design of algal film photobioreactors for algal biomass ...€¦ · je tiens à remercier mon...
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Design of Algal Film Photobioreactors for Algal Biomass Production
by
Scott Nicholas Genin
A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy
Graduate Department of Chemical Engineering and Applied Chemistry University of Toronto
© Copyright by Scott Nicholas Genin 2016
ii
Design of Algal Film Photobioreactors for Algal Biomass
Production
Scott Nicholas Genin
Doctor of Philosophy
Department of Chemical Engineering and Applied Chemistry
University of Toronto
2016
Abstract
Microalgae has been identified as a potential feedstock for both biofuels and biochemicals but
dewatering algae limits the economic viability. By growing algae as a biofilm, the cost of
dewatering can be reduced. Current design of algal film photobioreactors is limited to algal turf
scrubbers and rotating algal biofilm systems. There is opportunity to explore new designs based
on growing algal biofilms on a light emitting waveguide.
The growth of algal films on transparent surfaces with polar surface energy ranging from 7-11.3
mJ/m2 was tested in a Parallel Plate Airlift Reactor. Overall algal biofilm productivity is
correlated to the colonization time of the biofilm, with algal films grown on cellulose acetate
having the highest productivity of 2.1 g/m2 day. When colonization time was accounted for, the
approximate 2 g/m2 day algal biofilm productivity was independent of material. Colonization
time was correlated to the polar surface energy and not the water-material contact angle. Lipid
content of algal biofilms ranged from 6-8 w%/w and were independent of the material it was
grown on.
To demonstrate the feasibility of growing algal biofilms on light emitting waveguides, five
different waveguide designs were fabricated and the light emission from all the surfaces was
iii
measured. Light intensity distribution on the waveguides could be adjusted by surface
modification. Algal biofilms grown on these waveguides had overall non-linear growth kinetics
and the highest surface area productivity was 2.9 g/m2 day. The productivity was dependent on
the light intensity (incident photon flux from 1600-12600 μmol/m2 sec) and CO2 concentration
(0.04-3% partial pressure), but saturation effects were observed. The interaction effects between
light intensity and CO2 concentration on algal biofilm productivity was non-linear.
A fundamental model was developed to describe light and inorganic carbon dependent algal
biofilm growth. Incident light direction, intensity, and inorganic carbon concertation was varied.
A complimentary model based on a partial differential equation was also developed which
describes light limited growth. Predicted growth kinetics were sigmoidal in shape and showed
agreement with experimental data. Effects such as light-dark cycles were not fully captured by
the model, which suggests there is room for improvement.
iv
Acknowledgments
I am grateful for the support of my supervisors Professors Allen and Aitchison and to the
committee consisting of Professors Saville and Sinton. Without their help this thesis would not
be possible. I would like to thank the Ontario government and NSERC for the scholarships and
our industry partners: MARA renewables, Biox Corp. and Pond Biofuels. Now that the important
points are out of the way and since few people read this section I have chosen to write it in other
languages. Please enjoy:
日本語：はじめまして。スッコトゲニンです。どおぞよろしく。僕は博士課程の学生。
ダグーラス先生、僕はあなたの私を与えると約束した犬をお待ちしております。ともだ
ちは、ありがとございます。ビンセントさんは すごいです。ビンセントさんと一緒に
ゲームであそぶ時間はたのしかったです。
Français: Je tiens à remercier mes parents et amis. Merci de touts vos bontés. Je tiens à remercier
mon frère pour moi logement et brassage de la bière avec moi. Remerciement spéciaux à mon
ami Jon pour aller à la gym tous les jours avec moi et Sam pour… étant présent. Un merci
spécial à Pedro pour être un bon ami et pour l’aide à la mathématque.
Deutsch: Ich danke meinen Eltern für ihre Freundlichkeit. Ich möchte Sofia und Peter für ihre
Unterstützung danken. Ich danke Steven für das Lesen das obigen Absatzes. Algenforschung ist
schwierig daher, fühle ich mich schlecht für Tim. Ich hoffe, dass er Erfolg mit dem Algen hat.
Dansk: Dette markerer afslutningen på en rejse og begyndelsen på en ny rejse. Det var
vanskeligt, men nu er det slut. Jeg lærte, at alger forskning er trist. Jeg håber, at ingen andre gør
de samme fejl, som jeg har gjort.
Omnem dimittite spem, o vos intrantes.
v
Table of Contents
Acknowledgments .......................................................................................................................... iv
Table of Contents ............................................................................................................................ v
List of Tables .................................................................................................................................. x
List of Figures ................................................................................................................................ xi
List of Abbreviations and Acronyms ........................................................................................... xvi
List of Appendices ........................................................................................................................ xx
Chapter 1 Introduction .................................................................................................................... 1
1.1 Statement of Research ......................................................................................................... 1
1.2 Hypothesis ........................................................................................................................... 3
1.3 Research Objectives ............................................................................................................ 4
1.4 Industrial Significance ........................................................................................................ 4
1.5 Overall Approach and Outline of Thesis ............................................................................ 5
1.6 List of Contributions ........................................................................................................... 7
Chapter 2 Literature Review ........................................................................................................... 9
2.1 Algal Fundamentals ............................................................................................................. 9
2.1.1 Algal Growth Factors ............................................................................................ 10
2.1.2 Products from Algae ............................................................................................. 12
2.2 Algal Biofilms ................................................................................................................... 16
2.3 Algal Biofilm Growth Factors .......................................................................................... 17
2.3.1 Nutrients and Light ............................................................................................... 18
2.3.2 Biotic Factors ........................................................................................................ 20
2.3.3 Material and Surface Effects ................................................................................. 21
vi
2.4 Photobioreactors ............................................................................................................... 24
2.4.1 Open Photobioreactors .......................................................................................... 24
2.4.2 Closed Photobioreactors ....................................................................................... 25
2.5 Algal Film Photobioreactors ............................................................................................. 27
2.6 Photobioreactor Economics .............................................................................................. 31
2.7 Light Transport ................................................................................................................. 32
2.7.1 Waveguide Optics ................................................................................................. 33
2.8 Summary of the Literature and Significance of the Objectives of the Thesis .................. 35
Chapter 3 Material and Surface Energy Effects on Algal Film Growth Kinetics, Colonization
and Lipid Content ..................................................................................................................... 36
3.1 Introduction and Significance ........................................................................................... 36
3.2 Materials and Methods ...................................................................................................... 37
3.2.1 Reactor Design and Setup ..................................................................................... 37
3.2.2 Sessile Drop Tests ................................................................................................. 40
3.2.3 Sampling and Analysis ......................................................................................... 40
3.3 Results and Discussion ..................................................................................................... 41
3.3.1 Algal Biofilm Growth Kinetics on Various Materials .......................................... 41
3.3.2 Algal Biofilm Productivity ................................................................................... 44
3.3.3 Colonization Time Analysis ................................................................................. 48
3.3.4 Lipid Analysis ....................................................................................................... 51
3.4 Conclusions ....................................................................................................................... 55
Chapter 4 Waveguide Reactor for Growing Algal Biofilms ........................................................ 56
4.1 Introduction and Significance ........................................................................................... 56
4.2 Experimental Methods ...................................................................................................... 58
4.2.1 Waveguide Design and Fabrication ...................................................................... 58
4.2.2 Light Intensity Measurements ............................................................................... 59
vii
4.2.3 Waveguide Reactor Setup and Operation ............................................................. 61
4.2.4 Sampling and Analysis ......................................................................................... 63
4.3 Results and Discussion ..................................................................................................... 64
4.3.1 Waveguide Light Emission ................................................................................... 64
4.3.2 Waveguide Reactor – Suspended Reactor ............................................................ 67
4.3.3 Growth Kinetics of Algal Biofilms on Light Emitting Waveguides .................... 68
4.3.4 Algal Biofilm Productivity on Light Emitting Waveguides ................................. 71
4.3.5 Substrate and Light Limitations ............................................................................ 75
4.3.6 Photon to Biomass Conversion ............................................................................. 77
4.3.7 Lipid Content ........................................................................................................ 78
4.3.8 Comparison of Algal Film Photobioreactors ........................................................ 79
4.4 Conclusions ....................................................................................................................... 80
Chapter 5 Modeling Light and CO2 Growth Kinetics Dependence in Algal Biofilms ................. 81
5.1 Introduction ....................................................................................................................... 81
5.2 Theory ............................................................................................................................... 83
5.2.1 Model Development .............................................................................................. 83
5.2.2 Model Solution ...................................................................................................... 86
5.2.3 Parameters ............................................................................................................. 87
5.2.4 Analytical Simplification of Model ...................................................................... 88
5.3 Results and Discussion ..................................................................................................... 89
5.3.1 Model Stability ...................................................................................................... 89
5.3.2 Analytical Model Analysis ................................................................................... 90
5.3.3 Comparison to Experimental Data ........................................................................ 96
5.3.4 Numerical Model: Growth Kinetics ...................................................................... 98
5.3.5 Numerical Model: Inorganic Carbon Profiles ..................................................... 102
5.3.6 Numerical Model: Productivity .......................................................................... 104
viii
5.3.7 Model Limitations ............................................................................................... 107
5.4 Conclusions ..................................................................................................................... 107
Chapter 6 Analytical Model of Substrate Profiles in Phototrophic Biofilms ............................. 109
6.1 Introduction ..................................................................................................................... 109
6.2 Model Description .......................................................................................................... 110
6.2.1 PDE Solution ...................................................................................................... 113
6.2.2 ODE Solution ...................................................................................................... 117
6.2.3 Parameters ........................................................................................................... 120
6.3 Discussion ....................................................................................................................... 120
6.3.1 Steady State Analysis .......................................................................................... 120
6.3.2 Transient Analysis .............................................................................................. 122
6.3.3 Model Limitations ............................................................................................... 124
6.4 Conclusions ..................................................................................................................... 125
Chapter 7 Overall Discussion ..................................................................................................... 126
7.1 Introduction ..................................................................................................................... 126
7.2 Design Considerations .................................................................................................... 127
7.2.1 Material Considerations ...................................................................................... 128
7.2.2 Waveguide Based Algal Film Photobioreactors ................................................. 129
7.2.3 Modeling Light Dependency of Algal Biofilms ................................................. 131
7.3 Modeling a Hypothetical Waveguide Reactor ................................................................ 132
7.3.1 Modeling the PPAL Waveguide Reactor ............................................................ 137
7.3.2 Productivity and Economics of an Idealized Packed Waveguide Reactor ......... 140
Chapter 8 Conclusions and Recommendations ........................................................................... 149
8.1 Conclusions ..................................................................................................................... 149
8.2 Recommendations ........................................................................................................... 151
8.3 Engineering and Industrial Significance ......................................................................... 152
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Chapter 9 References .............................................................................................................. 154
x
List of Tables
Table 2.1 – Lipid, protein and carbohydrate composition of several freshwater and marine
algae species (Fernandez-Reirza et al. 1989, Becker 2004)………………………………... 10
Table 2.2 - Comparison of energy products derived from algae………………………....... 15
Table 2.3 - Other non-fuel products from mircoalgae & cyanobacteria…………………… 16
Table 2.4 - Operational comparison of open and closed PBRs …………………………… 27
Table 3.1 – Fortified Bold’s Basal Medium……………………………………………….. 39
Table 4.1 – Waveguide specification………………………………………………………. 59
Table 4.2 – Suspended and attached estimation of productivities in the reactor at the
following conditions: 7200 μmol/m2 s, 1% partial pressure of CO2. (95% confidence
intervals shown)…………………………………………………………………………….. 75
Table 4.3 – Algal film photobioreactor productivity comparison……………………......... 79
Table 5.1 – List of parameters used in the model………………………………………….. 88
Table 5.2 – Fitted parameters to data presented in literature by Schnurr et al. (2014) (95%
confidence levels presented)………………………………………………………………... 97
Table 7.1 - Capital cost inputs for algal film waveguide reactor ………………………….. 146
xi
List of Figures
Figure 1.1 – Microalgal biorefinery concept……………………………………………… 2
Figure 1.2 – Hypothetic waveguide reactor for growing algal biofilms…………………… 3
Figure 1.3 – Flow chart of experimental work. Tasks with an asterisk next to them have
been compiled into contributions…………………………………………………………... 6
Figure 2.1 – Transesterification of a triglyceride (modified from Ma & Hanna, 1999)…… 13
Figure 2.2 – Diffusion of inorganic carbon and light profile within an algal biofilm with
boundary layer (Reprinted from: Liehr et al. 1990, Biotechnology and Bioengineering,
35(1), with permission from John Wiley and Sons)………………………………………... 18
Figure 2.3 – Re-growth of a biofilm compared to suspended and initial growth (Reprinted
from: Christenson 2012, Biotechnology and Bioengineering, 109(7), with permission
from John Wiley and Sons)…………………………………………………........................ 23
Figure 2.4 - Photobioreactors used in growing algae: (a) raceway pond, (b) flat-plate, (c)
inclined tubular and (d) horizontal tubular (Reprinted from: Bitog et al. 2011. Application
of computational fluid dynamics for modeling and designing photobioreactors for
microalgae: A review, Computers and Electronics in Agriculture, 76(2):131-147 with
permission from Elsevier)………………………………………………………………….. 24
Figure 2.5 – Schematic of an ATS used for the treatment of dairy manure effluent
(Modified from Mulbry et al. 2008. Bioresource Technology, permission obtained from:
Elsevier)…………………………………………………………………………………...... 28
Figure 2.6 – A modified raceway pond consisting of triangle and vertical patterned RAB
systems (Modified from: Gross and Wen 2014. Bioresource Technology, permission
obtained from Elsevier)…………………………………………………………………….. 29
Figure 3.1 – PPAL reactor configuration and setup……………………………………….. 38
Figure 3.2 – Growth kinetics of algal biofilms grown on various materials………………. 43
Figure 3.3 – Overall algal biofilm productivity. Error bars show standard deviation.
(Calculated from a linear regression from 45 data points collected during 3 runs)………... 45
Figure 3.4 – Revised algal biofilm productivity. Error bars show standard deviation.
(Calculated from a linear regression from 30 data points collected during 3 runs)……....... 46
xii
Figure 3.5 – Algal biofilm productivity on the four types of embossed acrylic. Error bars
show standard deviation (n = 5)……………………………………………………............. 48
Figures 3.6 - Colonization time vs. water-material contact angle and material polar
surface energy (n = 3)………………………………………………………………………. 49
Figure 3.7 – Overall productivity in relation to the calculated colonization time………..... 51
Figure 3.8 – Lipid content of algal biofilms grown on different materials. Error bars show
standard deviation. (6 samples were taken for 3 replicate experiments, n = 18)………….. 52
Figure 3.9 – Lipid productivity of algal biofilms grown on different Materials. Error bars
show standard deviation (6 samples were taken from 3 replicate experiments, n = 18)........ 53
Figure 4.1 – Waveguide schematics for a) single wedge large notch, b) single wedge, c)
double wedge, d) single wedge small notch, e) double wedge small notch (Side view)….. 59
Figure 4.2 – Waveguide light emission experimental setup a) schematic representation, b)
electrical circuit diagram of photodiode, c) electrical circuit diagram of power circuit…… 60
Figure 4.3 – Waveguide reactor schematic………………………………………………… 61
Figure 4.4 a-e - Light emission profiles of the waveguides, a) – single wedge large notch,
b) single wedge, c) double wedge, d) single wedge small notch, e) double wedge small
notch………………………………………………………………………………............... 66
Figure 4.5 – Average TSS for the reactor runs using single wedge large notched
waveguides with varying light intensity and CO2 partial pressure…………………………. 67
Figure 4.6 – Nitrogen and phosphorous concentrations for the inlet and outlet of the
waveguide reactor (Light: 7200 μmol/m2 sec, CO2: 1%) (Standard deviations shown)…… 68
Figure 4.7 – Algal growth kinetics on the large notch waveguides: a) Growth kinetics on
the various faces of the waveguide at 1% CO2 and 7200 μmol/m2 sec, b) Growth kinetics
on the front with CO2 = 1%, c) Growth kinetics on the front with CO2 = ATM, d) Growth
kinetics on the front with CO2 = 3%. Error bars show standard deviation........................... 69
Figure 4.8 – Algal biofilm growth kinetics on a) single wedge waveguides b) double
wedge waveguides, c) single wedge small notches and d) double wedge small notches
(7200 μmol/m2 sec, CO2 = 1%). Error bars show standard deviation……...………………. 70
xiii
Figure 4.9 – a) Algal biofilm productivity on the front of the single wedge large notch
waveguide at different conditions b) Algal Biofilm productivity per single wedge large
notch waveguide at different conditions (95% confidence intervals shown)………………. 72
Figure 4.10 - Algal Biofilm productivity on single wedge, double wedge, single wedge
small notch and double wedge small notch, on each side and including regrowth (CO2 =
1%, 7200 μmol/m2 sec)…………………………………………………………………….. 73
Figure 4.11 – Biomass photon conversion ratios from algal biofilms grown on the single
wedge large notch waveguide. Error bars show the 95% confidence intervals calculated
from a linear regression (n = 18)…………………………………………………………… 78
Figure 5.1 – Schematic of the model showing light and inorganic carbon profiles……….. 83
Figure 5.2 – Predicted algal film biomass (left vertical axis) and growth rate (right
vertical axis) using the analytical model with varying light intensities…………………..... 91
Figure 5.3 – Predicted algal film biomass (left vertical axis) and growth rate (right
vertical axis) with constant light intensity and light intensity which varies linearly with
time………………………………………………………………………………………..... 92
Figure 5.4 – Predicted algal biofilm growth kinetics with varying a) extinction
coefficient, b) Monod maximum constant and c) the estimated productivity with varying
both parameters. Io = 100 μmol/m2 sec and other parameters are as is in Table 5.1……….. 94
Figure 5.5 – Algal biofilm growth kinetics with a light-dark cycle of 12h:12h compared
to algal biofilm growth under constant illumination with a maximum light intensity of 100
μmol/m2 sec a) over a period of 150 days, b) over a period of 22 days……………………. 95
Figure 5.6 – Comparison between experimental data (Schnurr et al. 2014) and model
predictions for inorganic carbon saturated biofilms (zero order kinetics) for the following
conditions: a) & b) light incident from the water side, c) & d) light incident from the
material side…………………………………………………………………….................... 97
Figure 5.7 – Predicted growth kinetics of algal biofilms at various carbon dioxide partial
pressures and different incident light directions: a) water side, b) material side, and c)
both sides…………………………………………………………………………................ 99
Figure 5.8 – Growth kinetics of algal biofilms at different light intensities and directions
a): ATM-Water side, b): 2% CO2 –Water Side, c): ATM-Material Side, d): 2% CO2-
Material Side, e): ATM-Both Sides, f): 2% CO2-Both Sides………………………………. 101
xiv
Figure 5.9 – Inorganic carbon profiles in algal biofilms with Io = 100 μmol/m2 sec a) light
from the water side, CO2: 2%, b) light from the water side, CO2: ATM, c) light from
material side, CO2: 2%, d) light from the material side, CO2: ATM, e) light from both
sides, CO2: 2%, and f) light from both sides, CO2: ATM…………………………………..
103
Figure 5.10 – Predicted algal biofilm productivities with varying light intensity and CO2
partial pressure with different incident light directions: a) water side, b) material side c)
both sides…………………………………………………………………………………… 105
Figure 6.1 – Schematic for diffusion of a substrate S in a biofilm with boundary layer
with two scenarios: a) light originating from the material of attachment, and b) light
originating from the water side……………………………………………………………... 110
Figure 6.2 – Steady state solution for inorganic carbon profiles in algal biofilms for the
numerical solutions and analytical solution for 600 μm biofilms under the following
condition’s: a) light incident from material side, μmax = 1.2 1/day, Cb = 0.045 mgC/cm3, b)
light incident from material side, μmax = 2.1 1/day, Cb = 0.05 mgC/cm3, c) light incident
from water side, μmax = 1.2 1/day, Cb = 0.045 mgC/cm3, a) light incident from water side,
μmax = 2.1 1/day, Cb = 0.05 mgC/cm3………………………………………………………. 121
Figure 6.3 – Transient solution for inorganic carbon profiles at different times
(parameters from Table 5.1) with an initial concentration of 0.015 mgC/cm3 and a bulk
concentration of 0.045 mgC/cm3 with varying mass transfer biot number and incident
light direction: a) material side, Bim = 1.78, b) water side, Bim = 1.78, c) material side,
Bim = 0.37, d) water side, Bim = 0.37, e) material side, Bim = 5.26, f) water side, Bim =
5.26………………………………………………………………………………………..... 123
Figure 7.1 – Waveguide reactor schematics for a) a plug flow reactor and b) packed
waveguide reactor…………………………………………………………………………... 127
Figure 7.2 – Cross section diagram of light being refracting within a) waveguide as
fabricated and b) waveguide with a polycarbonate layer…………………………………... 130
Figure 7.3 – a) 2D Schematic of waveguide reactor and b) 2D schematic of algal
biofilm……………………………………………………………………………………… 135
Figure 7.4 – 3D Schematic for waveguide reactor………………………………………… 135
Figure 7.5 – Schematic representation of an a packed waveguide reactor with two designs
for supplying light a) LEDs and b) a solar collector……………………………………….. 141
Figure 7.6 – Schematic representation of an ideal packed waveguide reactor for the
productivity and cost model………………………………………………………………... 142
xv
Figure 7.7 – Model predictions for photobioreactor land productivity with respect to the
cross sectional area of a single waveguide with varying the photons into each waveguide
and variable spacing between waveguides a) 0.004 m, b) 0.01 m, c) 0.05 m and d) 0.002
m. Defined Variables: Photonflux out: 150 μmol/m2
sec.…………………………………..
144
Figure 7.8 – Bioreactor capital cost estimates for different waveguide cross sectional
areas (single waveguide) and different reactor configurations to produce 1 kg of dried
algal biomass per day……………………………………………………………………..... 147
xvi
List of Abbreviations and Acronyms
ADH Aldehyde Dehydrogenase
ATM Atmospheric
ATS Algal Turf Scrubber
BS Both Sides
C6H12O6 Glucose
CO2 Carbon Dioxide
CO32-
Carbonate ion
CSTR Continuously Stirred Tank Reactor
EPS Extra-cellular Polymeric Substance
FAME Fatty Acid Methyl Ester
H2CO3 Carbonic Acid
HCO3-
Bicarbonate ion
NO3- Nitrate ion
MS Material Side
O2 Oxygen
ODE Ordinary Differential Equation
PBR Photobioreactor
PDC Pyruvate Decarboxylase
PDE Partial Differential Equation
PFR Plug Flow Reactor
PO43-
Phosphate
PPAL Parallel Plate Air Lift
RAB Rotating Algal Biofilm
xvii
STP Standard Temperature and Pressure
WS Water Side
xviii
List of Variables
β Eigenvalue Unitless
γ Light Attenuation 1/cm
Γ- Base Component of Surface Energy J/m
2
Γ+
Acid Component of Surface Energy J/m2
ΓLW
Lifshitz-van der Waals Component of the Surface Energy J/m2
Γpolar
Polar Surface Energy J/m2
Γs Total Surface Energy J/m2
θ Liquid-Material Contact Angle Degrees
θc Critical Angle for Total Internal Reflection Degrees
λ Wavelength of Light nm
μmax Monod Max Constant 1/day
ρ Density g/cm3
b Respiration Coefficient 1/day
Bim Mass Transfer Biot Number Unitless
C Total Inorganic Carbon mgC/cm3
D Diffusion cm3/cm day
dp Characteristic Length cm
F Flow rate g/day
Fl Steele Relationship Unitless
h Mass Transport Coefficient cm/day
Io Initial Light Intensity μmol/m2 sec
xix
Is Light Saturation μmol/m2 sec
Ki Inhibition Constant mgS/cm3
Ks Monod Carbon Saturation Constant mgC/cm3
L Length of Fibre Optic m
Lf Biofilm Thickness cm
M Biofilm Mass per Area g/m2
ni Refractive Index of a Medium i Unitless
Pi Optical Input Power W
Po Optical Output Power W
Q Yield Coefficient mgBiomass/mgC
Re Reynolds Number Untiless
S Substrate Concentration of S mgS/cm3
Sc Schmidt Number Unitless
Sh Sherwood Number Unitless
x, y, z Spatial Variables cm
xf Substrate Concentration in Film Biomass mgS/cm3
xs Substrate Concentration in Suspended Biomass mgS/cm3
Y Respiration Yield Coefficient mgCbiomass/mgC
xx
List of Appendices
Appendix A – Original Waveguide Schematics……………………………………….. 169
Appendix B – Parallel Plate Air Lift Reactor Physical Properties and Calculations….. 171
Appendix C – Numerical Shooting Method and Matlab Code®……………………… 176
Appendix D – Light Calibration Curves………………………………………………. 193
Appendix E – Environmental Scanning Electron Microscopy Images………………... 197
Appendix F – Sessile Drop Test Data…………………………………………………. 199
1
Chapter 1 Introduction
1.1 Statement of Research
There is an increasing research effort to understand and develop alternative fuels and
technologies capable of reducing the human ecological foot print. Algae are a promising solution
since they can be a feedstock for the production of biodiesel and can be used as a carbon
capturing technology. Algae has significant advantages over terrestrial crops since they grow
significantly faster, consume less land, and do not compete with the global food supply. Algae
can also be used in the treatment of wastewater. Wastewater streams from municipal and
industrial sources are rich in nutrients (i.e., nitrogen and phosphrous) which, when released
untreated into the environment often cause eutrophication of the water system (Anderson et al.
2002). It is possible to use algae to remove these nutrients during the water treatment processes
and harvest the algae to produce value added products such as nutraceuticals, livestock feed,
proteins, lipids, and pigments (Barowitzka 1992, Lam and Lee 2012). A biorefinery capable of
utilizing waste streams to produce algal biomass and then processed the biomass into value
added products (Figure 1.1) could help improve the economic feasibility of algal biomass
production.
One of the major challenges that algae production faces is the high cost of de-watering the algae,
which is estimated to be 20-30% of the total biomass production costs (Gudin and Therpenier
1986, Uduman et al. 2010). To improve the economic viability of algae as a feedstock for
biofuels, there is a need to reduce the biomass production and harvesting costs. Algae grown as a
biofilm presents an opportunity to reduce dewatering costs since the biomass is more
concentrated (90-150 g/L) (Christenson and Sims 2012; Ozkan et al. 2012; Gross et al. 2013)
compared to suspended algae produced in raceway ponds (0.5-1 g/L) or photobioreactors (1-4
g/L) (Chisti 2007). Algal biofilms are a mixed community of many different algae and bacteria
species within a matrix of extracellular polymeric substances (EPS) (Hodoki 2005; Lawrence et
al., 1998). EPS is a matrix of polysaccharides, proteins, glycoproteins, glycolipids, and
2
extracellular DNA produced by the microorganisms that are imbedded in the biofilm (Flemming
et al. 2007).
Figure 1.1 – Microalgal biorefinery concept
Recent publications by various groups have demonstrated the scalability of algal turf scrubbers
(ATS) and rotating algal biofilm (RAB) systems for either the production of algal biomass or for
treatment of municipal wastewater (Christenson and Sims 2012, Ozkan et al. 2013, Gross and
Wen 2014). These systems have demonstrated high aerial productivities ranging from 15-31
g/m2 day of dry algal biomass, but have a number of design limitations. The designs require light
to be provided by an external source that is not directly integrated into the attachment material,
thereby limiting possible design configurations.
Using an external source of light has disadvantages such as: (1) opaque media can block light
transmission to the algal film and the separation of the attachment material and (2) light source
can result in a bulky reactor design. A possible solution would be to grow algae on a light
emitting waveguide. Light emitting waveguides are devices that distribute the light from a high
3
intensity source over a large surface area. An algal film photobioreactor that uses waveguides for
growing algal biofilms could be more compact and have better light transmission/efficiency
(Figure 1.2). The goal of this research is to demonstrate and evaluate the technical feasibility of
growing algal biofilms on light emitting waveguides.
Figure 1.2 – Hypothetical waveguide reactor for growing algal biofilms
1.2 Hypothesis
The specific hypotheses of this project are: (1) algal biofilms can grow on light emitting
waveguides; (2) material properties of the surface effect algal biofilm productivity in of
vertically oriented films; (3) increasing the light intensity emitted from the waveguide will
improve algal biofilm growth, and (4) there is an interaction between CO2 concentration and
light intensity on algal biofilm growth.
4
1.3 Research Objectives
The overall objective of this research is to explore the feasibility of growing algal biofilms on
light emitting waveguides. This will help determine if waveguide based photobioreactors are a
viable design for growing algal biofilms. In this, light can be delivered to the algal biofilms
without obstruction from suspended algae and other light absorbing substances and could
produce more compact reactors. To achieve this goal, the following objectives were formulated:
1. Determine the feasibility of growing algal biofilms on waveguides
2. Determine material surface property effects on algal biofilm growth
3. Determine how the processing parameters light intensity and carbon dioxide (CO2)
concentration will influence algal biofilm production
4. Develop a model to describe how light intensity and CO2 affect growth kinetics of algal
biofilms
5. Develop a reactor model to describe how the following reactor design parameters will
impact algal biofilm production: surface area, light intensity, waveguide packing density,
and configuration
1.4 Industrial Significance
The commercialization of algae for energy production or waste treatment is not widespread as
there are numerous challenges that prevent algae photobioreactors from becoming economically
viable (Chisti and Yan 2011, Pate et al. 2011). Areas identified as problematic for the
commercialization of algae are: high dewatering costs, availability of concentrated CO2 sources
and high capital cost of photobioreactors (Pate el al. 2011). Growing algae as an algal biofilm
can reduce dewatering costs, but further understanding of how the main photobioreactor design
factors affect algal biofilm growth are required to further advance the design concepts of algal
film photobioreactors.
5
A common problem with industrial wastewater is the colour, which, depending on the source,
can be opaque. Opacity prevents light from being transmitted to the algae for photosynthesis.
Biofouling, the formation of undesired algal biofilms in suspended photobioreactors also reduces
the light transmission efficiency. By growing algal biofilms on light emitting waveguides, the
light can be directly delivered to the algal biofilm without issues of opacity from the media. An
algal film photobioreactor that does this has never been developed and the idea never been fully
investigated.
1.5 Overall Approach and Outline of Thesis
The overall approach to address the objectives is outlined in Figure 1.3. The main objective for
this thesis is to determine the feasibility of growing an algal biofilm on a light emitting
waveguide. In order to achieve this, the feasibility of growing an algal biofilm on transparent
materials was first addressed (Chapter 3) followed by fabricating and characterizing waveguides
(Chapter 4). Once a suitable waveguide design was identified, multiple copies were fabricated
and algal biofilm growth on these waveguides was tested in a waveguide reactor. The interaction
effects of light intensity and CO2 were investigated as well (Chapter 4). During the
experimentation, a fundamental model was developed to describe algal biofilm growth with
respect to CO2 concentration and light intensity (Chapter 5). The development of a reactor model
was conducted after the fundamental algal biofilm growth model and reactor results were
finished (Chapter 7).
6
Figure 1.3 – Flow chart of experimental work. Tasks with an asterisk next to them have
been compiled into contributions
This thesis is comprised of nine chapters and four appendices, of which Chapters 3 and 4 are
based on publications. Chapter 1 provides the objectives of this thesis and their motivation.
Chapter 2 consists of a literature review, containing background on previous research on algal
biofilms, photobioreactors, and optics. Chapter 3 covers the effects of material surface energy
and embossing on algal film growth, productivity and lipid content. Chapter 4 covers the design,
and testing of the waveguide reactor, and the interaction effect of light intensity and carbon
dioxide concentration have on algal film productivity. Chapter 5 formulates a fundamental model
to describe algal biofilm growth and discusses the model predictions and simplifications. Chapter
7
6 covers a complimentary model that predicts the inorganic carbon concentration profiles within
an algal biofilm based on an analytical model. Chapter 7 discusses a proposed reactor model,
which is then used to assist in analyzing the economic and scale-up feasibility of a waveguide
reactor as outlined in Chapter 4, and contains a discussion of the overall results and how they can
be applied in industrial applications. Chapter 8 includes conclusions and recommendations for
future scientific, engineering and commercialization to fully develop the waveguide reactor.
Chapter 9 contains the references used in this thesis. The appendices include the following:
characterization of the LEDs used in Chapter 4, the properties of the PPAL reactor and CO2
solubility graphs, the MATLAB® code used to solve the model as described in Chapter 5, and
detailed drawings of the waveguides.
1.6 List of Contributions
Referred Journal Publications:
Suthamathy Sathananthan, Scott N. Genin, J. Stewart Aitchison, D. Grant Allen, Micro-
structured surfaces for algal biofilm growth. Proc. SPIE 8923, Micro/Nano Materials, Devices,
and Systems, 892350 (December 7, 2013); doi:10.1117/12.2033794.
Scott N. Genin, J. Stewart Aitchison, D. Grant Allen, Design of algal film photobioreactors:
Material surface energy effects on algal film productivity, colonization and lipid content,
Bioresource Technology, Volume 155, March 2014, Pages 136-143, ISSN 0960-8524,
http://dx.doi.org/10.1016/j.biortech.2013.12.060.
Scott N. Genin, J. Stewart Aitchison, D. Grant Allen, (2015) Novel waveguide reactor design for
enhancing algal biofilm growth, submitted to Algal Research, In-Press.
Book Chapters:
Scott N. Genin, J. Stewart Aitchison, D. Grant Allen, Chapter 18: Photobioreactor based energy
sources, Nano and Biotech based material for energy building efficiency, Springer Publishing
Patents:
Scott N. Genin, D. Grant Allen, J. Stewart Aitchison, April 2015. Systems and Methods for
Phototrophic biomass production, (Provisional Patent: US62/151,283)
8
Other Contributions:
Genin, S. N. Sathananthan, S., Bui, F., Aitchison, J. S., Allen, D. G. 2013. Design of algal film
photobioreactors: surface and pH effects on algal film growth kinetics, 3rd
International
Conference on Algal Biomass, Biofuels and Bioproducts, Toronto, ON.
Genin, S.N., Aitchison, J. S., Allen, D. G. 2012. Design of algal film photobioreactors: exploring
material effects on algal biofilm growth and productivity, 62nd
Canadian Society for Chemical
Engineering Conference, Vancouver, B.C.
Genin, S. N., Schnurr, P.J., Aitchison, J. S., Allen, D. G. 2014. Light deliver in algal film
photobioreactors, 4th
International Conference on Algal Biomass, Biofuels and Bioproducts,
Santa Fe, New Mexico.
9
Chapter 2 Literature Review
2.1 Algal Fundamentals
Interest in algae research has been increasing over time, due to its potential use as a feedstock for
biofuels and its potential use as a carbon capturing technology. Algae are photosynthetic
autotrophs which convert water and carbon dioxide (CO2) into glucose and oxygen (O2) via the
light reactions and Calvin cycle that can be represented by the simplified chemical reaction
found in equation (2.1). Algae are also capable of growing as heterotrophs when organic carbon
is present, where organic carbon and oxygen is converted to water and CO2. Algae encompass a
wide range of organisms including Eukaryotes and Prokaryotes.
