Temperature Influence and Heat Management

Requirements of Microalgae Cultivation in

Photobioreactors

A Thesis

presented to

the Faculty of California Polytechnic State University,

San Luis Obispo

In Partial Fulfillment

of the Requirements for the Degree

Master of Science in Agriculture, with Specialization in:

Agricultural Engineering Technology

by

Thomas Hagen Mehlitz

February 2009

© 2009

Thomas Hagen Mehlitz

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ABSTRACT

Temperature Influence and Heat Management Requirements of Microalgae Cultivation in

Photobioreactors.

Thomas Hagen Mehlitz

Microalgae are considered one of the most promising feedstocks for biofuel

production for the future. The most efficient way to produce vast amounts of algal

biomass is the use of closed tubular photobioreactors (PBR). The heat requirement for a

given system is a major concern since the best algae growth rates are obtained between

25-30 °C, depending on the specific strain. A procedure to determine temperature

influence on algal growth rates was developed for a lab-scale PBR system using the

species

Chlorella

. A maximum growth rate of 1.44 doublings per day at 29 °C (optimal

temperature) was determined. In addition, a dynamic mathematical model was developed

to simulate heating and cooling energy requirements of tubular PBRs for any desired

location. Operating the model with hourly weather data as input, heating and cooling

loads can be calculated early in the planning stage of a project. Furthermore, the model

makes it possible to compare the operation inside a greenhouse to the outdoor operations,

and consequently provides fundamental information for an economic feasibility study.

The best configuration for a specific location can be evaluated easily. The model was

exemplary tested for a hypothetical 100,000 l photobioreactor located in San Luis Obispo,

California, U.S.A. Average algae productivity rates of 23% and 67% for outdoor and

indoor PBR operations, respectively, were obtained. Actual energy loads (heating and

cooling) needed to maintain the PBR at optimal temperature were determined and

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compared. Sensitivity analyses had been performed for abrupt temperature and solar

radiation steps, PBR row distances, ground reflectivities, and ventilation rates of the

greenhouse. An optimal row distance of 0.75 m was determined for the specific PBR. The

least amount of energy was needed for a ground reflectivity of 20%. The ventilation rate

had no major influence on the productivity rate of the system. Results demonstrated the

importance of a simulation model as well as the economic impact of a sophisticated heat

management system. Energy savings due to an optimized heat management system will

eventually increase proficiency of the systems, which will support a new sustainable

industry and future developmental potential.

Keywords: Microalgae, photobioreactor, temperature influence, heat management,

biodiesel, ethanol, biofuel, algal biomass

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ACKNOWLEDGMENTS

I would like to thank my faculty advisors for their support while working on this

thesis. I would like to thank Dr. Ilhami Yildiz for his inspiration, hard work and

friendship throughout my time at Cal Poly. Thank you for dozens of meetings, hundreds

of coffees and thousands of laughs. Please keep your high standards and amazing ways of

energizing people. Dr. Yildiz, I thank you for your great influence and shaping me to the

person I am now. I have had nothing but a great time, and am grateful for this lifetime

friendship.

I would also like to thank Dr. Richard Cavaletto, Dr. Brian Hampson, Dr. Shaun

Kelly and Dr. Shikha Rahman for their unlimited support and constant belief in me as

well as the project.

Furthermore, I would like to thank my co-workers and green-friends here at Cal

Poly: Bryan Brooker, Diana Durany and John Karamanlis for their enthusiasm and

support, their contributions to this thesis and for continuing the Algae-to-Biofuels project

at Cal Poly.

Finally, I would like to thank Burkhard, Elke, Linda, Kathrin and Sandra for their

love, support and sacrifice throughout my time on the other side of the world.

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TABLE OF CONTENTS

Page

ABSTRACT ii

ACKNOWLEDGMENTS iv

LIST OF TABLES viii

LIST OF FIGURES ix

LIST OF SYMBOLS xii

CHAPTER

I. INTRODUCTION 1

II. BACKGROUND 7

2.1 Overview 7

2.2 Algae Classification 8

2.3 Cell Theory 10

2.4 Green Algae 12

2.5 Algae Specification 13

2.7 Algal Photosynthesis 14

2.7 Growth Kinetics 16

2.8 Carbon Source (CO2) 19

2.9 Nutrients 20

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2.10 Temperature 24

2.11 Photobioreactors 26

2.11.1 Function of a Photobioreactor 29

2.11.2 Types and Usage 31

2.11.3 The PBR used for Simulation in this Study (BioFence) 34

III. MATERIALS AND METHODS 37

3.1 Experimental Set-up 37

3.1.1 Culturing Techniques 38

3.1.2 Applications 41

3.1.3

Data Collection and Analyses 47

3.2 Heat Management Simulation Model 49

3.2.1 Introduction 49

3.2.2 Physical Model and Photobioreactor Architecture 52

3.2.3 Energy Balances 52

3.2.4 General Equations 58

3.2.5 Outdoor Photobioreactor 67

3.2.6 Indoor Photobioreactor 74

3.2.7 Sensitivity Analyses and Evaluations 79

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IV. RESULTS AND DISCUSSION 80

4.1 Temperature Experiments 80

4.2 Heat Management Model 88

V. CONCLUSIONS 107

5.1 Temperature Experiments 107

5.2 Heat Management Model 109

BIBLIOGRAPHY 112

APPENDICES

A. Energy requirements per day for standard transmissivity. 120

B. Energy requirements per day for 60% transmissivity. 122

C. Energy requirements per day for 80% transmissivity. 124

D. Effects of different Nitrogen concentrations on the chemical

composition of various algae strains. 126

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LIST OF TABLES

Table

Page

1. Chemical Composition of Different Algae Strains on a Dry Matter Basis (%) 13

2. Basic fertilizer composition 41

3. Photobioreactor and greenhouse characteristics 51

4. Key model parameters and their values used in the sensitivity analyses... 79

5. Mean growth rates at different growth medium temperatures ... 85

6. Values incorporated into the heat management model 85

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LIST OF FIGURES

Figure

Page

1. Schematic view of a photobioreactor system 1

2. A tubular photobioreactor in outdoor environment. 2

3. Algae paste freshly harvested through filter technology 7

4. Scheme of an algal cell.. 11

5. Green algae as seen under the microscope 12

6. Growth phases of algal cultures.. 17

7. Variation of maximal growth rate (maxT) versus temperature 24

8. A horizontal tubular Photobioreactor 27

9. Open Pond System. 28

10. Flow chart of a photobioreactor. 30

11. Schematic view of the dark zone 32

12. Schematic view of the BioFence system 34

13. BioFence Manifold configuration. 35

14. The actual BioFence during installation. 36

15. A lab-scale PBR in use 39

16. Schematic view of the photobioreactor set-up. 40

17. Optical microscope 42

18. CO2 control valves (left) and pH computer (right) 43

19. An older spectrophotometer with analog reading. 44

20. A modern spectrophotometer with PC control 44

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21. Hanna Instruments Multimeter. 45

22. Screen view of the online database where all available data were collected. 48

23. Flow chart of the simulation model. 50

24. Dimensions of the photobioreactor. 53

25. Heat losses and gains from an outdoor PBR 54

26. Heat losses/gains from an indoor PBR and a greenhouse 56

27. Zenith angle, slope, surface azimuth angle, and solar azimuth angle for a tilted

surface. 60

28. Photobioreactor tube configuration used in determining the critical sun angle, TC.

The upper tube shades the lower tube. 62

29. Angles of incidence and refraction in media with refractive indices n1 and n2. 65

30. Photobioreactors during operation 81

31. Online database where all observed data were collected. 82

32. Sample size for each temperature experiment. 83

33. Mean growth rates and standard deviations at different temperatures 84

34. Relative productivity rates with respect to growth medium temperature. 87

35.

Chlorella

growth curve with respect to growth medium temperature. 87

36. Sensitivity analyses on outside temperature (top) and solar radiation (bottom). 89

37. Responses to a step change in outdoor temperature 90

38. Responses to a step change in solar radiation. 91

39. Energy requirements and average productivity for different ground reflectivities 92

40. Energy requirements and average productivity for different PBR distances. 93

41. Energy requirements and average productivity for ventilation rates. 95

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42. Energy requirements and average productivity for different shading material

transmissivities 95

43. Temperature variations for outdoor (top) and indoor (bottom) PBR operations. 99

44. Temperature distribution on a clear day (April 10th, 2007). 100

45. Temperature distribution on an overcast day (April 20th, 2007) 100

46. Algae productivity with respect to the temperature in each hour in the outdoor

PBR operation. 102

47. Algae productivity with respect to the temperature in each hour in the indoor

PBR operation. 103

48. The hypothetical algae productivity with respect to the temperature in each

hour for indoor PBR operation, when losses due to overheating were ignored 104

49. Required heating and cooling loads for the indoor PBR operation. 106

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LIST OF SYMBOLS

AEH

Infiltration rate

AGH

Total surface area of the greenhouse

AGHSUR

Total surface area of the floor

ATSUR

Total outside surface of the PBR tubes

ATSURPRO

Total projected surface area of the PBR

b

Distance between ground & first PBR tube

CpAIR

Specific heat of air

CpWAT

Specific heat of water

CvF

Specific volumetric heat capacity for the floor

D Dilution

rate

DAP

Specific testing vial diameter according to Bouguer′s law

DFLOOR1

Floor layer thickness of the top layer

DFLOOR2

Floor layer thickness of the middle layer

DFLOOR3

Floor layer thickness of the bottom layer

dt

Distance between PBR tube centers

dTFL1

Ground temperature change for top floor layer

dTFL2

Ground temperature change for middle floor layer

dTFL3

Ground temperature change for bottom floor layer

dTGH

Greenhouse air temperature change

dTPBR Photobioreactor

temperature

change

dtt

Distance between PBR twin tube centers

E Calculation

parameter

EF

Extinction factor according to Bouguer′s law (also known as K)

GHG Greenhouse

gable

height

GHL Greenhouse

length

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GHN

# of greenhouse bays

GHW Greenhouse

width

GHWH

Greenhouse wall height

hHTC

Heat transfer coefficient

HILL1

Illuminated height of a column n

HSPBR

Heat storage component of the PBR

IRAIR

Index of refraction n for the air

IRTUBE

Index of refraction n for the glass tube

IS

Outside solar radiation

IT

Total solar radiation reaching the tubes

JD Julian

Day

K

Thermal conductivity of floor layers

FLOOR

Ks Half-saturation

constant

lt

PBR tube length

na

# of PBR columns axial

nc

# of PBR parallel columns

Percent shading of tubes illuminated in the nth column (fully

PERCNILL

illuminated)

PERCNSHADE

Total percentage of shading received in column n

PERCNSHADE1

Percent shading of tubes in the nth column (not fully illuminated height)

PL

Actual pathlength in the algae medium

Pr

Prandtl number

Q10

Temperature coefficient

QCLBOTF

Conductive heat transfer of bottom floor layer

QCLMIDF

Conductive heat transfer of middle floor layer

QCLTOPF

Conductive heat transfer of top floor layer

QGHCL

Heat transfer due to free convection between the inside air and PBR

QGHHG

Greenhouse heat gains due to solar radiation

xiii

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QGHHLC

Greenhouse heat transfer due to conduction

QGHHLI

Greenhouse heat transfer due to infiltration

QGHHLR

Radiation exchange with the ground and sky

QGHTSRA

Total solar radiation absorbed by the PBR in the greenhouse

QOS

Outside longwave radiation exchange with the sky and the ground

QOSCL

Outside convective heat transfer due to convection

QRLF

Radiation exchange between the sky and floor

QTSRA

Total solar radiation absorbed by the PBR

QTSRAF

Total solar radiation absorbed by the floor

RALGAE

Reflectivity of the algae algae

Re Reynolds

number

REFT

Total reflection of the PBR tube

RGROUND

Reflectivity of the ground

RPARA

Parallel reflection of the PBR tube

RPERP

Perpendicular reflection of the PBR tube

SF

Shade factor

SFR

Percent shading of the first PBR column

SFtt

Overall shading factor for twin tube PBR

SFtt1

Shading factor for one twin tube column

STIME

Solar time on a specific day of the year

t

# of tubes per PBR column

T Temperature

TALG

PBR or algae temperature

TALGNEW

New PBR temperature

TC Critical

sun

angle

TFLOOR Floor

temperature

TFLOORBOT

Bottom floor layer temperature

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TFLOORMID

Middle floor layer temperature

TFLOORNEW

New floor temperature

TG

Deep ground temperature

TGH Greenhouse

temperature

TIME

Time on a specific day

Tinf

Temperature at 10% of maximum growth rate (lower end)

Topt

Optimal temperature

TOS

Outside air temperature

TSKY

Sky temperature

Tsup

Temperature at 10% of maximum growth rate (upper end)

Switch to decide whether twin tubes (1) or single tubes (0) are used in

tt

PBR columns

UFL

Heat transfer coefficient - poured concrete 152 mm

UG

Heat transfer coefficient - single layer glass

VFL1

Volume of the top floor layer

VFL2

Volume of the middle floor layer

VFL3

Volume of the bottom floor layer

VGH

Total greenhouse volume

VPBR

Total photobioreactor volume

WS Wind

speed

x

Distance between PBR columns (parallel)

xa

Distance between PBR columns (axial)

Absorptivity of the floor

FLOOR

Slope of virtual surface for beam incidence

Surface azimuth angle

Declination, the angular position of the sun at solar noon

xv

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Emissivity of the glass/Plexiglass tubes

f

Flow rate photobioreactor

max

Maximum growth rate

maxT

Temperature dependent maximum growth rate

Angle of incidence

AIR

Density of air

WAT

Density of water

Total transmissivity PBR

GH

Transmissivity of the greenhouse cover

A

Transmissivity of algae water

T

Transmissivity of PBR tubes

Latitude for location (San Luis Obispo)

Hour angle, the angular displacement of the sun

xvi

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CHAPTER I

INTRODUCTION

As we enter into the 21st century, the world is faced with two major problems: the

depletion of fossil fuels and the resulting dependency on fossil fuel exporting countries,

as well as the aspect of global warming through emissions of greenhouse gases (Hinrichs

and Kleinbach, 2006). Alternative, renewable, and environmentally friendly energy

sources in combination with energy conservation practices are key elements in solving

these problems. A lot of research has been done in various fields of alternative energy

such as bioethanol and biodiesel production from crops, development of hydrogen as a

Figure 1. Schematic view of a photobioreactor system.

