ISOBUTANOL PRODUCTION IN A BIOREACTOR FOR INCOMPATIBLE GASES (BIG)
By
YANGMU CHLOE LIU

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Chemical Engineering—Doctor of Philosophy
2014

ABSTRACT
ISOBUTANOL PRODUCTION IN A BIOREACTOR FOR INCOMPATIBLE GASES (BIG)
By
YANGMU CHLOE LIU
Electrofuels are carbon-neutral, renewable transportation fuels generated using nonphotosynthetic CO2 fixation. Biological conversion of H2, CO2 and O2 into alcohols is emerging
as a promising strategy for producing electrofuels while reducing greenhouse gas emission.
However, development of this process presents significant bioreactor-design challenges. First,
these fermentations have unusually high demands for gas mass transfer. Second, the need to
simultaneously deliver H2 and O2 creates safety issues, because these gases are incompatible,
forming a flammable mixture over the range of 4 to 94% H2. Third, alcohols are typically
inhibitory to the microbial biocatalysts, making their in situ removal desirable for continuous
bioreactor operation.
This dissertation describes development of a novel Bioreactor for Incompatible Gases
(BIG) to address these challenges. The BIG features a hollow fiber configuration, in which the
microbial biocatalysts are immobilized in the porous fiber walls. A liquid phase containing
microbubbles of one gaseous reactant is pumped through the hollow fibers, and a gas phase
containing another gaseous reactant(s) incompatible with the first is maintained outside the fibers.
In this way, rapid mass transfer to the immobilized cells of both gaseous reactants is achieved
without creating hazardous gas mixtures. In situ product removal can be achieved from the liquid
stream (for nonvolatile products) and/or the gas stream (for volatile products).
A prototype bench-scale BIG was designed, fabricated, and integrated with an Opto22based control system that monitored and controlled the composition of the gas phase, dissolved

oxygen concentration in the liquid phase, and temperature. The control system was programmed
to make intelligent operational decisions in response to process contingencies. The BIG system
was inoculated with an isobutanol (IBT)-producing strain of Ralstonia eutropha and operated
stably for up to 19 days, during which continuous, autotrophic IBT production from H2, CO2 and
O2 was achieved for the first time.
A dynamic mathematical model was developed to describe the interplay of multispecies
and multidirectional gas mass transfer, along with complex cellular kinetics involving mixed-gas
substrates. The simulation results were used to interpret experimental findings and simulate BIG
performance under a range of operating conditions. The experimental and modeling results
established the unexpected finding that R. eutropha cells both produced and consumed IBT,
depending on the local H2 concentration. The BIG prototype reactor and associated mathematical
models are generic and could describe production of a variety of biofuels from incompatible
gases.

Copyright by
YANGMU CHLOE LIU
2014

To my parents,
and
To Aaron

v

ACKNOWLEDGEMENTS

There are so many people without whose help and support I would not have made it this
far. First and foremost I would like to thank my advisor R. Mark Worden for the opportunity to
join his lab, and for his support, guidance and patience throughout my study. Your optimism has
helped me through the most difficult part of this project. I would also like to thank Scott
Calabrese-Barton, Claire Vieille and Dennis Miller for their time and guidance as members on
my Ph.D. committee.
Part of this dissertation is the result of collaboration with my former colleague Soumen
Maiti, whom I would like to thank for his contribution to the experimental work. I would also
like to thank the undergraduate students I have worked with on the project, Derek Montgomery,
Jillian Robertson, and Dexter Gregg, for their help.
I would also like to express my gratitude to people who have helped me with various
aspects of my work: Anthony Sinskey’s research group at Massachusetts Institute of Technology
for their help in understanding the metabolic characteristics of the biocatalyst, especially Chris
Brigham and Jingnan Lu; Carol Flegler for her indispensable assistance with microscopy
imaging; and Lee Alexander for training me in various sterile techniques.
I know I would not be where I am without my parents. Thank you Mom and Dad for
making me believe that I am capable of anything I put my mind to, and for believing in me.
Thank you for doing what might be the most difficult thing for a parent—letting your only
daughter move half way across the globe to a country you’ve never been to, knowing fully that
our conversations will be subjected to the whims of the intercontinental internet connection.

vi

Special thanks to Aaron for his love, support and words of encouragement. You have
been the best companion I could have asked for in my life.
Finally, I wish to extend my sincerely gratitude to all my family and friends for being
there for me during the past few years.

vii

TABLE OF CONTENTS

TABLE OF CONTENTS .......................................................................................................... viii
LIST OF TABLES ....................................................................................................................... xi
LIST OF FIGURES .................................................................................................................... xii
KEY TO SYMBOLS.................................................................................................................. xvi
1

INTRODUCTION................................................................................................................... 1
1.1 Motivation and Problem Description ............................................................................ 1
1.2 Background ...................................................................................................................... 4
1.2.1 Alternative Fuels and Strategies for Production ........................................................... 4
1.2.2 Isobutanol Production by Ralstonia eutropha .............................................................. 5
1.2.3 Fermentation of Gases with Low Aqueous Solubilities ............................................... 6
1.3 Organization of This Dissertation .................................................................................. 7
1.3.1 Continuous Isobutanol Production in A Bioreactor for Incompatible Gases (BIG) ..... 7
1.3.2 Mass Transfer in a Bioreactor for Incompatible Gases (BIG) ...................................... 7
1.3.3 Simulation of Isobutanol Production in a Bioreactor for Incompatible Gases (BIG) ... 8
1.4 Acknowledgments ............................................................................................................ 8

2 CONTINUOUS ISOBUTANOL PRODUCTION IN A BIOREACTOR FOR
INCOMPATIBLE GASES (BIG)................................................................................................ 9
2.1 Introduction ..................................................................................................................... 9
2.2 Materials and Methods ................................................................................................. 12
2.2.1 Microorganisms and Media ........................................................................................ 12
2.2.2 Bioreactor for Incompatible Gases (BIG) ................................................................... 13
2.2.3 Hollow Fiber Membrane Selection ............................................................................. 15
2.2.4 Cell Immobilization and Hollow Fiber Membrane Cleaning ..................................... 21
2.2.5 Measurement of Biomass, Ammonium and IBT Concentration ................................ 23
2.2.6 Operation of Bioreactor for Incompatible Gases (BIG) ............................................. 24
2.2.6.1 Heterotrophic Operation with Immobilized Cells.............................................. 24
2.2.6.2 Autotrophic Operation with Immobilized Cells ................................................ 26
2.2.6.3 Autotrophic Operation with Planktonic Cells .................................................... 27
2.2.6.4 Opto22-based Control Network and Safety Measures....................................... 29
2.2.6.5 IBT consumption ............................................................................................... 31
2.3 Results and Discussion .................................................................................................. 32
2.3.1 Cell Immobilization .................................................................................................... 32
2.3.2 BIG Operation with Immobilized Cells ...................................................................... 34
2.3.3 IBT Consumption by R. eutropha ............................................................................... 36
2.3.4 Autotrophic Operation with Planktonic Cells ............................................................. 38
2.4 Conclusions .................................................................................................................... 41

viii

3

MASS TRANSFER IN THE BIOREACTOR FOR INCOMPATIBLE GASES (BIG) 43
3.1 Background .................................................................................................................... 43
3.1.1 Measurement of Diffusion Coefficients in Membranes.............................................. 43
3.1.2 Diffusion in Porous Membrane ................................................................................... 44
3.2 Experimental Setup ....................................................................................................... 48
3.2.1 Measuring O2 Membrane Diffusivity ......................................................................... 48
3.2.2 Measuring CO2 Membrane Diffusivity....................................................................... 49
3.2.3 Measuring IBT Membrane Diffusivity ....................................................................... 51
3.3 Data Analysis ................................................................................................................. 52
3.3.1 O2 ................................................................................................................................ 52
3.3.1.1 Simplistic calculation ......................................................................................... 53
3.3.1.2 Rigorous Calculation ......................................................................................... 54
3.3.1.3 COMSOL Simulation ........................................................................................ 55
3.3.2 CO2.............................................................................................................................. 57
3.3.3 Isobutanol .................................................................................................................... 58
3.4 Results............................................................................................................................. 59
3.5 Discussion ....................................................................................................................... 66
3.5.1 Effect of Membrane Type ........................................................................................... 66
3.5.2 Effect of Simplifying Assumptions ............................................................................ 66
3.5.2.1 Membrane Curvature ......................................................................................... 66
3.5.2.2 Axial Gradient and Dead Volume...................................................................... 68
3.5.2.3 Lumen Radial Gradient ...................................................................................... 68
3.5.2.4 Effect of Pressure Fluctuation ............................................................................ 69

4 SIMULATION OF ISOBUTANOL PRODUCTION IN A BIOREACTOR FOR
INCOMPATIBLE GASES (BIG).............................................................................................. 71
4.1 Introduction ................................................................................................................... 71
4.2 Materials and Methods ................................................................................................. 72
4.2.1 Model Setup ................................................................................................................ 72
4.2.2 Mass Transfer Parameters in the Hollow Fiber Membrane ........................................ 74
4.2.3 Estimation of Stoichiometry ....................................................................................... 76
4.2.4 Structured Cellular Kinetic ......................................................................................... 77
4.2.5 Mixed Substrate Cell Kinetics .................................................................................... 79
4.2.6 Estimation of Kinetic Parameters ............................................................................... 80
4.3 Results and Discussion .................................................................................................. 82
4.3.1 Evolution of Cell Density and Reaction Profile ......................................................... 82
4.3.2 Predicted Effect of Experimental Conditions on IBT Production .............................. 87
4.3.2.1 Initial Cell Density ............................................................................................. 87
4.3.2.2 Effect of Membrane Thickness .......................................................................... 89
4.3.2.3 Effect of Initial Ammonium Concentration ....................................................... 90
4.3.2.4 Effect of H2 Pressure .......................................................................................... 91
4.3.2.5 Effect of Lumen Flow Rates .............................................................................. 93
4.3.2.6 Effect of Substrate Preference ........................................................................... 97
4.3.2.7 Effect of Product Removal................................................................................. 98
4.4 Conclusions .................................................................................................................. 101
CONCLUSIONS ....................................................................................................................... 102
ix

APPENDIX ................................................................................................................................ 104
REFERENCES .......................................................................................................................... 115

x

LIST OF TABLES

Table 2.1 Comparison of mass transfer challenges posed by the three gas substrates. ............... 11
Table 3.1 Summary of the experimental setups used to measure diffusion coefficients of O2, CO2
and IBT. ........................................................................................................................................ 52
Table 3.2 Comparison of the assumptions made in three different types of calculation. ............ 57
Table 3.3 Apparent diffusion coefficients for O2 transport across the spongy layer of the hollow
fiber membrane. ............................................................................................................................ 59
Table 3.4 Apparent diffusion coefficients for CO2 transport across the spongy layer of the
hollow fiber membrane. ................................................................................................................ 60
Table 3.5 Apparent diffusion coefficients for IBT transport across the spongy layer of the hollow
fiber membrane. ............................................................................................................................ 60
Table 3.6 Summary of membrane diffusivities of O2, CO2 and IBT obtained from film theory
fitting using simplistic and rigorous calculation results, compared to their aqueous diffusivities.
....................................................................................................................................................... 62
Table 3.7 Comparison of
measured in mixed cellulose ester membrane and XM-50 hollow
fiber membrane ............................................................................................................................. 66
Table 3.8 Effects of simplifying assumptions on apparent diffusion coefficients ....................... 69
Table 4.1 Mass transfer parameters used in simulations. ............................................................. 74
Table 4.2 Kinetic parameters used in simulations........................................................................ 82

xi

LIST OF FIGURES

Figure 1.1 Schematic comparison between biomass-based alternative fuel platform (left) and
electrofuel platform (right). For interpretation of the references to color in this and all other
figures, the reader is referred to the electronic version of this dissertation. ................................... 2
Figure 2.1 Design concept for a bioreactor for incompatible gases (BIG) for autotrophic IBT
production. .................................................................................................................................... 14
Figure 2.2 SEM image of immobilized R. eutropha cells (Re2061). .......................................... 16
Figure 2.3 SEM images of (a) cross section, (b) inner surface and (c) outer surface of
polysulfone hollow fiber membrane. This type of polysulfone hollow fiber membrane showed
relatively uniform size distribution on the scale of 1 µm and is therefore not suitable for cell
immobilization by embedding. ..................................................................................................... 17
Figure 2.4 SEM images of (a) cross section, (b) inner surface and (c) outer surface of
polypropylene hollow fiber membrane. The membrane showed pore size in the 1-5 µm range and
therefore is not optimal for cell immobilization by embedding. .................................................. 18
Figure 2.5 SEM images of (a) cross section, (b) inner surface and (c) outer surface of
polyvinylidene fluoride hollow fiber membrane. Even though the membrane has large internal
“pockets” large enough to accommodate cells, the pores on its inner and outer surface exhibit
submicron sizes, making it unsuitable as immobilization matrix. ................................................ 19
Figure 2.6 SEM images of (a) cross section, (b) inner surface and (c) outer surface of mixed
cellulose ester hollow fiber membrane. The pore sizes exhibited are also non-ideal for cell
immobilization. ............................................................................................................................. 20
Figure 2.7 Illustration for cell immobilization/membrane inoculation. LEFT: inoculation by
incubation; RIGHT: inoculation by filtration. .............................................................................. 22
Figure 2.8 Hetetrophic operation setup with flow through configuration at the shell side.......... 25
Figure 2.9 Experimental setup for autotrophic operation flow-through configuration at the shell
side. ............................................................................................................................................... 26
Figure 2.10 Autotrophic setup for planktonic cells with dead-end configuration on the shell side.
....................................................................................................................................................... 27
Figure 2.11 Schematic of the Opto22-based control network. ①Opto22 controllers; ②ENMET
gas sensors; ③environmental H2 sensor; ④mass flow controller; ⑤pressure controller. Black
lines indicate tubings for gas and liquid transporation. Colored lines indicate the electric wirings:
blue-mass flow controller; orange-gas sensors; red-solenoid valves; green-pressure controller. 30
Figure 2.12 System configuration for IBT feeding experiment. .................................................. 31
xii

Figure 2.13 Comparison of initial cell density achieved by incubation and filtration. ................ 32
Figure 2.14 Scanning Electron Microscopy (SEM) image of XM-50 membrane cross-section (a)
after filtration inoculation (b) after incubation in exponentially growing R. eutropha culture for
48 h................................................................................................................................................ 33
Figure 2.15 Experimental results from heterotrophic and autotrophic operation with immobilized
cells. .............................................................................................................................................. 34
Figure 2.16 Fructose, NH4Cl and IBT concentrations from an IBT feeding experiment using R.
eutropha strain Re2425. ................................................................................................................ 37
Figure 2.17 Experiment results of BIG autotrophic operation with planktonic cells. ................. 38
Figure 2.18 Experiment results of BIG autotrophic operation with planktonic cells. ................. 40
Figure 3.1 Summarized relative diffusion coefficient of O2 in biofilm.[70].................................. 46
Figure 3.2 (a)SEM image of XM-50 membrane cross section. Upper left side is the lumen
surface. The support layer has a macroporous structure with size on the order of 10 nm. (b) Inner
surface of XM-50 hollow fiber membrane. (c) Outer surface of XM-50 hollow fiber membrane.
....................................................................................................................................................... 47
Figure 3.3 Schematic of the experimental system used to measure O2 mass transfer between the
gas phase in the shell and the aqueous phase circulating through the fiber lumen. ...................... 48
Figure 3.4 Schematic of the experimental system used to measure CO2 mass transfer between
the gas phase in the shell and the aqueous phase circulating through the fiber lumen. ................ 50
Figure 3.5 System configuration for measuring IBT apparent diffusion coefficient across the
XM-50 membrane. ........................................................................................................................ 51
Figure 3.6 Geometry of a single fiber in the hollow fiber reactor. .............................................. 55
Figure 3.7 Dissolved O2 versus time data used to determine the apparent diffusion coefficient for
oxygen through the spongy layer of the hollow fiber membrane. ................................................ 59
Figure 3.8 The apparent diffusion resistance across the hollow fiber membrane consists of
resistance of the membrane (
, is the thickness of membrane and
is the
diffusivity in the membrane) and a liquid film on the membrane inner surface (the reciprocal of
mass transfer coefficient ). The liquid film gets thinner as the liquid flow rate rises, and its
resistance to diffusion becomes insignificant at very high flow rates. ......................................... 61
Figure 3.9 Calculated apparent diffusion coefficients of O2 at different liquid flow rates with
simulated correlation between apparent diffusion coefficients and liquid flow rates. ................. 63
Figure 3.10 Calculated apparent diffusion coefficients of CO2 at different liquid flow rates with
simulated correlation between apparent diffusion coefficients and liquid flow rates. ................. 64

xiii

Figure 3.11 Calculated apparent diffusion coefficients of IBT at different liquid flow rates with
simulated correlation between apparent diffusion coefficients and liquid flow rates. ................. 65
Figure 3.12 Effect of neglecting membrane curvature. For diffusion from lumen to shell (left), if
using inner membrane area as basis for calculation, the concentration gradient will be
underestimated, causing diffusion coefficients to be overestimated. The opposite occurs with
diffusion from shell side to lumen when using outer membrane area for calculation. ................. 67
Figure 4.1 Experimental setups and results for measuring the membrane diffusivities of: (a) O2,
(b) CO2, and (c) IBT ..................................................................................................................... 75
Figure 4.2 The trend for total immobilized cell mass in the BIG resembles the growth curve in a
chemostat-exponential growth at low cell density follow by a plateau when mass transfer
becomes limiting. .......................................................................................................................... 83
Figure 4.3 Evolution of cell density profile in the membrane at (a) inlet, (b) mid-point and (c)
outlet of the hollow fiber reactor. ................................................................................................. 85
Figure 4.4 The evolution of O2 and H2 profiles as well as IBT production, consumption and net
reaction rates at membrane inlet in the case with H2 membrane diffusivity at 1 10-9 m2/s. ....... 86
Figure 4.5 IBT concentration versus time at different initial cell densities in a recirculation
mode.............................................................................................................................................. 88
Figure 4.6 IBT concentration at various biofilm thicknesses. ..................................................... 89
Figure 4.7 IBT concentration at various initial ammonium concentrations. ............................... 91
Figure 4.8 Average IBT outlet concentration at various H2 pressures......................................... 92
Figure 4.9 H2 and O2 concentration profiles at the reactor inlet, midpoint and outlet at 200 h. At
the highest shell pressure, H2 becomes excessive at the outlet, resulting in H2 and O2 mixing in
the lumen liquid. ........................................................................................................................... 93
Figure 4.10 Effect of lumen flow rates: (a) reservoir IBT concentration, inset-reservoir NH4Cl
concentration; (b)-(e) cell density distribution at fiber outlet at 2.5h, 50h, 200h and 400h. into the
biofilm, where the cell density peak occurs. ................................................................................. 95
Figure 4.11 (a) Reservoir IBT concentration with an initial NH4Cl concentration of 0.05g/L at
various H2 preferences. Inset: corresponding reservoir NH4Cl concentrations. (b) Outlet cell
density profiles at 200h. ................................................................................................................ 96
Figure 4.12 (a) IBT production rate; (b) NH4Cl concentration under various flow rates without
IBT recovery. ................................................................................................................................ 99
Figure 4.13 (a) IBT production rate; (b) NH4Cl concentration under various flow rates with IBT
recovery....................................................................................................................................... 100

xiv

Figure A.1 Cross section of a hollow fiber with inner radius R1 and outer radius R2. .............. 105
Figure A.2 A thin slice of lumen space with thickness Δz. ....................................................... 107
Figure A.3 A thin slice of the annular shell space with thickness Δz. ....................................... 111

xv

KEY TO SYMBOLS

Membrane inner area
Membrane outer area
δ

Membrane thickness
O2 concentration in the reservoir
Apparent diffusion coefficient
Apparent O2 diffusion coefficient
Apparent H2 diffusion coefficient
Apparent (measured) CO2 diffusion coefficient