6𝐶𝑂2 + 6𝐻2𝑂 + 𝐿𝑖𝑔ℎ𝑡 → 6𝑂2 + 𝐶6𝐻12𝑂6 (2.1)
Algae are found in both freshwater and saltwater ecosystems. They are capable of growing 100
times faster than terrestrial plants and some strains are capable of accumulating large quantities
of lipids, usually inside their cells in the range of 15-77% dry weight depending on the
conditions and species (Chisti 2007, Lam and Lee 2012). The approximate stoichiometric
elemental composition of algae based on the Redfield Ratio is C106H181O45N15P (Clarens et al.
2010). The lipid, protein, and carbohydrate fractions of algae are species dependent as shown in
Table 2.1. The growth phase and conditions under which the algae are grown in can also affect
the relative proportions of lipids, proteins and carbohydrates in algae (Fernandez-Reirz et al.
1989, Lynn et al. 2000).
10
Table 2.1 – Lipid, protein and carbohydrate composition of several freshwater and marine algae
species (Fernandez-Reirza et al. 1989, Becker 2004)
Species Lipid (w%/w) Protein
(w%/w)
Carbohydrate (w%/w)
Freshwater Algae
Euglena gracilis 14-20 39-61 14-18
Chlamydomonas
reinhardtii
21 48 17
Chlorella pyenoidosa 2 57 26
Chlorella vulgaris 14-22 51-58 12-17
Dunaliella salina 6 57 32
Spirulina maxima 6-7 60-71 13-16
Spirulina platensis 4-9 46-63 8-14
Scenedesmus obliquus 12-14 50-56 10-17
Marine Algae
Pavlova lutheri 29 33 18
Isochrysis galbanna 28 40 15
Tetraselmis suecica 17 30 9
Chaetoceros
calcitrans
14 9 9
Phaeodactylum
tricornutum
20 17 25
Rodomanas sp. 28 16 12
Heterosigma
akashiwo
29 16 10
The current metabolic model that describes oxygenic photosynthesis was proposed by Hill and
Bendall (1960), which is commonly referred to as the Z-scheme of linear electron transport. In
this model, photons are absorbed by pigments, such as chlorophyll a and b, which are then used
to remove electrons from water to power an electron transport chain across a membrane in the
cell (Metis 2009). The model predicts a minimum of 8 mol photons are required to evolve 1 mol
of oxygen , however there are exceptions, as some algae species require less photons as
demonstrated by Osborne and Geider (1987).
2.1.1 Algal Growth Factors
The main factors which affect the growth rate of planktonic algae are: temperature, light
intensity, pH, and nutrient concentration (e.g. phosphorous, nitrogen, and CO2) (Dauta et al.
1990, Chisti 2007, Lam and Lee 2012). For most algae species, there is a maximum light
11
intensity, known as the saturation light intensity that yields the maximum growth rate. Increasing
the light intensity beyond the saturation point can cause adverse effects such as photo oxidation
which reduces the maximum growth rate (Codd 1984, Dauta et al. 1990). Temperature also
yields a similar trend with an optimum growth temperature and Dauta et al. (1990) noticed there
was a relationship between the optimal light intensity and temperature for some algae species
such as Chlorella vulgaris.
Phototrophic organisms, such as algae, have the ability to assimilate inorganic carbon such as
CO2 and process it into organic carbon which is used for growth. Some algae species are capable
of using organic carbon for growth. From a stoichiometry perspective, algae require 1.85 g of
CO2 for 1 g of algae biomass (Posten 2009). Experiments conducted by Takeuchi et al. (1992)
have demonstrated growth rates of Oocystis sp. are enhanced by carbon dioxide loading, but
higher carbon dioxide loadings were demonstrated to increase the lag phase of the algae growth
cycle. Nutrients such as nitrogen, sulfate, and phosphorous are also important for maximizing the
growth rate of algae (Grover 1989).
Algae cell or biomass growth rates is often represented by equation (2.2) below:
𝑑𝑋
𝑑𝑡= 𝜇𝑋 (2.2)
Where X is the cell concentration or biomass, t is time, and μ can be represented by the Monod
model (Monod 1949) in equation (2.3) or by the Haldane model equation (Andrews 1968)
equation (2.4)
𝜇 = 𝜇𝑚𝑎𝑥𝑆
𝐾𝑠+𝑆 (2.3)
𝜇 = 𝜇𝑚𝑎𝑥𝑆
𝐾𝑠+𝑆+𝑆2
𝐾𝑖
(2.4)
12
Where μmax is the maximum growth rate, Ks is the Monod half saturation constant, S is growth
limiting substrate concentration and Ki is the inhibition constant.
Growth rates of phototrophic organism are affected by the light intensity. The Steele
relationship, equation (2.5), is commonly used to represent light limitations in algal cultivation
for the Monod model (Steele 1965, Liehr et al. 1990):
𝐹𝑙 =𝐼
𝐼𝑠𝑒
(1−𝐼
𝐼𝑠) (2.5)
Where Fl is the light limitation fraction, I is the light intensity, and Is is the saturation light
intensity. In the case of the Haldane model, light is considered to be a substrate and is
represented in equation (2.6)
𝜇 = 𝜇𝑚𝑎𝑥𝐼
𝐾𝐼+𝐼+𝐼2
𝐾𝑖
(2.6)
The variation of light intensity in algal solutions or films is often described by the Beer-Lambert
law which describes the light attenuation as:
𝐼 = 𝐼0𝑒−𝛾𝑧 (2.7)
Where I0 is the incident light intensity at the surface, γ is the extinction coefficient, and z is the
depth into the media or biofilm.
2.1.2 Products from Algae
Algae can be used to produce multiple bio-based fuels and products. Common products derived
from algae are biodiesel, bio-crude oil from hydrothermal liquefaction, high value bioproducts,
ethanol, and biomass (Minowa et al. 1995, Sawayama et al. 1999, Chisti 2007, Collet et al.
13
2011). The reactor and process design considerations are different depending on what type of
product is produced, since energy products such as biodiesel have lower profit margins per unit
mass of product compared to high value added products such as nutraceuticals. A summary of
the state, heating values, and location relative to the cell of the various energy products from
algae are summarized in Table 2.2.
Biodiesel produced from algae is a conventional bio-based fuel derived from the lipids in algal
biomass (Chisti 2007, Demirbas and Demirbas 2011, Lam and Lee 2012). Lipids extracted from
the algae are reacted with methanol or another alcohol using an acidic or basic catalyst to
produce fatty acid methyl esters (FAMEs) and glycerol (Figure 2.1). Biodiesel is considered to
be favourable since the lipid (w%/w) of algae can range from 5-50% lipids (Chisti 2007). After
the lipids are extracted from the algae, the remaining biomass could be sold for agricultural
purposes such as cattle feed (Demirbas and Demirbas 2011). Compared to other feedstocks for
biodiesel such as soybean and canola, algae has several advantages such as a higher lipid
content, can be grown on non-arable land, and they have a faster growth rate. A study by Chisti
(2007) estimated in order to meet the demand of 50% of the United States transport fuel need,
algae with 30% lipids (w%/w) would need 4.5 M ha of land, compared to 594 M ha of land
required by soybean and 223 M ha of land required by canola.
Figure 2.1 – Transesterification of a triglyceride (modified from Ma & Hanna, 1999)
An alternative approach to producing a petroleum fuel from algae is to subject the algae to a
process called hydrothermal liquefaction. In this process, the algal biomass is subjected to
temperatures between 200-350 oC for 5-30 min at high pressures and sodium carbonate is used as
a catalyst (Minowa et al. 1995, Sawayama et al. 1999). In this process, the algal biomass is
14
converted directly into a biocrude oil which typically has a high nitrogen (6 w%/w) and oxygen
content (12 w%w). The main benefits of hydrothermal liquefaction over transesterification of
lipids into biodiesel is that hydrothermal liquefaction does not require the biomass to be
dewatered entirely and does not require a solvent extraction (Brown et al. 2010). The bio-crude
oil produced from this process can then be refined into various petroleum products.
Hydrothermal liquefaction of algae into biocrude is considered to be a new process compared to
producing biodiesel from algae, but similar processes to produce bio-based petroleum such as
hydrocracking of oils from algae have been investigated (Hillen et al. 1982). Hillen et al. (1982)
demonstrated the hydrocarbon oils from Botryococcus braunii could be hydrocracked into
transport fuels. B. braunii produces branched hydrocarbon oils (C27-C34) which have a similar
chemical structure and properties to heavy crude oil (Wold et al. 1985).
Ethanol is another fuel product that can be produced by genetically modified cyanobacteria
undergoing photosynthesis (Deng and Coleman 1999). In the genetically modified cyanobacteria,
genes from E. coli were inserted into the cyanobacteria genome add the expression of the
enzymes PDC (pyruvate decarboxylase) and ADH (aldehyde dehydrogenase), which convert
pyruvate into ethanol through an acetaldehyde intermediate (Gao et al. 2012). This genetic
modification enables the conversion of CO2 into ethanol. Gao et al. (2012) reported their
genetically modified cyanobacteria (Synechocystis sp. PCC6803) could produce and excrete 212
mg/L day of ethanol. In context, however, it does not compare as favourably to sugar to ethanol
fermentation, but is comparable to biodiesel production. Some yeast strains, such as
Saccharomyces cerevisiae strain KF-7, are capable of producing ethanol at a rate of 0.146 g/L
day (Morimura et al. 1997). Based on volumetric productivities estimated by Chisti (2007), the
maximum potential FAME production from raceway ponds and photobioreactors - assuming 30
w%/w lipid – would be 0.0351 g/L day and 0.4605 g/L day. The ethanol produced ends up in
solution and is not stored in the cells, which has advantages over intracellular products that
require the algal biomass to be processed.
Algal biomass can be burned directly instead of extracting or converting the algal biomass. In
this case, the algal biomass needs to be dried before combustion as water will lower the potential
15
energy extracted from the combustion. A study conducted by Sturm and Lamer (2011) estimated
that the direct combustion of algal biomass is a more efficient energy source compared to the
overall energy balance required to produce biodiesel if the lipid content of the algae was at 10
w%/w. If algal biomass is used for combustion, the opportunity to take the residual biomass and
feed it into an anaerobic digester is lost when compared to biodiesel production (Sturm and
Lamer 2011, Collet et al. 2011).
An alternative to processing the algal biomass into a fuel or having the algae produce a fuel is to
digest the algal biomass using anaerobic bacteria to produce biogas. Anaerobic digestion of algal
biomass residues is often conducted in life cycle analysis (Sialve et al. 2009, Collet et al. 2011).
Multiple studies on anaerobic digestion of algal biomass have shown the quality of biogas
(methane composition by volume) range from 46-76% (Samson and LeDuy 1986, Chen 1987,
Yen and Brune 2007). The composition of algal biomass has a significant effect on the energy
produced from the methane as increased lipid composition increases the energy of the biogas;
however a theoretical study by Sialve et al. (2009) predicted that converting the lipids into
biodiesel and then anaerobically digesting the residual algal biomass will yield a higher total
energy in the two products compared to anaerobic digestion alone.
Table 2.2 - Comparison of energy products derived from algae
State at room
temperature
Heating Value
(MJ/kg)
Location in
Cell
Biodiesel (FAME) Liquid 39.5-41 Intracellular
Bio-crude Liquid 35-50 Conversion
Ethanol Liquid 29.7 Extracellular
Biomass (dry) Solid 21.1-25.1 Biomass
Methane Gas 50-55 Conversion
Microalgae and cyanobacteria are capable of producing a wide range of bioproducts that have
commercial applications (Table 2.3). These products have higher commercial value compared to
biodiesel and other fuels, but the production of some of these compounds such as Astaxanthin is
significantly lower. Astaxanthin is a high valued carotenoid produced from algae species such as
Haematococcus sp. and is used as a pigmentation source in aquaculture. In 2000, Astaxanthin
sold for ~US$2500 per kg and had an annual worldwide market estimated at US$200 million
16
(Lorenz and Cysewski 2000). Haematococcus sp. can contain between 1.5-3 w%/w of
astaxanthin, which is lower than the lipid content of most algae species.
Table 2.3 - Other non-fuel products from microalgae & cyanobacteria
Chemical Usage Product type Reference
Phycobiliproteins Medical Diagnostics Intracellular Eriksen (2008)
Astaxanthin Food supplement Intracellular Lorenz and Cysewski
(2000)
Xanthophyll Fish Feeds Intracellular Baroli and Niyogi (2000)
Beta-carotene Food Supplement Intracellular Deangleis et al. (1977)
Health
Supplements
Dietary Supplements Intracellular
Saxitoxin and
Microcystin
Insecticides Extracellular Becher and Jüttner (2005)
Folate and Biotin Extracellular Deangleis et al. (1977)
2.2 Algal Biofilms
An algal biofilm is a mixed community of many different algae and bacteria species within a
matrix of extracellular polymeric substances (EPS) (Lawrence et al. 1998, Hodoki 2005, Johnson
and Wen 2010). EPS is a matrix of polysaccharides, proteins, glycoproteins, glycolipids, and
extracellular DNA produced by the microorganisms that are imbedded in the biofilm (Flemming
et al. 2007). Biofilm composition varies between different films depending on the
microorganisms present, shear forces, temperature, and availability of nutrients (Flemming and
Wingender 2010). The EPS matrix bonds the cells to each other and the attachment material
which immobilizes the cells. The cells within these biofilms often exist in a symbiotic
relationship with other species in the matrix, where metabolites from one species can serve as
nutrients for other organisms (Hodoki 2005, Flemming et al. 2007). There is evidence to suggest
that EPS is a product of overflow metabolism and is continuously produced once algae enter the
stationary phase (Brouwer and Stal 2002, Barranguet et al. 2005)
The current state of research on algal biofilms is mainly limited to ecological studies, but there
are a few papers that investigate and discuss the use of algal biofilms for biodiesel production
(Johnson and Wen 2010, Christenson and Sims 2012, Young 2011, Gross et al. 2014). There is
limited research on the design aspects of algal biofilm photobioreactors. As stated earlier, algal
17
biofilms have a potential competitive advantage over suspended algae in regards to dewatering
and harvesting since the concentration of biomass is higher concentration of biomass than a
suspended system (Irving and Allen 2011, Ozkan et al. 2012, Christenson and Sims 2012).
2.3 Algal Biofilm Growth Factors
Algal biofilms are more complex than suspended algae. Not only do they consist of mixed
communities (Hodoki 2005, Flemming et al. 2007), but factors such as light and mass transport
become more important due to the fixed nature of the film (Liehr et al. 1990). In thick algal
biofilms, it is not reasonable to assume the biofilm is a well-mixed system and thus it would be
affected by mass transport (Liehr et al. 1988). Differences in phototropic biofilm growth are
attributed to the following factors: the chemical environment (i.e. nutrients, light, and pollution);
biotic factors (i.e. species composition and grazing by other organisms) (Hillebrand 2003,
Hodoki 2005); and material effects (i.e. material of attachment) (Sekar et al. 2004). Compared to
suspended algae, the factors which effect algal biofilm growth are less understood due to the
more complex nature of algal biofilms.
Growth of biofilms is characterized by going through various stages of growth: colonization,
growth, stabilization and biomass decrease through sloughing or senescence (Cooksey &
Wigglesworth-Cooksey 1995, Palmer 2007). The colonization phase of phototrophic biofilm
growth is characterized by the predominance of EPS and heterotrophic bacteria and the relative
lack of algae. There is evidence which supports the notion that bacteria condition the attachment
surface prior to the growth phase (Palmer 2007). During the growth phase, the bulk of organic
mass in the biofilm is represented by algae (Barranguet et al. 2005). During the stabilization
phase the rate of biofilm growth slows, in which the portion of EPS, bacteria and algae stabilizes,
but the ratio is dependent on environmental conditions (Barranguet et al. 2005). The sloughing or
senescence phase is not as well understood as the other phases, but it is reported that biofilms in
this stage are unable to uptake enough nutrients to meet their demand for growth (Cooksey &
Wigglesworth-Cooksey 1995). In this phase the cells will reach a steady state (net rate of
inorganic carbon uptake is equal to respiration) or slough.
18
2.3.1 Nutrients and Light
Like suspended algae, algal biofilms require nutrients such as inorganic carbon, nitrogen and
phosphorus to grow. Unlike suspended algae, the nutrients need to diffuse along a concentration
gradient into the biofilm since biofilm systems are not well mixed. This can complicate the mass
transport problems already present in bioprocessing systems. The addition of light transport into
algal biofilms can cause new challenges, since transporting light from the source to the algal
biofilm can be obstructed by suspended algae found in the bulk liquid and boundary layer
(Figure 2.2).
Figure 2.2 – Diffusion of inorganic carbon and light profile within an algal biofilm with
boundary layer (Reprinted from: Liehr et al. 1990, Biotechnology and Bioengineering, 35(1),
with permission from John Wiley and Sons)
The diffusion of inorganic carbon into algal biofilms is complicated by the addition of pH
gradients within algal biofilms (Kuenen et al. 1986, Liehr et al. 1990). The pH of algal biofilms
can reach 10 when undergoing photosynthesis due to the production of oxygen from the light
reaction of photosynthesis (Kuenen et al. 1986). Due to the pH change in algal biofilms, the ratio
of inorganic carbon species (CO2, HCO3-, and CO3
2-) would be a function of depth into the algal
biofilm. Past experiments by (Goldman and Graham. 1981, Thielmann et al. 1990, Watson 2009)
showed that algae have mechanisms for consuming HCO3- and CO3
2-, and Wolf-Gladrow and
19
Riebesell (1997) showed that neglecting the consumption of HCO3- by algal cells results in
significant deviations in predicted algal growth rates and inorganic carbon profiles.
Phototrophic organisms utilize photosynthetically active radiation (PAR) (wavelengths range
from 400-700 nm) as an energy source for the light cycle (Steele 1965, Rabinowitch and
Gouindjee 1969, Melis 2009). Wavelengths outside of the PAR spectrum are not useable for
photosynthesis. Of the solar radiation which reaches earth, 53% is in the PAR spectrum
(Rabinowitch and Gouindjee 1969, Hall and Rao 1999). Chlorophyll a has an approximate
absorption peak of 465 nm and 665 nm, while chlorophyll b has absorption peaks at 450 nm and
640 nm. 70% of the PAR is absorbed by the chlorophyll and photosynthetically active pigments,
of which 24% of the absorbed photon energy is lost due to degrading short wavelength photons
to the 700 nm energy level (Hall and Rao 1999). This leaves approximately 28% of total solar
radiation available to provide energy to the cell before metabolic inefficiencies are accounted for.
Several researchers have reported that light diminishes exponentially with depth of a biofilm,
similar to the Beer-Lambert law as shown in Figure 2.2 (Zieppel and Neu, 2005, Jorgensen et al.
1987, Barranguet et al. 2004). In thick biofilms, algae have been reported to adapt to the lower
light intensities (Jorgensen et al. 1987), implying the extinction coefficient in the Beer-Lambert
law for an algal biofilm would not be constant, but would vary with depth. The effect of light
saturation on algal biofilms is not well understood compared to the effects of light saturation on
suspended or individual algae cells (Henly 1993, Melis 2009). The light intensities which result
in saturation for suspended algae are wavelength dependent (Picket and Myers 1965). Suspended
algae cells will adjust their chlorophyll antenna size and concentration of pigments depending on
light intensity either to absorb more photons or to prevent damage to the cell from photo
oxidation (Melis 2009).
A recent study by Schnurr et al. (2014) demonstrated that algal biofilms grown at 2% sparged
CO2 and constant photon flux of 100 μmol/m2 sec (provided by red LEDs) did not have
significant variations in productivity when the direction of the light was changed from water
side, material side, and both sides. The direction of incident light did affect the measured
suspended algae concentration in the study. This could imply that at some conditions the light
20
direction is not an important factor in algal biofilm growth, which as significant implications for
future reactor design.
Nutrients such as phosphorous and nitrogen are important for algae growth, and there is
sufficient literature which demonstrates that starving suspended algae of key nutrients such as
nitrogen in improve lipid content (w%/w), but not always the lipid productivity (Shifrin and
Chisholm 1981, Ho et al. 2012, Schnurr et al. 2013). Results by Schnurr et al. (2013)
demonstrated that nitrogen was a critical nutrient in algal biofilm growth, as algal biofilms
starved of nitrogen suffered from sloughing compared to algal biofilms which were supplied
sufficient levels of nitrogen. This implies algal biofilms do not respond in the same manner as
planktonic algae when under nitrogen limitations, and there is little evidence to support that
nitrogen starvation will improve algal biofilm lipid yields.
2.3.2 Biotic Factors
Biotic factors such as relative abundance of bacteria to algae, and population of grazing
organisms can have a profound impact on algal biofilm growth. Initial settlement of bacteria onto
an attachment surface can affect the overall algal biofilm growth rate (Hodoki 2005, Irving and
Allen 2011) and the relative abundance of bacteria, algae and EPS (Barranguet et al. 2004,
Hodoki 2005). Irving (2011) showed that algal biofilms grown on glass wool in the absence of
bacteria and EPS have lower productivities and adhesion to the glass wool. Abiotic growth
conditions such as shear rate, temperature, bulk nutrient concentration, light intensity and pH
will not only affect the growth rate of the biofilm, but also the relative abundance of bacteria and
algae in the biofilm (Sekar et al. 2004, Hodoki 2005, Besemer et al. 2007).
External biotic and abiotic factors impact the internal biotic composition of algal biofilms.
During the growth of algal biofilms organic carbon, chlorophyll and EPS production are usually
correlated, even under different light intensities. This indicates a close coupling between
autotrophic carbon production and EPS (Barranguet et al. 2005). The effect of grazing on algal
biofilms can cause deviations from this correlation, as algal biofilms which have been grazed
tend to have higher EPS to cell ratios. This indicates that algal biofilms which are grazed upon
21
favour EPS rich algae, firmly attached diatoms and filamentous cyanobacteria (Barranguet et al.
2005). This shows that algal biofilms are capable of responding to external stimuli and the biotic
composition of a biofilm represents the environmental conditions.
2.3.3 Material and Surface Effects
Attachment of cells onto surfaces is widely attributed to the hydrophobicity of the surface (Sekar
et al. 2004, Palmer et al. 2007), but there are other factors that affect cell attachment onto
surfaces such as the pH of the bulk liquid, surface charge and cell charge (Palmer et al. 2007).
The literature is inconclusive about the material surface properties that impact algal biofilm
growth. Irving and Allen (2011) reported that water-material contact angle did not affect algal
biofilm growth on materials for the species C. vulgaris and S. obliquus, but Sekar et al. (2004)
reported that water-material contact angle was important for the initial attachment for C. vulgaris
when comparing metals and glass. The disparity may be due to differences in time scales of the
experiments.
To further the discussion on material surface energy and contact angles a brief discussion on the
fundamentals of surface energy is as follows. The contact angle of a material and a liquid can be
described by the Good Van Oss model (1) which relates the Interfacial Lifshitz-van der Waals
and Polar interactions of surface energy with the contact angle (Van Oss et al. 1988).
cos 𝜃 = −1 +2√𝛤𝑠𝑟
𝐿𝑊𝛾𝑙𝐿𝑊
𝛤𝑙
⁄+
2√𝛤𝑠𝑟+𝛤𝑙
−
𝛤𝑙⁄ +
2√𝛤𝑠𝑟−𝛤𝑙
+
𝛤𝑙⁄ (2.8)
where θ is the contact angle of the liquid and material, Γl is the total surface energy of liquid,
ΓlLW
is the Lifshitz-van der Waals component of liquid surface energy, Γl+ is the acid component
of liquid surface energy, Γl- is the base component of liquid surface energy, Γsr
LW is the Lifshitz-
van der Waals component of material surface energy, Γsr+ is the acid component of material
surface energy and Γsr- is the base component of material surface energy. The polar component
22
of the surface energy is a combination of the acid and base surface energies, which is represented
by equation (2).
𝛤𝑠𝑟𝑝𝑜𝑙𝑎𝑟 = 2√𝛤𝑠𝑟
−𝛤𝑠𝑟+ (2.9)
where Γsrpolar
is the polar surface energy component of a material’s surface energy.
There has been research into the surface and wettability effects of materials on bacteria and
algae, particularly from a biofouling perspective (Finlay et al. 2002, Palmer et al. 2007). These
studies, such as the one conducted by Finlay et al. (2002) on two marine algae species,
Enteromorpha and Amphora, set out to determine which surface properties affect attachment and
adhesion of microbes. They found that primary adhesion and settling of the spores of
Enteromorpha were promoted by hydrophobic surfaces, while the adhesion strength of the
settled spores was greatest on hydrophilic surfaces. For the species Amphora, hydrophobicity did
not influence the initial settling, but the cells were more strongly adhered to hydrophobic
surfaces. Work by Ozkan and Berberoglu (2013) on algal cell attachment onto surfaces showed
that acid-base interactions between algae and surface were the dominating mechanism.
Schumacher et al. (2007) demonstrated that materials could be designed to reduce the adhesion
and attachment of algae by manipulating the geometry of the surface without affecting the
surface energy.
The effect of attachment material on algal biofilm productivity has been investigated, but has not
been fully described. Johnson and Wen (2010) reported significant differences in algal biomass
productivity between polystyrene foam (2.57 g/m2day), cardboard (1.47 g/m
2day), polyethylene
fabric (0.58 g/m2day), and Loofah sponge (1.28 g/m
2day). This is not in direct disagreement
with the results from Irving and Allen (2011), considering the materials tested by Johnson and
Wen (2010) were foams and fabrics with pores that may help facilitate biofilm growth.
Christenson and Sims (2012) demonstrated algal biofilms grown on a rotating biofilm reactor
have a preference for growth on cotton rope when compared to polyester, jute and acrylic. They
concluded the differences in substrata performance were likely due to the differences in initial
23
attachment of bacteria. Orientation of the biofilm (e.g. vertical vs. horizontal) may be another
important in the development of algal biofilms.
Regrowth of algal biofilms is another factor that has been investigated in some detail (Johnson
and Wen, 2010, Christenson, 2011). Christenson (2011) found that mixed consortium algal
biofilms that are harvested and then allowed to regrow demonstrated faster growth rates
compared to initial growth (Figure 2.3). Johnson and Wen (2010) tried a similar experiment with
Chlorella sp. and found that regrowth does appear to increase the biofilm productivity. Johnson
and Wen (2010) and Christenson (2011) suspected that the increase in productivity was a result
from the harvesting process since the process leaves some residual bacteria, algae, and EPS
remains. These remnants act as a seed for the next film.
Figure 2.3 – Re-growth of a biofilm compared to suspended and initial growth
(Reprinted from: Christenson 2012, Biotechnology and Bioengineering, 109(7), with permission
from John Wiley and Sons)
Currently, there is very little research on the impact of biofilm orientation (i.e. vertical vs.
horizontal) on algal biofilm growth, but there have been studies on bacterial biofilms in vertical
orientation ranging from wastewater treatment to plasmid transport (Krol et al. 2011, Rodgers et
al. 2003, Kolari et al. 2002, Munoz et al. 2009).
24
2.4 Photobioreactors
The most common method of growing algae on a pilot or commercial scale is using a
photobioreactor (PBR) such as raceway pond or a variation of a closed photobioreactor (Figure
2.4) (Chisti 2007, Ugwu et al. 2008, Bitog et al. 2011, Wang et al. 2012). A PBR is a reactor
which uses light as one of the inputs to grow photosynthetic organisms. The PBR can be
illuminated either from artificial light, natural light or both.
Figure 2.4 - Photobioreactors used in growing algae: (a) raceway pond, (b) flat-plate, (c)
inclined tubular and (d) horizontal tubular (Reprinted from: Bitog et al. 2011. Application of
computational fluid dynamics for modeling and designing photobioreactors for microalgae: A
review, Computers and Electronics in Agriculture, 76(2):131-147 with permission from
Elsevier)
2.4.1 Open Photobioreactors
Open raceway ponds are the oldest and simplest systems for algal cultivation. They are
constructed by either constructing low walls (usually made from poured concrete) or are dug into
the ground and lined with a plastic liner. The typical depth for a raceway pond is approximately
25
20-50 cm (Doucha and Livansky 2006, Chisti 2007), but the length and width can vary
depending on scale and design. Water circulation in induced through the use of paddle wheels or
pumps, and the system can be sparged, but this is often not the case (Boussiba et al. 1988, Hase
et al. 2000, Ugwu et al. 2008).
Ugwu et al. (2008) considers raceway ponds to have low capital costs, easy to clean and good for
mass cultivation of algae, but they are difficult to control. Due to poor mixing, mass transfer
rates tend to be low, often resulting in low productivity (Chisti 2007, Ugwu et al. 2008). For
similar size reactor and operating conditions, raceway pond productivity is typically around 0.05
– 0.32 g/L day, where conventional closed photobioreactors produce around 1.5 g/L day of dry
biomass (Pushparaj et al. 1997, Jimenez et al. 2003, Doucha and Livansky 2006, Chisti 2007).
Raceway ponds also suffer from contamination of algal cultures, which can manifest in two
forms: contamination by other photosynthetic organisms and contamination by organisms that
prey upon algae (Chisti 2007, Pate et al. 2011, Wang et al. 2012). Contamination of by other
photosynthetic species is a problem when the desired product is required to meet a certain
specification, which usually occurs when the algae are grown for a specific chemical (e.g. β-
carotene) or for biodiesel production. In these cases, contamination by a more competitive algae
strain will cause the end product to be off specification, which could increase the cost of
downstream processing. Contamination by organisms that prey upon algae causes multiple
problems as it will decimate the entire culture and will delay the production cycle.
2.4.2 Closed Photobioreactors
Closed photobioreactors are often characterized according to their geometry which are vertical
column (bubble column or airlift), horizontal tubular, and flat plate (Bitog et al. 2011, Wang et
al. 2012). The design considerations for closed photobioreactors are: light distribution, CO2/O2
gas exchange, temperature, pH, mixing, and sterility. Some of the design considerations such as
light distribution are more dependent on the geometry of the reactor, while other such as
temperature and pH are more dependent on operating conditions (de Vasconcelos Barbosa 2003,
Wang et al. 2012). An efficient PBR design should achieve the following: 1) have a high
26
biomass productivity and selectivity; 2) efficient utilization of PAR and nutrients; 3) allow for
precise control of operational parameters; 4) minimize capital and operational costs.
Light transport and distribution into algae photobioreactors are considered to be the main barriers
to improved productivity (de Vasconcelos Barbosa 2003, Chisti, 2007, Ugwu, 2008, Erikson et
al. 2011, Chen et al. 2011). As light enters a suspended algae culture the intensity decays
according to the Beer-Lambert law as the algae closer to the illuminated surface shade the algae
farther away, which inhibits their growth (de Vasconcelos Barbosa 2003, Chen et al. 2011). This
leads to larger dark zones in the reactor, where the photobioreactor is considered to be
unproductive. The approaches currently implemented for reducing dark zones within a reactor
are to make the reactor as thin as possible, improving mixing, or adding internal light sources (de
Vasconcelos Barbosa 2003, Ono and Cuello 2004, Posten 2009, Maor and Appelbaum, 2011,
Wang et al. 2012).
CO2 is a required nutrient for algal growth, and O2 can be inhibitory to algal growth at high
concentrations (Miyachi et al. 1955, Weissman et al. 1988). At high dissolved oxygen levels
(DO), ribulose 1,5-bisphosephate carboxylase-oxygenase will convert O2 into CO2, and thus
reduces the rate of CO2 assimilation into the Calvin cycle (Jensen and Bahr 1977). Also DO may
convert into oxygen radicals under exposure to strong sun light radiation, which may damage the
cell and organelle membranes in the cell. Tubular photobioreactors in the literature tend to suffer
from the ability to deliver sufficient CO2 and remove O2 due to their configuration (Weissman et
al. 1988, Bitog et al. 2011, Wang et al. 2012).
Temperature and pH are important in algal culture systems since both affect the maximum
growth of algae. The ideal temperature range for algae ranges from 10-30 oC (Chisti 2007) and
the ideal pH ranges from 7-9, although there are species that can tolerate higher pH values
(Vieira Costa et al. 2004). In addition to affecting the maximum growth rate they affect the
solubility of CO2 and the ratio of species of inorganic carbon (i.e., HCO3-, CO3
2-). Over the range
of 10-30 oC, the solubility of CO2 and oxygen decrease as temperature increases. The total
capacity of water to hold dissolved inorganic carbon increases with increasing pH.
27
The general considerations for open photobioreactors and closed photobioreactors as discussed
above are summarized in Table 2.4. Currently, open photobioreactors such as raceway ponds are
more favourable when producing low value products such as biodiesel because of their low
capital and operating costs, where closed photobioreactors are preferred for producing high value
products since the potential for contamination is reduced.
Table 2.4 - Operational Comparison of Open and Closed PBRs
Open PBR Closed PBR
Mass Transport Poor Good
Contamination Possibility High Low
Algae biomass concentration 1-4 g/L (Chisti 2007) 0.1-1 g/L (Chisti 2007, Ugwu
et al. 2008)
Aerial productivity 11.1-35 g/m2 day 20-72 g/m
2 day
Water loss due to
evaporation
High Low
Temperature control Dependent on weather Can be controlled
Possible Design
Configurations
Few Multiple
2.5 Algal Film Photobioreactors
Algal biofilms grown on bench, pilot and commercial scales are grown in algal film
photobioreactors. These often take the forms of algal turf scrubbers (ATS) or rotating algal
biofilm (RAB) systems. Previous experiments related to algal biofilm production (Johnson and
Wen 2010, Irving and Allen 2011, Schnurr et al. 2013) have mostly been conducted on a small
scale while neglecting reactor design conditions. Research conducted by Mulbry et al. (2008)
and Kebede-Westhead et al. (2006) has tested the viability of nutrient removal from waste
streams but they have not been concerned with measuring algal biomass production. Christenson
and Sims (2012) designed and tested a rotating algal film photo bioreactor for waste treatment
and algal biomass production to be used in conjunction with raceway ponds.
Algal turf scrubbers (ATS) utilize algal biofilms attached to a material for the main purpose of
nutrient removal. A shallow layer of wastewater is passed over a sloped surface allowing
microorganisms to attach and form a mixed biofilm community and, remove compounds and
28
nutrients from the water (Craggs et al. 1996). Water is recycled and the entire system is exposed
to the atmosphere (Figure 2.5). The biomass from the algal turf scrubbers is harvested regularly
and which the resulting algal mass is often used for fertilizer (Mulbry et al. 2008, Kebede-
Westhead et al. 2006). Large ATS are housed outdoors, which leads to their performance often
being dependent on non-controllable factors such as the weather.