Source: After Algaelink, 2007.

fuel alternative, and biogas upgrades for use in gas fired vehicles. All of these new

technologies however, have a number of disadvantages (Antoni et al., 2007). Thus far,

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they are either not productive enough, stand in contrast to public interests, or lack an

abundance of a vital resource (mainly water and land). Therefore, several prudent

questions need to be addressed. Can biomass be supplied without impacting the cost of

agricultural land, competing with food production or harming the environment? Do we

have sufficient land here or elsewhere?

Growing algae as a biofuel feedstock can be the solution to all of these problems.

It has emerged as a viable resource for biodiesel and bioethanol production. Algae can be

grown in two different systems, in photobioreactors (PBR) (Figure 1 and Figure 2) or in

raceway ponds. Since the raceway ponds are less productive, land area extensive and

uncontrollable, the PBRs will be the favorable application for the future (Chen, 1996).

The PBR technology itself is quite new; therefore, much more research and

improvements need to be done to optimize and enhance the existing systems for

Figure 2. A tubular photobioreactor in outdoor environment.

Source: After Algaelink, 2007

commercial applications (NREL, 1998; Richmond, 2000; Pulz, 2001; Chisti, 2007;

Huntley and Redalje, 2007). The major technical challenges are how to sustain the

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highest photosynthesis and biomass productivity levels, reduce cell damage due to

hydrodynamic stress, reduce costs in fabrication and installation maintenance, and how to

increase the capability of the system to expand to an industrial scale (Barbosa, 2003;

AlgaeLink, 2007).

Unlike other crops that are currently being used for oil production such as

soybean, oil palm, corn, and jatropha, some strains of algae contain as much as 70% oil.

They are capable of producing more than 30-times the amount of oil (per year per unit

area of land) when compared to oil seed crops (Chisti, 2007). Another advantage is that

since algae use CO2 as a carbon source to grow, algae can extract the carbon dioxide from

power plant exhausts or any other CO2 emitting process when the PBR is integrated into

such a plant. A yield of 200 to 400 tons of oil/hectare/year can be considered reachable

with a standard PBR system (Oilgae, 2006; Huntley and Redalje, 2007).

Theoretically, biodiesel produced from algae appears to be the only feasible

solution today for replacing petrodiesel completely. No other feedstock has an oil yield

high enough to be in a position to produce such large volumes of oil. It has been found

that approximately 10 million acres of land would be needed for biodiesel production in

order to produce enough biodiesel that could replace all the petrodiesel currently used in

the U.S. (Oilgae, 2006). This is just 1 to 3% of the total land used today for both farming

and grazing in the United States (about one billion acres). Clearly, algae biomass is a

superior alternative as a feedstock for large-scale biodiesel production. One of the

byproducts of the biofuels production from algae is a protein rich algae cake that can be

used as an animal feed. Photobioreactors make it possible to supply biomass without

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impacting the cost of agricultural land, competing with food production and harming the

environment. Co-production of biofuel and animal protein makes this resource efficient

system a very attractive environmentally friendly alternative.

Impacts

Photobioreactors have two main functions: i) produce biomass in the form of

algae, and ii) the use of carbon dioxide (CO2) from the atmospheric environment in order

for the algae to grow. CO2 is the most emitted greenhouse gas; and therefore, is widely

considered responsible for global warming and its consequences. About 85% of the

released CO2 in California comes from fuel combustion. Other sources of CO2 emission

specific to California include the production of ethanol, cement, lime and waste

combustion (Climatechange CA, 2005). Companies are not allowed to release as much

CO2 as they would like to. Instead, they have to pay for every emitted ton of CO2.

Different scenarios estimate a CO2 price of $15 to $95 per ton (Spicher, 2008) in the

coming years. It is currently about $10 per ton of CO2. Large systems are able to utilize

about 150 tons of CO2 to produce 100 tons of dry biomass per day. The dry biomass is

then pressed to obtain the end products: algae vegetable oil and algae cake. Vegetable oil

can be converted to biodiesel. The market price for vegetable oil is currently about $3.00

per gallon. The algae cake is worth about $0.50 per kg and highly demanded by

agricultural and food industry. Algae cake is highly nutritious and is used as food

supplements and feedstock for animals (AlgaeLink, 2007).

The feasibility of photobioreactors is therefore mainly dependent on the algae

productivity as well as energy consumption during the algae production and processing.

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Revenue is generated simply by operating the plant; from the biological sequestration of

greenhouse gases, and marketing the value-added products (biodiesel, algae cake, and

others).

The overall research goal in this field is the development and optimization of

photobioreactors for microalgae cultivation to produce biofuels. The PBR technology is

only a few years old; therefore, further research and improvements are needed to optimize

and enhance the existing systems for commercial applications (NREL, 1998; Richmond,

2000; Pulz, 2001; Molina-Grima et al., 2004; Schulz, 2006; Chisti, 2007; Huntley and

Redalje, 2007; Antoni, 2007). The major technical challenges are how to sustain highest

photosynthesis and biomass productivity levels, reduce cell damage by hydrodynamic

stress, reduce costs in fabrication and installation maintenance, and how to increase the

capability of the system to expand to an industrial scale (Barbosa, 2003; AlgaeLink,

2007). The main goal is to make the systems economically feasible to produce algae on a

large-scale.

The specific objective of this study was to evaluate temperature influences on

algae cultivation in photobioreactors and the resulting heat management practices by

developing a dynamic simulation tool. The simulation shall provide fundamental data for

planning the best location and layout of commercial algae production plants. This study

investigates the effects of location, local climate and algae strain yield to analyze the

feasibility of a given PBR system. The results of this study are valuable for people

planning a business and operators of algae production systems using photobioreactors. It

answers the following questions: Where (geographically) can photobioreactors be placed?

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Are greenhouses necessary for housing photobioreactors? Is it feasible to heat the system

to get a better yield? At what temperatures is heating (or cooling) necessary?

General Approach

An experimental study was executed using a lab-scale photobioreactor. While

growing microalgae in the PBR, the system′s temperature was varied. The algae yield

differences due to temperature change was gathered and analyzed to find the optimal

temperature for algae growth. A comprehensive dynamic mathematical model for a

horizontal tubular PBR was developed and executed using the location of San Luis

Obispo, California, USA. Heat requirements of a virtual commercial-scale system were

calculated using the model and analyzed for indoor and outdoor growing conditions to

study heat management practices and improve the system efficiency.

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CHAPTER II

BACKGROUND

2.1 Overview

Microalgae are single celled microscopic organisms, which (like plants) use

photosynthesis to convert the sun′s energy into chemical energy. They are much more

efficient converters of solar energy than any known plant, because they grow in

suspension where they have unlimited access to water and more efficient access to CO2

and dissolved nutrients.

Microalgae are the fastest growing photosynthesizing organism on earth (Figure

3). They can complete an entire growing cycle in as short as one day only. Over 100,000

different strains of algae are known and many are still not discovered (NREL, 1998).

Three hundred species, mostly green algae and diatoms are winnowed and considered

Figure 3. Algae paste freshly harvested through filter

technology. Source: After Algaelink, 2007.

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viable for the production of biofuels. Some of those contain as much as 70% lipids (oil).

Many species can grow in brackish water, that is, water that contains high levels of salt.

Therefore, a competition with drinking water could be avoided by choosing the right

algae strain (NREL, 1998).

The cultivation of algae is nevertheless a complex process. The nutrient level in

the water must be in a specific range, the pH must always be under control. Nutrients

must be controlled so algae will not be "starved", and so that nutrients will not be wasted

either. Light must neither be too strong nor too weak. Algae only need 10% the amount of

light they receive from direct sunlight (Barbosa, 2003).

2.2 Algae Classification

Algae are a diverse group of organisms. They vary in size from single-celled

microalgae (as small as one micrometer) to several meter long seaweeds. Most algae are

photoautotrophic, however, some are facultative or obligate heterotrophs (Darley, 1982;

Becker, 1994). Photoautotrophs conduct photosynthesis, sequestering CO2, and using

light as the energy source. Heterotrophs receive their energy from organic carbon

compounds, instead. For the purpose of large-scale biofuel production, photoautotrophic

microalgae are the favorable kind, unless large amounts of chemically bound energy is

readily available for algae production (NREL, 1998).

Many different characteristics describe a single alga. The classification system is based

on attributes like (Jonathan et al., 2007):

- Presence or absence of flagella (tail)

- Flagellar characteristics (length, number, hairs, point of insertion)

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- Cell-wall composition, and

- Type of stored photosynthetic product

Over 100,000 different microalgae are classified in a variety of classes. The most

common classification of algae is shown below (NREL, 1998):

· BACILLARIOPHYTA (diatoms)

· CHAROPHYTA (stoneworts)

· CHLOROPHYTA (green algae)

· CHRYSOPHYTA (golden algae)

· CYANOBACTERIA (blue-green algae)

· DINOPHYTA (dinoflagellates)

· PHAEOPHYTA (brown algae)

· RHODOPHYTA (red algae)

About 300 species (mostly green algae and diatoms) show a potential (oil yield,

growing parameters) for different biofuel applications (NREL, 1998). This work will

therefore focus only on these two classes. Since they are single-celled organisms, some

background about cell theory is necessary to understand the complex interrelations.

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2.3 Cell Theory

The cell is the fundamental building block of life. It is the structural and

functional unit of all known living organisms. It is the smallest unit of an organism that is

classified as living (Alberts, 2002). Some organisms, such as bacteria and microalgae are

unicellular (consist of a single cell) (Figure 4). Other organisms, such as humans, are

multicellular. The cell theory, first developed in 1839 by Matthias Jakob Schleiden and

Theodor Schwann, states that all organisms are composed of one or more cells. All cells

come from preexisting cells. Vital functions of an organism occur within cells, and all

cells contain the hereditary information necessary for regulating cell functions and for

transmitting information to the next generation of cells (Espinasse, 1962). Cells are:

capable of growth and reproduction; that is, they can reproduce another entity

essentially identical to themselves.

highly organized and selectively restrict what crosses their boundaries. Thus, cells

are at low entropy compared to their environment.

composed of major elements (C, N, O and S, in particular) that are chemically

reduced.

self-feeding. They take up necessary elements, electrons and energy from their

external environment to create and maintain themselves, as reproducing,

organized and reduced entities. They require sources of elemental building blocks

that they use to reproduce themselves. They require a source of energy to fuel the

chemical processes leading to all three properties. In addition, they require a

source of electrons to reduce their major element. How cells obtain elements,

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energy and electrons is called

metabolism

, and is one essential way to characterize

a cell.

Cells can be divided into two main groups: the Prokaryotes and the Eukaryotes.

The main difference is that the Prokaryotes do not have a cell nucleus, and the DNA

floats freely in the cell (Shuler and Kargi, 2002).

Microalgae are made up of eukaryotic cells. These are cells with nuclei and

organelles. All algae have plastids, the bodies with chlorophyll that carry out

photosynthesis. However, various lines of algae can have different combinations of

chlorophyll molecules; some have just Chlorophyll A, some have a combination of A and

B, or A and C (Becker, 1994; Degen, 2003).

Figure 4. Scheme of an algal cell.

Source: After Sparknotes, 2007.

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2.4 Green Algae

The green algae are probably the most important class for the biofuel production

(NREL, 1998). They are one of the larger groups of algae in terms of variety of species.

Green algae (Figure 5) live mostly in fresh water. Some species can also live in moist soil

or in brackish water.

Figure 5. Green algae as seen under the microscope.

Source: After Esapub, 2006.

The two main characteristics of green algae are i) the use of chlorophyll A and B

in their photosynthesis (which gives them their green color), and ii) the enclosure of the

chloroplast in a double membrane. These characteristics make green algae the most plant-

like algae (Darley, 1982).

Green algae include unicellular and colonial flagellates, usually but not always

with two flagella per cell, as well as various colonial, coccoid, and filamentous forms

(Thomas, 2002). Many species live most of their lives as single-cells, other species form

colonies or long filaments. All green algae have mitochondria with flat cristae. When

present, flagella are typically anchored by a cross-shaped system of microtubules, but

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these are absent among the higher plants and charophytes. Flagella are used to propel the

organism. Green algae usually have cell walls containing cellulose (Hoek et al., 1995).

2.5 Algae Specification

The typical chemical algae composition contains proteins, carbohydrates, fats

(lipids), and nucleic acids in varying proportions. The percentages vary with the type of

algae, but also within a specific strain based on the nutrient supply. Table 1shows a range

of each compound for a number of important strains.

Table 1. Chemical composition of different algae strains on a dry matter basis (%).

Source: After Becker, 1994.

Strain Protein

Carbohydrates

Lipids

Nucleic

acid

Scenedesmus obliquus

50-56

10-17

12-14

3-6

Scenedesmus quadricauda

47 -

1.9

-

Scenedesmus dimorphus

8-18

21-52

16-40

-

Chlamydomonas rheinhardii

48 17

21

-

Chlorella vulgaris

51-58

12-17

14-22

4-5

Chlorella pyrenoidosa

57 26

2 -

Spirogyra sp.

6-20

33-64

11-21

-

Dunaliella bioculata

49 4

8 -

Dunaliella salina

57

32

6

-

Euglena gracilis

39-61 14-18

14-20

-

Prymnesium parvum

28-45

25-33

22-38

1-2

Tetraselmis maculata

52 15

3 -

Porphyridium cruentum

28-39

40-57

9-14

-

Spirulina platensis

46-63 8-14

4--9 2-5

Spirulina maxima

60-71

13-16

6-7

3-4.5

Synechoccus sp.

63 15

11

5

Anabaena cylindrica

43-56

25-30

4-7

-

13

---

2.6 Algal Photosynthesis

Photosynthesis is the process by which plants utilize the energy of the sun′s

radiation to produce energy and new biomass. Photosynthesis is the base reaction

supplying the vast majority of energy used by plants. Energy absorbed by chlorophyll

from the sun is captured in the form of ATP (adenosine triphosphate) and NADPH

(nicotinamide adenine dinucleotide phosphate), and later used to convert carbon dioxide

to carbohydrates plus oxygen. The carbohydrate can then be converted to protein or fat

(Hoek et al., 1995). The following simplified chemical reaction describes the process

quantitatively:

6 CO2 + 12 H2O + photons

C6H12O6 + 6 O2

(2.1)

Solar energy is spread along a wide range of wavelengths, of which only a portion

is useable for photosynthesis. The wavelengths useable by plants are known as

Photosynthetically Active Radiation (PAR), covers the spectral range from 0.4 to 0.7

micrometers, which includes about 45 to 50% of the total solar energy. Energy

requirements of the photosynthesis reaction reduce the usability of that 45 to 50% by

another factor of 4. The theoretical energy use is therefore roughly 11% of the overall

solar energy. This photosynthetic efficiency is translated into biomass including fats,

proteins, simple and complex carbohydrates (cellulose, lignin, etc.) and simple

carbohydrates (Luening, 1981; GreenFuel Technologies Corporation, 2008).

