CLAs allow for very high concentrations of the oil phase to be
dispersed in water. Phase volume ratios (PVR) up to 20 have been prepared without
phase inversion or coalescence from kerosene (Sebba, 1984). CLAs have been used for
predispresed solvent extraction in a kerosene-water system (Matsushita, 1992) and in
enzyme extraction (Save, 1993). They have also been used to separate a hydrophobic
organic dye from water through a combination CGA/CLA ﬂoatation process (Zhang,
1996b). Finally, in liquid-liquid extraction, an increase of 16 fold in the mass transfer rate

over conventional extraction was obtained using CLA (Matsushita, 1992).
3.4 Coalescence

Bubble size in a stirred vessel is dependent on a balance between the coalescence
and break-up rates in the vessel. Coalescence is the process by which two (or more)
bubbles, particles, drops, etc come together to with sufﬁcient energy and remain together
for a long enough time for a single unit to form. Breakage (or break-up) is the process by

which sufﬁcient energy is applied to shear the unit into multiple daughter units. The

27

coalescence and breakage in complex systems, such as fermentation broths are functions
of many parameters, such as surface characteristics of the bubbles or drops, dynamic
surface tension, bulk and dispersed phase properties, energy dissipation, size, etc.

In the analysis of dispersive systems, the population-balance-equation (pbe)
approach has been used extensively to model coalescence and breakage (Coulaloglou and
Tavlarides (1977), Das et al. (1987), and Prince and Blanch (1990)). This approach
describes the history of a population such as size, age, and concentration, during the
course of interaction events between particles, bubbles, or drops, and with the
surrounding environment. A pbe model is also effective in that it can accommodate
continuous mass transfer between phases, ﬂow in and out of the systems, as well as
coalescence and breakage events. This model consists of three major parameters, the
breakage frequency, the collision frequency and the collision efﬁciency.

3.4.1 Breakage Frequency

The breakage frequency is how often bubbles and drops undergo a breakage
event. Breakage has been proposed to occur through a number of mechanisms such as
drop elongation in a shear ﬂow ﬁeld (Taylor, 1934), turbulent pressure ﬂuctuations
(Hinze, 1955), relative velocity ﬂuctuations (Narismhan et al., 1980) and drop-eddy
collisions (Coulaloglou and Tavlarides, 1977). A number of mechanistic models have
been developed that provide simple mathematical expressions for drop breakage rates.
These models are based on the physical properties of the system such as drop diameter,
interfacial tension, and dispersed phase density, the geometry of the vessel, and the

energy provided to the dispersion by agitation.

28

3.4.2 Collision Frequency

The collision frequency is the rate at which bubbles or drops collide. Commonly
the bubble-bubble (or drop-drop) collision frequency is modeled assuming that the
bubbles behave like gas molecules in a turbulent ﬂow (Coulaloglou and Tavlarides,
1977) and that their collision processes can be described by an analogy to the kinetic
theory of gasses (Kennard, 1938). Making these assumptions, the collision frequency
becomes a function of the bubbles' size, their velocities (and therefore the energy
dissipation in the system) and the number of bubbles in the system.
3.4.3 Coalescence Efficiency

The coalescence efﬁciency is the percentage of collision events in a system that
will result in a coalescence event. The coalescence efﬁciency is a function of two
characteristic parameters: the contact time and the coalescence time. Once bubbles have
collided, they will stay in contact for some time period, known as the contact time, in
which they will either coalesce or separate. The contact time between bubbles has
typically been determined to be dependent on the energy dissipation in the system and the
bubbles' sizes (Coulaloglou and Tavlarides, 1977). Coalescence occurs if the contact time
is long enough that the liquid ﬁlm between the two bubbles drains away until a critical
ﬁlm thickness where rupture occurs. This is the coalescence time (Tsouris and
Tavlarides, 1994). Therefore, coalescence will occur when the contact time is greater
than the coalescence time.

A number of different models for the coalescence efﬁciency have been proposed.
Coulaloglou and Tavlarides (1977) used an expression that was developed from models

for ﬁlm drainage between pairs of drops immersed in an incompressible stagnant viscous

29

liquid. Sovova (1981) suggested that the model used by Coulaloglou and Tavlarides
(1977) favored the coalescence of smaller drops and replaced it with an expression that
describes the ratio of the interfacial energy in the system to the energy of collision. It has
been suggested by Tsouris and Tavlarides (1994) that this form of the coalescence
efﬁciency favors the coalescence of larger drops. Das et al. (1987) introduced a white—
noise model, which considers the ﬁlm drainage between two colliding drops as a
stochastic process driven by a suitably idealized random process for the ﬂuctuating force.
According to this model, the drops are considered nondeformable, and the critical
thickness of the ﬁlm before rupture is assumed to be speciﬁc for a given system.
Muralidhar and Ramkrishna (1986) employed a time-scale analysis in order to understand
the signiﬁcance of factors affecting drop coalescence. They considered both deformable
and nondeformable drops and under which conditions the white-noise model and a band-
limited model are valid. Muralidhar et al. (1988) studied the coalescence of rigid drops in
a stirred dispersion and developed a colored-noise model. The white noise, band-limited,
and colored-noise models have a large number of parameters that are difﬁcult to measure
or estimate (Tsouris and Tavlarides, 1994) and are computationally difﬁcult. Tobin et al.
(1990) studied the effect of drop size on coalescence frequencies and concluded that the
coalescence of small drops is not as frequent as the model of Coulaloglou and Tavlarides
(1977) predicts. Tsouris and Tavlarides (1994) suggest a kinetic collision mechanistic

model to describe the coalescence.

30

4. Formation and Stability of Microbubbles

4.1 Introduction

Fermentations that involve a gaseous substrate are inherently rate-limited by mass
transfer from the gaseous to the liquid phase. Synthesis gas fermentations are a primary
example of such mass-transfer-limited fermentations. The traditional approach to enhance
gas-to-liquid mass transfer is to increase the impeller rate, thereby increasing the
interfacial area available for mass transfer. However, this approach results in a dramatic
increase in power consumption, especially for large-scale systems, because power
consumption is proportional to the impeller rate to the third power and the impeller
diameter to the ﬁfth power (McCabe et al., 1985). Microbubble dispersions offer an
alternative, providing high interfacial area with the potential for low power input. In
aerobic fermentations with yeast, the transport of oxygen from a gas to a liquid, reported
in terms of kLa, was found have a 4-fold increase in using microbubble sparging over
conventional air sparging (Kaster, 1990).

In order to study microbubbles in fermentations, it is ﬁrst necessary to identify
criteria that deﬁne parameters such as stability and formation. The stability parameters
have been suggested by Amiri and Woodburn (1990) to be dependent on the drainage rate
of the liquid ﬁlm between microbubbles. The formation rate of microbubbles, and the
size distribution are suggested to be dependent on the salt concentration or ionic strength

of the solution (J auregi, 1996)

31

4.2 Materials and Methods

4.2.1 Microbubble Generator
Microbubble dispersions were formed using a spinning-disc device ﬁrst described by
Sebba (1985) and shown schematically in Figure 1. This device employs a high—speed
electric motor (Talboys #37830, Cole Partner, Chicago, IL) to spin a 5-cm-diameter by l-
cm-thick disk at speeds above 4000 rpm. Stationary bafﬂes located within 5 mm of the
spinning disk result in a localized high-shear zone. The stainless-steel disk and bafﬂes are
mounted in a 6 L fermentation vessel with the motor attached to the headplate. The
generator was adjusted to determine the optimal conﬁguration in terms of disk placement
based on visual observation of microbubble formation.
4.2.2 Bubble Size Distributions

Bubble-size distributions were measured with a Malvem Mastersizer (Malvem,
Inc.) particle size analyzer, which uses a light scattering technique (Chaphalkar, 1993).
Bubbles were loaded into the recycle ﬂow 100p containing water with surfactant until an
obscuration of 8-12% was obtained. Data were taken for 60 seconds. The Mastersizer
uses a light-scattering technique that gives accurate size distribution data within seconds
of injecting the sample. In contrast, microscope-based image-analysis methods are
relatively slow and require many individual measurements to give statistically
meaningful results.
4.2.3 Formation Studies

In the formation-rate experiments, the dispersion was considered fully formed
when an equilibrium foam volume was obtained. Dispersions were formed at 7000 rpm.

Experiments were done with three types of surfactant: non-ionic Triton X-100 (Sigma

32

Chemical Co., St. Louis, MO), anionic sodium dodecyl sulfate (SDS) (Sigma Chemical
Co.) and cationic cetyl pyridinium chloride (CPC) (Sigma Chemical Co.). Salt (NaCl)
was added to the microbubble generator (MBG) in runs with Triton to determine its
effects on microbubble formation.
4.2.4 Stability Studies

In the drainage and stability experiments, the microbubble dispersion was
generated, poured into a 1 L graduated cylinder, and allowed to drain. The heights of the
air-foam and foam-liquid interfaces were measured as a ﬁrnction of time. Runs with salt
(NaCl) dissolved in the liquid phase were done in a similar fashion.
4.2.5 Immobilization Studies

Immobilized microbubbles were made by generating by using a 2.0% (w/v)
solution of alginic acid with the addition of 240 mg/L of Tween 20 surfactant. The alginic
acid solution was prepared by allowing the material to mix for 24 hours on a magnetic
stirrer until homogeneous. Microbubbles were then formed from the alginic acid solution
in the MEG. The expected 3-fold volume expansion was not obtained; rather a 2-fold
expansion was obtained. The solution was then dripped into a 25 g/L calcium chloride
(CaCl2) solution that was agitated by a magnetic stirrer. The immobilized microbubbles

were allowed to cure for 30 nrinutes prior to removal from the CaCl2 solution.
4.3 Results and Discussion
4.3.1 Particle Size Distribution
The number-averaged bubble diameter was 58.9 pm for Triton X-100 at a

concentration of twice that of the CMC (135 mg/L) and a temperature of 25°C. The

average bubble size measured by the Mastersizer is in the range of literature values of 40

33

to 80 um (Longe, 1989). A sample of the data obtained from the particle size analyzer is
shown in Figure 3 below. The bubble size distribution was unaffected by the distance the
spinning disk was to the bafﬂes within 5 mm. The results from those experiments are

summarized in Table 1.

12.

10.

Percentage
O)

 

 

 

 

0 50 100 150 200

Bubble Size (um)

Figure 3: Bubble size distribution using dynamic light scattering

Table 1: Effect of disk distance on bubble diameter

 

 

Disk Distance from Bafﬂes Bubble Diameter
1 mm 57.50 um
3 mm 68.55 pm
5 mm 54.45 pm

 

 

 

34

4.3.2 Formation Studies

Figure 4 shows the equilibrium formation time for microbubble dispersions as

function of surfactant type and dimensionless surfactant concentration (DSC), which is

deﬁned as the ratio of surfactant concentration to its critical micelle concentration.

Time of Microbubble Formation (min

  
 
 

 

  

 

 

 

 

 

16 .
14 _ -a—Triton, non-ionic
+808, anionic
12 .. +CPC, cationic
10 .
8 .
6 .
4 . \Z~\ .
‘0
2 .
0 : : : : : : : : :
O 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Dimensionless Surfactant Concentration

Figure 4: Equilibrium formation time for microbubbles

35

Figure 5 shows the effects of the addition of NaCl to the generation media on the

equilibrium formation time.

16..
14 ..
12 u-

10.,

   
 

 

-5- RO Water

 

 

 

Time of Microbubble Formation (min
CO

 

 

6 .. —a—0.08 g/L NaCl
+0.8 g/L NaCl
4 ..
2 "r
0 : : : : : : : i :
o 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Dimensionless Surfactant Concentration
Figure 5: Equilibrium formation time in the presence of salts
Experiments were conducted at DSC values down to 0.25, but stable dispersions did not
always form. If a stable dispersion did not form after 20 minutes, no data are shown for
that concentration. A stable dispersion was indicated by a three-fold volume expansion
during foam formation.

The surfactant concentration is an important variable in the formation of stable
dispersions. There is believed to be a double layer of surfactant around each nricrobubble
(Sebba, 1987); however, when the surfactant concentration is much below the CMC,
stable microbubble dispersions do not form. In such cases, there is insufﬁcient surfactant
present to stabilize the large amount of interfacial area (Longe, 1989). Figure 4 indicates

that as the surfactant concentration was increased above the CMC, the dispersion

36

formation time decreased asymptotically to a value that is characteristic of the surfactant
used. This trend is thought to be due to saturation of the surfactant-adsorption capacity of
the nricrobubbles. Further addition of surfactant has a negligible effect because the
additional surfactant molecules remain suspended in the ﬂuid ﬁlm surrounding the
microbubbles. For ionic surfactants such as CPC and SDS, the amount of surfactant
necessary to achieve this asymptotic formation time was approximately the CMC. For
non-ionic surfactants, the asymptote occurred at a higher concentration. This result may
be due in part to CMCs of ionic surfactants typically being higher than that of non-ionic
surfactants. In this study the CMCs were 0.24 mM for Triton, 0.90 mM for CPC, and
8.27 mM for SDS. Ionic surfactants need to overcome the electrical repulsion of charged
groups to form micelles (Rosen, 1989). The number of surfactant molecules present at the
CMC for ionic surfactants is therefore greater than that for non-ionic surfactants. The
addition of an electrolyte changes the CMC for ionic surfactants (Rosen, 1989),
presumably because charge shielding reduces intermolecular repulsion. However, salts
have little effect on the CMC of non-ionic surfactants (Sebba, 1987). This trend is
reﬂected in Figure 5, in which dispersion-formation time was found to be independent of

salt concentration.

37

4.3.3 Stability Studies

Figure 6 shows a typical time course for the drainage and stability experiments for

 

 

 

  

 

 

 

 

a SDS foam with a DSC of 2.
1200 ..
*Foam
1000 " ““““““ . . , ‘ ‘ . +|nterface
.. 800 .. ““““
.l
.5.
E, 600 w
2
>°
400 ..
200 ..
0 " : i : : : :
0 10 20 30 4O 5O 60

Time (min)

Figure 6: Foam and Foam-Liquid interface level in drainage experiments

38

Figure 7 shows the effects of surfactant concentration on initial gas void fraction
(eg°). The value of ago was unaffected by NaCl in the range of 0.2 to 2.4 g/L for all

surfactant concentrations tested (data not shown).

 

 

 

 

 

 

1 .-

0.9 .-

0.8 u.
c
.9
*5 0.7 ..
E W0
U- 0.6 -- 1'
E
o
> 0-5 .-
3 o 4
(D ' " -a-Triton, non-ionic
E 0.3 .. —A-SDS, anionic
“
'E -o-CPC, cationic
_ 0.2 .-

Oo1 .-

0 : 'ﬁ : 1'. F i
0 1 2 3 4 5 6

Dimensionless Surfactant Concentration

Figure 7: Initial foam gas void fractions of microbubbles

39

Figure 8 shows foam stability, deﬁned as the ratio of the volume of liquid drained

after four minutes to the initial volume of foam, as a function of surfactant type and

  
  
  

 

 

 

 

 

 

   

 

 

 

 

 

 

concentration.
0.7 .-
0.6 ..
+Triton, non-ionic
0-5 -- +Triton, with 0.08 g/L NaCl
,2 +CPC, cationic
:73 0.4 .. -e-SDS, anionic
E
(D
E 0.3 ..
as
o
u.
0.2 ..
0.1 J- A # ﬂ
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Dimensionless Surfactant Concentration

Figure 8: Microbubble Stability

Microbubble dispersions are an aggregate of spherical bubbles surrounded by a
thin liquid ﬁlm called the lamella. When the dispersion is ﬁrst formed, the microbubbles
are spherical, and the lamella is thick. Such dispersions are termed 'wet' and have good
stability (Sebba, 1987). As the dispersion is allowed to drain, the liquid in the lamella
drains into the plateau borders, regions where several bubbles meet. The liquid in the
lamella drains in two different stages. Drainage occurs by gravity while the lamella are
still thick and the microbubbles are still spherical. As the lamella thins, the microbubbles

lose their spherical shape and begin to become polyhedral (Sebba, 1987). At this stage,

40

drainage of the dispersion is a result of surface-tension differences that depend on
pressure differences throughout the lamella. The pressure differences arise from
differences in the radius of curvature of the lamella. The greater the bubble size in the

dispersion, the greater the drainage rate as a result of surface tensions differences (Vold,

1983), (Rosen, 1989). At some critical thickness of the lamella (50-100 1:1), the
surrounding ﬁlm will rupture (Rosen, 1989).

When foam is poured into the graduated cylinder, buoyancy also contributes to
foam settling. Microbubble dispersions will "cream" (i.e. faster rising bubbles will
migrate to the surface). The time required for crearning is depends on the rise velocity of
the bubbles, which, according to Stokes law is proportional to the bubble radius squared
(Vold, 1983). The crearning process leads to a gradient in bubble size across the height of
the column. Amiri and Woodbum (1990) have shown that buoyancy effects result in a
gradual increase in gas void fraction and bubble diameter from the bottom to the top in a
column of microbubble dispersion.

Another factor contributing to the degradation of microbubble dispersions is
"bubble ripening" (i.e. the grth of larger bubbles at the expense of smaller ones). The

difference in the interior pressures (AP) between two bubbles having radii R1 and R2, is

given by the Laplace equation,

AP=20(—1—-—1—) (10)
R1 R2
where 0' is the surface tension. Because the pressure is greater inside smaller bubbles,
there will be net transport of gas molecules through the liquid phase ﬁom smaller to

larger bubbles. As the larger bubbles grow, they rise more rapidly and thus migrate to the

top of the foam column.

41

The initial gas void fraction, ego, is a measure of the amount of gas initially
trapped in the microbubble dispersion. Figure 7 shows ego to be independent of surfactant
type and concentration and approximately constant. The value of eg", between 0.65 and
0.70, approaches 0.741, the tightest packing arrangement for monosized spheres in a
face-centered cubic cell (Amiri, 1990), (Brown, 1981). The theoretical void fraction
based on a body-centered cubic cell is 0.68 (Brown, 1981), (Weaire, 1993). For the non-
ionic surfactant, ago did not change with the addition of sodium chloride. The addition of
salt also has little effect on the CMC for non-ionic surfactants, as mentioned earlier
(Sebba, 1987).

Spherical bubble foams (also known as early or wet foams) are very stable, and
will break only when the bubbles rise to the surface under the inﬂuence of gravity. As the
foam begins to cream and drain, the bubbles grow larger and change their shape from
spherical to polyhedral. Polyhedral bubbles can achieve a tighter packing; thus the gas
void fraction increases with not only height along the column but also with time.
Polyhedral foams (also known as late or dry foams) are much less stable. The lamellae of
these foams thin as they drain and break when they can no longer resist the upward
movement of the less dense gas trapped in the cells. The gas void fraction at which foams
typically burst is 0.89 (Weaire, 1993). Foam stability depends primarily on two factors:
the rate of drainage of liquid from the lamella and strength of the ﬁhn that encapsulates
each bubble (Sebba, 1987). At concentrations below the CMC, foam stability was found
to increase with increasing surfactant concentration. At concentrations above the CMC,
foam stability did not change appreciably with surfactant concentration. A possible

explanation for this observation is that as the concentration of surfactant in the liquid

42

 

 

phase increased, the density of surfactant adsorbed on the interface also increased until
saturation was reached.
4.3.4 Immobilization Studies

Successful immobilization of microbubbles with a size range of 50 to 80 um
(observed by electron microscopy) was obtained through the usage of calcium alginate. A
large number of easily distinguishable microbubbles was seen in each sphere. These
immobilized microbubbles have potential for future studies where changes in bubble size
could be observed. They also have potential uses in the efforts to probe the outer structure
of a microbubble. The alginate microbubble foam drainage (without curing) was
measured and is presented in Figure 9 below. The lamella drains at a more constant and
slower rate than microbubbles formed without alginate most likely due to increased
viscosity in the surrounding lamella. Increased viscosity slows the rate of coalescence in

the system by increasing the coalescence time of microbubbles (see Chapter 9).

43

1200 ..

 

 

 

 

 

 

 

         

 

1000 1N
v v v v : t 3 Cw

800 ..
Z?
.5.
g 500 __ +Foam Volume
2 + Liquid Volume
§

400 ..

200 .

0 : i i : i
0 5 10 15 20 25 30 35 40 45
Time (min)

Figure 9: Drainage experiment using alginate microbubbles

4.4 Conclusions

The size distribution of microbubble dispersions can be rapidly measured using a
light-scattering method. The number-averaged diameter for the microbubbles used in this
study was 60 um. Formation times of microbubble dispersions decreased with increasing
surfactant concentration to an asymptotic value that varied with surfactant type. This
asymptotic value was usually achieved at surfactant concentrations around the CMC.
Foam stability also exhibited saturation behavior; stability increased asymptotically with

surfactant concentration to a constant value near the CMC.

Microbubble foams were found to have a constant initial gas void fraction that
was independent of surfactant concentration and type. The experimental eg" value of 0.66

approaches the theoretical packing limit for mono-sized spheres. Salt concentrations from

44

0 to 2.4 g/L had virtually no effect on either the void fraction or the formation time for
the non-ionic surfactant.

Finally, by increasing the viscosity of the continuous phase, a decreased drainage
rate was seen, and therefore increased bubble stability. It was also possible to immobilize

microbubble in a calcium alginate matrix for later future studies.

45

5. Surfactant Biocompatibility

5.1 Introduction

The obligate anaerobe Butyribacterium methylotrophicum consumes carbon
monoxide, CO, to produce acetate, ethanol, butyrate and butanol (Worden, 1989) as
described previously in Chapter 2. Its broad range of useful products and its ability to
grow on 100% CO make B. methylotrophz’cum one of the most versatile
unicarbonotrophs. One of the key disadvantages of using this microorganism is low
product concentration and slow growth rates (Grethlein, 1991b). Another key
disadvantage to fermentation is that most fermentations are gas-to-liquid mass transport
limited (Worden, 1989).

Microbubbles have the potential to signiﬁcantly increase the rate of gas-to-liquid
mass transfer. Microbubbles are made in the presence of a surfactant that acts to stabilize
microbubbles and reduce the rate of coalescence through imparting an electric charge to
the bubble’s surface. As determined in Chapter 4, the addition of a surfactant is necessary
to generate a microbubble dispersion. Results ﬁom Chapter 4 indicated that the
concentration of the surfactant should be near or above its critical micelle concentration
(CMC) in order for a stable dispersion to form. To be of use for fermentation, the
surfactant should not be toxic to cellular growth, inhibit the formation of key products, or
signiﬁcantly change fermentation parameters (such as pH)

This chapter examines the growth and product formation of B. methylotrophicum
during CO fermentations in the presence of surfactants that are suitable for generating
microbubble dispersions. This information is needed to select surfactants for use in

microbubble-sparged synthesis gas fermentations.