Figure 2.5 – Schematic of an ATS used for the treatment of dairy manure effluent
(Modified from Mulbry et al. 2008. Bioresource Technology, permission obtained from:
Elsevier)
Rotating algal biofilm (RAB) systems are photobioreactors in which algae are attached to a
surface is then rotated so part of the algal biofilm is submerged in the media and the other part is
exposed to the air (Figure 2.6). The shear acting on the algal biofilm is generated by the motion
of the attachment material. Christenson and Sims (2012) reported that cotton rope was the best
candidate for use in their RAB system since it had the highest algal biofilm productivity. Algal
biofilms grown in these systems can be scraped off the attachment surface mechanically. These
systems have been used to treat municipal wastewater (Christenson and Sims 2012) and for the
mass production of algal biofilms (Gross et al. 2013).
29
Figure 2.6 – A modified raceway pond consisting of triangle and vertical patterned RAB
systems (Modified from: Gross and Wen 2014. Bioresource Technology, permission obtained
from Elsevier)
Current biofilm photobioreactor designs used in the literature tend to resemble raceway ponds
compared to traditional bioreactors. The films are grown horizontally (Craggs et al. 1996,
Kebede-Westhead et al. 2006, Mulbry et al. 2008, Johnson and Wen, 2010) or on paddles and
spools (Young 2011, Christenson and Sims 2012,) for the main purpose of wastewater treatment.
Vertically oriented algal turf scrubber reactors are rarely reported in literature, but Shi et al.
(2007) demonstrated that Chlorella vulgaris was capable of growing on a porous sheet when the
cells were forced onto the sheet. Designs such as airlift or tubular reactors are absent with the
exception of some research conducted by Munoz et al. (2009), where six different reactor
designs were tested with the biofilm immobilized either onto Poraver® carriers or on the reactor
wall itself. For some of the reactors, the algal biofilms were grown vertically while others were
grown horizontally, but the study did not cover production rates and was interested in BOD and
nutrient removal rates.
30
Algae film reactors have also been developed around the idea of active immobilization of algae
with the use of flocculating agents, chemical attachment, and gel entrapment (Moreno-Garrido
2008). Flocking agents and chemical attachment methods are intended to be used as harvesting
methods. Algae immobilized in gel entrapment are viable, capable of absorbing nutrients and
growing. Algae are often entrapped in gels and polymers such as alginate, but very little research
on this method for algae growth has been conducted as most are concerned with metal ion and
nutrient removal (Moreno-Garrido 2008, Lam and Lee 2012). Immobilization of bacteria is much
more common than immobilization of algae, but one would expect that the methods and
principles are similar. Immobilization of algae into alginate particles does cause problems with
nutrient transport and the algae inside is often light limited (Moreno-Garrido 2008).
Algal film photobioreactors are often considered unsterile because algal biofilms by nature often
consist of multiple different species of algae and contain other microorganisms (Hodoki 2005,
Barranguet et al. 2005, Besemer et al. 2007). Examples of algal film photobioreactors in the
literature do not attempt to control or measure the microbial community (Johnson and Wen 2010,
Christenson and Sims 2012, Gross et al. 2013, Schnurr et al. 2013), but there are examples of
chemically or mechanically fixing algae cells onto surfaces (Shi et al. 2007, Young 2011). In
both cases, contamination of the algal biofilm by other algae species is not considered to be an
issue.
Designing algal film photobioreactors has not been explored in-depth for ATS and RAB systems.
Studies of algal film photobioreactors in the literature usually explore either operational
parameters such as nutrient loading (Mulbry et al. 2008, Kebede-Westhead et al. 2006, Schnurr
et al. 2013) or design parameters such as attachment material (Johnson and Wen 2010,
Christenson and Sims 2012, Gross et al. 2013). The studies conducted on operational parameters
such as those by Kebede-Westhead et al. (2006) and Mulbry et al. (2008) were concerned with
nitrogen and phosphorus loading in an ATS system or were concerned with extreme cases such
as nitrogen starvation, as conducted by Schnurr et al. (2013). Studies which explore the design of
algal film photobioreactors such as determining suitable material of attachment such as those
conducted by Johnson and Wen (2010), Christenson and Sims (2012), Gross et al. (2013) could
31
only concluded that algae has a preference for growth on certain materials such as cotton over
other materials such as acrylic.
Productivity of algal film photobioreactors in the literature is calculated using two methods: (1)
single point productivity where the algal biomass harvested per unit area is divided by the total
time (Johnson and Wen 2010, Christenson and Sims 2012, Gross et al. 2013, Gross and Wen
2014) or (2) by conducting a linear regression over the entire data set of algal film biomass yield
(Schnurr et al. 2013, Schnurr et al. 2014). The first method for measuring productivity distorts
the reported productivities and lacks significant information about the overall growth kinetics of
the algal biofilm. In both measurement methods, it implicitly assumes that algal biofilm growth
will be linear, and while there is empirical evidence to support that while regions of algal biofilm
growth are linear (Christenson and Sims 2012, Schnurr et al. 2013, Gross et al. 2013), it is not all
encompassing of algal biofilm growth kinetics.
2.6 Photobioreactor Economics
There have been multiple studies that have examined the economic potential of biodiesel from
algae (Amer et al. 2011, Collet et al. 2011, Davis et al. 2011, Harun et al. 2011, Nagarajan et al.
2013). Most techno-economic studies of algae systems found in the literature are based
suspended algae as opposed to film algae. It is possible to find studies that conclude that the
price of biodiesel from algae is cost competitive with petroleum diesel (Nagarajan et al. 2013)
and those which conclude it is not cost competitive (Amer et al. 2011, Davis et al. 2011). In
some techno-economic analysis of algae production into biodiesel or other products the authors
assume that the algae does not have an ash content even though the ash content of algae can
range from 3-15% (Amer et al. 2011), or the algae grown has a high lipid content > 50 w%/w
(Nagarajan et al. 2013). Davis et al. (2011) estimated that the change to production cost of algal
biodiesel was most dependent on the lipid content of the algae followed by the growth rate.
Experimental studies seem to indicate that there is a tradeoff between the growth rate and the
lipid accumulation (Solovchenko et al. 2008), so it may be difficult to have high growth rate and
high lipid content.
32
The economic feasibility of algal biomass production is dependent on photobioreactor
costs and operational costs. Studies conducted by Amer et al. (2011) and Davis et al. (2011)
concluded that open raceway ponds have a significant cost advantage over photobioreactors even
though photobioreactors have higher aerial and volumetric productivities. For a photobioreactor
based algal cultivation system, the capital cost of the photobioreactor was the largest contributor
in both studies. Amer et al. (2011) predicted that photobioreactors illuminated with LEDs would
have higher operational costs than those illuminated by the sunlight, even though it was
estimated that an LED-lit photobioreactor would have a photon utilization efficiency of 90%,
while a solar-lit one would have an efficiency of 50%. These values for photon conversion are
based on the theoretical quantum efficiency of 8 photons to consume 1 molecule of CO2, which
as discussed in section 2.1, is not a reliable metric.
Other major costs for the production of algal biomass were the transportation and acquisition of
CO2, dewatering of algal biomass, and nutrient supply (i.e. nitrogen and phosphorus). Studies
assume that an algal production facility will be co-located next to an industrial process which
produces flue gas and wastewater rich in nitrogen and phosphorus (Amer et al. 2011, Harun et al
2011, Nagarajan et al. 2013). In other studies, it is suggested that the residual biomass can be
used to feed an anaerobic digester to produce biogas for electricity generation or to sell the
biomass for agricultural purposes (Collet et al. 2011, Harun et al. 2011). Sialve et al. (2009)
suggested that anaerobically digesting algae residue from the solvent extraction process was
necessary to make algal biodiesel sustainable and even estimated that on an energy balance basis
if the lipid content of the algae was below 40 w%/w, then the whole algal biomass should be
anaerobically digested as the optimal strategy on an energy balance.
2.7 Light Transport
Visible light is part of the electromagnetic radiation spectrum ranging from 400 – 700 nm.
Electromagnetic radiation consists of photons and the energy each photon carries is dependent on
the wavelength of the photon, where photons that have shorter wavelengths have more energy
than photons with longer wavelengths. This relationship is defined by the following equation:
hc
E hf
(2.10)
33
where E is the energy a photon contains [J], h is the Planck’s constant [6.62607040x10-34
J·s], f
is the frequency [Hz], λ is the wavelength of the photon [m], and c is the speed of light
[299792458 m/s].
Light transport in the application of photobioreactors is concerned with the modes of light loss
which occur as light propagates through the mediums of air and water. Light loss through a
media is caused either through reflection (light propagating from one media to other), scattering
(mie, raylay etc...), and absorption (Grima et al. 1999). It is possible to estimate the average solar
irradiance on the surface of the earth as described by Grima et al. (1999).
2.7.1 Waveguide Optics
Optical waveguides are structures which transmit light typically in a material with a higher
refractive index than the surrounding medium. The refractive index of a material is a
dimensionless number that describes the speed of light propagation through the medium. Optical
fibres work on the basis of acting as a waveguide with total internal reflection. Total internal
reflection occurs when a ray of light strikes a medium boundary at an angle larger than the
critical angle with respect to the normal surface. The critical angle of a boundary between two
media is given by Snell’s law (equation 2.11)
𝜃𝑐 = arcsin (𝑛2
𝑛1) (2.11)
Where θc is the critical angle, n1 is the refractive index of the media with the higher refractive
index and n2 is the media with the lower refractive index. When the incident angle of light is
greater than the critical angle, the light it totally internally reflected, while incident angles less
than the critical angle are only partially transmitted.
Attenuation in an optical fiber is defined as the loss of optical power as light travels along the
fiber. Attenuation in an optical fiber is caused by absorption, scattering, and bending losses
associated with the optical properties of the waveguide and the wavelength of the wave being
34
propagated. Equation (2.12) describes signal attenuation as a unit of length (Integrated
Publishing 2012):
𝑎𝑡𝑡𝑒𝑛𝑢𝑎𝑡𝑖𝑜𝑛 = (10
𝐿) log10 (
𝑃𝑖
𝑃𝑜) (2.12)
Where Pi is the optical input power, Po is the optical output power, L is length, and attenuation in
this equation is in units of decibels per length.
The application of fibre optics in algal photobioreactors has been used before in suspended
cultures (Burgess et al. 1993, Erickson et al. 2011). Burgess et al. (1993) used optical fibres to
improve light distribution while growing marine algae which led to a culture dry mass of 1.9 g/L,
while cultures grown with an external light source only reached 0.8 g/L over the same time
period. Zijffers et al. (2008) has proposed a model and procedure for determining the light ray
distribution in tapered waveguides that can also apply to sandblasted surfaces.
When a light wave meets the boundary between two indexes and the incident angle of light is
greater than the critical angle, the standing wave penetrates into the external medium while still
being total internal reflection. This phenomenon is called an evanescent wave and it decays
exponentially with distance from the interface, typically with a characteristic penetration depth
of 50 to 100 nm (Nath and Anand 1998). Evanescent-wave coupling is a process where
electromagnetic waves are transmitted from one medium to another using an evanescent wave.
The process is mathematically similar to particle in a box, except using electromagnetic waves
instead of quantum-mechanical wave functions.
A recent publication by Ooms et al. (2012) demonstrated that cyanobacteria can be grown on an
evanescent field. The recorded evanescent field penetration was between 1-5 μm from the
surface depending on the incident angle. The conditions in which the cyanobacteria were grown
in did not provide indication of whether a biofilm had formed, or whether the biomass
accumulated resulted from settling. Ooms et al. (2012) did not record the growth rates of the
cyanobacteria or provide a precise thickness of the cyanobacteria film. Based on the results,
35
evanescent fields will not be useful in growing photosynthetic biofilms thicker than
approximately 10 μm, which would imply they cannot be used in a photobioreactor with the
intent of producing large quantities of algal biomass.
2.8 Summary of the Literature and Significance of the Objectives of the Thesis
The literature review has outlined the current state of algal biofilms and algal film
photobioreactors from a bioprocessing perspective. Compared to their suspended counterparts,
there is limited understanding on light transport within algal film photobioreactors. Algal film
photobioreactors found in the literature often take the form of algal turf scrubbers or rotating
algal biofilm systems, whose primary role in most of the studies is the removal of nutrients.
There are few attempts to understand the effects of fundamental surface properties of the
attachment material on algal biofilm growth. There have been attempts at growing a phototrophic
biofilm with evanescent field, but not on a light emitting waveguide. The effects of light
intensity and CO2 on algal film growth have not been investigated, nor has their combined
interaction effects been analyzed.
Due to the lack of studies on algal film photobioreactors, there are opportunities to expand the
scientific literature on this topic. Important questions which are absent from the literature, are the
feasibility of growing algal films on a light emitting waveguide, the effects material surface
properties have on algal biofilm growth, the effects of light and CO2 on algal biofilm growth. By
demonstrating the feasibility of grown an algal biofilm on a waveguide it will enable new
configurations of reactors to be tested for algal biofilms.
36
Chapter 3 Material and Surface Energy Effects on Algal Film Growth
Kinetics, Colonization and Lipid Content
Scott N. Genin, J. Stewart Aitchison, D. Grant Allen
Some of the contents of this chapter were published have been published in Bioresource
Technology (Published March 2014); ISSN: 0960-8524, and in Proceedings of SPIE 8923; DOI:
10.1117/12.2033794
Abstract
A parallel plate air lift reactor was used to examine the growth kinetics of mixed culture algal
biofilms grown on various materials (acrylic, glass, polycarbonate, polystyrene, cellulose acetate
and three types of embossed acrylic). The growth kinetics of the algal biofilms were non-linear
overall and their overall productivities ranged from 1.10-2.08 g/m2 day, with those grown on
cellulose acetate having the highest productivity. Overall algal biofilm productivity was largely
explained by differences in the colonization time which in turn was strongly correlated to the
polar surface energy of the material, but weakly correlated to water-material contact angle. When
colonization time was taken into account, the productivity for all materials except acrylic was not
significantly different, at approximately 2 g/m2 day. Lipid content of the algal biofilms ranged
from 6-8% (w/w) and was not correlated to water-material contact angle or polar surface energy.
Embossing V-grooved acrylic coupons resulted in a higher productivity from 1 g/m2 day to 1.7
g/m2 day. The results have potential application for selecting appropriate materials for algal film
photobioreactors.
3.1 Introduction and Significance
In previous studies of algal film photobioreactors, suitable materials for algal film growth were
chosen based on high single point productivities of many different materials (Johnson and Wen
2010) or high surface energies or high-water material contact angles (Christenson and Sims
2012). Each of these methods has disadvantages: it is costly and impractical to measure single
37
point productivity for all potential materials; there are multiple types of surface energies; and
water-material contact angle is a course measurement which accounts for multiple types of
surface and material interactions. While a single point productivity measurement can determine
the overall the productivity of algal biofilms, the colonization and conditioning phases of biofilm
formation, which are expected to have lower productivities, are aggregated into these values. It
has been shown by Sekar et al. (2004) and Finlay et al. (2002) that during the initial attachment
phase, different algal species show preferential attachment to different materials based on the
intrinsic material properties, therefore leading to differences in overall algal biofilm productivity
on different materials reported by Johnson and Wen (2010), Irving and Allen (2011) and
Christenson and Sims (2012) could be the result of different colonization times.
The objective of this study is to improve material selection for algal biofilm photobioreactors by
determining which intrinsic material surface energy properties affect algal biofilm productivity,
colonization and lipid content. To complete this objective, a parallel plate air lift (PPAL) reactor
was designed and built. The reactor consists of a glass case with two internal plates to which
various material coupons can be attached to rapidly test the productivity of algal biofilms grown
on various materials. The parameters measured in these experiments were biomass production,
fatty acid methyl ester (FAME) content, temperature and pH.
3.2 Materials and Methods
3.2.1 Reactor Design and Setup
The PPAL reactor (Figure 3.1) used in this study was designed to provide vertically grown algal
biofilms with consistent lighting, nutrients, and shear. The reactor case was constructed of glass,
with two vertical internal plates of cast acrylic which were secured by a silicone adhesive. The
reactor can hold 15 L of media and has the following dimensions: 41 x 20 x 25 cm3. Up to 20
coupons each with two different materials were placed in the reactor for each run, giving a total
of 40 samples. The materials were clipped to the internal plates with each material coupon size
approximately 2x8 cm2. The materials were weighed before the experiments and then again after
being cleaned and dried.
38
Figure 3.1 – PPAL reactor configuration and setup
The coupon materials tested were: glass, cellulose acetate, acrylic, polystyrene, polycarbonate
and silicone rubber. A separate test was conducted using three types of embossed acrylic
(horizontal lines, vertical lines, and v-grooves), which were designed, fabricated and
characterized as described by Sathananthan (2014). The selection criteria for the materials were
based on transparency, toxicity towards algae, and water-material contact angle. The material
coupons were placed in the reactor in a random order determined by a random number generator.
Past work by Irving and Allen (2011) determined that the presence of wastewater is an important
factor in enhancing the formation of an algae biofilm. In order to introduce the bacteria and EPS
required to form the biofilms, unsterile wastewater from Ashbridge’s Bay Wastewater Treatment
Facility, Toronto, ON, was blended with Fortified Bold’s Basal Media (FBBM) (Bold 1949) in a
ratio of 1:2. FBBM was buffered to pH 6.8 and prepared to have the following concentration of
nutrients as described in Table 3.1.
39
Table 3.1 – Fortified Bold’s Basal Medium
Chemical Initial Concentration
(mg/L)
NaNO3 250
CaCl2 18.9
MgSO4 36.8
K2HPO4 75
KH2PO4 175
NaCl 25
Na2EDTA 10
FeSO4 2.72
H3BO3 11.42
Na2SiO3 26.2
Trace metals
ZnSO4 4.95
MnCl2 0.92
MoO3 0.70
CuSO4 1
Co(NO3)2 0.31
Compressed air was provided at a constant rate of 0.990 L/min (Standard Temperature and
Pressure; 0o C and 1 bar) STP, where it was mixed with CO2 flowing at 10 mL/min to give a
total CO2 content of 1% by volume. The solution was sparged with air at 1 L/min in the reactor
for 24 hours before being inoculated. The inoculum contained seven algal species that were
purchased from the Canadian Phycological Culture Centre (CPCC) or the Culture Collection of
Algae and Protozoa (CCAP). The species used in this experiment were: S. obliquus (CPCC 157),
C. vulgaris (CPCC 147), Coccomyxa sp.(CPCC 508), Nannochloris sp. (CCAP 251/2), Nitschia
palea (CPCC 160), Oocystis sp. (CPCC 9) and Oocystis polymorpha. The cultures were
cultivated in a light incubator at 25 oC in 250 mL Erlenmeyer flasks on an orbital shaker set to
110 rpm before being used to inoculate the reactor.
A peristaltic pump (Cole Parmer Masterflex, Model# 7520-35) was used to add and remove
media from the reactor at a dilution rate of 0.96 day-1
. The dilution rate was set to be higher than
the growth rate of the suspended algae in order to wash out suspended algae which would
otherwise obstruct light from reaching the films and to ensure there is enough nutrients provided
to the biofilm. White light was provided by four 8 Watt Light Emitting Diodes (LEDs) that are
positioned outside of the reactor. A Variner Tris-buffer pH probe and stainless steel temperature
40
probe were used to record pH and temperature data continuously over the course of the
experiment.
The reactor operated in batch mode for 48 hours after inoculation before the pumps were started
to introduce fresh FBBM. The day the pumps were started was considered day zero, and three
samples of each material were removed from the reactor on days 0, 3, 5, 7, and 10. Suspended
algae samples were also taken from the reactor in triplicate. Each experiment was repeated three
times. The experiment involving the embossed acrylic was conducted differently due to the low
number of embossed coupons available. In the study, five coupons each of smooth acrylic,
horizontal lines, vertical lines and v-groove were placed into the reactor and the reactor was
prepped as described above. The coupons were only harvested on day 10, and a single point
productivity analysis was used to describe the productivity of the algal biofilms.
3.2.2 Sessile Drop Tests
To determine the polar and Lifshitz-van der Waals components of the surface energy, sessile
drop tests were conducted using reverse osmosis (RO) water, glycerol (Sigma Aldrich #G5516),
and hexadecane (Sigma Aldrich #H6703) on the following materials: glass, cellulose acetate,
acrylic, polystyrene, polycarbonate, and silicone rubber. Five μL of each liquid was pipetted onto
each material using a 10 μL pipette and a picture was taken using a Nikon D3000 camera with a
macro lens (model number: AF-S DX Micro Nikon 40 mmf/256) (Results in Appendix F). This
process was repeated three times for each material and the resulting pictures were processed
using imageJ v. 1.46. The Lifshitz-van der Waals and polar surface energies were then calculated
using the Good Van Oss model (Van Oss et al. 1988).
3.2.3 Sampling and Analysis
The harvested coupons were scraped clean and the biofilms were suspended in RO water. A
vacuum filtration unit was used to filter the suspended algal mass through Supor®-450 47mm
filters with a pore size of 0.45 μm. The filters were baked at 103 oC for 3 hours and weighed
before and after filtration to measure the difference in dry mass.
41
A minimum of three coupons on day 10 were harvested, the algal film biomass was then freeze
dried and the lipids were extracted using the Folch method (Folch et al. 1956) using 1:2 (v/v)
chloroform to methanol as the solvent. The methanol phase and polar lipids solution was
discarded to target the neutral lipids. The neutral lipids were then methylated using the Fatty
Acid Methyl Ester (FAME) technique based on the Microbial Identification System, Microbial
ID Inc. (MIDI Method) (Smid and Salfinger 1994). The samples were analyzed using gas
chromatography (Perkin Elmer Clarus 680 GC) with a special performance capillary column
(Hewlett Packard model # HP-5 MS, 30 m x 0.25 mm x 0.25 μm) and a flame ionization
detector. Hexadecane (Sigma Aldrich #H6703) was used as the internal standard and olive oil
was used as a calibration standard.
Scanning electron microscopy (SEM) was used to observe the presence of microbes and EPS
within the algae biofilm. Samples of live biofilm were taken while still attached to the substrate
and were submersed in a 1% (v/v) solution of osmium tetroxide for 10 min. Osmium tetroxide
bonds to lipids and increases the cell’s electron density. The samples were then loaded into a
Hitachi S-3400 N scanning electron microscope, frozen to -20 oC to preserve the biofilm
structure at a pressure of 220 Pa. At these conditions, the algal biofilm remains hydrated and
biofilm structures can be seen. Backscattering electron (BSE) mode was used to observe
microbes which had accumulated significant quantities of osmium tetroxide, which were
predominantly algae cells, while secondary electron (SE) mode was used to image the entire
biofilm including bacterial cells, EPS and inert solids (Results in Appendix E).
3.3 Results and Discussion
3.3.1 Algal Biofilm Growth Kinetics on Various Materials
The pH and temperature of the reactor was stable at 6.9 ± 0.2 and 23 ± 1 oC respectively
throughout the experiment. The stability of the pH in the system is likely due to the continuous
addition of fresh media into the PPAL system. The total suspended solids in the PPAL were
below 0.050 g/L, which represents an algal productivity in the suspended phase of 0.048 g/L day
or 0.72 g/day. Qualitative observations of the SEM images showed the biofilms predominantly
contained algae, particularly S. obliquus, Oocystis sp., C. vulgaris, and N. palea. Algal biofilms
42
grown on cellulose acetate tended to slough off the material when harvested on day 10, but the
biofilm remained intact in a detached state. The overall growth kinetics of the algal biofilms
grown on the various materials appear to be initially non-linear with lower productivities
followed by linear regions of growth with higher productivities (Figure 3.2). This trend is
observable in results by Schnurr et al. (2013) and Gross et al. (2013) which show periods of
initial slow growth followed by increased linear growth.
43
Figure 3.2 – Growth kinetics of algal biofilms grown on various materials. Error bars
show the standard deviation.
Linear growth curves for microorganisms in conventional bioprocessing systems suggest
chemical or mass transport limitations to growth. This implies there is either a nutrient diffusion
or light limitation within the biofilm. Modeling of algal biofilms by Flora et al. (1995) showed
the CO2 concentration within an algal biofilm dropped to zero by 200 μm depth. If this were the
0
5
10
15
20
25
0 2 4 6 8 10 12
Alg
al
Fil
m B
iom
ass
(g
/m2)
Time (days)
Glass
Run 1 Run 2 Run 3
0
5
10
15
20
25
0 2 4 6 8 10 12
Alg
al
Fil
m B
iom
ass
(g
/m2)
Time (days)
Silicone Rubber
0
5
10
15
20
25
0 2 4 6 8 10 12
Alg
al
Fil
m B
iom
ass
(g
/m2)
Time (days)
Polycarbonate
0
5
10
15
20
25
0 2 4 6 8 10 12Alg
al
Film
Bio
mass (
g/m
2)
Time (days)
Acrylic
0
5
10
15
20
25
0 2 4 6 8 10 12
Alg
al
Fil
m B
iom
ass
(g
/m2)
Time (days)
Cellulose Acetate
0
5
10
15
20
25
0 2 4 6 8 10 12Alg
al
Film
Bio
mass (
g/m
2)
Time (days)
Polystyrene
44
case, the algae up to the depth of 200 μm would be providing the bulk of growth of the algal
biofilm which would suggest algal biofilms thicker than 200 μm would exhibit linear growth
kinetics. The same concept could also be applied to light limitations.
3.3.2 Algal Biofilm Productivity
Past studies calculated overall algal biofilm productivity based on single point measurements
(Johnson and Wen 2010, Irving and Allen 2011, Christenson and Sims 2012, Gross et al. 2013)
or linear regressions over the entire growth period including the initial colonization time
(Schnurr et al. 2013). Figure 3.3 shows the algal biofilm productivities for this study based on
linear regressions conducted over the entire growth period. The productivity of the algal biofilms
on the materials were for 1.12 g/m2 day for glass, 0.97 g/m
2 day for acrylic, 1.25 g/m
2 day for
polycarbonate, 1.34 g/m2 day polystyrene and 1.52 g/m
2 day silicone rubber. Algal biofilms
grown on cellulose acetate had the highest overall productivity of 2.08 g/m2 day. The
productivities of the algal biofilms grown on cellulose acetate were statistically significantly
higher than those grown on all other materials except for silicone rubber at the 95% confidence
level. The overall productivity of the algal biofilms does not correlate to the water-material
contact angle (P=0.33) which is consistent with results obtained by Irving and Allen (2011), but
it does correlate to the polar surface energy of the material (P=0.01).
45
Figure 3.3 – Overall algal biofilm productivity. Error bars show standard deviation.
(Calculated from a linear regression from 45 data points collected during 3 runs)
In order to take into account the potential differences due to colonization, we subsequently
considered the overall growth period to consist of two phases: the initial colonization during
which the cells attach to the coupon material; and, the subsequent growth phase after the material
is covered by at least one layer of cells. To test whether the impact of the material persisted after
the initial colonization phase, a linear regression was conducted on the data from the kinetic
study where algal film biomass yields above 1 g/m2 were used. This 1 g/m
2 cut off point is the
approximate algal film biomass yield on a surface if the film was 10 μm thick. This is the
approximate thickness of an algal biofilm that is a single algae cell thick. Once a layer of cells is
established on the material of attachment, the cells growing or being recruited will interact with
the algal biofilm and not the material, and we’d expect this could reduce the effect of the
material surface properties on algal biofilm growth and attachment. The new calculated
productivity is shown in Figure 3.4.
0
0.5
1
1.5
2
2.5
Glass (33.7 ) Cellulose
Acetate (63.1)
Acrylic (66.8) Polystyrene
(72.8)
Polycarbonate
(79.1)
Silicone
Rubber (93.6)
Alg
al
Bio
film
Pro
du
ctiv
ity
(g
/m2 d
ay
)
46
Figure 3.4 – Revised algal biofilm productivity. Error bars show standard deviation.
(Calculated from a linear regression from 30 data points collected during 3 runs)
The revised productivities of the algal biofilms grown materials are not statistically different at
the 95% confidence level from each other when data points below 1 g/m2 are removed with the
exception of those grown on acrylic. The revised productivities for the materials are: 1.96 g/m2
day for glass, 1.92 g/m2 day for cellulose acetate, 1.21 g/m
2 day for acrylic, 1.96 g/m
2 day for
polystyrene, 1.58 g/m2 day for polycarbonate and1.79 g/m
2 day for silicone rubber. The revised
productivities do not correlate to the water-material contact angle (P= 0.32) or the polar surface
energy (P=0.45)
The algal biofilm productivity values are on par with those obtained by Johnson and Wen (2010)
(2.57-0.58 g/m2 day) Schnurr et al. (2013) (2.1-2.8 g/m
2 day), and Gross et al. (2013) (1-1.5 g/m
2
day). The algae cells in the PPAL reactor are not able to settle on the materials unlike the reactor
configurations presented by Schnurr et al. (2013), Irving and Allen (2011) and Johnson and Wen
(2010). Since the conditions between reactor operations are so different between this experiment
and the literature, it is difficult to conclude whether algal biofilms grown in a vertical orientation
have any disadvantage over algal biofilms grown in horizontal configurations.
0
0.5
1
1.5
2
2.5
Glass (33.7 ) Cellulose
Acetate (63.1)
Acrylic (66.8) Polystyrene
(72.8)
Polycarbonate
(79.1)
Silicone Rubber
(93.6)
Alg
al
BIo
film
Pro
du
ctiv
ity
(g
/m2 d
ay
)
47
The highest reported overall algal biofilm productivity in this study was 2.08 g/m2 day for those
grown on cellulose acetate which would result in an estimated total productivity for the reactor
of 0.12 g/day if all 40 coupons were cellulose acetate. The suspended algae productivity from the
reactor is calculated to be 0.72 g/day which is about 6 times greater than the algal biofilm
productivity for this reactor. The higher suspended algae productivity is due to the fact that the
reactor’s design and operation are not optimized for algal biofilm growth, but for the rapid
testing of many different material coupons.
Algal biofilms grown on the V-groove embossed acrylic had statistically significantly higher
single point productivity at the 95% confidence level than algal biofilms grown on smooth
acrylic or the acrylic with horizontal or vertical lines (Figure 3.5). The higher algal biofilm
productivity on the V-groove could be attributed to the presence of larger surface area of
attachment for algal biofilm growth. There is 48% more surface area for attachment on the V-
groove surface (23.71 cm2) compared to the smooth acrylic (15.98 cm
2). Algal biofilms grown
on the horizontal and vertical line patterns did not have a statistically significantly different
productivity than algal biofilms grown on smooth acrylic. The depths of the horizontal and
vertical lines were small (1.5 μm) compared to the size of the algae species (5 μm is the smallest
size).
48
Figure 3.5 – Algal biofilm productivity on the four types of embossed acrylic. Error bars
show standard deviation. (n = 5)
3.3.3 Colonization Time Analysis
Conceptually, colonization time is defined as the point at which at least one cell layer covers the
entire material, which is estimated to be 1 g/m2. This point can be determined from the linear
regressions described above using only algal biofilm yields greater than 1 g/m2, then by
determining the time when the algal biofilm yield of the regression is equal to 1 g/m2. The
colonization time is plotted for each material against the water-material contact angle and the
polar surface energy (Figures 3.6a and 3.6b, respectively). The negative colonization time for
cellulose acetate is a result of the fact that some colonization may have occurred during the two
days the algae are given to acclimatize to the reactor before the pumps are started, which was
chosen to be time zero. The negative colonization time for the cellulose acetate implies that
bacteria are able to colonize the material rapidly. Hodoki (2005) demonstrated that algal biofilms
had a higher growth rate on materials which were initially colonized with bacteria, thus bacteria
may be attracted to cellulose acetate and will attach and grow faster than the other materials,
which in turn would lead to a higher algal biofilm growth rate and lower colonization time.
0
0.5
1
1.5
2
2.5
Smooth V-groove Horizontal Vertical
Alg
al
Bio
film
Pro
du
ctiv
ity
(g
/m2 d
ay
) Run 1 Run 2 Run 3
49
Figures 3.6 - Colonization time vs. a) water-material contact angle and b) material polar
surface energy. Error bars show standard deviation. (n = 3).
Colonization time as defined in this study is poorly correlated to the water-material contact angle
(P=0.12), but is strongly correlated to the polar surface energy of the material (P=0.0001) as
shown in Figures 3.6a and 3.6b, respectively. This is counter to what Christenson and Sims
(2012) claimed regarding algal biofilm preferential attachment towards materials with a high
surface energy, but is in agreement with the results from Finlay et al. (2002) and those of Ozkan
and Berberoglu (2013). Ozkan and Berberoglu (2013) showed that green algae attachment is
very dependent on acid-base interactions between algae cells and surfaces, with charge and
Lifshitz-van der Waals forces being less important. Since the colonization time is a significant
fraction of the algal biofilm growth period for some materials, it has an impact on the overall
productivity. The correlation between colonization time and polar surface energy suggests that
acid-base surface energy interactions still play an important role in the growth of algal biofilms.
Cellulose acetate is known to degrade and undergo hydrolysis (Buchannan et al 1993). The
acetate film used in this experiment is a mixture of cellulose di-acetate and cellulose tri-acetate.
50
It was observed that cellulose acetate coupons lost 5±1% of their mass over the course of the
experiment, which suggests that microorganisms may be using cellulose acetate as a carbon
source. Buchannan et al. (1993) reported that cellulose di-acetate degrades to 20% of mass in a
wastewater treatment system within 4-12 days depending on acetate substitution, but cellulose
tri-acetate did not have any notable degradation after 28 days. If the data point for cellulose
acetate is removed on the basis that it maybe feeding the algal biofilm and therefore is not purely
a surface interaction, there is a correlation between water-material contact angle and colonization
time (P= 0.002, R2
= 0.67) and the correlation between polar surface energy and colonization
time remains strongly correlated (P= 0.0001, R2 = 0.80).
The overall algal biofilm productivity is negatively correlated to the colonization time (P=
0.0001), which implies differences in productivity of algal biofilms grown on the materials used
in this experiment are caused by differences in colonization time (Figure 3.7). Colonization
time, as described in this study, is a useful measurement for assessing algal biofilm formation on
materials. It can be used to assess the rate at which algal biofilms are capable of establishing a
foundation and at which material affects will have limited impact growth. The colonization time
of the algal biofilm represents the initial phases of microbial colonization and surface
conditioning. Palmer (2007) described the conditioning of a surface as the accumulation of
molecules at the solid-liquid interface on surfaces. Colonization time takes into account the
surface conditioning of the attachment material in addition to the cell attachment.