14

---

Algae have been grown at a photosynthetic efficiency of approximately 5.4%

under natural sunlight. Crops in general grow at a photosynthetic efficiency of

approximately 1%. Algae can be grown much more efficiently because of the nature of

the photobioreactor and the removal of factors that might limit growth such as lack of

nutrients or CO2 (Luening, 1981; Pirt et al., 1983; Kirk, 1994; Ogbonna et al., 1995;

GreenFuel Technologies Corp., 2008).

Understanding the basics, one can easily assume that the algae growth rate can be

improved by using artificial lighting for 24 hours. However, this needs to be determined

for each individual application. In most cases, it is not economically feasible due to high

energy costs of artificial lighting.

The issue of lighting brings rise to the topic of photoinhibition. Algae must

receive sufficient light to exceed their light compensation point for their net growth.

Increasing light beyond the compensation point results in an increase in the growth rate

until the culture becomes light saturated, and higher light intensities can lead to

photoinhibition. Photoinhibition is a reduction in an alga′s capacity for photosynthesis

caused by exposure to strong light. Photoinhibition is not necessarily caused by intense

light, but rather absorption of too much light energy compared with the photosynthetic

capacity (Acien Fernandez et al., 1998; Yun and Park, 2001; Wu and Merchuk, 2002;

Barbosa, 2003).

15

---

2.7 Growth Kinetics

Unicellular microalgae do not grow in size or weight as regular plants or animal

cells. Rather, the growth is accomplished by increasing the number of single cells. For

filamentous algae, growth can also mean the elongation of the chain. However, since

every alga could also live alone and functions in the same way whether on or off the

chain, the elongation of the chain can be seen and measured by simply counting the

number of cells.

Commonly, populations of unicellular algae can be measured by the number of

single cells or by their mass. The former is then called "cell concentration", defined as the

number of individual cells per unit volume; the latter is called "cell mass" or "cell

density", defined as the weight of cells or biomass per unit volume. The growth kinetics

can be determined in a homogenous batch culture, where the nutrient supply is limited

and nothing is added or removed from the media. The algal growth passes through several

different phases as given in Figure 6 (Becker, 1994; Shuler and Kargi, 2002):

1. Adaption (lag phase)

2. Accelerating growth phase

3. Exponential growth (log phase)

4. Decreasing log growth (linear growth)

5. Stationary phase

6. Accelerated death

7. Log death

16

---

5

4

6

dN/dt = k

3

dN/dt = kN

BIOMASS

2

1

TIME

Figure 6. Growth phases of algal cultures. Source: After Shuler and Kargi, 2002.

The different phases are not always as clear as shown in the Figure 6. The slope

may vary in magnitude, length or height. Also, the transitions from one phase to another

may be shaped differently. The actual shape is based on the inoculation material, the

nutrient concentration, and the environmental conditions such as light intensity,

temperature, pH, etc. (Shuler and Kargi, 2002).

Phase 1:

When the medium is inoculated with the algae culture, the culture is not

adapted to the new environment. It takes some time for the culture to adjust to the new

conditions, before the algae can start growing.

Phase 2 and 3:

After the cells have adapted themselves to the new environment,

the exponential (logarithmic) growth begins. During this phase the increase in algal

biomass per time is proportional to the biomass in the population at any given time,

17

---

provided that neither light nor nutrient is limited. A steady-state is reached. The cells are

divided at a constant rate.

Phase 4:

The logarithmic growth declines at the point when nutrients get

depleted, and even more significant, when the culture density reaches its critical point.

Shading comes into play and a dark zone in the center of the bioreactor evolves. Light

becomes the limiting factor to the growing conditions. The increase in algal biomass

becomes almost linear. In well maintained, nutrient rich environments, this phase

continues, however, when one of the nutrients gets depleted, respiration effects occur.

Phase 5:

The light supply per algal cell becomes limited. Equilibrium is reached

between the maximum concentration of biomass and loss due to degradation processes.

The growth curve approaches a limiting value ­ the maximum attainable biomass

concentration in a closed system.

Phase 6:

Reduced viability in the cell population; the algal cells begin to release

organic, growth-inhibiting, materials into the medium. The phase is caused by

unfavorable conditions, over-age of the cultures and limited supply of light and nutrients,

or infection by other microorganisms.

Phase 7:

Death phase becomes exponential, leading to a complete breakdown of

the population.

As already mentioned, the growth kinetics curve came from a batch culture. For

mass production of algae, a continuous process is desirable (as realized in

photobioreactors) to obtain a high productivity. In that case, the algal growth has to be

kept at a steady-state (exponential) phase. Nutrients, therefore, have to be added

18

---

continuously and biomass has to be removed respectively, to keep the cell density at an

optimal level (avoid light limitation). The ratio of the flow rate

f

, at which the fresh

medium (nutrients) is supplied to the culture volume,

V

becomes important. This ratio is

called dilution rate,

D

=

f/V

. Its reciprocal, 1/

D

is called the mean residence time of an

algal cell in the system. For the size of the algal population to remain constant in the

system, the following equations have to be fulfilled: d

N

/d

t

= 0 and

=

D

, meaning that a

steady state is reached (Becker, 1994).

2.8 Carbon Source (CO2)

Like all autotrophic organisms, algae require an inorganic carbon source to

perform photosynthesis. In the case of a photobioreactor, the easiest way would be the

aeration with ambient air; however, the natural CO2 concentration (0.03%) in air is too

low to sustain optimal growth and high productivity. Freshwater algae, growing under

low salinity and at near neutral pH conditions, must be supplied with additional CO2 to

ensure satisfactory growth rates. Usually, CO2 enriched air is supplied to the systems.

In water, CO2 appears in different forms, depending on the pH, temperature and the

concentration of nutrients (Becker, 1994):

CO

-

2-

2 + H2O H2CO3 H+ + HCO3 2H+ + CO3

(2.2)

When growing algae in continuous flow, the pH tends to elevate due to the

excretion of OH- ions by the algae into the water. A sophisticated CO2 dosing system will

maintain the pH near neutral (Aqua Medic, 2007).

19

---

Algal biomass consists of about 50% carbon, which means that about 1.8 kg of

CO2 is required to produce 1 kg of biomass based on the chemical reaction described in

Chapter 2.6. Since pure CO2 is expensive, a production plant would need to look for

cheap alternatives. As already mentioned in the introduction, this is a good opportunity to

utilize flue gas from power plants, combustion processes, or cement plants. Ethanol plants

are considered to be the ideal carbon source for algal growth since it can be used without

a costly purification process (Aqua Medic GmbH, 2007; GreenFuel Technologies Corp.,

2008).

2.9 Nutrients

In addition to carbon, algae need some additional nutrients to grow and reproduce.

The most critical elements are nitrogen, phosphorous and silicon due to the high amount

required to produce the biomass. Trace elements are also important because they often are

used as catalysts and therefore, accelerate the process significantly. General information

about the uptake and limitation of nutrients are presented here, hoping to help in

understanding principles to come later.

Uptake kinetics

The nutrient supply can affect the algal growth rate, especially when the nutrient

concentration is low. Michaelis-Menten (1913) developed an empirical equation for

enzyme kinetics that can also be used to describe the relationship between the nutrient

concentration and the uptake rate (Darley, 1982). This relationship follows a hyperbolic

function:

20

---

V = Vm (S/(KS

+

S))

(2.3)

where V is the nutrient uptake rate, Vm is the maximum nutrient uptake rate, S is the

concentration of nutrient, and KS is the the half-saturation constant or substrate

concentration at which V = Vm/2. The half-saturation constants for nitrate, ammonia,

phosphate and silicate are in the mol l-1 range (0.1 - 5 mol l-1). It should also be noted

that KS may vary with environmental parameters such as temperature (Darley, 1982).

Nitrogen

From a quantitative view, nitrogen is, beside carbon, the most important nutrient.

It can be utilized by algae in organic (urea) or inorganic (nitrate, nitrite, ammonia) forms.

Nitrite (NO -

2 ) is toxic when used in larger amounts (higher concentrations) and thus not

very convenient to use (Darley, 1982). The growth rate is generally the same for every

nitrogen source. The best nitrogen assimilation can be reached using organic urea

((NH

+

-

2)2CO). Using inorganic sources, ammonia (NH4 ) is preferred over nitrate (NO3 ).

However, high ammonia concentrations (> 0.5 to 1.0 mol/l) will inhibit the uptake of

nitrate. The assimilation of inorganic nitrogen is highly related to the pH, since nitrogen

absorption changes the pH. Ammonia as a source of nitrogen may decrease to a low pH

of 3.0. The cells can only take up NH +

-

4 , so NO3 has to be reduced by an enzyme first

before incorporation into amino acids is possible (Darley, 1982):

NO -

-

+

3

NO2

NH4 (2.4)

The mean nitrogen requirement for many green algae is approximately 5 to 10%

of the dry weight or 5 to 50 mM (Millimolar) (Becker, 1994). Nitrogen deficiency results

21

---

in a growth limitation, but also in a higher proportion of lipids in every cell (Appendix

D). For biodiesel production, this is an opportunity to increase the oil yield per unit

weight (Eppley and Renger, 1974).

Phosphorous

Phosphorous is another significant nutrient for algal growth; it is essential for

almost all cellular processes. A limitation in phosphorous will also cause a decreased

growth rate. The phosphate forms PO 3-

-

2-

4 , H2PO4 and HPO4

are the most important

inorganic phosphorous sources for algae (Darley, 1982; Becker, 1994). However, algae

can obtain phosphorous from organic compounds, which has to be hydrolyzed by

extracellular phosphatases. This process is comparably slow and organic phosphorous is

not available all the time. The ideal phosphorous concentration in the growth medium

varies among the different species. The average concentration (tolerance) is in a range of

50 g/l to 20 mg/l (Becker, 1994). The phosphorous uptake rate is influenced by factors

such as pH and the concentration of Na+, K+, Mg+ and various heavy metals. Similar to

the starvation of nitrogen, a phosphorous deficiency increases the proportion of produced

lipids.

Silicon

Silicon is necessary for the growth of diatoms (silicon is part of the cell wall).

Usually, the orthosilicic acid (Si(OH)4) is used in artificial media. The assimilation takes

place in the later phase of cell growth (when the cell walls are built) (Sullivan, 1977).

22

---

Trace Elements

Only very small amounts (micro-, nano-, pictograms per liter medium) of trace

nutrients are needed for optimal growth. The most important elements are manganese,

nickel, zinc, boron, vanadium, cobalt, copper and molybdenum. Properties of essential

trace elements are as follows (Becker, 1994):

- Influence algal growth in a representative number of species,

- Have a positive effect on total growth,

- Show a direct physiological effect on algal growth,

- Cannot be replaced by another element, and

- Show reversible signs of deficiency in cultures lacking this element.

Vitamins

Some algae require additional vitamins for optimal growth. The most common

vitamins are B12, thiamine, and biotin. Concentrations may range from 1/10 to 1/100 ng/l

(Provasoli, 1974).

23

---

2.10 Temperature

The yield of algae production can be described through the specific growth rate .

The specific growth rate declares the doubling of cells per day (1/day). The maximum

specific growth rate, max, describes the highest value of the specific growth rate, ,

which also indicates the optimum algal growth rate under a specific condition.

Temperature is a widely measured environmental variable, and an important

factor that affects the performance of algal growth (Raven and Geider, 1988; Shuler and

Kargi, 2002). Determining the affect of strictly temperature on algal growth rate, can be

identified by keeping all other variables constant. The growth rate reaches a maximum at

a specific temperature. For microalgae, the growth rate, and therefore the yield, will

1.4

0.7

Maximal growth rate (1/day)

0.0

0

10

20

30

40

Temperature (°C)

Figure 7. Variation of maximal growth rate (maxT) versus temperature for

four different algae strains. Source: After Dauta et al., 1990.

24

---

follow a skewed normal distribution (Lehman et al., 1975; Dauta et al., 1990), where max

is the peak (Figure 7). Every single algae strain has a different specific growth rate, which

needs to be determined. The skewed normal distribution can be described through the

Eqn. 2.5 and 2.6, one for the specific growth rate below the maximum and one for the

specific growth above the maximum. The temperature dependent growth rate (maxT)

reaches a maximum at the optimal temperature (Topt). The growth rate declines therefore,

when the temperature rises or falls. Temperature limits are reached when maxT = 10% of

the maximum growth rate max under optimal conditions. The lower temperature limit

was expressed as Tinf, whereas the upper limit was shown as Tsup (Dauta et al., 1990):

maxT = max * EXP {- 2.3 * [(T ­ Topt) / (Tsup ­ Topt)]2}

(2.5)

for T > Topt

maxT = max * EXP {- 2.3 * [(T ­ Topt) / (Tinf ­ Topt)]2}

(2.6)

for T < Topt

The temperature coefficient (Q10) represents the factor by which the rate (R) of a

reaction increases for every 10-degree rise in the temperature (T). The rate (R) may

represent any measure of the progress along the process. If the rate of the reaction is

temperature independent, it can be seen in Eqn. 3 that the resulting Q10 will be equal to

1.0. If the reaction rate increases with increasing temperature, Q10 will equal greater than

1.0. Thus, the more temperature dependent a process is, the higher the Q10 value will be

(Eskandari, 2008):

25

---

Q

-T ))

10 = (R2/R1) (10/(T2

1 (2.7)

The Q10 value for microalgae grown in batch cultures is 1.88 at the maximum

growth rate, max. For continuous cultivation in large-scale photobioreactors, the Q10

value is between 2.08 - 2.19 at max. A number of researchers reported that the Q10 value

becomes greater below the optimal growth rate (Eppley, 1972; Goldman and Carpenter,

1974; Raven and Geider, 1988).

2.11 Photobioreactors

A Photobioreactor (PBR) is a bioreactor that incorporates some type of light source.

Photobioreactors are therefore fermenters in which phototrophic microorganisms such as

microalgae are cultivated. This type of technology implements a closed system that

introduces carbon dioxide to the algae in order to enhance its growth in the presence of

light, water and nutrients. Closed photobioreactors are culture systems which restrict the

exchange of gases, water, and contaminants between the culture and the outside

environment (Figure 8). They have several advantages over open pond systems (Figure 9)

for the cultivation of microalgae (Chen, 1996), such as

-

higher biomass concentrations due to shorter light paths,

-

reduced contamination,

-

better control of algae culture,

-

large surface-to-volume-ratio,

26

---

-

better control of gas transfer,

-

reduction in evaporation of growth medium,

-

uniform temperature, and

-

higher cell densities possible.