46

5.2 Materials and Methods

5.2.1 Culture Techniques

All chemicals and vitamins were obtained from Sigma Chemical Company (St.
Louis, MO), except for sodium dodecyl sulfate which was obtained from Boehringer
Mannheim (Mannheim, Germany). The nitrogen (N2) and CO gases were purchased from
AGA Gas and Welding (Lansing, MI). Butyribacterium methylotrophicum was obtained
from the Michigan Biotechnology Institute (Lansing, MI) and was grown anaerobically at
37 °C in a phosphate buffered (PB), sulﬁde-reduced medium prepared as previously
described (Kerby, 1987) on 100% carbon monoxide. Table 2 gives the media components
and their concentration. Resazaurin was used as an oxygen indicator in maintaining stock
cultures but was not used in the experimental fermentations due to interference with
measuring optical density. The medium was dispersed into 125 mL serum bottles
(Wheaton, Millville, NJ) at 50 mL per bottle and sealed with butyl rubber stoppers and
aluminum crimps (Wheaton, Millville, NJ). For the experimental runs with surfactant
present in the media, the surfactant was added to the media prior to autoclaving. A 1%
innoculum of an actively growing culture of B. methylotrophicum was used. The cultures
were incubated in an Innova 4000 shaker (New Brunswick Scientiﬁc, New Brunswick,

NJ) at 100 rpm in the dark.

47

Table 2: Phosphate buffered basal salts media composition

 

 

Component Concentration
NaCl 0.9 g/L
MgCl2-2H2O 0.2 g/L
CaCl2-2H2O 0.1 g/L
NH4C1 1.0 g/L
Yeast Extract 1.0 g/L
Trace Mineral Solution 10 mL/L
Vitamin Solution 10 mL/L
Phosphate Stock 25 mL/L
2.5% Na2S-9H2O Stock 25 mL/L
0.2% Resazurin 1.0 mL/L

 

 

 

The composition of the trace mineral solution is given in Table 3, the composition of the
Vitamin solution is given in Table 4, and the composition of the phosphate stock is given

in Table 5.

48

Table 3: Composition of trace mineral solution

 

 

 

Component Concentration
Nitrilotriacetic acid 12.8 g/L
FeSO407H2O 0.10 g/L
MnCl204H2O 0.10 g/L
CoCl206H2O 0.17 g/L
CaCl202H2O 0.10 g/L
ZnCl2 0.10 g/L
CuCl20H2O 0.02 g/L
H3303 0.01 g/L
NaMbO4 0.01 g/L
NaCl 1.00 g/L
Na2Se03 0.017 g/L

NiSO4o6H2O 0.026 g/L

 

49

 

Table 4: Composition of vitamin solution

 

 

Component Concentration
Biotin 2.0 mg/L
Folic acid 2.0 mg/L
Pyridoxine HCl 10.0 mg/L
Thiamine HCl 5.0 mg/L
Nicotinic acid 5.0 mg/L
Pantothenic acid 5.0 mg/L
Cyanocobalamin 0.1 mg/L
p—aminobenzoic acid 5.0 mg/L
Thioctic acid 5.0 mg/L
Riboﬂavin 5.0 mg/L

 

 

 

Table 5: Composition of phosphate stock solution

 

 

Component Composition
KH2PO4 150 g/L
K2HPO4 290 g/L

 

 

 

5.2.2 Culture Analysis
5.2.2.1 Gas Chromatography

Liquid samples (2 mL) were taken throughout the duration of each experiment.
To prepare samples for product analysis, 10% (v/v) of 1 M phosphoric acid was added.

After a ten-minute incubation at 37 °C, the samples were centrifuged and analyzed by gas

50

chromatography for acetate, ethanol, butyrate, and n-butanol. The separation was done
with a Perkin-Elmer Autosystems GC (Perkin Ehner, Norwalk, CN) with a Hayesep R, 6’
x 'A” x 2 mm deactiglass column (Alltech, Waukeegen, WI) and a ﬂame-ionization
detector. The injector, column, and detector were 220 °C, 170 °C, and 220 0C
respectively. The mobile phase was helium at 25 mL/min.
5.2.2.2 Spectroscopy

Growth was analyzed using a Lambda 3 spectrophotometer (Perkin Elmer,
Norwalk, CN) at 660 nm immediately after withdrawing the sample. A calibration curve
of optical density versus dry weight was constructed. After measuring optical density, the
samples were vacuum ﬁltered through a tared 0.22 pm ﬁlter disk (Millipore). The
samples were then dried at 85 °C for 24 hours. The ﬁlter was allowed to cool in a
desicator for 30 nrinutes prior to weighing.
5.2.2.3 pH Measurements

The pH was monitored through a phenol red spectroscopic method. A 1 mL
sample of cells was centrifuged in a Fisher Microcentrifuge 235C (Fisher Scientiﬁc,
Chicago, IL) at 15,000 rpm for 10 minutes. Phenol red was then added to the sample to
20 uM, and the optical density was measured at 560 nm to determine the pH of the
sample. The phenol red assay was calibrated using larger samples with a pH electrode.
5.2.3 Surfactant Studies

The primary surfactants used for this study were Tween (polyoxyethylene
sorbitans) and Brij (polyoxyethylene alcohols). The structures of these surfactants are

shown in Figure 10. The number of ethylene oxide adducts is indicated by EC.

51

(OCHZCH2)n40H
CH E0adducts=20=n1+n2+n3+n4
0 /\ . __
/ \ Tween 20. R — monolaurate
HZC CH CHZ(OCH2CHZ)TI30CR Tween 40: R = monopalmitate
\ / Tween 80: R = monooleate
HC— CiH

H0(CH2CH20>n1 (OCHZCHanZOH

CH CH O CH CH O H 3'7752: "=2
3( 2)is l 2 2 ln Brij56: ":10
321758: n=20

Figure 10: Chemical Structure for Tween and Brij surfactant (Ash, 1981).
DSC values up to 3 were used because previous studies (Chapter 4) indicated that
microbubble dispersions needed DSC values of at least 1 for the formation of stable
dispersions. Increasing DSC values above 3 had no effect on the dispersion’s stability,
presumably because the surfactant absorption saturation value of the available gas-liquid
interface had been reached. The critical micelle concentrations and aggregation numbers

for the surfactants used in these experiments are listed in Table 6 (Ash, 1981).

52

Table 6: Surfactant critical micelle concentration

 

 

 

Surfactant Critical Micelle Concentration
Brij 52 < 7 uM
Brij 56 7 uM
Brij 58 77 uM

Tween 20 60 mg/L

Tween 40 29 mg/L

Tween 80 13 mg/L

 

53

 

5.3 Results and Discussion

5.3.1 Dry Weight Calibration Curve

The dry weight-optical density calibration curve is given in Figure 11.

0.0005 '1'
0.00045 ..
0.0004 ..
0.00035 -.
0.0003 ..
0.00025 ..
0.0002 ..
0.00015 ..
0.0001 ..
0.00005 .

  
  
  
  
  
  
  
  
 
 

y = 0.000742X + 0.000013
R2 = 0.973290

Cell Dry Weight (gImL

 

0 0.1 0:2 0:3 0:4 0:5 0.6 0.7
Optical Density (at 660 nm)
Figure 11: Dry weight calibration curve

5.3.2 Tween Surfactants
Figure 12 shows growth curves for B. methylotrophicum with Tween surfactants
as a function of surfactant concentration. The control culture containing no surfactant was
prepared and inoculated at the same time and under the same conditions as the
experiment bottles. The medium for the entire experiment was made from the same
batch. The data in Figure 12 are the average of triplicate runs. Figure 13 shows the
speciﬁc growth rate of B. methylotrophicum determined from the exponential growth

phase data in Figure 12.

54

Cell Concentration (gIL)

0.9 ..
0.8 u
0.7 ..
0.6 ..
0.5 ..
0.4 ..
0.3 ..
0.2 ..

0.1 ..

 

 

 

—e—Control

—o—Tween 20, DSC=1
—e—Tween 20, DSC=2
+Tween 20, DSC=3
- o- .Tween 40, DSC=1
- 0- .Tween 40, DSC=2
. A. .Tween 40, DSC=3
—o—Tween 80, DSC=1
+Tween 80, DSC=2
+Tween 80, DSC=3

 

 

 
 
 
 
 

: ,G"O
- = "
/\"'°~
r. = ‘ 3

150 200 250 300 350
Time (hours)

Figure 12: Growth of B. methylotrophicum in batch bottles with Tween

55

 

0.015 ..

 

-e—Tween 20
0.01 .1. _a—Tween 40
+Tween 80

Specific Growth Rate (h '1)

 

 

0.005 ..

I l I I I
I I I I

0 0.5 1 1.5 2 2.5 3 3.5
Dimensionless Surfactant Concentration

 

Figure 13: Speciﬁc growth rate of B. methylotrophicum with Tween

None of the Tween surfactants strongly inhibited growth of B. methylotrophicum
in batch bottle fermentations. However there did seem to be an effect of the length of the
hydrophobic end of the surfactant on the growth curves. Tween 20 has a lauric acid group
(C12), Tween 40 has a pahnitic acid group (C16), and Tween 80 has an oleic acid group
(C18-1). In general, the shorter the chain length, the lower the growth rate (see Figure
10). However, for the Tween surfactants, most cultures obtained approximately the same
ﬁnal cell density. It has been suggested that longer chain lengths slow surfactant diffusion
into the cellular membrane and thereby result in lower toxicity (Schwuber, 1980). Tween
surfactants have also been found to be non-toxic to other types of culture systems (e.g.

soy and carrot suspension cultures) and in some cases Tween 20 actually enhanced the

56

growth of the culture (T.T. Ames, unpublished data). Higher surfactant concentrations
(10 to 20 DSC) were found to be toxic to the plant suspension cultures.

There was no inhibition from the products formed at the concentrations seen in
this study (Grethlein, 1990). The deviations from typical exponential growth are believed
to be due to mass-transfer limitations of the gaseous substrate.

5.3.3 Brij Surfactants

Figure 14 shows the growth of B. methylotrophicum in the presence of Brij
surfactants. The control experiments were performed in the same manner as the Tween
run. Similarly, the data in Figure 14 are an average of triplicate runs. Figure 15 shows the

speciﬁc growth rate as a function of Brij surfactant concentration.

1..

 

—a—Control
+Bri, 52, DSC=1 e

0-9 " +36, 52, DSC=2 o
0 8 +36, 52, DSC=3 - ,. .~ 4’
. .. . o. .36, 56, DSC=1 Ir - -

 
 
 
 
 
 

- o- .Brij 56, DSC=2

 

 

 

 

 

 

3
B: 0.7.. .x..Bri, 56, DSC=3 .'
V +36, 58, DSC=1 _ ,'
S 05 +Bri, 58, DSC=2 ”a
g ' .. +Bri, 58, DSC=3 "
h
*5 0.5..
0
2 04
o . 'P
o
= 0.3..
0
o
0.2 .. '1 A
,, ___.-o
0.1.. , z; A .--'c-> _ .
MA.:‘2:'.A """" ﬁ---A.‘-A-"A-— A
O l . ‘ l l 1 I
0 50 100 150 200 250 300

Time (hours)

Figure 14: Growth of B. methylotrophicum in batch bottles with Brij

57

0.05 ..
0.045 ..
0.04 ..
0.035 ‘4
0.03 ..
0.025 ..
0.02 ..

0.015 ..

Specific Growth Rate (h")

-e- Brij 52
-¢— Brij 56

0.01 ..

 

0.005 4 +30 58

 

l I I
I

1.5 2 2.5 3 3.5
Dimensionless Surfactant Concentration

0 i e
0 0.5 1

Figure 15: Speciﬁc grth rates of B. methylotrophicum with Brij

The Brij surfactants did strongly inhibit growth in some cases, but the inhibitory
effect again depended on the chain length. The Brij surfactants are polyoxyethylene
(polyethylene glycol -PEG) alcohols (see Figure 10) and had the following characteristics
(in order of increasing chain length): Brij 52 - PEG(2) Cetyl alcohol, Brij 56 - PEG(10)
Cetyl alcohol, and Brij 58 - PEG(20) Cetyl alcohol. As shown in Figures 14 and 15, the
speciﬁc growth rate and ﬁnal cell densities are much lower than those for the control for
increasing amounts of the two longer chain surfactants, Brij 56 and Brij 58. In general,
the higher the surfactant concentration the lower the speciﬁc growth rate and ﬁnal cell
density. The Brij surfactants are apparently more inhibitory to the growth of B.
methylotrophicum in concentrations necessary to form microbubbles than are the Tween

surfactants.

58

 

 

Growth experiments were also done with a few ionic surfactants (e.g. sodium
dodecyl sulfate, cetyl pyridinium choride, and sodium dodecyl benzene sulfonate). The
growth of B. methylotrophz'cum was strongly inhibited by these surfactants even at the
lowest concentrations tested (0.5 DSC) (data not shown). Both anionic and cationic
surfactants strongly bind proteins. The charged groups of ionic surfactant form relatively
strong ionic bonds with charged groups on the proteins. Non-ionic surfactants, on the
other hand, lacking the charged groups, bind through much weaker hydrophobic
interactions with the protein chain and thus are less likely to inactivate or denature
enzymes and proteins (Schwuber, 1980). Non-ionic surfactants would thus be expected to

have the least inﬂuence on cellular metabolism in fermentation.

59

 

5.3.4 Products and pH
The acetate, ethanol and butyrate fermentation proﬁles are shown in Figures 16,

17 and 18 respectively as a function of surfactant type and chain length.

 

 
  
 
  
 
  

1.6 ..
—a—Dontrol
—o—Tween 20, DSC=1
1'4 " —e—Tween 20, DSC=2
+Tween 20, DSC=3
1.2 + - o- .Tween 40, DSC=1

- o. .Tween 40, DSC=2
- A- .Tween 40, DSC=3
1 -- +Tween 80, DSC=1
—o—Tween 80, DSC=2
+Tween 80, DSC=3

 

 

0.8 ..

 

0.6 -r

0.4 ..

Acetate Concentration (glL)

0.2 .

 

db
-

0 50 100 150 200 250 300 350
Time (hours)

Figure 16: Acetate production

60

 

Ethanol Concentration (glL

0.18

 

0.16 4.
0.14 ..
0.12 ..

0.1 ..
0.08 ..
0.06 .
0.04 .

0.02 .

 

 

—e—Control

+Tween 20, DSC=1
—e—Tween 20, DSC=2
+Tween 20, DSC=3
- o- Tween 40, DSC=1
- o- .Tween 40, DSC=2
- a, Tween 40, DSC=3
—o—Tween 80, DSC=1
+Tween 80, DSC=2
+Tween 80, DSC=3

 

 

 
 
 
 
 
 
 
 
 
   

 

150 200 250
Time (hours)

Figure 17: Ethanol production

61

 

 

0.35 1F
—a—Control

—e—Tween 20, DSC=1
0.3 .. —e—Tween 20, DSC=2
—¢—Tween 20, DSC=3
- o- -Tween 40, DSC=1
0.25 .. - o- -Tween 40, DSC=2
- A. .Tween 40, DSC=3
—o—Tween 80, DSC=1 G
0.2 i. +Tween 80, DSC=2
+Tween 80, DSC=3

   
   
   
   

 

 

 

0.15 ..

0.1 HP

Butyrate Concentration (gIL

0.05 .

 

150
Time (hours)
Figure 18: Butyrate production
The remainder of the product concentration data (carbon dioxide) was calculated using
carbon and electron balances for each run (Erickson, 1978). The data shown in Table 9
for Tween surfactants, represent the average of triplicate values. The abbreviations in
used in Table 9 are summarized as the following; Ace indicates acetate, Et indicates
ethanol, Bu indicates butyrate, CM indicates cell mass, and DSC indicated the

dimensionless surfactant concentration.

62

 

 

 

 

 

Table 7: Carbon and electron balance results for Tween surfactants

 

 

 

Control 4 CO —> 0.40 Ace + 0.076 Et + 0.065 Bu + 0.61 CM + 2.17 CO2
Tween 20 4 CO —> 0.48 Ace + 0.050 Et + 0.028 Bu + 0.70 CM + 2.12 C02
(1 DSC)
Tween 20 4 CO —> 0.43 Ace + 0.114 Et + 0.039 Bu + 0.58 CM + 2.18 C02
(2 DSC)
Tween 20 4 CO ——> 0.45 Ace + 0.163 Et + 0.012 Bu + 0.52 CM + 2.20 C02
(3 DSC)
Tween 40 4 C0 —+ 0.41 Ace + 0.083 Et + 0.057 Bu + 0.61 CM + 2.17 C02
(1 DSC)
Tween 40 4 CO —> 0.34 Ace + 0.076 Et + 0.079 Bu + 0.66 CM + 2.19 C02
(2 DSC)
Tween 40 4 CO —) 0.37 Ace + 0.068 Et + 0.082 Bu + 0.62 CM + 2.18 C02
(3 DSC)
Tween 80 4 CO ——> 0.43 Ace + 0.085 Et + 0.047 Bu + 0.62 CM + 2.16 C02
(1 DSC)
Tween 80 4 CO ——> 0.43 Ace + 0.063 Et + 0.031 Bu + 0.77 CM + 2.13 C02
(2 DSC)
Tween 80 4 C0 —+ 0.37 Ace + 0.096 Et + 0.078 Bu + 0.55 CM + 2.20 C02
(3 DSC)

 

 

A typical plot of pH as a function of time during the experiment is shown in
Figure 19. The pH proﬁles for other runs (data not shown) had the similar proﬁles to the

one presented here.

63

7.2 -.

 

 

 

 

 

7
6.8 .
6.6 -
I
a.
6.4 .
6.2 ..
-S—Control
+Tween 20, DSC=1
6 .. -e—Tween 20, DSC=2
—¢—Tween 20, DSC=3
5.8 : i ' ' i i :

 

0 50 100 150 200 250 300 350
Time (hours)

Figure 19: pH proﬁle of a Tween 80 fermentation

The pH decrease as the fermentation proceeded is due to the production of acetic
and butyric acids. The metabolic pathways for acid production have been well-
characterized (Grethlein, 1992b). A shift in the product ratios for B. methylotrophicum
has been observed, in which less acetate and more butyrate and alcohols are produced at
lower pH (Grethlein, 1992b); (Grethlein, 1990). Moreover, a pH shift from 6.8 to 6.0 as
the cells entered the stationary phase has been shown to induce formation of butyrate as
the primary product (Grethlein, 1991a); (Worden, 1989). Consistent with this trend,
Figures 12 and 16 show that acetate is produced throughout the fermentation, but the
butyrate production starts after 70 hours. The acetate, ethanol and butyrate proﬁles in
Figures 16, 17 and 18 are the averages of triplicate data sets. In the averaged sets of data

the variability was as great as +/- 25% between bottles. Due to the post-autoclave

64

 

 

 

additions done to each bottle and individually inoculating each bottle, these variations are
not unexpected.

The carbon and electron balance results for the Tween surfactant experiments,
shown in Table 7, show the ratio of the primary products, acetate, ethanol, and butyrate,
were not affected by the presence of the surfactant in the media. This result suggests that

the Tween surfactants are a good choice for microbubble-sparged CO fermentations.
5.4 Conclusions

The effect of Tween surfactants on growth of B. methylotrophicum on C0 varied
With the chain length. Longer chain lengths had negligible effects on growth in a DSC
range of 0 to 3. Shorter chain lengths slowed growth somewhat, but did not affect the
ﬁnal cell density. None of the Tween surfactants signiﬁcantly affected the product
stoichiometry. Brij surfactants were more inhibitory over the same concentration range,
in some cases reducing both the growth rate and the ﬁnal cell density. An increase in the
ratio of butyrate to acetate observed late in the fermentations coincided with a decrease in

the fermentation pH and the onset of the stationary phase.

65

6. Mass Transfer Properties of Microbubbles

6.1 Introduction

The commercial feasibility of synthesis-gas fermentations is limited by the:
relatively low volumetric productivities. Several studies have indicated that the rate
limiting step in these fermentations is the inherently slow transfer of synthesis gas int
the liquid phase (Worden, 1997). The driving force for synthesis-gas mass transfer is lovr
on a mass basis, the aqueous solubilities of CO and H2 are only 60% and 4% that c
oxygen, respectively. Moreover, per carbon equivalent consumed, more moles c
synthesis gas must be transferred than for an aerobic fermentation. Consequently, th
well-known gas mass-transfer issues that are central to bioreactor design for aerobi
fermentations are even more critical for synthesis-gas fermentations.

A common approach used to enhance gas-to-liquid mass transfer is to increase th
impeller rate. The resulting increase in average shear rate enhances bubble breakuj
increasing the interfacial area for mass transfer. Although effective, this approach i
costly for large ferrnenters, because power consumption is proportional to impeller rate t
the third power and impeller diameter to the ﬁfth power (McCabe, 1985). In addition, th
increased power input can be detrimental to shear-sensitive cells.

Sparging with microbubbles is another approach that has the potential to enhanc
mass transfer while maintaining low power consumption and shear rates. Microbubble
offer the potential for orders-of-magnitude higher mass-transfer rates due to the sma‘
size and higher interfacial areas. Microbubble mass transfer should be most effective fc
gases having a high consumable ﬁaction, such as synthesis gas, which can consist of ove

95% CO and H2 (Worden, 1998). As the consumable gas is transferred into the liqui

66

 

 

phase, the microbubble shrinks, further increasing the interfacial area per unit gas
volume. Additionally, the gas pressure inside a bubble is greater than that outside due tc
the surface tension. The magnitude of this pressure differential, known as Laplace
pressure, increases as the microbubbles shrink (Rosen, 1989). Because the gas solubility
is proportional to the intrabubble pressure, the Laplace pressure increases the driving
force for mass transfer.

The lack of electrodes to measure liquid-phase, carbon-monoxide concentration:
suggests the use of oxygen as a model gas for the mass-transfer studies. The high rate 0:
mass transfer from microbubbles makes measurement of volumetric mass-transfer
coefﬁcients (KLa) challenging. Unsteady-state methods that use oxygen electrodes tc
measure changes in liquid-phase oxygen concentration as a function of time are poorl)
suited, because the response times of the probes are too slow to follow the rapic
dynamics of the liquid-phase oxygen concentration (V an't Riet, 1979). Sulﬁte-oxidatior
methods are also poorly suited due to signiﬁcant rate of reaction that can occur in the
liquid ﬁlm surrounding the slowly rising bubble (Bailey, 1986). Consequently, a methoc
based on measuring the steady-state oxygen concentration proﬁle through a bubble
column was developed. A mathematical model was developed to predict changes in the
bubble diameter across the bubble column, so that the mass-transfer coefﬁcient (KL) am
the interfacial area per unit volume (a) could be computed individually. The effects or
gas void fraction and the concentration of surfactant in the bulk liquid on KL were
determined. Power requirements to produce the microbubbles were experimentally
measured and used to estimate the power required for microbubble sparging of a large-

scale, synthesis-gas fermentation. This chapter describes the experimental studies tc

67

determine the mass transfer properties of microbubbles and the power consumption

necessary to produce them.
6.2 Materials and Methods

6.2.1 Microbubble Generation

The microbubble dispersions were formed using a spinning-disk apparatus
described in Chapter 2. Microbubble size distributions were measured by laser-light
scattering using a Malvem Mastersizer, also described in Chapter 2. The surfactant used
in all studies was Tween 20 (Sigma Chemical Co., St. Louis, M0) at two times the
critical micelle concentration (CMC) (120 mg/L). This surfactant was chosen from the
studies done in Chapters 4 and 5. The cost of the surfactant was not a major consideration
in the selection due to the low concentration used and the typically low cost of the
common polysorbates. The microbubbles were formed with 100% oxygen for the axial-
dispersion and mass-transfer studies.
6.2.2 Axial-Dispersion

The degree of axial dispersion of the water/microbubble dispersion passing
through the bubble column was measured to determine a suitable mixing model for
calculating the Km values. The experimental system, shown schematically in Figure 20,
consisted of a 60-cm-long by 2.5-cm-ID glass column. The column had ports at 7 cm, 22
cm, 37 cm, and 52 cm along its length. A 1/30 hp centrifugal pump was used to supply
the carrier liquid (distilled water). A peristaltic pump delivered microbubbles from the
generator to the column. Standpipes were used to reduce pressure ﬂuctuations from the

peristaltic pump.