51
Figure 3.7 – Overall productivity in relation to the calculated colonization time
3.3.4 Lipid Analysis
The neutral lipid content for the algal biofilms grown on the various materials was 6-8% (w/w)
and was not statistically significantly different between materials at the 95% confidence level, as
shown in Figure 3.8. These results are consistent with the findings of Johnson and Wen (2010)
(6-9% w/w) and Schnurr et al. (2013) (5-10% w/w). The neutral lipid content in algal biofilms
was lower than those reported for suspended algae cultures, which is typically reported to be
between 10-50% depending on growing conditions and species (Chisti 2007). The neutral lipid
content for algal biofilms is likely lower compared to algae grown in a suspended culture due to
either the presence of bacteria and/or EPS. Bacteria and EPS could add to the total mass of the
biofilm while not significantly contributing to the overall lipid content.
y = -0.1861x + 1.9217
R² = 0.6187
P = 0.0001
0
0.5
1
1.5
2
2.5
3
-3 -2 -1 0 1 2 3 4 5 6 7
Ov
era
ll P
rod
uct
ivit
y (
g/m
2 d
ay
)
Colonization Time (days)
52
Figure 3.8 – Lipid content of algal biofilms grown on different materials. Error bars
show standard deviation. (6 samples were taken for 3 replicate experiments, n = 18)
The similarity of lipid content between algal biofilms grown on different materials, suggests that
algal species composition did not vary significantly between the biofilms and that material of
attachment does not affect algal biofilm lipid content. Seven different species of algae with a
range of lipid contents were used as the inoculum. If the species composition of the algal
biofilms grown on different materials varied significantly, it could cause the lipid content of the
algal biofilms to be different between materials. Results from Schnurr et al. (2013) demonstrated
that for algal biofilms inoculated with S. obliquus the neutral lipid content of the biofilm (5%
w/w) was significantly lower than those inoculated with N. palea (10% w/w).
Using the neutral lipid content, the lipid productivity was calculated (Figure 3.9). The lipid
productivity ranges from 0.06-0.13 g/m2 day and the differences in lipid productivity between
algal biofilms grown on different materials can be attributed to differences in algal biofilm
productivity. The surface area lipid productivities are lower than those of terrestrial crops (0.25
g/m2 day (Mata et al. 2010)), likely because the operating conditions for the reactor have not yet
been optimized and the algae in the suspended phase has been flushed out of the reactor and not
accounted for.
0
2
4
6
8
10
12
Glass Cellulose Acetate Acrylic Polystyrene Polycarbonate Silicone Rubber
Lip
id C
on
ten
t (%
w/w
)
53
Figure 3.9 – Lipid productivity of algal biofilms grown on different materials. Error bars
show standard deviation. (6 samples were taken for 3 replicate experiments, n = 18)
The lipid content of the algal biofilms grown did not correlate with the water-material contact
angle (P = 0.19) for each material and nor did it correlate with the polar surface energy (P =
0.68). Lipid productivity of the algal biofilms does not correlate to the water-material contact
angle (P = 0.74) nor to the polar surface energy of the material (P = 0.85). This is expected since
material properties should affect the rate of attachment and adhesion of algal biofilms to the
material and not affect the internal lipid content of the algae. It may not be possible to select or
design materials that can improve the lipid productivity of algal biofilms, and therefore, other
factors such as species or conditions that influence algal lipid content should be investigated
instead.
Algae species can have a preference in initial attachment depending on the material properties as
shown by results from Sekar et al. (2004), Finlay et al. (2002) and Ozkan and Berberoglu (2013).
Since the amount of biomass on the coupons was too low to conduct a lipid analysis at day zero,
results presented here cannot confirm this. The results from this study imply that while it is
possible that different algae species may initially (over 24-48 hours) colonize different materials
at different rates, the algal biofilms have a tendency to become more or less uniform in species
composition irrespective of the material properties.
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Glass Cellulose
Acetate
Acrylic Polystyrene Polycarbonate Silicone
Rubber
Lip
id P
rod
uct
ivit
y (
g/m
2 d
ay
)
54
Cellulose acetate appears to be an ideal material to grow algal biofilms but there was notable
difficulty in harvesting. Occasionally, on days 7 and 10, the entire film would fall off the
material and fall into the reactor; this likely indicates that the biofilm became too thick and the
adhesion between the material and the algal biofilm was not strong enough to maintain the algal
biofilm when disturbed.
While algal biofilms have a higher biomass concentration than suspended algae, they tend to
have a lower lipid content compared to suspended algae, as shown in this study and by others
(Johnson and Wen 2010, Schnurr et al. 2013). This is problematic for fuels derived from lipids
as it increases surface area requirements to meet the same demand. This could be improved with
reactor designs that maximize surface area to land area ratios. Based on the algal biofilm
productivity and lipid results from this experiment and the reactor configuration presented, an
algal biofilm grown on cellulose acetate, it would require 521 m2 of surface area or 347 m
2 of
land area to produce 1 kg of algal biomass on cellulose acetate. Assuming 6% neutral lipid
content, it would require 8680 m2 of surface area or 5710 m
2 of land area to produce 1 kg of
neutral lipids. With the reactor configuration presented by Christenson and Sims (2012), which
has an aerial biomass productivity of 21-30 g/m2 and lipid productivity of 2.2-2.5 g/m
2, would
require 400 m2 of land to produce 1 kg/day of algae oil. This land use is better than the lipid
productivity of open ponds, but there is potential to improve these ratios.
Demonstrating that algal biofilms can be grown in an airlift reactor has significant implications
for the scaling of algal biofilm photobioreactors. The design considerations, operating
parameters and scaling of airlift reactors is well known and documented (Chisti and Moo-Young
1987). The hydrodynamic flow in the PPAL reactor is similar to those which would be on a pilot
or commercial scale. The observations of algal biofilm growth kinetics and colonization time
found in the PPAL have potential to be translated to pilot or commercial scale airlift algal film
photobioreactors.
The results on how colonization time affects algal biofilm productivity have significant impacts
on future design considerations for algal film photobioreactors with respect to the material
selection and reactor configuration. Understanding that polar surface energy is strongly
55
correlated to the colonization time of algal biofilms, it is possible to select or engineer materials
that have low polar surface energies to reduce colonization time or select materials with high
polar surface energies to prevent the initial colonization of algal biofilms. It is possible to grow
algal biofilms in a vertical air lift reactor and get algal biofilm surface area productivities
comparable to those with a horizontal configuration. Growing algal biofilms in a vertical
orientation has potential to enable more efficient land use for algal biomass and lipid production.
3.4 Conclusions
The attachment material affects the overall algal biofilm productivity; with biofilms grown on
cellulose acetate had the highest overall productivity (2.08 g/m2 day) among the materials tested.
Differences in the overall productivities between algal biofilms grown on different materials
were largely explained by differences the colonization time; after the colonization time, biofilm
growth rate was independent of material at ~2 g/m2 day for all materials except acrylic at 1.2
g/m2/day. Embossing acrylic with V-grooves increased the observed productivity from 1 g/m
2
day to 1.7 g/m2 day. The colonization time was positively correlated to the polar surface energy
of the material. The lipid content of algal biofilms grown on different materials was not
statistically different among the materials tested.
56
Chapter 4 Waveguide Reactor for Growing Algal Biofilms
Scott N. Genin, J. Stewart Aitchison, D. Grant Allen
Some of the contents of this chapter published in Algal Research (ISSN: 0960-8524), and are
contained in a Provisional Patent: US62/151,283
Abstract
To enhance light delivery to algal biofilms, five different waveguide designs were developed.
Light emitting waveguides are capable of distributing a bright light source over a larger surface
area. The light emission from these waveguide designs was characterized and the algal biofilm
growth on waveguides was characterized in a parallel plate airlift reactor (17L). The light
intensity and CO2 concentration were varied in a 32 factorial design experiment to determine if
there were any interaction effects. Light emission from the waveguides could be altered by
changing the tapper angle or by notching the surfaces. Algal film growth kinetics on the
waveguides were overall non-linear, but had linear regions of growth. The waveguides achieved
an algal biofilm surface area productivity of 2.8 g/m2 day and an aerial productivity of 33.6 g/m
2
day. Algal film productivity displayed saturation kinetics with respect to light intensity and CO2
concentration, but the interaction effect of light and CO2 on productivity is likely non-linear.
Algal film biomass per photon consumed decreased with increasing light intensity when the
reactor was not CO2 limited. The results indicate the potential for algal biofilms to be grown on
light emitting waveguides which opens up the opportunity to explore new algal film
photobioreactor configurations.
4.1 Introduction and Significance
Algal film photobioreactors have the potential to reduce dewatering costs and have a comparable
productivity to raceway ponds. Current designs have focused on maximizing productivity and
nutrient removal through material selection and design. However, fewer studies have focused
analyzing the effects of illumination and carbon dioxide (CO2) concentration on algal film
57
growth. The transport of light in suspended photobioreactors is considered a serious problem due
to cell shading, light scattering and non-uniform optical absorption. Current research on algal
film photobioreactor design focuses on rotating algal biofilm (RAB) systems (Christenson and
Sims 2012; Gross et al. 2013; Blanken et al 2014) or on algal turf scrubbers (Craggs et al. 1996;
Mulbry et al. 2008; Johnson and Wen 2010; Ozkan et al. 2012). These reactors are based on the
principle of growing an algal biofilm on a rough attachment surface in which either the surface
or the water is moving. These RAB systems show promise as their reported aerial biomass
productivities are higher than those of raceway ponds (Christenson and Sims 2012; Gross et al.
2013). The design considerations for these systems have been investigated from algal film
productivity and nutrient removal standpoint, but have not investigated effects of light intensity
and CO2 concentration on algal film growth.
Recent studies by Schnurr et al. (2014) and Pierobon et al. (2014) have provided new insight into
new photobioreactor designs. In experiments by Schnurr et al. (2014) algal biofilms were grown
where light was incident through glass and the productivity was compared to algal biofilms
which were grown in a conventional manner where light was incident from the water side. The
results demonstrated that at the conditions tested, light direction did not impact algal biofilm
growth. Oms et al. (2012) demonstrated the possibility of growing cyanobacteria in the
evanescent field associated with an optical waveguide. While the biofilms only reached a
thickness of 10-15 μm, the results showed by both these studies demonstrate the potential to
grow algal biofilms on a light emitting surface.
Growing an algal biofilm on a light emitting surface presents a series of potential advantages:
When the attachment material and light source are integrated, the light is directly delivered to the
algal biofilm without shading from suspended algae to produce a more compact bioreactor.
However, the effects of CO2, illumination intensity and light direction on the growth kinetics of
an algal biofilm on a light emitting surface have not been investigated.
The objective of this study is to demonstrate the feasibility of growing algal biofilms on light
emitting waveguides and determining the combined effects of varying light intensity and CO2
concentration. To complete this objective, five different acrylic waveguides and a parallel plate
58
airlift (PPAL) reactor were designed and built. The parameters measured were biomass
production, fatty acid methyl ester (FAME) content, total nitrogen, total phosphorous,
temperature and pH.
4.2 Experimental Methods
4.2.1 Waveguide Design and Fabrication
Five different waveguide designs were fabricated out of optically transparent cast acrylic
(McMaster Carr #) with a top cross sectional area of 1.27x1.27 cm2 and a length of 25 cm
(Figures 4.1 a-e). Dimensions, tapering and notching specifications are provided in Table 4.1.
The tapper and notches in the waveguide cause light to leak or scatter out of the waveguide. The
taper in the waveguide dimension along the direction of propagation prevents total internal
reflection and as a result light leaks from the waveguide. The notches provide local scattering
centres and cause light trapped in the waveguide to scatter into the bioreactor. Red LEDs (3.5V
and 700 mA, 635 ±10 nm, see Appendix D for more information) provided by Pond Biofuels
Inc. were mounted to the top of the waveguide.
59
Figures 4.1 – Waveguide schematics for a) single wedge large notch, b) single wedge, c)
double wedge, d) single wedge small notch, e) double wedge small notch (Side view)
Table 4.1 – Waveguide specification
Angle of Taper
(degrees)
Number of
Notches
Notch Depth
(mm)
Notch spacing
(mm)
Single Wedge
Large notch
1.88 6 5.0 7.5
Single Wedge 1.88 0 0 0
Double Wedge 1.11 0 0 0
Single Wedge
small notch
1.88 167 0.25 0.2
Double Wedge
small notch
1.11 334 0.25 0.2
4.2.2 Light Intensity Measurements
The light emission from the waveguide was characterized by a photodiode (Thor Labs model#:
FDS010) which was scanned along the direction of light propagation in the waveguide at a
distance of 2.4 mm from the surface (Figure 4.2 a). The current and voltage provided to the LED
60
by a Pyramid brand variable power supply (model #: PS-32lab) was measured using a volt and
amp meter (Figure 4.2 c). The electrical input power to the LED was adjusted to control the light
emission and was calibrated using a Newport Silicon photometer (model #: 818-SL) which was
set to 635 nm, to confirm that over the electrical power range used in these experiments, the light
emission was linearly correlated to the electrical input power. The photon flux from the LEDs at
different input electrical power was measured using a Fieldscout Quantum Light Meter (model #:
3415F) and a calibration curve was generated. This calibration curve was used to estimate the
photon flux emitted from the surfaces of the waveguide.
Figure 4.2 – Waveguide light emission experimental setup a) schematic representation,
b) electrical circuit diagram of photodiode, c) electrical circuit diagram of power circuit
61
4.2.3 Waveguide Reactor Setup and Operation
The PPAL reactor (Figure 4.3) used in this study was designed to provide a constant shear force
on each waveguide, adequate mixing, and nutrients. The reactor case was constructed of glass,
with two vertical internal plates of cast acrylic which were secured by a silicone adhesive. The
reactor was filled with 17 L of media and has the following dimensions: 41 x 20 x 25 cm3.
Twenty-four waveguides were placed vertically in the down-comer of the PPAL for each run.
The red LEDs were mounted to the top of each waveguide in four parallel circuits and power
was supplied by a Pyramid brand variable power supply (model #: PS-32lab).
Figure 4.3 – Waveguide reactor schematic
Past work by Irving and Allen (2011) determined that the presence of wastewater is an important
factor in enhancing the formation of an algae biofilm. To introduce EPS and bacteria, unsterile
wastewater from Ashbridge’s Bay Wastewater Treatment Facility, Toronto, ON, was blended
62
with Fortified Bold’s Basal Media (FBBM) (Bold 1949) in a volumetric ratio of 1:2. FBBM was
buffered to pH 6.8 and prepared to have the following concentration of nutrients (Table 3.1):
NaNO3 250 mg/L, CaCl2 ⦁2H2O 25 mg/L, MgSO4⦁7H2O 75 mg/L, K2HPO4 75 mg/L, KH2PO4
175 mg/L, NaCl 25 mg/L, Na2EDTA 10 mg/L, FeSO4⦁7H2O 4.98mg/L, H3BO3 11.42 mg/L,
Na2SiO3⦁7H2O 58 mg/L, ZnSO4⦁7H2O 8.82 mg/L, MnCl2⦁4H2O 1.44 mg/L, Na2MoO3 0.70
mg/L, CuSO4⦁5H2O 1.57, and Co(NO3)2⦁6H2O 0.49 mg/L. The solution was sparged with air at
1 L/min in the reactor for 24 hours before being inoculated. The inoculum contained seven algal
species which were purchased from the Canadian Phycological Culture Centre (CPCC) or the
Culture Collection of Algae and Protozoa (CCAP). The species used in this experiment were: S.
obliquss (CPCC 157), C. vulgaris (CPCC 147), Coccomyxa sp.(CPCC 508), Nannochloris sp.
(CCAP 251/2), Nitschia palea (CPCC 160), Oocystis sp. (CPCC 9) and Oocystis polymorpha
(CPCC 35) and was prepared as described in Chapter 3. The reactor operated in batch mode for
48 hours before the pumps were started to introduce fresh FBBM. The day the pumps were
started was considered day zero, and the algal biomass on three waveguides was harvested from
the reactor on days 0, 3, 5, 7, 10, 12, and 14. The cleaned waveguides were then placed back into
the reactor. Suspended algae samples were also taken from the reactor in triplicate. Regrowth
experiments were conducted by placing the waveguides back into the reactor after harvesting,
then harvesting the front of all the waveguides on the final day (day 14).
For the single wedge large notch waveguides, the reactor was operated under different light
intensities and CO2 to compressed air ratios at a total flow rate of 1 L/min STP in a 32 factorial
experimental design, with triplicate experiments conducted at the center point (1% CO2, 7200
μmol/m2 sec). A dark control experiment, where the PPAL reactor was covered, was conducted
to determine whether an algal biofilm could grow in the reactor conditions without the presence
of light and at 1% CO2. For the single wedge, double wedge, single wedge small notch and
double wedge small notch waveguides, the reactor was operated under the same light intensity
(7200 μmol/m2 sec) and CO2 partial pressure (1%). A peristaltic pump (Cole Parmer Masterflex,
Model# 7520-35) was used to add and remove media from the reactor at a dilution rate of 0.90
day-1
to was out the suspended algae.
63
4.2.4 Sampling and Analysis
The algal biomass on the waveguides was harvested and suspended in RO water. A vacuum
filtration unit was used to filter the suspended algal mass through Supor®-450 47mm filters with
a pore size of 0.45 μm. The filters were baked at 103 oC for 4 hours and weighed before and after
filtration to measure the difference in dry mass.
Algal film biomass harvested from the single wedge large notch waveguides on day 14 was
freeze dried and the lipids were extracted using the Folch method (Folch et al. 1956) using 1:2
(v/v) chloroform to methanol as the solvent. The methanol phase and polar lipids solution was
discarded to target the neutral lipids. The neutral lipids were then methylated using the FAME
technique based on the Microbial Identification System, Microbial ID Inc. (MIDI Method) (Smid
and Salfinger 1994). The samples were analyzed using gas chromatography (Perkin Elmer
Clarus 680 GC) with a special performance capillary column (Hewlett Packard model # HP-5
MS, 30 m x 0.25 mm x 0.25 μm) and a flame ionization detector. Hexadecane (Sigma Aldrich
#H6703) was used as the internal standard and olive oil was used as a calibration standard.
The removal of nitrogen and phosphorous by the algal biofilms was evaluated at 1% CO2 partial
pressure and 7200 μmol/m2 sec. Nitrogen and phosphorous in the inlet and outlet streams were
measured using Hach reagent kits for total nitrogen (TNT 827) and total phosphates (TNT 844).
The total phosphorus concentration in the media was calculated based on the total phosphates.
During the experiment, algal biofilms were harvested at the same intervals to determine growth.
Algal biofilm productivity is calculated by either using a single point measurement (Johnson and
Wen 2010; Irving and Allen 2011; Christenson and Sims 2012; Gross et al. 2013), a linear
regression over the entire growth period (Schnurr et al. 2013) or through colonization time
analysis (Chapter 3). In this study, productivity was calculated using the colonization time the
method used as described in Chapter 3 which removes bias that colonization can introduce into
the productivity measurement.
64
The percent of nitrogen and phosphorous removed was calculated using equation (4.1) below:
𝑆𝑖𝑛−𝑆𝑜𝑢𝑡
𝑆𝑖𝑛× 100 = 𝑝𝑒𝑟𝑐𝑒𝑛𝑡 𝑟𝑒𝑚𝑜𝑣𝑎𝑙 (4.1)
where Sin and Sout are the concentration of the nutrients (nitrogen and phosphorous) in the inlet
and outlet respectively. All productivity confidence intervals are the 95% confidence interval
assuming a student-t distribution.
The gram biomass per mol photon was calculated using the following formula:
𝑔𝐵𝑖𝑜𝑚𝑎𝑠𝑠
𝑚𝑜𝑙𝑝ℎ𝑜𝑡𝑜𝑛=
𝑁𝑒𝑡 𝑊𝑎𝑣𝑒𝑔𝑢𝑖𝑑𝑒 𝑎𝑙𝑔𝑎𝑙 𝑓𝑖𝑙𝑚 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦
𝑇𝑜𝑡𝑎𝑙 𝑝ℎ𝑜𝑡𝑜𝑛 𝑓𝑙𝑢𝑥 𝑒𝑚𝑖𝑡𝑡𝑒𝑑 𝑓𝑟𝑜𝑚 𝐿𝐸𝐷 (4.2)
The area underneath the waveguide light emission profiles was calculated using the trapezoid
method of integration.
4.3 Results and Discussion
4.3.1 Waveguide Light Emission
The results shown in Figures 4.4 a-e were normalized to an input electrical power of 0.67W (at
this power the red LED produces 7200 μmol/m2 sec). For the single wedge large notch
waveguide (Figure 4.4a), the light emission from the front shows a regular cycle in light intensity
peaks, which coincide with the notches in the waveguide. A smaller cycle of light intensity was
also measured on the back. The light emission from the side of the waveguide decreased along
the length of the waveguide and did not show a cyclical pattern in light intensity. The highest
light intensity emitted from any waveguide was measured for the single wedge, large notch
waveguide at 3320 μmol/m2 sec at a distance of 40-45 mm along the waveguide on the input
surface. The light emission for the single wedge (Figure 4.4b) and single wedge small notch
waveguides (Figure 4.4d) followed similar exponential decay trends for all sides. The light
emission for the double wedge waveguide (Figure 4.4c) was more uniform compared to the light
65
emission from the other waveguides, but the light emission for the double wedge small notch
waveguide followed an exponential decay after 50 mm, which is based on a line of best fit
(Figure 4.4e). The ratio of light emitted from each waveguide to the incident light intensity did
not change with varying light intensity for all waveguide designs. The ratios are: 0.81, 0.89, 0.85,
0.68, and 0.83 for the single wedge large notch, single wedge, double wedge, single wedge small
notch, and double wedge small notch waveguides respectively. These results demonstrate the
ability to change the light emission profile of a waveguide by the addition of notches.
66
Figure 4.4 - Light emission profiles of the waveguides, a) – single wedge large notch, b)
single wedge, c) double wedge, d) single wedge small notch, e) double wedge small notch
67
4.3.2 Waveguide Reactor – Suspended Reactor
The pH and temperature of the reactor was stable at 6.8 ± 0.3 and 23 ±2 oC respectively
throughout the duration of the experiments. During the experiment, the total suspended solids
after day 3 remained below 0.025 g/L. In every experiment, it was observed that the total
suspended solids (TSS) decreased from day 1 to day 3, and then remained relatively stable
afterwards. The average TSS did not increase with increasing CO2, but did increase from low
light intensity (1600 μmol/m2 sec) to medium (7200 μmol/m
2 sec), then plateaued at high (12600
μmol/m2 sec) (Figure 4.5). The outlet nitrogen concentration decreased from day four to six, but
afterwards remained between the values of 19-23 mgN/L for the remainder of the experiment
(removal efficiency from day 6-13 was 40-49%) (Figure 4.6). The outlet phosphorous
concentration remained more consistent over the course of the experiment, ranging from 25-30
mgP/L (removal efficiency varied from 16-30%).
Figure 4.5 – Average TSS for the reactor runs using single wedge large notched
waveguides with varying light intensity and CO2 partial pressure. Error bars represent 95%
confidence intervals
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0 2000 4000 6000 8000 10000 12000 14000
Av
era
ge
TS
S (
g/L
)
Incident Photon Flux into Waveguide (μmol/m2 day)
ATM
1%
3%
68
Figure 4.6 – Nitrogen and Phosphorous concentrations for the inlet and outlet of the
waveguide reactor (Light: 7200 μmol/m2 sec, CO2: 1%). Error bars show standard deviation.
4.3.3 Growth Kinetics of Algal Biofilms on Light Emitting Waveguides
The overall growth kinetics of the algal biofilms grown on the waveguide notches, back and
sides were non-linear overall, but have did linear portions (Figures 4.7 a-e and 4.8 a-d). The
growth appears to be linear and then is followed by a plateau or sloughing. This trend is
consistent with data presented by Schnurr et al. (2013), and Gross et al. (2013). Linear (as
opposed to exponential) growth curves for microorganisms in conventional bioprocessing system
suggest chemical or mass transport limitations to growth. For the algal biofilms, this implies a
nutrient, diffusion, or a light limitation within the biofilm. Modeling of algal biofilms by Flora et
al. (1995) and Liehr et al. (1990) show the CO2 concentration within an algal biofilm drops to
zero at a depth of 200 μm and that light intensity drops off to 6.1% of the initial light intensity.
This implies that the fundamental growth kinetics of algal biofilms are likely limited by either
inorganic carbon or light at the low light intensity conditions tested. At the medium and high
light intensities, the algal biofilms are not entirely light limited, but since there are still regions of
linear growth, this suggests that light saturation of algal biofilms also induces linear growth
curves in algal biofilms. There also seems to be a photo inhibition effect when the CO2 partial
0
10
20
30
40
50
60
70
80
90
100
0
5
10
15
20
25
30
35
40
45
50
0 2 4 6 8 10 12 14
Rem
ov
al
%
Co
nce
ntr
ati
on
(m
g/L
)
Time (days)
Nitrogen Inlet
Nitrogen
Oulet
Phosphorous
Inlet
Phosphorous
Outlet
Nitrogen
Phosphorous
69
pressure was atmospheric since the algal film biomass was less on day 14 when the incident
photon flux into the waveguide was increased from 1600 μmol/m2 sec to 7200 μmol/m
2 sec. In
the dark control experiment (Figure 4.7b), the algal biofilm yield was not statistically
significantly different than zero, which implies that algal biofilms were not capable of growing
in the reactor without light.
Figure 4.7 – Algal growth kinetics on the large notch waveguides: a) Growth kinetics on
the various faces of the waveguide at 1% CO2 and 7200 μmol/m2 sec, b) Growth kinetics on the
front with CO2 = 1%, c) Growth kinetics on the front with CO2 = ATM, d) Growth kinetics on
the front with CO2 = 3%. Error bars represent standard deviation.
The growth overall growth kinetics as shown in Figures 4.7 b showed that increasing light
intensity (12600 μmol/m2 sec) caused the algal biofilms to reach a plateau at around 20 g/m
2.
70
Plateauing was common for algal biofilms grown at 7200 μmol/m2 sec at 1% CO2, but the
plateaus occurred at biomass yields above 30 g/m2 day. Algal biofilms grown on the single
wedge large notch waveguide reached higher algal biofilm yields, compared to algal biofilms
grown on the other types of waveguides (single wedge, double wedge, single wedge small notch,
double wedge small notch) (Figure 4.8 a-d).
Figure 4.8 – Algal biofilm growth kinetics on a) single wedge waveguides b) double
wedge waveguides, c) single wedge small notches and d) double wedge small notches (7200
μmol/m2 sec, CO2 = 1%). Error bars represent standard deviation.
Adding small notches to the waveguides appeared to increase the yield on the notched sides and
decreased the yield on the non-notched sides (Figures 4.8 a-d).This implies that algal biofilms
preferred to grow on the notched surface even though for the single wedge and single wedge
71
with small notches the light emission profiles did not vary significantly. This implies that
embossing the surface with structured surfaces larger than the algae cell enhances biomass
accumulation to the surface which is agreement with results observed in Chapter 3. Sloughing of
the algal biofilms on the back of the double wedge small notch was observed on days 12 and 14
(Figure 4.8 d).
The regrowth of algal biofilms on the front of the different styles of waveguides had similar
profiles to the initial growth (Figures 4.8 a-d), but the yields did not exceed the initial growth in
contrast to results by Christenson and Sims (2012), which show that the algal biofilm yield for
regrowth was significantly higher than the initial growth.
4.3.4 Algal Biofilm Productivity on Light Emitting Waveguides
The algal biofilm productivities on the front of the large notched waveguide ranged from 0.25-
2.9 g/m2 day depending on conditions (Figures 4.9 a and b). The highest productivity observed in
this study (2.9 g/m2 day) was at the conditions of 3% CO2 partial pressure and high light
intensity (12600 μmol/m2 sec); however this was not statistically different compared to the
following conditions: 1% CO2 with medium (7200 μmol/m2
sec) and high light intensity (12600
μmol/m2 sec), and 3% CO2 at medium light intensity (7200 μmol/m
2 sec). These productivities
were significantly higher than those reported by Christenson and Sims (2012) (1.4 g/m2 day) and
in Chapter 3 (1.2 g/m2 day) for algal biofilms grown on acrylic. The surface area productivities at
these conditions were also higher than for similar algal biofilms grown on other materials (Gross
et al. 2013) (1-1.5 g/m2 day on cotton in a RAB reactor), and comparable to the maximum values
reported by Schnurr et al. (2013) (2.1-2.8 g/m2 day on glass in a horizontal plate reactor).
72
Figure 4.9 – a) Algal biofilm productivity on the front of the single wedge large notch
waveguide at different conditions b) Algal biofilm productivity per single wedge large notch
waveguide at different conditions. Error bars show 95% confidence intervals.
Algal biofilm productivity on the large notch waveguide front was significantly higher than
growth on the sides or back of the waveguide (Figure 4.7 a). This observation was consistent
across all conditions tested for the large notch waveguide. This is in contrast to algal biofilms
grown on the single, double wedge waveguides, and double wedge waveguides with small
notches (Figure 4.10), where the growth on the front, sides and back of the waveguides were
73
similar even though the light emission from the sides of the waveguides is statistically
significantly lower than the front or the back (Figures 4.4 b and c).
Figure 4.10 - Algal biofilm productivity on single wedge, double wedge, single wedge
small notch and double wedge small notch, on each side and including regrowth (CO2 = 1%,
7200 μmol/m2 sec). Error bars show 95% confidence intervals.
The algal biofilm productivity on front, back, sides and regrowth of the single wedge (0.82 g/m2
day, 0.81 g/m2 day, 0.71 g/m
2 day, 0.86 g/m
2 day respectively) and on the double wedge
waveguide (0.57 g/m2 day, 0.61 g/m
2 day, 0.69 g/m
2 day, 0.68 g/m
2 day respectively) were not
statistically different (Figure 4.10). The light intensity emitted from the front and back surfaces
of the double edge waveguides was ~2 – 3 times larger than that emitted from the side surfaces
(Figures 4.4 b and c). It is possible that the light intensity emitted from the sides is sufficient
enough to saturate the algal biofilm. Algae grown in suspension under white light becomes light
saturated between 400-500 μmol/m2 sec (Melis 2009). Previous results from Johnson and Wen
(2010) and Christenson and Sims (2012) demonstrated that regrowth on materials, improved
algal biofilm productivity, but this result was not replicated in this study, possibly due to the
difference in materials used or the vertical orientation of the waveguides. In chapter 3, it was
demonstrated that acrylic was a poor material to grow algal biofilms on, and had the lowest
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Single Wedge Double Wedge Single Wedge Small
Notch
Double Wedge Small
Notch
Alg
al
Fil
m P
rod
uct
ivit
y (
g/m
2 d
ay
)
Front Back Side Regrowth
74
productivity out of the materials tested (glass, cellulose acetate, polycarbonate, polystyrene,
acrylic, and silicone rubber).
The algal film productivity on the front of the single wedge small notched waveguides (1.12
g/m2 day) was statistically significantly higher than the productivity on the back (0.44 g/m
2 day)
and the side (0.33 g/m2 day) (Figure 4.10). The light emission from the single wedge small
notched waveguides was similar to the light emission from the single wedge waveguides (Figure
3 b and d). The improvement in algal film productivity from the front of the single wedge small
notch waveguide compared to the back, sides and the front of the single wedge waveguide may
be the result of improved attachment of the algal biofilm. Chapter 3 saw a similar trend, where
embossing acrylic with microstructures in a parallel plate airlift reactor resulted in a 70%
increase in algal film productivity. The increase in algal film growth on the front of the single
wedge small notch waveguide appears to have come at the expense of growth on the back and
sides of the waveguide. The total algal biofilm growth on the waveguide decreased when the
single wedge was notched with small notches (Table 4.2).
At the operation conditions of 1 % CO2 and medium light intensity (7200 μmol/m2 sec), the
algal biofilm productivities on the front, back and side of the waveguide were 2.8 g/m2 day, 0.26
g/m2 day and 0.57 g/m
2 day respectively, which yields an overall algal film productivity of
0.00572 g/day on a single waveguide. With 24 waveguides in the reactor, the net reactor
productivity was 0.14 g/day and when considering the aerial foot print of the reactor, the
productivity was 1.7 g/m2 day. If the waveguide aerial foot print is considered, the aerial
productivity of the waveguide was 35.5 g/m2 day. It would be unreasonable to assume that the
ideal waveguide reactor would contain waveguides which were not spaced apart, so if a reactor
was designed in which the waveguides were spaced 1.27 cm apart, and the productivity obtained
in this study was transferable to the other reactor, the aerial productivity of the reactor could be
15.2 g/m2 day, which is comparable to results obtained by Christenson and Sims (2012) (21-30
g/m2 day). This implies that important design parameters for scaling up a waveguide algal film
photobioreactor would be waveguide size, packing, light emission and CO2 concentration.
75
The total algal film productivity per waveguide was not statistically significantly different except
between the single wedge vs. single wedge small notch at the 95% confidence level (Table 4.2).
For all waveguide reactor runs at 7200 μmol/m2 sec and 1% CO2 partial pressure, the suspended
productivity was not statistically significantly different from the total biofilm productivity
(defined as the algal film productivity on the waveguides only). The suspended productivity was
statistically significantly lower in the waveguide reactors than the productivity in the PPAL in
Chapter 3 (suspended productivity of 0.72 g/day). The total reactor productivity from the single
wedge waveguide reactor was statistically significantly greater than the productivity from the
single wedge small notch waveguide reactor. The light emission profiles from these two
waveguides are similar, so this suggests that the notched surface had a significant impact on the
productivity.
Table 4.2 – Suspended and attached estimation of productivities in the reactor at the following
conditions: 7200 μmol/m2 s, 1% partial pressure of CO2. (95% confidence intervals shown)
Waveguide
Type
Productivity
Per
Waveguide
(g/day)
Total
Biofilm
Productivity
(g/day)
Suspended
Productivity
(g/day)
Total
reactor
Productivity
(g/day)
Biofilm
Productivity
Percentage
Single Wedge
Large Notch
0.0057±0.001 0.14 ±0.02 0.19 ±0.03
0.33 ±0.05 42%
Single Wedge 0.0071±0.001 0.17 ±0.03 0.20 ±0.04 0.37 ±0.07 46%
Double
Wedge
0.0055 ±0.002 0.13 ±0.05 0.20 ±0.04 0.33 ±0.09 39%
Single Wedge
Small Notch
0.0038 ±0.001 0.09 ±0.03 0.11 ±0.02 0.20 ±0.05 45%
Double
Wedge Small
Notch
0.0038 ±0.002 0.09 ±0.05 0.14 ±0.03 0.23 ±0.08 39%
4.3.5 Substrate and Light Limitations
Algal biofilms grown at atmospheric CO2 demonstrated a statistically significant decrease in
productivity from low light intensity (0.52 g/m2 day) to medium (0.21 g/m
2 day) and high light
intensity (0.23 g/m2 day) as shown in Figure 4.7a. Increasing the light intensity from low (1600
μmol/m2 sec) to medium (7200 μmol/m
2 sec) at 1% and 3% CO2 resulted in statistically
significant increases in algal biofilm productivity from 0.61 g/m2 day to 2.8 g/m
2 day for 1%
76
CO2 and 1.2 g/m2 day to 2.8 g/m
2 day for 3% CO2. Increasing the light intensity to high (12600
μmol/m2 sec) did not improve the productivity of the algal biofilms at 1% and 3% CO2. A
multiple linear regression on the algal biofilm productivity does not yield a statistically
significant correlation for the front (P = 0.097), back (P = 0.163), or sides (P = 0.559) which
implies algal film productivity on the waveguide is a non-linear function of CO2 partial pressure
and light intensity or the number of data points is insufficient. A modeling study by Liehr et al.