Figure 8. A horizontal tubular Photobioreactor.

Source: After Mehlitz, 2008.

27

---

Figure 9. Open Pond System.

Source: After Seambiotic, 2008.

The ability of a pond to grow algae is limited by its surface area, not by its

volume. Receiving just enough solar radiation, algae can only grow in the top 6 mm layer

of the water (Chen, 1996).

The microalgae production can be divided into two main substrate usages: the so

called "clean process" and the "wastewater process". The clean process uses fresh water

with artificial fertilizers (nutrients) at specific concentrations. The wastewater process on

the other hand uses filtered wastewater. The main advantage of wastewater use is the

abundance of inexpensive substrate (avoiding the use of artificial fertilizers) and the

synergies with wastewater treatment plants. The main disadvantage, however, is the

uncontrollability due to the vast amount of different and unknown bacteria, viruses and

algae. Thus, growing a single species in wastewater is almost impossible.

28

---

2.11.1 Function of a Photobioreactor

A photobioreactor is a closed loop system. The algae grow in water, which is

pumped through different stages (Figure 10). The heart of a PBR is where the

photosynthesis occurs; where the algae is illuminated and absorbs solar radiation or

artificial light through glass, transparent plastic tubes, bags or plates. The water is

transported by a pump from the photosynthesis part of the PBR to the main feeding

vessel. The vessel is usually manufactured from stainless steel or plastic to avoid

corrosion and ensure a sanitary environment. The algae are not illuminated in the vessel,

so that a natural light­dark cycle between the photosynthesis part and the vessel can

occur. This enhances algal growth because the algae have time for respiration in the dark.

The vessel also makes it possible to supply nutrients and initial algae strains (inoculation

material) to the system. Also, a temperature control can be mounted in the feeding vessel.

The CO2/air mix is supplied through a valve connected on a tube right after the vessel.

Harvesting takes place through a bypass in the system. When a critical cell density is

reached, a valve flips over, and the algae water is directed through a filter or centrifuge

system that extracts the algal biomass from the water. The water that now hardly contains

algae is directed back to the system. The extracted algae mass can then be processed

further by methods such as drying and pressing.

29

---

l

ow chart of a photobioreactor.

Figure 10. F

30

---

2.11.2 Types and Usage

Photobioreactors can be divided into five major groups: vertical tubular,

horizontal tubular, plate, plastic bag system, and combinations of these.

Tubular Systems

There are numerous ways to construct tubular reactors although they all perform

the same function. The tube is transparent and can be flexible, which is either laid out in a

serpentine manner, coiled, or rigid structure. When laid out rigid, the tubes are either

joined at the end by U joints or by manifolds. There is a substantial amount of literature

that presents efficient ways of growing large quantities of various species of algae. An

increasing number of hatcheries and algal production facilities are using tubular reactors

because of their production benefits such as higher yield, better environmental control,

and savings of labor.

Advantages of a tubular reactor include:

- Maximum light efficiency, and therefore, significantly improved productivity.

Compared to bag cultures, the productivity is about 10-20 times higher.

- Self cleaning mechanisms can be implemented.

- Space saving. They can be mounted vertically, horizontally or at an angle, indoors

or outdoors.

- Less labor requirements that reduces or eliminates handling problems.

- Systems can be operated for long periods of time without culture death.

31

---

- Good controllability. They usually have automated systems where cultures can

easily be kept hygienic. All environmental parameters are controlled.

One limitation of tubular systems is the dark zone in the center of the tubes as the

diameter gets larger (Figure 11). Narrow diameter tubes avoid this problem since the light

can penetrate all the way to the center of the tubes. This maximizes the available surface

area for photosynthesis. Another system limitation is the pump. In order to reduce the

problems of algae fouling as well as avoiding the tube cleaning, the flow rate through the

tubing needs to be sufficient to induce appropriate turbulent flow. The AlgaeLink system

avoids the need for this by having pig-like cleaners which are used frequently; however,

the downside is the loss of productivity.

Zone of light penetration of

algae penetration

Dark zone

Tank or bag culture

Small diameter PBR

tube

32

---

The simplest and cheapest means of achieving turbulent flow is with a centrifugal

pump. This has been shown very effective with tough cell walled algae such as

Nannochloropsis

and

Chlorella

(Varicon Aqua Solutions, 2004)

.

These are probably the

most successful species to grow in tubular reactors where they are able to grow to

extremely high densities. A centrifugal pump will however act like a liquidizer on many

algal species and could destroy them completely. Diaphragm pumps and very low shear

pumps and good for pumping flagellate genera such as T

tetraselmis

and

Isochrysis

(Varicon Aqua Solutions, 2004)

.

Diaphragm pumps are cheap, but often require a high

pressure compressed air supply, which may not always be available. Low shear pumps

need to be larger in size than a centrifugal pump, in order to produce the same flow,

Figure 11. Schematic view of the dark zone

which means that Diaphragm pumps can therefore be expensive.

The system size is a critical measure as well and must be analyzed. As the length

of tubes increase so does the friction of the liquid in the tubing. The head pressure

required to pump the water, therefore, increases as well. For that reason, bigger and more

expensive pumps are required in larger systems. In addition, as the amount of time the

algae spends in the light increases, the carbon dioxide consumption increases, too.

Oxygen poisoning combined with bleaching from the excess light can occur as a result

(Varicon Aqua Solutions, 2004).

33

---

2.11.3 The PBR used for Simulation in this Study (BioFence)

About a dozen or so firms have been developing and selling photobioreactors. The

dynamic simulation tool developed in this Master′s Thesis was based on a system known

as "BioFence". The BioFence system was developed by Varicon Aqua Solutions Ltd, UK

(Figure 12 and Figure 14). Horizontal plastic tubes are stacked in a rack to allow a high

surface-to-volume ratio. The focus and benefit of this system is the easy to assemble

modular and simple design. The expandability (for example by simple tube joiners) of the

system allows a scale-up to basically all desired sizes. A sophisticated manifold assembly

design reduces the size of the pump required, and therefore saves both cost and algal

damage. Due to the manifold design shown in Figure 13, an inhibition of algal growth

caused by water supersaturated with oxygen can be avoided. The BioFence has the tubes

Figure 12. Schematic view of the BioFence system.

Source: After Varicon Aqua Solutions Ltd., 2008.

34

---

arranged on manifolds which dramatically increase the path length that can be taken by

the algae. For that reason, large systems can be built. Patented special cleaning beads that

continuously circulate with the algae, clean the tubes from the inside and avoid algae

sticking on the inside of the tubes.

Due to the beads, the process does not have to be stopped for cleaning purposes, thus

higher productivity and a more stable process can be reached due to avoided cell crashes.

According to Varicon Aqua Solutions Ltd., the BioFence can produce an equivalent of

2000 l of bag grown algae per day in an array of tubes of 10 m x 1.8 m. Since the

BioFence is automatically controlled and delivers algae either continuously or at set

intervals, the equipment requires little attention. In addition, the algae can be delivered

Figure 13. BioFence Manifold configuration. Source: After Varicon

Aqua Solutions Ltd., 2008.

35

---

either directly to where it will be used or into easy to handle containers. The system′s

volume can be easily calculated. Each meter of transparent tube has an internal volume of

0.66 liters and an internal surface area of 0.1 square meters. The BioFence is expandable

in blocks of 16 x 5 m tubes, i.e. 53 liters. A light-to-dark ratio of at least 50% is

recommended. The tank size required is therefore equal or greater than the internal tube

volume. The total system volume is 100 liters per block of 16 tubes (Varicon Aqua

Solutions, 2004).

Figure 14. The actual BioFence during installation.

Source: After Varicon Aqua Solutions, 2004.

36

---

CHAPTER III

MATERIALS AND METHODS

3.1 Experimental Set-up

In this study, three lab-scale photobioreactors made by Aqua Medic GmbH were

set-up, inoculated and operated over a period of 50 days. The temperature was varied

from 9 °C to 39 °C by an off-the-shelf aquarium chiller and an aquarium heater.

Contamination with other algae strains as well as any sort of bacteria had to be

avoided. Therefore, an optical microscope was used to ensure the purity of algae cultures.

Samples were checked for purity once a week. In case of a contamination, the complete

batch was eliminated, to ensure the work on a single strain.

The CO2 supply was controlled by an Aqua Medic GmbH pH meter, which was

connected to an electric valve. An optimal pH of approximately 7.2 was maintained by

supplying the right amount of CO2. As soon as the pH rose over 7.25, the valve opened

and CO2 dosing was provided, which decreased the pH below 7.15. This procedure

ensured an optimal CO2 supply as well as optimal pH in the algal growth medium.

A Bausch & Lomb Spectronic 21 spectrophotometer was used to monitor algal

growth. Samples from each PBR were taken twice a day. The optical density of each

sample was determined by measuring the transmittance at 560nm. Since the density is a

limiting growth factor (too high of a density can limit growth), the growth medium was

diluted as soon as the transmittance reached 10%. The danger of false readings and

misinterpretable data was too high when going under 10%, too.

37

---

A Hanna instruments® multimeter was used to measure phosphate and nitrate

concentration at each start of a new batch (approximately every forth day). In case of a

lack of nutrients, the specific nutrient was supplied. This procedure avoided a growth

inhibition due to a lack of nutrients. The minimum amount of phosphate was 10 ppm; the

minimum amount of nitrate was 15 ppm.

3.1.1 Culturing Techniques

A vial with pure

Chlorella

cultures in a medium called "ALGGRO" was obtained

from UTEX, the University of Texas, Austin, Texas, U.S.A. The vial was opened and put

into the lab-scale photobioreactor (Figure 15) together with 100 ml of distilled water and

5 drops of composed fertilizer called "PLANT FOOD", containing all important nutrients

with a N-P-K ratio of 10-15-10 (Table 2). The nutrient concentration was kept above 10

mg/l for Phosphorous and above 50 mg/l for Nitrogen.

The PBR was a vertically mounted, transparent plastic tube with the air supplied

from the bottom. The air supplied a small amount of CO2 (content in ambient air about

0.03%) and accounted for the necessary turbulences (water mixture) in the bioreactor.

Additional CO2 was supplied by an external CO2 bottle, controlled by a pH monitoring

computer. An optimal pH of 7.2 was maintained by regulating the CO2 supply. Since CO2

forms carbonic acid in the water, the CO2 dosing reduced the pH. An electrode placed in

the bioreactor sensed the pH in the algae water and transmitted it to the pH computer,

which regulated the valve of the CO2 bottle. Figure 16 shows a schematic view of the

PBR set-up.

38

---

The algal growth was monitored by optical density measurements using a

spectrophotometer. A low density condition (transmittance larger than 10%) was

maintained by adding distilled water to the bioreactor as soon as the density increased to a

transmittance smaller than 10%. Another optical density reading was taken after adding

water in order to monitor the change and keep continuous data analysis. A new batch was

started accordingly. This has to be considered later on when selecting the data.

Artificial lighting was also supplied by a fluorescent light bulb (6,700K, 8 W,

1300 lm) hung up parallel to the PBR. The lighting was controlled by a timer providing

16 hours of light and 8 hours of dark periods, respectively. The location of the PBR

offered almost no natural daylight. All bulbs that are above 5600K are considered

Figure 15. A lab-scale PBR in use.

39

---

pH Computer

Thermometer

CO2

pH electrode

CO2 valve

Check valves

Air

pump

Sample

discharge

Figure 16. Schematic view of the photobioreactor set-up.

daylight bulbs, offering a clean, bright light condition. These bulbs are used to simulate

outdoor conditions.

As soon as stable conditions and a continuous growth rate were obtained at room

temperature, a chiller connected to one of the PBR systems was activated, decreasing the

temperature slowly. In order to get the temperature function as described in Chapter II,

the temperature with a growth rate of 10% of the maximum growth rate had to be

determined. The experiments with colder water, therefore, focused on a region between 9

40

---

°C and 14 °C to determine the 10% growth rate temperature. The PBR was operated over

several weeks within this temperature range, increasing and decreasing the temperature

frequently (approximately every forth day).

The same procedure was performed on another PBR by heating the water until a

temperature with a growth rate close to 10% of the maximum growth rate (32 °C ­ 39 °C)

was determined. The optimal temperature (usually between 23 °C and 30 °C), however,

was determined by heating the third PBR at smaller temperature increments.

Table 2. Basic fertilizer composition.

Analysis

Total Nitrogen

10%

1.6% Ammoniacal Nitrogen

0.2% Nitrate Nitrogen

8.2% Urea Nitrogen

Available Phosphate (P2O5) 15%

Soluble Potash (K2O)

10%

Iron (Fe)

0.1%

Manganese (Mn)

0.05%

Zinc (Zn)

0.05%

3.1.2 Applications

Optical Microscope

A type of microscope which uses visible light and a system of lenses to magnify

images of small samples is optimal. Optical microscopes are the oldest and simplest of

microscopes. A stereomicroscope was used to examine the algae samples. Figure 17

shows the basic components of a typical research stereomicroscope. The total

41

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magnification equals the product of the ocular (eye) and objective lense. A "Köhler

illumination" was used in these types of microscopes which means that the incident light

shines on the specimen from below. The total magnification was "1000x".

Figure 17. Optical microscope.

Source:After Molhave, 2006.

pH-Computer and Valve

The pH value indicates the measure of the free carbonic acid in the

photobioreactors. The carbonic acid fertilization is the basis for a well thriving algae

growth. A pH-Computer (Figure 18) maintained the pre-set pH value automatically by

supplying CO2 through a controlled valve. In this study, the pH-Computer was used to

regulate the level of carbonic acid in the photobioreactor.

42

---

Figure 18. CO2 control valves (left) and pH computer (right).

Source: After Aqua Medic GmbH, 2007.

Spectrophotometer

An ultraviolet-visible spectrophotometry (UV/VIS) uses light in the visible and

adjacent near ultraviolet (UV) and near infrared (NIR) ranges. In this region of energy

space molecules undergo electronic transitions. The device measures the intensity of light

passing through a sample, and compares it to the intensity of light before it passes through

the sample. The ratio is called the transmittance, and is usually expressed as a percentage.

The basic parts of a spectrophotometer (Figure 20 and Figure 19) are a light source, a

holder for the sample, a diffraction grating or monochromator to separate the different

wavelengths of light, and a detector. The detector is typically a photodiode. Photodiodes

are used with monochromators, which filter the light so that only the light of a single

wavelength reaches the detector. Samples are typically placed in a transparent cell, known

as a cuvette. Cuvettes are typically rectangular or cylindrical in shape, commonly with an

43

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internal width of one cm or one inch. This width becomes the path length, PL, in the

Beer-Lambert law. The use will be discussed later in the Thesis.