68

OUtlet <——-]—

 

Surfactant
Solution (I.
Oxygen Gas 1 L

 

 

 

 

 

 

 

 

 

 

 

Carrier )1 ‘
Water /

.6" Vi.
1: /...————:a‘ :,\ l“;
K ’

\\\ :K‘rjg/

 

 

Figure 20: Experimental apparatus used in axial dispersion and mass transfer

Two conductivity probes were made by mounting a 1 mm diameter brass roe
inside of a 2-mm-ID brass tube with a 0.5-mm-thick plastic, non-conductive spacer ir
between. Wires soldered to the ends of the inner rod and outer tube were connected te
conductivity meters (Cole Partner, Chicago, IL). The ends of the probes were ﬁled ﬂa
and polished (Thompson, 1993). The probes were mounted in ports 7 cm and 52 en
above the base of the column. Five mL of a 25 g/L CaCl2 tracer was injected into the bull
liquid stream just upstream of the column. The probes’ responses were recorded on the

hard disk of a PC at 20 Hz using LabTech Notebook software and a Data Translation I/C

69

 

card. Voltage isolators were used to eliminate a current loop between the probes.
Between 5 and 10 replicates were done for each set of conditions.
6.2.3 Mass Transfer

A Clark-style oxygen electrode (Diamond General, Ann Arbor, MI) attached to a
Chemical Microsensor II (Diamond General, Ann Arbor, MI) was used to measure the
steady-state, liquid-phase oxygen concentration at several positions in the column.

The electrode was calibrated at 0% oxygen with nitrogen-sparged water and at
100% with oxygen-sparged water. The water was maintained at a constant temperature of
22 °C in a water bath during the calibration.

The bulk liquid phase was initially degassed to prevent stripping of nitrogen gas
into the microbubbles by maintaining distilled water under a vacuum created by a water
aspirator for 24 hours prior to the experiment. The degassed water gave an oxygen
reading of 0% using the calibrated electrode. The surfactant was added to the bulk liquid
prior to degassing. Experiments were run at several ﬂow rates and surfactant
concentrations. Between three and ﬁve replicates were performed for each set of
conditions.

6.2.4 Power Consumption

The power consumption of the microbubble generator was measured using a
Lightnin mixer, model L1U08 (Lightnin, Rochester, NY), that gives simultaneous
readouts of rpm and power input. The power input for the generator was measured at the
maximum mixing rate of the mixer (1800 rpm) in air, water, and microbubble
dispersions. The volumetric-uptake rate of synthesis-gas components was obtained from

the continuous fermentation.

70

6.2.5 Dynamic Gassing Out

Experiments were done in a 100 gallon fermenter vessel to estimate the mass
transfer coefﬁcient from microbubble sparging using a dynamic gassing out method. The
fermenter was a Pfaudler vessel equipped with Rushton-bladed turbines for mixing. The
vessel diameter was 3 feet with an impeller diameter of 1 foot. The vessel also had a
sparger for the delivery of compressed air or nitrogen from a tank. The impeller was
driven by an overhead drive and was calibrated using a strobe gun. Since typical oxygen
probe response times were felt to be inadequate to handle the rapidly changing liquid-
phase oxygen concentration, conditions were set so that the liquid-phase concentration
would not change as rapidly. The use of a large-scale fermenter and low gas ﬂow rate
were kept the liquid-phase concentration from changing rapidly.

The oxygen electrode (Ingold) was attached to an ampliﬁer/interface and then to a
data acquisition system (Camile Data Acquistion). The microbubbles were made from air
and were sparged to the fermenter through silicon tubing. The microbubbles were made
in an aqueous, 2 DSC solution of Triton X-100 that was reﬁlled into the generator
through a peristaltic pump. The oxygen electrode was calibrated at 0% saturation after
sparging the liquid phase with nitrogen gas, and 100% saturation after sparging with air
at the beginning of each day of experimentation. The liquid inside the vessel was changed
between each run with tap water. The temperature was monitored on several occasions
during the run and was found to remain relatively constant at 14 °C. Gas holdup was
estimated by immersing a ﬂask of known volume into the vessel, capturing a known
volume of liquid/ gas dispersion, and allowing the gas phase to settle out. The experiment

was performed by stripping the oxygen concentration down to 0% with nitrogen and then

71

starting the ﬂow of microbubbles to the system. The liquid-phase oxygen concentration
was monitored with time.
6.2.6 Mathematical Models
6.2.6.1 Axial Dispersion

The tracer peak for each probe was normalized using a calibration curve. If the
areas under the input and response peaks differed by more that 15%, that data set was
discarded. An unsteady-state mass balance on the tracer in the liquid phase is shown

below, along with the appropriate boundary conditions for an open vessel.

ac, a"- C, ac,
_ Dar 2 — u—— (11)
81‘ 52 é’z

 

 

t=0 z=0 CL=C0
t>O z=0 CL=0

t> 0 z = 00 CL = 0
This model is based on the assumptions that the salt tracer exists only in the liquid

phase and that the salt concentration is uniform. in the radial direction. A computer
program originally developed by Wakao and Kaguei (1982) and later modiﬁed by
Thompson (1993) was used to determine the optimal values of the dispersion coefﬁcient
and interstitial velocity for each data set by minimizing the least-squares error. The
program converted the experimental data into Fourier series and calculated a predicted
outlet tracer curve using the Fourier series from the input probe (at 7 cm) as an input

function and the transfer functions from Equation 11.

72

6.2.6.2 Mass Transfer

The gas phase was assumed to pass through the column in plug ﬂow. This
assumption is typically satisfactory in systems having a large length-to-diameter ratio
(F ogler, 1992). The length-to-diameter ratio for the bubble column is 24.

A steady-state, liquid-phase mass balance on oxygen assuming plug ﬂow is
shown below, along with the appropriate boundary conditions.

dCL KLa .
———— C —C =0
dz u ( L L) (12)

The interfacial area per unit gas volume is given by:

 

3R280 (13)
a :
R3
where the gas void fraction varies with the bubble radius according to the equation:
3
R
50 = 50,0(R_0] (14)

The interfacial oxygen concentration varies with the atmospheric pressure, depth in the

column, and bubble radius as shown below:

C; = H[p(—g—](L — z) +P0 + 2—0] (15)
g. R

The rate of microbubble shrinkage varies signiﬁcantly across the length of the column

and is described by the following equation and boundary conditions.

73

 

 

3K . RT
4in— L(c,_c,) g
dR gc u M

 

g 40'

3P0 + 2(L — z)p(—) + —
gc R (16)

z = O R = R0
This equation accounts for hydrostatic pressure, Laplace pressure, and loss of gas via
transfer into the liquid phase.

Equations 12 through 16 were solved using Simusolv modeling software (Dow
Chemical Company, Midland, MI) using a Gears stiffness method with a generalized
reduced-gradient optimization on KL. The average value of R of 60 um was determined
with the dynamic light scattering method (Chapter 4) and used, together with the ﬂow
rates of the degassed water and microbubble dispersion, to calculate the initial value of a.
6.2.6.3 Dynamic Mass Transfer

An unsteady-state mass balance for oxygen on the liquid phase, assuming a well-

rnixed gas phase for a CSTR is shown below.

dc, (t)
dt

 

= K,a[—CI7G — C, (1)] (17)

which can be integrated to give a linear form shown below.

 

ln[l — :L j = —KLat (18)

*
L

Equation 18 can be plotted to give a slope of —KLa.

74

6.3 Results and Discussion

6.3.1 Axial Dispersion

The dispersion coefﬁcients for the microbubble dispersions in the bubble column
are shown in Figure 21 as a function of liquid velocity and microbubble gas ﬂow rate.
The error bars represent the average deviation from the mean of the replicates. The
literature correlation for a conventional bubble column given below (Deckwer, 1974) is

also shown.

1),, = 2.7D}-4u§-3 (19)

 

25

20 ul-

 

— Deckwer et. al.
a 7.22 mI/min

A 12.73 ml/min
o 26.5 ml/min

0 40.26 ml/min
x 54.0 ml/min

+ 67.8 ml/min

   
 
 

_\
(II
I
I

_I.
O
I

 

 

 

Dispersion Coefficient (cmzls)

t. 4M

6 8 10 12 14 16
Velocity (cm/s)

 

 

Figure 21: Axial dispersion coefﬁcients
Figure 21 indicates that axial dispersion for the microbubble dispersions was
considerably lower than in conventional bubble systems. In conventional systems, the

much larger bubbles rise at an appreciable rate relative to the surrounding liquid. Liquid

75

trapped in the bubble wake is transported through the column at a higher velocity than the
bulk liquid, contributing to axial mixing. The very low rise velocities of microbubbles do
not induce such wakes. The dispersion coefﬁcients were used to calculate Peclet
numbers. The lower bound on the Pe values was 42, which is indicative of low degrees of
axial mixing (Fogler, 1992). Consequently, the plug-ﬂow mixing model was deemed
appropriate for calculating KL values from the oxygen-proﬁle data.
6.3.2 Mass Transfer
6.3.2.1 Plug Flow Model

Figure 22 shows an example of the agreement between the experimentally
measured liquid-phase oxygen concentration proﬁle across the bubble column and that
predicted by the mathematical model for the optimal KL value. The error bars represent
the average deviation from the mean of the replicates. The predicted change in R across
the bubble column is also shown for this run. Even though the residence time of the
microbubbles in the column was only a few seconds, R, CL”, 80, and a all are predicted to

change signiﬁcantly, demonstrating the need to include Equations 13 - 16 in the model.

76

 

3.50E-02 3.50E-05

 

 

 

 

 

A 3.00E-02 .. 3.00E-05

15

CD

5’ 2.50E'02 -- -- 2.50E‘05 A

r: .5.

.2 en

‘5' 2.00E-02 .. .. 2005-05 .2

J:- "o

N

5 a:

8 1.50E-02 .. ..1.50E-05 2

O .D

o '3

S: 1.00E-02 .. —Optimized Fit .. 1.00E-05 m

>. A Experimental Data

X .

0 5005-03 .. -*- Rad'us .. 5.00E-06
0.00E+00 ; - . - : 0.00E+00

 

0.00 0.10 0.20 0.30 0.40 0.50 0.60
Column Position (m)

Figure 22: Optimized ﬁt for KL using a plug ﬂow model
6.3.2.2 Void Fraction and Surfactant Effects
The experimentally determined KL values are shown in Figure 23 as a function of
so, for different concentrations of surfactant in the bulk liquid. Also shown in this ﬁgure
are KL correlations published by Waslo and Gal-Or (1971), and Calderbank and M00-
Young (1961) for small, rigid—surface bubbles. The well—known theoretical correlation for

diffusion from a sphere into an inﬁnite pool of stagnant ﬂuid (Sh=2) is also shown.

77

0.00025

 

 

0 0x Tween 20

a 1x Tween 20

0-0002 1- A 5x Tween 20
—.—Calderbank and Moo-Young
—Waslo and Gal-Or

0.00015 .. 0 —--3h = 2

 

 

 

 

KL (mls)
C

vvvvvvrr-vv vvvvvvvtvvv vvvvvvvvivvvvvvvvvvvvvvvvv‘v’v vvvvvvvv
l .-

\U \
0.00005 .

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
Gas Void Fraction, 89

/

 

 

 

Figure 23: Mass transfer coefﬁcients from microbubbles

The experimentally determined KL values are similar in magnitude to those
predicted by the correlations. However, there is a signiﬁcant decrease in KL with
increasing surfactant concentration. This trend suggests that adsorption of the surfactant
at the gas-liquid interface creates additional resistance to gas mass transfer. Such
resistance can arise through several mechanisms. First, surfactant molecules can retard
surface ﬂow by the surface tension gradient at the interface. Second, they can act as
physical barriers to the passage of gaseous molecules at the interface (Koide, 1976). For
soluble surfactant monolayers, Princen et al. (1967) suggests that gas transfer occurs by
simple Fickian diffusion through aqueous pores between the surfactant molecules. Third,
the surfactant concentration may inﬂuence the thickness (h) of the liquid shell

surrounding the bubble. Amiri et al. (1990) estimated the shell of microbubbles to be

78

about 0.75 pm thick. Assuming mass transfer is limited by the rate of diffusion across the
shell, h can be estimated. from KL using the following expression (Princen, 1965).

DOZHO

h
kL,S

(20)

For the range of KL values shown in Figure 23, the range of h values predicted by this
equation is 0.2 pm to 3 pm. This calculation assumes the diffusivity of oxygen in the
shell is equal to that in pure water. The presence of soluble surfactants has been reported
not to signiﬁcantly affect diffusion of small molecules (Quintana, 1990). Also, the gas-
side ﬁhn resistance has been shown to be negligible for a sparingly soluble gas, such as
oxygen (Motarjemi, 1978). The effect of surfactants, gases, and composition on the
thickness of the water shell has not been determined to this date. The effects of these
conditions could be addressed at some later date.

The KL values measured when no surfactant was initially present in the bulk
liquid were higher than the values predicted by the three correlations based on the data
presented in Figure 23. One explanation for this trend is that bubble shrinkage enhances
mass transfer relative to conventional bubbles through the Laplace pressure effect and a
steepening of the oxygen concentration gradient outside the bubble. These ideas are
explored more thoroughly using a dynamic model of a single microbubble (Worden and
Bredwell, 1998).

The KLa values for the experiments shown in Figure 23, calculated using

Equation 21, ranged from 200 h'1 to 1100 h".

KLa = -—gKL (21)

79

Table 8 contains the KL, a, and KLa values determined in this study using the bubble

 

 

 

column.
Table 8: Mass Transfer Results
Surfactant Microbubble Liquid Flow KL a KLa
(DSC) Flow (mL/min) (m/s) (m'l) (11")
(mL/min)
0 39.8 1033.6 1.1426e-4 2531.8 1041.22
0 39.8 1810.4 1.4717e-4 1453.1 769.9
0 39.8 2587.1 2.1418e-4 1019.1 785.8
0 81 1033.6 5.2524e-5 5091.8 962.8
0 81 1810.4 7.7295e-5 2939.1 817.8
0 81 2587.1 1.1925e-4 2065.8 886.9
1 39.8 1033.6 6.0244e-5 2531.3 549.0
1 39.8 1810.4 7.5274e-5 1453.1 393.8
1 39.8 2587.1 1.2353e-4 1019.1 453.2
5 39.8 1033.6 2.9325e-5 2531.3 267.2
5 39.8 1810.4 4.3340e-5 1453.1 226.7
5 39.8 2587.1 5.5200e-5 1019.1 202.5

 

 

These values are considerably higher than those reported for mechanically agitated,
commercial-scale fermentations, yet they were measured in an unagitated bubble column.
Thus, despite the reduction in KL seen at high surfactant concentrations, the large

increase in a due to the exceedingly small bubble diameter resulted in high KLa values.

80

6.3.3 Power Consumption
6.3.3.1 Power Consumption in Fermenters

The measurements of power required to drive the microbubble generator in w:
and in the nricrobubble dispersion at 1800 rpm were used to calculate a Power numbe:
0.036 for the microbubble generator. Power numbers are typically constant in
turbulent regime (Rushton, 1950). Consequently this value could be used to calculate
expected power consumption at the operating rpm (4000 rpm) from the deﬁning equat

for Power number, shown below.

Pg.
PM = pN 1’ D?

 

(2:

The measured rate of microbubble formation in the generator (300 mL/rnin of gas) 1
used, together with the volumetric CO consumption rate for B. methylotrophic
(0.02573 mol/h*L) (Grethlein, 1991b), to calculate a power requirement of 0.01 kW
m3 of fermentation broth to form the microbubble dispersions. It was assumed that
power number was constant in the turbulent regime, that the power consumption in
foam was 1/3 of the power consumption in the liquid, and that there was 10
consumption of synthesis gas components (CO) from the microbubble. A small amo
of additional power would be required to maintain adequate liquid mixing in the reac
In comparison, typical P/V values for commercial-scale, stirred-tank ferrnenters are
the order of 1 kW/m3 (Van't Riet, 1979). An estimated P/V value for synthesis-.
fermentations using conventional sparging in stirred-tanks is 2 kW/m3 (E.N. Kaufm

personal communication).

81

6.3.3.2 Comparison of Reactor Type
The dependence of KLa on P/V has been well—studied for conventional bubble

For stirred tanks, a commonly used correlation is (Van't Riet, 1979)

P

KLa = K(?) (ug )ﬂ (23)

For bubble-coalescing media, or = 0.4 and 0:05; for non-coalescing media, 0t=0.7 and
= 0.2 (V an't Riet, 1979), where P is in W/m3, V is in L, and ug is in m/h. For airli

reactors a comparable correlation is (Margaritis, 1981), (Siegel, 1988).

KLa = [(9 0(3)!) (24)

Reported values of 0t and B are 1.0 (Siegel, 1988) and 0.9 (Bello, 1985), respectively. Tb
correlations shown in Equations 23 and 24 (for a superﬁcial gas velocity of 60 cm/mir
are plotted in Figure 23, along with the range of KLa values measured in this study, t
show the performance enhancement possible using microbubble sparging
Comparatively, the superﬁcial gas velocity for the microbubble study ranged from 180 t
500 cm/min. Relatively high power inputs are needed in conventional gas-sparge
systems to break up bubbles and provide adequate KLa values. However fc
microbubbles, only enough power is required to provide adequate liquid mixing. Thu:
microbubble sparging offers the possibility of simultaneously providing both high KL
values and low power inputs. The energy savings arise because the high shear levels use
to provide bubble breakup are applied only to the small liquid volume contained in th
microbubble generator, rather than the entire contents of the bioreactor. The only powe
delivered to the liquid contents of the main bioreactor is that needed for mixing. In large

scale fermenters, the microbubbles could be generated in an external vessel as in thi

82

study. Increased ﬁltration capacity would then be required to handle the larger scai
liquid entering the reactor through the microbubble foam. Alternatively, the microbu
generator could be housed directly in the larger fermenter to create a local
“microbubble generation zone” within the fermenter, thereby removing the cost of 12

scale ﬁltration necessary to regenerate the solution to make microbubbles.

1 00000

 

10000 .

 

1000 .. Microbubble Range

 

 

 

 

 

 

 

 

 

 

 

 

X,
!? x/X’

.: x/X/
v x/ 1 1 i—+.-

“h x/‘r 4' ' I
-“ 100 4r/W

x
10 -o—CSTR - Bubble Coalescing
" _i_csrR - Bubble Non-coalescing
—x—Airlift - with draft tubes (Margaritis et. al.,1981)

1 I I I I I I I I :I
100 1‘

(PN) (W/m3)

Figure 24: Comparative KLa values for varying reactor types
The simultaneous advantages of reduced power and increased producti
demonstrated in synthesis-gas fermentations could, in principle, also be realized
variety of other unit operations in which gas-to—liquid mass transfer is rate limit
Examples include aerobic fermentations, soil washing, stripping of volatiles from a lie

Phase, and ﬂotation.

83

 

6.3.4 Dynamic Gassing Out

A sample of the raw data obtained from the absorption of oxygen into nitrogen-
stripped water is shown in Figure 25 below in terms of percent air saturation. The
temperature remained constant at 14 OC throughout the experiment. The probe was

calibrated on a daily basis and fresh tap water was used for each run.

60-

   
 
 
   

50.

40.

304

°/o Air Saturation

20.

10.

 

 

 

'—

400 600 800 1000 1200 1400
Time (sec)

0 200

Figure 25: Experimental data from a dynamic gassing out run

 

C . . . .
The data were plotted as the ln[l — I; J versus trme, as shown 1n Equation 19 to obtain a
L

KLa value. A sample of these plots is given in Figure 26.

84

200 400 600 800 1000 1200
-0.1 .

I

'0.2 III-

  

y = -0.000638x + 0.026814

2 _.
_0.3 __ R — 0.999961

-0.4 ..

‘0.5 III-

‘0.6 II-

 

-0.7 .-

Time (sec)

Figure 26: Linear form of Equation 19
To evaluate whether the assumption that the composition of the gas phase changes as
function of time in the reactor, a calculation was done to compare the maximum amount
of oxygen gas that could be transferred to the actual amount of gas that was transferred.
The maximum amount of gas transferred was determined by calculating the total amount
of oxygen coming into the reactor and assuming it was all transferred into the liquid
phase. Other assumptions made include that the gas behaves as an ideal gas and the
pressure inside of the bubble is atmospheric. The results from this comparison are shown

for a feed of 300 mL/min gas phase from microbubbles at 50 RPM in Figure 27.

85

10-. .- 100

 

 

 

 

 

 

9 .. .. 90
d 8 .. .. 80
3’
V 7 -I- III- 70 U
c o
.2 t
a 6 .. -- 60 £2
4: 8
5 5 . .. 50 ea

5

g I-
o 4 .. 40 g
0 o
S: 3 . .. 30 g
Q 2 _ _ —Theoretical .. 20
0 / x Experimental

1 -- ——Percent Transferred -- 10

0 i i i 4 0

0 10 20 30 40 50

Time (minutes)

Figure 27: Percent of oxygen transferred to liquid phase
The results in Figure 27 indicate that for such small bubbles, there is a considerable
fraction of gas transferred into the liquid. The maximum percentage of inlet oxygen
transferred to the liquid phase was 86% at 300 mL/min, 60% at 600 mL/min, and 50% at
900 mL/min. This indicates that the assumption that the gas phase concentration in the
reactor did not change is most likely not valid.

To properly account for the changing composition of the gas phase, accurate data
regarding the gas holdup of the reactor and the outlet gas composition would be needed.
Using such data, gas-phase and liquid-phase mass balances could be written using the
well-mixed liquid phase balance in Equation 18 and a well-mixed gas phase mass balance
given below. The model could then be subsequently solved to give a KLa value from this

type of experiment.