(1990) on the effects of light intensity and CO2 on algal biofilm growth would imply that the
relationship is highly non-linear, which is in agreement with the results of this study.
The results from Figures 4.7 a and b show that algal biofilm productivity increases with light
intensity and CO2 concentration, but experience a saturation effect with respect to CO2 and light
intensity. Increasing the CO2 partial pressure from atmospheric (0.04%) to 1% improved algal
biofilm productivity at medium and high light intensities. This is counter to what Gross et al.
(2013) observed with their RAB system, where an increase in CO2 partial pressure beyond
atmospheric did not result in an increase in productivity, but is consistent with Blanken et al.
(2014). In both studies, the algal biofilms were partially exposed to the atmosphere. Modeling
studies by Liehr et al. (1990) and Flora et al. (1995) showed algal biofilms experienced
inorganic carbon diffusion limitations when the dissolved inorganic carbon concentrations
expected at atmospheric CO2 partial pressure.
Previous studies on the influence of light intensity on algal biofilm growth are limited. A study
by Schnurr et al. (2014) demonstrated that a decrease in light intensity from 100 μmol/m2 sec to
50 μmol/m2 sec resulted in a decrease in productivity from 1.7 g/m
2 day to 0.9 g/m
2 day. The
study did not examine light intensities or the possibility of light saturation. Planktonic algal
cultures will become light saturated and increasing the light intensity beyond the light saturation
point does not improve algal growth (Steele 1965, Melis et al. 1999, Melis 2009) and past the
saturation light intensity, there can be a decrease in algal cell growth (Baroli and Melis 1995).
When the algal biofilms were grown at 1% and 3% CO2, increasing light intensity past the
saturation point did not improve algal film growth, but did not decrease it either, whereas
increasing light intensity when atmospheric CO2 was sparged in, algal film productivity
decreased. This implies that when algal biofilms are carbon starved, increasing light intensity
77
past the light saturation point will hinder growth rates; whereas non-carbon starved biofilms will
not see a decrease or increase in growth rates. This suggests that increasing CO2 concentration
can offset the effects that high light intensity has on photo inhibition of algal biofilms. Pope
(1975) observed that for suspended microalgae inhibition of photosynthesis (CO2 fixation and
growth) increases with increasing light intensity beyond the light saturation point, but increasing
CO2 concentrations can decrease the effect that high light intensities have on photo inhibition.
There is evidence to suggest that an active photosynthetic carbon metabolism in the algae cell
prevents photoinhibition (Powles 1984).
4.3.6 Photon to Biomass Conversion
The grams of biomass produced per mol of photon emitted from the LEDs decreased with
increasing inlet photon flux (Figure 4.11). The highest biomass to photon ratio (0.074
gbiomass/molphoton) occurred at 1600 μmol/m2 sec and 1% CO2, while the lowest biomass to
photon ratio (0.003 gbiomass/molphoton) occurred at atmospheric CO2 and photon flux of 12600
μmol/m2 sec, which was statistically significantly different than the biomass to photon ratio with
the same CO2 conditions and lower photon flux of 7200 μmol/m2 sec. The gram biomass per mol
photon ratio was not statistically significantly different for the CO2 partial pressures at the same
photon flux (1600 μmol/m2 sec). This implies that the photon to biomass conversion is most
efficient at low light intensities and when the biofilm is not carbon limited. This is consistent
with the fundamental theories outlined by Osborne and Geider (1987), Melis (2009) and the
results on suspended algae which were reported by Melis et al. (1999). The photon to biomass
conversion ratio can be a helpful metric for understanding the light efficiency of algal film
photobioreactors.
78
Figure 4.11 – Biomass photon conversion ratios from algal biofilms grown on the single
wedge large notch waveguide. Error bars show the 95% confidence intervals calculated from a
linear regression (n = 18)
The biomass photon conversion ratio for algal biofilm systems is not presented in the literature,
but a comparison can be made to the theoretical maximum for suspended algae. The theoretical
maximum photon to CO2 conversion for C. vulgaris is reported to be 1 mol of CO2 sequestered
per 8 mol of photons (Melis 2009) and the CO2 to biomass conversion is 1.85 g of CO2 per 1 g of
biomass. Based on these numbers it is estimated that the theoretical maximum biomass ratio is
2.97 g/mol photon. The biomass photon conversion ratios calculated here are significantly lower
than this value.
4.3.7 Lipid Content
The neutral lipid content for the algal biofilms grown on the waveguides ranged from 12-15%
(w/w) and was not statistically significantly different at the 95% confidence level depending on
the CO2 partial pressure or light intensity. The results are higher than those reported by Johnson
and Wen (2010) (6-9% w/w) and results from chapter 3 (6-8% w/w), but are similar to those
found by Schnurr et al. (2013) (5-10% w/w) and by Christenson and Sims (11-12% w/w). For
the conditions of 1% CO2 partial pressure and 7200 μmol/m2 sec, the lipid productivity for algal
biofilms grown in the notch was 0.34-0.42 g/m2 day; aerial reactor productivity was 0.19-0.24
g/m2 day, and the waveguide aerial productivity was 4-5 g/m
2 day. The aerial reactor
79
productivity is lower than those of terrestrial crops (0.25 g/m2 day) and values reported by
Christenson and Sims (2012) (2.2-2.5 g/m2 day). The results in this study suggest that the lipid
content of algal films may not be affected by light intensity, which is consistent with the results
presented by Ho et al. (2012) for S. obliquus grown in suspension; however Guedes et al. (2010)
showed a decrease in lipid content of Pavlova lutheri with increasing light intensity.
4.3.8 Comparison of Algal Film Photobioreactors
Table 4.3 compares the algal film productivities, attachment material, light source and neutral
lipid content of the reactor in this study to other algal film photobioreactors reported in literature.
RAB reactors such as the ones designed by Christenson and Sims (2012) and Gross and Wen
(2013) continue to have the highest reported aerial productivity (20-31 g/m2 day and 10.5 g/m
2
day respectively), but direct comparisons can be difficult, because attachment material, light
intensity, algal culture composition, reactor configuration, and nutrient loads can impact algal
biofilm productivity (Christenson and Sims 2012, Schnurr et al. 2013, Genin et al. 2014). When
examining surface area productivity, the single wedge large notch waveguide (2.8 g/m2 day)
performs just as well as reactors developed by Christenson and Sims (2012) (2.5 g/m2 day),
Schnurr et al. (2013) and Gross et al. (2013). This indicates that light emitting waveguides
present a promising approach to the production of algal biomass.
Table 4.3 – Algal Film Photobioreactor Productivity comparison
Reactor Material Surface Area
Productivity
g/m2 day
Lipid
content
(w/w)
Species Light source Reference
Waveguide
Reactor
Acrylic 2.9 12-15% Mixed Red LEDs This Chapter
PPAL Cellulose
Acetate
2.1 6-8% Mixed White LEDS Chapter 3
Flat Plate Glass 2.8 5-10% S. obliquus Red LEDs Schnurr et al.
(2013)
RAB Cotton 3.51 7-8% C. vulgaris White Light Gross et al.
(2013)
Bench
scale RAB
Cotton
Rope
2.5 11.2-
12.4%
Mixed White light Christenson and
Sims (2012)
Turf
Scrubber
Concrete 0.7 20-25% B. braunii White light Ozkan et al.
(2012)
80
4.4 Conclusions
In this chapter, growth of algal biofilms on light emitting waveguides was demonstrated. The
design of the waveguides impacts the light emitted from the waveguides, which in turn, impacts
the algal biofilm productivity. The highest measured surface area productivity recorded was on
front of the single wedge large notch waveguides which was 2.9 g/m2 day, a FAME productivity
of 0.34-0.42 g/m2 day, a nitrogen removal efficiency of 40-49% and a phosphorus removal
efficiency of 15-30%. Algal biofilm productivity showed a dependency on light intensity and
CO2 concentration; however, algal biofilms became light and CO2 saturated. The interaction
effects that light and CO2 have on algal biofilm productivity is complex. The negative effect of
increasing light intensity beyond the saturation point on algal biofilm growth can be reduced by
increasing the CO2 concentration. Algal biofilms grown on the light emitting waveguides did not
show changes in neutral lipid content with the various light and CO2 conditions tested. The
results indicate the potential for algal biofilms to be grown on light emitting waveguides which
opens up the opportunity to explore new algal film photobioreactor configurations.
81
Chapter 5 Modeling Light and CO2 Growth Kinetics Dependence in Algal
Biofilms
Abstract
A model was developed to describe algal biofilm growth and estimate productivity based on
inorganic carbon concentration, illumination intensity and incident light direction. The model
considers the inorganic carbon utilization and production from photosynthesis, respiration and
diffusion. The overall pseudo-steady state material balance yielded a second order nonlinear
ordinary differential equation (ODE). This system was solved as a transient partial differential
equation (PDE) with a 4th
order Runge-Kutta algorithm until the steady state inorganic carbon
profile was reached. The results showed that algal biofilm growth kinetics followed saturation
kinetics with respect to inorganic carbon concentration and light intensity. Light direction did
affect algal biofilm productivities at certain conditions. A simplification of the model was
derived in which the biofilm was assumed not to be inorganic carbon limited which results in
zero order consumption kinetics with respect to inorganic carbon. This model was compared to
experimental data and the Monod maximum coefficient was estimated, which showed strong
agreement with values of the Monod maximum constant found in literature for algae.
5.1 Introduction
Models describing algal biofilm growth are not as well studied or understood as compared with
suspended systems where there are a number of models. Models developed by Liehr et al. (1988,
1989, 1990) and Flora et al. (1993, 1995) have studied diffusion and concentration profiles of
nutrients such as inorganic carbon, phosphorous, and pH into algal biofilms, but did not generate
algal growth profiles. The models proposed by Liehr et al. (1988, 1989, 1990) and Flora et al.
(1993, 1995) take into consideration the limitations imposed by carbon, light, and pH in algal
biofilms while using ion charge to modify the diffusion profiles. Liehr et al. (1988, 1989, 1990)
and Flora et al. (1995) based their model on the assumption that only CO2 was consumed by the
algal biofilm while the other species of inorganic carbon, HCO3- and CO3
2-, were not consumed.
Past experiments by Goldman and Graham (1981), Thielmann et al. (1990), and Watson (2009)
82
showed that algae have mechanisms for consuming HCO3- and CO3
2-, and Wolf-Gladrow and
Riebesell (1997) showed that neglecting the consumption of HCO3- by algal cells results in
significant deviations in the growth and inorganic carbon concentration profiles. The model
developed by Liehr et al. (1988, 1989, 1990) assumed that alkalinity was comprised of HCO3-,
CO32-
, H+, and OH
-, however, in algal film photobioreactor systems, Bold’s Basic Media (BBM)
contains phosphates which contribute to alkalinity. A model developed by Lin et al. (2003)
estimated the growth of algal biofilms, but neglected the effects of light intensity on algal biofilm
growth and assumed that only HCO3- was consumed by the algae.
While these models have been useful, they have not been compared to experimental data, nor
have analytical models for algal biofilm growth been developed. Most models are focused on the
diffusion of inorganic carbon species and pH profiles into the biofilm and do not address algal
biofilm growth. All models for algal biofilm growth (Liehr et al. 1988, 1989, 1990, Flora et al.
1993, 1995, Wolf et al. 2007) assume that light originates from the water side, which means the
algal biofilm is not attached to a light emitting source. A recent study by Schnurr et al. (2014)
demonstrated that algal biofilms not only grow on a light emitting surface, but the direction of
light does not affect algal biofilm growth kinetics. The study did not vary carbon dioxide
concentration or check whether there was an interaction effect between carbon dioxide and light
intensity.
Most of the models that have investigated the growth of algal biofilms have focused on the ion
and nutrient diffusion profiles within algal or phototrophic biofilms (Liehr et al. 1990, Flora et
al. 1995, Wolf et al. 2007), but have not focused on the effects of light direction and intensity on
the growth of algal biofilms. To help size future algal film photobioreactors, simple models that
can relate the important parameters to algal biofilm growth kinetics and productivity are needed
with preference for analytical models which can be applied to reactor design equations.
While many models have enhanced our understanding of light-inorganic carbon interactions in
algal biofilms, there are no rigorous comparisons between the models and experimental data. The
purpose of this study is to develop a model that describes the growth of algal biofilms and
examines the effects of inorganic carbon and light intensity on the growth kinetics and
83
productivity. The predicted growth kinetics were compared to experimental data presented in the
literature.
5.2 Theory
5.2.1 Model Development
The model developed describes inorganic carbon utilization in the algal biofilm, which is
assumed to have a uniform density and composition. Inorganic carbon and light are considered to
be the limiting conditions and all other nutrients are assumed to be in excess. In this pseudo-
steady state problem, the model assumes that microorganisms are not being removed or added to
the biofilm through attachment or detachment. In the model, the inorganic ion species, CO2,
HCO3-, and CO3
2- are aggregated into a single term representing all inorganic carbon (Figure
5.1).
Figure 5.1 – Schematic of the model showing light and inorganic carbon profiles
84
The model begins with the transient material balance of inorganic carbon at a point in the biofilm
that includes mass transfer by diffusion and generation/consumption:
𝐷𝜕2𝐶
𝜕𝑥2 + 𝑟𝑖 =𝜕𝐶
𝜕𝑡 (5.1)
Where, C [mg/cm3] represents the concentration of inorganic carbon, D [cm
2/day] is the
diffusion of inorganic carbon in the biofilm, t [day] is time, x [cm] is distance, and ri is the rate of
inorganic carbon generation or consumption [mg/day]. It is assumed that the steady state
diffusion of inorganic carbon into an algal biofilm can be reached faster than the algal biofilm
can grow. The transient problem was used because the solution for the steady state system using
the shooting method failed to converge at certain conditions. A further discussion of this can be
found in Appendix C.
For algal biofilms, the Monod model combined with the Steele relationship and a first order
respiration model is used, which is represented by equation (5.2).
𝑟 = −𝜇𝑚𝑎𝑥𝑥𝑓𝐶
𝐾𝑠+𝐶𝐹𝑙 + 𝑏
𝑥𝑓
𝑌 (5.2)
Where μmax is the Monod max constant for algae [1/day], xf is the biomass density as mass of
inorganic carbon [mgC/cm3], Ks is the Monod half-saturation constant for inorganic carbon
[mgC/cm3], b is the respiration coefficient [1/day], Y is the yield coefficient [mgBiomass/mgC]
and Fl is a ratio which is expressed by the Steele relationship (Steele 1965). Compared to past
models developed by Liehr et al. (1988, 1989, 1990) and Flora et al. (1993, 1995), the inorganic
carbon species are lumped together in one term, C. The Steele relationship is represented below
(Steele 1965):
𝐹𝑙 =𝐼
𝐼𝑠𝑒
(1−𝐼
𝐼𝑠) (5.3)
85
Where Fl is the light limitation fraction, I is the light intensity [μmol/m2 sec], and Is [μmol/m
2
sec] is the saturation light intensity. The Steele relationship describes the photoinhibition effect
that algae experience (Steele 1965, Melis et al. 1999, Melis 2009).There are alternative
relationships to describe the photo-inhibition effect such as the Haldane-type model; however,
these models are significantly more complex and are dependent on multiple parameters that must
be determined from experimental data. The light intensity in algal solutions or films is often
described by the Beer-Lambert law for light attenuation:
𝐼 = 𝐼0𝑒−𝛾𝑥 (5.4)
Where Ii is the light intensity at the surface of the biofilm or material [μmol/m2 sec], and γ is the
extinction coefficient [1/cm]. Most models on phototrophic biofilms that account for light (Liehr
et al. 1989, Flora et al. 1995, Wolf et al. 2007) use the Beer-Lambert law to describe light
attenuation. The light direction can be specified in the model as three possibilities: from the
water side, the material side, or from both sides.
The total flux of a substrate in an algal biofilm is represented by:
𝐽𝐶 = ∫ (𝜇𝑚𝑎𝑥𝑥𝑓𝐶
𝐾𝑠+𝐶∙
𝐼
𝐼𝑠𝑒
(1−𝐼
𝐼𝑠)
− 𝑏𝑥𝑓
𝑌) 𝑑𝑥
𝐿𝑓
0 (5.5)
where Jc is the inorganic carbon flux [mgC/cm2], and Lf is the thickness of the biofilm [cm]. The
growth of an algal biofilm is then described as the conversion of the inorganic carbon into
biomass as described below:
𝑑𝑀
𝑑𝑡= 𝑄𝐽𝑐 (5.6)
where M is the algal film biomass per surface area [g/m2], and Q is the yield coefficient of
inorganic carbon to biomass [mgBiomass/mgC].
86
Finally, the total inorganic carbon flux into the biofilm is represented by:
𝐽0 = −𝐷𝜕𝐶
𝜕𝑥|𝑥=0 (5.7)
There are alternative mathematical models for describing algal growth such as Droop kinetics
(Droop 1968); however, this model was not used because Goldman and Graham (1981) reported
that the Droop kinetics did not adequately describe inorganic carbon dependent growth of green
algae on a mass basis. The model as described above assumes inorganic carbon and light are the
two limiting growth factors, of which the Droop kinetics does not describe well.
5.2.2 Model Solution
The model uses a finite difference method assuming a transient state and solve until steady state
is reached. To solve this, the following equation is the transient diffusion into the algal biofilm:
𝑑𝐶
𝑑𝑡= 𝐷
𝑑2𝐶
𝑑𝑥2−
𝜇𝑚𝑎𝑥𝑥𝑓𝐶
𝐾𝑠+𝐶𝐹𝑙 + 𝑏
𝑥𝑓
𝑌 (5.8)
The transient equation is solved to steady state by using the finite discretization method on the
right hand side (RHS) and solving for dC/dt. A 4th
order Runge-Kutta is used to iterate the time
setup until steady state was reached based on a convergence criteria. The time step and
convergence were set to be adaptable within the following ranges: time: 0.0001-0.0002 days, and
convergence: 10-8
- 10-6
. This method was used instead of the shooting method because it was
capable of converging under all conditions tested. A detailed description of the shooting method
along with the issues of using the method can be found in Appendix C.
The boundary conditions applied were: [C] = [C]bulk at x = 0 and that d[C]/dx = 0 at x=Lf. The
flux of inorganic carbon into the biofilm (D*d[C]/dx at x = 0) is set to be equal to the reaction
rate integrated over the depth of the biofilm (equation 5.5). After the total inorganic carbon
87
consumed by the biofilm was calculated, the growth of the biofilm over a defined time period
was calculated by using a discretized form of equation (5.6).
5.2.3 Parameters
The parameters used in this model include an aggregate diffusion coefficient of inorganic carbon
in the biofilm (D), growth kinetics coefficients (μmax, Ks, Is), light extinction coefficient (γ),
biomass density (xf), and yield coefficient (Q). The light direction is also specified with three
possible light origins: water side, material side, and both sides. Values for these parameters were
taken from literature based on averaged values and are summarized in Table 5.1 along with
references.
Growth kinetics parameters used in the model are dependent on the algal species being modeled.
The Monod max constant for algae can range from 0.5-3 1/day depending on the spices
(Goldman 1974, Watson 2009). In this model, the value chosen is based on the average values of
the algal species present in the biofilm. For the simulations conducted in this paper, the Monod
max constant and saturation constant were based on average values for S. Obliquus (1.2 ± 0.4
1/day and 3*10-4
mgC/cm3) (Watson 2009). The light saturation coefficient for the algal biofilm
(Is) is based on values reported by Melis et al. (1999), which for white light is 400 μmol/m2 sec
(Melis 2009). Light attenuation through the biofilm was based on values used by Liehr et al.
(1990) and Flora et al. (1995). The yield coefficient was chosen to be 1 mgCBiomass/mgC,
which means that one gram of carbon in the algal biomass, was fixed from one gram of inorganic
carbon. A respiration rate of 0.1 1/day was chosen (Bowie et al. 1985).
The diffusion coefficient for inorganic carbon through a biofilm was adapted from the diffusion
coefficients reported by Flora et al. (1995) by taking the average of the diffusion coefficients for
each inorganic carbon species. The yield coefficient is derived from assuming a carbon to dry
weight ratio of 0.5 (Liehr et al. 1990) and assuming that one gram of carbon biomass results
from each net gram of inorganic carbon fixed. Experimental results place the density of the
biofilm between 90-160 g/L (Christenson and Sims 2012, Ozkan et al. 2012) and so value of 10
g/L was chosen for the model.
88
Table 5.1 – List of Parameters used in the Model
Parameter Units Value Reference
μmax days-1
1.2 Goldman (1974), Bowie
(1985), Watson (2009)
D cm2/day 1.14 Flora et al. (1995)
xf mgC/cm3 50 Liehr et al. (1990)
γ cm-1
140 Liehr et al. (1990)
Is μmol/m2 s 200 red, 400
white
Liehr et al. (1990), Melis
(2009)
Q mg Biomass/mgC 0.5
Ks mgC/cm3 3*10
-4 Watson (2009)
ρ mg/cm3 100 g/L Christenson and Sims (2012),
Ozkan et al. (2013)
b 1/day 0.1 Bowie et al. (1985)
Y mgC/mgC 1 Bowie et al. (1985)
5.2.4 Analytical Simplification of Model
A special condition arises when the algal biofilm is assumed to be saturated with inorganic
carbon in such that C >> Ks. Under this condition, the algal biofilm follows zero order growth
kinetics with respect to inorganic carbon and thus is light limited. Liehr et al. (1990) discussed
this condition and modeled the case when light was on the water side. Under these conditions, it
is possible to derive analytical expressions for the algal biofilm growth under two conditions,
namely with light direction from the water side or from the material side. These expressions are
summarized in the equations below:
𝑑𝑀
𝑑𝑡= 𝑄 ∫ (𝜇𝑚𝑎𝑥𝑥𝑓
𝐼0
𝐼𝑠𝑒−𝛾𝑥𝑒
(1−𝐼0𝐼𝑠
𝑒−𝛾𝑥)− 𝑏
𝑥𝑓
𝑌)𝑑𝑥
𝐿𝑓
0 (5.9)
𝑑𝑀
𝑑𝑡= 𝑄 ∫ (𝜇𝑚𝑎𝑥𝑥𝑓
𝐼0
𝐼𝑠𝑒(𝛾𝑥−𝛾𝐿𝑓)𝑒
(1−𝐼0𝐼𝑠
𝑒(𝛾𝑥−𝛾𝐿𝑓)
)− 𝑏
𝑥𝑓
𝑌)𝑑𝑥
𝐿𝑓
0 (5.10)
Integrating the right hand side (RHS) of equations (5.9) and (5.10) yields the following
equations:
89
𝑑𝑀
𝑑𝑡= 𝑄 (
𝜇𝑚𝑎𝑥𝑥𝑓
𝛾(𝑒
(1−𝐼0𝐼𝑠
𝑒−𝛾𝐿𝑓)
− 𝑒(1−
𝐼0𝐼𝑠
)) − 𝑏
𝑥𝑓
𝑌𝐿𝑓) (5.11)
𝑑𝑀
𝑑𝑡= 𝑄 (−
𝜇𝑚𝑎𝑥𝑥𝑓
𝛾(𝑒
(1−𝐼0𝐼𝑠
)− 𝑒
(1−𝐼0𝐼𝑠
𝑒−𝛾𝐿𝑓)
) − 𝑏𝑥𝑓
𝑌𝐿𝑓) (5.12)
Equations (5.10) and (5.11) are identical and are referred to as analytical equations because they
are analytical with respect to the growth rate. This implies that algal biofilms grown under light
limited conditions will have similar growth kinetics regardless of light direction. Results from
Schnurr et al. (2014) demonstrated that algal biofilms grown under their operating conditions,
light direction did not affect algal biofilm growth which is consistent with the analytical model.
Equation (5.10) was solved by using ode45 in MATLAB®, which uses a 4th
or 5th
order Runge-
Kutta numerical method. The MATLAB® function lsqcurvefit was used to estimate the Monod
maximum constant (μmax) to experimental algal biofilm growth data found in the literature, using
equation (5.11) and the parameters found in Table 5.1.The MATLAB® function lsqcurvefit uses
a least squares method for adjusting parameters. To determine the thickness of the biofilm when
respiration was equal to consumption of inorganic carbon, a GRG non-linear root solving method
was used on equation (5.10). The MATLAB® code used to solve these models is contained
within Appendix C.
The analytical model as described by equations (5.11) and (5.12) describe the algal biofilm
growth rate as a definable function. This does not describe the inorganic carbon profile within
the biofilm. In Chapter 6, a complimentary model which describes the transient and steady state
solution for inorganic carbon profiles within algal biofilms is presented and discussed.
5.3 Results and Discussion
5.3.1 Model Stability
The initial mass of the biofilm was kept constant throughout the simulation with a value of 1.5
g/m2. This value is greater than 1 g/m
2, which is reported to be the minimum amount of algal
biomass required to negate the effects that the material surface energies have on algal biofilm
90
colonization (Chapter 3). The bulk pH was held constant at 7.0 and all inorganic carbon
concentrations were calculated as such.
The stability of the model was affected by the step size (time) and the box size (distance). Failure
to converge could be remedied by changing the step size when needed. The transient model
would converge to steady state after 1 hour worth of time steps were taken, but this was
dependent on the inorganic carbon concentration at the biofilm-water interface.
5.3.2 Analytical Model Analysis
Algal biofilm growth rate as predicted by the analytical model (Figure 5.2) have an initial region
exponential growth, which then reaches the maximum growth rate followed by an exponential
decline in the growth rate that asymptotically approaches zero. This results in a predicted growth
curve which follows a sigmoidal pattern. The model suggests that even without considering cell
detachment from the algal biofilm that the biofilm will eventually stop growing in thickness. In
the equations (5.11) and (5.12), growth of the algal biofilm occurs when the rate of inorganic
carbon utilization is greater than the rate of respiration. The plateau as shown in Figure 5.2
occurs when the rate of inorganic carbon utilization is equal to the rate of respiration. There have
been observations of a plateau in algal biofilm growth (Gross et al. 2013, Chapter 3), but it is
unknown whether this plateau is caused by shear or whether the inorganic carbon respiration in
the biofilm is equal to the inorganic flux into the biofilm which can be represented by equation
(5.13).
∫𝜇𝑚𝑎𝑥𝑥𝑓𝐶
𝐾𝑠+𝐶𝐹𝑙𝑑𝑥
𝐿𝑓
0= 𝑏
𝑥𝑓
𝑌𝐿𝑓 (5.13)
In the case described by equation (5.13), the cellular respiration is equal to the consumption
which is a steady state condition. At this condition, the net flux of inorganic carbon into the
biofilm is zero, since the biofilm is consuming inorganic carbon at the same rate which it is
producing it. When this is reached, the biofilm has reached its maximum thickness for the
provided conditions. The growth rate of the algal biofilm is related to the thickness of the algal
91
biofilm. This suggests there is an optimal time to harvest the algal biofilm just after it has
reached its maximum growth rate and that allowing some algal biomass to remain after
harvesting would enable the algal biofilm to continue to grow at its maximum growth rate.
Figure 5.2 – Predicted algal film biomass (left vertical axis) and growth rate (right
vertical axis) using the analytical model with varying light intensities
The analytical model predicts that there is a maximum growth rate which is dependent on the
parameters and conditions (Figure 5.2) (Table 5.1). The maximum growth rate of the algal
biofilm increases with light intensity, but under very high light intensities (>1200 μmol/m2 sec),
the analytical model predicts that a thin film of algae will have a negative algal biofilm growth
rate. This occurs because the thin biofilm is so light saturated that the inorganic carbon
consumption within the algal biofilm is smaller than the inorganic carbon respiration. In essence,
the model predicts that photobleaching has occurred at these conditions. Biofilms that are already
established (i.e. thick), do not experience such phenomena, which suggests that under very high
light intensities, algal biofilms can grow, but regions close to the light source are non-productive
92
(not contributing to growth). It also implies that as the algal biofilm grows, the light intensity
should be increased to ensure the maximum growth rate at that light intensity is achieved. This
idea is tested in Figure (5.3), where the light intensity is varied starting from 50 μmol/m2 sec and
increased linearly with respect to time in such a way that the area underneath the light intensity
as a function of time is equal as if the light intensity were set to a constant 100 μmol/m2 sec.
Figure 5.3 – Predicted algal film biomass (left vertical axis) and growth rate (right
vertical axis) with constant light intensity and light intensity which varies linearly with time.
By varying the light intensity with time, the growth rate of the algal biofilm can be kept closer to
its maximum value. This results in a higher algal biomass yield in the long term. This can be
further manipulated to optimize the growth of algal biofilms by keeping the algal biofilm
continuously growing near its maximum growth rate.
While the analytical model suggests algal biofilm growth kinetics are non-linear, it is possible
that over a small time range, experimental observations would suggest that algal biofilm growth
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0
20
40
60
80
100
120
140
160
180
0 20 40 60 80 100 120 140
Alg
al
Fil
m G
row
th R
ate
(g
/m2 d
ay
)
Alg
al
Fil
m B
iom
ass
(g
/m2)
Time (days) Biomass Constant Light Intensity Biomass Increasing Light Intensity
Growth Rate Constant Light Intensity Growth Rate Increasing Light Intensity
93
kinetics are linear. Assuming that experimental measurements of productivity have a 95%
confidence interval of ±0.25 g/m2 day (Schnurr et al. 2013, 2014, Gross et al. 2013), using the
parameters listed in Table 5.1 with an initial light intensity of 100 μmol/m2 sec, the range at
which the measured productivity would within this range for approximately 28 days.
The analytical model shows that important parameters which contribute to algal biofilm growth
are μmax, xf and γ since they appear in the form:max fx
. Increasing the Monod max constant
(μmax) can be achieved by selecting faster growing algal strains. The reported range of Monod
max constants for algae are 0.8-3 1/day (Bowie et al. 1985). The carbon density of the algal
biofilm is dependent on the carbon composition of the algae along with the biomass density,
which could potentially be accomplished through strain selection. Decreasing the light
attenuation coefficient (γ) by decreasing the pigment density or the antenna size of the
chlorophyll would improve algal biofilm growth. The attenuation coefficient also appears in the
exponential. The most important parameters in in this combined term are the Monod maximum
constant and the extinction coefficient, since these parameters are known to be dependent on
algae species (Bowie et al. 1985). These two parameters impact the algal biofilm growth kinetics
and the maximum algal film biomass yield (Figure 5.4).
94
Figure 5.4 – Predicted algal biofilm growth kinetics with varying a) extinction
coefficient, b) Monod maximum constant and c) the estimated productivity with varying both
parameters. Io = 100 μmol/m2 sec and other parameters are as is in Table 5.1
Algal biofilm productivity decreases with increasing extinction coefficient and increases with
increasing Monod maximum constant (Figure 5.4 a and b). There is an observed interaction
effect between the extinction coefficient and the Monod maximum constant on the algal biofilm
productivity; however this interaction effect is non-linear (Figure 5.4 c). These coefficients are
predicted to have profound impacts on algal biofilm productivity since a change of the Monod
maximum constant from 1.2 1/day to 2.0 1/day can yield a 50-100% increase in productivity,
depending on the other parameters.
A potentially interesting variation on the model is to investigate light-dark cycles and how that
effects algal biofilm growth. In this analysis, the light intensity was made into a function of time
95
such that a 12h:12h light-dark cycle was constructed and there results were compared to growth
without dark-light cycles (Figure 5.5).
Figure 5.5 – Algal biofilm growth kinetics with a light-dark cycle of 12h:12h compared
to algal biofilm growth under constant illumination with a maximum light intensity of 100
μmol/m2 sec, a) over a period of 150 days, b) over a period of 22 days
The model suggests that algal biofilms which are exposed to alternating light cycles
would have a significantly lower growth rate than those exposed to constant illumination (Figure
5.5). This phenomena was also explored in the PHOBIA model (Wolf et al. 2007) and a cyclical
pattern in the growth rate was also observed. Experimental evidence has shown that algae grown
under alternating light-dark cycles had improved growth rates depending on the frequency and
ratio of light (Kok 1956, Degen et al. 2001). The model does not agree with experimental results
from the literature which may be because the model is not able to capture the light and dark
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0
10
20
30
40
50
60
70
0 20 40 60 80 100 120 140 160
Gro
wth
Ra
te (
g/m
2 d
ay
)
Alg
al
Fil
m B
iom
ass
(g
/m2)
Time (days)
a Biomass 12h:12h Biomass Constant Illumination
Growth Rate 12h:12h Growth Rate constant illumination
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0
5
10
15
20
25
0 5 10 15 20 25
Gro
wth
Ra
te (
g/m
2 d
ay
)
Alg
al
Fil
m B
iom
ass
(g
/m2)
Time (days)
b
96
cycles present within algae. Future models should be developed which can capture this
relationship.
5.3.3 Comparison to Experimental Data
The analytical model (equation 5.11) was compared to experimental data obtained by Schnurr et
al. (2014) (Figures 5.6 a-d). Current literature lacks sufficient data to estimate more than one
parameter. In the literature, the most common way to represent algal biofilm growth kinetics is
by single point productivity (Christenson and Sims 2012, Ozkan et al. 2012, Gross et al. 2013).
A few recent publications (Schnurr et al. 2013, 2014) provide values for biomass yield over
multiple time points. Equation (5.11) was used to fit the Monod max constant (μmax) to data from
the literature (Schnurr et al. 2014) summarized in Table 5.2. The predicted Monod max constants
for data obtained at 100 μmol/m2 sec (ranged from 1.45-1.88 1/days) were not statistically
different at the 95% confidence level and the values were in agreement with the Monod max
constant reported for S. obliquus grown in suspension by Goldman and Graham (1981). The
Monod constant was estimated to be statistically significantly different when the light intensity
was 50 μmol/m2 sec. This may be caused by the fact that data for the experiment conducted by
Schnurr et al. (2014) contained data points which were below the 1 g/m2 threshold discussed in
chapter 3 and thus, material-algae interactions and colonization may be contributing to the
growth of the algal biofilm. The model presented here, does not factor in attachment,
colonization or material-algae interactions, and thus may provide incorrect estimated parameters
for data with values below 1 g/m2.
97
Figure 5.6 – Comparison between experimental data (Schnurr et al. 2014) and model
predictions for inorganic carbon saturated biofilms (zero order kinetics) for the following
conditions: a) & b) light incident from the water side, c) & d) light incident from the material
side. Incident photon flux in all cases was 100 μmol/m2 sec.
Table 5.2 – Fitted parameters to data presented in literature by Schnurr et al. (2014) (95%
confidence levels presented)
Parameter 100 μmol/m2
sec - Water
Side - 1
100 μmol/m2
sec - Water
Side - 2
100 μmol/m2
sec - Material
Side - 1
100 μmol/m2
sec - Material
Side - 2
50 μmol/m2
sec - Water
Side
μmax 1.54 ±0.15 1.45 ±0.16 1.49 ±0.13 1.88 ±0.24 2.25 ±0.07
R2 0.77 0.97 0.94 0.91 0.98
The R2 value for the model fitted to experimental data (Schnurr et al. 2014), varied from 0.77 to
0.98. This suggests the model is capable of fitting experimental data. Unfortunately, there is not
enough data presented in the literature to accurately model and fit all the parameters.