Figure 19. An older spectrophotometer with analog reading.

Source: After Mehlitz, 2008.

Figure 20. A modern spectrophotometer with PC control.

Source: After Mehlitz, 2008.

Multimeter

A Hanna Instruments® Multimeter (Figure 21) was used in the experiments to

measure the amount of different nutrients in the growth media. Essentially, the instrument

is a multiparameter bench photometer dedicated for aquacultural analysis. It can measure

13 different methods (nutrients) using specific liquid or powder reagents. The amount of

reagent is precisely dosed to ensure maximum reproducibility.

44

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Absorption of light is a typical phenomenon of interaction between

electromagnetic radiation and matter. When a light beam crosses a substance, some of the

radiation may be absorbed by atoms, molecules or crystal lattices. If pure absorption

occurs, the fraction of light absorbed depends both on the optical path length through the

matter and on the physical-chemical characteristics of substance according to the

Lambert-Beer law.

The concentration can be calculated from the absorbance of the substance once

other factors are known. Photometric chemical analysis is based on the possibility to

develop an absorbing compound from a specific chemical reaction between sample and

reagents. Given that the absorption of a compound strictly depends on the wavelength of

the incident light beam, a narrow spectral bandwidth should be selected as well as a

proper central wavelength to optimize measurements.

Figure 21. Hanna Instruments Multimeter.

Source: After Hanna Instruments®, 2008.

A microprocessor controlled special tungsten lamp emits radiation which is first

optically conditioned and beamed to the sample contained in the cuvette. The optical path

is fixed by the diameter of the cuvette. Then the light is spectrally filtered to a narrow

spectral bandwidth, in order to obtain a light beam intensity. The photoelectric cell

45

---

collects the radiation that is not absorbed by the sample and converts it into an electric

current, producing an electrical potential in milivolts.

The microprocessor uses this potential to convert the incoming value into the

desired measuring unit and then displays it on the liquid crystal display (LCD). The

measurement process is carried out in two phases: first the meter is zeroed; and then the

actual measurement is performed. The cuvette has a very important role, because it is an

optical element; and thus requires particular attention. It is important that both the

measurement and the calibration (zeroing) cuvette are optically identical to provide the

same measurement conditions. Most techniques use the same cuvette for both, so that the

measurements take place in the same optical point. The instrument and the cuvette cap

have special marks that must be aligned in order to obtain better reproducibility. The

surface of the cuvette must be clean and not scratched. This is to avoid measurement

interference due to unwanted reflection and absorption of light. Therefore, it is

recommended not to touch the cuvette walls with hands. Furthermore, in order to

maintain the same conditions during the zeroing and the measurement phases, it is

necessary to close the cuvette to prevent the possibility of contamination. Due to the

turbid algal water in this study, the measurements had to be taken at the very beginning of

each batch cultivation, when the water was still clear (Hanna Instruments, 2008). This

instrument could not be used when the transmittance was under 50%.

46

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3.1.3 Data Collection and Analyses

All data were collected and reported by a research team in a limited online

database, which was updated daily (Figure 22). Even slight changes or outlying data

points could be monitored and evaluated very quickly. The online access enabled the

team members to update or download data at all times. Microsoft Excel software was

used to perform a number of data analyses.

Three PBRs were operated over a period of 50 days. With two readings per day,

the sample size summed up to 300 entries. The data evaluated were manually chosen

from the entire set. Recorded data from lag phases with no or hardly growth were deleted.

Every single data set was examined and checked for plausibility. Over 150 samples were

deleted from the database in order to examine only pure culture findings. Main criteria for

this purpose were:

- pH lower than 5.5 or higher than 8.0

- 3 data sets after changing an environmental factor (delete lag phase)

- Transmittance below 7% (density too high)

The measured temperatures were rounded to full degrees Celsius (e.g. 15.3 °C to

15 °C). In accordance with Eqn. 2.5 and 2.6 (Chapter II), only the temperature for the

maximum growth (anticipated to be between 23 °C and 31 °C), the temperature at 10% of

the maximum growth rate at the lower end (anticipated to be between 9 °C and 14 °C),

and the temperature at 10% of the maximum growth rate at the upper end (anticipated to

47

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be between 34 °C and 40 °C) were to be determined. The research therefore mainly

focused on these regions.

For the evaluation, the time interval ( t in hours) from the previous reading to the

current and the corresponding change in transmittance (

) were calculated. The growth

rate per day (24 hours) was interpolated from these two parameters and reported with the

corresponding temperature. Then, a mean growth rate for each temperature experiment

was determined.

Figure 22. Screen view of the online database where all available data were collected.

48

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3.2 Heat Management Simulation Model

3.2.1 Introduction

A dynamic simulation model was developed to provide an accurate prediction of a

horizontal tubular photobioreactor as a function of dynamic environmental factors such as

solar energy, outside temperature, and wind speed. This dynamic prediction model was

developed in Microsoft Excel using VBA (Visual Basic for Application), from basic

energy conservation and heat transfer principles for a single glass glazing greenhouse.

The model incorporated a dynamic simulation of algae growth. The photobioreactor and

greenhouse characteristics used in the simulation model for this study are presented in

Table 3. The model was used to predict heating and cooling loads and the benefits

associated with heating and cooling. A flow chart of the simulation model is presented in

Figure 23. This chapter discusses the techniques employed as well as the assumptions

made throughout the system analysis.

Hourly weather data (temperature, solar radiation, wind speed, relative humidity)

were downloaded from the California Irrigation Management Information System

(CIMIS) weather station for San Luis Obispo (35o 17′N; 120o 39′W), California, U.S.A.

for the month of April 2007 (http://wwwcimis.water.ca.gov). However, the simulation

model is flexible enough to simulate any other location, any other month, or even any

year. Simulations were performed starting at the beginning of the fifth day and ended at

the end of 30th day of the month providing 26-day simulations.

49

---

START

INPUT

Read weather file and

input parameters

Initialize

t = 0

Perform Basic

Calculations

Solve System Equations

Activate Control Routine

Compute Energy Cons.

Compute Algal Prod.

NO t = t + t

t = tend?

YES

Print Result

STOP

Figure 23. Flow chart of the simulation model.

50

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Table 3. Photobioreactor and greenhouse characteristics.

Parameter

Description

Value

IRAIR

Index of refraction n for the air

11

IRTUBE

Index of refraction n for the glass tube

1.5261

Latitude for location (San Luis Obispo)

35.23°

Surface azimuth angle

0° 3

Slope of virtual surface for beam incidence

45° (assumed)

RGROUND

Reflectivity of the ground

20% (assumed)

RALGAE

Reflectivity of the algae algae

5% (assumed)

GH

Transmissivity of the greenhouse cover

60%2

CpWAT

Specific heat of water

1.16278 Wh/kg.K4

CpAIR

Specific heat of air

0.2811 Wh/kg.K4

WAT

Density of water

996 kg/m3 4

AIR

Density of air

1.2 kg/m3 4

Emissivity of the glass/Plexiglass tubes

94%3,4

AEH

Infiltration rate

1.5 ( air exchanges per hr)2

UG

Heat transfer coefficient - single layer glass

0.00628 kW/m2.K2

UFL

Heat transfer coefficient - poured concrete 0.000872 kW/m2.K2

152 mm

TOPT

Temperature at max growth rate

29 °C

max

Maximum growth rate

1.44 /day

TSUP

Temp. at 10% of max growth rate - upper

35 °C

TINF

Temp. at 10% of max growth rate - lower

11 °C

nc

# of PBR parallel columns

19

na

# of PBR columns axial

10

d

PBR tube diameter

0.03 m

lt

PBR tube length

10 m

dt

Distance between PBR tube centers

0.18 m

dtt

Distance between PBR twin tube centers

0.06 m

b

Distance between ground & first PBR tube

0.3 m

x

Distance between PBR columns (parallel)

1.5 m

xa

Distance between PBR columns (axial)

1.5 m

t

# of tubes per PBR column

32

GHW Greenhouse

width

7.2

m

GHL Greenhouse

length

57.6

m

GHWH

Greenhouse wall height

2.4 m

GHG Greenhouse

gable

height

1.8

m

GHN

# of greenhouse bays

12

Switch to decide whether twin tubes (1) or

tt

0 or 1

single tubes (0) are used in PBR columns

1Duffie and Beckman, 2006; 2Aldrich and Bartok, 1992; 3Iqbal, 1983; 4Incropera et al.,

2007

51

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3.2.2 Physical Model and Photobioreactor Architecture

A description of the photobioreactor as a series of parallel rows was extended to

an overall greenhouse model for indoor operation, whereas the same parallel rows were

modeled without a greenhouse for the outside operation, as schematically shown in

Figure 25 and Figure 26. In dealing with the energy exchanges, the outside weather

conditions and the deep ground temperature served as boundary conditions. The bulk air

was analyzed by adopting the assumption of "perfect mixing".

All dimensions of the PBR were variables in the model. This feature allowed

optimization and flexibility for different PBR configurations possible. Figure 24 shows

the basic dimensions used in the simulation model.

3.2.3 Energy Balances

Many factors influence the heat losses and gains of tubular photobioreactors

(PBRs). To understand the developed simulation model, general approaches employed in

heat transfer calculations and basic principles are explained in this section. The

simulation model is able to determine the heating requirements for an outdoor operation

as well as for an indoor (greenhouse) operation. Different heat transfer modes occur under

the two different conditions. In the case of an outside operation, heat losses due to forced

convection (wind) and radiation (ground and sky), and gains due to solar radiation are

present (Figure 25). The photobioreactor and ground have thermal masses; therefore, heat

storage has to be considered.

52

---

GHL

GHG

na = # of columns

axial

nc = # of columns

parallel

dtt

GHWH

dt

h

d

lt

xa

b

x

GHW

Figure 24. Dimensions of the photobioreactor.

53

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Solar radiative

Radiative

Gains

Losses

Convective

Losses/gains

Radiative

Losses/gains

Ground

Figure 25. Heat losses and gains from an outdoor PBR.

The energy balance for an outdoor photobioreactor can be symbolically expressed as:

Energy storage = Ein - Eout

(3.1)

WAT * VPBR * CpWAT * dTPBR/dt = QTSRA - QOS - QOSCL

(3.2)

where

WAT was the density of water (996 kg/m3); VPBR was the total photobioreactor

volume (m3); CpWAT was the specific heat capacity of water (1.16278 Wh/kg.K); dTPBR

was the photobioreactor temperature change (K) over a period of time dt (one hour);

QTSRA was the total solar radiation absorbed by the PBR (kW); QOS was the outside

longwave radiation exchange with the sky and the ground (kW); QOSCL was the outside

convective heat transfer due to convection (wind), and HSPBR was the heat storage

54

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component of the PBR. The details of these individual components are explained in the

upcoming sections.

For the inside conditions, an interaction between inside and outside air

temperatures as well as between inside air and reactor temperatures were considered.

Heat storage in the inside air, the ground and the PBR were taken into account. The

greenhouse lost heat due to conduction through the walls, roof and ground, and also due

to infiltration (air exchange). Heat gains are mainly due to incoming solar radiation. The

heat transfer between the PBR and the greenhouse was due to free convection (no air

movement around the tubes), and radiation between the PBR and the ground and sky as

shown in Figure 26.

The energy balance for the greenhouse air was expressed as the following:

AIR * VGH * CpAIR * dTGH/dt = QGHHG - QGHHLI - QGHHLC

(3.3)

where AIR was the density of air (1.2 kg/m3); VGH was the total greenhouse volume (m3);

CpAIR was the specific heat capacity of water (0.2811 Wh/kg.K); dTGH was the

greenhouse air temperature change (K) over a period of time dt (one hour); QGHHG was

the greenhouse heat gains due to solar radiation (kW); QGHHLI was the heat transfer due to

infiltration (kW), and QGHHLC was the heat transfer due to conduction (kW). The details

of these individual components are explained in the upcoming sections. In this study, it

was assumed that the greenhouse air was well mixed and had negligible temperature

gradients.

55

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Photobioreactor Solar

Radiative Gains

Radiative

Losses

Greenhouse Solar

Radiative Gains

Convective

Losses/gains

Infiltration

Losses

Conductive

Radiative

Losses/

Losses/

gains

gains

Ground

Figure 26. Heat losses/gains from an indoor PBR and a greenhouse.

The energy balance for the PBR in the greenhouse can be written as the following:

WAT * VPBR * CpWAT * dTPBR/dt = QGHTSRA - QGHHLR + QGHCL

(3.4)

where

WAT was the density of water (996 kg/m3); VPBR was the total photobioreactor

volume (m3); CpWAT was the specific heat capacity of water (1.16278 Wh/kg.K); dTPBR

was the photobioreactor temperature change (K) over a period of time dt (one hour);

QGHTSRA was the total solar radiation absorbed by the PBR in the greenhouse (kW);

QGHHLR was the radiation exchange with the ground and sky (kW), and QGHCL was the

56

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heat transfer due to free convection between the inside air and PBR (kW). The details of

these individual components are explained in the upcoming sections.

A one-dimensional heat conduction equation was used in dealing with the energy

balance of the floor for inside and outside conditions, by dividing the floor into three

layers with the assumption of homogeneous thermal and hydraulic properties within each

layer (Kindelan, 1980; Avissar and Mahrer, 1982; Arinze, 1984; Akhter, 1988, Yildiz,

1993). The ground was divided into three layers having thicknesses of 0.05, 0.10 and 0.50

m for the top, middle and bottom layers, respectively. It was assumed that the deep

ground temperature was constant at 15 °C (Takakura et al., 1971). It was also assumed

that the floor layers had identical thermal properties. Considering these assumptions, the

energy balance equations for the three floor layers were written as:

Top layer:

VFL1 * cvF * dTFL1/dt = QTSRAF ­ QRLF ­ QCLTOPF

(3.5)

Middle layer:

VFL2 * cvF * dTFL2/dt = QCLTOPF - QCLMIDF

(3.6)

Bottom layer:

VFL3 * cvF * dTFL3/dt = QCLMIDF - QCLBOTF

(3.7)

where VFL1, VFL2, and VFL3 were the volumes of the three floor layers (m3); cvF was the

specific volumetric heat capacity for the floor (0.8139 kWh/m3.K); dTFL1, dTFL2, and

dTFL3 were the ground temperature changes (K) for each layer over the time interval dt

57

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(one hour); QTSRAF was the total solar radiation absorbed by the floor (kW); QRLF was the

radiation exchange between the sky and floor (kW); QCLTOPF was the conductive transfer

to the next floor layer (kW); QCLMIDF and QCLBOTF were the conductive heat transfer

components of the middle and bottom floor layers, respectively. These individual terms

are explained further in the upcoming sections.