86

dCG Cl—C, . V,
= —K C —C — 25
dt (VG/G) ‘al ‘ JV, ( )

 

where C1 and C2 are the gas-phase oxygen concentrations at the reactor inlet and outlet,
respectively. It would be necessary to use an average gas ﬂow rate if the inlet and out
ﬂows were not constant. It would also be necessary to use an average value for CL. since
there will be bubbles with a wide variety of oxygen gas compositions. Van’t Reit (1979)
has suggested that the data from making the assumption of a constant composition gas
phase can become a signiﬁcant problem if the gas phase residence time is not much
smaller the l/KLa. In the experimental system used the gas phase holdup was only
roughly estimated. A gas void fraction of 0.0303 was measured for a 300 mL/min ﬂow
rate of microbubbles into the reactor. The gas void fraction did not seem to vary
signiﬁcantly for different sparging rates or different measurement times past 15 minutes.
Using the estimate of gas holdup, the gas phase residence times for the three different
ﬂow rates, 300 mL/min, 600 mL/min, and 900 mL/min were 38.4 min, 19.2 min, and
12.8 min respectively, and were obtained by dividing the reactor gas holdup by the inlet
gas ﬂowrate. Comparatively, the 1/KLa values ranged from 20.5 min to 50.3 min. These
numbers verify the results seen earlier that the gas-phase dynamics are important to
consider in this situation and should be included in the analysis of the data and
determination of KLa.

Dunn and Einsele (1975) have constructed correction charts for the determination
of more accurate KLa values where only the gas void fraction and the KLa determined
from the liquid-phase model are known. The correlation charts were constructed from
plotting the relationship between KLa determined using only liquid-phase dynamics and

the KLa determined from using both liquid-phase and gas-phase dynamics at different

87

gas-phase residence times. Extrapolating the gas-phase residence times, the correction
chart given in literature (Dunn, 1975), the corrected KLa values were determined. The
results are presented in Figure 28, along with the correlation describing mass transfer

coefﬁcients in a bubble non-coalescing media (Van't Riet, 197 9).

20 .-

18 ..

    
 
  
  

16..

14.

 

 

 

 

+Bubble Non CozaTes—Eingj
+300 mL/min 1
+600 mL/min l

KLa (h 1)
(Corrected values)
8

 

 

 

4 J +900 mL/min
2 ..
0 i : i + i i
0 100 200 300 400 500 600
(PN) ratio (W/m3)

Figure 28: Dynamic mass transfer coefﬁcients of microbubbles
The power-to-volume input was estimated by calculating the impeller Reynolds number,
Re, from Equation 26 and determining the power number, Pno from correlation charts
(Bailey, 1986). The impeller Reynolds number was calculated to be 700, and the
subsequent power number was determined to be 3.9. The system was operated in the
transition region between the laminar and turbulent ﬂow regimes (between a Re 50 and

5000)

88

_ pIIViDi2
#1

Re.

i

(26)

The power was then calculated from Equation 22. The effect of the aeration rate on the
power requirements was determined through calculating the dimensionless aeration rate,
Na.

N, = G
MD;

 

(27)

The effect of aeration on the power requirements was small; N,l was never higher than
104, suggesting that there was no power loss due to aeration.

Figure 25 indicates that for an equivalent P/V ratio mass transfer coefﬁcients from
microbubbles are higher than those for conventional bubbles described by the bubble
non-coalescing correlation at lower power to volume inputs. (The literature correlation
used a gas ﬂow rate of 300 mL/min.) This trend. is similar to that seen in Figure 24.
Increasing power input generally increases bubble breakup, giving smaller average
bubble sizes, and this trend is seen in the literature correlation. Microbubbles, on the
other hand, have very small diameters entering the vessel and are unlikely to break up
further. Thus, the KLa values determined from microbubbles should be independent of
the power input to the vessel. This trend has been seen previously in fermentations
(Kaster, 1990). The small increase in KLa seen in Figure 25 may be due to greater surface
mixing at higher (P/V). The KLa curves for microbubbles cross the KLa value determined

from the literature correlation at a similar (PN) ratio as in Figure 24.
6.4 Conclusions

A steady-state method was developed to measure KL and KLa values for

microbubble dispersions. The KL values obtained were comparable to those predicted by

89

correlations for small, rigid-surface bubbles. An increase in the concentration of
surfactant in the bulk liquid decreased the KL value by as much as 75%, presumably due
to increased mass-transfer resistance in the rrricrobubble shell. The KLa values ranged
from 200 to 1100 h], verifying that microbubble dispersions can provide extremely high
mass-transfer rates.

The Power number of the microbubble generator was measured to be 0.036.
Based on this value, an incremental power-to-volume ratio to make microbubbles for a
synthesis-gas fermentation was estimated to be 0.01 kW per m3 of fermentation capacity.
Thus, the projected power input to microbubble sparged fermenters is low, with little
power required beyond what is necessary to keep the liquid mixed.

The mass transfer coefﬁcients from microbubbles were also measured in a
dynamic gassing out method in a 100 gallon fermenter. Difﬁculties in the measurement
of the gas holdup and exiting gas composition did not allow for accurate measurements of
KLa. Correlation charts were used to account for the change in gas composition with
bubble residence time. The results from this dynamic study show similar trends when
compared with the KLa values versus power input obtained in the steady-state
experiments.

6.5 Nomenclature

6.5.1 Symbols

(1 = Interfacial area/unit gas volume (m!)

b = Constant for physical properties of the ﬂuids and reactor geometry in
airlift fermenters

C1 = Gas—phase oxygen concentration at inlet (mg/L)

90

C2
C0
CL

CL

CT

Dt

D02

Dax

DSC

gc

Ho

KL
kL,s

KLa

Gas-phase oxygen concentration at outlet (mg/L)
Gas-phase oxygen concentration (mg/L)

Liquid-phase oxygen concentration (mg/L)
Equilibrium liquid-phase oxygen concentration (mg/L)
Initial salt tracer concentration (g/L)

Concentration of calcium chloride tracer in liquid phase (g/L)
Tube diameter (m)

Bubble diameter (m)

Diffusion Coefﬁcient (mZ/s)

Axial dispersion coefﬁcient (mz/s)

Impeller diameter (m)

Dimensionless surfactant concentration = surfactant concentration/critical
micelle concentration

Gravity constant (9.81 m/sz)

Conversion factor

Reactor inlet gas ﬂow rate (mL/min)

Surfactant ﬁlm thickness (m)

Henry’s law constant (Kg/m3 Pa)

Ostwald coefﬁcient of gas solubility

Constant for reactor geometry in stirred tanks
Mass-transfer coefﬁcient (In/s)

Mass-transfer coefﬁcient of surfactant layer (m/s)

Volumetric mass-transfer coefﬁcient (s'l)

91

ZZZ”

O:

'11

R02
RC.’

Sh

UG

VG

Column length(m)

Molecular weight (g/mol)

Impeller rate (rpm)

Dimensionless aeration number

Power input (W)

Power number

Atmospheric pressure (N/mz)

Reactor inlet partial pressure of CO (atm)
Reactor outlet partial pressure of CO (atm)
Peclet number (radius)

Bubble radius (m)

Initial bubble radius (m)

Gas constant

Reaction rate of oxygen in the liquid phase
Impeller Reynolds Number

Sherwood munber

Liquid velocity (m/s)

Gas velocity (m/s)

Time (sec)

Temperature (C)

Volume (m3)

Reactor liquid volume (L)

Reactor gas volume (L)

92

7.5.2

So

80,0

Position in column (m)

Greek Symbols

Exponent for the (PN) term in stirred tank and airlift correlations

= Exponent for the gas ﬂow rate term in stirred tank and airlift correlations
= Gas void fraction

= Initial gas void fraction

= Bulk liquid density (g/m3)

= Continuous phase density (g/m3)

= Surface tension (N/mz)

93

7. B. ME T HYLOT ROPHIC UM FERMENTATIONS

7 .1 Introduction

In the previous chapter, the mass transfer coefﬁcients from microbubbles were
measured to be very high, in the range from 240 h'1 to 1100 h]. This chapter describes
experiments to determine whether the use of microbubbles would enhance synthesis gas
fermentations. The obligate anaerobe, B. methylotrohicum is capable of consuming CO to
produce liquid fuels and chemicals such as ethanol and acetate. These fermentations have
previously been shown to be mass transport limited (Worden, 1989) and could potentially
beneﬁt form microbubble sparging.

A dynamic model describing the mass transfer of nricrobubbles has been
developed (Worden and Bredwell, 1998). This model predicts that for a gas with a high
consumable fraction, such as synthesis gas, the mass transfer rate from a microbubble
increases rapidly as the bubble shrinks. This effect is less signiﬁcant for gases with a 20%
consumable fraction, such as air, where the amount of bubble shrinkage is not as large.
The increase in mass transfer due to shrinkage is partially due to increased interfacial area
per volume and partially due to increased internal bubble, which increases the saturation
concentration. These results indicate that synthesis gas fermentations could beneﬁt more

than aerobic fermentations from microbubble sparging.
7.2 Materials and Methods

7.2.] Media and Cultures
B. methylotrophicum cells were grown in serum bottles as described in Chapter 5,
and after one week were used to inoculate the reactor (5% by volume). A phosphate-

buffered, basal media was used in the reactor with half the concentration of yeast extract

94

used by Grethlein (1991b). The composition of the enhanced phosphate buffered media is
given in Table 9 below.

Table 9: Composition of the enhanced PBB media

 

 

Component Concentration
NaCl 0.9 g/L
MgC12°2HzO 0.2 g/L
CaCl202H2O 0.1 g/L
NH4C1 1.0 g/L
Yeast Extract 1.0 g/L
Trace Mineral Solution 50 mL/L
Vitamin Solution 100 mL/L
Phosphate Stock 25 mL/L
2.5% Na2S-9H2O Stock 25 mL/L
0.2% Resazurin 1.0 mL/L
(NH4)2SO4 2.0 g/L

 

 

 

The vitamin solution, trace elements solution, and phosphate stock are the same as
described in Chapter 4, Tables 3, 4, and 5.
7.2.2 Reactor

A synthesis-gas fermentation using Butyribacterium methylotrophicum was run in
a 1.5 L Multigen fermenter (NBS, Edison, NJ) using a Minitan stainless steel ﬁltration
unit containing eight Durapore 0.2 pm ﬁlter plates (Millipore, Bedford, MA) for total cell

recycle. A schematic diagram of the apparatus is shown in Figure 29.

95

Fresh
Media

 

 

 

 

 

 

 

 

 

v __
Reactor 1 i Microbubble
_, ‘ _, , Filter I Generator

 
 

Figure 29: Flow diagram for a B. methylotrophicum fermentation

A peristaltic pump delivered fresh media to the reactor at a rate of 0.2 mL/min.
The pH was controlled at 6.6 using a pH 4000 controller (NBS, Edison, NJ) with 6 N
NaOH and 6 N H3PO4. The CO was sparged into the fermentation through a stainless
steel ﬁit having a 10 um pore size with the ﬂow rate being controlled through a needle
valve (Cole Parmer, Chicago, IL). The impeller rate was 200 rpm during the entire
fermentation. Gas ﬂow rates were measured using a wet test meter (GCA/Precision
Scientiﬁc, Chicago, IL).
7.2.3 Analytical Techniques

Gas compositions were measured using a Perkin-Elmer Autosystems gas
chromatograph equipped with a thermal conductivity detector (Perkin—Elmer, Norwalk,
CT) and a Hayesep DB 30’ by 1/8” column (Alltech Assoc, Deerﬁeld, IL). The ﬂow rate
0f the carrier gas (He) was 30 mL/min. The inlet and detector temperatures were 110 OC.

The temperature program was 40 0C for 6 minutes, followed by a ramp at 45 °C/min to

96

 

275 °C for 1.5 minutes. The biomass concentration was measured using optical density
(OD) at 660 nm. A calibration curve was used to convert OD into dry cell weight. Liquid-
phase products were measured using gas chromatography with a ﬂame ionization
detector with a 4% Carbowax 20M on Carbograph IDA 80/120 mesh 6’ by %”
deactiglass column (Alltech Assoc., Deerﬁeld, IL). The ﬂow rate of the carrier gas (He)
was 20 mL/min. The injector and detector temperatures were 220 °C, and the column
was maintained at 180 °C for 7 minutes.
7.2.4 Models

A mass balance on C0 in the gas phase in the reactor assuming an ideal gas
phase, mass-transfer-limited operation, and perfect mixing in both the gas and liquid
phases is shown in Equation 28 (Klasson, 1992).

Pi: = K.a V‘Rgf
PCO HG (28)

 

 

7.2.5 Carbon and Electron Balances

Carbon and electron balances have previously been done on B. methylotrophicum
fermentations (Grethlein, 1991b). They were used in the product analysis in Chapter 5,
and are presented in more detail here. The carbon and electron balance equations are

given in Equations 29 and 30, respectively.

N150 =NC0 +NC02 +2Nace +2Neth +4Nbut +Ncells (29)

out out

yCONCO : yCOz NC02 +7H20NH20 +yaceNace +7erhNeth +ybu’Nbu! +766”ch6113 (20)

con verr prod prod

The reductance degrees, y, are given in Table 10 below.

97

 

Table 10: Reductance degrees

 

 

Component Reductance Degree
Yco 2
Ycoz 0
Yace 4
Yeih 6
7601 5
Yceiis 4.2
71120 0

 

 

 

The reductance degrees are from Erickson (1978).
7.3 Results and Discussion
7.3.1 Products

The concentration of the fermentation products for both conventional and

microbubble sparging in the reactor are shown in Figure 30.

98

.I.
O
N
0|

 

 

 

 

 

 

 

 

 

 

, ‘ -_ 20 g,

.1 i ..
3’ ' W s
z .. 15 E
9 .9. Cell ’5
° 8
3 .5. Acetate c
g 1,. Butyrate -- 10 8
= + Ethanol *6
° 5
U -. 5 e
LLlEEEEéa n.

. i : O
60 70

 

Time (Days)

Figure 30: Fermentation product proﬁle
Similar concentrations of acetate, ethanol, and butyrate have been reported in previous
CO fermentation studies using B. methylotrophicum (Grethlein, 1991b). The volumetric
productivity for acetate, the primary product, was 3.84 g/L*day prior to microbubble
sparging. Butanol is typically not produced to a signiﬁcant degree at the pH used. The dip
in the reactor productivity at day 26 was due to the installation of new ﬁlter packets and
subsequent resterilization of the reactor. Conventional sparging through the 10 um
stainless steel frit produced bubbles on the order of 0.5 to 1 mm in diameter. On day 48
of the fermentation, conventional sparging was replaced by microbubble sparging. The
microbubble sparging was run for 8 days prior to the termination of the experiment due to
ﬁlter fouling. This problem prevented obtaining a maximum productivity from the reactor

with microbubble sparging. Fogler (1992) suggests that a minimum of three residence

99

times are required for a steady-state to occur. The liquid-phase residence time in the
reactor and microbubble generator combined was 10.4 days. In order for a liquid-phase
steady-state to be achieved, it would require 31.3 days. The spinning disk microbubble
generator and ﬁlter units were not capable of completing this task. The gas-phase on the
other hand, had an approximate residence time of 30 minutes. Therefore, to obtain a gas-
phase steady-state, a minimum of only 1.5 hours would be required.

The carbon and electron balances were done both on the fermentation with
conventional and microbubble sparging. For both conventional and microbubble
sparging, between 60% and 80% of the incoming CO was converted. The carbon balance
closed to 96.3% and the electron balance closed to 97.1% with conventional sparging.
With microbubble sparging the closure was lower; the carbon balance closed to 88.3%
and the electron balance to 91.1%. The lower closer may be due to some product loss in
the microbubble generator. When started initially, and when ﬁlters were adjusted, there
was some overﬂow of the microbubble generator. This overﬂow caused loss of
fermentation liquid from the microbubble generator at various times, thereby losing some
of the products from the fermentation. At times during the fermentations (approximately
once per day), the ﬁlters were backﬂushed to maintain maximum ﬁltration capacity.
During those operations the liquid was allowed to accumulate in the reactor. After
completing a backﬂush, the pumps were restarted, and the excess liquid from the reactor
was ﬁltered back into the generator. On occasion, the rapid increase in the liquid
concentration would cause the microbubble foam to expand, and some liquid would

overﬂow the generator.

100

7.3.2 Mass Transfer Coefﬁcients
Mass-transfer coefﬁcients were obtained by varying the inlet gas ﬂow rates and

plotting the results as shown in Figure 31.

 

   
    

 

 

 

 

 

 

4.5
4 " 0 Conventional Sparging
3.5 __ a Microbubble Sparging
3 _-
’6
0° 2.5 --
E Kla = 90.64 h'1
8 2 .. 2
a R = 0.9944
V 1.5 --
1 _ M
O 5 KLa = 14.2 h-1
' R2 = 0.9433
0 : . : i
0 0.05 0.1 0.15 0.2 0.25

1/G (min/mL)

Figure 31: Mass transfer coefﬁcients from fermentation

By inspection of Equation 28, the data should be linear if the fermentation is mass-

KLa

 

transfer limited, with a slope of VLRgT . Results for both conventional and

microbubble sparging are shown in Figure 31. The Km for microbubble sparging was
four times higher than for conventional sparging, even though the gas throughput for the
microbubbles was only about one half that for the conventional bubbles.

A lower gas ﬂow rate was used for microbubble sparging to avoid exceeding the
liquid-handling capacity of the ﬁlters. The microbubble foam had a signiﬁcant liquid

void fraction, approximately 0.32 (Bredwell, 1995), which increased the liquid ﬂow rate

101

 

through the ﬁlter. The KLa value measured in the fermentation is lower than that
measured in the bubble column studies, probably because of the very low microbubble
ﬂow rate used in the fermentation. The low ﬂow rate gave lower 80 values than were
used in the bubble column studies. A comparable four-fold increase in the volumetric
mass-transfer coefﬁcient due to microbubble sparging was reported previously in an
aerobic Saccharomyces cerevisiae fermentation by Kaster et al. (Kaster, 1990).

Filter fouling prevented long—tenn operation of the reactor with microbubble
sparging. Since microbubbles have a signiﬁcant liquid fraction associated with them, the
use of microbubbles increased the liquid ﬂow rate into the reactor, especially at higher
gas ﬂow rates. This signiﬁcantly increased the requirements of the ﬁlter used for cell
retention. Other experiments using microbubbles to deliver synthesis gas to a sulfate-
reducing bacteria culture have used dual hollow ﬁber membranes in parallel to
successfully handle the increased ﬁltration requirements (Selvaraj, 1997b).

7 .4 Conclusions

The six-fold increase in the volumetric mass transfer coefﬁcient despite lower gas
ﬂow rates, indicates that microbubbles can enhance the gas-to-liquid mass transfer in
synthesis gas fermentations. The results demonstrated that microbubble technology can

enhance synthesis gas fermentations.

7 .5 Nomenclature

7.5.1 Symbols

Gi = Inlet gas ﬂow rate (mL/min)
H = Henry’s law constant (atrrr/mol*L)
KLa = Volumetric mass transfer coefﬁcient (h'l)

102

N = Number of moles (moles)

Pico = Inlet partial pressure of CO (atm)
POCQ = Outlet partial pressure of CO (atm)
Rg = Gas constant

T = Temperature (K)

VL = Reactor volume (L)

y = Reductance degree

7.5.2 Subscripts and Superscripts

in = inlet

out = outlet

prod = produced
convert= converted

CO = Carbon monoxide
CO2 = Carbon dioxide
H2O = Water

ace = Acetate

eth = Ethanol

but = Butyrate

cells = Cell mass

103

8. SRB FERMENTATIONS

8.1 Introduction

Sulfur dioxide ($02) is one of the major air pollutants in the US, with 70% of
total SO2 emissions coming from the combustion of fossil fuels, primarily from coal-ﬁred
power plants. The quantity emitted in the US in 1992 was estimated to be 22.73 million
tons (1992). In the atmosphere, SO2 reacts photochemically or catalytically with other
constituents to form sulfuric acid which contributes to acid rain. Conventional ﬂue gas
desulfurization (F GD) processes are based on wet-scrubbing techniques that use
disposable sorbents such as dolomite or limestone or regenerable sorbents such as copper
oxide. Microbial processes, such as sulfate reducing bacteria (SRB), have found potential
application in treatment processes of sulfur-laden wastes.

Under anaerobic conditions, sulfur compounds (sulﬁte, sulfate, thiosulfate) can
act as a terminal electron acceptor for SRB. Organic acids and alcohols (Colleran, 1995),
sewage digest (Selvaraj, 1995), and hydrogen and synthesis gas (du Preez, 1994), (van
Houten, 1994) have all been used as electron donors for SRB. While organic acids and
alcohols (such as lactic acid and ethanol) may be utilized, they are most likely too costly
to use as feedstocks for this process. Synthesis gas, therefore, is an attractive alternative
feedstock for SRB fermentations.

Bioreactor design for synthesis gas fermentations centers around the issue of
providing high gas-to-liquid mass transport rates while trying to maintain economic
feasibility. Techniques typically used to increase mass transfer rates, such as increasing
the impeller rate to promote bubble breakup, are expensive, especially in large-scale

fermenters because power consumption is proportional to the impeller rate to the third

104

 

power and impeller diameter to the ﬁfth power (McCabe, 1985). Power consumption can
be a critical cost in synthesis gas fermentations, because the bioreactors used are expected
to be very large. Based on the reactor productivities using sewage digest as a feedstock,
in order to biodesulﬁuize the efﬂuent from a 1000 MW coal-ﬁred power plant, a total
reactor volume of 410,000 gallons would be required (Selvaraj, 1996b).

Increasing volumetric productivity can reduce the reactor size needed in
biodesulfurization. This chapter describes the development of a microbubble—sparged
CSTR for the biodesulﬁuization of ﬂue gases by SRB using a synthesis gas feedstock.
Gas-to-liquid mass transport limitations of synthesis gas sparging SRB fermentations are
also discussed.

The work with SRB fermentations was done at Oak Ridge National Laboratory
(ORNL) in the laboratory of Eric Kauﬁnan. Work was done in collaboration with Punjai

Selvaraj, Mark Little, and Miguel Rodriguez.
8.2 Materials and Methods

8.2.1 Microbubble Generation

A new microbubble generator was built at ORNL. It was similar in design and
construction to the previous generator. The average bubble size was measured ex situ
with a Coulter LS 130 particle size analyzer (Coulter, Hialeah, FL) using both a
microvolume module (MVM) and a ﬂow-through hazardous ﬂuids module (HFM). The
MVM is a vessel into which the microbubbles were loaded into water with surfactant and
agitated with a magnetic stirrer. The HFM module continuously pumps liquid in a
recirculation loop to maintain suspension of the sample. The microbubbles were added to

the 15 mL MVM until an obscuration of 8 to 15% was obtained, and the particle size was

105

 

 

measured via dynanric light scattering. A similar procedure was done using the HFM.
Between each run, the MVM was drained and cleaned, and the ﬂuid in the HFM was
ﬁltered. Particle size distributions were obtained for 60 seconds.
8.2.2 Media and Cultures

Mixed SRB cultures were isolated ﬁom sewage solids obtained from the
dissolved air ﬂoatation (DAF) unit of a municipal sewage treatment plant in Oak Ridge,
TN as described previously (Selvaraj, 1997a). The cultures were grown in lactic acid
(LA) media for seed cultures and 10 L batch reactor runs. Chloroform was added to the
LA media at 25 ppm to inhibit the growth of methanogens. The composition of this
medium is given in Table 11. A minimal salts (MS) medium was used for mass transport

limitation studies and as the primary reactor media. Its components are listed in Table 12.