98
5.3.4 Numerical Model: Growth Kinetics
The numerical model predicted that algal biofilm growth kinetics were initially non-linear with
low, but increasing productivities, followed by a distinct region of linear growth (Figures 5.7 a-c
& 5.8 a-f). The model predicts that the growth kinetics of algal biofilms at all tested condition
begin to plateau as time increases. This is consistent with experimental observations about algal
biofilm growth (Schnurr et al. 2013, Gross et al. 2013). For very thick biofilms, the model
predicts that the flux of inorganic carbon entering the biofilm will reach zero, which is consistent
with the model developed by Liehr et al. (1988, 1989, 1990). Linear growth curves for
microorganisms in bioprocessing systems suggest a chemical or mass transport limitation to
growth. In the case for this model, this implies that the biofilms become either light limited,
carbon limited or a combination of both, depending on the conditions.
99
Figure 5.7 – Predicted growth kinetics of algal biofilms at various carbon dioxide partial
pressures and different incident light directions: a) water side, b) material side, and c) both sides
100
Results from Figure 5.8 show that light intensity has a substantial effect on algal biofilm growth
kinetics, but there is an interaction effect with CO2 on the overall growth kinetics. When the light
intensity is increased beyond the saturation light intensity, the algal biofilms continue to have
faster growth kinetics up to a point. Figures 5.8 a-f shows that at 600 μmol/m2 sec, the predicted
algal film biofilm biomass at day 10 is lower compared to algal biofilm growth at 350 μmol/m2
sec. At day 26, the algal film biomass at 600 μmol/m2 sec is comparable to that of 350 μmol/m
2
sec. This initial slow growth is caused by the thin algal biofilm (15-100 μm thick) being over
saturated by light, which results in slow growth This occurs since the Steele relationship
produces values less than 1 when the light intensity at a given point in the biofilm is greater than
the light saturation.
101
Figure 5.8 – Growth kinetics of algal biofilms at different light intensities and directions
a): ATM-Water side, b): 2% CO2 –Water Side, c): ATM-Material Side, d): 2% CO2-Material
Side, e): ATM-Both Sides, f): 2% CO2-Both Sides
102
5.3.5 Numerical Model: Inorganic Carbon Profiles
The inorganic carbon concentration profiles within the algal biofilm were estimated for different
bulk inorganic carbon concentrations and different light directions (Figures 5.9 a-f). This was
done by solving the inorganic carbon profile for a prescribed film thickness using methods
described in section 5.2.2. The inorganic carbon concentration profile when the bulk inorganic
carbon concentration was set to 0.045 gC/L (approximately 2% partial pressure at pH 7) was
dependent on the thickness and on the light direction (Figures 5.9 a, c, and e). In the cases when
light was incident from the material side and when light was originating from both sides, the
inorganic carbon concentration in the algal biofilm did not surpass the initial inorganic carbon
concentration, unlike the cases when the light was incident from the water side. The inorganic
carbon profiles, in the case when light is entering from the water side were similar in shape to
those described by Liehr et al. (1990) (Figures 5.9 a and b).
103
Figure 5.9 – Inorganic carbon profiles in algal biofilms with Io = 100 μmol/m2 sec a)
light from the water side, CO2: 2%, b) light from the water side, CO2: ATM, c) light from
material side, CO2: 2%, d) light from the material side, CO2: ATM, e) light from both sides, CO2:
2%, and f) light from both sides, CO2: ATM.
104
The inorganic carbon profiles show that the profile is dependent on the thickness of the algal
biofilm. Algal biofilms with a thickness of 655 μm had inorganic carbon concentrations which
were greater than the inorganic carbon at the water-biofilm interface (Figures 5.9). Algal
biofilms 655 μm thick which were illuminated from both sides had a positive inlet flux, while
algal biofilms illuminated from the material side had a negative inlet flux. The light direction had
a significant impact on whether the algal biofilm had a positive inlet flux, even though the total
photon flux entering the algal biofilm is the same in Figures 5.9 a-f. Inorganic carbon profiles in
this case were similar to those calculated by Aquasim. This suggests that algal biofilms which
are illuminated from both sides have the potential to reach a greater maximum thickness than
algal biofilms illuminated from the material side when at low bulk inorganic carbon
concentrations. The results also indicate that light direction does the flux of inorganic carbon into
the algal biofilm at low inorganic carbon concentrations (0.0009 gC/L).
5.3.6 Numerical Model: Productivity
The model predicts that the relationship between productivity and light intensity for algal biofilm
is non-linear and is dependent on light intensity, incident light direction and inorganic carbon
concentration (Figures 5.10 a-c). For all light directions and carbon concentrations, the
productivity increases linearly at low light intensities (<1/2 light saturation). The estimated
productivities at high inorganic carbon concentrations (0.045 g/L to 0.09 g/L) are not statistically
different and represent the biofilm being saturated with inorganic carbon. The productivity
plateaus at high light intensities and the plateau is dependent on the inorganic carbon
concentration and light direction. Algal biofilms which have light supplied from both directions,
plateau at higher productivities at a given inorganic carbon concentration than algal biofilms
with light provided from the water or material side only. Algal biofilms with light provided from
the water side experience a decrease in productivity at very high light intensities, where the
maximum productivity is dependent on inorganic carbon concentration. When light is provided
from the material side, a plateau is reached, but a decrease in productivity is not observed.
Increasing the light intensity beyond the plateau continues to see marginal increases in
productivity.
105
Figure 5.10 – Predicted algal biofilm productivities with varying light intensity and CO2
partial pressure with different incident light directions: a) water side, b) material side c) both
sides
106
Predicted productivity values suggest that algal biofilms which are illuminated on both sides are
capable of reaching higher productivities when the algal biofilm would be considered light
saturated. When light originates from both the water and material sides at high light intensity
(600 μmol/m2
sec) and inorganic carbon saturated, the potential productivity is estimated to be
significantly higher which is estimated to be 7 g/m2 day. This implies that surface area
productivity could be improved by illuminating algal biofilms from the material and water sides.
Productivity values predicted by the model were on the same order of magnitude as
productivities found in the literature. The model predicts that for conventional algal biofilm
photobioreactors such as those developed by Christenson and Sims (2012) and Gross et al.
(2013), where light originates from the water side, at high light intensities (600 μmol/m2
sec), it
is possible to reach high productivities of 4.3 g/m2 day at high light intensities and saturated
inorganic carbon concentrations. This surface area productivity is higher than most reported in
the literature. The model predictions in Figures 5.10 a-c used red light as the saturation light
intensity.
The model suggests that productivity shows saturation kinetics with respect to inorganic carbon
at values greater than 1% CO2 partial pressure. Past experiments performed by Gross et al.
(2013) demonstrated that algal biofilms grown on the rotating film photo bioreactor did not
experience an improvement in productivity when the carbon dioxide partial pressure was
increased from 0.03% to 1%. This result implies the algal biofilms were saturated with inorganic
carbon. The light intensity used by Gross et al. (2013) was 110-120 μmol/m2
s and at this light
intensity the model predicts there would be a significant improvement in productivity from
0.03% to 1%. This difference may be caused by the design they implemented, which exposes the
algal biofilm to the atmosphere. This may improve the diffusion of carbon dioxide and inorganic
carbon into the algal biofilm and hence saturate the biofilm.
The estimated algal biofilm productivity does not follow the trend which was observed in chapter
4, where algal biofilms grown at atmospheric CO2 experienced significant decreases in
productivity as light intensity was increased. In the model, there is no direct interaction between
the light intensity component (the Steele relationship) and the inorganic carbon consumption (the
107
Monod kinetics). The combined Monod kinetics and Steele relationship is not adequate in
describing all the aspects of algal growth. More advanced descriptions of algal growth will be
needed, such as model based on the fundamental metabolisms of algae.
5.3.7 Model Limitations
The model has made significant progress in developing tools for predicting algal biofilm growth
which are dependent on the limiting conditions for growth. The model currently does not have a
method for estimating algal biofilm growth under dark conditions. Another problem is that there
is insufficient data within the literature to estimate the growth parameters: μmax, γ, and xf. In the
literature the number of data points rarely exceeds 18, or 9 non duplicated results, which makes
estimation of more than one parameter difficult.
The model had troubles with predicting inorganic carbon profiles under the following
circumstances: when a light source was present on the material side, low inorganic carbon
concentration such that C ~ Ks, and when the biofilms were thick. Numerical techniques such as
decreasing the step size and adaptable tolerances did not resolve the issues. Building in manual
checks into the algorithm did eventually resolve these issues.
5.4 Conclusions
A mathematical model was developed that describes algal biofilm growth as a function of
inorganic carbon and light intensity. The results showed that algal biofilms exhibit regions of
linear growth, which is consistent with experimental observations, but the growth approaches an
asymptote, where the cellular respiration is equal to the inorganic carbon consumption, upon
which the flux of inorganic carbon into the biofilm is zero. The predicted growth kinetics showed
saturation effects with respect to light intensity and inorganic carbon concentration, regardless of
light direction. An analytical simplification of the model assuming the concentration of inorganic
carbon was significantly higher than Ks showed that the light direction could not affect algal
biofilm growth rates. The predicted productivities of the model are in agreement with those
observed in the literature.
108
The analytical model was compared to algal biofilm growth data found in the literature, but due
to the scarcity of data, only one parameter (Monod maximum growth constant) could be
estimated. The R2 for the model ranged from 0.77 to 0.98 and the predicted Monod maximum
constant was consistent with the values reported for the literature. The analytical model
predictions were identical to those predicted by the numerical model when the inorganic carbon
concentration was set to excess.
109
Chapter 6 Analytical Model of Substrate Profiles in Phototrophic Biofilms
Abstract
An analytical model was developed to describe the concentration of a substrate in a phototrophic
biofilm. The model proposes a non-homogenous partial differential problem with one
homogeneous boundary condition which is then separated into two problems. This creates a
partial differential equation and an ordinary differential equation. The solutions to the associated
problems are then found using the separation of variables method and a double integration
respectively. A final solution is found as the sum of both problems. In the model, the substrate
was assumed to be inorganic carbon. The predicted steady state conditions were in agreement
with the numerical model presented in Chapter 5. For a uniform initial concentration, steady state
conditions were reached on the time scale of minutes. The inorganic carbon profiles within the
algal biofilms were found to be dependent on the direction of the incident light (material side vs.
water side). Varying the mass transfer Biot number changed the magnitude of the concentration
within the algal biofilm, but not the general shape of the profile, as expected.
6.1 Introduction
As discussed in Chapter 5, it is possible to derive an analytical expression for the growth rate of
an algal biofilm, but an analytical model describing the diffusion and consumption of the
nutrients in the biofilm has yet to be developed (Liehr et al. 1990, Flora et al. 1995, Wolf et al.
2007). Analytical solutions for biofilms models can be obtained if zero order consumption
kinetics are assumed; however, these require a calculation of the minimum substrate
concentration. This is not possible in an algal biofilm that is light limited, due to the asymptotes
existing in the minimum substrate calculations (detailed explanation in Appendix C). This
chapter compliments the discussions in Chapter 5, but focuses on the mathematical development
of an analytical solution. The work here was developed in partnership with Pedro Isaza from the
Department of Mechanical and Industrial Engineering at the University of Toronto. Pedro
contributed to the analytical mathematics presented in this chapter.
110
6.2 Model Description
An analytical solution for the transient diffusion equation in an algal biofilm can be derived if the
rate of consumption term is of zero order. This condition has applications in algal biofilm
systems where light is considered an input (examples include entrapped photosynthetic
organisms). In this section, various solutions are explored and shown how they apply to the case
of phototrophic biofilms. The intent is to derive a model with a broad application where light is
incident from two different sides (material and water). Consider the phototrophic biofilm
systems with a liquid boundary layer shown in Figures 6.1 a and b.
Figure 6.1 – Schematic for diffusion of a substrate S in a biofilm with boundary layer
with two scenarios: a) light originating from the material of attachment, and b) light originating
from the water side.
111
For this problem, a PDE can be formulated describing the transport via diffusion for a generic
substrate (in the biofilm), subject to generation/consumption, as follows:
2
max
2
( , )( , )( )
( , )
f f
l
s
x S x t xS S x tD F x b
t x K S x t Y
(6.1)
In equation (6.1) Fl(x) is a function accounting for the effect light on the reaction kinetics, D is
the diffusion coefficient of the substrate in the biofilm [cm2/day], μmax is the Monod maximum
constant [1/day], xf is the concentration of the substrate in the algal biomass [mgS/cm3], Ks is the
Monod saturation constant for substrate S [mgS/cm3], b is the respiration coefficient for S
[1/day], and Y is the substrate conversion coefficient [mgSbiomass/mgS]. Typically Fl(x) is
unitless, and can be represented by the Steele relationship (Equation 5.3) or other mathematical
expressions such as those presented by Bannister (1979) and Aiba (1982). In this chapter Fl(x)
will be expressed by the Steele relationship and the Beer-Lambert law.
Boundary and initial conditions are also formulated for the problem depicted in Figure 6.1, and
are the following:
B.C #1:0
0x
S
x
@ x = 0 (6.2)
B.C. #2: f
fx L bx L
SD h S S
x
@ x = Lf (6.3)
I.C: 0( , 0)S x t S @ t = 0 (6.4)
Where h is the mass transport coefficient in the boundary layer [cm/day], and Lf is the thickness
of the biofilm [cm]. Boundary condition #2 arises from the assumption of a thin film diffusion
model in the aqueous phase. Boundary condition #1 requires symmetry at the origin, thereby
assuming that the substrate cannot diffuse into the attachment material.
112
For the zero order reaction kinetics considered here, Equation (6.1) simplifies to:
2
max2
( , ) ( , )( )
f
f l
xS x t S x tD x F x b
t x Y
(6.5)
Since the non-homogeneous term in the PDE is a function of the spatial direction only, and the
non-homogeneity (bS ) at the boundary is a constant, a solution can be found by proposing two
problems as follows (Hahn and Özişik, 2012, Chapter 3):
*( , ) ( , ) ( )S x t S x t x (6.6)
Substituting equation (6.6) into equation (6.5) yields:
* 2 * 2
max2 2
( , ) ( , ) f
f l
xS x t S x t dD D x F x b
t x dx Y
(6.7)
The problem can now be separated into two, with a PDE describing *( , )S x t and an ODE
describing 𝜑(𝑥). For convenience, all of the non-homogeneous terms are retained in the φ(x)
problem.
Applying equation (6.6) onto the boundary conditions and initial conditions (Equations: 6.2-6.4)
yields:
B.C #1:*
0 0
0x x
S
x x
@ x = 0 (6.8)
B.C. #2: * ( )f f
fx L f bx L x L
S dD h S L S
x dx
@ x = Lf (6.9)
I.C: *
0( , 0) ( )S x t S x @ t = 0 (6.10)
113
The summarized resulting problems can be separated into the time dependent (transient) and
non-time dependent (steady state). These are presented below:
Transient Problem:
S*(x,t) PDE.: * 2 *
2
( , ) ( , )S x t S x tD
t x
(6.11)
BC: *
0
0x
S
x
,
**
f
fx Lx L
SD h S
x
(6.12a&b)
IC: *
0( , 0) ( )S x t S x (6.13)
Steady State Problem:
φ(x) ODE: 2
max20
f
f l
xdD x F x b
dx Y
(6.14)
BC: 0
0xx
, ( )
f
f bx L
dD h L S
dx
(6.15a&b)
6.2.1 PDE Solution
Since S*(x,t) consists of a homogeneous PDE and with homogeneous B.Cs., the method of
separation of variables can be applied directly. Begin by assuming that:
* ( ) ( )S X x G t (6.16)
Substituting equation (6.16) into (6.11) one obtains:
2
2
2
1 ( ) 1 ( )
( ) ( )
dG t d X x
DG t dt X x dx (6.17)
114
where λ is the separation constant and is assumed to be negative in order force the desired a
boundary value problem in the x direction (Hahn and Özişik, 2012, Chapter 3). Isolating the
temporal ODE section of the problem results in:
Time Problem:
2( )
( )
dG tDdt
G t
which can be easily shown to solve to:
2
1( ) exp( )G t C Dt (6.18)
The spatial ODE can also be isolated from equation (6.17) as follows:
Spatial Problem:
2
2
2
( )( )
d X xX x
dx
Which solves to (Hahn and Özişik, 2012, Chapter 3)
2 3( ) sin( ) cos( )X x C x C x (6.19)
Applying now equation (6.16) onto the first boundary condition given by equation (6.12a) one
finds:
𝑑𝑋(𝑥)
𝑑𝑥|𝑥=0 = 0
Which upon substitution of equation (6.19) yields:
2 3cos( 0) sin( 0) 0C C
115
The above requirement can only be satisfied when C2 = 0, and simplifies equation (6.19) to:
3( ) cos( )X x C x (6.20)
Following a similar procedure, and applying equation (6.19) onto the second boundary condition
(6.12b) yields:
( )
( )f
fx L
dX xD h X L
dx (6.21)
Substituting equation (6.20) into (6.21) yields:
3 3sin( ) cos( )f fD C L hC L
Where 𝐶3 ≠ 0 as it will yield the trivial solution. Rearranging the equations, and allowing 𝜆 to
satisfy the boundary condition, one arrives at the transcendental equation for the problem:
tan( ) where 1,2,3,...n n f
hL n
D (6.22)
Note that the subscript n is introduced as there are infinity eigenvalues,n , which will satisfy this
requirement.
Letting βn = λn*Lf yields another form of the transcendental equation:
tan( )f
n n m
h LBi
D
(6.23)
Where hLf/D is the mass transfer Biot number Bim. This represents the ratio of resistance to mass
transport imparted by diffusion in the biofilm relative to convection in the boundary layer.
Having identified the eigenvalues, the most general solution to the problem is comprised of the
116
sum of all the solutions (sum of the product of equations 6.20 and equation 6.18 for every λn ) as
described by Hahn and Özişik (2012, Chapter 3):
* 2
1
( , ) cos( )exp( )n n n
n
S x t C x Dt
The non-homogeneous initial conditions given by equation (6.13) is then applied yielding:
*
0
1
( , 0) ( ) cos( )n n
n
S x t S x C x
(6.24)
The above expression is a Fourier series expansion of So – φ(x) in terms of the orthogonal
function cos( )nx over the interval 0 ≤ 𝑥 ≤ 𝐿𝑓. As described in Hahn and Özişik (2012), due to
orthogonality, when both sides are multiplied by the orthogonal function cos( )mx for an
arbitrary eigenvalue (m ), and integrated from 0 to Lf, the result is the following:
0
0 cos( )cos( )
( )
fL
m n
n
if n mx x dx
N if n m
(6.25)
Where N(λn) is the norm. The implication of applying this operations on equation (6.25) is that
all the terms of the summation will be zero when 𝑛 ≠ 𝑚. As such it becomes possible to identify
the coefficients (nC ) in the summation as follows:
0
0
2
0
( ) cos( )
cos( )
f
f
L
n
n L
n
S x x dx
C
x dx
(6.26)
Where ( nC ) is dependent on the function 𝜑(𝑥). This needs to be solved for two different cases:
(1) light incident from the material side and (2) light incident from the water side.
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6.2.2 ODE Solution
Consider the ODE problem as detailed by equation (6.10) and 6.11 a-b. Recall equation 6.10 as
the following:
2
max2
( )( )
f
f l
xd xD x F x b
dx Y
(6.27)
Which for simplicity can be represented as the following:
2
2
( ) ( )d x g x
dx D
Where:
max( ) ( )
f
f l
xg x x F x b
Y
The solution to the Ode can be found by converting to a double integral to find:
1 2
1( ) ( )x g x dxdx C x C
D (6.28)
Where C1 and C2 are integration constants to be identified by the boundary conditions of the
problem. Again for brevity of the solution, let the double integral of g(x) with respect to x be f(x)
and now which equation (6.28) can be written as:
1 2
1( ) ( )x f x C x C
D (6.29)
Applying the first transformed boundary conditions given by equation (6.15a) yields:
10 0
( ) 1 ( )0
x x
d x df xC
dx D dx
118
By rearranging for C1 yields the following expression:
10
1 ( )
x
df xC
D dx (6.30)
Substituting equation (6.29) into equation (6.15b) yields the following equation:
1 1 2
( )( )f f b
f
df x hDC f L hC L hC hS
x Ldx D
Solving again for C2 yields:
2 1 1
( )( )
f
f f bx L
df x hC DC f L hC L hC
dx D (6.31)
6.2.2.1 ODE Solution for Scenario a) (Light Incident from Material Side)
In the case where light is incident from the material side, the expression for the Steele
relationship (𝐹𝑙(𝑥)) is represented by the flowing equation:
( ) exp( ) exp(1 exp( ))l f fF x I x I x (6.32)
Where If = I0/Is. Know the expression for Fl(x), it is now possible to use equation (6.32) to solve
for C1:
𝐶1 = −𝜀
𝐷∗ exp (1 − 𝐼𝑓) (6.33)
Where ε = μmaxxf/γ is defined for brevity
Solving for C2 requires f(x) to be solved. Recall that ( ) ( ) ( )f
f l
bxf x g x dxdx x F x dxdx
Y
Solving for f(x):
119
2exp(1) 1( ) (1, exp( ))
2
f
f
bxf x Ei I x x
Y
(6.34)
Where Ei is the exponential integral function which is represented by: (1, )t
x
eEi x dt
t
.
Substituting equation (6.33) and (6.34) into (6.31), C2 can now be solved:
2
2
1 1exp(1 exp( )) exp(1 )
exp(1) (1, exp( )) 1exp(1 )
2
f
f f f f
f f f
f f f b
bxC I L L I
h Y h
Ei I L bxL I L S
D YD D
(6.35)
By combining equations (6.21), (6.22) and (6.23) into equation (6.17) yields the ODE solution
for φ(x) as follows:
2
2
1 exp(1) 1( ) (1, I exp( )) exp(1 )
2
1 1exp(1 exp( )) exp(1 )
exp(1) (1, exp( )) 1exp(1 ) L
2
f
f f
f
f f f f
f f f
f f f b
bxx Ei x x L x
D Y D
bxI L L L
h Y h
Ei I L bxL L S
D YD D
(6.36)
6.2.2.2 ODE Solution for Scenario b) (Light Incident from Water Side)
A second case can be explored when light is incident from the water side of the algal biofilm. In
this case the expression for the Steele relationship is modified to:
( ) exp( ( ))exp(1 ( ( )))l f f f fF x I x L I x L (6.37)
Repeating the procedure of 6.2.2.1 of identifying C1, C2, and f(x), and back substituting these
findings into equation (6.17), the ODE solution for φ(x) becomes:
120
2
2
1 exp(1) 1( ) (1, exp( ( ))) exp(1 exp( ))
2
1exp(1 ) exp(1 exp( ))
1 1exp(1) (1, ) exp(1 exp( ))
2
f
f f f f
f
f f f f
f
f f f f f b
bxx Ei I x L x I L x
D YD D
bxI L I L
h Y h
bxEi I L I L L S
D Y D
(6.38)
By inspection, it can be readily seen that equations (6.36) and (6.38) are different.
6.2.3 Parameters
The parameters used in the model are described in Chapter 5 (Table 5.1) with the exception of
the mass transfer coefficient h. A value for h of 21.9 cm/day was estimated based on
hydrodynamic conditions in the waveguide reactor described in Chapter 4. A detailed calculation
can be found in Appendix B.
6.3 Discussion
6.3.1 Steady State Analysis
The solutions of φ(x) for both scenarios are the steady state solution for the model. As time
approaches infinity, the transient part of the solution becomes zero. This enables a direct
comparison between the two solutions for φ(x) and the numerical solutions presented in Chapter
5 (Figure 6.2). The steady state substrate concentration profile is of particular interest since this
is what has been investigated in past models (Liehr et al. 1990, Flora et al. 1995, Wolf et al.
2007), which enables a comparison to the literature as well.
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Figure 6.2 – Steady state solution for inorganic carbon profiles in algal biofilms for the
numerical solutions and analytical solution for 600 μm biofilms under the following condition’s:
a) light incident from material side, μmax = 1.2 1/day, Cb = 0.045 mgC/cm3, b) light incident from
material side, μmax = 2.1 1/day, Cb = 0.05 mgC/cm3, c) light incident from water side, μmax = 1.2
1/day, Cb = 0.045 mgC/cm3, a) light incident from water side, μmax = 2.1 1/day, Cb = 0.05
mgC/cm3. Bim = 1.78.
The steady state solution for the total inorganic carbon in Figures 6.2b and d are similar to those
presented by Liehr et al. (1990) under similar conditions. The analytical solution deviates from
the numerical solution as the inorganic carbon concentration approaches the value for Ks. The
results from this simulation imply the light direction has a significant impact on the general
shape of the inorganic carbon profile, but that changing parameters such as the Monod maximum
does not change the overall shape, but does change the absolute concentration in the algal
biofilm.
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6.3.2 Transient Analysis
The transient solution is solved by numerically calculating the first 150 eigenvalues using the
transcendental equation (6.23) then by numerically integrating the resulting expression for Cn
(equation 6.26). The transient solution provides information regarding the time it takes to reach
steady state (Figures 6.3 a-f). The time to reach steady state was on the order of minutes, but was
dependent on the input parameters (such as mass transfer coefficient) and light direction. The
numerical solution described in Chapter 5 converged on the time scale of about 1 hour which is
different than the transient model presented here. A detailed discussion is presented in Chapter 7.
The Monod maximum constant for algae is measured on the order of days with the highest cited
value being approximately 3 1/day (Liehr et al. 1990). This suggests that the inorganic carbon
concentration quickly reaches steady state faster than the algal biofilm is capable of growing
even when the mass transfer coefficient is low. It supports the pseudo steady state assumption
used in Chapter 5 to grow the biofilm.
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Figure 6.3 – Transient solution for inorganic carbon profiles at different times
(parameters from Table 5.1) with an initial concentration of 0.015 mgC/cm3 and a bulk
concentration of 0.045 mgC/cm3 with varying mass transfer biot number and incident light
direction: a) material side, Bim = 1.78, b) water side, Bim = 1.78, c) material side, Bim = 0.37, d)
water side, Bim = 0.37, e) material side, Bim = 5.26, f) water side, Bim = 5.26.
The mass transfer Biot number (Bim) has a significant impact on the inorganic carbon
concentration within the biofilm even when the bulk concentration is kept constant. The overall
shape of the inorganic carbon profile is similar even when the mass transfer coefficient is varied
(Figures 6.3 a-f). The mass transfer Biot number represents the ratio between the resistance to
diffusion of the substrate in the liquid boundary vs. the resistance to diffusion in the biofilm. As
the mass transfer Biot number decreases, the time to reach steady state increases (Figures 6.3 a-
f). The resistance of diffusion of a substrate in the biofilm itself is harder to control than the
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resistance of diffusion of a substrate in the boundary layer from a reactor engineering
perspective.
The model suggests that while the growth kinetics of algal biofilms which are carbon saturated
(i.e. zero order with respect to inorganic carbon) are independent of light direction (as shown in
Chapter 5), the inorganic carbon profiles are dependent on light direction (Figures 6.2 and 6.3).
This is because the assumption of zero order growth kinetics reduces the inorganic carbon
consumption term to be a function of light intensity and not a function of the inorganic carbon
profile.
The model as presented here has applicability in algal biofilm reactor environments, where the
concentration of inorganic carbon species in the bulk phase is likely to be greater than the Monod
saturation constant. Algal film photobioreactor systems found in the literature are often sparged
with gas that has a CO2 partial pressure a one hundred times greater than atmospheric (Schnurr et
al. 2013 and 2014). Other systems have shown that the algal biofilm systems exhibit zero order
growth kinetics with respect to changing the CO2 partial pressure (Gross et al. 2013). Results
from Chapter 4 suggests that algal film photobioreactors sparged with air with a CO2 partial
pressure greater than 1% have zero order growth kinetics with respect to inorganic carbon. This
suggests that the zero order consumption models derived in Chapter 5 and 6 will be applicable in
algal film photobioreactor environments where it is desirable to have the highest growth kinetics
possible.
6.3.3 Model Limitations
The model as described in this Chapter has several limitations, in that the concentration of the
substrate must be significantly greater than the Monod saturation constant (Ks) or else it is
possible the model can predict negative concentrations. Also, unlike the analytical growth model,
the light intensity in this model cannot be varied with time since the Steele relationship (Fl) was
solved only as a function of the spatial variable x.
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6.4 Conclusions
The zero order consumption kinetic problem in phototrophic biofilms is solvable as a PDE. The
resulting steady state solution of the PDE is in agreement with the numerical steady state
solution. The transient solution suggests that steady state conditions within an algal biofilm are
reached on the time scale of minutes. The mass transfer coefficient has a significant impact on
the absolute inorganic carbon concentration within the algal biofilm, but not the overall profile.
The transient solution demonstrates the feasibility of modeling algal biofilms in reactor
environments, where the bulk concentration of CO2 is likely to be significantly greater than the
Monod saturation constant value.
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Chapter 7 Overall Discussion
7.1 Introduction
With the growth of algal biofilms on light emitting waveguides having been demonstrated on a
proof of concept basis, the next steps for taking the algal film photobioreactors from the lab to a
pilot scale demonstration or a commercial scale is to develop in-depth models which will enable
reactor performance to be predicted and the validation of such models. In this Chapter the
combined lessons and observations from the previous chapters will be combined to discuss algal
film photobioreactor design concepts and how they are applied specifically onto waveguide
reactors. The waveguide photobioreactor can take multiple possible configurations, such as a
plug flow reactor (PFR) style where media flows past an algal biofilm on a waveguide, where the
waveguide takes the form of a sheet, or a packed waveguide reactor where individual
waveguides (in the form of wedges or tubes) are packed into a container (Figure 7.1 a and b).
The reactor configurations are examples of potential configurations for a waveguide based algal
film photobioreactor. There are multiple potential ways to deliver the media and nutrients to the
biofilms in these configurations. One approach is to submerge the waveguide in previously
fabricated container such as an open raceway pond or a flat plate photobioreactor. An alternative
would be to cascade the media over the film which is already done in some algal turf scrubbers
(Mulbry et al. 2008). Having the waveguide rotate such as in a rotating algal biofilm system
might prove to be more difficult, but is still technically possible. All of these systems can be
considered and modeled further, but the PFR model for estimating nutrient absorption into the
biofilm can be applied.
127
Figure 7.1 – Waveguide reactor schematics for a) a plug flow reactor and b) packed
waveguide reactor
The two reactor diagrams as shown in Figure 7.1 are representative of two designs that will be
considered in this chapter for further calculations. The two designs are not mutually exclusive,
but present a foundation to estimate the algal biofilm productivity, nutrient consumption rates
and capital costs.
7.2 Design Considerations
The main design considerations which were covered in this thesis were material selection and
waveguide configuration/design. Models were developed to predict algal biofilm growth so that
such models could then be used in reactor design equations to predict algal biofilm growth. This
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section contains a discussion on these and how they relate to the design of algal film
photobioreactors.
7.2.1 Material Considerations
In Chapter 3 it was demonstrated that material affects algal film productivity and the correlation
between polar surface energy and algal film productivity was demonstrated, although the exact
relationship is still unknown. There are sources in the literature which support the concept that
algal attachment to surfaces is correlated to the water-material contact angle (Finlay et al. 2002,
Sekar et al. 2004) and other studies show that there is no correlation (Irving and Allen 2011). A
comprehensive study by Ozkan and Berberoglu (2013) demonstrated that algal attachment was
dependent on the polar surface energy which agreed with the results obtained in Chapter 3. The
results from this thesis show that the small scale observations of algal cell attachment as
observed by Ozkan and Berberoglu (2013) are related to larger scale observations such as
colonization of surfaces by cells.
Large scale studies of algal film growth on different materials did demonstrate that algal biofilms
have higher overall productivity (as defined by single point analysis discussed in Chapter 3)
depending on the material of attachment (Johnson and Wen 2010, Christenson and Sims 2012
and Gross et al. 2013), but none of these were able to demonstrate why. Based on single point
productivity analysis, multiple possible explanations for higher productivities on materials could
arise: (1) material affects adhesion, such that algal biofilms with lower productivity were more
likely to slough off over the observed time scale; (2) material properties affect algal metabolism
such that algae attached to certain materials will have higher growth rates; or (3) initial
colonization is affected by material properties. In Chapter 3 it was demonstrated that the latter is
the most consistent explanation. Understanding adhesion and colonization time affect the overall
productivity is important in improving algal film reactor design guidelines and to help bridge the
gap between micro-scale algal attachment experiments (Sekar et al. 2004, Ozkan and Berberoglu
2013) and large scale algal film photobioreactor studies (Christenson and Sims 2012, Gross et al.
2013).
129
The effect of material surface energy on the microbial and algal population within the algal
biofilm was not explored in this thesis. In Chapter 3, the lipid content (w%/w) of the algal
biofilms grown on the different materials was not statistically significantly different, but this
does not imply whether the communities in the biofilms were different. Future research should
explore the microbial communities within algal biofilms grown on different materials.
7.2.2 Waveguide Based Algal Film Photobioreactors
Chapter 4 covered the research on algal biofilms that were growing on light emitting
waveguides. Five different waveguide designs were proposed and fabricated. The single wedge
large notch waveguide emitted the highest light intensity, while the double wedge waveguide
design had the most uniform light emission. The experiment demonstrated the possibility of
growing algal biofilms on light emitting waveguides, which opens up various new possible
configurations for algal film photobioreactors. Algal biofilms showed saturation kinetics with
respect to light intensity and CO2; however algal biofilms grown at low carbon dioxide
concentrations, increasing light intensity had a negative impact on algal biofilm growth.
The light emission from the waveguides was dependent on the engraved features and the
tapering. Based on the light emission profiles, the double wedge waveguide had the most
uniform light emission; however, adding 0.25 mm deep grooves resulted in a non-uniform light
emission profile. If the objective is to construct a waveguide with uniform light intensity, then
the double wedge waveguide should act as a starting point. In principle a combination of tapering
and structuring would result in the optimum waveguide design, but this was not explored in this
thesis. Future development of waveguide reactors should focus on simulating and developing
waveguides that have optimal light distribution.
Past research by Schnurr et al. (2014) and results in Chapter 5 indicate that light direction
doesn’t affect algal biofilm productivities when comparing light incident directions of water and
material sides. This has applicability in new reactor configurations and helps validate the concept
that growing algal biofilms on light emitting waveguides is a possible approach for algal film
photobioreactors. Waveguides have an added advantage as light is able to be transported through
130
opaque media without significant intensity loss to the algal biofilms. This could have
applications in treating opaque wastewater, such as that which is discharged from anaerobic
digesters.