3.2.4 General Equations

For both inside and outside operations, general equations used in developing the

simulation model are presented here.

Julian Day

For all the following equations, the Julian Day for a specific date of the year had

to be determined. The Julian Day is the consecutive number of days in a year. Each year

has therefore 365 Julian Days; January 1st being the first day and December 31st being the

365th day. February 1st, for example, would be the 32nd Julian Day.

Solar Time

The solar time is the time based on the apparent angular motion of the sun across

the sky, with solar noon being the time the sun crosses the meridian of the observer

(Duffie and Beckman, 2006). The solar time was calculated using the following equations

(Iqbal, 1983):

STIME = TIME + 2.4 + E

(3.8)

with

58

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E = 229.2 * (0.000075 + 0.001868 * Cos (b * / 180)

- 0.032077 * Sin (b * / 180) - 0.014615 * Cos (2 * b * / 180)

- 0.04089 * Sin (2 * b *

/

180))

(3.9)

and

b = (JD - 1) * 360 / 365

(3.10)

where STIME was the solar time on a specific day of the year; JD was the Julian Day

number, TIME the time of that specific day, and b and E were calculated parameters.

Solar Radiation / Sun Angle

One major parameter of the model was the direction of the sunlight, and

consequently the sun angle with respect to the PBR. Figure 27 shows main angles of solar

radiation that were considered:

= Latitude, the angular location north or south of the equator, north positive;

- 90° <=

<= 90°, for San Luis Obispo, CA, U.S.A.: = 35.23°.

= Declination, the angular position of the sun at solar noon (i.e., when the sun is

on the local meridian) with respect to the plane of the equator, north

positive; - 23.45° <= <= 23.45°.

= Slope, the angle between the plane of the surface in question and the

horizontal; 0° <= <= 180°. ( > 90° means that the surface has a downward-

facing component).

59

---

= Surface azimuth angle, the deviation of the projection on a horizontal plane of

the normal to the surface from the local meridian, with zero due south, east

negative, and west positive; --180° <= <= 180°.

= Hour angle, the angular displacement of the sun east or west of the local

meridian due to rotation of the earth on its axis at 15° per hour; morning

negative, afternoon positive.

= Angle of incidence, the angle between the beam radiation on a surface and the

normal to that surface.

Figure 27. Zenith angle, slope, surface azimuth angle, and solar azimuth

angle for a tilted surface. Source: After Duffie and Beckman, 2006.

In this study, approximate equations developed by Cooper (1969) were used to

determine the declination ( ), hour angle ( ), and angle of incidence ( ):

= 23.45 * Sin (360 * ((284 + JD) / 365 * / 180))

(3.11)

60

---

= (STIME - 1200) / 100 * 15

(3.12)

= Acos (Sin ( * / 180) * Sin ( * / 180) * Cos ( * / 180)

- Sin ( * / 180) * Cos ( * / 180) * Sin ( * / 180)

* Cos ( * / 180) + Cos ( * / 180) * Cos ( * / 180)

* Cos ( * / 180) * Cos ( * / 180) + Cos ( * / 180)

* Sin ( * / 180) * Sin ( * / 180) * Cos ( * / 180)

* Cos ( * / 180) + Cos ( * / 180) * Sin ( * / 180)

* Sin ( * / 180) * Sin ( * / 180))

(3.13) (3.13)

Shading

Shading (received solar radiation) of the PBR had a major impact on the

performance of the system since the tubes shade each other differently throughout the

day. An equation construct was developed, covering all possible shading options within

every PBR column, and also through multiple columns standing next to each other. A

shade factor (SF) as a function of the Julian Day (JD) and the time of the day (TIME)

were derived and later multiplied by the incoming solar radiation. A critical sun angle

(TC) existed, where the tubes shade each other (Figure 28). This angle was estimated by

the following equation:

TC

=

Atan

(dt

/

d)

(3.14)

where d was the tube diameter (m); and dt was the distance between the tubes within one

column (m).

61

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Critical sun angle

dtt

PBR tubes

dt

Sun ray

d

Center line tube column

Figure 28. Photobioreactor tube configuration used in determining the critical sun

angle, TC. The upper tube shades the lower tube. Source: After Mehlitz, 2008.

For the angle of incidence ( ) greater than the critical angle (TC), no shading

occurs. For an angle of incidence less than the critical angle, however, the following

equation was used to determine the percentage of shading (SFR):

SFR = (TC - )

*

100

/

TC

(3.15)

where SFR was the percentage of shading the first column received.

For the second to the nth column, the illuminated height was calculated based on

the following equation:

HILL1 = x / Tan ( *

/

180)

(3.16)

62

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where HILL1 was the illuminated height (m from the top) of a column n within a field of

multiple columns set-up parallel, and x was the distance between columns (m). The

illuminated height should not be greater than the total height of tubes stacked over each

other (i.e. total height (h) minus the distance of the tube next to the ground (b)). Turning

this height into a percentage value of illuminated tubes, delivered the following equation:

PERCNILL = HILL1 * 100 / (h - b)

(3.17)

where PERCNILL was the percentage of tubes illuminated in the nth column.

The remainder of tubes in column n was not illuminated fully, however, received

solar rays through the gaps of tubes of the previous column:

PERCNSHADE1 = ddr * (100 - PERCNILL)

(3.18)

where PERCNSHADE1 was the shading percentage of tubes in a column n receiving solar rays

through the gaps of the previous columns, expressed by the diameter to distance ratio, ddr

= d / dt.

Related to the critical sun angle, the total percentage of shading was expressed as:

PERCNSHADE = PERCNILL * PERCNILL / 100 + PERCNSHADE1

(3.19)

where PERCNSHADE was the total percentage of shading received in column n.

Putting all columns together, and considering that the top tube of each column

receives solar radiation without shading all day long, the final equation for total shading

was developed:

63

---

SF = ((((SFR + (nc - 1) * PERCNSHADE) / nc) * (t - 1) + 1 / t) / t) / 100

(3.20)

where SF was the total shading factor for the PBR; nc was the number of columns

standing parallel to each other, and t was the number of tubes per column.

Shading for the second half of the day (i.e. after solar noon) was treated the same

as the first half of the day.

Since the simulation model had an option to handle twin tubes within one column

(i.e. two tube rows were hold by one frame), the shading factor had to be adjusted to this

case. Eqns. 3.14 through 3.20 were used to calculate the shading factor for one twin tube

column (SFtt1). Therefore, the distance between two different columns (x) were

substituted by the distance between the twin tubes (dtt). Then, the usual shading factor

(SF) for the entire PBR setting was determined as described above. The shading factor for

one twin tube column was then multiplied by the remaining illumination height

(1 ­ SF). Adding this percentage to the usual shading factor resulted in an overall shading

factor for twin tubes (SFtt). In general, the twin tubes will increase the total shading

factor.

Air / PBR Interface

Further steps had to be considered to handle the air and PBR interface: The total

incoming solar radiation were partly reflected or transmitted through the PBR tubes.

Absorption of the glass or plexiglass tubes was neglected. The transmitted portion was

partly absorbed by the growth media (algae water). The reflected portion was exposed to

the other tubes consequently. Figure 29 shows the relationships between total incoming

64

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beams and refraction at a surface of a different media. The refraction angle ( 2) was

calculated by using Snell′s Law (Dietz, 1963):

2 = Asin ((IRAIR / IRTUBE) * Sin ( * / 180)) / * 180

(3.21)

where

2 was the refraction angle, IRAIR the refraction index of air, IRTUBE was the

refraction index of the tube; and was the angle of the total incoming solar radiation.

Figure 29. Angles of incidence and refraction in media with refractive

indices n1 and n2. Source: After Duffie and Beckman, 2006.

In order to determine how much radiation was transmitted through the tube and algae

water, the transmittance of the tube and water was multiplied:

= T * A

(3.22)

where was the total transmittance (%); T was the transmittance of the tube (%); and A

was the transmittance of the algae water (%).

65

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The transmittance of the tube was a function of the parallel and perpendicular

reflection of the tube in accordance with Fresnel′s equation (Duffie and Beckman, 2006):

T = 0.5 * ((1 - RPARA) / (1 + RPARA) + (1 - RPERP) / (1 + RPERP))

(3.23)

where RPARA was the parallel reflection of the tube (%); and RPERP was the perpendicular

reflection of the tube (%).

Consequently, the parallel and perpendicular reflections were calculated as

follows:

RPARA = (Tan ( 2 - ) * / 180)2) /((Tan( + 2) * / 180)2)

(3.24)

RPERP = ((Sin (( 2 - ) * / 180))2)/((Sin(( + 2) * / 180))2) (3.25)

where and 2 were the incoming and refracted angles at the surface, respectively.

The total reflection (REFT) of the tube was calculated using the following equation

with the assumption that the mean angle the beams hit the tubes was 45°:

REFT = 0.5 * (RPERP + RPARA)

(3.26)

The transmittance of the algae water was calculated using Bouguer′s law (Duffie

and Beckman, 2006), which is based on the assumption that the absorbed radiation was

proportional to the local intensity in the medium and the distance the radiation has

traveled in the medium:

dI

=

-

I

*

K

dx

(3.27)

66

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where K was the proportionality constant, the extinction factor (EF), which is assumed to

be a constant in the solar spectrum (Duffie and Beckman, 2006). Integrating along the

actual pathlength (PL) in the medium (i.e. from zero to PL/cos 2) yielded:

A = Exp (-EF * PL / Cos( 2 *

/

180))

(3.28)

The pathlength was assumed to be approximately 60% of the tube diameter (d in m).

In Eqn. 3.28, the extinction factor (EF) needed to be calculated from experimental

data:

EF = - Ln ( AP) / DAP

(3.29)

where AP was the transmittance (%) of an algae probe examined in a spectrophotometer

using a specific testing vial with a specific diameter DAP (m). For this study, a mean

transmittance (optimal density for algae) of 0.3 as well as a vial with a diameter of

0.00127 m was used.

3.2.5 Outdoor Photobioreactor

As previously described, three major heat transfer modes occur in outdoor

conditions: Heat gain due to absorbed solar radiation (QTSRA), heat loss due to convection

(QOSCL), and heat loss due to radiation with the sky and ground (QOS). The total solar

radiation absorbed was calculated using the following equations:

IT = (1 - SF) * IS + IS * RGROUND + IS * REFT + IS *

(3.30)

67

---

QTSRA = IT * ATSURPRO * (1 - - RALGAE)

/

1000

(3.31)

where IT was the total solar radiation reaching the tubes (W/m2), consisting of four

components: The first component was the solar radiation, IS (W/m2), at a specific time.

The second was the reflected solar radiation from the ground (W/m2), and the reflectivity

of the ground, RGROUND, was assumed to be 0.2. The third one was the reflected solar

radiation from the tubes (W/m2), and the forth component was the transmitted radiation

from the tubes (W/m2).

Then, the amount of absorbed solar radiation, QTSRA, was determined as the

product of the total solar radiation (W/m2), the total projected surface area of the PBR,

ATSURPRO (m2), and the absorptivity of the algae water which was assumed to be 1 minus

the total transmittance ( ) minus the reflection of single algae cells (RALGAE assumed to be

0.05). Finally, the product was divided by 1000 to convert the dimension to kW.

Heat losses due to convection were calculated for the forced convection

conditions since the wind was the main driver for the heat losses. According to Newton′s

law of cooling, the heat transfer q can be expressed as:

Qconv = h * A * T

(3.32)

where h was the heat transfer coefficient (W/m2.K); A was the area (m2); and T was the

temperature difference between the tube and ambient air (K). For the PBR convective

heat transfer, the equation was modified to:

QOSCL = hHTC * ATSUR * (TALG - TOS)

/

1000

(3.33)

68

---

where QOSCL was the total convective heat transfer (kW); hHTC was the heat transfer

coefficient (W/m2.K); ATSUR was the total outside surface of the PBR tubes (m2); TALG

was the PBR or algae temperature (K); and TOS was the outside temperature (K). To

convert QOSCL from W to kW, the product was divided by 1000. In Eqn. 3.33, the heat

transfer coefficient, hHTC, was calculated using the following equation (Incropera et al.,

2007):

hHTC

=

Nu

*

k

/

d

(3.34)

where Nu was the Nusselt number; d was the tube diameter (m); and k was an air constant

(0.0263 W/m.K) (Vargaftik, 1975).

The value of the Reynolds number (Re) provided the information about the flow

conditions (i.e. laminar or tubulent flow over a tubular surface), and it was calculated as

follows (Incropera et al., 2007):

Re

=

WS

*

d

/

v

(3.35)

where WS was the wind speed (m/s); and v was an air property. With a maximum wind

speed of 5.2 m/s obtained from the weather file, a tube diameter of 0.003 m, and v being

0.00001589 m2/s at room temperature (Vargaftik, 1975), the Reynolds number resulted in

9820, which was smaller than 107, hence a laminar flow condition was assumed

(Incropera et al., 2007).

For laminar flow, the following Nusselt equation was used (Incropera et al.,

2007):

Nu = c * Rem * Pr(1/3)

(3.36)

69

---

where c and m were constants; for the range of Reynolds numbers for the given

conditions, their numerical values were 0.193 and 0.618, respectively (Incropera et al.,

2007). The Prandtl number (Pr) for air at 300 K was 0.707 (Vargaftik, 1975). The

Reynolds number was calculated each time as a function of the wind speed.

The radiative heat transfer with the sky and ground were determined using the

simplified radiation equations for an object in a large enclosure (in this study, small

diameter tubes under the sky and exposed to the ground) (Incropera et al., 2007):

Q

4

4

rad = * A * * (T1 ­ T2 )

(3.37)

where Qrad was the radiative heat transfer (W); was the emissivity of the small surface;

was the Stefan-Boltzman constant (5.67 * 10-8 W/m2.K4); and T1 and T2 were the

temperatures of the relevant surfaces (K). For the outside PBR, Eqn. 3.37 was modified

to:

Q

4

4

SKY = * AGH * * (TALG - TSKY )

/

1000 (3.38)

Q

4

4

FLOOR = * AGH * * (TALG - TFLOOR )

/

1000

(3.39)

QOS = 0.5 * QSKY + 0.5 * QFLOOR

(3.40)

where it was assumed that the total outside radiative heat exchange (QOS) was 50% with

the sky (QSKY) and 50% with the ground (QFLOOR). was the emissivity of the glass (or

plexiglass) tubes, which was 0.9 (Vargaftik, 1975); AGH was the total surface area of the

greenhouse (m2); TALG was the temperature of the PBR tubes (K); TFLOOR was the floor

temperature (K); and TSKY was the sky temperature (K).