106

 

 

Table 11: Lactic acid media

 

 

Component Concentration
Citric acid 3.6 g/L
CaCl2 0.8 g/L
NH4C1 1.0 g/L
K2HPO4 0.5 g/L
FeCl2 0.52 g/L
Yeast Extract 1.0 g/L
Cysteine HCl 0.05 g/L
Sodium Lactate
(60% Syrup) 5.8 mL/L
Butyric acid 0.52 mL/L

 

Table 12: Minimal Salts Media

 

 

 

Component Concentration
Na2HPO4 1.2 g/L
KH2PO4 1.8 g/L

MgClz 0.7 g/L

NH4C1 0.2 g/L

Fer 0.04 g/L

Mineral Water 50 mL/L
Batch Vitamin Solution 0.2 mL/L
Heavy Metal Solution 15 mL/L

 

107

 

 

 

The batch Vitamin solution and the heavy metal solution are given in Tables 13 and 14
respectively.

Table 13: Batch vitamin solution

 

 

Component Concentration
Biotin 2.0 mg/L
Folic acid 2.0 mg/L
Pyridoxine HCl 10.0 mg/L
Thiamine HCl 5.0 mg/L
Riboﬂavin 5.0 mg/L
Nicotinic acid 5.0 mg/L
DL-calcium pantothenate 5.0 mg/L
Cyanocobalamin 0.01 mg/L
p-amino benzoic acid 5.0 mg/L
Thioctic acid 5.0 mg/L

 

 

 

Table 14: Heavy metal solution

 

 

Component Concentration
EDTA 1.5 g/L
ZnSO407H2O 0.1 g/L
Trace Elements 6 mL/L

 

 

 

108

 

Table 15: Trace elements 11

 

 

Component Concentration
AlCl3 0.0507 g/L
KI 0.139 g/L
KBr 0.139 g/L
LiCl 0.139 g/L
H3BO3 3.060 g/L
ZnCl2 0.280 g/L
CuCl202H2O 0.326 g/L
NiCl206H2O 0.513 g/L
CoCl206H2O 0.513 g/L
SnCl202H2O 0.139 g/L
BaCl202H2O 0.163 g/L
Na2MoO402H2O 0.139 g/L
CuSeO405H2O 0.139 g/L
NaVO3 0.024 g/L

 

 

 

In serum bottles, the sulfate source was provided by the addition of up to 4.0 g/L
of Na2SO4 or MgSO4. In the CSTR, the sulﬁte source was provided by a 5% 802, 5%
CO2, and balance N2 gas. For growth on synthesis gas, a mixture of 47% CO, 36% H2,
10% C02, 5% CH4, and the balance N2, (Air Liquide, Houston, TX) was used. This gas

composition is typical of a coal-ﬁred, oxygen blown Texaco gasiﬁer (Simbeck, 1983).

109

For bottle studies, 100 mL of MS media in a 150 mL serum bottle with butyl rubber
stopper was made anaerobic by gassing with nitrogen followed by steam sterilization.
The synthesis gas was bubbled through the media after sterilization. The headspace was
monitored for synthesis gas components and hydrogen sulﬁde and was replenished with
fresh synthesis gas when needed. The bottles were usually shaken at 100 rpm at 30°C.
Tween 20 surfactant was used in the reactor studies at 4 times the surfactant critical
micelle concentration (240 mg/L).
8.2.3 Mass Transfer Limitation Studies

A 10 L glass carboy was used for a batch reactor for biomass growth. The carboy
had a stainless steel headplate that allowed for pH control, gas sparging, venting, and
liquid inlet/outlet ports. A pump cycled liquid through a loop with a pH probe, and the
pH in the reactor was controlled at 7.0 with Chemcadet controller (Cole Parmer
Instrument Company, Niles, IL) with 6 N NaOH and 6 N H3PO4. Nitrogen gas was
bubbled through the system to strip off the biologically generated H2S. LA medium was
used with the addition of 25 ppm chloroform and 4 g/L of sodium sulfate as a sulfur
source. The lactate concentrations were monitored by a model 2700 Dual Channel
Biochemistry Analyzer (Yellow Springs Instrument Co., Yellow Springs, OH). Sulfate
concentrations were also monitored. The reactor was stirred using a magnetic stirrer and
stirbar. When the lactate concentration dropped below 0.5 g/L, the reactor was stopped
and the biomass harvested with a IEC Chemical Centrifuge (International Equipment Co.,
Needham, MA) at up 5200 rpm with N2 gas to ﬁll the basket. The centrifuge was opened

in an anaerobic glove box under a nitrogen atmosphere, and the biomass was collected

110

from the centrifuge basket. The biomass was then resuspended in MS media and used for
mass transfer limitation experiments.
8.2.4 Fermentations
8.2.4.1 Conventional Sparging

A 2 L Virtis Omni-culture chemostat (Virtis Co., Gardiner, NY) with temperature
and agitation control was used as the primary reactor vessel. The vessel headplate was
modiﬁed for acid/base additions and gas and liquid inlets and outlets. The pH was
controlled at 6.6 with a Chemcadet controller (Cole Parmer Instrument Company, Niles,
IL) with 6 N NaOH and 6 N H3PO4. The reactor was agitated at 300 rpm. The reactor was
operated in a continuous mode with a feed rate of fresh MS medium at 0.2 mL/min. A
ﬁltration system consisted of two Amicon Diaﬂo hollow ﬁber cartridges (Amicon, Inc.,
Beverly, MA) operated in parallel. All pumps used were Masterﬂex peristaltic pumps
(Cole Parmer Instrument Company, Niles, IL). Nitrogen was sparged at 50 mL/min to the
reactor vessel to strip the produced H2S from the reactor. Synthesis gas was added

directly to the reactor through a stainless steel ﬁit. A ﬂow diagram is given in Figure 32.

111

(D
./e——>Vent

 

 

 

 

 

 

 

 

 

 

 

 

 

KT Synthesis
MS Medra ——.—6 1 Gas
soz/N2 H3PO4
| I I'— NaOH
I.
i v v i
l — '
/, :1—-—>< D
Figure 32: SO2 reducing fermentation ﬂow diagram
8.2.4.2 Microbubble Sparging

The reactor scheme used for microbubble sparging is similar to the apparatus used
for conventional sparging. The synthesis gas was supplied directly to the microbubble
generator. The synthesis gas microbubbles were delivered to the reactor through a
peristaltic pump. The liquid in the reactor was ﬁltered, with the solids being returned to
the reactor and the liquid being returned to the microbubble generator.
8.2.4.3 Mass Transfer Studies

The mass transfer characteristics of the fermentation were measured while the
system was under continuous sparging. The inlet synthesis gas ﬂow rate was changed,
and the resulting conversion of CO and H2 was monitored. A mass balance on the two

consumed gas components in the fermentation is given below (Klasson, 1991b).

112

L

[552.51% = K a“) __VLRT (31)

 

P50 P,” HG"
P‘ P’ V RT
i——’ =K,a”2 L _ (32)
P132 P,” HG‘

8.2.5 Analytical Techniques
8.2.5.1 Gas Chromatography

Hydrogen sulﬁde in the efﬂuent gas was analyzed using a gas chromatograph
(Hewlett Packard HP 5890 Series II) equipped with a teﬂon column (30 in x 1/8 in)
packed with Super Q (80/ 100 mesh) (Alltech, Waukeegen, WI). Temperatures of the
column, injection port, and thermal conductivity detector were 70 0C, 125 °C, and 125 0C
respectively. The canier gas was helium at 25 mL/min. The calibration was based on 1%,
5%, and 10% H23 in nitrogen standards. Synthesis gas components were measured using
a gas chromatograph (Hewlett Packard HP 5890 Series II) equipped with a HP PLOT
molecular sieve 5 A capillary column (30 m x 0.32 mm) with a 12 um ﬁlm thickness.
Temperatures on the column, injection port, and thermal conductivity detector were 55
°C, 100 °C, and 240 °C respectively. Liquid samples were ﬁltered through a 0.22 pm
syringe ﬁlter and analyzed by gas chromatography using a HP 5890 Series II with a HP
WAT (crosslinked PEG) capillary column (30 m x 0.53 mm) with a 1.0 pm ﬁlm
thickness. The column temperature program was initially 70 °C followed by ramping to
200 °C at 25 oC/min with a 1.2 min hold then ramping to 225 °C at 25 °C/min with a 3.0
min hold. The injection port temperature was 245 °C while that of the ﬂame ionization

detector was 265 °C.

113

.____.. __..-.. _._._ .. _ .. .. ._. --....___ _.. W,

3.2.5.2 Sulfur Chemistry

The sulﬁte in the reactor was analyzed spectrophotometrically by the reaction of
fuchsin and formaldehyde in sulfuric acid (Steigrnan, 1950). The sulﬁde in the reactor
was precipitated using zinc acetate in a basic solution. The resulting zinc sulﬁde was
resuspended and reacted with dimethyl-p-phenylenediamine and ferric chloride to form
methylene blue. The concentration of sulﬁde was then measured spectrophotometrically
at 660 nm and compared to a sulﬁde calibration curve. The concentration of a sulﬁde
solution was determined from potentiometric titration with a standard lead chlorate
solution until an endpoint was reached. From this known sulﬁde concentration an
calibration curve was constructed. A sample of the potentiometric titration is given in

Figure 33 below.

~780 '

ii) 1 2 3 4 5 6 7 8
-800 -.

‘-
I
It
._
-
-
I.
-

   
 

-820 ..

-840 .1 i-

'860 u- u-

-880 ..

Potential (mV)

-900 ..

-920 .1-

-940 .

 

4
-960 .1.
mL 1000 ppm Pb(CIO4)2 added

Figure 33: Potentiometric titration of sulﬁde

114

8.2.5.3 Most Probable Number (MPN) and Misc. Analytical

In all runs the reactors were monitored for 8032' and suspended solids. Efﬂuent
gas was also monitored for H2S and synthesis gas components. Efﬂuent gas ﬂow rates
were monitored with a wet test meter (GCA/Precision Scientiﬁc, Chicago, IL) for two
hour periods. For solids determination, the liquid samples of known volume were ﬁltered
through tared Whatrnan glass microﬁber ﬁlters (Grade GF/C) using a Gelman 25 mm
polysulfone ﬁlter funnel. The ﬁlters were then dried in for 2 h in an oven at 60 OC
followed by cooling to room temperature. The SRB in the liquid samples were
enumerated by the MPN method using SRB medium from Bioindustrial Technologies,
Inc. (Houston, TX) as described previously (Selvaraj, 1997a).
8.2.6 Carbon and Electron Balances

Mass balances on sulfur and carbon were done with 99.6% conversion of SO2 to

H2S and no liquid-phase products assumed.

C0”' + C05" = C0“ + cog“ (33)

S0321 : HZSout + SZ—,out + 8032-011! (34)
An electron balance was done around the reactor and is shown below.

CO H, .90? _ C02 HZO
yCOnconvert + 7H2 ”convert + 7503* ”convert _ ySZ- nS2- + yCOanrod + 7H20nprod (35)

The reductance degrees, y, for CO, H2, SO32} S2", CO2, and H20 were 2, 2, -8, -2, 0, and 0

respectively as suggested by Erickson (1978).

115

 

 

8.3 Results and Discussion

8.3.1 Conﬁrmation of Mass Transfer Limitations

Biomass was grown in a 10 L batch reactor on lactate and was harvested and
resuspended in the MS. The cultures were then switched to a synthesis gas feedstock and
adapted to it over a period of two or three days. At the start of the experiment, the
headspace and liquid of each biomass concentration (0.45 g/L, 2.40 g/L and 5.45 g/L)
was sparged with fresh synthesis gas for 5 minutes prior to monitoring by GC. The
headspace in each bottle was sampled and analyzed every 30 minutes. The pressure
inside of the serum bottles was monitored using an inert tracer gas, CH4. Since the
bacteria did not consume or produce this gas, the amount in each sealed serum bottle
would not change during the fermentation. Therefore, using a ratio of ﬁnal concentration
of CH4 to initial concentration of CH4, the pressure inside of the serum bottles could be
adjusted. Carbon monoxide depletion is shown in Figure 34, and hydrogen depletion is

shown in Figure 35.

116

 

[cm/[c0]o

1.2

.._.—_C_. .—

 

 

 

 

 

 

 

0.8 .. I
o
A
. . _
0.6 .. . g o 0.45 g/L solids {
A . 2 2.4 g/L solids
7 g 5.45 g/L solids ;
0.4 I. . L— " hi
A I
02.. ’-
A
A I
0 ‘ ' ' . . - iH‘LH—l—H—
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

Time Elapsed (hours)

Figure 34: CO uptake by SRB in batch serum bottles

117

9.00

1.2 ,

 

 

 

 

1 A
I
‘- ‘I I I O. ‘
I t
0.8 .-
r 0.6 ..
'1': _ I
E, ,9 0.45 g/L solids ; °
04 .2AgAsmMsi
' 1. 5.45 g/L solids f
" t I
0.2 .. o '
A
0 .L : : ' s 4 :: :

 

 

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00
Time Elapsed (hours)

Figure 35: H2 uptake by SRB in batch serum bottles
The uptake pattern of synthesis gas components by SRB is typical of other
synthesis gas consuming bacteria (Vega, 1989b). Typically CO is consumed ﬁrst to some
critical concentration before H2 uptake begins. This pattern may be due in part to
inhibition of the hydrogenase enzymes by CO (Ragsdale and Ljungdahl, 1984). The
inhibition of the hydrogenase enzymes by CO is through reversible binding of CO to the
iron-sulfur active site of the enzyme (Adams, 1987). Also, this trend could be due in part

to the production of H2 from the CO metabolism by SRB (Yagi, 1959).
The uptake rates of both carbon monoxide and hydrogen did not show signiﬁcant
variation for the different concentrations of biomass. Vega et al. (1989b) and Worden et
al. (1989) show similar results for other synthesis gas consuming bacteria where the

uptake rate became independent of biomass concentration. As shown in Table 16, an

118

 

order of magnitude change in concentration of biomass did not cause signiﬁcant changes

in the uptake of the CO component of synthesis gas.

Table 16. Synthesis Gas Uptake from Serum Bottles

 

 

 

Suspended Solids CO (mmol/h) H2 (mmth)
0.45 g/L 19.0 i 9.9% 28.7 i 11.0%
2.40 g/L 17.8 i 10.4% 24.3 i 0.1%
5.45 g/L 18.8 i 2.7% 14.6 i 3.6%

 

This indicates that the serum bottles were mass transfer limited for CO at all three of the
biomass concentrations tested. However, decreased H2 uptake was observed at the higher
biomass concentration of 5.45 g/L. This may be due to mechanism in the system where
the hydrogenase enzymes are more inhibited by CO and higher biomass concentrations,
an artifact, or analytical errors. These data show that the serum bottle was also mass
transfer limited for H2 at all three of the concentrations tested. The MPN number was
determined from the 0.45 g/L serum bottle and was found to be 1.10 x 10H cells/L. The
average mean weight of a dry cell of SRB is 3.125 x 10'13 g/cell (Postgate, 1984).
Therefore the dry weight of the SRB in the serum bottle was 3.44 x 10'2 g/L, indicating
that the viable SRB concentration in the bottle was only 7.6% of the total solids.
8.3.2 Conventional Sparging

A CSTR was operated for extended periods of time using synthesis gas as a
feedstock. The SO2 ﬂowrate was gradually increased until the efﬂuent concentration of
8032' began to increase. At this point the ﬂow of SO2 to the reactor was decreased until
100% conversion of SO2 was achieved. Sulﬁte, S037”, is toxic to SRB. Concentrations of

40 ppm seem to have signiﬁcant inhibitory or toxic effects on SRB observed when the

119

 

S03 concentration in the reactor was increased above 40 ppm. Sulﬁte is formed when
SO2 is dissolved in water. An increase in the 8032' concentration indicates that the
maximum SO2 conversion rate has been obtained. The reactor was capable of a maximum
throughput of SO2 of 1.23 mmol/h*L with 100% conversion of SO2 to H2S. The reactor
utilized 1.8 mmol H2 and 2.3 mmol CO per mole of SO2 reduced.

The suspended solids concentration was measured to be 3.17 g/L, and the MPN
was determined to be 2.3 x lOlZ/L when the reactor was determined to operate at steady-
state. These numbers indicate that 22% of the suspended solids are viable SRB. While the
mass transfer characteristics of the CSTR are certainly different than the serum bottles,
the comparable biomass concentrations in both systems suggests that the CSTR could be
mass transfer limited, i.e. the effective concentration of the liquid-phase substrates were
approximately zero.

A N2 sparge directly into the reactor was necessary to insure adequate stripping of
H28 from the reactor vessel to prevent inhibition of culture growth and productivity. Reis
et al. (1992) found a concentration of 547 ppm was capable of totally inhibiting grth in
SRB and suggests that this toxicity is reversible. The pH was maintained at 6.6 to give
good growth characteristics while keeping the produced H2S as hydrogen sulﬁde that was
capable of being stripped. At higher pH, much of the H2S exists as S2" (Grethlein, 1992b)
and cannot be stripped from the liquid. The equilibrium reaction under aqueous

conditions is given in Equation 36 below (Grethlein, 1992).

HZS¢:>H++HS' pKa1=7.04

(36)
HS‘c>H++S2' pKa2=12.0

The mass transfer characteristics of the reactor with conventional sparging were

determined. Once again, the inert methane tracer was used to adjust for changes in

120

 

 

 

 

pressure and dilution of the component gases by N2. The volumetric mass transfer
coefﬁcients for CO and H2 were calculated from the slopes in Figure 36 and Figure 37,

respectively. The data are plotted as suggested by Equations 31 and 32. Under mass

VLR T

g

 

transfer limited conditions, the slope should be equal to K La

4.5 ..
4 ..

3.5 ..

    

 

 

3:
l
>-
O.
. 2-5 -r y = 22.749x + 0.6764
8 R2 = 0.8896
3 2 ..
7) O
0
"9:15 .1.
1 ..
0.5 --
0 1 : k 1 4' i 1 :
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
1N (min/mL)

Figure 36: Mass transfer coefﬁcient for CO

121

 

 

 

 

  

y = 47.211x - 0.2524

   

(PIHZIPOHZ'PiIIPOI)
A

 

 

3 .. R2 = 0.9946

2 ..

1 ..

0 : : : i I. i : :
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

1N (min/mL)

Figure 37: Mass transfer coefﬁcient for H2
The subsequent calculated KLa values calculated from the slopes of Figures 36 and 37
with conventional sparging were 30 h’1 and 75 h'1 for CO and H2, respectively. These
values are similar to the KLa value for CO measured in a mass transfer limited 1 L CSTR
for a mixed triculture synthesis gas fermentation (28.1 h'l at 300 RPM (Klasson, 1992)).
The KLa values for CO and H2 are related through their diffusion coefﬁcients (Cussler,
1984) as shown by the deﬁning equation for the mass transfer coefﬁcient based on ﬁlm

theory.

k,=

D
I (3 7)

The ratio between diffusion coefﬁcients calculated by the Wilke-Chang equation is 1.93

for H2 to CO. The ratio of the experimental mass transfer coefﬁcients measured is 2.5.

122

 

8.3.3 Microbubble Sparging

In the control run, a separate liquid reservoir bottle with surfactant was used to
simulate the microbubble generator; the liquid was pumped from the reservoir bottle to
the reactor at a ﬂowrate that would be comparable to the rate liquid would be carried over
in the microbubbles, i.e. from 3 mL/min to 7 mL/min. The dual ﬁlter system was capable
of handling the increased liquid processing requirements. Fresh feed was added to the
reactor at 0.2 mL/min and removed from the reservoir bottle at 0.2 mL/min.

The system was brought to a maximum productivity of 1.25 mmol/h*L with
conventional sparging and maintained for two days. The microbubble generator replaced
the liquid recycle bottle, and the synthesis gas was added to the reactor as microbubbles.
The synthesis gas ﬂow rate to the reactor remained at a constant 10 mL/min (of gas
phase) for both conventional and microbubble sparging. The ﬂow rate of 802 was slowly
increased over the period of 24 hours until a maximum productivity was obtained with
microbubble sparging. The SO2 throughput in both phases of this experiment and the

subsequent 8032' concentration are shown in Figure 38.

123

400 .. .. 2.5

  
  
 
 
 
 
   

350 ..
.2---~______ _. _ _ _ _. .. 2 A
300 .. -a-Sulﬁte (mg/L) 1 g.
—o— 802 Throughput (mmol/h.L) l a
d 250 "' .. 1.5 a
g: ::
v 5
3 200 .. a

2.:
.. .. 1 =
0:) 150 .. e
.4:
[-1
100 .. N
. 0.5 8
50 ..

 

 

 

 

Figure 38: Reactor productivity

The maximum reactor productivity obtained using microbubble sparging is similar to the
value of 1.27 mmol/h*L obtained by Selvaraj et al. (1997a) using soluable substrate;
sewage digest medium. This result indicates that at the maximum reactor productivity
using microbubble-sparging the reactor might no longer be in the mass transfer limited
regime. These results also provide more evidence that the CSTR under conventional
sparging was mass transfer limited. By keeping the ﬂowrate of the gaseous substrate
constant and only decreasing the average bubble size entering the reactor, a 2-fold
improvement in the maximum SO2 throughput was obtained.

To obtain the mass transfer coefﬁcients using microbubble sparging, the same
approach as conventional sparging was used. The derivations of Equations 31 and 32 did

not account for the small amount of dissolved CO or H2 that is carried into the bioreactor

124

 

by the interstitial liquid of the microbubble foam. However, this amount of dissolved

gases was calculated to be negligible compared to the amount of gas that enters with the
microbubbles and is transferred to the medium. Due to the difﬁculty of maintaining long-
term (more than 2 or 3 days), high-productivity, microbubble-sparged fermentations, only
two data points have been obtained for the evaluation of KLa values. Using those two
data points, an estimate of the KLa value for CO was 104 h’1 and for H2 was 190 h].
These numbers represent a 3.4-fold increase for CO and a 2.6-fold increase for H2 with a
H2/CO ratio of 1.85. These numbers compare well with the mass transfer coefﬁcient
determined in Chapter 6 of 91 h'1 for CO. These numbers are comparable regardless of
impeller speed, because the volumetric mass transfer coefﬁcients from microbubbles
have been shown to be independent of impeller rate (Chapter 6, Kaster 1990).

The difﬁculty in maintaining long-term, high-productivity SRB fermentations is
the potential instability due to the rapid build-up of a toxic compound, 8032', if the
fermentation fails. Once the SO32" concentration begins to rise, the reaction rate slows
down, causing the S032" concentration to rise faster. At the maximum productivity using
microbubble sparging, toxic levels (>40 ppm) can build up within 20 minutes if a failure
in the bioconversion occurs.

8.3.4 Carbon and Electron Balances

The sulfur, carbon and electron balances were calculated for the data giving the
maximum productivity for both conventional and microbubble sparging. For
conventional sparging, the inlet sulﬁlr was recovered to 98% in the outlet sulfur
compounds, with 99.6% of the outlet sulfur being H28 and 0.4% being 82’. There was no

measurable SO32" present in the reactor. The available carbon was 95% recovered in the

125

outlet carbon dioxide. The remainder of the carbon may have been incorporated into
various liquid phase products such as acetate, propionate, and cell mass. Of the available
electrons, 88% were recovered in the H2S and 82'.