DCW

Dry cell weight
Effective diffusion coefficient (in biofilm)
Diffusion coefficient of solute in solvent
Membrane diffusion coefficient
O2 membrane diffusion coefficient
H2 membrane diffusivity
CO2 membrane diffusivity

DO

Dissolved oxygen
Membrane porosity
Flow rate in the lumen
Flow rate in the shell

xvi

IBT

Isobutanol
Henry's coefficient of CO2 at 298K

L

Fiber length [m]

N

Number of fibers
|

Diffusion flux at membrane inner surface
CO2 partial pressure in reservoir
Gas constant, 8.314[J/K/mol]
Inner radius of hollow fiber
Outer radius of hollow fiber

T

Temperature [K]

VR

Reservoir volume [m3]
Total volume [m3]

xvii

1
1.1

INTRODUCTION
Motivation and Problem Description
With the global energy demand rising and instability in oil-exporting countries, the

scientific community has been searching for environmentally responsible and economically
viable approaches to harvest energy and convert it into forms suitable to meet societal needs (e.g.,
transportation fuels). Solar, wind, geothermal and hydropower energy sources are being
considered as alternatives to conventional fossil fuels.[1, 2]
Solar energy holds great potential because of its ubiquitous availability. Currently, the
alternative fuel industry is based largely on the photosynthetic capture of solar energy as
carbohydrates in food crops, wood, switchgrass, and corn stover.[3] The carbohydrates are then
recovered from the plant material, converted into sugars, and then used in fermentations to
produce bioethanol, biobutanol, etc.
However, the biomass refining processes required to convert the plant material (biomass)
into a fermentable sugar stream can be costly because the biomass typically needs to be
harvested, pre-treated then hydrolyzed with enzymes.[4, 5] Moreover, photosynthesis is inherently
inefficient; a typical crop plant has a sunlight-to-biomass efficiency of only 1%-3% of the overall
solar radiation.[6] On the other hand, with advances in photovoltaic technology, commercial solar
panels have reached efficiencies up to 21.0%,[7] suggesting that transportation fuels could be
produced more efficiently via mature electrofuel technologies.
In the electrofuel platform, solar energy is harvested and converted into liquid fuels
without the involvement of photosynthesis. In one approach, photovoltaic materials convert solar
energy into electricity, which is then used to electrolyze water into H2 and O2. The storage,
transportation, and use of H2 as a transportation energy source are energy intensive. However, by
1

using engineered microbes as biocatalysts, H2 and CO2 can be converted into a convenient,
energy-rich liquid fuel, such as isobutanol (IBT). Thus, the electrofuel platform has the potential
to circumvent inefficient photosynthetic solar energy collection, as well as energy intensive
biomass pre-treatment and carbohydrate hydrolysis to potentially generate higher yields.[8]

Figure 1.1 Schematic comparison between biomass-based alternative fuel platform (left) and
electrofuel platform (right). For interpretation of the references to color in this and all other
figures, the reader is referred to the electronic version of this dissertation.
In most cases, microbes that can utilize H2 or CH4 as a source of energy need an electron
acceptor, such as O2,[9,

10]

sulfate[11] or nitrate[12] to receive the electrons generated when

2

oxidizing H2 and CH4. For economic reasons, O2 is preferred in industrial processes.
Conventional fermentation vessels are poorly designed for using flammable gases and O2 as
substrates for several reasons. First, the traditional method to increase the gas mass transfer rates
is to increase the impeller power in stirred tanks, which reduces bubble size and increases
interfacial area. However, this approach scales up unfavorably, resulting in unaffordable power
requirements in commercial-scale bioreactors.[13] Second, these fermentations require many more
moles of gas to be transferred per mole of product than conventional aerobic fermentations.
About 9 moles of H2 would be consumed per C-mole of IBT produced by Ralstonia. eutropha.[14]
In contrast, only about 0.25 moles of O2 are consumed per C-mole of product in a typical aerobic
fermentation.[15] Thus, gas mass transfer, which is already rate-limiting in most aerobic
fermentations, is much more challenging for gas-intensive fermentations. Third, most microbes
used for the electrofuel fermentations simultaneously require both a flammable gas (CO, H2, or
CH4) and O2.[9, 14] Existing methods to rapidly deliver both a flammable gas and O2 to the cells
would generate potentially explosive gas mixtures. Thus there is an urgent need for a scalable
bioreactor system that can cost-effectively achieve extremely high mass transfer rates without
gas-phase mixing of incompatible gases.
As solar-derived H2 is made more available by increased efficiency achieved by
photovoltaic materials, a bioreactor where biosynthesis of liquid fuels can be safely carried out
with high yields remain the key piece of technology that can make the Electrofuel platform
feasible.
The goal of this project includes two aspects: 1) to construct a prototype bioreactor
system that would allow simultaneous enhanced mass transfer of incompatible gaseous feeds to
the bacterial culture without creating an explosive mixture with an integrated in situ product

3

recovery system, and 2) to develop a comprehensive mathematical model to obtain insights on
the interplay between mass transfer and cellular kinetics in the system to design strategies for
performance improvement and future system scale-up.
1.2

Background

1.2.1 Alternative Fuels and Strategies for Production
Alternative liquid fuels of current research interests include ethanol,[16] IBT,[17] nbutanol,[17] etc. IBT has advantages over ethanol, includinghigher energy content (33 MJ/kg for
IBT versus 27 MJ/kg for ethanol[18]) and better compatibility with current pipeline infrastructure
due to its lower tendency to cause stress corrosion cracking.[19] Moreover, they can also be
converted to alkenes, which are gateway chemicals that can be hydrogenated, esterified or
polymerized to synthesize a diverse group of compounds with various applications.[17]
Intensive research is being carried out to develop and improve production methods for
these alternative fuels, and many of the approaches use microbes as the catalyst. These
“biocatalysts” have several advantages over their inorganic counterparts:[20] (1) using metabolic
engineering, the microbes could be “tailored” to utilize certain substrate(s) as the carbon or
energy source; (2) microbes produce fewer by-products (higher product specificity); (3)
microbial fermentations usually take place under mild conditions as opposed to some inorganic
catalytic reactions; and (4) well-designed fermentation processes typically do not generate
inorganic pollutants. As a result, using fermentation-based processes may reduce operating costs
and minimize the impact on the environment.
Microbes can produce fuels from a variety of substrates. The most common substrates are
sugars derived from biomass sources, including wood, switchgrass, corn stover, corn, etc.

4

However, the process of converting the biomass into sugars can be costly because the biomass
typically needs to be harvested, pre-treated, and then hydrolyzed with enzymes.
On the other hand, solar-derived H2 is predicted to be increasingly available with
technical advancements in solar water splitting,

[21-23]

suggesting that H2 may ultimately be an

economically viable substrate for microbial fuel production.
1.2.2 Isobutanol Production by Ralstonia eutropha
Ralstonia eutropha is a gram-negative bacterium that can use H2 as its energy source and
CO2 as its carbon source. This microbe has flexible metabolic pathways and therefore is able to
carry out both heterotrophic growth, where the microbe uses complex organic carbon substrates
(e.g., sugars), and autotrophic growth, where the microbe uses inorganic sources (e.g., CO2 and
H2).[12] When the nitrogen source is limited, this microbe accumulates poly-β-hydroxybutyrate
(PHB) in the form of intracellular storage granules, which can be harvested and used to
manufacture biodegradable thermoplastics.[16] Of all the bacteria that synthesize PHB, R.
eutropha is the most commonly used, owing to its ability to accumulate high levels of PHB (on
the order of 60 g/L[24]) when grown on a simple medium.[25]
The metabolic carbon flux in R. eutropha can be re-routed to synthesize IBT instead of
PHB. Our collaborators on this project, Dr. Anthony Sinskey’s team in the Massachusetts
Institute of Technology Biology Department, have removed the PHB-producing pathway in R.
eutropha and constructed an IBT synthesis pathway based on the native pathway for valine
biosynthesis from pyruvate.[26] By introducing a heterologous ketoacid decarboxylase, the valine
precursor 2-ketoisovalerate is converted to isobutyraldehyde and then reduced by an alcohol
dehydrogenase to IBT.[27]

5

Even though the technology to produce IBT from sugars is close to commercialization,[28]
the only published work on IBT production from CO2 is in photosynthetic cyanobacterium
Synechococcus elongatus, where the resulting IBT titer was less than 1 g/L.[27] The ability of
wild-type R. eutropha to accumulate PHB at a level of 60 g/L from autotrophic feeds[24] suggests
that engineered R. eutropha could achieve a high level of IBT productivity.
1.2.3 Fermentation of Gases with Low Aqueous Solubilities
Wild type R. eutropha is able to accumulate PHB using CO2 as the carbon source and H2
as the energy source.[10, 29-32] With the PHB synthesis pathway genetically deleted, and IBTproducing pathway inserted, the engineered R. eutropha strains are able to produce IBT both
heterotrophically[33] and autotrophically, as demonstrated in Chapter 2.
Developing a fermentation process in which the carbon and energy sources are all gases
presents significant engineering challenges. In fermentations with sparingly soluble gases such as
H2 or CO, the rate-limiting step is typically gas-to-liquid mass transfer.[34-36] Besides using highshear impellers and increasing impeller rates,[34, 37] engineering approaches commonly used to
enhance gas-liquid mass transfer in fermentations include 1) gas sparging through fritted glass[38,
39]

with intensive agitation; 2) gas delivery in microbubbles;[40] and 3) use of a continuous gas

phase, with counter flow of gas and liquid through a packed column containing immobilized
cells.[38, 41]
The incompatible nature of H2 and O2 gases presents other engineering challenges. H2 has
a wide explosive range (4%-75% in air), and therefore mixing H2 with O2 at virtually any ratio
raises serious safety concerns. Little guidance is provided in the literature on bioreactor designs
that simultaneously provide rapid mass transfer of incompatible gases while preventing
formation of explosive gas mixtures. In one published patent application, surfactants were used
6

to maintain an energy-rich gas (methane) and oxygen as discrete bubbles for fermentation
applications. However, this approach would add significant costs to the operation and
downstream product purification. The primary goal of this project is to design, assemble, and
operate a bioreactor that provides sufficient oxygen and hydrogen mass transfer to the cells
without creating a potentially explosive gas mixture.
1.3

Organization of This Dissertation

1.3.1 Continuous Isobutanol Production in A Bioreactor for Incompatible Gases (BIG)
Chapter 2 introduces the design concept of a Bioreactor for Incompatible Gases (BIG),
describes the design and fabrication of a prototype BIG system, and presents results documenting
the first continuous, autotrophic IBT production. This part of the project was carried out in
collaboration with Dr. Soumen Maiti (a postdoctoral researcher in the Department of Chemical
Engineering and Materials Science). Each of the collaborators made equal contributions to the
work, which demonstrated the system’s ability to produce IBT both heterotrophically and
autotrophically, and identified the key factors affecting the BIG’s IBT productivity. The R.
eutropha strains were provided by Dr. Anthony Sinskey at Massachusetts Institute of
Technology.
1.3.2 Mass Transfer in a Bioreactor for Incompatible Gases (BIG)
Chapter 3 describes efforts to measure the mass transfer rates of O2, CO2 and IBT in
hollow fiber membranes. Experimental methods were developed for each solute. Three
approaches for data analysis were applied, including two numerical derivations and simulations
in COMSOL Multiphysics®.

7

1.3.3 Simulation of Isobutanol Production in a Bioreactor for Incompatible Gases (BIG)
Chapter 4 describes a comprehensive mathematical model of the BIG system that takes
into account multiphase, multispecies gas mass transfer and includes a structured cell kinetic
model. The model was solved numerically using COMSOL Multiphysics® using various
parameters to obtain insights on the operation conditions’ impact on the systems performance.
1.4

Acknowledgments
Funding for this research was provided by the Department of Energy ARPA-E

Electrofuels program subaward No. 5710002852.

8

2

CONTINUOUS

ISOBUTANOL

PRODUCTION

IN

A

BIOREACTOR

FOR

INCOMPATIBLE GASES (BIG)
2.1

Introduction
Electrofuels are carbon-neutral, renewable transportation fuels produced via non-

photosynthetic CO2 fixation.[42,

43]

With the advancement in photovoltaic technologies, solar-

derived H2 is expected to become more available for use as electron donor to reduce CO2 and
store energy in C-H bonds within multi-carbon organic compounds, such as isobutanol (IBT).
IBT offers advantages over ethanol as a liquid fuel, including a lower vapor pressure, lower
hygroscopicity and higher energy density. It can be blended at any ratio with gasoline and used
as automotive fuel with existing infrastructure and engines.[44] Moreover, IBT can also be
converted to alkenes, gateway chemicals that can be hydrogenated, esterified or polymerized to
synthesize a diverse group of compounds with various applications.[17]
Most biofuel production strategies utilize heterotrophic carbon sources, such as sugars
derived from biomass, such as wood, switchgrass, and corn stover.[3] However, the biomass
refining to obtain sugars can be costly because the biomass needs to be harvested, pre-treated
then hydrolyzed with enzymes.[4, 5] Moreover, photosynthesis inherently has a lower solar energy
yield than photovoltaics, suggesting that transportation fuels could be produced more cheaply via
mature electrofuel technologies than via a photosynthetic platform. Photosynthesis of a typical
crop plant has a sunlight-to-biomass efficiency of only 1%-3% of the overall solar radiation,[6] as
opposed to 20.1%, the highest efficiency afforded by a commercial solar panel.[7] Also, carbonneutral electrofuels would not raise atmospheric CO2 levels as do fossil fuels.
Ralstonia eutropha, also known as Alcaligenes eutropha, Wausteria eutropha or
Cupriavidus necator, is a facultatively autotrophic Gram-negative bacterium that has been used

9

commercially to produce poly-β-hydroxybutyric acid (PHB), a biodegradable polymer,[25, 45, 46]
with a maximum titer of 60 g/L.[24] Nitrogen limitation is known to promote PHB accumulation
in the wild type[30] and the same regulation was used to trigger IBT production[33]. A native
valine biosynthetic pathway in the wild type R. eutropha was engineered by Lu, Brigham

[33]

to

produce IBT after the PHB-producing pathway was removed. The engineered strain retained the
wild type strain’s ability to utilize both heterotrophic and autotrophic carbon sources, with
carbon flux to IBT production being stimulated under nitrogen limitation.
Construction of a bioreactor system for autotrophic production of IBT poses a unique set
of engineering challenges. First, these fermentations are expected to be highly mass-transfer
limited. Although the overall stoichiometry for autotrophic IBT production will depend on a
number of factors, including how much ATP is consumed for cell maintenance, an approximate
stoichiometry based on known reaction pathways in R. eutropha (Equation 2.1)[10] indicates that
9 moles of H2 would be consumed per C-mole of CO2 reduced to IBT. In contrast, only about
0.25 moles of O2 are consumed per C-mole of glucose consumed in a typical aerobic
fermentation.[15] Moreover, both H2 and O2 have low aqueous solubilities, resulting in low
driving force for mass transfer. The combination of a higher demand for gas mass transport and a
small driving force indicates that the well-known challenges associated with achieving sufficient
gas mass transfer rates in aerobic fermentations would likely be at least one order of magnitude
more severe for fermentations that produce biofuels from H2 and CO2. Since the stoichiometric
coefficients represent the demand on the gas substrates, and the aqueous solubility and
diffusivity indicate the difference in each substrate’s mass transfer characterisitics, the ratio of
gas substrates’ stoichiometric coefficients versus the product of their aqueous solubilities and
diffusivities can be used as a qualitative gauge of their individual mass transfer challenge, as

10

summarized in Table 2.1. Even though H2 has a higher diffusivity in water, the mass transfer
challenge it poses is still more than twice of O2, making H2 mass transfer highly likely to be a
rate-limiting step. Second, the need to simultaneously deliver H2 and O2 creates safety issues
because these gases are incompatible, forming a flammable mixture over the range 4 to 94% H 2.
Third, like most alcohols, IBT is inhibitory to the bacterial cells, making its in situ removal
desirable for continuous bioreactor operations.
2.1

Table 2.1 Comparison of mass transfer challenges posed by the three gas substrates.