70

---

The sky temperature was determined as a function of the ambient air temperature

as defined by Swinbank (1963):

T

1.5

SKY = 0.0552 * TOS

(3.41)

where TOS was the outside air temperature (K).

The heat exchange done by the floor layers were calculated using the following

equations:

QTSRAF = AGHSUR * IS *

/

1000 (3.42)

FLOOR

where QTSRAF was the total solar radiation absorbed by the floor (kW); AGHSUR was the

total surface area of the floor equal to the area needed for a greenhouse (indoor) operation

(m2); IS was the incoming solar radiation (W/m2); and

was the absorptivity of the

FLOOR

floor layer.

The conductive heat transfers between floor layers were calculated using the

following equations:

QCLTOPF = K

* A

FLOOR

GHSUR * (TFLOOR - TFLOORMID) / DFLOOR1

(3.43)

QCLMIDF = K

* A

FLOOR

GHSUR * (TFLOORMID - TFLOORBOT) / DFLOOR2

(3.44)

QCLBOTF = K

* A

FLOOR

GHSUR * (TFLOORBOT - TG) / DFLOOR3

(3.45)

where QCLTOPF, QCLMIDF and QCLBOTF were the heat fluxes of the top, middle and bottom

layers, respectively (kW); K

was the thermal conductivity of floor layers (1.75

FLOOR

W/m.K) (Arinze et al., 1984); TFLOOR was the floor temperature (K), TFLOORMID was the

middle layer temperature (K), TFLOORBOT was the bottom layer temperature (K), and TG

71

---

was the ground temperature (K); DFLOOR1, DFLOOR2 and DFLOOR3 were the layer

thicknesses for the top, middle and bottom layers, respectively (m).

Solving differential equations

The ordinary differential equations, represented in a general form in Eqn. 3.46

with an initial value, were solved using Euler′s method (Eqn. 3.47).

d /dt = ( , t)

(3.46)

(0) = 0

j+1 =

j + (

j, tj) *

t

(3.47)

Eqn. 3.47 was used to advance in time and to obtain a new solution at the next

time step. In this study, a time interval of one hour was used. Because of the fairly large

time constants of the heat storage elements, no stability problems were observed using

Euler′s method.

With the knowledge of heat fluxes through all modes, the temperature of the

system was calculated as follows, taking the heat storage term into account:

Q = * V * Cp * dT/dt

(3.48)

where Q was the total net energy input (kW); was the density (kg/m3); V was the

system′s volume (m3); Cp was the specific heat capacity (kW/kg.K); dT the temperature

change (K); and dt was the time interval in which the temperature change dT occurred.

The floor temperature was calculated taking the heat storage term into account:

72

---

HSTOPF = AGHSUR * DFLOOR1 * CpvFLOOR * (TFLOORNEW ­ TFLOOR)

(3.49)

where HSTOPF was the heat storage term of the top layer (equal to total net heat flux) in

kW; AGHSUR was the total floor surface area (m2); DFLOOR1 was the thickness of the top

layer (m); CpvFLOOR was the volumetric heat capacity of the floor (2.93*106 J/m3.C)

(Takakura et al., 1971); TFLOORNEW was the new floor temperature; and TFLOOR was the

floor temperature at the previous integration step as discussed above. A time interval (dt)

of one hour was used.

Reorganizing Eqn. 3.49 resulted in the equation used to calculate the new floor

temperature, TFLOORNEW:

TFLOORNEW = HSTOPF / (AGHSUR * DFLOOR1 * CpvFLOOR) + TFLOOR

(3.50)

For the photobioreactor, the equation was modified to:

QTOSHR = WAT * VPBR * CpWAT * (TALGNEW ­ TALG)

(3.51)

where QTOSHR was the total energy balance of the photobioreactor system in one hour

time interval (kW); WAT was the density of water (kg/m3); VPBR was the total PBR

volume (m3); CpWAT was the specific heat of water (4186 J/kg.C); TALGNEW was the new

PBR temperature (K), whereas TALG was the PBR temperature at the previous step. The

time interval (dt) was one hour. Reorganizing Eqn. 3.51 resulted in the following equation

used to calculate the new PBR temperature, TALGNEW:

TALGNEW = QTOSHR ( WAT * VPBR * cpWAT) + TALG

(3.52)

73

---

3.2.6 Indoor Photobioreactor

The inside air of the greenhouse had a major influence on the PBR temperature

itself. Hence, the inside air temperature was calculated first and then used to calculate the

PBR temperature. At the greenhouse interfaces, three heat fluxes occurred: The heat gain

due to solar radiation (QGHHG), the heat loss due to infiltration (air exchange) (QGHHLI),

and the heat transfer due to conduction through the walls and roof (QGHHLC).

The gained heat due to solar radiation was estimated by using the following

equation in accordance with Aldrich and Bartok (1992):

QGHHG = GH * IS * (AGH + ATSURPRO * (1 - SF)) / 1000

(3.53)

where QGHHG was the greenhouse heat gain (kW); GH was the transmissivity of the

greenhouse walls of 94% (Aldrich and Bartok, 1992); IS was the hourly solar radiation

(W/m2); AGH was the total greenhouse floor surface area (m2); ATSURPRO was the projected

PBR surface area (m2); and SF was the shading factor of the PBR at each specific time of

the day (%).

The largest heat transfer component was by conduction through the greenhouse

cover. Conductive heat transfer was estimated by the following equation (Aldrich and

Bartok, 1992):

QGHHLC = AGHGSUR * UG * (TGH - TOS) + AGH * UFL * (TGH - TOS)

(3.54)

where QGHHLC was the greenhouse conductive heat transfer (kW); AGHGSUR was the total

greenhouse cover surface area (m2); UG was the heat transfer coefficient for the

74

---

greenhouse cover (0.00628 KW/m2.K); and UFL for the floor (0.000872 KW/m2.K)

(Aldrich and Bartok, 1992). TGH was the greenhouse temperature (K); and TOS was the

outside temperature at each specific time (K).

The greenhouse infiltration losses were estimated as followed (Aldrich and

Bartok, 1992):

QGHHLI = 0.02 * AEH * VGH * (TGH - TOS) * 0.0002928

(3.55)

where QGHHLI was the greenhouse heat loss due to infiltration (kW); AEH was the air

exchanges per hour (assumed to be 1.5 per hr); VGH was the greenhouse volume (m3); and

0.0002928 was a conversion factor used to convert Btu/h into kW.

With the knowledge of all the heat fluxes, the temperature response of the

greenhouse air was calculated taking the heat storage term into account and following the

approach described in Eqns. 3.46 through 3.48:

TGHNEW = QGHHLG / ( AIR * VGH * CpAIR) + TGH

(3.56)

where TGHNEW was the new greenhouse temperature (K); QGHHLG was the total net energy

input (kW); AIR was the density of air (1.2 kg/m3); VGH was the total greenhouse volume

(m3); CpAIR was the specific heat capacity of air (1.012 J/g.C); and TGH was the

greenhouse temperature of the previous integration step. The time interval (dt) was one

hour.

75

---

As previously described, three heat transfer modes were considered for the inside

photobioreactor. Heat gain due to absorbed solar radiation (QGHTSRA); convective heat

exchange (QGHCL); and radiative heat exchange with the sky and the ground (QGHHLR).

The total solar radiation absorbed, IT, was calculated using the following

equations:

QGHTSRA = GH * QTSRA

(3.57)

QTSRA = IT * ATSURPRO * (1 - - RALGAE)

/

1000

(3.58)

IT = (1 - SF) * IS + IS * RGROUND + IS * REFT + IS *

(3.59)

where QGHTSRA was the total solar radiation absorbed by the PBR in the greenhouse (kW);

GH was the transmissivity of the greenhouse cover of 94% (Aldrich and Bartok, 1992);

QTSRA and IT were the same as previously calculated for outdoor conditions in Eqn. 3.30

and 3.31.

Heat fluxes due to convection were calculated using equations for free (buoyancy)

convection, since no wind and hardly any air movement occurred around the tubes.

Newton′s law of cooling (Eqn. 3.32) was modified to calculate the convective heat

transfer for the indoor photobioreactor:

QGHCL = hHTC * ATSUR * (TALG - TGH)

/

1000

(3.60)

Where QGHCL was the total convective heat transfer (kW); hHTC the heat transfer

coefficient (W/m2.K); ATSUR was the total outside surface area of the PBR tubes (m2);

TALG was the PBR or algae temperature (K); and TGH was the greenhouse air temperature

76

---

previously calculated (K). To convert QGHCL from W to kW, the product was divided by

1000.

The heat transfer coefficient, hHTC, was calculated using the simplified equation

for buoyancy-induced convection to air at atmospheric pressure and moderate

temperatures for horizontal cylinders (Incropera et al., 2007):

hHTC = 1.32 * ((TALG - TGH) / d) 0.25

(3.61)

where d was the tube diameter (m).

The radiative heat exchange with the sky and ground were calculated using the

simplified radiation equations as discussed before (Eqn. 3.37). For the indoor

photobioreactor, the equations were modified to:

Q

4

4

SKY = GH * * ATSUR * * (TALG - TSKY )

/

1000 (3.62)

Q

4

4

FLOOR = * ATSUR * * (TALG - TFLOOR )

/

1000

(3.63)

QGHHLR = 0.5 * QSKY + 0.5 * QFLOOR

(3.64)

where it was assumed that the total radiative heat exchange (QGHHLR) was 50% with the

sky (QSKY) and 50% with the ground (QFLOOR). was the emissivity of the glass (or

plexiglass) tubes, which was 0.9 (Aldrich and Bartok, 1992); ATSUR was the total surface

area of the PBR tubes (m2); was the Stefan-Boltzman constant (5.67 * 10-8 W/m2.K4);

TALG was the temperature of the PBR tubes (K); TFLOOR was the floor temperature (K);

and TSKY the sky temperature (K), which was calculated in Eqn. 3.41.

77

---

The floor temperatures were calculated using the same approach as in outdoor

conditions, however, now the long and shortwave transmittance of the greenhouse roof

was considered, too.

With the knowledge of all the heat fluxes, the temperature response of the

photobioreactor was calculated, taking the heat storage term into account and following

the approach described in Eqns. 3.46 through 3.48:

QTGHHR = WAT * VPBR * CpWAT * (TALGNEW ­ TALG) (3.65)

where QTGHHR was the total energy balance of the photobioreactor system in one hour

time interval (kW); WAT was the density of water (kg/m3); VPBR was the total PBR

volume (m3); CpWAT was the specific heat of water (4186 J/kg.C); TALGNEW was the new

PBR temperature (K), whereas TALG was the PBR temperature at the previous step. The

time interval (dt) was one hour. Reorganizing Eqn. 3.65 resulted in the following equation

used to calculate the new PBR temperature, TALGNEW:

TALGNEW = QTGHHR / ( WAT * VPBR * CpWAT) + TALG

(3.66)

78

---

3.2.7 Sensitivity Analyses and Evaluations

After developing the simulation model, sensitivity analyses were performed on the

indoor photobioreactor system, which had a glass greenhouse glazing. The shading

system was not operational. The default values are shown in Table 4.

Table 4. Key model parameters and their values used in the sensitivity analyses.

Parameter Values

Outside Air Temp. (°C)

- 20

-5

10

25

40

55

Outside Solar Radiation (W/m2) 0 300 600* 900 1200

Ground Reflectivity (%)

20

40*

60

80

PBR column distance (m)

0.25

0.5

0.75

1.0

1.5*

2.0

Transmissivity

Shading

Mat.(%)

20 40 60 80

100*

Infiltration Rate (m3/s.m2)

0.001*

0.01 0.02 0.03 0.04

*Default values, the default value for outside temperature was 18 °C

Table 4 shows some of the key model parameters and their deviations from the

standard value used in the sensitivity analyses. Each parameter was varied individually

while all other parameters were held at their standard values.

In addition to the sensitivity analyses, responses of some key parameters to step

inputs in outside air temperature and outside solar radiation were also determined and the

findings were presented in Chapter IV.

79

---

CHAPTER IV

RESULTS AND DISCUSSION

This section presents the results for the temperature experiment first, and is

followed by the results and analysis of the developed heat management model.

4.1 Temperature Experiments

The overall goal of the temperature experiments was to develop a procedure to

find out the temperature influence on algal growth. Later on, this procedure was used to

determine out the temperature properties of the algae strain

Chlorella

. The data were

needed to supply the heat management model with information about the algae growth as

a function of temperature.

Observations

The visible color of the algae water changed as the density changed due to

increased chlorophyll content in the water. Also, the color of each alga changed over

time, especially when they were exposed to stress conditions (i.e. high or low

temperature, high or low nutrient level). After almost 8 months of algae research in this

project, the research team was able to guess what happened to the algae just by visual

examination. Generally, a "healthy"

Chlorella

alga would look fresh to dark green,

whereas stressed algae would turn to bright green first, and later on to yellow. Especially

in the accelerated death phase (Figure 6) the algae looked bright green and soon turned to

yellow before turning to white dead biomass, eventually.

80

---

A lag (adaption) phase was observed after almost all environmental changes

(temperature, density, pH, nutrients), which was indicated by hardly any or no growth for

several hours up to two days.

Figure 30. Photobioreactors during operation

Results

Optical density (OD) measurements were made twice a day, and reported in an

online database (Figure 31) together with the temperature, date, time, and pH. The

nutrient content was controlled about every fifth day and adjusted (nutrients added) as

needed.

Three PBRs were operated over a period of 50 days. With two readings per day,

the sample size summed up to 300 entries. The data evaluated were manually chosen

from the entire set. Recorded data from lag phases with no or hardly growth were deleted.

Every single data set was examined and checked for plausibility. Over 150 samples were

81

---

Figure 31. Online database where all observed data were collected.

deleted from the database in order to examine only pure culture findings. Main criteria for

this purpose were:

- pH lower than 5.5 or higher than 8.0

- 3 data sets after changing an environmental factor (delete lag phase)

- Transmittance below 7% (density too high)

The distribution of sample sizes for each temperature experiment was shown in

Figure 32. The temperatures were rounded to full degrees Celsius (e.g. 15.3 °C to 15 °C).

In accordance with Eqns. 2.5 and 2.6 (Chapter II), only the temperature for the maximum

growth (anticipated to be between 23 °C and 31 °C), the temperature at 10% of the

maximum growth rate at the lower end (anticipated to be between 9 °C and 14 °C), and

the temperature at 10% of the maximum growth rate at the upper end (anticipated to be

82

---

between 34 °C and 40 °C) were to be determined. The research therefore mainly focused

on these regions.

Figure 32. Sample size for each temperature experiment.