For microbubble sparging, the inlet sulfur was recovered to 91.6% with 97.2% of
the available sulfur recovered in H2S. The available carbon was recovered to 88.4% in
outlet carbon dioxide. Similarly, 86.2% of the electrons were recovered in the outlet

sulfur compounds.
8.4 Conclusions

Experiments in both serum bottles and stirred-tank reactors provided evidence
that synthesis-gas-fed sulfate reducing bacteria fermentations are typically mass transport
limited. In the serum bottles experiments, increasing biomass concentrations did not
increase the rate of synthesis gas uptake. In the stirred tank reactor, the maximum
productivity increased signiﬁcantly upon switching from conventional bubbles to
microbubbles. The KLa values for the conventionally-sparged SRB fermentations in the
stirred tanks were 31 h'1 for CO and 75 h'1 for H2. These values are comparable to
literature values for synthesis gas fermentations in lab-scale stirred tanks. The maximum
productivity was 1.25 mmol/h*L.

Upon switching from conventional sparging to microbubble sparging, with no
change in the ﬂow rate of the synthesis gas, a 2-fold increase in reactor productivity was
obtained within 24 hours. By increasing only the interfacial area available for mass
transfer, a maximum reactor productivity of 2.5 mmol/h*L was obtained. Finally,

preliminary mass transport coefﬁcients obtained during microbubble sparging indicate a

126

 

3.4 fold increase in Km for CO and a 2.6 fold increase for H2 over the conventionally
sparged-stirred tank.
8.5 Nomenclature

8.5.1 Symbols

a = interfacial area per unit gas volume (ml)
CO = ﬂow of moles CO (mol/min)

CO2 = ﬂow of moles CO2 (mol/min)

G = Total gas ﬂow rate (mL/min)

H2S = ﬂow of moles H2S (mol/min)

H = Henry’s Law coefﬁcient (atm/mol‘L)
H = stagnant layer ﬁlm thickness (m)

KL = mass transfer coefﬁcient (m/s)

n = number of moles (mol)

R = gas constant

S2' = ﬂow of moles SZ‘ (mol/min)

SO2 = ﬂow of moles SO2 (mol/min)

8032' = ﬂow of moles SO32' (mol/min)

T = Temperature (K)

t = Time (h)

VL = Volume (L)

8.5.2 Greek Symbols
y = reductance degree

8.5.3 Subscripts and Superscripts

127

in,i
out,o
C0
C02

SO2

H28

H20

so32'
convert

prod

inlet

outlet

Carbon monoxide
Carbon dioxide
Sulfur dioxide
Hydrogen
Hydrogen sulﬁde
Water

Inert component
Sulﬁde

Sulﬁte

converted

produced

128

9. COALESCENCE

9.1 Introduction

Coalescence in stirred vessels has been extensively studied for liquid—liquid
dispersions by Coulaloglou and Tavlarides (1977), Tsouris and Tavlarides (1994), and
Sovova and Prochazka (1981) among others. The above authors have successfully used
the population balance equation (PBB) model to describe the relative rates of breakage
and coalescence in dispersive systems. The pbe model has also been used to describe
ﬂocculation in colloidal systems (Tsouris, 1995b; Tsouris, 1995a) and for bubbles
(Prince, 1990; Oolman, 1986b). This model is very useful in describing the history of a
pOpulation in terms of properties such as size, age, and concentration, and interaction
events with themselves and their environment.

Prince and Blanch (1990) studied bubble coalescence in a bubble column under
laminar, buoyant, and turbulent shear. They considered that the coalescence of two
bubbles in turbulent ﬂow occurs through three steps. The ﬁrst step is the collision of two
bubbles, which traps a thin ﬁlm of liquid between them. The rate of collisions is a key
kinetic parameter during this step. The second step is drainage of the liquid ﬁlm between
the two bubbles until a critical thickness is reached, and the third step is the rupture of the
thin ﬁlm, at which point the two bubbles become one. The coalescence efﬁciency is a
second paramater that controls whether two bubbles will coalesce and is deﬁned as the
fractional probability that two colliding bubbles will undergo a coalescence event. For
two bubbles to coalesce, the time the bubbles remain in contact must be greater than the
time required for the drainage of the liquid ﬁlm between the bubbles. The same

mechanism for drop coalescence was proposed by Coulaloglou and Tavlarides (1977).

129

 

The effects of surfactants in both liquid-liquid and gas-liquid dispersions have
also been studied. Koshy et al. (1988) studied the breakage of droplets in a water-styrene-
Teepol (surfactant) system. They reported that the breakage of drops in stirred
dispersions is affected by the surfactant not only through the reduction of the surface
tension, but also through the generation of an interfacial surface tension gradient along
the drop surface through drop deformation (Koshy, 1988). The surface tension gradient
results in an extra stress (Maragoni stress) that adds to the turbulent stress, increases the
breakage rate, and thereby reduces the average droplet size formed. This idea is also
supported by work in gas-liquid dispersions by Zahradnik et al. (1995), which found that
there is an overall smaller bubble size in an electrolyte-laden system over a ‘clean’
system. This observation indicates decreased bubble coalescence in the presence of the
electrolyte due to surface immobilization. These observations support the earlier work of
Prince and Blanch (1990), who also studied the effects of electrolytes in bubble columns.
One of the assumptions made in the development of the Prince and Blanch model was
that bubble coalescence does not occur in systems where the salt concentration is
sufﬁcient to immobilize the gas-liquid interface. Therefore, in their model, the
coalescence efﬁciency of bubbles with immobile interfaces is taken to be zero. This
assumption is based on ﬁlm thinning times. The ﬁlm thinning time for bubbles with
immobile interfaces has been predicted by Prince and Blanch to be on the order of
seconds, and even in the case that surfactant transport is incorporated to give a partially
mobile gas-liquid interface, the coalescence times are still on the order of hundreds of

milliseconds (Prince and Blanch, 1990). Comparatively, the contact time in turbulent

130

dispersions was calculated to be 10 ms, which is much smaller than the coalescence time
that is needed for coalescence to occur.

Because the proposed structure of microbubbles generated in this work includes a
stagnant water shell, there should be minimal coalescence, according to the assumptions
from Prince and Blanch (1990). However, microbubbles do coalesce, as shown by the
dynamic measurements of bubble size performed in this study. Therefore, the assumption
that coalescence is negligible in systems with immobile surfaces was rejected. However,
the coalescence rate of microbubbles is low in comparison to conventional bubbles. It is
the purpose of this chapter to describe the dynamic coalescence phenomena of
microbubbles in a stirred tank. The effects of increasing the amount of surfactant present

in the surrounding liquid was investigated through both experiments and modeling.
9.2 Mathematical Model

9.2.1 Population Balance Equation Model
The population balance equation model is presented below with terms for both

coalescence and breakage.

6n(v, t)

at
where n(v,t) is the number of bubbles of volume v at a given time t, and D, B represent

+D—B=O o&

the death and birth rates of bubbles from coalescence and breakage. These terms are

given in the following equations:

D = n(v,t) f1(1),v')h(v,v')n(v')dv'+g(v)n(v,t) (39)

and

B = VJMV — v' )h(v — v' )n(v — v’ )n(v' , t)dv'+oj[ﬂ(v, v' )U(v' )g(v' )n(v' , t)dv' (40)

0

131

where u(v’) is the number of bubbles formed from the breakage of a drop of volume v’;
,B(v,v’) is the probability density of the daughter bubbles, which represents the probability
of forming bubbles of size v from breakage of drops of size v’; g(v’) is the breakage
frequency of bubbles of volume v’; h(v,v) is the collision frequency of bubbles of
volumes v and v’; l(v,v’) is the coalescence efﬁciency once collision occurs between
bubbles of volumes v and v’. Volume discretization of equation 38 gives a system of
integro-differential equations that represent an initial value problem that can be solved
numerically (Coulaloglou and Talvarides, 1977; Tsouris and Talvarides, 1994). This
model describes the history of the bubble population in terms of bubble properties, such
as size, age, and concentration, during the course of bubble interaction events with
themselves and the surrounding environment.

Since the microbubbles formed in this work are very small in comparison with
typical bubbles, the rate of breakage may be negligibly small and hence neglected in the
pbe model. The small size of the bubbles would require extremely high levels of shear in
order for further breakage to occur. In order to evaluate whether breakage may be
signiﬁcant, the maximum stable bubble size, dcr, can be estimated using the following

correlation (Shinnar, 1961),

EN2
dc, = Cm We‘o'éD, We = LL— (39)
0'
where We is the Weber number, deﬁned as the ratio of surface tension forces to dynamic
pressure forces, and Cm is a constant in literature (Sprow, 1967) as 0.125. For dilute

suspensions, the critical diameter below which bubbles do not break, def, is the same as

the maximum stable drop size, domax (Shinnar, 1961). To account for the holdup effect on

132

the maximum stable drop size for a non-dilute suspension, considering Kolmogorov’s

3
microscale (with the ratio K— ), Doulah (1975) showed the following,
5

8: = (”—1 (42)
8 V

. . . . . . '3 .
where 8C 15 the energy drssrpatron rate per unit mass for the pure contrnuous phase, 8 rs

 

the energy dissipation rate per unit mass of the dispersion, and v. and vc are the
kinematic viscosities for the dispersion and continuous phase, respectively. Taylor (1932)

derived the following relationship for the apparent viscosity of a liquid dispersion.

g‘ = )1, 1+ 2.54%] (43)
lud + Iuc

Using Equations 42 and 43, and the assumption that for dilute suspensions, pc = pi, the

following expression can be used to describe the effect of holdup on the maximum stable

bubble size (Tsouris and Tavlarides, 1994).

1.2
dc, = cm We‘0-6D, [1 + 25¢[WJ] (44)
#d + #c

For the experimental system used in this work, dcr was calculated to be 356 um, above

which bubble breakup becomes signiﬁcant enough that it can no longer be neglected.

From the dynamic experimental data obtained over six minutes, the mean bubble size was
found to range between 66 um and 130 pm with 98% of all bubbles measured to be

below the calculated dcr. Thus breakage was neglected in the population balance

equations over the time frame examined. The simpliﬁed birth and death terms are shown

below.

133

 
 

 

D = n(v,t)?ﬂ.(v,v‘)h(v, v')n(v')dv’ (45)

v/2
B: JA(v—v',v')h(v—v',v')n(v—v',t)n(v',t)dv' (46)
0
9.2.2 Collision Frequency
Energy dissipation in the system is how much mechanical energy is being
supplied to the ﬂuid in the vessel. In the experimental system used in this work, the
energy dissipated is supplied by the impellers. The amount of energy dissipated depends

on the impeller size, speed, and tank geometry as shown below.

N31).5
T4; (47>

 

8(x,y,z) = kl (x, y, z)

where T and H represent the vessel diameter and height respectively. Assuming that the
constant, k1 is not a function of position in the vessel, the mean energy dissipation can be

determined. Bertrand (1980) used the following relation if T=H=2Di.
.1} = 0.81N3Df (48)

where 1:: is the average energy dissipation in the system. The inﬂuence of inhomogeneity
of the turbulence in stirred vessels on the coalescence and breakage has been studied
(Coulaloglou and Talvarides, 1977; Tsouris and Talvarides, 1994). The inhomogeneity of
the turbulence is an important factor in the determination of the breakage ﬁequency,
which however, was neglected in the experimental system used here. The model in this
study uses the mean energy dissipation as suggested by Bertrand (1980), but with the
result doubled to account for the presence of dual impellers in the experimental system
used in this study. Since the system has a low gas hold-up, the gassed power draw on the

second impeller is the same as the power draw on the ﬁrst impeller (Tatterson, 1991).

134

The assumption that the bubbles are in the inertial subrange is necessary to
neglected short-range forces such as Van der Waals and that energy is transferred from
eddies to bubbles. In order to verify this assumption, the wave number of the bubbles (the
inverse of the bubble diameter) is compared with the limits of the eddy wave number.
The lower limit on the size of the eddies in the vessel is given by the Kolmogorov

microscale and it is given by:

3 H4
r" = 2(3) (49)

For a mean energy dissipation of 24,000 cmz/S" which corresponds to 500 rpm agitation
speed in our system, rn=0.0025 cm and kn=398 cm'l (upper limit of the eddy wave
number). The largest possible eddy size in the vessel is on the order of the impeller
radius. For a 5 cm diameter impeller, ke=1/re=0.4 cm]. The number-averaged bubble size
in the vessel ranged from 60 pm to 165 pm during the study, which gives a kd from 60
cm’1 to 167 cm". Therefore, ke<kd<kn which shows that the bubble size range is in the
inertial subrange.

The bubble-bubble collision frequency can be obtained by making the assumption
that the bubbles in the turbulent flow behave like gas molecules. The following
expression can then be used to describe the collision frequency (Tsouris and Tavlarides,

1994),
72' 2 — —' I/2
h(d,d')=—Z(d+d') (u2 +u'2) 1111' (50)

where 17 , the average velocity of a bubble, is given by:

17:1.0732’3d2’3 (51)

135

9.2.3 Coalescence Efﬁciency

The binary coalescence efﬁciency of bubble collisions has been described through
the physical events occurring. The efﬁciency is a function of the contact time between
bubbles, which can be described through hydrodynamics and bubble size, and the
coalescence time, which can be described through energy, surface and ﬁlm characteristics
of the bubble and bubble size. An expression for coalescence efﬁciency given by

Coulaloglou and Tavlarides (1977) is given below:

202,1») = e'”; (52)

where tis the average contact time and ris the average coalescence time between
bubbles of volumes v and v’.

The contact time between bubbles depends on the energy dissipation and the
bubble size. High levels of turbulence increase the likelihood that an eddy will separate
the two bubbles. Large bubble surfaces provide larger areas for contact between bubbles.
The following equation gives an estimate of the contact time in turbulent ﬂows (Levich,

1962).

t — (53)

 

The coalescence time, E, has been described by Coulaloglou and Tavlarides
(1977) through drainage of the continuous phase ﬁlm between bubbles. If the contact
time between the bubbles is sufﬁcient for the ﬁlm to drain and thereby longer than the
coalescence time, coalescence will occur. Making the assumptions of a pure system (a
system without surface active agents that can absorb at the interface) where Van der

Waals and double-layer forces are not present and retard rupture which arise from the

136

absorption of surface active agents, the following model for the coalescence time was
derived (Coulaloglou and Tavlarides, 1977).

— 82/3d.+d. ” dd. 4
TZI—toz’ucpc (I j)2 1 1 l} (54)

0'2 23.—207 di+dj

 

which results in the ﬁnal expression for the coalescence efﬁciency.

 

4
#1 P8 did}
/l(di,d.)=exp -k C c (55)
l j 10(1+¢)3[di+dj]

Sovova (1981) suggested that Equation 55 favors the coalescence of smaller
bubbles and suggested the following model based on the assumption that the forces of
adhesion are weak in comparison with the turbulent forces in the system and are

consequently unable to control the coalescence rate (Howarth, 1964).

226,1»): exp[— k2 “(’m ”23”") l (56)

pdN2D4/3W.(v2/9 + v.2/9)

 

In this expression, the bracketed term is proportional to the interfacial energy of the drops
and inversely proportional to the energy of collision. Tsouris and Tavlarides (1994)
present that the following represents a more exact representation of ratio of the interfacial

energy and the energy of collision.

 

, 0' V2/3 +V'2/3
22(v,v)=exp[—k3 ,0 N2g4/3(v11/3 +1.11/3):| (57)
d i

In reality, a combination of both expression may accurately describe the system. The

following expression is suggested by Sovova (1981).

/l(v, v') = 211 (v, v') + A, (v, v') — xi, (v, v')/l2 (v, v') (58)

137

Tsouris and Tavlarides (1994) proposed a modiﬁcation of the Coulaloglou model
(Coulaloglou and Tavlarides, 1977) for coalescence efﬁciency that is based on a kinetic
collision model with the assumption of spherical nondeformable drops rather than on a

dynamic, active surface model to be applicable for more dense dispersions.

 

xi d,d' =ex —
( ) pI: p682/3(d+d')2/3 (TzHy/B

where g is deﬁned by the following expression:

h“2 1.378 h“2 0.12
5:1.8721n[ 0‘ + q]+0.127ln[ ° + 3 q] (60)

h)” +1.378q hyz +0.312q

 

 

and q, the ratio of the continuous phase to the dispersed phase viscosities normalized by

the geometric average of the bubble diameters, is deﬁned by the following expression:

6 rr' ”2
#1771 ‘6”

Other researchers have proposed more complex models to describe the
coalescence of droplets. Das et al. (1987) proposed a white-noise model, which considers
ﬁhn drainage between two colliding droplets as a stochastic process. Muralidhar et al.
( 1986) looked at the white noise model with large drainage rates and later proposed a
band-limited noise model after studying the coalescence of droplets in a stirred dispersion
(Muralidhar, 1988).

Prince and Blanch (1990) developed a model for the coalescence time of bubbles
in a bubble column that was used in this study. The thinning of a liquid ﬁlm between two

bubbles of equal size can be given as (Oolman, 1986a):

138

 
 

 

 

 

2 l/2
—__. 8 42(2) .22. .3 (.2)
dt Rip, RgT dc rb 67th

In the following analysis, the effect of Hamaker forces in equation 62 have been
neglected. These forces generally become more signiﬁcant just prior to rupture at very
thin ﬁlm thicknesses. Numerical solutions to equation 62 with the assumptions that
bubble deformation by turbulent eddies is neglected and that the thickness of the liquid
disk between coalescing bubbles (Rd) is a constant fraction of the bubble radius leads to
the following expression for the coalescence time (Prince and Blanch, 1990).

r3 1/2 h
2: '—"p" 111—°— (63)
160' hf

where rij is the equivalent radius of the two bubbles, which is given by the following

—1
j 2 rm. ’12.;

which results in the ﬁnal expression for coalescence efﬁciency (Prince and Blanch,

expression.

1990).

 

3/2p1/281/3
_ ‘1' "
21(di’dj)_exp|:-k5 01/2db2/3 ] (65)

The values of the initial ﬁlm thickness, ho, and the ﬁnal ﬁlm thickness, hf, have been
given in literature at 10'2 cm and 10'6 cm respectively (Prince and Blanch, 1990), and are
system speciﬁc. The initial ﬁlm thickness for microbubbles may be signiﬁcantly thicker
than the literature value for conventional bubbles due to the shell surrounding and

stabilizing the microbubble.

139

2.4 Solution Technique

Several different models for the coalescence efﬁciency were examined in this
study. The ﬁrst model examined was that developed by Coulaloglou and Tavlarides
(1977) using Equations 38, 45, 46, 50, and 55. The second model used the coalescence
efﬁciency suggested by Prince and Blanch (1990) which was obtained by modeling the
ﬁlm drainage between two bubbles and its solution is given Equation 65. Discretization
of the PBE equation (Equation 38) gives a system of nonlinear ordinary differential
equations that form an initial value problem. The bubble size was discretized using
volume (Tsouris and Tavlarides, 1994), enabling tighter closure of mass balances on the
system than if discretization based on bubble diameter had been used. Therefore, two
bubbles in the ﬁrst or smallest volume class will coalesce to give a bubble of volume
class two. So, the discretization is via the minimum bubble volume (vmin): where class 1
is vmin, class 2 is 2*vmin, class 3 is 3*Vmim etc. One hundred individual volume classes
were used in the discretization for all simulations. The system of equations was solved
using the EPISODE package by Byme and Hindrnarsh (1976) with the computational
results being tested by the closure of the mass balances. The mass balances were done by
calculating the volume of dispersed phase (gas) present before the time step used and
calculating the volume of dispersed phase present after computation. If the mass balances

did not close, it indicated a computational error or bad input data.
9.3 Materials and Methods

9.3.1 Coalescence Measurements
Measurements of bubble coalescence were made in a stirred tank. The tank was

constructed of optical quality plexiglas and was built as a 10-sided vessel to maintain

140

approximate geometric similarity to cylindrical stirred tanks. The vessel was 4" in
diameter with a height of 8". Liquid was ﬁlled to the 4" height during the experiments.
The vessel had four 0.4" wide bafﬂes that were constructed from Plexiglas and fused to
the inside of the tank. Mixing was maintained via an electric motor (Talboys #37830,
Cole Parmer, Chicago, IL) with dual Rushton type impellers having a 2" diameter. The
impellers were mounted 1" and 3" above the bottom of the vessel. The microbubbles
were injected into the vessel at the wall through a port at the base of the vessel using a
syringe.
9.3.2 Particle Size Distributions

Particle size distributions were obtained using a long-range microscope Questar —
Model QM100 (Questar, New Hope, PA). The long focal length of the microscope
allowed focusing in a particular section of the vessel at a distance of 2 cm from the wall
of the vessel to avoid any obvious wall effects. Selection of a wide-angle lens for the
microscope allowed for a signiﬁcant ﬁeld of view, capable of giving bubble sizes that
range from 5 pm to 1000 um in the viewing area. The microscope was attached to a
digital camera of a shutter speed up to 10,000 per second (Burle, Lancaster, PA). The
camera was set at the maximum speed of 10,000 frames/second to freeze the motion of
the bubbles and obtain the best possible images for later analysis. An example of the
images obtained is shown in Figure 39. The images were recorded using a Panasonic
Super VHS videocassette recorder.

The microbubble generator used for these studies was constructed at ORNL and is

described in both construction and performance in Chapter 8.

141

 

The system was calibrated by placing a 70 um wire into the system and focusing
on the calibration wire. The experiment was then run after the wire was withdrawn
without changing the position or focal length of the camera/microscope arrangement.
After the images were acquired, they were analyzed by capturing each frame from the
videotape (which acquires the data at 50 frames/second) and examining each captured
image using imaging software (Global Lab Image). Each bubble in focus was then
measured and compared with the calibration wire to give the size of each bubble. Bubbles
that were not in focus were not included in the count. Three hundred bubbles were
measured at each time point to give a representative sample. The data were acquired at
each time point for a period of 5 seconds. All data obtained were analyzed with none
being discarded.

9.3.3 Experimental Variables

The ﬁrst run had no surfactant present in the bulk liquid in the agitated vessel, the
second run had three times the critical micelle concentration of Tween 20 (Sigma
Chemical Co., St. Louis, MO) (180 mg/L) and the ﬁnal run had ﬁve times the critical
micelle concentration of Tween 20 (300 mg/L). The surfactant Tween 20 was chosen
because it was used in the mass transfer studies from microbubbles that were described
previously in Chapter 6 (Bredwell and Worden, 1998). The microbubbles were made
from two times the critical micelle concentration of Tween 20 (120 mg/L) as determined
in Chapter 4. All experiments were done at 23 °C.

To avoid gas mass transfer into the liquid phase that might lead to bubble
shrinkage, the bulk liquid was sparged with air for ten minutes prior to beginning the

experiment. The microbubbles were made with air. At 500 rpm, the majority of the

142

 

 

microbubbles seemed to remain suspended in the continuous phase. Entrainment of larger
bubbles from the surface of the liquid in the vessel did not seem to occur due to the
break-up of the surface waves by the bafﬂes. When the agitation to the vessel was turned
off, the microbubble foam began to rise to the surface.
9.3.4 Surface Tension

Surface tension measurements were done with a Fisher Autotensiomat with a
platinum- irridium ring in the DuNouy ring method. The surface tension was measured at
zero, one, three, and ﬁve times the critical micelle concentration in deionized, distilled
water at 23 °C. The resulting surface tensions are given below in Table 17.