Gas

Amount
required
(mole/mole of
isobutanol)

Solubility in
water
(1 atm, 25°C)
(mole gas/kg
water)[47]

Diffusivity in
water
(×10-5 cm2/s)

H2

36

7.90×10-4

4.50[48]

1.01×109

O2

12

1.32×10-3

2.10[49]

4.33×108

CO2

4

3.45×10-2

1.92[49]

6.04×106

Mass transfer resistance
(stoichiometric
coefficient/(solubility ·diffusivity))
(kg·s/(mole ·cm2))

Existing bioreactor systems and strategies are not well suited to address this unique set of
engineering challenges. The strategy of simply mixing the gases at a ratio out of explosive limit
results in severe O2 limitations.[45] In addition, error in controlling the gas mixture or fluctuations
in cell metabolic activity could allow formation of explosive gas mixtures. A second approach is
to use a potentially explosive gas mixture, but contain it within an explosion-proof reactor
designed to withstand the pressure increase that would result if the gas phase ignited.[50] A
disadvantage of this approach is that fermenters able to withstand extremely high internal
pressures are expensive to fabricate and scale up. Another strategy used excessive gas in the

11

form of emulsions stabilized with surfactants, which would add significant costs to the operation
and downstream product purification.
This chapter presents a novel Bioreactor for Incompatible Gases (BIG) concept that
facilitates simultaneous and rapid mass transfer of two sparingly soluble and incompatible gases
while preventing formation of explosive gas mixtures. A prototype BIG system was developed
that uses Opto-22 control system to monitor and regulate the feeding gas flow rates in the system
to ensure safe operation and minimize wasted gas. The prototype BIG system was used with a
recombinant strain of R. eutropha, and it is the first to continuously produce IBT autotrophically
on H2, CO2 and O2.
2.2

Materials and Methods

2.2.1 Microorganisms and Media
Methods used to develop the R. eutropha strains Re2061 and Re2425/pJL26 used in this
study have been reported previously.[33] Briefly, Re2061 is a derivative of the wild type strain
with the PHB-producing pathway removed, and Re2425/pJL26 uses the overexpression of
plasmid-borne, native branched-chain amino acid biosynthesis genes and the overexpression of
heterologous ketoisovalerate decarboxylase gene to channel excess carbon from the PHB
production to biosynthesis of IBT. Re2061 was used in experiments on immobilization
techniques, while Re2425/pJL26 was used in all the IBT-producing and -consumption
experiments presented in this work.
The strains were cultivated at 30°C in either rich media consisting of 2.75 % (w/v)
dextrose-free tryptic soy broth (TSB) (Becton-Dickinson, Sparks, MD, USA) or minimum media
that contained per liter: 4.0 g NaH2PO4, 4.6 g Na2HPO4, 0.45 g K2SO4, 0.39 g MgSO4, 0.062 g
12

CaCl2, and 1 mL/L of a trace metal solution. The trace salt solution contained 15 g/L
FeSO47H2O, 2.4 g/L MnSO4H2O, 2.4 g/L ZnSO47H2O, 0.48 g/L CuSO45H2O and 0.1 M HCl.
For heterotrophic growth, 2% (w/v) fructose was added as carbon and energy source. For
autotrophic growth, H2, CO2 and O2 gases were provided from compressed-gas cylinders. Two
initial ammonium chloride concentrations were used, 0.1% (w/v) was used to promote growth
while 0.01% (w/v) was used to facilitate product formation. All media used for Re2061
contained a final gentamicin concentration of 10 μg/mL, and additionally, all media used for
Re2425/pJL26 also contained 200 μg/mL kanamycin.
The stock culture was grown on TSB agar plates, from which a single colony was picked
and cultured in 2-mL TSB medium. After overnight incubation, the 2-mL TSB culture was then
used to inoculate 100 mL minimal growth medium in a flask, which was shaken in an incubator
until it reached exponential growth phase before it was used as inoculum for three 1-L minimal
medium cultures in Erlenmeyer flasks.
2.2.2 Bioreactor for Incompatible Gases (BIG)
The proposed hollow-fiber bioreactor (Figure 2.1) has the biocatalyst immobilized on, or
entrapped within, the walls of hollow fiber membranes that separate the bioreactor housing into a
lumen side (inside the hollow fibers) and a shell side (outside the hollow fibers).
H2 and O2 are provided from opposite sides of the membrane with H2 in gas phase and O2
dissolved in the liquid medium. If necessary, the H2 mass transfer rate can be enhanced by
increasing the pressure, thus increasing the solubility (
dissolution, as suggested by Equation 2.2, where

13

) and raising the driving force for gas

is the total flux of gas-liquid mass transfer,

is the mass transfer coefficient,

is the interfacial area, and

is the aqueous concentration of

dissolved gas.
2.2

Figure 2.1 Design concept for a bioreactor for incompatible gases (BIG) for autotrophic IBT
production.

On the other hand, the mass transfer of O2 can be enhanced by using microbubble
dispersion. Microbubbles, which have been used to enhance gas transportation in
fermentations,[40,

51-53]

can improve the mass transfer rate by orders of magnitudes. As

demonstrated in Equation 2.3, the volumetric gas mass transfer rate is dependent on the specific
interfacial area and the concentration gradient. The specific interfacial area of spherical bubbles
(a) is inversely correlated with the bubble diameter, as is the gradient of gas concentration
around the bubbles at steady state.[40] Therefore, a 100-fold decrease in bubble size could
potentially enhance the mass transfer rate by ten thousand fold.

14

2.3

Moreover, the surface tension between aqueous and gaseous phases also results in a
difference in pressure inside and outside a bubble, denoted Laplace pressure. Laplace pressure is
proportional to the surface tension

and inversely proportional to the bubble radius r (Equation

2.4); therefore the very small r values of microbubbles make Laplace pressure effects potentially
significant. As O2 dissolves in the water, the bubble size decreases, further elevating the Laplace
pressure and thus further aiding the O2 dissolution process.
2.4

By feeding H2 and O2 from opposite sides of the membrane, the bioreactor design allows
bacterial culture sufficient access to both gases while keeping them separate. Significant mixing
of H2 and O2 due to transport across the membrane is unlikely to happen for these reasons: 1)
The pores of the hollow fiber membrane are filled with bacterial cells in aqueous environment,
and both of the gases are sparsely soluble in water, limiting the flux between the lumen and shell
side of the membrane; 2) The bacteria will consume most of the gas that diffuses into the
membrane; 3) The selected membrane will have a pore size that won’t allow O2 microbubbles to
pass.
Hollow fiber membrane reactors have been extensively used in industrial scale
wastewater treatments. The reactor designs are modularized and highly scalable, reaching a
processing capacity up to 3×107 gal/day.[54, 55]
2.2.3 Hollow Fiber Membrane Selection
To select a suitable hollow fiber membrane for this application, the following criteria
were used: 1) the material should be hydrophilic so that the membrane can provide a humid
15

environment for the bacteria; 2) Based on scanning electron microscopy (SEM, JEOL JSM6610LV) image (Figure 2.2), the rod-shape R. eutropha cells have a typical diameter of 0.5 µm
and an average length of about 1.5 µm. To allow the cells to be embedded at a high density, the
membrane should have asymmetric pore size distribution with pores significantly larger than the
cells on one side and smaller pores (submicron size) on the other side so that the bacterial cells
can be retained in the larger pores; 3) for analytical purposes, the membrane material should be
chemically resistant to the reagents used to extract protein from immobilized cells and should not
interfere with protein assays.

Figure 2.2 SEM image of immobilized R. eutropha cells (Re2061).
Initially, a number of hollow fiber membranes were considered, including polysulfone
(CLF2E110, GE Healthcare, Pittsburg, PA), polypropylene, polyvinylidene fluoride (PVDF) and
mixed cellulose ester hollow fiber membranes (Spectrum Laboratories, Inc., Rancho Dominguez,
CA). However, preliminary SEM examinations found that the pore sizes of all the membranes
are too small for cells to be embedded into the pores (Figure 2.3-Figure 2.6).

16

(a)

(b)

(c)

Figure 2.3 SEM images of (a) cross section, (b) inner surface and (c) outer surface of
polysulfone hollow fiber membrane. This type of polysulfone hollow fiber membrane showed
relatively uniform size distribution on the scale of 1 µm and is therefore not suitable for cell
immobilization by embedding.

17

(a)

(b)

(c)

Figure 2.4 SEM images of (a) cross section, (b) inner surface and (c) outer surface of
polypropylene hollow fiber membrane. The membrane showed pore size in the 1-5 µm range and
therefore is not optimal for cell immobilization by embedding.

18

(a)

(b)

(c)

Figure 2.5 SEM images of (a) cross section, (b) inner surface and (c) outer surface of
polyvinylidene fluoride hollow fiber membrane. Even though the membrane has large internal
“pockets” large enough to accommodate cells, the pores on its inner and outer surface exhibit
submicron sizes, making it unsuitable as immobilization matrix.

19

(a)

(b)

(c)

Figure 2.6 SEM images of (a) cross section, (b) inner surface and (c) outer surface of mixed
cellulose ester hollow fiber membrane. The pore sizes exhibited are also non-ideal for cell
immobilization.

20

Ultrafiltration membranes fulfill the requirement on pore size distribution since they
typically have anisotropic pore size distributions with a skin layer with the designated nominal
pore size and a “spongy layer” with macroporous structure to provide extra mechanical strength
without adding resistance to the permeate flow. XM-50 hollow fiber membrane has been
successfully

used

for

whole

cell

immobilization,

and

the

material,

a

polyacrylonitrile/polyvinylchloride copolymer, is reasonably hydrophilic. Therefore, an XM-50
ultrafiltration hollow fiber cartridge was chosen as the reactor (hereafter noted as HFR, HF,
1018-1.0-45-XM50, Koch Membrane System, Wilmington, MA). The membrane has a skin
layer on the lumen side with a nominal pore size of 50 kDa, while the shell-side pore size is on
the 10-100 µm scale and large enough for the cells to enter and become entrapped in the fiber
wall.
2.2.4 Cell Immobilization and Hollow Fiber Membrane Cleaning
Prior to experiments, the hollow fiber cartridge was sanitized by incubating the HFR
lumen, fiber wall, and shell space with 500 ppm aqueous sodium hypochlorite (NaClO) solution
for at least 2 h. Afterwards, the HFR was thoroughly rinsed with sterile water. The experiments
on immobilization techniques were carried out with strain Re2061.
The cells were grown on fructose-based minimal medium until they reached exponential
growth phase and then used to inoculate the HFR. For incubation immobilization method, 1-cm
fiber segments were incubated in the exponentially growing culture at 30˚C for 48 h (Figure 2.7
left).
For filtration immobilization, cells from 3-L exponentially growing culture were
harvested, rinsed 3 times with 0.1 M phosphate buffer saline (PBS) at pH 7.4 to prevent carryover of fructose and metabolic intermediates from the spent heterotrophic medium, and re21

suspended in 200-250 mL fructose-free minimal media. The concentrated R. eutropha culture
was placed in a 300 mL sample cylinder (AA0359 304L-HDF4-300CC, Swagelok, Solon, OH)
connected to the HFR shell side, and the cells were forced into the pores of the membrane
spongy layer from the lumen by applying pressure on the shell side using compressed air (Figure
2.7 right). Because pores on the inner membrane skin were too small to allow cell passage, the
cells were filter-immobilized within the large pores of the membrane spongy layer.

Figure 2.7 Illustration for cell immobilization/membrane inoculation. LEFT: inoculation by
incubation; RIGHT: inoculation by filtration.

After experiments, the hollow fibers were rinsed repeatedly by forcing sterile water from
lumen to shell in order to flush out embedded cells. The water rinsate (rinsate 1) was collected.
To further remove cell mass from the hollow fibers, the lumen, fiber wall, and shell side were
filled with 1M NaOH aqueous solution and incubated at room temperature for 6~8 h to lyse the
cells and extract the protein.[56] After the incubation, the protein extract was collected, and the
membrane was rinsed with copious de-ionized water until the rinsate reached neutral pH. All the
alkaline rinsate (rinsate 2) was collected for protein quantitation.
22

2.2.5 Measurement of Biomass, Ammonium and IBT Concentration
For planktonic cultures, the cell density was measured using an HP 8452 diode array
spectrophotometer (Hewlett-Packard, Palo Alto, CA).
For experiments with cell immobilization techniques, 1-cm hollow fiber segments were
collected and incubated in 1 M NaOH at 125˚C for 15 min to lyse the cells before the protein
contents were quantitated with fluorescamine assay.
For experiments with immobilized cells in hollow fiber modules, the final cell mass was
measured by totaling the cell mass in the rinsates. Cell mass in rinsate 1 was quantified by its
optical density at 600 nm (OD600) before the cells were collected by centrifugation and lysed
using the same alkaline incubation as for the hollow fiber membrane. The protein content in this
extract was used as a reference to measure the cell mass in rinsate 2 (Equation 22.5).
2
2.5

is the total cell mass in rinsate 2,
and
and

and

are the cell density and volume of rinsate 1,

are the protein concentration and volume of the protein extract from rinsate 1, and
are the protein concentration and volume of the rinsate 2 protein extract.
Immobilized cell mass was estimated by total protein content as quantitated using

fluorescamine assay. Fluorescamine reacts with primary amines in proteins and forms highly
fluorescent moieties. The intensity of the fluorescent response correlates linearly with protein
concentration at lower protein concentrations (0-500 µg/mL). The assay procedure has been
described by Held. Briefly, 50 µl aliquots of 10.8 mM (3mg/ml) fluorescamine (F9015, SigmaAldrich Corporation, Missouri, MO) dissolved in acetone were added to 150 µL of diluted
samples and bovine serum albumin (BSA, 05470, Sigma-Aldrich, Missouri, MO) standards in a

23

96-well plate (82050-728, Greiner Bio-One, Monroe, NC) and mixed immediately before the
fluorescence responses were determined using a 400 nm, 30 nm bandwidth, excitation filter and
a 460 nm, 40 nm bandwidth emission filter. The protein concentrations of the samples were
determined using the BSA standard curve.
The concentration of NH4+ was measured using an assay kit (AA0100, Sigma-Aldrich, St.
Louis, MO). IBT was measured using a Bruker® GC-450 gas chromatograph (Bruker
Corporation, Billerica, MA) outfitted with a Varian® CP7416 column and an flame ionization
detector.
2.2.6 Operation of Bioreactor for Incompatible Gases (BIG)
The components used in the BIG system included two ENMET GSM-60 gas sensors
(ENMET Corporation, Ann Arbor, MI), a Sartorius BIOSTAT® Bplus Fermenter with a 1-L
vessel (Sartorius Stedim Biotech, S.A., Göttingen, Germany), an Opto22 SNAP-PAC-R1
programmable automation controller (Opto22, Temecula, CA), MasterFlex Pumps (Model 752300 and 77200-12, Cole-Parmer, Vernon Hills, IL), a hollow fiber reactor (HF, 1018-1.0-45XM50, membrane area 1 ft2, Koch Membrane System, Wilmington, MA), Omega FMA6500
digital mass flow controllers (Omega Engineering, Inc., Stamford, CT), and solenoid valves
(Clark-Cooper Division, Magnatrol Valve Corporation, Cinnaminson, NJ ).
2.2.6.1 Heterotrophic Operation with Immobilized Cells
Heterotrophic operations were carried out in the first stage of some experiments to
rapidly increase the immobilized cell density and to verify the ability of the immobilized cells to
heterotrophically produce IBT. The system was set up as illustrated in Figure 2.8, with a flowthrough configuration on the shell side and 0.4 L fructose-based minimal medium circulated in

24

the lumen. The pressure at the shell side was maintained by a 1-psig check valve at the vent. Air
was supplied through a Millex HA 0.45 μm filter (EMD Millipore, Billerica, MA) to the shell
side at 5 psig. No gas was fed to the reservoir. The IBT in the shell effluent gas was recovered
using a Graham style condenser (Z531405, Sigma-Aldrich, Milwaukee, WI) with 0˚C ethanol as
coolant. Samples were collected from the reservoir for measurement of fructose, IBT and NH4Cl.

Figure 2.8 Hetetrophic operation setup with flow through configuration at the shell side.

25

2.2.6.2 Autotrophic Operation with Immobilized Cells
The BIG system was modified for autotrophic operations as depicted in Figure 2.9.
Instead of air, H2 and CO2 were fed to the shell at 0.1 L/min and 0.02 L/min respectively. A
peristaltic pump recirculates 0.4 L fructose-free minimal medium from the reservoir through the
lumen. A flow-through configuration was used on the shell side, with the exiting gas sent to an
ENMET sensor (GSM-60, ENMET Corporation, Ann Arbor, MI) to monitor O2 concentration.
The pressure at the shell side was maintained by using a 1-psig check valve at the vent.

Figure 2.9 Experimental setup for autotrophic operation flow-through configuration at the shell
side.
26

A mixture of air and CO2 was fed to the medium reservoir in a 9:1 ratio. The gas flow
rate into the reservoir was regulated by the fermentor control tower to maintain dissolved O2 (DO)
level at 80% air saturation. To minimize IBT loss to gas stripping, a cold trap was attached to the
reservoir exhaust. A second ENMET gas sensor was installed to monitor the O2, CO2 and H2
concentrations in the exhaust gas from the reservoir vent. Liquid samples were collected from
the reservoir for IBT and NH4+ analysis.
2.2.6.3 Autotrophic Operation with Planktonic Cells

Figure 2.10 Autotrophic setup for planktonic cells with dead-end configuration on the shell side.