Creating multi-layered waveguides could be another approach to control the light emission
profiles from the waveguides. Light scattering is dependent on the refractive index of the
material, so by coating the waveguide with a material of a different refractive index, the critical
angle can be adjusted. To demonstrate this point, the following example is proposed in Figure
7.2:
Figure 7.2 – Cross section diagram of light being refracting within a) waveguide as
fabricated and b) waveguide with a polycarbonate layer
Using Snell’s law to calculate the critical angle, in the current waveguide setup, the critical angle
is approximately 63.5o, but by adding a layer of polycarbonate the critical angle becomes 70.1
o.
Coating the waveguides with a thin layer of a material with a different refractive index would
change the light emission spectrum. If the proposed waveguide had an acrylic core and a
polycarbonate outside layer, based on results from chapter 3, the overall productivity of the
waveguide would be expected to be higher. Another possibility for controlling the light emission
from the waveguide is to adjust the tapper of the waveguide as a function of the length. At the
inlet of the waveguide, there would be a relatively low light intensity leakage, while further
along the waveguide, as the internal light intensity decreased, the larger taper angle would
increase the amount of light escaping from the waveguide.
131
7.2.3 Modeling Light Dependency of Algal Biofilms
The few models of algal biofilms are similar in nature, focusing on multi-ion species diffusion
within the algal biofilm (Liehr et al. 1990, Flora et al. 1995, Wolf et al. 2007). As results from
chapter 4 have shown, saturating an algal biofilm in an airlift reactor with inorganic carbon can
be done with 1% CO2 partial pressure. The models proposed by Liehr et al. (1990), Flora et al.
(1995) and Wolf et al. (2007) would be well suited for predicting algal biofilm growth at low
concentrations of inorganic carbon such as those experienced in a natural environment in a
stream. In reactor environment for the mass production of algal biomass, it is desirable to have
high inorganic carbon concentrations so that the algal biofilms are not carbon limited. This
would mean that the model derived in Chapter 5 (Equation 5.12) has applicability to modeling
algal biofilms in reactor environments for biomass production and CO2 capture (where inlet
streams of gas have a CO2 partial pressure greater than 1%).
In Chapter 5, it was noted that the numerical model estimated the algal biofilm would reach
steady state in less than one hour, where the analytical transient model in Chapter 6 would reach
steady state in less than 30 min. The numerical model in Chapter 5 uses Monod kinetics to
describe the inorganic carbon consumption and thus, as the inorganic carbon concentration in the
biofilm approaches the Monod saturation value, the time to reach steady state is affected. The
second is that the numerical model can overshoot the steady state condition and thus, it can
appear as if the time to reach steady state takes longer than the analytical model. This
discrepancy arises from issues with the solver algorithm and the difficulty associated with
selecting convergence values.
There are further improvements to the model to better predict and model the metabolism of algae
cells. The model described here represents the consumption of inorganic carbon as a function of
the inorganic carbon concentration and light intensity. The Calvin cycle, also known as the dark
cycle, is responsible for the uptake and integration of CO2 into glucose. This cycle can occur in
the absence of light, something which the model here does not describe. An alternative would be
to model the light dependent and light independent as two differential equations and link the two
via an energy storage term. A similar approach was used in the PHOBIA model (Wolf et al.
132
2007), but the model was unable to describe the light cycling effect. O2 inhibition is also an
effect which was not explored in the model, but that should be included in future models.
Oxygen production and consumption would be coupled to the light dependent reaction and
cellular respiration.
The model that describes algal growth (Chapters 2 and 5) can be applied onto the suspended
algae in the waveguide reactor. The theoretical maximum suspended phase productivity of the
waveguide reactor can be estimated using equations (2.2, 2.3, 2.5 and a cellular respiration term).
The maximum productivity occurs when the alga is not light or nutrient limited. Based on the
highest average TSS in the waveguide reactor from Chapter 4 (0.015 g/L), the maximum
productivity is 0.048 g/day and if the Monod max constant is doubled to 2.4 day-1
, the maximum
possible productivity is 0.103 g/day. These values are lower than the suspended productivities
measured in the waveguide reactor (Table 4.2). Since the suspended phase is likely light limited
in some parts of the reactor, the actual productivity is likely lower than the maximum
productivity estimated. This implies a significant algal biomass detachment from the biofilm to
the suspended phase, and the rate of detachment is significantly greater than the rate of
attachment when the biofilm is established.
7.3 Modeling a Hypothetical Waveguide Reactor
Algal film photobioreactors can be modeled using the equations for algal biofilm growth derived
in Chapter 5. The following derivation can be applied for the mass growth of algal biofilms or
for modeling for nutrient removal. In such an application, the focus of the reactor would be for
wastewater treatment and the removal of nutrients. In such an application, the mass balance of
the nutrients is important to describe and model. The derivation of models will mainly though be
focused on using the analytical expressions for algal biofilm growth, which assumes that algal
biofilm growth is light limited and not nutrient limited.
The following derivations for the nutrient balances can be applied to any nutrient (inorganic
carbon, PO43-
, NO3- etc…) which will be consumed by an algal biofilm. The underlying
assumptions are: diffusion is represented by a second order diffusion in one dimension, and the
133
consumption can be described using Monod kinetics coupled with the Steele relationship. In an
algal film photobioreactor for maximum biomass production or for CO2 capture, it is desirable
not to operate under nutrient limited conditions. In applications such as nitrogen or phosphorous
removal, these nutrients may be the limiting, and thus, the reactor would be operating under a
nutrient limited condition. If the reactor in question is being operated in carbon saturated
conditions, the flux entering the algal biofilm is described by:
( )b f
dSD h S S x L
dx (7.1)
Where D is the diffusion coefficient of the substrate in the biofilm, h is the mass transfer
coefficient, and Sb is the concentration of the nutrient in the bulk phase.
In this example, a steady state solution will be examined as opposed to the transient case
solution. In this case example, the algal biofilm is not nutrient limited and therefore is subject to
zero order kinetics. The flux entering the algal biofilm must be equal to the inorganic carbon
consumed and therefore:
( )c b fJ h S S x L (7.2)
max
0
exp(1 ) ( )
fL
f
f b f
s s
xI Ix b dx h S S x L
I I Y
(7.3)
As shown in Chapter 5, the left hand side (LHS) of equation (7.3) is solvable. This yields the
following expression:
max 0 0exp(1 exp( ) exp(1 ( ) ( )
f f
f f b f
s s
x xI IL b L h S S x L
I I Y
(7.4)
134
The rate of the nutrient uptake can be solved directly in the reactor environment. The external
mass transfer coefficient (h) can be estimated from the dimensionless Sherwood number (Sh)
(Seader and Henley 2006):
𝑆ℎ = ℎ𝑑𝑝
𝐷
Where dp is a characteristic length and D is the diffusion of the nutrient in the liquid. The
Sherwood number (Sh) can be expressed as a function of the dimensionless Reynolds number
(Re) and the Schmidt number (Sc) for flow over a flat plate (Seader and Henly 2006):
𝑆ℎ = 𝐴 + 𝐵 ∗ 𝑅𝑒𝑚𝑆𝑐𝑛
In this expression, A, B, m and n are determined empirically from experimental data for a
specific system/geometry. Re and Sc are represented by the following equations:
𝑅𝑒 = 𝑈𝑑𝑝
𝑣, 𝑆𝑐 =
𝑣
𝐷
This enables the inorganic carbon concentration at the interface of the algal biofilm to be solved
for depending on the reactor conditions.
Consider the scenario, as expressed in Figures 7.3 and 7.4, of a single fluid cross-section in a
hypothetical algal film photobioreactor. In this example, the PFR waveguide reactor case (Figure
7.1 a) is applied onto the waveguide reactor developed in Chapter 4. Zero order kinetics are
assumed with respect to the substrate (i.e. algal biofilm growth is light dependent only). The time
scale at which these equations apply needs to be significantly lower than the algae grows (on the
time scale of minutes opposed to hours or days).
135
Figures 7.3 – a) 2D Schematic of waveguide reactor and b) 2D schematic of algal
biofilm
Figure 7.4 – 3D Schematic for waveguide reactor
136
In this case, the general equation for a plug flow reactor will be applied, including the
assumption that, in the axial direction (in this case the x-z plane), the substrate is uniformly
mixed. The region of plug flow is in the control volume suspended phase, where the
concentration of the substrate can vary with respect to the y direction. For the single substrate S,
the general PFR equation is shown below:
0
0
V
sS s s
dMF F r dV
dt (7.5)
When applied onto the scenario in Figure 7.3, there are two sources of reaction: in the algal
biofilm and in the media. The consumption of the substrate in the suspended phase will be
equivalent to the consumption and respiration of the algae. The consumption of substrate S in the
algal biofilm will be equal to the flux of substrate entering the algal biofilm at a given point at
pseudo steady-state. The consumption of the substrate in the suspended phase is assumed to be
zero order Monod kinetics. This can be described as:
max
0
( ) exp(1 )
fL
fF
S b f
s s
xI Ir h S S x L x b dx
I I Y
(7.6)
max ( ) ( )S s
S s l
xr x y F x b
Y (7.7)
Where xs is the concentration of algal biomass in the suspended phase as a function of y
[mgS/cm3]. (rs
F is the rate of consumption of S in the biofilm [mgS/day cm
2], rs
S is the rate of
consumption of S in the suspended phase [mgS/day cm3]) As discussed before, the flux entering
into the biofilm is equal to the rate of substrate consumption in the algal biofilm (equation 7.3).
Therefore the general equation to describe the removal of substrate S in the proposed reactor:
0
0 0
V A
S FsS S S S
dMF F r dV r dA
dt (7.8)
Equation (7.8) is the general equation for describing the rate of consumption of the material. The
control volume is assumed to have the following dimensions in the x, y and z direction
137
respectively: X, Y and W. Assuming steady state conditions (i.e. dM/dt = 0) the following
equation can be derived:
𝐹𝑆0 − 𝐹𝑠 + 𝑊 ∫ ∫ 𝑟𝑆𝑆𝑑𝑥𝑑𝑦
𝑋
𝐿𝑓
𝑌
0
+ 𝑊 ∫ 𝑟𝑠𝐹𝑑𝑦
𝑌
0
= 0
Substituting the reaction rates for their respective equations, the description for this system is:
0 max
0
max 0 0
0
( ) ( )
exp(1 exp( )) exp(1 ) 0
f
Y X
S sS S s l
L
Yf f
f f f
f s s
xF F W x y F x b
Y
x xI IW L b L dy
I I Y
(7.9)
Where; γf is the extinction coefficient of light in the algal film, xs is the substrate concentration in
the suspended biomass, and Fls is the Steele relationship in the liquid phase. The equation
derived in (7.9) represents a general solution to a plug flow description of the substrate
consumption in the waveguide reactor. Approximating the downcommer of the waveguide
reactor as a PFR may not be the best model, but this can be tested.
7.3.1 Modeling the PPAL Waveguide Reactor
In Chapter 4, a PPAL waveguide reactor demonstrated the possibility of growing algal biofilms
on light emitting waveguides. In this section, the equations derived in Chapters 5 and 6 will be
applied onto the reactor as a demonstration of the application.
Consider the scenario presented in Figure 7.3 and 7.4. As shown in Figure 7.3 a and b, the
control volume encompasses the algal biofilm and the suspended phase in the downcommer and
not the riser. The riser is ignored because it is assumed that not enough light is transmitted to the
riser of the airlift, but this assumption will be tested later on. To further the development of the
reactor model, additional assumptions were made: (1) the plates which separate the riser from the
downcommer do not obstruct light transmission, (2) the concentration of suspended algae is
uniform throughout the reactor, (3) the reactor is symmetrical in the vertical direction, and (4)
138
the substrate S is well mixed in the z direction. It should be mentioned that often air lift reactors
are considered CSTRs with respect to substrate production/consumption on a bulk scale (Chisti
and Moo-young 1987). This assumption can be tested by applying a PFR model on to the
waveguide reactor developed in Chapter 4 and estimating the change in nutrient concentration
from the top of the downcommer to the bottom.
To start, assume that xs is constant (or so low that variations in the concentration are not
significant). Therefore, equation (7.9) can be integrated to with respect to x:
0max 00
0
max 0 0
0
exp( )exp( )exp 1 exp(1 exp( ( ))
( ) exp(1 exp( )) exp(1 ) 0
Yf f ss
S S f f s
s S s
Yf fs
f f f f
f s s
I L Xx IF F W L
I I
x xx I Ib X L dy W L b L dy
Y I I Y
(7.10)
In differential form, (7.10) becomes:
00max
max 0 0
exp(exp( )exp( )exp(1 ) exp(1
( ) exp(1 exp( )) exp(1 )
f f sf f ss
s s sS
f fsf f f f
f s s
I LI L Xx
I IdFW
dy x xx I Ib X L L b L
Y I I Y
(7.11)
If the light intensity is uniform, then I0 is not a function of y. In this case the resulting equation
for the chance in mass flow rate across has the form of a linear expression:
𝐹𝑠𝑜𝑢𝑡 = 𝑚 ∗ 𝑦 + 𝐹𝑠
𝑖𝑛 (7.12a)
Where F is the mass flow rate (mgS/day) of compound S either in or out of the system and m is a
constant of the slope which is represented by equation (7.12b), assuming that the extinction
coefficients are constant and the initial light intensity does not vary along the length of the
waveguide. Where in this case, m has the units of [mgS/cm day] for a substrate and is
represented by the following equation:
139
0max 0
max 0 0
exp( )exp( )exp 1 exp(1 exp( ( ))
( ) exp(1 exp( )) exp(1 )
f f ssf f s
s S s
f fsf f f f
f s s
I L Xx IL
I Im W
x xx I Ib X L L b L
Y I I Y
(7.12b)
The final equation is represented by:
0max 0
max 0 0
exp( )exp( )exp 1 exp(1 exp( ( ))
( )
( ) exp(1 exp( )) exp(1 )
f f ssf f s
s S sout in
S S
f fsf f f f
f s s
I L Xx IL
I IF y W y F
x xx I Ib X L L b L
Y I I Y
(7.13)
If the parameters from Table 5.1 are used in conjunction with the light emission data from the
double wedge waveguide (approximate uniform light emission is 150 μmol/m2 sec). At 1%
partial pressure of CO2, the estimated change in inorganic carbon concentration is 0.0005 g/L
from the inlet to the outlet (i.e., the top of the downcommer to the bottom). The gradient change
in the inorganic carbon is so small with respect to the y direction of the downcommer (vertical
direction). Since the x and y directions are assumed to be well mixed, the change of nutrient
concentration in any special direction is not significant and therefore, the nutrients in the reactor
can be assumed to be well mixed. This implies that the nutrient balance in the reactor can be
modeled as a CSTR instead of a PFR.
The parameters for the model are found in Table 5.1, with the exception of the required biofilm
thickness, which was assumed to be 100 μm which is approximately 10 g/m2. The PFR model
developed here predicts that the total algal biofilm productivity for the waveguide reactor is
0.289 gbiomass/day, which is approximately double what was measured in Chapter 4 (0.13
±0.05 gbiomass/day). When combining both the suspended phase productivity and the algal
biofilm productivity, the value was 0.33 ±0.09 gbiomass/day, which is not statistically different
from the model predictions at the 95% confidence level.
140
The model estimates that the suspended phase does not produce significant quantities of algal
biomass (-0.064 mg/day) when the thickness of the algal biofilm is 100 μm, or at approximately
10 g/m2. The negative biomass growth occurs because the rate of cell death in the suspended
phase is greater than the growth. This implies that the only source of algal growth in the reactor
is supplied by the algal biofilm. Results from Chapter 4 suggested that the majority of algal
productivity from the waveguide reactor came from the suspended phase, but the model derived
here suggests this is not likely. Therefore, it would appear that algal biofilm shedding is a
significant contributor to the suspended phase productivity.
7.3.2 Productivity and Economics of an Idealized Packed Waveguide Reactor
7.3.2.1 Reactor Model Description
A reactor model was developed based on the algal biofilm productivity estimates from the
fundamental model derived in Chapter 5 which assumed that light was the only limiting nutrient.
The reactor model assumes that incoming light can be evenly distributed on the surface area of
the waveguide. In this example, the bulk fluid phase will be considered to be well mixed. For the
productivity and economic analysis, a packed waveguide reactor will be considered which has
two different designs for lighting: LED powered and solar powered (via a solar collector) (Figure
7.5).
141
Figure 7.5 – Schematic representation of an a packed waveguide reactor with two
designs for supplying light a) LEDs and b) a solar collector
For both of these configurations, a reactor model to determine the productivity which includes
the incident photon flux, surface area photon flux, cross sectional area of the top of the
waveguide, and the spacing between each waveguide. The model is based upon a schematic as
presented in Figure 7.6.
142
Figure 7.6 – Schematic representation of an ideal packed waveguide reactor for the
productivity and cost model
Depending on the geometry of the waveguide (cylinder or rectangular prism), the diameter or
length of the waveguide is fixed. For a rectangular prism waveguide, the height of each
waveguide is calculated based on the following equation (rectangular prism was chosen since the
models derived in Chapter 5 are based on Cartesian coordinates):
𝐻𝑒𝑖𝑔ℎ𝑡 = 𝑃ℎ𝑜𝑡𝑜𝑛𝑠 𝑖𝑛
4×𝑃ℎ𝑜𝑡𝑜𝑛𝑓𝑙𝑢𝑥𝑜𝑢𝑡 (7.14)
Equation (7.14) assumes that all photons are leaked out through the sides of the waveguide and
the photonflux through the bottom of the waveguide is zero. In these estimates, the incident
photons into the waveguides are a fixed value (in units of μmol/sec per waveguide). The number
of waveguides which can be packed into a 1 m2 land area is calculated based on an assumed
separation distance between each waveguide.
#𝑜𝑓 𝑊𝑎𝑣𝑒𝑔𝑢𝑖𝑑𝑒𝑠 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑎𝑟𝑒𝑎 =1
(𝐿𝑒𝑛𝑔𝑡ℎ+𝑆𝑝𝑎𝑐𝑖𝑛𝑔 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒)2 (7.15)
143
The number of waveguides is per unit area. Based on the emitted light intensity, the fundamental
model described in section 4.1 was used to generate waveguide surface area productivity values.
𝑆𝑢𝑟𝑓𝑎𝑐𝑒𝐴𝑟𝑒𝑎𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦 = 𝑓(𝑃ℎ𝑜𝑡𝑜𝑛𝑓𝑙𝑢𝑥𝑜𝑢𝑡) (7.16)
The productivity is calculated using equation (5.12). From combining equations (7.14), (7.15)
and (7.16), the land area productivity of the reactor is then calculated using the following
equation:
𝐿𝑎𝑛𝑑 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦 = 4 × 𝐿𝑒𝑛𝑔𝑡ℎ × 𝐻𝑒𝑖𝑔ℎ𝑡 × #𝑜𝑓𝑊𝑎𝑣𝑒𝑔𝑢𝑖𝑑𝑒𝑠 ×
𝑆𝑢𝑟𝑓𝑎𝑐𝑒𝐴𝑟𝑒𝑎𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦 (7.17)
Where land productivity is in units of [g/m2 day], length and height are in units of [m], number
of waveguides [waveguides/m2] and surface area productivity is [g/m
2 day].
7.3.2.2 Productivity Estimates
Based on equations (7.14-7.17), estimates for land productivity for the theoretical reactor can
now be estimated. The model predicts the land productivity for square rectangular waveguides.
The dependency between land productivity and cross sectional area of the waveguide and
spacing is shown in Figure 7.7. The quantity of photons to the waveguides can be varied and the
spacing can be adjusted in the model. In the following cases the waveguides are assumed to be of
rectangular prism geometry.
144
Figure 7.7 – Model predictions for photobioreactor land productivity with respect to the
cross sectional area of a single waveguide with varying the photons into each waveguide and
variable spacing between waveguides a) 0.004 m, b) 0.01 m, c) 0.05 m and d) 0.002 m. Defined
Variables: Photonflux out: 150 μmol/m2 sec.
For each spacing and incident light there is a maximum land productivity that the model predicts.
The value of the maximum and at what waveguide cross sectional area it occurs at varies with
the photons supplied to each waveguide and the spacing between each waveguide. A maximum
land area productivity implies there is an optimal packed waveguide reactor design which can be
obtained. The estimated land area productivity increases with decreasing waveguide spacing, but
the spacing of the waveguide represents the doubled value of the maximum possible biofilm
thickness which could be obtained (i.e. if the waveguides are spaced 2 mm apart the algal biofilm
can only grow to 1 mm before unknown growth conditions will happen because the two biofilms
could merge).
145
Under the defined conditions, the reactor model predicts that the maximum land productivity is
75 g/m2 day, which is higher than the 20-31 g/m
2 day land area productivity reported by
Christensen and Sims (2012). The estimated land area productivity is higher than open raceway
ponds (8-25 g/m2 day) (Shen et al. 2009, Christensen and Sims 2012), and greater the range
given for tubular photobioreactors (35-48 g/m2 day) (Chisti 2007). Land productivity is
dependent on waveguide cross sectional area, but for cross sectional areas larger than 0.1 m2 in
some of the simulations, the height of the waveguides surpassed values of 6 m, which may not be
structurally or economically feasible. The estimated land productivities by the model should be
assumed to be an idealized maximum productivity.
7.3.2.3 Capital Cost Estimate
Capital cost estimates are important in scaling reactors from the bench/pilot scale to commercial
scale. The capital cost of a hypothetical waveguide reactor for growing algal biofilms was
estimated in this section. At this stage in development it is not possible to estimate the operating
costs with reasonable certainty. In this section, the cost estimates are presented based on the
following ideal photobioreactor configurations: open pond with waveguides and airlift
photobioreactor with waveguides. Furthermore, two possible light supply sources will be
estimated: light provided by a series of LEDs and a solar collector.
146
Table 7.1 - Capital Cost Inputs for Algal Film Waveguide Reactor
Item Unit Cost per unit Source
Land $/acre 3000 Davis et al. 2011
Open Pond $/m2
10 Benemann 2008
Air lift $/m2 100 Benemann 2008
Solar Collector1 $/m
2 90 Energy.gov (2015)
Red Rebel LEDs2 $/waveguide 5 Luxeonstar (2015)
Waveguide3 $/m
3 of Acrylic 1945 McMaster Carr (2015)
The capital costs for the four configurations are plotted against the waveguide cross-sectional
area (Figure 7.8), assuming that each waveguide requires a single LED, the solar collector is
being irradiated with 1000 μmol/m2 sec, photonflux on the surface of the waveguide is set to 150
μmol/m2 sec, 35 μmol photons/sec into each waveguide, and a waveguide spacing of 2 mm. The
capital cost is referenced to the production of 1 kg of algal biomass per day. The cost of acrylic
waveguides in this cost estimate was based on the price of acrylic from McMaster Carr. Cost
estimates are on the higher side since the cost of acrylic and LEDs are based on retail cost
estimates and not on wholesale costs.
1 Price is estimated by an aggregate then multiplied by 1.1 for an estimate. Difficult to price a solar collector for this
specific application
2 Price is rounded up to include costs associated with electrical work
3 Price of waveguides is assumed to be independent of design, but costs are based on a 50% markup of the cost of
acrylic
147
Figure 7.8 – Bioreactor capital cost estimates for different waveguide cross sectional
areas (single waveguide) and different reactor configurations to produce 1 kg of dried algal
biomass per day
The capital cost estimate predicts there is a minimum capital cost based on the waveguide cross
sectional area for all types of configurations. The cost for the solar collector and LEDs remain
constant for all waveguide cross sectional areas. The underlying reason is that the number of
photons required to produce 1 kg of algal biomass remain constant regardless of the
configuration. The minimum estimated capital cost for the waveguide reactors occurs at a
waveguide cross sectional area (0.01 m2 for open pond and 0.004 m
2 for PBR) which is not the
same as the cross sectional area which results in the highest land area productivity (occurs at
0.00001 m2 cross section for both reactor configurations). This is caused due to the cost of the
acrylic for the waveguides. The volume of the waveguides decreases with increasing cross
sectional area while the total number of waveguides required to produce 1 kg of algal biomass
per day remains constant.
The estimated bioreactor capital costs for open raceway styles and closed photobioreactors tend
to have overlaps when the waveguide cross sectional area is less than 0.0025 m2 provided the
0
5,000
10,000
15,000
20,000
25,000
30,000
0.000 0.005 0.010 0.015 0.020 0.025
Bio
rea
cto
r C
ost
($
/m2)
Waveguide Cross Sectional Area (m2)
Open Pond
with LEDs
PBR with
LEDs
Open Pond
with Solar
Collector
PBR with
Solar
Collector
148
light source is the same. This is because the waveguide costs are significantly larger than the cost
for the open raceway pond or the photobioreactor. At very small waveguide cross sectional areas
(0.000025 m2) for both open raceway and closed photobioreactor style with LEDs the cost of the
waveguides and LEDs make up 99.99% of the total estimated costs. When a solar collector is
used, the waveguide cost and solar collector total cost is approximately 99.8% of the total cost.
This suggests that future work should be focused on reducing the manufacturing costs of the
waveguides.
The capital costs estimated here are not favourable as compared to estimates by Davis et al.
(2011) which predict that an open raceway pond in upfront capital costs is estimated to cost
approximately $550 to produce 1 kg of algal biomass per day (excluding land and capital costs of
harvesting equipment). Even if the harvesting costs could be negated, the estimated total capital
cost for a packed waveguide reactor would then be estimated to be $8,700 to produce 1 kg of
algal biomass.
The capital cost estimates shown in Figure 7.8 are approximations since the algae
photobioreactor industry is not well established and quotes for photobioreactors are not readably
available. Other factors integrated into capital costs, such as installation, taxes, import fees etc…
have not been accounted for. These could have a significant impact on the overall capital cost of
any photobioreactor; however; general trends in capital costs can still be inferred from Figure
7.8. The operational costs such as labour, electricity and nutrient requirements are not covered in
the estimate. At the current stage in the development of the waveguide based algal film
photobioreactor, the design has not yet been optimized, nor has a pilot scale demonstration been
achieved. This could lead to inaccuracies in the operation and capital costs, but once a pilot scale
waveguide reactor has been built, operating costs can be estimated.
149
Chapter 8 Conclusions and Recommendations
8.1 Conclusions
The research demonstrated the feasibility of growing algal biofilms on light emitting waveguides
and addressing the material selection of such reactors and modeling the growth of algal biofilms
in such systems. The conclusions from the work of this thesis are listed below:
1. Material of attachment affects the overall algal biofilm productivity. Differences in
the overall productivities between algal biofilms grown on different materials were
largely explained by differences the colonization time; after the colonization time was
accounted for, biofilm growth rate was independent of material at ~2 g/m2/day for all
materials except acrylic at 1.2 g/m2/day. Algal biofilms grown on cellulose acetate had
the highest overall productivity (2.08 g/m2 day) among the materials tested. Acrylic
embossed with 15 μm v-grooves showed a 70% improvement in algal biofilm
productivity compared to smooth acrylic and acrylic embossed with 2 μm features.
2. The colonization time was positively correlated to the polar surface energy of the
material, while it was not correlated to water-material contact angle. The lipid
content of algal biofilms grown on different materials was not statistically different
among the materials tested.
3. Algal Biofilms can grow on light emitting waveguides. The design of the waveguides
impacts the light emitted from the waveguides, which in turn, impacts the algal biofilm
productivity. The highest measured surface area productivity recorded was on front of the
single wedge large notch waveguides, at 2.9 g/m2 day, a lipid productivity of 0.34-0.42
g/m2 day, a nitrogen removal efficiency of 40-49% and a phosphorus removal efficiency
of 15-30%.
150
4. Algal biofilm productivity showed a dependency on light intensity and CO2
concentration, however algal biofilms became light and CO2 saturated. The
interaction effects that light and CO2 have on algal biofilm productivity are complex. The
negative effect of increasing light intensity beyond the saturation point has on algal
biofilm growth can be reduced by increasing the CO2 concentration.
5. The model predicts that algal biofilm growth kinetics are non-linear and follow a
sigmoidal shape. The model shows that growth of an algal biofilm stops when the
inorganic carbon respiration term is equal to the inorganic carbon consumption. When the
model was compared to experimental data while allowing the Monod maximum constant
(μmax) to be varied, the predicted growth kinetics compared to experimental data had an
R2 value from 0.77 to 0.98. The model predicts that algal biofilms that have zero order
consumption with respect to inorganic carbon (when the concentration of inorganic
carbon is much greater than the Monod saturation constant), have growth kinetics that are
independent of light direction.
6. It is possible to solve the inorganic carbon profile with film depth so long as the
consumption kinetics are assumed to be zero order. The growth rate of such algal
biofilms is independent of light direction, but the concentration profiles of inorganic
carbon are not identical when light is incident from the material side and water side. The
model predicts the steady state condition is reached on the time scale of minutes,
depending on the initial concentration and the parameters.
7. Shedding of algal biofilms appears to be a significant contributor to the overall
productivity of the waveguide reactor. Modeling the growth of the suspended phase in
the waveguide reactor suggests that the suspended phase productivity is close to zero
mg/day and should be washed out entirely if algal film shedding did not occur.
151
8.2 Recommendations
The research presented here acts as the starting point for further photobioreactor engineering and
further scientific analysis of algal biofilms. There are multiple paths which can be pursued due to
the applied nature of the research which either involves further fundamental scientific studies or
applied research with the end goal of commercialization. The recommendations are as follow:
1. Further research should be conducted on exploring the optimum waveguide design
for waveguide based reactors. Due to the relatively high cost and current long
production cycles (due to the small production runs), using ray tracing software to predict
light scattering is recommended for saving time. The design parameters of the
waveguides to investigate would be: tapering angle (can also be a function of the
waveguide length), notch size, angle, spacing and waveguides constructed from multiple
layered polymers.
2. The combined biofilm and suspended phase productivity in algal film
photobioreactors needs to be further investigated. Most literature does not report the
suspended concentration of algae in the algal film photobioreactors, thus making
comparative analysis difficult. Results from this thesis show that apparent suspended
phase productivity is a large contributor to the overall productivity of the algal film
photobioreactor, but it is not known whether this suspended phase was produced via
shedding of the algal biofilm. Modeling of the waveguide reactor suggests shedding is an
important contributor in the suspended productivity.
3. Alternative light sources for the waveguide photobioreactor should be examined and
implemented. While LEDs are a convenient way of generating red light for the algal
biofilms, a preferred alternative would be to use solar light for growing the algal biofilms.
A capital cost estimate predicted that a waveguide reactor which uses a solar collector has
a lower capital cost than one which uses LEDs for the light source. This implies that
152
methods for solar light collection should be investigated and combined with the
waveguides.
4. The community of the algal biofilms grown on different materials and the
waveguides should be investigated. The lipid analysis indicated that material does not
affect the total weight composition of the lipids, but it did not analyze the composition of
the fatty acids or the composition of the proteins/carbohydrates. Understanding the how
the microbial community changes over the course of the reactor run will be beneficial.
One application this information would yield is how to seed the material with the best
microbes for enhancing algal biofilm growth/attachment.
5. The fundamental mathematical relationships used to model algal biofilms needs to
be redefined to describe more aspects of algal biofilm growth. The analytical model
developed in this thesis was capable of describing light dependent growth of algal
biofilms, but some phenomena such as light-dark cycling of light could not be explained.
The model predicted that algal biofilms which underwent any light-dark cycle would
have lower growth rates than those which were constantly illuminated. Experimental
observations show that algal growth does benefit from the light-dark cycle under certain
conditions.
6. Commercialization of the waveguide reactor still requires further work and
development of the reactor to improve the productivity. The reactor system developed
in this thesis was not optimized for maximum production of algal biomass, but further
development of such reactors is feasible based on the information contained within this
document. The following should be considered in optimization: light intensity, light-dark
cycles, CO2 concentration, pH, and harvesting schedules.
8.3 Engineering and Industrial Significance
The findings of the material comparison experiment can be applied to photobioreactor
construction and to biofouling. For the application of algal film photobioreactors, it is desirable
153
to have materials that attract algae and bacteria to colonize the surface quickly. The results can
also be applied onto biofouling, where materials which have a long colonization time are more
desirable than materials which have a short colonization time. The results from this thesis,
suggest that materials with a high polar surface energy are desirable for avoiding biofouling
applications and materials with a low polar surface energy are desirable for enhancing algal
biofilm productivity. The colonization time method also sets a benchmark for how algal biofilm
surface area productivity should be calculated to eliminate the effects of material properties on
the colonization of the algal biofilm.
The fact that algal biofilms can be grown on light emitting waveguides has a significant impact
on future algal film photobioreactor design. The research here shows the productivity of algal
biofilms grown on light emitting waveguides was comparable to other traditional algal film
photobioreactors. This implies that the light source and the attachment material can be integrated
and that productivity will not be impacted. Waveguides can be used to transmit light through
opaque liquids to deliver light directly to algal biofilms. This has direct applications in designing
algal film photobioreactors for wastewater treatment where the water is opaque.
The observation of saturation effects of the algal biofilm growth kinetics with varying light
intensity and CO2 concertation is important in optimizing the operating parameters of algal film
photobioreactors. It was observed that there are interaction effects of light intensity and CO2
concentration on algal biofilm productivity was a non-linear relationship. The saturation kinetics
shows that there is an optimal light intensity for algal biofilm growth and that increases in light
intensity beyond this value will not improve the productivity.
The solution for the zero order inorganic carbon consumption kinetics PDE shows that it is
mathematically possible to solve such a solution, which in literature is often solved only though
numerical methods. This has a significant impact on the field of modeling algal biofilms as
relatively simple analytical models can be used to adequately describe algal biofilm growth,
which has applications in bioprocess engineering. From a scientific standpoint, the models
derived in this thesis provide insight into the inorganic carbon concentrations in the algal
biofilms.
154
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170
171
Appendix A – Original Waveguide Schematics
Figure A.1 – Original schematic for single wedge waveguide
172
Figure A.2 – Original schematic for double wedge waveguide
173
Appendix B – Parallel Plate Air Lift Physical Properties and Calculations
B.1 – Schematics
Figure B.1 – PPAL reactor schematics a) front view and b) top view
B.2 – Velocity in the downcommer
The velocity in the downcommer of the PPAL was measured by observing the velocity of beads
with a density of 1 g/cm3.
Table B.1 – Average time and velocity of beads in the airlift with varying air flow
Airflow (LPM) Average Time (s) Error Average Velocity (cm/s) Error
0.8 4.47 1.606964 3.288591 0.591124
1 3.19 0.709382 4.60815 0.512373
1.8 2.08 0.364539 7.067308 0.619306
3.2 1.48 0.297396 9.932432 0.997928
174
Figure B.2 – Average velocity in the downcomer with varying airflow (standard
deviation shown)
Total inorganic carbon as a function of CO2 partial pressure and pH as estimated using Henry’s
law and the disassociation constants for the inorganic carbon species.