Table 19: Surface tension measurements

 

 

Concentration (DSC) o (dyn/cm)
0 71.8
3 35.4
5 37.2

 

 

 

9.4 Results and Discussion

9.4.1 Data Quality
Figure 39 shows an image captured from the videotape for bubble size

measurements. The bubbles are seen as clear, focused black spheres.

143

 

.lnoolv.|

 

 

Figure 39: Captured video image of microbubbles

The microbubbles were injected into the vessel through the injection port at t=0 s, and
data were obtained at t=120 s, 240 s, and 360 s. Figure 40 shows the experimental bubble
size distributions in a continuous phase of water with no surfactant present. The data

were broken down into even-sized categories for the histogram plot.

—

w.

 

 

 

 

 

 

 

 

0.12 T

0.1]
g gTime = 0.0 minutes
"3 0.08- .Time = 2.0 minutes
2 aTime = 4.0 minutes
“L o 06— . .
3 - .Tlme = 6.0 minutes
‘5‘
3 0.04-
2

0.02-

0- 22:12.11 ll iii

 

 

 

 

     

         

 

111.12

1.11". llll
male. 4% l‘l 1
N 1%
‘— 3 8 O 0 ($ny 3
. ‘— ‘— O 743 ‘9
Bubble Dlameter (um) N E

g g (8)
Figure 40: Bubble size distribution histogram

Greater than 97% of the microbubbles measured, even at the end of the
experiment, were of a size smaller than the dcm, thereby supporting the assumption that
breakage in the system can largely be neglected. The video technique for the acquisition
of particle size data was found to be effective and relatively simple, although it is time-
consuming. It has been used previously in the measurement of both droplets (Tsouris and
Talvarides, 1994) and gas bubbles (Pacek, 1994). The accuracy of the measurements
obtained using video microscopy have been estimated by Pacek et al. (1994) to depend
on two sources of error: the sizing of bubbles that are out of focus and inaccuracies in the
measurement of the bubble diameter during the image analysis step. The error estimated
from the former is i5% and the error associated with the later have been estimated to be

typically i10% (Pacek, 1994).

145

9.4.2 Deformable Drop Efﬁciency Model

The ﬁrst efﬁciency model examined was proposed by Coulaloglou and Talvarides
(1977) (Equation 55) with the collision frequency described by Tsouris and Tavlarides
(1994) (Equation 50). The collision frequency model is appropriate for bubbles in the
inertial subrange. The form of the collision frequency suggested by Tsouris and
Talvarides (1994) was used rather than the form suggested by Coulaloglou because the
Tsouris form does not have a ﬁttable parameter, leaving the ﬁnal models with only 1
parameter that describes the efﬁciency.

Figure 41 shows both the modeled and experimental data for no surfactant present
in the surrounding bulk liquid in terms of cumulative number fraction. The parameter k1
was best ﬁt by a least squares method on the average bubble volume to obtain an optimal

value (Perry, 1984).

146

Cumulative Number Fraction

1.20 .
1.00 l
0.80 q
0.60 ..
0.40 .

0.20 .

 

0.00

o'o'o 1w'111'..'1'.1.11:1::11:.-'1 1 1-1-1-1.1-1_1_111;112

"""""

A'A. ‘‘ : s . ﬂo u 0‘. ‘‘‘‘ .........---....--i=

 

0 Time = 0.0 minutes (Data)
—Time = 0.0 minutes (Model)
A Time = 2.0 minutes (Data)

- - - .Time = 2.0 minutes (Model)
0 Time = 4.0 minutes (Data)
—Time = 4.0 minutes (Model)
((3 Time = 6.0 minutes (Data)
- - - .Time = 6.0 minutes (Model)

 

 

 

 

2:;za'o’oo:‘
. AAAA
I’. I AA 000 U333
I ‘A mﬂ
,, O
" O
o A, O
l A'.O
‘ A." OD
. A . U
A O, (:1
A o' (:1
A I
O A O I.
O "
0 A00 1
0 D, I
0 A0 0 I I
- 1 592't"
4 —32_ l l
50 100 150

200 250 300

Bubble Diameter (um)

Figure 41: Coalescence using efﬁciency modeled with Equation 53

147

 

 

 

Figure 42 shows the Sauter mean bubble size as a function time (both data and model

results).

140 .

130- O

 

o 0.0 mg/L Tween 20 in Bulk (Data)
—0.0 mg/L Tween 20 in Bulk (Model)

_x
N
O
I

 

110.

100 .

90.

80.

70.

Average Bubble Diameter (um)

60.

 

50

 

l I I I I I

Time (min)

Figure 42: Average bubble size using efﬁciency modeled with Equation 53
The model seems to overpredict the coalescence rate for small bubbles, yielding high

coalescence efﬁciencies for small bubbles. The predicted coalescence efﬁciency is much
smaller for larger bubbles, approaching 10’6 % for bubbles over 100 um. The coalescence
rate is directly proportional to the coalescence efﬁciency, given by the following
equation.

F(d, d') = 2(d, d')h(d, d')n(d)n(d') (64)
The coalescence rate is also a function of the collision frequency, which is described by
h(d,d')n(d)n(d). As bubbles coalesce, in order to preserve the closure of the mass

balance, the number of bubbles in the system drops. This decreases the collision

148

frequency and thus, the coalescence rate. This trend has been noted by Sovova (1981)
who offers a different form of the coalescence efﬁciency, given by Equation 56. Tsouris
and Tavlarides (1994) suggest that Sovova’s efﬁciency term favors the coalescence of
larger bubbles and was unable to effectively predict the coalescence in a system where
larger average bubble sizes were found.

9.4.3 Film Drainage Efﬁciency Model for Bubbles

9.4.3.1 Model Results

The coalescence efﬁciency model proposed by Prince and Blanch (1990) for
bubbles, given in Equation 65 was also examined. Figure 43 shows both the modeled and

experimental data for no surfactant present in the surrounding bulk liquid in terms of

cumulative number fraction

 

 

 

 

 

‘LZO-
: 100 d 2 — ‘ v 0 o e a 11):: 4; _111..1..1:.'1'..'1-.'1-‘ :.:1 1.1.1.1‘1;1;1_1_1-1.‘.1._. J;
.2 1’ . ' (AAA!) 0...;J1- .......... II;i-‘----~
‘6 I, O A .009
E ' A95 '9 -'
u- 0.80 1- . o A, 00.
E 1 AAIéo Ill!J 0 Time = 0.0 minutes (Data)
§ 050 _ 2 ,5 (2)9 —Time = 0.0 minutes (Model)
E ' A.'0 U A Time = 2.0 minutes (Data)
0
E, «2 A.’ . - . .Time = 2.0 minutes (Model)
(B 0.40 -1 Al 0 d
'5 AA” 13’ 0 Time = 4.0 minutes (Data)
as; o ,’ 0. ,8 ——Time = 4.0 minutes (Model)
0'20 ' 0 {ago (3 Time = 6.0 minutes (Data)
A
0 60' 20 - - - .Time = 6.0 minutes (Model)
0200 WU .

 

50 1 00

150

200 250 300

Bubble Diameter (um)

Figure 43: Coalescence in 0 mg/L Tween 20 using Equation 63

149

 

 

The parameter k5 was adjusted to best ﬁt the average bubble size through a least squares
approach by minimizing the squares of the errors between the model and the
experimental data. The optimal value was 9.51 x 102. This parameter, k5, is related to the
initial and ﬁnal ﬁlm thickness of the liquid ﬁlm surrounding the bubble. This parameter
is dependent on interfacial tension, viscosity in the continuous and dispersed phases, and
contaminants, such as surface active agents, in the continuous phase (Howarth, 1964).
Results for 180 mg/L of Tween 20 surfactant present in the bulk liquid (3 times the
CMC) and 300 mg/L of Tween 20 surfactant present in the bulk liquid (5 times the CMC)

are shown in Figures 44 and 45 , respectively.

 

 

 

 

 

 

1.20 .
to: 1'00 ‘ .' 2. 2 = 39.31.11.111» nil-i alufglg;1:E-‘Eéil?3i"3‘---v'
'13 1" 099m A‘AAAAgéeé
E 0 Ball A, 0000
u- 0.80 - ' D , ‘ I’OOO
h 1 ,’ A O
a) Cl , A 29
.a . . 0 . .
E 0 60 D , , (,7 l 0 Time = 0.0 mlnutes (Data)
.3 ' " " 13 {A}? l —Time = 0.0 minutes (Model)
1; o 13 .' 1 ,' ( (3 Time = 2.0 minutes (Data)
“3 0.40 4 o D; 1' l . . - Time = 2.0 minutes (Model)
'2 Cl" " ,' l A Time = 4.0 minutes (Data)
3 0°01, 1 —Time = 4.0 minutes (Model)
0 0.20 - 000 r ,1 l 0 Time = 6.0 minutes (Data)
or] 6' - - - Time = 6.0 minutes (Model)
oggoga
0-00 "8&09 l I I I I I
0 50 100 150 200 250 300

Bubble Diameter (um)

Figure 44: Coalescence in 180 mg/L Tween 20 using Equation 63

150

1.20 .

1.00 .

0.80 .

0.60 .

0.40 .

Cumulative Number Fraction

0.20 .

 

0.00 M836

 

 

 

, .2 . 11 -_- .1"; I. .39415 = -_'- 311-. 9 2 21.2.1.1. .1, 3, ,1, .1. .1. .1. .1...‘. 3.999
.. . 1,1,5...an go".-.
.35451,868888
A 5' 1‘ b0
(2A I '.
A ,II Q r————— ——~* -- ~—~
.°'. l 0 Time = 0.0 minutes (Data) 1
t .u. 'l ‘ ——Time = 0.0 minutes (Model) l
_ 'I ' A Time = 2.0 minutes (Data) i
. 2’5 . . . - Time = 2.0 minutes (Model) ‘
”- 2' a Time = 4.0 minutes (Data)
I1 ,' ——Time = 4.0 minutes (Model)
Ael .' 0 Time = 6.0 minutes (Data) l
(’5; t - . - Time = 6.0 minutes (Model) 1
50 100 150 200 250 300

Bubble Diameter (um)

Figure 45: Coalescence in 300 mg/L Tween 20 using Equation 63

The best ﬁt parameters from these two cases were determined to be 7.52 x 102 for 180

mg/L and 8.20 x 102 for 300 mg/L. The average bubble size for all three conditions is

given in Figure 46.

151

 

140 . o 0.0 mg/L Tween 20 in Bulk (Data)
—0.0 mg/L Tween 20 in Bulk (Model)
130 - A 180 mg/L Tween 20 in Bulk (Data) 0
- - - 180 mg/L Tween 20 in Bulk (Model)
120 - :1 300 mg/L Tween 20 in Bulk (Data)
—— 300 mg/L Tween 20 in Bulk (Model)

 

 

 

 

 

 

E
3
L-
d)
*5110.
E
(U
5100.
2
g 90.
5
a, 80.
8
'5 7055
>
<
60
50' r I I I I I I
0 1 2 3 4 5 6 7

Time (min)

Figure 46: Dynamic average bubble size

Since the coalescence efﬁciency is dependent on the bubble size, smaller bubbles
are predicted to have higher coalescence efﬁciencies and were observed to have such
behavior with the efﬁciency model by Coulaloglou and Tavlarides (1977). However, the
trend is not as pronounced in this model as the previous model; in the Coulaloglou and
Tavlarides (Equation #55) model the coalescence time is proportional to the bubble
volume to the fourth power, while in the Prince and Blanch (Equation #65) model the
coalescence time is proportional to the bubble volume to the one-half power. The
coalescence efﬁciency calculated by the Prince and Blanch model is given (as a function

of both bubble sizes in binary coalescence) in Figure 47.

152

0.18% .

 

 

 

 

    

      
  

 

 
 

 

 

0.16% 1 °
0140/ oD2=60.0 um
. 0 -l
g 02 = 75.6 um
0.12% . A D2 = 86.5 um
> 0 D2 = 95.2 um
0 0.10% . x02: 102.6 um
C
.3 0 - 02 = 109.0 um
15 0.08% .
Lu
0.06% . °
0
0.04% . D 0 0
Cl 000
0.02% . A U
6 DUE] I 11",” .............
000% I '96 . IIIEEMIWISUI'I-I11111111.......... . .. , .,
0 50 100 150 200 250 300

Bubble Diameter (um)

Figure 47: Coalescence efﬁciency

The efﬁciency had a maximum of 0.17%, indicating that out of every 1000
collisions, there will be 17 occasions of coalescence. The efﬁciency is a function of the
starting minimum bubble size and drops off signiﬁcantly for larger bubbles. The collision
frequency increases with bubble size (larger bubbles are more likely to have a collision
with another bubble) and with the number of bubbles present in the system. A higher rate
of collision is most likely to occur with microbubbles since for a constant volume of gas,
there will be more bubbles in the system due to their small size.

Another factor that contributes to reduced coalescence rates is the reduction in the
number of bubbles in the system available for coalescence. Of the 10 mL of microbubble
dispersion initially injected, 68%, or approximately 6.8 mL was gas (Bredwell, 1995).

Assuming an average diameter of between 65 um and 75 um (depending on the data set),

153

 

 

this volume corresponds to approximately 28,000 bubbles present. At the end of the
experiment, there were signiﬁcantly fewer bubbles in the system, due to bubble
coalescence. Basing the starting conditions on the experiment (where 28,000 bubbles
were determined at time zero based on the average initial bubble size and the amount of
gas injected into the system) the number of bubbles as a function of time that are

predicted by the model are given in Figure 48.

 

 

 

 

30000 1

8 -
_ 25000 . o g A A A 0.0 mg/L Tween 20 in Bulk
$ 0 A A A g 180 mg/L Tween 20 in Bulk
8 o D A A A A 300 mg/L Tween 20 in Bulk
> 1:1 A A 2
.E O D U A A A A
U) 0 D D D A A A A A A
e o D D AAAAAAA
3 o o '3 D A A A A
.6 15000. 0 DDDDDD
: 00 000000
m 0 O o O D D D U C] C]
H- O O O o o
O 0 O o o o 0 0 O
a; 10000. 000066
.o
E
:3
z 5000 .

O I I I I I I I
0 1 2 3 4 5 6 7
Time (min)
Figure 48: Number of Bubbles in Vessel
9.4.3.2 Physical Signiﬁcance of Fitted Parameters

The ﬁtted parameters have physical signiﬁcance in terms of ﬁlm thickness and
other surfactant properties, such as bulk hindrance due to steric effects. Also, the surface
tension, which was measured in a static system, may not accurately describe the dynamic

surface tension that occurs at the interface between the two bubbles. As mentioned

154

previously, a surface tension gradient (Koshy et al., 1988) can form when a bubble is
deformed in the presence of surfactant. The main difference in the three cases studied
was the surfactant concentration, which manifests itself both in the surface tension and in
terms of steric hindrance and/or ﬁhn thickening. In order to investigate the effects of
surface tension in the value of k5 obtained for all three surfactant concentrations, the

following group was calculated.

k5

C1 = 401/2

 

(68)

The form of C1 was determined by the form of the model for coalescence time (Equation
#63). This normalization combines the effects of surfactant properties into one ﬁttable
parameter. Since it is difﬁcult to obtain a true measure of the surface tension in a
dynamic system, the dynamic effects are lumped into C]. The effect of surfactant

concentration on C1 is shown in Figure 49.

155

 

36.

341

32.

   
 

30 .
y =1.12x + 28.09

2 ._
28 4 R — 0.9979

26..

C1 (cm/dyn)“2

24.

22.

20

 

 

0 1 2 3 4 5 6
Dimensionless Surfactant Concentration

Figure 49: Effect of surfactant on C1

The increase in C1 with DSC can be related to the initial and ﬁnal ﬁlm thickness between

h
two bubbles. Prince and Blanch (1990) proposed that k5 is related to In —°— , where ho and
f

hf are the initial and ﬁnal ﬁlm thickness between two bubbles. It is not clear how to
incorporate into the model the effects of the physical size and presence of surfactant in
the liquid ﬁlm, either absorbed at the gas-liquid interface, or present as micelles in the
liquid layer. Therefore, the absolute value of k5 is not signiﬁcant, but the general trends
are signiﬁcant. The increasing trend seen in Figure 48 suggests that the surfactant causes
either increased ﬁlm thickness in the liquid ﬁhn surrounding a bubble, or the higher

concentration of surfactant becomes a greater physical barrier to coalescence, or both.

156

The increasing trend continues beyond the critical micelle concentration, which would
lend evidence to the presence of a greater concentration of micelles and surfactant in the
surrounding liquid. This might cause an increased resistance to coalescence through a
larger amount of bulk hindrance and electrostatic effects in the system. The predicted
coalescence time calculated using the optimal k5 values for a pair of 75 um bubbles is
18.2 ms in the presence of no surfactant and 21.8 ms at 300 mg/L of surfactant with
coalescence efﬁciencies on the order of 0.04%. In contrast, the coalescence time for a
conventional bubble calculated using ﬁlm thicknesses suggested by Prince and Blanch
(1990) was 0.2 ms, giving a coalescence efﬁciency of 87.5%.

The absolute value of C1 is not meaningful in this study because this parameter is
thought to be dependent on other, poorly characterized inﬂuences. For instance, the
model developed by Li (1996) could not explain data for systems containing high
concentrations of surfactant. He suggested that the discrepancies could be due to
electrostatic forces. In addition, steric hindrance and surface blocking could be involved.
While these phenomena may not be important in turbulent systems due to high inertial
energy, they could have a signiﬁcant role in processes involving microbubbles. The C]
parameter does not distinguish the various inﬂuences, but rather includes them all into
one term.

These data from the coalescence studies support the trends seen in Figure 22 in
which increasing the surfactant concentration in the bulk liquid reduced the mass transfer
coefﬁcient, KL. This trend is most likely due to thickening of the liquid ﬁlm or shell
around the microbubbles and physical (steric) hindrance by the surfactant molecule in the

shell. The mass transfer resistances around a microbubble can be considered using a

157

resistances in series model as proposed by Worden and Bredwell (1998) in the following

Equation 69.

—=—+— (69)

where l/kL,S is the resistance due to the total shell of a microbubble (surfactant layers and
liquid layer), and RL is the local resistance of the bulk liquid. Using a dynamic model of a
single microbubble, Worden and Bredwell (1998) found that for a kl”, value of 0.0001
m/s or less, the shell resistance is expected to dominate. The mass transfer coefﬁcients
calculated in Chapter 6 and shown on Figure 22 are all less than 0.00013 m/s in the
presence of surfactant. This indicates that shell resistance is most likely to dominate
resistance in this system.

Princen and Mason (1967) suggested that gas transfer through soluble surfactant
monolayers occurs through simple Fickian diffusion, and Quintana et al. (1990) has
reported that the presence of soluble surfactants does not signiﬁcantly affect the diffusion
of small molecules. Also, gas-side ﬁlm resistances have been shown to be negligible for
sparing soluble gases (Motarjemi, 1978). These results suggest that the primary resistance
to mass transfer in the microbubble shell would be in the stagnant water layer around the
microbubble. The thicker this shell of water, the lower the mass transfer coefﬁcient.
Therefore, the evidence from the coalescence data suggests that the liquid shell around a
microbubble has been effectively thickened by increased concentrations of surfactant.
However, other phenomena, such as surface blocking and electrostatic forces may also

contribute signiﬁcantly.

158

9.5 Conclusions

The coalescence rate of microbubbles in batch stirred vessels has been measured
through video microscopy and found to decrease with increasing bulk surfactant
concentration. Bubble size versus time data were analyzed using a population balance
approach with two different mathematical models: one giving the coalescence efﬁciency
for deformable drops and one based on the dynamic drainage of the liquid ﬁlm between
two colliding bubbles. The deformable drop model grossly underpredicted the
coalescence efﬁciency for larger bubbles. The liquid drainage model reasonably modeled
the data, although it still underpredicted the coalescence of larger bubbles. Therefore,
better models should be developed.

The ﬁlm drainage model suggested that the liquid ﬁlm between two colliding
bubbles is thicker in the presence of higher concentrations of surfactant. This result is
consistent with the mass transfer results, where KL decreased with increasing surfactant
concentration in the bulk liquid. The resistance to coalescence was increased through
possible mechanisms such as steric hindrance and physical blocking in the liquid ﬁlm.
Modeling work done by other researchers indicates the majority of the mass transfer
resistance from microbubbles occurs in the surrounding liquid shell, and the thickening of

that shell would therefore decrease the mass transfer coefﬁcient.

9.6 Nomenclature

9.6.1 Symbols

A = Hamaker constant
B = Birth term of bubbles
Cm = Constant for maximum stable bubble size

159

 

 

 

D

Di
d°m.x.dcr
d

g(V)

H
h(d,d’)
h(V,v’)

hf

kL,s

0°70

rearn

Constant (cm/dyn)”2

Concentration of surfactant molecules (mol/L)
Death term of bubbles

Impeller diameter (m)

Maximum stable bubble size

Bubble diameter (rn)

Breakage frequency (8")

Liquid height in vessel (m)

Collision frequency (s'l)

Collision frequency (5")

Final ﬁlm thickness (m)

Initial ﬁlm thickness (m)

Eddy wavenumber (m'l)

Constant

Overall mass transfer coefﬁcient (m/s)
Bulk liquid mass transfer coefﬁcient (m/s)
Shell mass transfer coefﬁcient (m/s)
Agitation speed (3")

Number of bubbles

Term used to simplify Equation 60
Radius of the liquid disk between bubbles (m)
Gas constant (L*atm/K*mol)

Length scale (m)

160

r, rb = Bubble radius (m)

T = Vessel diameter (m)

t = Time (s)

i = Average contact time (s)
u = Velocity (m/s)

1; = Average velocity (m/s)
v,v’ = Bubble volume (m3)

We = Weber number

9.6.1 Greek Symbols

B(v,v’) = Probability density of breakage

s = Energy dissipation (mZ/s)

2 = Average energy dissipation (mz/s)
q; = Holdup

7L(d,d,) = Coalescence efﬁciency

k(v,v’) = Coalescence efﬁciency

u = Viscosity (Kg/m*s)

n(v) = Number of bubble formed from breakage
v = Kinematic viscosity (mZ/s)

p = Density (kg/m3)

o = Surface tension (N/m)

1 = Average coalescence time (s)

161

9.6.3 Subscripts and Superscripts
c, l = Continuous phase
(1 = Dispersed phase

*

= Dispersion (both phases)

 

162

10. SUMMARY AND CONCLUSIONS

Microbubbles, or colloidal gas aphrons, have been characterized in terms of
formation time, stability, gas void fraction, and bubble size. The minimum formation
time was obtained at the critical micelle concentration for the surfactants tested and was
unaffected by the addition of salts. Microbubble dispersions were most stable at the
critical micelle concentration. The gas void fraction was found to be independent of
surfactant concentration and approached the maximum packing limit for monosized
spheres in a face-centered cubic cell, or 0.67. The average bubble size was measured to
be approximately 60 um using dynamic light scattering techniques.