27

Figure 2.10 shows the system configuration used for autotrophic operations with
planktonic (suspended) cultures of R. eutropha. Several improvements were made on the basis of
the setups used with immobilized cells. A dead-end configuration was used for shell gas feeding
to reduce the amount of gas required for the process and minimize the IBT loss in the effluent
gas stream. The dead-end configuration also allows more accurate pressure control with a digital
back pressure controller (Alicat Scientific, Tucson, AZ). Pure H2 was fed to the system to avoid
dilution by CO2. The reservoir DO was controlled at 80%-100% air saturation using a mixture of
air (0.4 L/min) and pure O2. Carbon dioxide (0.2-0.3 L/min) was sparged into the reservoir liquid.
The 0.5-L planktonic culture was circulated through the system using a peristaltic pump.
Two variations were used with this setup. In Setup 1, the reservoir liquid was recirculated
through the lumen of the HFR, while pure H2 was fed to the shell in a dead-end configuration at
15 psig. The recycled liquid returning from the HFR was delivered into the headspace above the
reactor vessel liquid, so that any H2-containing gas bubbles generated within the HFR would
disengage from the returning liquid stream and enter the Sartorius headspace without being
entrained into the agitated liquid in the Sartorius vessel. In Setup 2, H2 was delivered to the
lumen side in a dead-end configuration with pressure controlled at 15 psig, while the reservoir
liquid was circulated through the shell. The recycled liquid was injected directly into the liquid
within the Sartorius vessel, so that any H2-containing gas bubbles generated within the HFR
would be entrained into the agitated liquid in the Sartorius vessel. A small amount of the H2 gas
stream was vented from the BIG at designated intervals to purge any gases (e.g. CO2) that might
accumulate and dilute the H2. The vented gas was sent through an ENMET gas sensor to ensure
that O2 never exceeded a critical level. There was no gas flow through the shell except during the
occasional venting periods. The liquid stream exiting the HFR was directly injected into the

28

liquid in the reservoir, rather than dispensing it into the gas headspace above the liquid, as was
done in Setup 1.
In both setups, the system was equipped with a glass column (I.D. 10 mm, length 50 cm,
Omnifit®, Diba Industries, Danbury, CT) packed with Dowex® Optipore SD-2 polymeric resin
(The Dow Chemical Company, Midland, MI) to recover IBT from the reservoir effluent gas.
Samples were collected from the reservoir for measurement of cell density, IBT and
ammonium. Ammonium chloride was added as needed to avoid nitrogen limitation. Samples
were collected from the culture vessel for measurement of cell density, IBT and NH4+. Methanol
was used periodically to desorb IBT from the resin column and thereby measure the amount of
IBT adsorbed. Two resin columns were alternately used for either adsorbing or desorbing IBT,
so the reactor could be operated continuously without IBT accumulation to toxic levels.
2.2.6.4 Opto22-based Control Network and Safety Measures
Due to safety concerns when using H2 gas in an aerobic environment, solenoid valves,
mass flow controllers and gas sensors were used to monitor and regulate gas flow rates and
composition in various regions of the BIG system. To implement centralized control over the
instruments, an Opto22-based control network was constructed, as shown in Figure 2.11. The
Opto22 SNAP-PAC system consisted of an automation processor and 10 I/O modules. The input
modules received the analog or digital readings from the instruments and passed them on to the
I/O processor, which ran the user-defined control strategies and adjusted the output signal
accordingly. The output signals were then relayed to the instruments via the output modules.
Figure 2.11 shows an Opto22 control strategy used for autotrophic operation of the BIG
system described in Figure 2.9. The sensors closely monitored the gas composition in the
reservoir head space and HFR shell. If any mixing of H2 and O2 were detected, a pre-defined set
29

of actions would be executed to flush out the potentially hazardous mixture. If a H2 leak were
detected in the walk-in fume hood, the control system would trigger an alarm and shut the
solenoid valves on the gas cylinders.

Figure 2.11 Schematic of the Opto22-based control network. ①Opto22 controllers; ②ENMET
gas sensors; ③environmental H2 sensor; ④mass flow controller; ⑤pressure controller. Black
lines indicate tubings for gas and liquid transportation. Colored lines indicate the electric wires:
blue-mass flow controller; orange-gas sensors; red-solenoid valves; green-pressure controller.

30

2.2.6.5 IBT consumption
To measure the rate of IBT uptake by the cells, IBT was fed to a 0.5 L high density
culture that was initially grown on fructose to a reservoir OD of approximately 7 before the
carbon feed was switched to IBT.
The fermenter’s control strategy monitored the DO level in the culture. When the energy
source became depleted, the cells’ metabolism rapidly decreased, causing a spike in DO level.
The control system was programmed to respond to such spikes by adding an aliquot of the
energy source (IBT). The subsequent increase in cellular metabolism caused the DO level to
drop again. In this way, the control system allowed the IBT level to be maintained at a low level
to avoid toxicity, and the rate of IBT consumption to be measured by the average rate of IBT
delivery to the reactor.
To avoid loss of IBT by gas stripping, an HFR was used to provide O2 via diffusion
across the membrane from the shell side in a dead-end configuration (Figure 2.12).

Figure 2.12 System configuration for IBT feeding experiment.
31

2.3

Results and Discussion

2.3.1 Cell Immobilization
Figure 2.14 shows cross-sectional SEM images of hollow fiber membranes inoculated by
filtration (a) versus incubation (b). With filtration, the cells were embedded in the macroporous
structure of the fiber wall, achieving a much higher cell density (Figure 2.14a) than a membrane
incubated in R. eutropha culture for 48 h (Figure 2.14b). A similar result was obtained from
fluorescamine assay (Figure 2.13). A high initial cell density could shorten the growth phase and
increase the culture’s resistance against contamination.

Inoculum (μg protein/cm2 )

1200
1000
800
600

400
200
0

Incubation

Filtration

Figure 2.13 Comparison of initial cell density achieved by incubation and filtration.

32

(a)

(b)

10 µm

Figure 2.14 Scanning Electron Microscopy (SEM) image of XM-50 membrane cross-section
(a) after filtration inoculation (b) after incubation in exponentially growing R. eutropha
culture for 48 h.

33

2.3.2 BIG Operation with Immobilized Cells
The experimental results are summarized in Figure 2.15. This experiment comprised of
three stages. The first stage spanned 0-168 h, when only heterotrophic feed was present. The
second stage started when autotrophic operation was initiated at 168 h with fructose still present
in the liquid medium and ended when the medium was replaced with fructose-free medium at

40

4

30

3

20

2

10

1

0
0.00

NH4Cl concentration (g/L)
IBT concentration (mg/L)

Fructose concentration (g/L)

244 h. In the third and last stage only autotrophic substrates were present in the system.

0
100.00

200.00
Time (h)

Fructose
IBT in shell cold trap
NH₄Cl

300.00

400.00

IBT in reservoir
IBT in reservoir cold trap

Figure 2.15 Experimental results from heterotrophic and autotrophic operation with immobilized
cells.

During the first stage, IBT production occurred at low levels, most likely due to the high
NH4+ concentration maintained to facilitate cell growth on fructose. After the autotrophic
operation was initiated at 168 h, a spike in the IBT concentration in the shell side cold trap was

34

observed, suggesting an increase in the local IBT concentration on the outer surface of the
membrane, possibly due to the addition of CO2 as a second carbon source. A second increase in
the IBT concentrations in both the shell side and reservoir exhaust cold traps was observed after
the liquid in the culture was replaced with fructose-free medium at 244 h, providing preliminary
evidence of IBT autotrophic production in the BIG system. The IBT concentration in the liquid
reservoir reached a maximum of 1.05 mg/L at 268 h. The increased IBT concentration was
accompanied by a drop in NH4+ concentration from 0.13 g/L to undetectable levels (< 2×10-4
g/L).
As NH4+ concentration dropped below 0.05 g/L, the IBT concentration also
decreased,suggesting that a threshold concentration of NH4Cl may be required for IBT
production during the transition from heterotrophic to autotrophic operation to sustain enzyme
synthesis while the cells are adapting to new carbon and energy sources. Growth of planktonic
cells was first observed in lumen liquid at the same time, possibly a result of either autotrophic
growth, or cell growth in the liquid phase using autotrophically produced IBT.
The BIG system was continuously operated first heterotrophically then autotrophically
for a total of 19 consecutive days without contamination. Protein assays showed that the total
immobilized cell mass grew from 1.56 ± 0.02 to 4.22 ± 0.58 g dry cell weight (DCW) during the
experiment. Ammonium chloride concentrations suggested that most of the growth occurred
during Stage 1. IBT production was measured during all stages. Initial IBT concentrations were
lower than anticipated. Possible explanations for the low IBT production include a non-optimum
autotrophic medium, gas mass transfer limitations, and consumption of IBT produced in one
region of the hollow fiber by cells in another region.

35

Subsequently, two experiments with higher initial cell densities did not yield higher IBT
concentrations. Various combinations of operating conditions (H2 pressure, DO set point, NH4+
concentration) were also tested but did not yield a significant increase in IBT concentration.
2.3.3 IBT Consumption by R. eutropha
A hypothesis was formulated to explain the observations that the IBT production was low,
was weakly influenced by the substrate concentrations, and decreased as the cell density
increased. The hypothesis was that in regions of the reactor where the autotrophic carbon and
energy sources were available, the cells would produce IBT, but in regions where the carbon
and/or energy sources were depleted, the cells would consume IBT. In principle, the cells only
need an electron acceptor (O2) to utilize IBT as a carbon and energy source, whereas all three of
the gaseous substrates (H2, CO2 and O2) must be present for autotrophic IBT synthesis. Because
H2 and O2 are provided to the cells by diffusion from opposite sides of the fiber wall, and H2 has
the highest mass-transfer challenge parameter (Table 2.1), it is conceivable that there would be
regions within the fiber walls where the cells were producing IBT and other, H2 depleted, zones
that were consuming IBT. In addition, growth of cell mass within the fiber walls would
simultaneously increase the gas uptake rate and decrease the gas diffusion rate by blocking pores
through the fiber wall. Consequently, H2 depletion, and thus IBT consumption, would be
expected to increase at higher cell densities, consistent with the experimental trends.
To test the hypothesis, experiments were conducted to assess IBT consumption by the R.
eutropha cells. During the fed-batch growth experiments, IBT was added on demand as the only
carbon and energy source. Figure 2.16 shows the fructose, NH4Cl and IBT concentration curves
marked with arrows. IBT was added to the culture several times and immediately consumed, as
indicated by the spikes in IBT concentration. The highest IBT consumption measured was 62 mg
36

IBT/ (g cell·h), a significant rate compared to the observed IBT production. The maximum
specific growth rate on IBT was 0.033 h-1 with a yield of 2.13 g IBT/g DCW cell.

5

10

4

8

3

6

2

4

1

2

0

0
0

50

100

150

200
Time (h)

250

300

350

400

OD
DO(%)

35
30

100

25

80

OD (AU)

20

60

15
40

DO (%)

Fructose (g/L)

12

Fructose (g/L)
NH₄Cl (g/L )
IBT (g/L)

NH4Cl and IBT (g/L)

6

10

20

5
0

0
0

100

200
Time (h)

300

400

Figure 2.16 Fructose, NH4Cl and IBT concentrations from an IBT feeding experiment using R.
eutropha strain Re2425.

37

2.3.4 Autotrophic Operation with Planktonic Cells
The finding that the cells consumed IBT under aerobic conditions in the absence of other
energy sources suggested that higher reactor productivity might be achieved by operating the
BIG under autotrophic conditions that reduced the likelihood of forming H2 depleted zones.
Because the high cell density achieved in the hollow fiber walls could lead to rapid H2 uptake
and sharp H2 concentration gradients in the radial direction, additional fermentation experiments
were conducted using Setup 1 in which the R. eutropha Re2425/pJL26 cells were grown in
suspension rather than being immobilized in the fiber wall. This mode of operation allowed the
cell density to be readily measured by OD and adjusted if desired.

80

2

70

1.8
1.6

60
50
OD600
IBT

1.2

40

1

30

0.8

0.6

20

NH4Cl(g/L)

1.4

0.4

10

0.2

0

0
0

100

Time (h)

200

300

Reservoir OD

IBT in resin (mg)

IBT in reservoir (mg/L)

IBT productivity (mg/(L day))

NH₄CL(g/L)
Figure 2.17 Experiment results of BIG autotrophic operation with planktonic cells.

38

Early in the experiment, the specific growth rate during autotrophic growth was 0.053 h-1,
and the IBT production rate was 48 mg/ (Lday). After 70 h (Figure 2.17) the culture’s OD600
was 6.8 and nitrogen was limiting. To increase the productivity, cell growth was encouraged by
adding NH4Cl. The cells resumed growing at slower rate, but the net production of IBT became
very low even after NH4+ had been depleted.
At 129 h, to confirm that minerals were not rate limiting, CaCl2, MgSO4 and trace
elements were added, but there was no increase in IBT production. At 170 h, the culture medium
was replaced with fresh medium to eliminate potentially inhibitory metabolic intermediates that
might have accumulated in the liquid during fermentation. This step was achieved by
centrifuging the lumen liquid at 2455 g in an Avanti® J-E centrifuge (Beckman Coulter, Inc.,
Pasadena, CA), and then re-suspending the cells in an equal volume of fresh medium and then
returning the cell suspension to the reservoir. However, medium replacement had virtually no
effect on IBT formation.
To test the hypothesis that the lack of IBT production was caused by high cell density
that would cause H2 depletion and IBT consumption, the culture was diluted to an OD600 of 2.2
at 199 h. After dilution, the cells began growing autotrophically again at a rate of 0.057 h -1 with
concurrent IBT production that peaked at about 60 mg/ (L day) at an OD of about 8. The cells
were diluted again at 263 h to an OD600 of 0.76, leading to resumption of cell growth at a specific
rate of 0.084 h-1 and IBT production. A peak IBT production rate of about 68 mg/ (L day) was
measured with specific production rate at 1.39 mg/ (g DCW h) when NH4+ became limiting at an
OD of about 6 (Figure 2.17).
These results provided strong support for the hypothesis that H2 limitation at high cell
density causes the drop in IBT production, and are consistent with other experimental results

39

suggesting that IBT consumption when H2 becomes depleted greatly reduces the net IBT
production rate. In this case, as the cell density increased beyond a threshold value, IBT
generation dropped precipitously.
Another autotrophic experiment was carried out with Setup 2 (Figure 2.18). The initial
specific growth rate of Re2425/pJL26 under autotrophic conditions was 0.11 h-1. As ammonium
became limiting at 35 h, IBT was produced with a specific production rate of 6.20 mg/ (g DCW
h), and a peak volumetric production rate of 323 mg/ (L day). Both of these values are higher
than those achieved in Setup 1, possibly because the direct injection of the recycled liquid into
the reservoir liquid allowed small bubbles of H2 from the HFR to be dispersed throughout the
liquid contents of the vessel, thereby achieving some degree of H2 transfer to the culture in the
vessel as well as the HFR.
400

IBT in reservoir (mg/L)
IBT in resin (mg)
IBT productivity(mg/L/day)

150

300

100

200

50

100

0

0
0

20

40

-50

60

80

100

120
-100

Time (h)

12

1.2
NH₄Cl (g/L)

1

8

0.8

6

0.6

4

0.4

2

0.2

0

0
0

20

40

60

80

100

Time (h)
Figure 2.18 Experiment results of BIG autotrophic operation with planktonic cells.

40

120

NH4Cl(g/L)

OD

10

OD (AU)

IBT productivity
(mg/L/day)

IBT in reservoir
(mg/Ll) and resin
column (mg)

200

However, when the OD reached about 10, the net IBT production plummeted, even under
ammonium-limiting conditions. At around 92 h, when the BIG was not producing IBT, the CO2
and O2 sparging rate into vessel liquid and liquid flow rate through the shell side of HFR were
increased, but IBT production did not increase. Pyruvic acid was produced at a level of about 8
g/L at low cell density, but this metabolic intermediate was also taken up by the cells at higher
cell density.
The higher IBT production achieved with planktonic cells compared to immobilized cells
can be attributed to the prevention of H2-depleted zones within the reactor. The filtrationinoculation method achieved high initial cell densities, a typical inoculum used for cell
immobilization was 220 mL of concentrated culture at OD600 of 24. The enhanced H2 mass
transfer was not sufficient to sustain such high cell density. In addition, growth of cell mass
within the fiber wall would simultaneously increase the gas uptake rate and decrease the gas
diffusion rate due to cell blockage of pores in the fiber wall. As a result, H2 depletion, and thus
IBT consumption, would be expected to increase at higher cell densities, consistent with the
experimental trends. Also, H2 mass transfer was enhanced by a higher supply pressure (15 psig)
in experiments with planktonic cells.
2.4

Conclusions
A novel bioreactor system was constructed for autotrophic IBT production. To our

knowledge, the BIG is the first bioreactor to facilitate mass transfer of two sparingly soluble,
incompatible gaseous reactants without forming hazardous gas-phase mixtures. The reactor
design simultaneously addresses both the mass transfer and safety issues, and therefore helps
advance the Electrofuel initiative. This design could also be applied in methanotrophic
fermentations, or other fermentations that simultaneously consume O2 and a flammable gas. This
41

system can be operated with immobilized or planktonic cultures and offers a novel platform for
autotrophic production of liquid fuels directly from cheap gas substrates, such as CO2 and CH4.
The relative low levels of autotrophic IBT production observed with both immobilized
and planktonic cells is likely a result of consumption of cellular IBT consumption when H2 mass
transfer becomes limiting. Improved IBT production levels are likely to result if IBT
consumption pathways are identified and eliminated, or if H2 transport is further enhanced,
possibly by operating the HFR at a higher pressure when stronger membranes are used.