Henry’s law with respect to dissolved CO2 in water:
𝑃𝐶𝑂2= 𝐻𝐶𝑂2
[𝐶𝑂2]
Where HCO2 is the Henry’s constant for CO2 [units of pressure*length3/mol]
Equilibrium of inorganic carbon species is defined by the following series of equations:
𝐶𝑂2(𝑎𝑞) + 𝐻2𝑂 ⇌ 𝐻2𝐶𝑂3(𝑎𝑞)
𝐻2𝐶𝑂3(𝑎𝑞) ⇌ 𝐻(𝑎𝑞)+ + 𝐻𝐶𝑂3(𝑎𝑞)
−
𝐻𝐶𝑂3(𝑎𝑞)− ⇌ 𝐻(𝑎𝑞)
+ + 𝐶𝑂3(𝑎𝑞)2−
Of which the equilibrium constants for the disassociation of the inorganic carbon (K1 and K2) are
represented by the following equation:
𝐾1 =[𝐻+][𝐻𝐶𝑂3
−]
[𝐻2𝐶𝑂3]
0
2
4
6
8
10
12
0 0.5 1 1.5 2 2.5 3 3.5
Av
era
ge
Vel
oci
ty (
cm/s
)
Airflow (LPM)
175
𝐾2 =[𝐻+][𝐶𝑂3
2−]
[𝐻𝐶𝑂3−]
Total inorganic carbon can be represented by the following equation:
𝐶𝑇(𝑎𝑞) = [𝐶𝑂2(𝑎𝑞)] [1 +𝐾1
[𝐻(𝑎𝑞)+ ]
+𝐾1𝐾2
[𝐻(𝑎𝑞)+ ]2
]
Figure B.3 – Concentration of inorganic carbon species in water with varying partial
pressure at fixed pH of 6.8
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0 5 10 15
Co
nce
ntr
ati
on
(m
ol/
L)
Partial Pressure of Carbon Dioxide (%)
Dissolved Carbon
Dioxide
Dissolved Bicarbonate
Dissolved Carbonate
Total Inorganic Carbon
176
Figure B.4 – Log concentration of inorganic carbon species in water with varying pH at a
fixed partial pressure of 1% CO2
B.3 Detailed Calculation of the Mass Transfer Coefficient
Area of riser: 8.5x41 cm2
Area of downcomer: 4.5x41 cm2
Height of downcomer: 14.7 cm
Length of submerged portion of waveguide: 19.2 cm
The average velocity in the downcomer is calculated using the average time that micro beads
with 1 g/cm3 took to travel from the top of the downcomer to the bottom:
𝑈 =𝑑𝑑𝑐
𝑡=
14.7𝑐𝑚
3.19𝑠𝑒𝑐= 4.61
𝑐𝑚
𝑠𝑒𝑐
Reynolds number is calculated as such:
-16
-14
-12
-10
-8
-6
-4
-2
0
2
4
2 4 6 8 10 12
Lo
g C
on
cen
tra
tio
n (
Lo
g(m
ol/
L))
pH
Dissolved
Carbon Dioxide
Dissolved
Bicarbonate
Dissolved
Carbonate
Total Inorganic
Carbon
177
𝑅𝑒 =𝑈 ∙ 𝑑𝑐
𝜈=
0.0461𝑚
𝑠𝑒𝑐 ∙ 0.0810𝑚
1.004 × 10−6 𝑚2
𝑠𝑒𝑐
= 3,719
Schmidt number is calculated as such:
𝑆𝑐 =𝜈
𝐷=
1.004 × 10−6 𝑚2
𝑠𝑒𝑐
1.14𝑐𝑚2
𝑑𝑎𝑦
=1.004 × 10−6 𝑚2
𝑠𝑒𝑐 ×1002𝑐𝑚
𝑚2 ×86400𝑠𝑒𝑐
𝑑𝑎𝑦
1.14𝑐𝑚2
𝑑𝑎𝑦
= 760.9
The average Sherwood number can be represented by the following expression for this case
(Seader and Henly 2006):
𝑆ℎ = 0.664 ∙ (𝑅𝑒)1/2(𝑆𝑐)1/3
𝑆ℎ = 0.664(3719)1/2(760.9)1/3 = 369.8
The mass transfer coefficient is represented by:
ℎ =𝑆ℎ ∙ 𝐷
𝐿𝐹
Thus:
ℎ =369.8 × 1.14
𝑐𝑚2
𝑑𝑎𝑦
19.2 𝑐𝑚= 21.9
𝑐𝑚
𝑑𝑎𝑦
178
Appendix C – Numerical Shooting Method and MATLAB® Code
Recall the description of the problem as presented in Chapter 5. The model developed describes
inorganic carbon utilization in the algal biofilm. The film is assumed to have a uniform density
and composition. Inorganic carbon and light are considered to be limiting, so that all other
nutrients are assumed to be in excess. The light intensity and concentration profiles in the biofilm
are considered to be at steady state, while the growth of the biofilm is not. In this pseudo-steady
state problem, the model assumes that microorganisms are not being removed or added to the
biofilm through attachment or detachment. In the model, the inorganic ion species, CO2, HCO3-,
and CO32-
are aggregated into a single term representing all inorganic carbon.
The model begins a steady state material balance on inorganic carbon at a point in the biofilm
that includes mass transfer by diffusion and generation/consumption:
𝐷𝑑2𝐶
𝑑𝑥2 + 𝑟𝑖 = 0 (C.1)
C [mg/cm3] represents the concentration of inorganic carbon, x [cm] is distance, and r is the rate
of inorganic carbon generation or production [mg/day]. The steady state diffusion is used in this
case as it is assumed that steady state diffusion of inorganic carbon into an algal biofilm can be
reached quickly or faster than the algal biofilm can grow.
For algal biofilms, the Monod model combined with the Steele relationship and a first order
respiration model is used, which is represented by equation (2).
𝑟 = −𝜇𝑚𝑎𝑥𝑥𝑓𝐶
𝐾𝑠+𝐶𝑓𝐿 + 𝑏
𝑥𝑓
𝑌 (C.2)
Where μmax is the Monod max constant for algae [days-1
], xf is the biomass density as moles of
substrate [mgC/cm3], Ks is the Monod half-saturation constant for the substrate [mgC/cm
3], b is
the respiration coefficient [days-1
], Y is the yield coefficient [mgBiomass/mgC] and Fl is a ratio
179
which is expressed by the Steele relationship (Steele 1965). Compared to past models developed
by Liehr et al. (1988, 1989, 1990) and Flora et al. (1995), the inorganic carbon species are
lumped together in one term, C. The Steele relationship is represented below (Steele 1965):
𝐹𝑙 =𝐼
𝐼𝑠𝑒
(1−𝐼
𝐼𝑠) (C.3)
Where Fl is the light limitation fraction, I is the light intensity [μmol/m2 s], and Is [μmol/m
2 s] is
the saturation light intensity. The Steele relationship describes the photoinhibition effect that
algae experience (Steele 1965, Melis et al. 1999, Melis 2009).There are alternative relationships
to describe the photo-inhibition effect such as the Haldane-type model, however these models are
significantly more complex and are dependent on multiple parameters which must be determined
from experimental data. The light intensity in algal solutions or films is often described by the
Beer-Lambert law for light attenuation:
𝐼 = 𝐼𝑖𝑒−𝛾𝑥 (C.4)
Where Ii is the light intensity at the surface of the biofilm or material [μmol/m2 s], and γ is the
extinction coefficient [cm-1
]. Most models on phototrophic biofilms which account for light
(Liehr et al. 1989, Flora et al. 1995, Wolf et al. 2007) use the Beer-Lambert law to describe light
attenuation. The light direction can be specified in the model as three possibilities: water side,
material side, and both sides.
Total flux of a substrate in an algal biofilm is represented by:
𝐽𝐶 = ∫ (𝜇𝑥𝑓𝐶
𝐾𝑠+𝐶∙
𝐼
𝐼𝑠𝑒
(1−𝐼
𝐼𝑠)
− 𝑏𝑥𝑓
𝑌) 𝑑𝑥
𝐿𝑓
0 (C.5)
where Jc is the inorganic carbon flux [mgC/cm2]. The growth of an algal biofilm is then
described as the conversion of the inorganic carbon into biomass as described below:
𝑑𝑀
𝑑𝑡= 𝑄𝐽𝑐 (C.6)
180
where M is the algal film biomass per surface area [g/m2], and Q is the yield coefficient of
inorganic carbon to biomass [mg Biomass/mg C]. Combining equations (C.1-4) yields the
second order ODE:
𝐷𝑑2𝐶
𝑑𝑥2 −𝜇𝑥𝑓𝐶
𝐾𝑠+𝐶𝑓𝐿 + 𝑏
𝑥𝑓
𝑌= 0 (C.7)
The alternative to solving the equation is to non-dimentionalized the nonlinear differential
equation developed by the combined equations (C.1-4), then by resolving the second order non-
linear ordinary differential equation (ode) into two first order non-linear odes. These equations
were solved using a 4th
order Adam-Bashford predictor corrector method in combination with a
shooting method where the flux of inorganic carbon into the biofilm is the estimated parameter.
The boundary conditions applied were: [C] = [C]bulk at x = 0 and that d[C]/dx = 0 at x=Lf. The
flux of inorganic carbon into the biofilm (D*d[C]/dx at x = 0) is set to be equal to the reaction
rate integrated over the depth of the biofilm (equation C.5). After the total inorganic flux
consumed by the biofilm was calculated, the growth of the biofilm over a defined time period
was calculated by using a discretized form of equation (C.6).
C.1 Problems with the shooting method
In chapter 5 it was briefly mentioned that the shooting method encountered certain problems
which resulted in nonsensical results in terms of inorganic carbon profile. Using the shooting
method will enable the model to predict negative concentrations and fails to satisfy the boundary
conditions, while properly balancing the overall mass balance under certain conditions. This
problem has been discussed by Wong (2005) in enzymes embedded in particles. In diffusion into
particles with embedded enzymes, when the solution fails to converge, the method to follow is to
use an asymptotic analysis with a shooting method. In the application discussed by Wong (2005),
this occurs when the Thiele modulus is large so that the substrate consumption and enzymatic
reaction is significantly greater than the diffusion rate, which causes perturbations in the
solution. Using this method an intermediate layer where the concentration of the substrate is
assumed to reach zero is guessed, then the shooting method with the new boundary conditions
(Cs(x = l) = 0, opposed to dCs/dx|x=l = 0). In bacterial biofilm models, when assuming zero order
181
growth kinetics it is possible to estimate whether the biofilm has been fully or partially
penetrated (Wanner et al. 2006). With phototrophic biofilms which have a light dependency, this
estimation is impossible.
The inorganic carbon profiles from Figure C.1 show irregular/impossible inorganic carbon
profiles as estimated by the model, either showing negative concentrations, or profiles which do
not satisfy the boundary condition that dC/dx at x = Lf is not zero. This problem was observed
when the initial inorganic carbon concentration was low (0.0009 gC/L), when there was a light
source present from the material side and when the biofilm reached a certain thickness. Under
the conditions presented in Figures 5.8 d, and f, the inorganic carbon profiles were not physically
possible at biofilm thickness greater than 100 μm. Since the model convergence is dependent on
the inlet flux being balanced with the total flux consumed/produced in the algal biofilm, it is
possible that the model will suggest inorganic carbon profiles which are impossible (i.e. have
negative values or don’t satisfy the boundary condition). The model is programed to converge on
the criteria that the inlet flux has to balance with the total inorganic consumption and respiration
(equation C.5). Due to the input parameters listed in Table 5.1 it is possible that a negative
inorganic carbon concentration can yield a positive consumption term (carbon is calculated as
being consumed).
182
Figure C.1 – Inorganic carbon profile as estimated by the Shooting Method.
There were many challenges associated with simplifying the model, which are not encountered
in other biofilm modeling cases. In biofilm modeling, it is possible to derive a pseudo-steady
state model, which has many of the same underlying assumptions which were made in Chapter 5
(gel-like structure, known biofilm thickness, no external mass-transport resistance). In modeling
pseudo-steady state biofilms which have consumption and respiration, a key variable to know is
the minimum concentration of a given substrate as demonstrated by (Wanner et al. 2006):
𝑆𝑚𝑖𝑛 =𝑏
𝑌𝜇𝑚𝑎𝑥−𝑏 (C.7)
Where Smin is the minimum possible concentration of substrate S in the biofilm, b is the
respiration constant, Y is the yield coefficient and μmax is the maximum specific growth rate
according to Monod kinetics. In the case for algal biofilm the equation for the minimum is (Liehr
et al. 1990):
𝐶𝑚𝑖𝑛 =𝑏𝐾𝑠
𝑌𝜇𝑚𝑎𝑥𝐹𝑙(𝑥)−𝑏(C.8)
-0.004
-0.0035
-0.003
-0.0025
-0.002
-0.0015
-0.001
-0.0005
0
0.0005
0.001
0.0015
0 50 100 150 200 250
Ino
rga
nic
Ca
rbo
n C
on
cen
tra
tio
n
(mg
C/c
m3)
Depth into biotilm (μm)
183
The equation (C.8) has an asymptote as a function of distance into the biofilm (x). This creates
issues with the calculation the minimum concentration, since Cmin can approach infinity and
negative infinity depending on Fl(x). It can also yield a negative value for the minimum
concentration, a physically impossible answer. This creates additional problems for modeling
substrate diffusion in phototrophic algal biofilms, since the transferability of equations from non-
phototrophic biofilms is non-applicable. The relationship of minimum total inorganic carbon
(equation C.7) was first presented by Liehr et al. (1990), but was only discussed in terms of how
the value affected the flux of inorganic carbon into the biofilm and only from one direction. To
demonstrate how equation (C.8) affects the convergence of the model, Figure C.2 was created as
shown below:
Figure C.2 – The minimum inorganic carbon estimated by the proposed model with
varying light direction and biofilm depth (assuming conditions outlined in Table 5.1 and
assuming a biofilm 800 μm thick)
-0.0025
-0.002
-0.0015
-0.001
-0.0005
0
0.0005
0.001
0.0015
0 100 200 300 400 500 600 700 800 900
Min
imu
m T
ota
l In
org
an
ic C
arb
on
(g
C/L
)
Depth in Biofilm (μm)
Water Side
Material Side
Both Sides
184
In the Figure C.2, asymptotes are present, which affects to minimum inorganic carbon
concentration possible and allows that value to approach infinity. This causes problems in the
computation, since the numerical model may predict a concentration of infinity or negative
infinity, which causes issues in the secant method.
The problem can also be shown in the following demonstration. In this case the initial slope of
the inorganic carbon is varied linearly from one set parameter to another set parameter and the
total inorganic carbon consumption is calculated for each guess. The values for the inorganic
carbon flux into the biofilm minus the consumption flux are plotted with each guess in addition
to the total inorganic carbon consumption (Figure C.3).
Figure C.3 – Variations in the difference between the inlet flux and the consumption flux
and the slope at the attachment material with varying initial slope.
Based on the results, it is clear that the model is having issues converging under these conditions.
For the model to converge the derivative at the wall must equal to zero to satisfy the boundary
condition and the flux in must equal the flux consumed. In this case there are points where one
condition will be satisfied but the other condition is not satisfied. What appears to be
“turbulence” in the inorganic carbon consumption does not disappear with taking smaller step
-5000
0
5000
10000
15000
20000
-1
0
1
2
3
4
5
6
-0.06 -0.055 -0.05 -0.045 -0.04 No
n-d
imen
tio
na
lize
d S
lop
e a
t th
e W
all
(un
itle
ss)
Dif
feren
ce i
n I
nle
t F
lux a
nd
Gen
era
tio
n
(mg
C/c
m2 d
ay
)
Non-dimentionalized Initital Slope Guess (unitless)
Difference in Flux in
and Consumption
Slope at the wall
185
sizes. The model will converge when both the difference in the flux and the slope at the wall are
close to zero for a given initial guess. As of currently, it appears to be related to the asymptotes
found in the minimum inorganic carbon concentration. Changing the solving algorithm to a
transient problem appeared to resolve the issue.
MATLAB® Code:
C.2 Analytical Solution
C.2.1 Core Solution
%Analytical Model by Scott Genin %calculates growth of carbon saturated algal biofilms %Input units must be in mg/cm^2 %Conversion factor from g/m^2 to mg/cm^2 is 10. filename = 'Analyticalalgalfilm.xlsx';
%define variables D = 1.14; %cm^2/day k = 2.6; %day^-1 Ks = 3*10^-4; %mg CO2/cm^3 xf = 50; %mg CO2/cm^3 Q = 0.5; %Fraction of carbon converted into biomass Is = 200; %saturation light intensity Io = 100; gamma = 200; b = 0.1; %day^-1 Y = 1; % mg C/mg C row = 100; %mg/cm^3 tspan = [0:0.2:150]; y0 = 0.15; dmdt = [];
%Declare function callmyfun = @(t,y)AFMass(t,y,Q,k,xf,gamma,Io,Is,row,b,Y);
%Solve function using ODE45 [t,y] = ode45(callmyfun,tspan,y0);
%Correction factor of 10 due to unit change biomass = y*10;
%Generate instantaneous rate of change for i = 1:numel(t); dmdt(i) = AFMass(t(i),y(i),Q,k,xf,gamma,Io,Is,row,b,Y); end dMdt = transpose(dmdt);
%Plot
186
plotyy(t,biomass,t,dMdt);
%Write xlswrite(filename,t,1,'A1'); xlswrite(filename,biomass,1,'B1'); xlswrite(filename,dMdt,1,'C1');
C.2.2 Core Biomass Function Where Light is Constant %Funtion where light intensity is constant
function dmdt = AFMass(t,m,Q,k,xf,gamma,Io,Is,row,b,Y)
dmdt = Q*((k*xf/gamma)*(exp(1-(Io/Is)*exp(-gamma*m/row))-exp(1-Io/Is))-
(b*xf*m)/(Y*row));
end
C.2.3 Core Biomass Function Where Light is Variable (example function of light intensity
is given) %Function for when light changes function dmdt = AFMass2(t,m,Q,k,xf,gamma,Io,Is,row,b,Y)
%Define function of how light changes I = (Io/2)+(2/3)*t;
dmdt = Q*((k*xf/gamma)*(exp(1-(I/Is)*exp(-gamma*m/row))-exp(1-I/Is))-
(b*xf*m)/(Y*row));
end
C.2.4 Curve Fitting Algorithm
%Analytical Model by Scott Genin %Calculates growth of carbon saturated algal biofilms %Input units must be in mg/cm^2 %Conversion factor from g/m^2 to mg/cm^2 is 10.
k = 2.1; %day^-1 Ks = 3*10^-4; %mg CO2/cm^3 xf = 50; %mg CO2/cm^3 Q = 0.5; %Fraction of carbon converted into biomass Is = 200; %saturation light intensity Io = 100; gamma = 140; b = 0.1; %day^-1 Y = 1; % mg C/mg C row = 100; %mg/cm^3
Params = [k]; %Define data from experiments xdata = [0;5;7;10;14;19;21;24;26];%data ydata = [0.02875;1.01125;1.3;1.4975;2.34;3.26875;3.81;3.995;4.46875];%data %define initial value
187
y0 = 0.02875;
%Solve
[y,resnorm,residual,exitflag,output,lambda,J] =
lsqcurvefit(@film_ode2,Params,xdata,ydata);
%Return values
ci = nlparci(y,residual,'jacobian',J);
C.3 Transient Code
C.3.1 Solution to Steady State %Model to attempt to describe the steady state solution %Variables %Light related ones Io = 100; %umol/m^2 s Is = 200; %umol/m^2 s gamma = 140; %1/cm %Growth related variables mu = 1.2; %1/day xf = 50; %mgC/cm^3 b = 0.1; %1/day Y = 1; %mgC/mgC %Diffusion D = 1.14; %cm^2/day k = 1.14; %cm^2/day h = 100; %cm/day %Amalgamated variables Kappa = b*xf/Y; epsilon = mu*xf/gamma; If = Io/Is;
%Defined variables L = 0.06; C = []; x = []; Cb = 0.045; %generate x matrix for q = 1:300 x(q) = q*0.0002;
end
%Individual term calculation
for j = 1:300 test2 = expint(If*exp(-gamma*x(j)));
term_1 = (epsilon*exp(1)/(D*gamma))*expint(If*exp(-gamma*x(j))); term_2 = -(1/2)*(Kappa/D)*x(j)^2; term_3 = -(epsilon/D)*exp(1-If); term_4 = -(k/(D*h))*epsilon*exp(1-If*exp(-gamma*L)); term_5 = (k/(D*h))*Kappa*L;
188
term_6 = (epsilon/D)*(k/h)*exp(1-If); term_7 = -(epsilon/(D*gamma))*exp(1)*expint(If*exp(-gamma*L)); term_8 = (1/2)*(Kappa/D)*L^2; term_9 = (epsilon/D)*exp(1-If)*L;
Test = term_4+term_5;
C2 = term_2+term_3*x(j)+term_4+term_5+term_6+term_7+term_8+term_9+Cb;
C(j) =
term_1+term_2+term_3*x(j)+term_4+term_5+term_6+term_7+term_8+term_9+Cb;
end
X = transpose(x); Carbon = transpose(C);
plot(X,Carbon);
C.3.1 Solution to Transient %Solver for the transient function S_star = zeros(1,100); S = zeros(1,100); Sstore = 0; %Variables for described polynomial for numerical integration a = 26866.4419; %5th order b = -2439.733266; %4th order c = 78.03726865; %3rd order d = -3.012793374; %2nd order e = 0.048096762; %constant So = 0.015; %Reactor/biofilm properties h = 100; D = 1.14; L = 0.06; %thickness of biofilm cm %define file name filename = 'CprofilesTfilm.xlsx'; %define time and space variables
x = 0:0.0005:L; t = 0:0.01:24;
%Get beta values
Beta = Efinder(h,L,D);
Lambda = Beta/L; n = numel(Lambda);
%Get value for Cn Cn = Cnsolver(Lambda,L,a,b,c,d,e,So,n);
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%Solver for each row of C % We know that S*(x,t) = Sum[1->infinity] of % (Cn*cos(lambda*x)*exp(-lambda^2*t) %And S = S* + phi, where phi = ax^5 + bx^4 + cx^3 + dx^2 + e for q = 1:numel(x)
phi(q) = a*x(q)^5 + b*x(q)^4 + c*x(q)^3 + d*x(q)^2 + e;
end %Define counters, remember that Lambda(1) = 0 j = 1; %lambda counter k = 1; %space counter w = 1; %time counter %Since phi is a fixed function S* is the only one which needs to be solved
for k = 1:numel(x) Sstore = 0; %Reset variable for j = 1:(n-1)
Stemp = Cn(j)*cos(Lambda(j+1)*x(k))*exp(-D*(Lambda(j+1)^2)*0); Sstore = Sstore + Stemp;
end S_star(k) = Sstore; end
for q = 1:numel(S_star)
S(q) = S_star(q) + phi(q);
end
for k = 1:numel(x) Sstore = 0; %Reset variable for j = 1:(n-1)
Stemp = Cn(j)*cos(Lambda(j+1)*x(k))*exp(-D*(Lambda(j+1)^2)*0.001); Sstore = Sstore + Stemp;
end S_star(k) = Sstore; end
for q = 1:numel(S_star)
S1(q) = S_star(q) + phi(q);
end for k = 1:numel(x) Sstore = 0; %Reset variable for j = 1:(n-1)
Stemp = Cn(j)*cos(Lambda(j+1)*x(k))*exp(-D*(Lambda(j+1)^2)*0.005);
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Sstore = Sstore + Stemp;
end S_star(k) = Sstore; end
for q = 1:numel(S_star)
S2(q) = S_star(q) + phi(q);
end for k = 1:numel(x) Sstore = 0; %Reset variable for j = 1:(n-1)
Stemp = Cn(j)*cos(Lambda(j+1)*x(k))*exp(-D*(Lambda(j+1)^2)*0.01); Sstore = Sstore + Stemp;
end S_star(k) = Sstore; end
for q = 1:numel(S_star)
S3(q) = S_star(q) + phi(q);
end plot(x,S);
X = transpose(x); Conct1 = transpose(S); Conct2 = transpose(S1); Conct3 = transpose(S2); Conct4 = transpose(S3); SSConc = transpose(phi);
xlswrite(filename,X,1,'A1'); xlswrite(filename,Conct1,1,'B1'); xlswrite(filename,Conct2,1,'C1'); xlswrite(filename,Conct3,1,'D1'); xlswrite(filename,Conct4,1,'E1'); xlswrite(filename,SSConc,1,'F1');
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C.4 Numerical Solution
C.4.1 Numerical Transient Solution
%Define Constants D = 1.14; %cm^2/day k = 2.1; %day^-1 Ks = 3*10^-4; %mg CO2/cm^3 xf = 50; %mg CO2/cm^3 n = 50; %Initial number of boxes depth = 1.2*10^-3; %width of each box Is = 200; %saturation light intensity Q = 0.5; %Fraction of carbon converted into biomass j = 2000; %number of time interations row = 100*10^-3; %biomass density g/cm^3 b = 0.1; %day^-1 Y = 1; % mg C/mg C Co = 0.03478; %mgC/cm^3 converge = 1; C = []; dcdt = []; delta_t1 = 0.0001; %step size filename = 'cprofilefilm.xlsx';
count = 1; checksum = 1; delta_t = delta_t1; %Generate initial matrix
for i = 1:n C(i) = (Co-Ks)/2;
end FL = Steele_const(n,depth,Is); while abs(converge) > 0.5e-7
i = 1;
%For the first box
dcdt(i) = Filmchange(D,Co,C(1),C(2),Y,b,FL(i),k,xf,Ks,depth/2,depth);
%For every other box for i = 2:n-1
dcdt(i) = Filmchange(D,C(i-
1),C(i),C(i+1),Y,b,FL(i),k,xf,Ks,depth,depth);
192
end
%Final Box i = n;
dcdt(i) = Filmchange(D,C(i-1),C(i),-0.15,Y,b,FL(i),k,xf,Ks,depth,depth);
%RungeKutta section
i = 1;
k1 = Filmchange(D,Co,C(1),C(2),Y,b,FL(i),k,xf,Ks,depth/2,depth); k2 =
Filmchange(D,Co+(delta_t1/2)*k1,C(1)+(delta_t1/2)*k1,C(2)+(delta_t1/2)*k1,Y,b
,FL(i),k,xf,Ks,depth/2,depth); k3 =
Filmchange(D,Co+(delta_t1/2)*k2,C(1)+(delta_t1/2)*k2,C(2)+(delta_t1/2)*k2,Y,b
,FL(i),k,xf,Ks,depth/2,depth); k4 =
Filmchange(D,Co+(delta_t1)*k3,C(1)+(delta_t1)*k3,C(2)+(delta_t1)*k3,Y,b,FL(i)
,k,xf,Ks,depth/2,depth);
C(i) = C(i) + (delta_t/6)*(k1+2*k2+2*k3+k4);
for i = 2:n-1 k1 = Filmchange(D,C(i-1),C(i),C(i+1),Y,b,FL(i),k,xf,Ks,depth,depth); k2 = Filmchange(D,C(i-
1)+(delta_t1/2)*k1,C(i)+(delta_t1/2)*k1,C(i+1)+(delta_t1/2)*k1,Y,b,FL(i),k,xf
,Ks,depth,depth); k3 = Filmchange(D,C(i-
1)+(delta_t1/2)*k2,C(i)+(delta_t1/2)*k2,C(i+1)+(delta_t1/2)*k2,Y,b,FL(i),k,xf
,Ks,depth,depth); k4 = Filmchange(D,C(i-
1)+(delta_t1)*k3,C(i)+(delta_t1)*k3,C(i+1)+(delta_t1)*k3,Y,b,FL(i),k,xf,Ks,de
pth,depth);
C(i) = C(i) + (delta_t/6)*(k1+2*k2+2*k3+k4);
end
i = n; k1 = Filmchange(D,C(i-1),C(i),-0.15,Y,b,FL(i),k,xf,Ks,depth,depth); k2 = Filmchange(D,C(i-1)+(delta_t1/2)*k1,C(i)+(delta_t1/2)*k1,-
0.15,Y,b,FL(i),k,xf,Ks,depth,depth); k3 = Filmchange(D,C(i-1)+(delta_t1/2)*k2,C(i)+(delta_t1/2)*k2,-
0.15,Y,b,FL(i),k,xf,Ks,depth,depth); k4 = Filmchange(D,C(i-1)+(delta_t1)*k3,C(i)+(delta_t1)*k3,-
0.15,Y,b,FL(i),k,xf,Ks,depth,depth);
C(i) = C(i) + (delta_t/6)*(k1+2*k2+2*k3+k4);
converge = sum(dcdt)*delta_t*n;
193
count = count + 1; checksum = checksum +1; if (C(1) - Co < 1e-2) if count > 10000 delta_t = delta_t*1.2; count = 0; end end if checksum > 100000 break; end
end x = []; x(1) = depth/2; for i = 2:n x(i) = depth*i-depth/2;
end
Carbon = transpose(C); X = transpose(x); plot(X,C);
xlswrite(filename,X,1,'A1') xlswrite(filename,Carbon,1,'B1')
C.5 General Function
C.5.1 Steele Function
function res = Steele_function(Io,Is,gamma,Lf,n,x) I = []; Fl = [];
for i = 1:n
I(i) = Io*exp(-gamma*x(i)); Fl(i) = (I(i)/Is)*exp(1-(I(i)/Is));
end res = Fl; end
C.5.2 Consumption
function res = C_consumption(Params,n,c,Lf,length) %fixed parameters D = Params(1); %day/cm^2 k = Params(2); %day^-1 Y = Params(3); %etc..
194
b = Params(4); %day^-1 Io = Params(5); %umol/m^2 sec Is = Params(6); %umol/m^2 sec Ks = Params(7); %mg/cm^3 gamma = Params(8); % cm^-1 xf = Params(9);
Fl = Steele_function(Io,Is,gamma,Lf,n,length); flux_tot = 0;
for i=1:n flux = Fl(i)*(k*xf*c(i))/(Ks+c(i))-b*xf/Y; flux_tot = flux*(Lf/n)+flux_tot; end res = flux_tot; end
C.5.3 Adam Bashford function [x y] = AdamBashford(a,b,h,con,fun,Co,Lf,Params) %4th- order predictor correct method of Adam-Bashford x = a:h:b; n = length(x); y = zeros(length(con),n);
y(:,1) = con; %Runge-Kutta initial Prediction
for k = 1:3 k1 = fun(x(k),y(:,k),Co,Lf,Params); k2 = fun(x(k)+0.5*h,y(:,k)+0.5*h*k1',Co,Lf,Params); k3 = fun(x(k)+0.5*h,y(:,k)+0.5*h*k2',Co,Lf,Params); k4 = fun(x(k)+h,y(:,k)+h*k3',Co,Lf,Params); y(:,k+1)=y(:,k)+h*(k1'+2*k2'+2*k3'+k4')/6; end
for k = 4:(n-1) %Predictor ab1 = fun(x(k),y(:,k),Co,Lf,Params); ab2 = fun(x(k-1),y(:,k-1),Co,Lf,Params); ab3 = fun(x(k-2),y(:,k-2),Co,Lf,Params); ab4 = fun(x(k-3),y(:,k-3),Co,Lf,Params); y(:,k+1) = y(:,k) + (h/24)*(55*ab1'-59*ab2'+37*ab3'-9*ab4'); %Corrector cab = fun(x(k+1),y(:,k+1),Co,Lf,Params); y(:,k+1) = y(:,k) + (h/24)*(9*cab' + 19*ab1' - 5*ab2' + ab3'); end
end
195
Appendix D – Light Calibration Curves
Figure D.1 – Light power emission from the red LEDs used in Chapter 4 as measured by
the Newport silicone Detector
Figure D.2 – Photon flux from the red LEDs used in Chapter 4 as measured by the
Fieldscout Quantum Light Meter
y = 150.08x
R² = 0.9813
0
50
100
150
200
250
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Lig
ht
Po
wer
Rea
din
g (
mW
/cm
2)
Electrical Power (W)
y = 10697x
R² = 0.9893
0
500
1000
1500
2000
2500
0 0.05 0.1 0.15 0.2 0.25
Ph
oto
n F
lux (
um
ol/
m2 s
ec)
Electrical Power (W)
196
Figure D.3 – Photodiode readings from the red LEDs used in Chapter 4
Figure D.4 – Light spectrum from red LEDs provided by Pond Biofuels with changing
electrical input power.
y = 2050374x
R² = 0.9879
0
50
100
150
200
250
300
0 0.00002 0.00004 0.00006 0.00008 0.0001 0.00012 0.00014
Ph
oto
dio
ide
rea
din
g (
mV
)
Electrical Power (W)
0.00E+00
2.00E-06
4.00E-06
6.00E-06
8.00E-06
1.00E-05
1.20E-05
1.40E-05
1.60E-05
1.80E-05
580 590 600 610 620 630 640 650 660 670 680 690 700 710 720
Inte
nsi
ty (
mW
)
Wavelength (nm)
2.180W
1.615W
0.818W
0.338W
0.133W
0.070W
0.024W
197
Appendix E – Environmental Scanning Electron Microscopy Images
Figure E.1 – ESEM image of an algal biofilm grown on glass tagged with Osmium
tetroxide (BSE3D Mag 250x, total width 11400 μm)
198
Figure E.2 – ESEM image of an algal biofilm growing on cellulose acetate tagged with
Osmium tetroxide (BSE3D Mag 75x, total width 12200 μm)
199
Appendix F – Sessile Drop Test Data
Table F.1 – Liquid-material contact angles for water, glycerol and hexadecane (n = 3, standard
deviations shown)
Material Water (o) Glycerol (
o) Hexadecane (
o)
Cellulose Acetate 63.1 (± 6.7) 74.0 (± 2.8) 29.9 (± 5.2)
Acrylic 66.8 (± 6.7) 64.8 (± 2.4) 15.7 (± 1.1)
Glass 33.7 (± 3.8) 43.1 (± 2.6) 15.5 (± 7.2)
Polycarbonate 79.1 (± 1.5) 68.4 (± 3.4) 9.8 (± 0.5)
Silicone Rubber 93.6 (± 3.2) 80.4 (± 1.9) 59.5 (± 5.0)
Polystyrene 72.8 (± 3.4) 54.2 (± 1.9) 15.5 (± 0.4)
Table F.2 – Dispersion surface energies of the materials used in Chapter 3
Material Dispersion Surface
Energy (mJ/m2)
STDEV
Cellulose Acetate 23.87466193 1.184088892
Acrylic 26.45141961 0.144072262
Glass 26.3555567 0.976506729
Polycarbonate 27.07246522 0.04324058
Silicone Rubber 15.61685074 1.539953997
Polystyrene 26.47994687 0.053987638
Table F.3 – Polar surface energies of the materials used in Chapter 3
Material Polar Surface
Energy (mJ/m2)
STDEV
Cellulose Acetate 7.109273393 0.413208388
Acrylic 8.239127804 0.339827272
Glass 10.90779024 0.323520256
Polycarbonate 7.612227481 0.509294616
Silicone Rubber 6.890278559 0.425203756
Polystyrene 9.620777768 0.216404759
200
Copyright Acknowledgements