Surfactants were tested for biocompatibility with Butyribacterium
methylotrophicum. Tween, or polysorbate surfactants, did not signiﬁcantly affect the
grth or product formation patterns. Similar results were obtained for some Brij
surfactants. An effect of chain length was noted on the toxicity of the surfactant, with
shorter chain surfactants generally being more toxic than longer chains. Most ionic
surfactants tested were toxic to the organism.

The mass transfer properties of microbubbles were studied using both a steady-
state method and an unsteady-state method in a large-scale fermenter. In the steady-state
method, the axial dispersion for ﬂow of microbubbles through a bubble column was
much lower than for conventional bubbles. The steady-state KL values were similar in
magnitude to literature values for small, rigid bubbles. Increasing concentrations of
surfactant decreased the KL as much as 75%. This decrease was presumed to be due to
shell thickening and steric hindrance. The resulting KLa values ranged from 200 h'] to

1100 h]. These values are an order of magnitude higher than those measured in synthesis

163

 

 

 

 

gas fermentations using conventional sparging. Dynamic mass transfer studies conducted
in a 100 gallon fermenter showed that the majority of the available gas was transferred
into the liquid phase. The corresponding KLa values were considerably higher than for
conventional sparging at low power to volume inputs. The calculation of the power input
required to generate microbubbles for synthesis gas fermentations gave a Power number
of 0.036 for the microbubble generator and a corresponding P/V value of 0.01 kW/m3 of
fermentation capacity.

Microbubble-sparged synthesis gas fermentations were run using both B.
methylotrohicum and sulfate reducing bacteria. The B. methylotrohz'cum fermentation
yielded a six-fold improvement in the volumetric mass transfer coefﬁcient over
conventional sparging: 91 h'1 vs. 14 h], even through a lower gas ﬂow rate was used for
the microbubbles. A two-fold improvement in SRB reactor productivity was obtained
upon switching from conventional bubbles to microbubbles. The maximum productivity
obtained with the microbubble—sparged fermentation was similar to that obtained using a
soluble substrate, in which there was no interphase mass transfer resistance.

The coalescence of microbubbles was studied in a stirred vessel. The bubble size
distribution was monitored over time using a high-speed video camera. A population
balance equation approach was used to analyze the data. The coalescence efﬁciency was
modeled using a ﬁlm drainage model. Results from these studies indicated that decreased
coalescence occurs with increased bulk liquid surfactant concentration. The decreased
coalescence is thought to be due to shell thickening and steric and physical hindrances at

higher concentrations of surfactants.

164

 

 

 

 

 

11. APPENDICES

165

 

 

11.1 Appendix A: Axial Dispersion

The program used to evaluate the axial dispersion in the system is listed here with

subroutine PATERN eliminated. A listing of the PATERN subroutine can be found in

 

Thompson (1993).
C
C
C
C SUBROUTINE PROC FOR PROGRAM CALLED PATERN
C
C PURPOSE: TO ESTIMATE DIFFUSION COEFFICIENTS BY READING
IN DATA
C CONTAINING TIME -VS- CONCENTRATION VALUES.
C
C MAIN PROGRAM
C
C
INTEGER NDATA,NP,NPASS,IO
integer ip, i, nin, nres, nterm
real pm(20), cdi(200), cwork(lO), toin, dtin, tores, dtres,
S cdr(200), tau, p(10), step(10)

common /mainl/cdi,toin,dtin
common /main2/cdr,tores,dtres
common /main5/nin,nres
common /pbparm/pm
common /main4/tau,nterm
open(2,file='file2.csv',status='old')
open(3,file='filel.csv',status='old')
open(4,file=’file3.csv',status='old')
OPEN (UNIT=30,FILE='FOR30.DAT',STATUS='NEW')

ip=3
read(2,*) (pm(i), i=1riP)
write(30,*) (pm(i), i=1rip)

300 format(8f10.0)
read(3,*) toin,dtin
write(30,*)toin,dtin

100 format(2f10.0)

nin=0

110 format(10f8.0)

I do 10 i = 1, 10

read(3,*) cwork(i)
if (cwork(i) .lt. 0.0) goto 90
nin=nin+l
if (nin .gt. 200) goto 90
cdi(nin)=cwork(i)
write(*,*) cdi(nin)
write(30,*) cdi(nin

)

10 continue
goto I
90 nres=0

166

20

read(3,*) tores,dtres

write(30,*) tores,dtres
do 20 i=1,10

read(3,*) cwork(i)
if (cwork(i) .lt. 0.0) goto 91
nres=nres+1
if (nres .gt. 200) goto 91
cdr(nres)=cwork(i)
write(*,*) cdr(nres)
write(30,*) cdr(nres
continue
goto 2

)

91 read(4,*) tau,nterm

200

C
C
C
C399

399

00000000000000

write(30,*) tau, nterm

format(f10.0,i10)

call norsig
call fouexp

SEARCH INITIALIZATION
P(l)= 0.01

p(2)= 1.0e-3
STEP(1)=0.01
step(2)=1.0e—3

NP=2

NPASS=3

IO=3

START SEARCH

CALL PATERN(NP,P,STEP,NPASS,IO,COST)

SEARCH COMPLETE, PRINT RESULTS
PRINT 399, P(l), P(Z), COST

FORMAT(F10.3,10X,FIO.3)

WRITE (30,399) P(l),P(2),COST
FORMAT(EIO.3,5X,F6.3,5X,ElO.3)
STOP
END

THIS FILE IS A PAIR OF SUBROUTINES WRITTEN TO BE
COMPATIBLE WITH THE OPTIMIZATION SUBROUTINE PATERN.
THEY SIMULATE A PROCESS USING DISCRETE DIFFERENCE
EQUATIONS AND COMPARE THE SIMULATION OUTPUT WITH

THE ACTUAL OUTPUT (READ IN THROUGH A DATA FILE),
CALCULATING AN ERROR OR "COST" ASSOCIATED WITH THAT
SIMULATION. PATERN USES THESE SUBROUTINES ITERATIVELY
IN ORDER TO FIND THE OPTIMUM SET OF TRANSFER FUNCTION

PARAMETERS TO FIT THE DATA.

SUBROUTINE PROC(P,COST)
dimension p(10)

167

 

 

common/pbparm/pm(20)
common/mainB/error
pm(2)=p(l)
Pml3l=p(2)

call precur
cost=error

RETURN
END

SUBROUTINE BOUNDS(P,IOUT)
DIMENSION P(10), STEP(10)
IOUT=O
IF(P(1).LE.O) IOUT=1
if(p(2).le.0) iout=1
RETURN
END

subroutine norsig

10

20

30

integer znin,znres

common /main1/ cdin,ztoin,zdtin

common /main2/ cdres,ztores,zdtres

common /main5/znin,znres

common /signal/toin,dtin,nin,cin(200),
tores,dtres,nres,cres(200)

dimension cdin(200),cdres(200)

nin=znin

toin=ztoin

dtin=zdtin

nres=znres

tores=ztores

dtres=zdtres

call normlz(dtin,nin,cdin,ain,cin)

call normlz(dtres,nres,cdres,ares,cres)

return

end

subroutine normlz(dt,n,cd,area,cn)
dimension cd(200),cn(200)
area = 0.0
do 10 i=1,n
area=area+cd(i)
continue
area=area*dt
if(area.eq.0.0) then
write(*,600)
do 20 i=1,n
cn(i)=cd(i)
continue
return
elseif(area.lt.0.0) then
write(*,610)
endif
do 30 i=1,n
cn(i)=cd(i)/area
continue

168

 

return

600 format(lh0,'area of curve is zero(returned signal is not normal
$ized).'/)
610 format(lh0,'area of curve is negative.'/)
end

subroutine fouexp
common /main4/ztau,znterm
common /signal/ toin,dtin,nin,cin(200),

$ tores,dtres,nres,cres(200)
common/fdata/ tau,nterm,aoin,ain(200),bin(200),

$ aores,ares(ZOO),bres(200)
tau=ztau

nterm=znterm
if(tau.lt.(tores+dtres*float(nres))/2.0) then
tau=(tores+dtres*float(nres))/2.0*1.5
write(*,610) tau
endif
if(nterm.lt.1.or.nterm.gt.ifix(tau/dtres+0.5)) then
nterm=ifix(tau/dtres+0.5)
write(*,620) nterm

 

endif
if(nterm.gt.200) then
nterm=200
write(*,620) nterm
endif

call foucoe(toin,dtin,nin,cin,tau,nterm,aoin,ain,bin)
call foucoe(tores,dtres,nres,cres,tau,nterm,aores,ares,bres)
return

610 format(lh0,'half period (tau) is replaced by',e15.7)
620 format(lh0,'number of terms (nterm) is replaced by',i5)
end

subroutine foucoe(to,dt,nt,cn,tau,nterm,ao,a,b)
dimension cn(200),a(200),b(200)
data pi/3.141593/
ao=0.0
sq=0.0
do 10 i=1,nt
ao=ao+cn(i)
sq=sq+cn(i)**2
10 continue
ao=ao*dt/tau
sq=sq*dt
cotest=ao/2.0
sqtest=2.0*(ao/2.0)**2*tau
do 20 n=l,nterm
x=0.0
y=0.0
sv=float(n)*pi/tau
do 30 i=1,nt
z=sv*(to+float(i-1)*dt)
x=x+cn(i)*cos(z)
y=y+cn(i)*sin(z)
30 continue

169

 

20

4O

10

a(n)=x*dt/tau
b(D)=y*dt/tau
cotest=cotest+a(n)
sqtest=sqtest+(a(n)**2+b(n)**2)*tau
if(mod(n,10).eq.0) then
rat=sqtest/sq

endif

continue

return

end

subroutine precur

common /main3/err

common/signal/toin,dtin,nin,cin(200),tores,dtres,nres,

cres(200)
common/fdata/tau,nterm,aoin,ain(200),bin(200),aores,
ares(200),bres(200)

common/pbparm/ pm(20)

dimension aclc(200),bclc(200)

call clccoe(pm,tau,nterm,nt,aoin,ain,bin,aoclc,aclc,bclc)

x=2.0*(aores/2.0-aocIc/2.0)**2

y=2.0*(aores/2.0)**2

do 40 i=1,nt
x=x+(ares(i)-aclc(i))**2+(bres(i)-bclc(i))**2
y=y+ares(i)**2+bres(i)**2

continue

err = sqrt(X/y)

return

end

subroutine clccoe(pm,tau,nterm,nt,aoin,ain,bin,aoclc,aclc,bclc)
dimension pm(20),ain(200),bin(200),ac1c(200),bclc(200)
data pi/3.141593/
call transf(0,0.0,pm,an,bn)
aoclc=aoin*an
do 10 n=1,nterm
w=float(n)*pi/tau
call transf(l,w,pm,an,bn)
aclc(n)=ain(n)*an+bin(n)*bn
bclc(n)=bin(n)*an-ain(n)*bn
if(an**2+bn**2.lt.1.0e-8) then
nt=n
return
endif
continue
nt=nterm
return
end

subroutine transf(ictl,w,pm,an,bn)
dimension pm(20)

real*8 d1,d2

save d1,d2

complex*16 cs,cphi,cex,coth,cf
if(ictl.eq.0) then
d1=Pm(3)/(pm(l)*pm(2))
d2=pm(1)/pm(2)

170

 

endif
if(w.eq.0.0) then
an=1.0
bn=0.0
return
endif
cs=cmplx(0.0,w)
cphi=cdsqrt(l+4.0*d1*d2*cs)
cex=1—cphi
coth=1.0/(2.0*d1)*cex
cf=cdexp(coth)
an=cf
bn=dimag(cf)
return
end

171

 

11.2 Appendix B: Bubble Coalescence

The program used to evaluate the bubble coalescence in a stirred tank is listed
below. The subroutine EDRIVB, the EPISODE B package, has been eliminated from the
listing. A complete listing of EPISODE can be obtained from Byrne and Hindmarch
(1976)

C======================================================================
C= THIS PROGRAM CALCULATES THE BUBBLE COALESCENCE IN STIRRED TANK. =
C: THE BUBBLE COLLISION FREQUENCY IS ESTIMATED FROM THE ISOTROPIC =
C= TURBULENT FLOW. THE COLLISION EFFICIENCY IS ESTIMATED FROM =
C: PRINCE AND BLANCH =
C: WRITTEN BY COSTAS TSOURIS, MODIFIED BY MARSHALL BREDWELL - 1.16.98 =

 

IMPLICIT DOUBLE PRECISION (A-H,O-Z)

DIMENSION FO(300),YO(300),VY(300),SY(300),VD(300),IWORK(IOOO)

DIMENSION D(300),CUMVY(300),CUMSY(300),R(300),WORK(4000)

INTEGER*2 IHR,IHRO,IMIN,IMINO,ISEC,ISECO,IIOOTH

COMMON/HISTRY/Y(I300)

COMMON/MODS/TOL,YREL,HBIG,NITCON,LOUT

COMMON/EPCOMl/T,H,HMIN,HMAX,EPSC,SS,UROUND,NC,MFC,KFLAG,JSTAR

COMMON/EPCOMZ/YMAX(300)

COMMON/EPCOM3/ERROR(300)

COMMON/EPCOM4/SAVE1(300)

COMMON/EPCOMS/SAVE2(300)

COMMON/EPCOM6/PW(IOOOO)

COMMON/EPCOM7/IPIV(300)

COMMON/EPCOM8/EPSJ,NSQ

COMMON/EPCOM9/HUSED,NQUSED,NSTEP,NFE,NJE

COMMON/DATl/F(300,300),VOL(300),EFFRQ(300,300)

DOUBLE PRECISION
VC,PI,A1,A2,SIGMA,ED,RPM,DNSC,C3,C4,DIMP,HO,HOLD2

DOUBLE PRECISION
D3,D2,CALL,DNSD,EFl,EF2,HOLDl,NUMBUB,DAVE2,TOT,D1

DOUBLE PRECISION EF3,EF4,COLFRQ

COMMON/DAT3/EPSI,JMAX

EXTERNAL FUNl

PI=3.1415926

 

C

C READ ALL REQUIRED PARAMETERS

C
OPEN(20,FILE='COLLEF.RES',STATUS='UNKNOWN')
OPEN(21,FILE='COLLEF2.RES',STATUS='UNKNOWN')
OPEN(22,FILE='POTENT.RES',STATUS='UNKNOWN')
OPEN(23,FILE='PSTATS.RES',STATUS='UNKNOWN')
OPEN(24,FILE='PBERES.RES',STATUS='UNKNOWN')
OPEN(25,FILE='TESTOUT.RES',STATUS='UNKNOWN')
OPEN(l,FILE='BUBBLE.DAT',STATUS='OLD')

C

CALL GETTIM(IHRO,IMINO,ISECO,IlOOTH)
WRITE(*,'(20H PROGRAM STARTED AT ,2(I3,1H:),I3)')IHRO,IMINO,ISECO

172

READ(l,*)OUTT,NCL,ICL,TEND,DMIN,PINIT,VC,SIGMA,RPM,C3,C4,DIMP,
+ HO,DNSC,DNSD,EPSABS,EPSREL,LIMIT,(FO(K),K=1,ICL)

CALCULATE ENERGY DISPERSION VIA BERTRAND
ED=2*(O.81*((RPM/60.)**3)*((DIMP/lOO.)**2))*lOOOO

TO=O.lE-5
HO=l.OD-4
MF=10
ML=NCL+l
MU=NCL+1

VMIN=PI*(DMIN**3)/6.

VMAX=VMIN*NCL*2

DMAX=(6.*VMAX/PI)**(1./3.)

HS=VMIN

DO 20 J=l,NCL
VOL(J)=VMIN+(J-l)*HS
D(J)=(VOL(J)*6./PI)**(l./3)

R(J)=D(J)/2

CONTINUE

 

GIVE INITIAL CONDITIONS

VP=O.

SDTD=O.

DO 22 K=1,ICL
Y0(K)=F0(K)*PINIT
VP=VP+Y0(K)*VOL(K)
SDTD=SDTD+Y0(K)*D(K)
D3=D3+Y0(K)*(D(K)**3)
D2=D2+Y0(K)*(D(K)**2)

CONTINUE

DAVEO=D3/D2

VSIM=VP*PDENS/PCONC

WRITE(*,*)DAVEO

DAVE=SDTD/PINIT

PRATIO=1.

TINIT=O.

DO 24 K=ICL+1,NCL

YO(K)=O.

CONTINUE

EPS=1.0

IERROR=2

TOUT=0.1D—5

INDEX=1

HBIG=O.1

YREL=EPS

LOUT=5

NITCON=3

TOL=EPS

DO 26 J=l,NCL
SY(J)=YO(J)/SDT

173

VY(J)=VD(J) /VDT
26 CONTINUE
CUMSY(1)=SY(1)
CUMVY(1)=VY(1)
DO 27 J=2,NCL
CUMSY(J)=CUMSY(J-l)+SY(J)
CUMVY(J)=CUMVY(J-1)+VY(J)

27 CONTINUE
WRITE(23,210)TO,(D(K),VOL(K),SY(K),CUMSY(K),VY(K),CUMVY(K),
+ K=1,NCL)

C

C CALCULATE COALESCENCE FREQUENCY

C

DO 28 J=l,NCL
DO 30 K=J,NCL
Al=D(J)
A2=D(K)
HOLD1=(O.5*(l./R(J)+l./R(K)))**(-l.0)
EFl=EXP(-C3*(HOLDI**3*DNSC/(16*SIGMA))**(l./2.)/
+ (HOLD1**(2./3.)/(ED**(l./3.))))
HOLDZ=(SIGMA)*(Al**(2./3.)+A2**(2./3.))
EF=EF1
EF3=1.07*ED**(2./3.)*Al**(2./3.)
EF4=l.O7*ED**(2./3.)*A2**(2./3.)
COL=3.1415926/4.0*(Al+A2)**2.0*(EF3+EF4)**(l./2.)
F(J,K)=COL*EF
P(KIJ)=F(JIK)
WRITE(20,212)A1,A2,COL,EF,F(J,K)
3O CONTINUE
28 CONTINUE
212 FORMAT(F20.14,3X,F20.l4,3X,F20.l4,3X,F20.l4,3X,F20.14,3X,F20.l4,
+ 3X,F20.l4)

 

C
C
10 CALL EDRIVB(NCL,TO,HO,YO,TOUT,EPS,IERROR,MF,INDEX,ML,MU)

SDT=O.

VDT=O.

D3=0.

D2=0.

D1=0.

RDT6=O.

SDTD=0.

tot=0.

DO 68 K=1,NCL
SDT= SDT+Y0
SDTD= SDTD+
D3= D3+Y0(K

(

Y D

) )
D2= D2+YO(K ) )

)

(

)

(

K) (K)
D( **3)
D( **2)
D1: D1+YO(K (K
TOT= TOT+YO
VD(K )= O<K

VDT= VDT+VD
CUMSY(K) =0.
CUMVY(K)=O.

68 CONTINUE

*
K
K
)

K)

0(

*(

*(

*D

K)
*VOL(K)
K)

174

 

 

 

DAVE=D3/D2

DAVE2=Dl/TOT

VRATIO=VDT/VP

PRATIO=SDT/PINIT

DRATIO=DAVE/DAVEO

WRITE(24,208)TO,DAVE,D1,DAVE2

WRITE(*,208)TO,DAVE,DI,DAVE2

DO 73 J=l,NCL
SY(J)=YO(J)/SDT
VY(J)=VD(J)/VDT

73 CONTINUE

CUMSY(1)=SY(1)

CUMVY(1)=VY(1)

DO 75 J=2,NCL
CUMSY(J)=CUMSY(J—1)+SY(J)
CUMVY(J)=CUMVY(J-1)+VY(J)

75 CONTINUE
C CALCULATE THE TOTAL NUMBER OF BUBBLES
NUMBUB=0.0

DO 150 K=1,NCL
NUMBUB=Y(K)+NUMBUB
150 CONTINUE

 

WRITE (23,*) NUMBUB

WRITE(23,210)T0,(D(K),VOL(K),SY(K),CUMSY(K),VY(K),CUMVY(K),

+ K=1,NCL)
208 FORMAT(F6.0,4X,F15.12,4X,F15.12,4X,F15.12)
210 FORMAT(//F6.0,/,(F10.5,2X,F10.5,2X,F10.5,2X,F10.5,2X,

+ F10.5,2X,F10.5))

TOUT=TOUT+OUTT

IF(TOUT. LE. (TEND+0.001))GOTO 10

C
CALL GETTIM(IHR,IMIN,ISEC,IlOOTH)
ISEC=(IHR-IHRO)*3600+(IMIN-IMINO)*60+ISEC-ISECO
WRITE(*,'(22H CPU TIME IN SECONDS: ,I4)')ISEC
C
STOP
END
C
C
C
SUBROUTINE PDB(N,T,Y,PD,MG,ML,MU)
RETURN
END
C
C
C
SUBROUTINE DIFFUN(NCL,T,Y,YDOT)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION Y(NCL),YDOT(NCL)
DIMENSION Sli300),SZ(300)
COMMON/DATl/F(300,300),VOL(300)
Z=Z+l
C
C ESTIMATION OF INTEGRALS NEEDED IN THE INTEGRAL-DIFFERENTIAL
C POPULATION BALANCE EQUATIONS
C

175

 

O 0 0 0‘0

93
92

O O 0<ﬁio

O O O O O

101

81 COALESCENCE TO LARGER BUBBLES

82 = COALESCENCE FROM SMALLER BUBBLES

Tl=T
T=Tl
DO 90 J=l,NCL

Sl(J)=0.0

82(J)=0.0
VSl=0.0
V82=0.0
CONTINUE

ESTIMATION OF INTEGRAL Sl
(LOSS DUE TO COALESCENSE TO LARGER BUBBLES)

DO 92 J=l,NCL-l
DO 93 K=1,NCL-J
Sl(J)=Sl(J)+F(J,K)*Y(J)*Y(K)
IF(K. EQ. J)THEN
Sl(J)=Sl(J)+F(J,K)*Y(J)*Y(K)
ELSE
ENDIF
CONTINUE

CONTINUE

DO 94 J=l,NCL-l

VSI=VSl+Sl(J)*VOL(J)
CONTINUE

ESTIMATION OF INTEGRAL 82
(SOURCE DUE TO COALESCENCE OF SMALLER BUBBLES)

DO 96 J=2,NCL
DO 98 K=1,J/2
82(J)=82(J)+F(K,J-K)*Y(K)*Y(J-K)
CONTINUE
CONTINUE
DO 99 J=2,NCL
VSZ=VS2+82(J)*VOL(J)
CONTINUE
VLOSS=VSl-VSZ
WRITE(25,*)VSI,V82,VLOSS

SPECIFY THE DIFFERENTIAL EQUATIONS

YDOT(l)=-Sl(l)

DO 101 J=2,NCL-1
YDOT(J)=-Sl(J)+SZ(J)

CONTINUE

YDOT(NCL)=SZ(NCL)

RETURN
END

176

 

12. BIBLIOGRAPHY

177

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