42

3
3.1

MASS TRANSFER IN THE BIOREACTOR FOR INCOMPATIBLE GASES (BIG)
Background

In the BIG design, the incompatible O2 and H2 gases are physically separated by the
hollow fiber walls. The gases diffuse into the spongy layer from opposite directions and are
consumed by the immobilized cells. Under conditions in which gas mass transfer is rate-limiting,
the diffusivities of the substrates and products will have a significant impact on the system
dynamics. To accurately describe the mass transfer in BIG system in a mathematical model
(Chapter 4) and subsequently optimize the system’s operating conditions, the apparent diffusion
coefficients (Dapp) of O2, CO2, and IBT in the hollow fiber membranes were measured for a
range of lumen liquid flow rates. The effect of flow rate on the apparent diffusion coefficients
was modeled using both empirical correlation and COMSOL simulations to separate the
diffusion resistance of the lumen flow and obtain accurate estimates of the diffusivities.
3.1.1 Measurement of Diffusion Coefficients in Membranes
The theoretical and experimental aspects of determining a diffusion coefficient (D) in
planar membranes have been thoroughly covered in a number of books and journal articles.[57-59]
A common experimental setup consists of two diffusion chambers separated by a membrane with
known surface area. The liquid in the chambers is assumed to be well mixed, so there is no film
resistance between the bulk liquid and the membrane. The volumes of the chambers are large
enough so that the solute concentration in the chamber initially devoid of the solute can be
assumed to be throughout the experiment. The solute concentration in the other chamber is
measured regularly, and the total amount of diffused solute is plotted versus time. The plot is
43

then analyzed using a mass balance equation to determine the membrane diffusion coefficient
from either the slope of the linear region (denoted steady state analysis) or the x-axis intercept of
the extrapolated linear line (as in time lag analysis).[59, 60]
3.1.2 Diffusion in Porous Membrane
There is a large body of research on diffusion and permeation in porous membranes.[60-64]
The apparent diffusion coefficient (
(

of a solute relative to the aqueous diffusion coefficient

is affected by the void fraction (porosity, ) and tortuosity (τ) of the pore structure. If the

solute partitions into the membrane, a partition coefficient, Kp, can be used to analyze the data. In
macroporous and microporous membranes with pore sizes ranging from 5 nm to 1.0 μm, the
apparent diffusion coefficient is described using Equation 3.1.
3.1
Since immobilized cells can occupy space in pores and thus reduce the membrane’s
porosity, the apparent diffusion coefficient is likely to be affected by the density of immobilized
cells. However, there is no consensus in the literature regarding how to compensate for such
effects. Mignot and Junter[59] found that diffusivities of L-malic acid and glucose in an agar
membrane decreased linearly with the logarithm of cell density for cell densities between 20 ng
and 2 mg dry cell wt./ cm3 agar. Linear and quasi-linear correlations between cell density and
diffusion coefficient were also reported for cell densities up to 300 mg wet wt. /g gel in
polyacrylamide gel membrane[65] and at 40 mg dry wt. /cm-3 gel in Ca-alginate beads[66].
Hannoun and Stephanopoulos[60] found no effect of 20 wt.% yeast cells on the apparent diffusion
coefficient of glucose and alcohol in 2% alginate membrane. However, the 2 % agar membranes
used in the studies mentioned above have an estimated nominal pore size of 500-700 nm[67], and

44

the alginate beads have surface pore sizes between 6.8 and 16.6 nm[68], much smaller than the
pore size in the XM-50 membrane spongy layer (Figure 3.2a). Moreover, the solutes used in
these studies are organic molecules such as fructose and L-malic acid, all of which are
significantly larger than the gas molecules used in BIG. It’s likely that in the macroporous
spongy layer of a membrane such as XM-50 with pore sizes on the order of 10 µm (Figure 3.2c),
the effect of porosity on gas diffusivity is very slight, and the majority of diffusion resistance
stems from the skin layer, which has a molecular weight cut-off (MWCO) at 50 kDa. According
to a correlation established by Guo and Santschi[69], a 50-kDa MWCO has a nominal pore size of
5 nm. Since the skin layer’s pore size is too small to allow R. eutropha cells to be embedded, its
diffusion resistance will not be affected by cell immobilization.
There is very little literature on immobilized cells in macroporous polymer membrane
with pore sizes significantly larger than that of gel membranes, but the effect of immobilized
cells on solute diffusivity in the spongy layer can be estimated using data from biofilms.
Stewart[70] reviewed experimental measurements of effective diffusion coefficients in biofilms,
as summarized in Figure 3.1. The general trend suggests that higher cell densities could result in
more significant diffusion retardation. The diffusion coefficient in biofilms with the highest cell
density, 400 g/L, is 9% of the aqueous value. However, at less extreme cell densities (up to 50
g/L) the diffusion coefficients through biofilm are on the same magnitude as in water. It is
reasonable to assume that the diffusion coefficients through the immobilized cells are similar to
that those obtained in biofilms with similar cell densities.
Therefore, the membrane diffusivities measured with empty membranes were measured
and used as reasonable estimates for model simulation at low cell densities.

45

Effective O2 diffusion coefficient
De/Daq

1.2
1
0.8
0.6
0.4
0.2
0
0

100

200

300

400

500

Biomass Density (g/L)
Figure 3.1 Summarized relative diffusion coefficient of O2 in biofilm.[70]
Figure 3.2b and c are SEM (JEOL JSM-6610LV Scanning Electron Microscopy) images
of inner and outer surfaces of XM-50 hollow fiber membranes, respectively. The inner surface
seems smooth at the magnification of 4500, suggesting very small pore size. The XM-50
membrane has a molecular weight cut-off (MWCO) of 50 kDa, which corresponds to a nominal
pore size of 5 nm according to Guo et al..[69] On the contrary, the outer surface of the membrane
exhibits pores on the order of 10-100 µm.
The SEM images of XM-50 membrane cross section (Figure 3.2a) show two distinct
layers: one with lateral pores facing the outer (shell) surface and one with comb-shape pores
residing closer to the inner (lumen) surface of the membrane. The comb-shape pores have sizes
large enough to embed R. eutropha cells, but in an image of membrane cross section with
immobilized cells (Figure 2.14a), very few cells are observed in the comb-shape layer. Therefore,
the interface between the two layers must also have small pore sizes as well as the inner surface.

46

(a)

(b)

(c)

Figure 3.2 (a)SEM image of XM-50 membrane cross section. Upper left side is the lumen
surface. The support layer has a macroporous structure with size on the order of 10 nm. (b) Inner
surface of XM-50 hollow fiber membrane. (c) Outer surface of XM-50 hollow fiber membrane.

47

3.2

Experimental Setup

3.2.1 Measuring O2 Membrane Diffusivity

Figure 3.3 Schematic of the experimental system used to measure O2 mass transfer between the
gas phase in the shell and the aqueous phase circulating through the fiber lumen.
The experimental system is shown schematically in Figure 3.3. The membrane diffusivity
of O2 was originally measured in mixed cellulose ester fiber (X32M-601-02N, Spectrum Labs,
Inc., Rancho Dominguez, CA), and additional measurements were made in XM-50
(polyacrylonitrile-polyvinyl chloride copolymer) membrane (HF, 1018-1.0-45-XM50, Koch
Membrane Systems, Wilmington, MA). Purified water was recirculated through the hollow fiber
lumen and a small, well-mixed liquid reservoir that contained a dissolved O2 (DO) sensor. When
measuring O2 diffusivity in cellulose ester membrane, the reservoir volume was 16 mL. An

48

optical dissolved O2 sensor was kindly provided by Prof. Ruby Ghosh[71]. The N2 flow rate
through the reactor shell was 385 mL/min. The O2 diffusivity in the XM-50 membrane was
measured using a Sartorius® Bplus fermentation vessel as the liquid reservoir with a 1.5 L
volume and the fermentor’s built-in dissolved O2 sensor. Liquid flow was circulated using a
peristaltic pump with a Masterflex standard pump head (Cole-Parmer, Vernon Hills, IL). N2 gas
was continuously fed through the shell at a flow rate of 1 L/min to provide a driving force for O2
diffusion. It is essential in the setup to leave no headspace in the liquid reservoir, since otherwise
the liquid-gas mass transfer between the reservoir liquid and headspace would interfere with the
measurement.

3.2.2 Measuring CO2 Membrane Diffusivity

The process of CO2 dissolution in water is complicated by its coupling with dissociation
of carbonic acid. High levels of dissolved CO2 can lead to a drop in pH value, and, as a result,
the rate of dissolution can be limited by the rate of bicarbonate formation from dissolved CO2.
To avoid these complications, the system shown schematically in Figure 3.4 was used to
measure the CO2 diffusion coefficient in cellulose ester membranes (X32M-601-02N,
SpectrumLabs, Inc., Rancho Dominguez, CA). Reverse-osmosis purified water equilibrated with
air (21% O2, 79% N2) was pumped through the lumen without recirculation using a peristaltic
pump (Model 7523-00 with Quick-load® pump head model 7021-20) while a gas mixture with
an initial composition of 5% CO2, 21% O2 and balance N2 was recirculated though the shell at
105 mL/min. Changes in the CO2 concentration in the gas phase were then monitored as a
function of time using a gas-phase CO2 sensor (Series 9500, Alpha Omega Instruments, Lincoln,
RI).

49

Figure 3.4 Schematic of the experimental system used to measure CO2 mass transfer between
the gas phase in the shell and the aqueous phase circulating through the fiber lumen.

By keeping the liquid flow rate through the lumen relatively high, a very low liquidphase CO2 concentration was maintained, circumventing the complication with carbonic acid
formation at high CO2 concentrations. Since the liquid was in equilibrium with 21% O2, there
was no driving force for O2 mass transfer across the membrane. Also, since the Henry’s law
constant of N2 (1,639 L·atm/mol) is much greater than that of CO2 (29.4 L·atm/mol)[72], the flux
of N2 desorbed into the gas was much smaller than that of CO2 adsorption and could be
neglected. As CO2 dissolved into the liquid stream, the total amount of gas in the reservoir was
reduced. To avoid a reduction in pressure, the reservoir was connected to an air cylinder with a
water trap that releases air (21% O2 and 79% N2) into the chamber as the CO2 diffused across the
membrane.

50

3.2.3 Measuring IBT Membrane Diffusivity

Figure 3.5 System configuration for measuring IBT apparent diffusion coefficient across the
XM-50 membrane.

The IBT diffusion coefficient in the XM-50 hollow fiber membrane was measured using
the experimental system shown in Figure 3.5. The system consisted of a hollow fiber module
(HF, 1018-1.0-45-XM50, Koch Membrane Systems, Wilmington, MA) and a well mixed 200mL reservoir that contained an IBT aqueous solution. The IBT solution had an initial
concentration, C0, of 5 g/L (0.068 M), and was continuously recycled through the fiber lumen at
various flow rates using a peristaltic pump with Masterflex Easy-Load® pump head (ColeParmer, Vernon Hills, IL). Since the water flow through shell was not recycled, the IBT
51

concentration in the shell was assumed to be zero, so the driving force for IBT diffusion was
only a function of IBT concentration in the lumen side. Liquid samples were taken from the
reservoir regularly and analyzed using a Bruker® GC-450 gas chromatograph (Bruker
Corporation, Billerica, MA) outfitted with a Varian® CP7416 column and an flame ionization
detector.
The setups used for measuring membrane diffusivities of O2, CO2 and IBT are
summarized in Table 3.1.
Table 3.1 Summary of the experimental setups used to measure diffusion coefficients of O2, CO2
and IBT.
Solute
O2
CO2
IBT

3.3

Diffusion Direction
Lumen liquid  Shell gas
Shell gas  Lumen liquid
Lumen liquid  Shell liquid

Measured Concentration
Dissolved O2 in lumen liquid
CO2 composition in shell gas
IBT in lumen liquid

Data Analysis

3.3.1 O2
Even though the systems used to measure diffusion coefficients of O2, CO2 and IBT
varied from one another, their designs all aimed to obtain a negligible solute concentration on
one side of the membrane, thus making the diffusion driving force only the function of
concentrations on the other side. Therefore the data analysis for the three solutes was similar.
The method used for the O2 diffusion coefficient measurement is described below as an example.
Three approaches were used (described in Sections 3.3.1.1-3.3.1.3). In the analysis, all the
membrane diffusion coefficients were assumed isotropic.

52

3.3.1.1 Simplistic calculation
An unsteady-state mass balance on O2 in liquid phase was developed to calculate the
apparent diffusion coefficient across the membrane (Equation 3.2).
in the system;

is the total liquid volume

is the O2 concentration as measured in the reservoir;

diffusion flux at membrane inner surface;
membrane, and

|

is the

is the apparent O2 diffusion coefficient in the

is the membrane area.
|

|

3.2

In the first approach, denoted “simplistic” derivation, the mass balance was based on the
following assumptions: 1) the curvature in the membrane fiber wall was negligible (

|

); 2) the liquid in the entire system, including the reservoir liquid and the dead volume in
the tubing and reactor, had a constant volume and was well mixed, with negligible axial and
radial dissolved O2 concentration gradient (

).

Based on these assumptions, Equation 3.2 can be integrated to give Equation 3.3, whose
form suggests that the natural log of dissolved O2 concentration should follow a linear
relationship with respect to time with N2 flow in the shell side, and that the slope is a function of
the apparent diffusion coefficient of O2 across the membrane (

(

).

)

3.3
3.4

In Equation 3.3,

is the apparent diffusion coefficient of O2 between the lumen

liquid stream and gas phase in the shell side, Amembrane1 is the hollow fiber membrane area, Δr is
53

the thickness of hollow fiber membrane, and

is the total liquid volume in the system (lumen,

tubing, and reservoir).
3.3.1.2 Rigorous Calculation
While the above-mentioned assumptions greatly simplify the derivation, they are not
strictly valid. First, the curvature of the membrane wall may not be negligible for the geometries
used. The thickness of the XM-50 hollow fibers is 0.033 cm, and the ID is 0.11 cm; also, the
thickness of the cellulose ester hollow fiber is 0.015 cm, and the fiber ID is at 0.1 cm. Second,
even though a significant portion of the liquid in the system is well-mixed, the rest of the liquid
in the lumen space doesn’t have a uniform concentration. Third, at lower lumen flow rates, there
is likely to be a significant drop in O2 concentration between the inlet and outlet. Taking all of
these factors into account but ignoring radial O2 concentration gradients within the lumen,
Equation 3.5 (denoted the “rigorous” calculation) was derived, and the detailed derivation is
included in Appendix A.

(

(

)

where:
FL = Flow rate of liquid in the lumen [m3/min]
VR = Reservoir volume [m3]
L = Fiber length [m]
= O2 Membrane diffusion coefficient [m2/min]
N = Number of fibers
= Fiber inner radius [m]
54

)

3.5

= Fiber outer radius [m]
3.3.1.3 COMSOL Simulation
The membrane diffusivity experiments were simulated using COMSOL Multiphysics®.
COMSOL Multiphysics® is a powerful commercial software package capable of simulating
coupled physics phenomena, ranging from chemical reactions and diffusion to acoustics and
electromagnetics, in a 3-dimensional space. The software creates a mesh in the model space and
uses finite element method (FEM) to solve the models, with the error controlled using a variety
of numerical solvers.

Figure 3.6 Geometry of a single fiber in the hollow fiber reactor.

55

The axisymmetric model constructed in COMSOL included 3 domains: lumen,
membrane and shell (Figure 3.6). The phase in each domain was assigned according to the
specific experimental setup, and the dimensions of each domain were defined according to the
membrane module used. Since in the experiments the membranes were saturated with water, the
membrane domain was assumed to be an aqueous phase. The calculated Reynolds number of the
lumen flow ranged between 5 and 160, and therefore the lumen flow was assumed to be fully
developed laminar flow with a parabolic velocity profile. Since the cross section of the reactor
shell had a highly irregular shape, the shell flow was assumed to be turbulent and have a uniform
concentration. Mass balance equations were used to describe both diffusive and convective mass
transfer in lumen and shell (Equation 3.6), whereas convection was considered negligible in the
membrane domain (Equation 3.7). An ordinary differential equation (Equation 3.8) was used to
update the reservoir concentration based on the reservoir volume, flow rate and effluent
concentration. The natural log of the reservoir concentration was plotted against time, and the
membrane diffusion coefficient was varied in the simulation until the slope matched the
experimental result.
𝜕
𝜕

𝛻
𝜕
𝜕

𝛻
𝛻

𝑢 𝛻
𝛻

0
0

3.6
3.7
3.8

In Equation 3.6 and 3.7,
coefficient

is the concentration of a chemical species with diffusion

. The flow velocity in either lumen or shell is represented by 𝑢. In Equation 3.11,

is the reservoir volume,

is the concentration in the reservoir,

56

is the

average concentration at the lumen outlet for O2 and IBT, and shell outlet concentration for CO2.
is the lumen flow rate for O2 and IBT, and shell flow rate for CO2.
The concentrations of all chemical species at the lumen-membrane interface are assumed
to be continuous. Instantaneous gas-liquid equilibria are assumed for gaseous substrates and
volatile chemical species, such as IBT, at the membrane-shell interface.
A comparison of the assumptions made in the three types of calculations is summarized
in Table 3.2. The COMSOL model used the fewest simplifying assumptions and took into
account the mass transfer in lumen radial and axial directions. The COMSOL results therefore
represent only the membrane diffusion coefficient instead of the compounded “apparent”
diffusion coefficient, so the COMSOL predictions are considered the most accurate of the three
approaches.
Table 3.2 Comparison of the assumptions made in three different types of calculation.
Type of Calculation
Simplistic
(Equation 3.3)

Rigorous
(Equation 3.5)

COMSOL

1)
2)
3)
1)
2)
3)
4)
1)
2)
3)
4)

Assumptions
No membrane curvature
No concentration gradient in the radial and axial direction
All the liquid in the system is well mixed (no dead volume in
the reactor lumen)
Membrane curvature accounted
No concentration gradient in the radial direction
Concentration gradient in the axial direction in the space
originally containing solute
Dead volume in the reactor lumen
Membrane curvature accounted
Concentration gradient in lumen radial direction
Concentration gradient in the axial direction
Dead volume in the reactor lumen

3.3.2 CO2
A mathematical model analogous to that previously described for measuring O2 transfer
was applied to determine the apparent CO2 diffusion coefficient (D) across the spongy layer. The
57

equations derived from simplistic (Equation 3.9) and rigorous (Equation 3.11) calculations are
listed below. The derivation is also attached in appendix A. Since the CO2 content was measured
in partial pressure, the variables used in the derivation have been adapted accordingly.

3.9

3.10

(

(

)

)

3.11

The slope was determined using linear regression and then used to calculate the
corresponding

value. The process was repeated three times for each of four different liquid

flow rates.
3.3.3 Isobutanol
The experimental setup of IBT apparent diffusion coefficient measurement was very
similar to that used for O2 in that they both measure the solute diffusion from lumen to shell, and
therefore the equations derived from simplistic (Equation 3.12) and rigorous (Equation 3.14)
calculations were also similar:

3.12

3.13

(

(

)

58

)

3.14

3.4

Results
An example of the natural log of dissolved O2 (DO) versus time plot is shown in Figure

3.7. As expected, the plot is highly linear. The slope was determined using linear regression and
then used to calculate the corresponding

value using both simplistic (Equation 3.3) and

rigorous (Equation 3.5) derivations. The results obtained from 4 different liquid flow rates are
summarized in Table 3.3.

-ln(DO)

0
266700
-0.5
-1

-1.5

266800

266900

267000

y = 3.16E-03x - 8.44E+02
R² = 9.91E-01

-2
-2.5

Time (s)
Figure 3.7 Dissolved O2 versus time data used to determine the apparent diffusion coefficient for
oxygen through the spongy layer of the hollow fiber membrane.

Table 3.3 Apparent diffusion coefficients for O2 transport across the spongy layer of the hollow
fiber membrane.
(×10-10 m2/s)

(×10-10 m2/s)

Liquid Flow Rates
(mL/min)

(simplistic calculation)

(rigorous calculation)

15

8.93 ± 0.03

5.05 ± 0.02

47

11.50 ± 1.17

5.97 ± 0.64

72

13.99 ± 0.92

7.16 ± 0.35

95

14.29 ± 0.38

7.27 ± 0.20

Data collected from CO2 and IBT diffusion measurement experiments were processed
using corresponding equations, with calculated results summarized in Table 3.4 and Table 3.5.

59

Table 3.4 Apparent diffusion coefficients for CO2 transport across the spongy layer of the
hollow fiber membrane.
(×10-10 m2/s)

(×10-10 m2/s)

Liquid Flow Rates
(mL/min)

(simplistic calculation)

(rigorous calculation)

15

3.30 ± 0.07

2.90 ± 0.06

49

4.52 ± 0.08

3.98 ± 0.07

73

5.01 ± 0.32

4.42 ± 0.28

100

5.27 ± 0.39

4.65 ± 0.35

Table 3.5 Apparent diffusion coefficients for IBT transport across the spongy layer of the hollow
fiber membrane.
(×10-10 m2/s)

(×10-10 m2/s)

Liquid Flow Rates
(mL/min)

(simplistic calculation)

(rigorous calculation)

22

1.42 ± 0.40

0.91 ± 0.03

45

2.03 ± 0.25

1.20 ± 0.05

58

2.15 ± 0.14

1.34 ± 0.09

80

2.86 ± 0.19

1.78 ± 0.12

132

3.61 ± 0.44

2.24 ± 0.28

184

3.42 ± 0.04

2.11 ± 0.03

The results showed that the diffusion coefficient was affected by the liquid flow rate at
low flow rates, but the effect decreased at higher flow rates. In a classic liquid film model,[49] this
phenomenon is considered a result of the shrinking diffusion boundary layer in laminar flows as
the flow rate increases. As demonstrated in Figure 3.8, the apparent diffusion resistance across
the hollow fiber membrane

consists of resistance across the membrane (

across a diffusion boundary layer on the membrane ( ) (Equation 3.15), where
60

and

is the thickness

of membrane,
and

is the apparent diffusivity,

is the diffusivity in the membrane,

is the mass transfer coefficient, which is affected by the liquid velocity. At low liquid flow

rates, the mass transfer coefficient is small, and the diffusion boundary layer is rate limiting.
However, as the flow rate is raised, the diffusion boundary layer becomes thinner, causing mass
transfer coefficient

to increase and eventually ceasing to limit the overall rate of diffusion.

Figure 3.8 The apparent diffusion resistance across the hollow fiber membrane consists of
resistance of the membrane (
, is the thickness of membrane and
is the
diffusivity in the membrane) and a liquid film on the membrane inner surface (the reciprocal of
mass transfer coefficient ). The liquid film gets thinner as the liquid flow rate rises, and its
resistance to diffusion becomes insignificant at very high flow rates.

The impact of liquid flow rate on diffusion resistance across the diffusion boundary layer
can be described by an empirical correlation of Sherwood number (
(

for laminar flow in a pipe[49] (Equation 3.163.18), where
61

) and Reynolds number

is the membrane thickness;

is

the solute diffusivity in water;
length and

is the density of fluid;

is the diameter of fiber;

is the fiber

is the fluid velocity. Given this correlation and the measured diffusion coefficients

at various flow rates, the membrane diffusivity can be extracted by fitting experimental data to
Equation 3.15. The dashed lines in Figure 3.9-Figure 3.11 represent the simulation results, which
show a similar trend as found in experimental results. The membrane diffusivity of O2, CO2, and
IBT obtained are summarized in Table 3.6.
3.15
3.16
( )
3.17
3.18

Table 3.6 Summary of membrane diffusivities of O2, CO2 and IBT obtained from film theory
fitting using simplistic and rigorous calculation results, compared to their aqueous diffusivities.
Solute

(×10-10 m2/s)
(simplistic calculation)

(×10-10 m2/s)
(rigorous calculation)

O2

24.3

8.56

21.0[49]

CO2

5.60

4.77

19.2[49]

IBT

2.44

1.68

8.40[73]

62

(×10-10 m2/s)

Dapp (x10-10 m2/s)

16
12
8
4
0

0

40
80
Liquid flow rates (mL/min)

120

Apparent diffusivity-simplistic calculation
Best fit to simplistic calculation
Apparent diffusivity-rigorous calculation
Best fit to rigorous calculation
Membrane diffusivity - COMSOL fitting

Figure 3.9 Calculated apparent diffusion coefficients of O2 at different liquid flow rates with
simulated correlation between apparent diffusion coefficients and liquid flow rates.

63

7

Dapp(×10-10 m2/s)

6
5
4
3
2

1
0
0

40

80

120

Liquid flow rates (mL/min)
Apparent diffusivity -simplistic calculation
Best fit to simplistic calculation
Apparent diffusivity - rigorous calculation
Best fit to rigorous calculation
Membrane diffusivity COMSOL fitting
Figure 3.10 Calculated apparent diffusion coefficients of CO2 at different liquid flow rates with
simulated correlation between apparent diffusion coefficients and liquid flow rates.

64

5

Dapp ( ×10-10 m2/s)

4
3
2
1
0
0

50
100
150
Lumen flow rate (mL/min)

200

Apparent diffusivity - simplistic calculation
Best fit to simplistic calculation
Apparent diffusivity - rigorous calculation
Best fit to rigorous calculation
Membrane diffusivity - COMSOL fitting results

Figure 3.11 Calculated apparent diffusion coefficients of IBT at different liquid flow rates with
simulated correlation between apparent diffusion coefficients and liquid flow rates.

65

3.5

Discussion

3.5.1 Effect of Membrane Type
O2 diffusion coefficient measurements were carried out with both mixed cellulose ester
membrane and XM-50 hollow fiber membrane to verify whether the difference between the two
membrane types would result in significant variation in membrane diffusivity. As shown in
Table 3.7, the calculated membrane diffusivities are roughly 50% to 90% higher in XM-50
membrane than in mixed cellulose ester membrane. Part of the increase is due to a higher lumen
velocity used in the measurement.
Table 3.7 Comparison of
fiber membrane

measured in mixed cellulose ester membrane and XM-50 hollow

Membrane type
Mixed cellulose ester,
pore size 0.2µm
XM-50, MWCO 50 kDa

Lumen flow
velocity
(cm/s)

(simplistic)
(× 10-10 m2/s)

(rigorous)
(× 10-10 m2/s)

2.3

8.93

5.05

3.1

13.5

9.75

3.5.2 Effect of Simplifying Assumptions
The deviations between diffusion coefficient results from the three approaches can be
interpreted in terms of the underlying assumptions/simplifications. As summarized in Table 3.8,
simplifications were made on four variables: membrane curvature, axial gradient, lumen radial
gradient and dead volume.
3.5.2.1 Membrane Curvature
Neglecting membrane curvature could lead to either overestimated or underestimated
apparent diffusion coefficient, depending on the membrane surface area used in calculation. In a
66

curved membrane, at pseudo steady state, the concentration gradient would be highest at the
membrane inner surface, where the area normal to diffusion flux is at the smallest, as indicated in
Figure 3.12.
For O2 and IBT, the solute diffuses from the lumen to the shell, and the simplistic
calculations were carried out on the basis of membrane inner surface. While the simplistic
calculation neglected the membrane curvature and assumed a linear concentration profile within
the membrane, in actuality the profile is curved to achieve a constant total flux through the
thickness of membrane: as the solute diffuses outward, the area normal to the diffusive flux
increases, and correspondingly the concentration gradient decreases. Therefore, simply using the
concentration difference divided by the membrane thickness causes the concentration gradient at
the inner surface to be underestimated, and hence the diffusion coefficient overestimated. The
curvature would cause a similar effect with CO2, when the solute diffuses from shell side to
lumen, but to an opposite effect---the apparent diffusion coefficient is underestimated.

Figure 3.12 Effect of neglecting membrane curvature. For diffusion from lumen to shell (left), if
using inner membrane area as basis for calculation, the concentration gradient will be
underestimated, causing diffusion coefficients to be overestimated. The opposite occurs with
diffusion from shell side to lumen when using outer membrane area for calculation.
67

3.5.2.2 Axial Gradient and Dead Volume
In this analysis, dead volume refers to the volume outside of the reservoir. The effect of
neglecting axial gradient and dead volume is somewhat convoluted since when assuming no
dead volume (the entire system is well mixed) and including the entire system volume in the
calculation, axial gradient is implicitly omitted. Intuitively, including the dead volume will result
in a higher apparent diffusion coefficient than only considering reservoir volume.
On the other hand, neglecting the axial gradient means assuming that the liquid
concentration remains at the same level as in the liquid reservoir as the flow travels down the
reactor length. However the assumption deviates further because for lower flow rates the longer
residence time causes a significant drop in concentration along the reactor length. Still applying
the reservoir concentration unrealistically overestimates the concentration driving force across
the membrane and therefore the resulting diffusion coefficient is likely to be lower than the
actual value.
3.5.2.3 Lumen Radial Gradient
In laminar flow, a concentration gradient exists between the center of the lumen liquid
and inner surface of membrane due to the parabolic velocity profile. Neglecting this
concentration difference would cause a similar effect as omitting axial gradient—underestimated
diffusion coefficient.
The effects of the simplifications, as summarized in Table 3.8, can be used to explain the
deviations of simplistic and rigorous calculation results from COMSOL simulation results:
1) Since the rigorous calculation omitted lumen radial gradient, its results were smaller than
COMSOL simulation results. However, as the flow rate increases, the diffusion resistance
in the model liquid film decreases, thus reducing the error.
68

2) The simplistic calculation resulted in higher

in the case of IBT and O2, indicating

that the effects of curvature and dead volume combined were significant enough to
overwhelm that of axial gradient. However, as the flow rate increases, the effect of axial
gradient becomes weaker, and therefore the simplistic calculation results deviate further
from COMSOL results.
3) Since the effect of membrane curvature is reversed in the case of CO2 diffusion, the
simplistic calculation underestimated Dapp.
4) In O2 diffusion coefficient measurements, since the reservoir used is very small (16 mL),
the error caused by including dead volume (12 mL) in the calculation was large enough
that the calculated Dapp was higher than aqueous diffusivity.

Table 3.8 Effects of simplifying assumptions on apparent diffusion coefficients
Simplistic
calculation

Simplification

Effect on calculated

No membrane
curvature

O2 and IBT: overestimation
CO2: underestimation

√

No axial gradient

Underestimation

√

No dead volume

Possible overestimation

√

No lumen radial
gradient

Underestimation

√

Rigorous
calculation

COMSOL

√

3.5.2.4 Effect of Pressure Fluctuation
The COMSOL simulation accounts for the effect of lumen radial gradient and the results
should not be affected by the lumen flow rates. However, an effect is still observed in the case of
CO2 and IBT (Figure 3.10 and Figure 3.11, respectively), where the membrane diffusivity seems
to increase with liquid flow rates. On the contrary, such effect is not observed with O2
69

measurements (Figure 3.9). This effect is likely a result of convective flow as a result of pressure
fluctuations caused by peristaltic pumps. Pressure pulsation is known to enhance mass transfer in
membrane processes by way of enhancing dispersion and permeation.[74-77] The pressure
fluctuation caused by peristaltic pumps increased in frequency as higher flow rates are delivered
by the pump head thus causing an apparent increase in membrane diffusivity.
Larger diameter tubing (3/16’’ I.D.) was used in IBT and CO2 setups than for O2 setup
(1/16’’ ID). All of the tubing had the same wall thickness (1/16’’). Since the pressure
fluctuations caused by peristaltic pumps stem from the deformation of tubing, with the same wall
thickness, it is speculated that tubings with larger diameters would likely result in more
prominent pressure fluctuations.
In conclusion, the diffusion coefficients of O2, CO2 and IBT were measured in hollow
fiber membranes Experimental data were analyzed to obtain a value for the diffusivity using
three methods. The values obtained using COMSOL simulations are considered to be the most
accurate results, because the COMSOL simulations most accurately capture the effect of a
laminar flow velocity profile on the concentration driving force for mass transfer. Due to the
pressure fluctuation caused by peristaltic pumps, the diffusion coefficients obtained from
COMSOL simulations are likely higher than the actual membrane diffusivity.

70

4

SIMULATION OF ISOBUTANOL PRODUCTION IN A BIOREACTOR FOR
INCOMPATIBLE GASES (BIG)

4.1

Introduction
The BIG system described in Chapter 2 addresses the engineering challenges associated

with aerobic fermentations with sparingly soluble flammable gases, such as H2. The biocatalyst
was immobilized in the porous walls of the hollow fibers, with O2 and H2 provided from
opposite sides of the membrane wall. The BIG system is the first bioreactor that allows
independent, enhanced mass transfer of O2 and H2 without creating hazardous gas-phase
mixtures of an energy-rich gas and oxygen. This novel design de-risks fermentations with
incompatible gases and may lead to an economically viable electrofuel platform. The BIG
system could also be applied in methanotrophic fermentations.
During the BIG experiments, unexpected trends in IBT production levels were observed,
including an initial spike in IBT concentration that subsequently disappeared, very low IBT
production despite high cell densities, and little effect of increased substrate availability on
reactor performance.
To help explain these results, it was hypothesized that under H2-limiting conditions IBT
was consumed by the R. eutropha cells as a carbon and/or energy source. Several of the
experimental trends were consistent with this hypothesis. However, due to the novelty of the BIG
design, very little literature exists to discuss the interaction between the reaction kinetics and
mass transfer in a system configuration where substrates diffuse from opposite sides of the
reaction site, changes in mass-transfer across the hollow-fiber wall due to cell growth, and
product formation in one part of the reactor accompanied by consumption in another part. To
validate the hypothesis and better understand the effects of operating conditions on IBT
71

production and obtain insights for future scale up of the bioreactor, a comprehensive, dynamic
mathematical model was constructed to describe both mass transfer and cellular kinetics in BIG.
The resulting partial differential equations were solved using COMSOL® Multiphysics, and the
results were used to explore the system dynamics under various conditions. Results presented in
this chapter explored the effect of cell density and H2 and ammonium availability on IBT
production.
4.2

Materials and Methods

4.2.1 Model Setup
The model was constructed to describe the conditions of the immobilized cells
experiments with flow-through configuration on the shell side. A single hollow fiber within the
reactor was described in cylindrical coordinates with 3 domains: lumen, membrane and shell.
The hollow fiber membrane has an inner radius of 0.57 mm, an outer radius of 0.9 mm with a
length of 42.5 cm. The lumen flow rates ranged between 160 mL/min and 800 mL/min, which
correspond to a Reynolds number between 48 and 240. The laminar flow in the lumen was
described with a parabolic velocity profile. Since the cross section of the reactor shell had a
highly irregular shape, the high velocity shell gas flow (0.5 L/min) was assumed to be turbulent
and have a uniform concentration. With immobilized cells, convection was considered negligible
in the membrane domain. Equation 3.6 was used to describe the diffusive and convective mass
transfer in lumen and shell space, and Equation 3.7 was used to describe the diffusion and
biocatalytic reactions.
𝜕
𝜕

𝛻
𝜕
𝜕

𝛻
𝛻

𝑢 𝛻

0

4.1
4.2

𝛻

72

In Equations 3.6 and 3.7,
coefficient

is the concentration of a chemical species with diffusion

and membrane reaction rate

. The flow velocity in either lumen or shell is

represented by 𝑢. The concentrations of all chemical species at the lumen-membrane interface
are assumed to be continuous. Instantaneous gas-liquid equilibria are assumed for gaseous
substrates and volatile chemical species, such as IBT, at the membrane-shell interface.
In the experiments, the BIG system was operated with liquid circulating from a reservoir,
where the dissolved O2 (DO) level was monitored and regulated, and CO2 and O2 flow rates were
set at a fixed ratio. Therefore, it was assumed in the simulations that O2 and CO2 concentrations
at the hollow fiber lumen inlet were fixed at 100% saturation and 20% saturation, respectively.
In contrast, inlet IBT and ammonium concentrations were equal to their reservoir concentrations,
which were dependent on the outlet concentrations and the liquid flow rate. Ordinary differential
equations (Equation 3.8) were included in the model to update the IBT and ammonium reservoir
concentrations, where

is the reservoir volume,

is the concentration in the reservoir,

is the average concentration at the hollow fiber outlet, and

is the lumen flow rate.
4.3

The modeling equations were solved using COMSOL Multiphysics®, which uses finite
element methods to solve for the coupled differential equations that describe the spatial profiles
and transient behaviors of the eight variables, including concentrations of substrates, products
and cells in the 3 domains. The model was used to help interpret experimental results, identify
rate-limiting steps, and optimize system performance, and it may also be suitable to help design
and scale up practical BIG reactors for IBT production.

73

4.2.2 Mass Transfer Parameters in the Hollow Fiber Membrane
The membrane diffusivities of O2, CO2 and IBT were measured experimentally. The
system setups (Figure 4.1) were designed so that the driving force for diffusion only depends on
the reservoir concentration, and the natural log of the concentration changes linearly with respect
to time. The experimental procedures and data analysis are detailed in Chapter 3.
Due to the low Reynolds number of the lumen flow, the parabolic profile of the liquid
was taken into account in determining the diffusivities. Simulations were done using COMSOL
Multiphysics to fit the experimental results and obtain the membrane diffusivities

, as

summarized in Figure 4.1. Since the membrane diffusivities vary slightly with flow rate due to
pressure fluctuations caused by peristaltic pumps,[74-76] the average value was used as the
membrane diffusivity.
Table 4.1 Mass transfer parameters used in simulations.
Parameter

Value
(×10-10 m2/s)
21.0[49]
45.0[49]

Value
(×10-10 m2/s)
11.2
19.5

Parameter

19.2[49]

4.87

19.6[49]

6.70

8.40[73]

2.13

Parameter

Value
(mL/min)
160
500

The highest cell density reached at the peak in the simulation is 50 g/L. As reviewed by
Stewart,[70] the reported diffusivities of solutes, such as glucose, acetate and O2, ranged between
30% and 45% of the corresponding value in water in biofilms with cell densities around 50 g/L.
Therefore, for the other chemical species (H2 and ammonium), the membrane diffusivities were
conservatively assumed to be 35% of their aqueous diffusivities. Also, cell density is assumed to

74

have no effect on the membrane diffusivities of O2, CO2 and IBT. A list of mass transfer
parameters used in the model is summarized in Table 4.1.
(a)

(b)

(c)

Figure 4.1 Experimental setups and results for measuring the membrane diffusivities of: (a) O2,
(b) CO2, and (c) IBT
75

4.2.3 Estimation of Stoichiometry
Ralstonia eutropha is a facultatively autotrophic gram-negative bacterium that can use H2
as an energy source to reduce CO2 in the presence of O2.[29, 78] The first part of the autotrophic
pathway used by R. eutropha involves fixation of CO2 and production of glyceraldehyde-3phosphate (G3P) via the Calvin-Benson-Bassham (CBB) cycle. These reactions consume
reducing equivalents (electrons) in the form of NADPH and energy in the form of ATP.[79] The
subsequent reduction of G3P to IBT also consumes NADH, NADPH and ATP. To generate the
electrons and ATP, R. eutropha uses a soluble hydrogenase (SH) that oxidizes H2 while reducing
NAD+ to NADH.4 It also uses a membrane-bound hydrogenase (MBH) to remove electrons from
H2 and direct them into an electron transport chain, which pumps protons across a membrane
against a concentration gradient. The resulting “proton motive force” drives the protons back
across the membrane in a process that generates ATP. Finally, the protons are recombined with
the electrons and the terminal electron acceptor (O2) to make water.[80] R. eutropha also has a
transhydrogenase (TH) that converts NADH produced by the SH to NADPH, which is needed
for CO2 fixation via the CBB cycle.[81]
The stoichiometry for cell growth and IBT production can be estimated by combining the
following reactions: (a) reduction of CO2 to G3P using NADPH and ATP in the CBB cycle, (b)
MBH-catalyzed H2 oxidation and subsequent ATP production via the electron transport chain, (c)
conversion of G3P to PYR via enzymatic reactions found in glycolysis, (d) conversion of
NADPH to NADH, (e) conversion of PYR to IBT or cell mass, whose elemental composition
can be approximated as CH1.8O0.5N0.2,[82] and (f) SH-catalyzed reduction of NAD+ to NADH by
H2. The final stoichiometry is affected by YP/O, the number of ATP molecules generated in the
electron-transport chain by per molecule of O2 consumed, which could range between 0.5 and 4
76

depending on the experimental conditions.[79] Assuming a YP/O of 2.3, the reactions for cell
growth and IBT productions were estimated as follows:
4.4
0

4.5

The metabolic pathways for IBT consumption by the cells, either for anabolism
(formation of cell mass) or catabolism (energy generation) are still unclear, but using energy and
material balances, the stoichiometry for cell growth on IBT was estimated based on yield
coefficient obtained experimentally (Equation 4.6), and the stoichiometry for IBT catabolism
(Equation 4.7) was assumed to be the same as that of IBT aerobic combustion:
0

4.6
4.7

4.2.4 Structured Cellular Kinetic
There are two types of kinetic models for microbial biocatalysts: unstructured and
structured. Unstructured models assume that the cell mass is invariant in its properties, whereas
structured models account for time-dependent changes in cellular composition and reactivity. For
example, the commonly used unstructured Monod model[83] describes the effect of substrate
concentration on microbial growth rate, but it cannot describe bacterial cells’ adjustment to
changes in growth conditions,[84] such as lag phases or transition between heterotrophic and
autotrophic growth. Structured models are able to describe more complex cell behaviors by
dividing biomass into compartments[85] and/or incorporating physiological variables such as
intracellular concentration of RNA.[86] By recognizing the changes in physiological state of cells,
structured models are able to more accurately describe various behaviors in cell growth and
product formation. Because R. eutropha exhibits dramatic changes in its metabolism based on

77

changes in the nitrogen/carbon ratio, and because the immobilized cells are expected to exhibit
variations in metabolic activity due to substrate gradient in the biofilm, a structured model was
developed for growth and IBT production by R. eutropha in the bioreactor.
A number of structured kinetic models have been constructed for poly-β-hydroxybutyrate
(PHB) production in wild type strains of R. eutropha. PHB is a biodegradable polymer and can
accumulate up to 80% of cell dry weight.[87, 88] Given the high contents of product in cells, most
of the models segregate the product (P) from the rest of biomass, which is denoted “rest mass”
(R). However, the engineered IBT-producing strain differs from the PHB-producing wild type in
that, instead of remaining part of the cell, the product IBT is secreted out of the cell membrane.
However, IBT production is dependent on the cells’ viability, which is described by Hills and
Wright
(

[89]

by introducing the total biomass per cell (

and defining a minimum cell weight

) below which the cell is no longer considered viable. Since a typical bacterial culture

contains around 1012 cells·L-1·OD-1,[90] and a robust autotrophic culture of wild type R. eutropha
H16 contains 0.383 g DCW L-1·OD-1,

was assumed to be 0.3×10-12 g/cell. The “excess cell

mass” is the difference between the minimum cell weight (

) and total cell mass ( ) and

contains the enzymatic components responsible for product synthesis, indicating the cell’s
metabolic activity. Only when excess cell mass is present does the cell reproduce (increase in
cell number

) and synthesize the product. The structured model is described in Equations 4.8-

4.10, where

and

are specific growth rates on autotrophic substrates and IBT;

are specific cell division rates on autotrophic substrates and IBT, respectively; and

and
and

represents cell mass and cell number degradation constants, respectively.
4.8

78

4.9

4.10
4.2.5 Mixed Substrate Cell Kinetics
Bacterial consumption of mixed substrates could be either sequential (diauxic growth) or
simultaneous (mixotrophic). It was assumed that the cells utilize IBT and H2 as energy and
carbon sources simultaneously. Several models have been proposed for mixotrophic growth, and,
as reviewed by Kovárová-Kovar and Egli

[91]

most of them were modified from Monod-type

saturation kinetics. One of the models[92] defines the mixotrophic specific growth rate to be the
function of Monod parameters from single-substrate growth and the percentage of each substrate
in the mixture. This model yielded the best fit for E. coli growth on multiple substrates, and
therefore its form was adopted in the kinetic model to account for the mix substrate growth.
(

)(
(

)(

)(

)(

)

4.11
)

4.12

(

)(

)(

)

4.13

(

)(

)(

)

4.14
4.15

4.16
[

][

]

79

4.17

(

)(

)

4.18
(

)

(

)(

)

The kinetic model is described in Equation 4.11-4.18, where
cell number density, and is excess cell mass.
O2 and NH4+;

is cell mass density,

is

are concentrations of H2, CO2,

are the corresponding Monod constants;

concentration above which the strain no longer grows;

and

is the IBT
are the maximum

specific autotrophic growth rate and maximum specific growth rate on IBT respectively;
and

represent the maximum specific cell division rates using CO2 and IBT as the only

carbon source. The strain’s relative preference to use H2 as energy source is represented with α,
with =0 meaning the strain does not utilize H2 at all and α=1 meaning the strain only utilizes H2.
The immobilized cells grow both autotrophically on H2, CO2, and O2 and heterotrophically on
IBT in the presence of nitrogen source, such as NH4Cl. Since H2 is most likely the limiting
substrate in autotrophic growth (Table 2.1), the contributions of growth on autotrophic substrates
and IBT in mixotrophic metabolism are assumed to be determined by the local ratio of H2 and
IBT concentrations. Growth on H2 and IBT are both inhibited by IBT in a linear form (
). IBT is also catabolized by the cells in the presence of O2.

4.2.6 Estimation of Kinetic Parameters
Some of the kinetic parameters were estimated from experimental data. The maximum
specific growth rate of R. eutropha on autotrophic substrates was estimated to be 0.065 ± 0.017
h-1, and since the autotrophic growth rate was likely affected by substrate limitations,

80

is

assumed to be 0.11 h-1 in the simulations, which is a conservative estimation compared to the
literature value of 0.29 h-1.[93]
The specific growth rate of R. eutropha on IBT (

and the corresponding yield

coefficient were estimated based on data from IBT-consumption experiments (2.3.3). The
maximum specific growth rate on IBT was 0.033 h-1 with a yield of 2.13 g IBT/g DCW cell.
The highest IBT consumption measured was 62 mg IBT/ (g DCW cell·h). IBT is known to be
toxic towards R. eutropha cells, and concentrations above 1% v/v (0.12 mol/L) results in no cell
growth,[33] and therefore

is set to be 0.12 mol/L.

The specific IBT production rate was estimated to be 1.22 mg/ (g DCW h). If the
maximum specific growth rate was used as a reference point for the carbon flux capacity of the
engineered strain’s metabolic pathways, the maximum IBT specific growth rate
, with

being the yield coefficient from CO2 to cell mass, and

would be
being

the yield coefficient from CO2 to IBT. Based on the estimated stoichiometries in Equations 4.4
and 4.5,

=1.8, and

=2.4, and therefore

In the model, however, a more ambitious value for

=0.0825 g/(g DCW h).
(0.25 g/ (g DCW h) ) was assumed to

simulate a much improved biocatalyst and assess mass transfer limiting scenarios that would
provide valuable guidance in process optimization for the bioreactor system.
It was not feasible to obtain exact values of all the kinetic values based on the limited
experimental data obtained. Due to limited quantitative studies on autotrophic growth of R.
eutropha, very little can be found concerning the other kinetic parameters. Monod constant for
ammonium chloride was estimated to be 0.167 mol/L from a paper by Patwardhan and
Srivastava.[31] Monod constants for H2 and O2, were assumed to be 1×10-6 mol/L based on
Monod constants obtained by Siegel and Ollis.[93] Monod constant for CO2 was assumed to be

81

the same as that of H2 and O2. The maximum specific cell division rate on autotrophic substrates
and IBT,

and

, are assumed to be slightly lower than the corresponding

maximum specific growth rate, since cell division is likely to occur at a slower pace than cell
mass accumulation. Reasonable values were assumed for the rest of the kinetic parameters and
are considered sufficient to elucidate trends in the performance properties of the novel BIG
reactor. A list of kinetic parameters used in the model is summarized in Table 4.2.
Table 4.2 Kinetic parameters used in simulations.
Parameter

4.3

Value

Parameter

Value

Parameter

Value

0.11 h-1

0.033 h-1

1×10-6 mol/L[93]

0.033 h-1

1×10-14 h-1

1×10-6 mol/L[93]

0.1 h-1

1×10-6 mol/L[93]

0.03 h-1

0.25 g/ (g DCW
h)
0.062 h-1

0.5

0.12 mol/L

0.014 mol/L[31]

1×10-3 mol/L

Results and Discussion

4.3.1 Evolution of Cell Density and Reaction Profile
Unlike planktonic culture in a continuous stirred tank reactor, in which the cells are
uniformly distributed throughout the reactor, the immobilized cells within the BIG do not reach a
steady state over the time period of the simulations. Even though the simulations were initiated
with a uniform cell density, the profile soon developed a cell concentration peak that grows
higher and thinner, as depicted in Figure 4.3. The peak formation is a result of the counterdirectional diffusion of H2 and O2, as illustrated in Figure 4.4.

82

H2 and O2 diffuse from opposite sides of the membrane, with their concentration profiles
overlapping in a finite “reaction zone” within the membrane. Only immobilized cells within the
reaction zone are predicted to grow, while cells outside of the reaction zone become deprived of
either O2 (near the shell surface) or H2 (in the vicinity of lumen surface) and degrade. The higher
consumptions of both H2 and O2 in the reaction zone cause the concentration gradients to
become steeper, resulting in a narrower reaction zone. Without nitrogen limitation, the cell
density in the reaction zone continues to grow, and the active immobilized cell layer becomes
thinner and more concentrated without reaching a true steady state. However, the total cell mass
under the density peak reaches a plateau as the cell density that can be sustained by the
maximum H2 diffusive flux (Figure 4.2). If the simulation were extended indefinitely, a steady
state could be reached when the cell density at the peak reached the maximum density allowed in
the system. The maximum cell density could be defined as the largest number of cells the porous
structures of the membrane could hold. However, as an extremely high cell density would
significantly impacts the membrane porosity, the maximum cell density is likely to be restricted
by local membrane diffusivities of the substrates and product.

Figure 4.2 The trend for total immobilized cell mass in the BIG resembles the growth curve in a
chemostat-exponential growth at low cell density follow by a plateau when mass transfer
becomes limiting.
83

The position of the concentrated cell layer is affected by the relative availability of H2
and O2. As O2 concentration drops along the length of the fiber, the reaction zone shifts closer to
the lumen (Figure 4.3). R. eutropha are motile and have shown chemotactic activity towards
certain nutrients.[12, 94] Random motility would tend to combat sharp cell concentration gradients.
However, the pore structures in the hollow fiber walls are relatively rigid and are not likely to
allow significant movement. Therefore, the cells’ mobility was assumed negligible in the model,
and the local cell density is only affected by cell growth and degradation based on local substrate
and product concentrations.
In systems with immobilized cells where nutrients diffuse from a single direction, the
active cell layer tends to migrate towards the nutrients and, eventually, out of the support
material. In contrast, in this hollow fiber system, the active cell layer is well confined within the
membrane.

84

Figure 4.3 Evolution of cell density profile in the membrane at (a) inlet, (b) mid-point and (c)
outlet of the hollow fiber reactor.

85

Figure 4.4 The evolution of O2 and H2 profiles as well as IBT production, consumption and net
reaction rates at membrane inlet in the case with H2 membrane diffusivity at 1 10-9 m2/s.

86

Figure 4.4 shows the evolution of IBT production, consumption, and net reaction rates in
the cross section of the fiber inlet at a H2 membrane diffusivity of 1x10-9 m2/s. As the cell
density increases, the cells at the lumen surface become depleted of O2 and start to consume IBT
(6 h). As the peak in cell density profile develops, it also becomes the point of highest IBT
production. However, due to high H2 consumption, part of this dense cell layer does not receive
enough H2, and therefore a peak for IBT consumption forms next to the IBT production peak. As
a result, a positive IBT net production only occurs in radial positions closer to the H2 source,
while IBT consumption (i.e., negative IBT production) is observed at positions farther from the
H2 source. Beyond a certain cell mass, the total IBT consumption by the cells overwhelms the
total IBT production, and the IBT concentration decreases. This trend is consistent with our
experimental observation that beyond a certain cell density, net IBT production decreases. Thus,
the model provides support for the hypothesis that H2 depletion by the cells triggers IBT
consumption.
The general development of immobilized cell density distribution, H2 and O2 profile in
the membrane and IBT production and consumption rates can be applied to explain the
simulation results.
4.3.2 Predicted Effect of Experimental Conditions on IBT Production
4.3.2.1 Initial Cell Density
The model was used to explore the effect of initial cell density on BIG dynamics. The
simulated results (Figure 4.5) show an initial increase in IBT concentration as cell concentration
increases, followed by a relatively rapid drop in IBT concentration as cell density passes a
threshold level. For higher initial cell densities, the rise in IBT concentration to the maximum

87

value and the onset of the decline in IBT concentration both occur sooner, and the final IBT
concentration is lower.

Figure 4.5 IBT concentration versus time at different initial cell densities in a recirculation
mode.
As demonstrated in Section 4.3.1, the higher the initial cell density, the sooner H2 mass
transfer becomes rate-limiting and significant net IBT consumption shows effect. While the rate
of IBT production is limited by H2 mass transfer, the rate of IBT consumption is not. The higher
the cell concentration, the more rapidly IBT is consumed. Also, in the region where H2 becomes
depleted, IBT production slows, leaving more O2 available for IBT consumption. At the highest
initial cell density (3 g/L), the IBT concentration drops the earliest, before the IBT concentration
could reach above 0.012 g/L. These results suggest that with a high enough initial cell density,
88

no IBT net production would be observed, providing a reasonable explanation for the very low
to no IBT production observed during experiments with high immobilized cell concentrations.
4.3.2.2 Effect of Membrane Thickness
Since all the gas substrates are delivered to the immobilized cells via diffusion through
the membrane, membrane thickness would be expected to be an important process parameter.
Immobilized-cell biocatalysts exhibiting standard Monod kinetics exhibit an optimum biofilm
thickness. Biofilms thicker than the optimum are diffusion-limited and biofilms thinner than the
optimum could be kinetically limited. IBT consumption further complicates the calculations and
data interpretation. With a thicker membrane, more severe H2 limitation results in more IBT
consumption, thereby reducing net IBT production. These trends are evident in Figure 4.6, which
shows simulation results for five biofilm thicknesses. The thinnest biofilm simulated gave the
highest IBT concentration, although a much longer time was required for the cells to grow to a
high enough cell mass within the thin membrane to achieve maximum IBT concentration.

Figure 4.6 IBT concentration at various biofilm thicknesses.
89

Cell density and membrane thickness both affect the initial total cell mass in the
membrane, but they influence IBT production in different ways. Cell density affects the
consumption of substrate in a unit volume of the membrane and, as a result, the substrate
concentration gradients. Moreover, extreme cell densities would affect the membrane
diffusivities of all chemical species. On the other hand, as the overlap between O2 and H2 profile
becomes thinner, membrane thickness determines the distance the substrates have to diffuse
through to reach the active cell layer, which impacts the maximum diffusive flux.
4.3.2.3 Effect of Initial Ammonium Concentration
While the presence of a nitrogen source is essential to maintain cells’ metabolic viability
and ability to produce IBT, it also encourages cell growth, which diverts resources away from
IBT formation. Therefore, BIG’s productivity is highly sensitive to ammonium concentration in
the lumen liquid.
Figure 4.7 summarizes the simulation results at various initial ammonium concentrations
without IBT recovery. Two distinctly different trend lines are predicted. At the 2 highest initial
ammonium concentrations, 1 g/L and 5 g/L, the ammonium is not depleted in the 100 hour time
frame, allowing cell growth to exceed the threshold cell mass beyond which H2 depletion occurs
and rapid IBT consumption takes place. As a result, the IBT concentration peaks and decays
rapidly, as was reported above. On the other hand, for the two lowest ammonium concentrations,
0.01 and 0.1 g/L, the nitrogen source becomes depleted, and cell growth stops at 5.6 h and 12.8 h,
respectively. Afterwards the cell densities decrease slowly due to cell degradation, causing the
IBT levels to gradually drop. However, because the cell density never achieves levels at which
H2 becomes depleted throughout much of the biofilm, the rapid drop in IBT concentration
attributed to consumption does not occur. These results suggest that an intermediate cell density
90

would maximize IBT production when using strains that catabolize IBT, and that the IBT
productivity is very sensitive to the effect of ammonium concentration. This result suggests that
in situ control of ammonium level might be useful in optimizing the system’s IBT productivity.

Figure 4.7 IBT concentration at various initial ammonium concentrations.
4.3.2.4 Effect of H2 Pressure
Since H2 has the lowest solubility and the highest mass transfer demand among the three
gaseous substrates, it is intuitively most likely to be the rate-limiting reactant. Therefore,
simulations were carried out to study the extent to which IBT production can be improved when
higher H2 pressure is used in the shell space. Increasing H2 mass transfer was predicted to
increase the predicted IBT concentration (Figure 4.8). Examination of the H2 and O2 profiles at
91

inlet, midpoint and outlet revealed that as the H2 pressure increases, the higher H2 availability
cause the H2-O2 overlap region to be closer to the lumen surface, shrinking the H2 depletion
region and thereby reducing IBT consumption.
However, further increasing H2 pressure could result in excessive mass transfer, as
demonstrated in Figure 4.9. At 200 h and a shell pressure of 4 atm, the H2 flux into the
membrane exceeds the consumption by the cells, leading to a non-zero concentration at the
lumen surface. Even though and elevated H2 level in membrane wall helps curb IBT
consumption, it can also result in H2 diffusion into the liquid flowing through the lumen and
subsequent mixing of H2 and O2 in the liquid reservoir head space, raising safety concerns.

Figure 4.8 Average IBT outlet concentration at various H2 pressures.

92

Figure 4.9 H2 and O2 concentration profiles at the reactor inlet, midpoint and outlet at 200 h. At
the highest shell pressure, H2 becomes excessive at the outlet, resulting in H2 and O2 mixing in
the lumen liquid.
4.3.2.5 Effect of Lumen Flow Rates
In most of the BIG experiments, O2 was provided via the liquid flowing through the
lumen. Therefore, the lumen’s liquid flow rate affects the O2 availability to immobilized cells.
Simulations were conducted to explore the effect of lumen flow rate on BIG performance. The
simulation was initiated with a relatively low ammonium concentration (0.05 g/L). The resulted
trends in IBT concentrations in Figure 4.10 showed two distinct inflection points as described
below.
In the presence of ammonium (0 h-100 h), increased O2 availability allows O2 to
penetrate deeper into the immobilized cell layer, and therefore the reaction zone is positioned
closer to the shell with higher lumen flow rate (Figure 4.10c), resulting in a larger H2-depleted
zone. Therefore, even though at 50 h a higher O2 availability yields a higher cell mass, as
evidenced by the faster ammonium consumption shown in Figure 4.10a inset and the cell density

93

distribution in Figure 4.10c, it also encourages IBT consumption. Therefore, the final IBT
concentration is lower.
After ammonium depletion (at 100 h, 200 h and 250 h in each case), cell mass generation
was immediately halted, causing the carbon flux to be re-directed, creating a surge in IBT
production, which soon slowed down due to cell degradation in the absence of ammonium.
Eventually IBT consumption became dominant, and the IBT concentration dropped again.
IBT consumption not only competes with IBT production for O2, it also makes increasing
O2 availability an unsuitable strategy for increasing IBT yield unless H2 mass transfer limitation
is removed. The extent to which IBT consumption is exacerbated by added O2 is determined by
the relative magnitudes of the rate constant for IBT consumption compared to that of IBT
production. If IBT consumption occurred at a lower rate, increased O2 availability would
presumably have a significant positive impact on IBT productivity.

94

(a)

(b)

(c)

(d)

(e)

Figure 4.10 Effect of lumen flow rates: (a) reservoir IBT concentration, inset-reservoir NH4Cl
concentration; (b)-(e) cell density distribution at fiber outlet at 2.5h, 50h, 200h and 400h. into the
biofilm, where the cell density peak occurs.
95

(a)

(b)

Figure 4.11 (a) Reservoir IBT concentration with an initial NH4Cl concentration of 0.05g/L at
various H2 preferences. Inset: corresponding reservoir NH4Cl concentrations. (b) Outlet cell
density profiles at 200h.
96

4.3.2.6 Effect of Substrate Preference
In the kinetic model, the immobilized cells grow both autotrophically on H2, CO2 and O2
and heterotrophically on IBT and O2 in the presence of NH4+ ions. The effects of growth on
autotrophic substrates are described by the expression

, a function of the local

ratio of H2 and IBT concentrations and the strains preference for autotrophic substrates . An
Increased

value could be used to represent progress in strain improvement, such as elimination

of carbon sinks in the IBT utilization pathway or increased dehydrogenase activity. An

value

of 1 would indicate a “perfect” strain that does not consume the product IBT in the presence of
O2.
Figure 4.11a summarizes the effect of strain improvement on IBT production. With
α=0.25-0.99, the reservoir IBT concentration exhibited the hallmark trend of an initial increase
followed by a precipitous drop. Even though an increase in the strain’s bias towards H2 from 0.25
to 0.99 increases the IBT peak value from 0.016 g/L to 0.16 g/L, as the reaction zone narrows,
the bias towards autotrophic metabolism becomes irrelevant in the H2-depletion zone as IBT
becomes the only source of energy. Since growth on H2 is faster than that on IBT, the higher cell
density as a result of a stronger H2 preference also causes IBT to be consumed faster. At 100 h,
the highest H2 preference yields the lowest IBT concentration before the trend reverses due to
NH4+ depletion. The most drastic change comes when the cells’ ability to consume IBT is
entirely eliminated. The IBT concentration in the reservoir steadily increases until NH4+ is
depleted and the IBT concentration starts to decrease due to halted production compounded with
IBT loss to gas stream in the shell.
The outlet cell density distribution at 200 h (Figure 4.11b) reveals that the more the strain
prefers H2 as the substrate, the faster the cells grow (specific growth rate on autotrophic
97

substrates are higher than that on IBT), which results in a higher O2 consumption rate and
therefore the H2-O2 overlap area lays closer to the lumen. However, with IBT consumption
eliminated (preference to H2 =1), O2 uptake is lessened and the oxygen profile penetrates further
into the biofilm, where the cell density peak occurs (Figure 4.11b).
4.3.2.7 Effect of Product Removal
The model was also used to explore the strategy of reducing IBT consumption by
removing IBT as it is produced. As discussed in 4.3.2.5, without IBT recovery, a higher O2
availability leads to lower IBT concentrations. However, the IBT consumption is encouraged by
the presence of IBT in the lumen flow. As the IBT concentration data in Figure 4.10a are
converted into IBT production as shown in Figure 4.12a, a negative IBT reaction rate is observed
immediately after the initial surge in IBT concentration. The IBT consumption then slows down
as IBT concentration significantly decreases, and the IBT net production reaches a dynamic
equilibrium with IBT consumption, resulting in a near zero productivity throughout the
simulation even under nitrogen limitation (Figure 4.12b).
However, when the simulations are carried out with total IBT recovery, IBT production is
strongly encouraged, as can be seen in Figure 4.13a. Because IBT consumption is suppressed by
the removal of this product, higher O2 availability as provided by the higher lumen flow results
in a higher productivity, regardless of the nitrogen availability (Figure 4.13b).

98

(a)

(b)

Figure 4.12 (a) IBT production rate; (b) NH4Cl concentration under various flow rates without
IBT recovery.

99

(a)

(b)

Figure 4.13 (a) IBT production rate; (b) NH4Cl concentration under various flow rates with IBT
recovery.

100

4.4

Conclusions
The dynamic mathematical model of the BIG takes into account both structured cell

kinetics and diffusional mass transfer in a novel hollow fiber based BIG system. The model was
used to explore the BIG’s dynamics and reproduce non-intuitive experimental results, including
a decrease in IBT productivity as the cell concentration increased. The model provides strong
support for the hypothesis that IBT consumption is triggered by H2 limitation, causing the
reduction in IBT production. The model’s predictions also provide valuable insights that would
help fully realize the potential of this reactor design. For example, the following strategies should
be considered in designing future generations of the BIG:
(1) optimize membrane thickness and immobilized cell mass based on the highest H2
flux deliverable by the system;
(2) utilize more robust membrane materials that can endure higher H2 pressure required
for enhanced mass transfer;
(3) monitor ammonium level and employ online control;
(4) recover the product IBT in situ to minimize consumption;
(5) if H2 mass transfer limitation cannot be overcome and IBT cannot be removed from
the system in situ, operate the reactor under O2-limiting conditions.
The model could also provide guidance in setting boundaries for operating conditions (O2
flow rate, ammonium concentration, etc.) and design parameters (fiber length and membrane
thickness, etc.) for scale-up of the BIG system.

101

CONCLUSIONS
The rising availability of CH4 and solar-derived H2 makes these gases promising low-cost
gas feedstocks for bioconversion processes that are able to produce liquid transportation fuels
such as IBT. These energy-rich gases have low aqueous solubilities and their utilization by
microbes often requires O2 as electron acceptor, creating engineering challenges in both mass
transfer and process safety. This dissertation focused on developing the first bioreactor that is
able to facilitate such processes with enhanced mass transfer and maximized safety. The BIG
design concept simultaneously enhances mass transfer of two incompatible gases while
preventing formation of hazardous gas-phase mixtures of those gases. The use of hollow fiber
membranes to separate a continuous gas phase and a continuous liquid phase that contains
microbubbles enables independent control on the mass transfer of each gas by pressurization
and/or increased interfacial area.
A bench-scale prototype BIG system was constructed and integrated with an in situ IBT
recovery system and an Opto22 control network. Continuous autotrophic IBT production by
engineered Ralstonia eutropha was demonstrated for the first time in both immobilized and
planktonic cultures. The IBT productivity was found to increase with cell concentration to a peak
value of 325 mg/ (L·day). The productivity then decreased as cell concentration increased further,
consistent with the hypothesis that the cells consumed IBT under H2 limiting conditions.
A dynamic mathematical model was constructed to describe the interactions between
mass transfer and cellular kinetics. The model’s constants, including using mass transfer
coefficients and kinetic constants for a structured kinetic model, were evaluated obtained from
experimental results whenever possible. The model was solved using COMSOL Multiphysics®,
and the model predictions were used to interpret experimental results from the bench-scale BIG

102

system under various operating conditions. The simulation results reproduced a counter-intuitive
peak in IBT productivity as cell mass increased, providing further verification for our hypothesis
that H2 limitation triggered product consumption in the BIG. The simulation results allowed the
effect of system parameters on BIG performance to be elucidated and provided guidance on
process optimization strategies to minimize the effects of product consumption and product
inhibition. Strategies considered in the modeling studies included enhancing H2 mass transfer,
controlling ammonium concentration regulation, and implementing in situ IBT recovery. The
mathematical model could be used to aid in future BIG system design and scale-up efforts.
The BIG system developed in this study is the first continuous bioreactor system with the
potential to achieve high product yields from incompatible gaseous substrates without forming
potentially hazardous gas mixtures, and therefore offers promise in making electrofuels an
economically viable option.

103

APPENDIX

104

A. Derivation of Rigorous Calculation of Membrane Diffusion Coefficient
The appendix details the derivation of Equation 3.5, 3.8 and 3.14, which describe
the relationship between the solute concentration in the reservoir and time. The derivation
takes into account the membrane curvature, axial concentration gradient, and system dead
volume.
For all species, at a certain reactor length , the mass balance on a very thin ring
in the membrane at a given radius gives the following equation.

(

)

0

A.1

R2
R1

Figure A.1 Cross section of a hollow fiber with inner radius R1 and outer radius R2.

(

)

A.2

0

A.3
A.4

105

A.5

A.1 O2
Boundary Conditions

|
|

0

is the O2 concentration on the inner surface of membrane
Use the boundary conditions to solve for

and

in A.5

Hence at a given length,

A.6

Where

is O2 concentration at the inner membrane surface at the given fiber

length.

106

The next step is to describe

as a function of fiber length assuming no radial

concentration gradient in the lumen liquid.

𝜐𝐶𝑂𝑜 |

𝑧

𝜋𝑅

𝜐𝐶𝑂𝑜 |

𝑧

𝐽

𝜋𝑅

𝑧

𝜋𝑅

𝑧

Figure A.2 A thin slice of lumen space with thickness Δz.
At steady state, for a very thin slice of lumen space (thickness

0

|

|

)

A.7

|

A.8

Substitute A.8 into A.7 gives

0

|

|

A.9

107

Dividing both sides by

and let

0

A.10

Rearranging gives

A.11

Integrate

∫

∫

A.12

A.13

A.14

A.15

Since the lumen liquid is recycled from a reservoir, consider the reservoir

A.16

Rearranging A.15

108

(

)

A.17

Substitute A.17 into A.16 yields

(

(

)

)

A.18

Rearrange and integrate

(

∫

(

∫

(

(

)

(

)

(

)

A.19

)

)

)

A.20

A.21

Therefore there is a linear relationship between natural log of reservoir
(

concentration and time, and the slope is

(

A.2 Isobutanol
The derivation for isobutanol is the same as O2.

109

)

)

A.3 CO2
Assuming the outer surface concentration is always in equilibrium with the partial
pressure in the shell.

Boundary Conditions

|

0

|
is the CO2 concentration on the outer surface of membrane
Use the boundary conditions to solve for

and

in A.5

Hence at a given length,

A.22

Where

is CO2 concentration at the outer membrane surface at the given fiber

length.

110

The next step is to describe

as a function of fiber length assuming no radial

concentration gradient in the shell gas.

|

𝐶𝑂𝑜 |

𝑧

𝑧

𝐹𝐺

Figure A.3 A thin slice of the annular shell space with thickness Δz.
At steady state, for a very thin slice of shell space (thickness

0

|

|

)

A.23

|

A.24

The negative sign here means the flux direction is towards the center of cross
section area where radius is smaller.
Substitute A.24 into A.23 gives
111

0

|

|

Dividing both sides by

A.25

0

and let

A.26

Rearranging gives

A.27

Integrate

∫

A.28

A.29

A.30

Since the lumen liquid is recycled from a reservoir, consider the mass balance on
the reservoir liquid:

A.31

A.32

112

Rearranging A.15

(

)

A.33

Substitute A.33 into A.32 yields

(

)

A.34

Rearrange and integrate

(

)

A.35

∫

A.36
∫

(

(

)

(

)

)
A.37

113

Therefore, there is a linear relationship between natural log of reservoir
concentration and time, and the slope is

114

(

(

)

) .

REFERENCES

115

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