For the evaluation, the time interval ( t in hours) from the previous reading to the

current and the corresponding change in transmittance (

) were calculated. The growth

rate per day (24 hours) was interpolated from these two parameters and reported with the

corresponding temperature. Then, a mean growth rate for each temperature experiment

was determined (Figure 33 and Table 5). The total growth rate distribution with respect to

temperature was as expected in the form of a skewed normal distribution (Figure 33). The

maximum growth rate (1.44 /day) was observed at a medium temperature of 29 °C

(Figure 33 and Table 5). The observed maximum growth rate was in agreement with the

previous studies; i.e. 1.44 doublings per day versus 1.0 to 2.0 doublings per day in the

literature (Reynolds, 1984; Raven and Geider, 1988; Dauta et al., 1990). For our study,

the goal was not to reach the maximum growth rate, rather to monitor the growth

distribution and develop a growth function as a function of temperature. The important

83

---

outcome was the percent losses and gains with respect to the maximum growth rate.

Beside the maximum growth rate, the upper and lower 10% maximum growth rates had

to be determined. Ten percent of 1.44 doublings per day was 0.144 doublings per day. For

the lower value, a growth medium temperature of 11 °C was determined from Table 5.

The upper value was determined at the temperature of 35 °C. Finally, all parameters

needed for the heat management model were determined and incorporated into the model

(Table 6).

Figure 33. Mean growth rates and standard deviations at different temperatures

84

---

Table 5. Mean growth rates at different growth medium temperatures.

TEMPERATURE

MEAN

TEMPERATURE

MEAN

(°C)

GROWTH

(°C)

GROWTH

RATE (1/day)

RATE (1/day)

9

-0.12

25

1.33

10

0.10

26

1.40

11

0.15

27

1.39

12

0.11

28

1.38

13

0.20

29

1.44

14

0.37

30

1.33

15

0.37

31

1.17

16

0.41

32

0.63

17

0.57

33

0.37

18

0.65

34

0.21

19

0.73

35

0.12

20

0.74

36

0.11

21

0.82

37

0.09

22

0.95

38

0.02

23

1.12

39

-0.25

24

1.17

40

Table 6. Values incorporated into the heat management model.

Temperature at max

TOPT

29 °C

Temperature at 10% max lower

TINF

11 °C

Temperature at 10% max upper

TSUP

35 °C

Maximum Growth rate max (1/day)

MGR

1.44

The results also showed some interesting deviations. The growth rates between 26

to 29 °C had similar values. In fact, the growth rate at 28 °C was less than those at 26 °C

and 27 °C. This unsteadiness could be due to the measurement techniques used as

discussed later. A similar unsteadiness occurred in the lower temperature range (14 °C to

16 °C). The growth rate at 12 °C was smaller than the one at 11 °C, which was not in

85

---

concurrence with the pattern of the skewed normal distribution. One reason could be

again the measurement techniques; another could be the slow growth rate itself. At such

critical temperatures, algae are more sensitive to all other environmental parameters, too.

Longer periods required for one doubling under these conditions allow more time for

other environmental factors (nutrients, pH, light, contamination, etc.) to interfere. At the

growth medium temperature of 9 °C and 39 °C, the growth rates were observed to be

negative, which means that the algae died due to environmental stress.

This study shows that

Chlorella

algae were very sensitive to high temperatures.

The range between the optimal temperature (29 °C) and death (38 °C) was very tight.

This indicates that special considerations with respect to the heat management of large

scale systems have to be taken into account.

Using the data presented in Table 6, a growth function as described in Chapter II

was generated and plotted accordingly (Figure 35). The differences in the mean growth

rates at specific temperatures could also be expressed as percent losses with respect to the

maximum growth rate. This is especially important for the productivity considerations.

Considering that the temperature at the maximum growth rate has a 100% productivity,

the temperatures below and above the maximum will be a fraction thereof and can be

presented as in Figure 34.

86

---

Figure 35.

Chlorella

growth curve with respect to growth medium temperature.

Figure 34. Relative productivity rates with respect to growth medium temperature.

87

---

4.2 Heat Management Model

Sensitivity Analyses

A sensitivity analysis was performed on the simulation model in order to show the

impact of outside temperature changes on the PBR and inside greenhouse air

temperatures. A second analysis was performed to determine the impact of outside solar

radiation on the PBR temperature and inside greenhouse air temperatures. Finally, the

energy consumption was monitored for different ground reflectivities and different

distances between the PBR columns.

For the temperature sensitivity analysis (Figure 36), the solar radiation was kept

constant at 600 W/m2 for nine hours each day. The outside temperature was kept the same

for five consecutive days at each temperature starting at -20 °C and ending at 40 °C. The

greenhouse air temperature and the PBR temperature responded accordingly. It took

roughly two days for the responding temperatures to adjust to the new climatic condition

as seen in Figure 36. Focusing on the critical region, where the outside temperature step

change took place (Figure 37), it was obvious to see that the maximum temperatures for

the greenhouse and the PBR had a gap of about two to three hours due to the difference in

their thermal masses. The distribution of the PBR temperature as well was shown in

detail. Due to shading effects within the PBR columns, the temperature rose rapidly until

the critical sun angle (TC) and slower afterwards due to less direct sun light reaching the

PBR tubes. The temperature differences at the maximums were between 8 °C and 10 °C.

88

---

).

89

perature (top) and solar radiation (bottom

e

nsitivity analyses on outside tem

Figure 36. S

---

Figure 37. Responses to a step change in outdoor temperature.

For the solar radiation sensitivity analysis, the outside air temperature was kept

constant at 18 °C for day and night (Figure 36). The solar radiation was varied in 300

W/m2 increments between 0 W/m2 and 1200 W/m2 for five days each. It was assumed

that the sun was shining at a constant radiation rate for 9 hours every day. The greenhouse

air temperature and the PBR temperature responded accordingly, and increased after each

step. Due to the difference in thermal masses, the maximum temperature of the PBR was

reached about one to two hours after the greenhouse air temperature reached its maximum

(Figure 38). Also, the temperature variability of the PBR was due to higher thermal mass

less than the one of the greenhouse temperature. The shape of the temperature distribution

looked similar to the previous sensitivity analysis, and was again a result of the shading

function, and therefore, of the sun angle. However, the magnitudes were different. The

90

---

temperature differences at the maximums were between 5 °C and 18 °C, depending on the

level of incoming solar radiation.

Figure 38. Responses to a step change in solar radiation.

For the ground reflectivity sensitivity analysis, the original weather file for San

Luis Obispo, CA, U.S.A. for April 2007 was used. The simulations were performed for

ground reflectivities of 20, 40, 60 and 80%. Associated energy requirements and average

productivities were monitored (Figure 39). The results showed that the higher the

reflectivity was, the lower the average productivity was (a function of the PBR

temperature). The higher the reflectivity, the less heating and the more cooling were

required. The total energy needs for heating and cooling rose with rising ground

reflectivity.

91

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Figure 39. Energy requirements and average productivity for different ground

reflectivities.

For the PBR column distance sensitivity analysis, the original weather file for San

Luis Obispo, CA, U.S.A. for April 2007 was used. The simulations were performed for

PBR column distances of 0.25, 0.5, 0.75, 1.0, 1.5, and 2.0 m. In each simulation, the

greenhouse size was kept the same, which means that there was the same number of

PBRs in the greenhouse, but they were closer or wider apart.

The distance between the PBR columns had a major impact on the energy

requirements and the average productivity (Figure 40). The most heating (18,331 MJ per

day) was required at a distance of 0.75 m, the least (16,474 MJ per day) at 2 m. The most

cooling (12,974 MJ per day) was required for a distance of 2 m, the least (10,531 MJ per

day) at 0.75 m. The total energy needs rose with larger distances and peaked at the 2 m

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distance with 29,448 MJ per day. However, the algal productivity was a function of the

PBR temperature and its distribution during the day. Too high and too low temperatures

had direct impact on the productivity. Shading had a major impact on the temperature

regime of the PBR. The distance between the PBRs influenced the shading factor as

previously described. Apparently, an optimal distance between columns existed, where

heat gains due to solar radiation and the shading at midday (avoid overheating) were in a

most advantageous ratio. For the examined PBR, the best distance seemed to be about

0.75 m. However, the total productivity (biomass output and price per area) is also a

measure of the price of greenhouse space. A smaller distance will eventually save space.

Whether space savings outweigh the higher productivity rate or not can now be

investigated.

Figure 40. Energy requirements and average productivity for different PBR distances.

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For the transmissivity of greenhouse shading material sensitivity analysis, the

original weather file for San Luis Obispo, CA, U.S.A. for April 2007 was used. The

simulations were performed for greenhouse shading material transmissivities of 20, 40,

60 and 80% as well as for a greenhouse without shading (100% transmissivity).

Associated energy requirements and average productivities were monitored (Figure 42).

The transmissivity of the shading material had a major impact on the energy

requirements and the average productivity. The most heating (59,678 MJ per day) was

required for a transmissivity of 20%, the least (15,830 MJ per day) for 100% (without

shading material). The most cooling (10,243 MJ per day) was required for no shading

material (100% transmissivity), the least (0 MJ per day) for a transmissivity of 20%. The

total energy needs rose with lesser transmissivity and was the least for 100%

transmissivity with 26,073 MJ per day. However, the algal productivity as a function of

the PBR temperature and its distribution during the day could not be correlated to the

energy consumption. The highest productivity (73.9%) was determined at 60%

transmissivity, whereas the lowest productivity (47.1%) was determined for a

transmissivity of 20%. Important for further considerations was the productivity rate of

66.9% for a transmissivity of 100% (no shading). Apparently, an optimal shading

transmissivity existed, where heat gains due to solar radiation and the shading at midday

(avoid overheating) were in a most advantageous ratio. The productivity can be increased

by 7% by using a shading material with 60% transmissivity. Whether more energy input

(using a shading material with less transmissivity) will outweigh the higher algal

productivity can now be determined by the photobioreactor operator. Further discussion

about the shading will follow later in this work.

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Figure 42. Energy requirements and average productivity for different shading material

transmissivities.

Figure 41. Energy requirements and average productivity for ventilation rates.

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For the ventilation rate sensitivity analysis, the original weather file for San Luis

Obispo, CA, U.S.A. for April 2007 was used. The simulations were performed for

ventilation rates of 0.01, 0.02, 0.03 and 0.04 m3/s.m2 as well as for the default value

(0.001 m3/s.m2) that reflected the natural ventilation only (no mechanical ventilation).

Ventilation was only supplied when the PBR (algae) temperature was over its optimum of

29 °C. Associated energy requirements and average productivities were monitored

(Figure 41).

The ventilation rate had an impact on the energy requirements and the average

productivity. The most heating (17,207 MJ per day) was required for the highest

ventilation rate (0.04 m3/s.m2), the least (15,830 MJ per day) for no ventilation. The most

cooling (10,243 MJ per day) was required for no ventilation, the least (8,942 MJ per day)

for the highest ventilation rate, as expected. The total energy needs rose with higher

ventilation rates and was the most at the highest ventilation rate with 26,149 MJ per day.

The algal productivity as a function of the PBR temperature and its distribution during the

day was directly correlated to the energy consumption. The higher the ventilation rate

was, the higher the average productivity. However, the magnitudes were very small. The

highest productivity (68.3%) was determined for a ventilation rate of 0.04 m3/s.m2,

whereas the lowest productivity (66.97%) was determined for no ventilation. The

productivity can be increased by approximately 1% by utilizing high ventilation. Whether

the savings in cooling and the small increase in productivity rectifies the costs of

ventilation can now be determined by the photobioreactor operators.

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Results

The model was run using the weather data for San Luis Obispo, CA, U.S.A. to

exemplify the process and possibilities of analysis. The weather file contained hourly

weather data for outside temperature, solar radiation, wind speed, and relative humidity

for April 5th to 30th, 2007. The month of April was chosen to represent an average month

of the year. A specific photobioreactor and greenhouse were chosen for this analysis as

described in Chapter III.

The first scenario studied was the DO-NOTHING scenario: how the PBR system

performed in local San Luis Obispo weather without heating or cooling. An outdoor PBR

operation was compared to a PBR operation in a greenhouse to be able to draw a

conclusion about feasibility in a future study. Since the time interval used in the

simulation was one hour, the calculated output temperature was based on the heat

exchange, which took place during the previous hour. The PBR system performance was

studied in the outdoor conditions first. The hourly temperature distributions were

presented for the entire evaluation period as shown in the upcoming figures presented in

this chapter.

Figure 43 shows the temperature variations for outdoor and indoor PBR

operations. For outdoor operation, the PBR temperature followed the outside temperature

closely. However, as expected, the PBR itself functioned as a thermal storage device due

to its thermal mass, and responded to the outside temperature change with a time lag. The

temperature of the PBR was higher during the day due to solar radiation heat gains. As a

result, the PBR temperature did not fall below the outside temperature. The same was true

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for the floor temperature. A longer time lag was observed due to a bigger thermal mass.

The bigger the thermal mass was, the slower the reaction of the component was to the

changes in outside weather conditions. The temperature peaks were skewed by about 1 to

3 hours. The maximum PBR temperature occurred about 2 hours after the greenhouse air

temperature reached its maximum. The floor temperature peaked about 1 to 2 hours after

the PBR temperature peaked; and this was because of the bigger thermal storage of the

ground compared to that of the PBR. For outdoor operation, four graphs were plotted

(Figure 43 bottom) to compare the outside temperature, the greenhouse air temperature,

the floor temperature and the PBR temperature over the entire period. In this case, the

greenhouse air functioned as a buffer, and therefore; the PBR temperature was

approximately 10 to 15 °C higher than the outside temperature. As for the outdoor

condition, the peak temperatures for the indoor conditions were a function of the thermal

masses, too. The floor temperature responded to the PBR temperature with a time lag of

approximately 2 to 3 hours. The PBR temperature responded to the greenhouse air

temperature with a time lag of approximately 1 to 3 hours. The greenhouse air

temperature responded to the outside air temperature with a time lag of 1 to 4 hours.

Due to a long time interval between simulation steps (one hour) in the model, it

took about 2 to 4 days to adjust the PBR and floor temperature to the outside conditions.

The temperatures of the first 5 days should not be considered reliable, and were not

considered in the evaluations. Some unsteadiness′ at the peaks of the outside temperature

during noon time were recorded. These jags were due to the typical California Central

Coast weather with a harsh wind (up to 7 m/s) during the midday hours. The temperatures

dropped accordingly and the temperature response of the PBR followed subsequently.

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) PBR operations.

99

erature variations for outdoor (top) and indoor (bottom

p

e

m

Figure 43. T

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Figure 44. Temperature distribution on a clear day (April 10th, 2007).

Figure 45. Temperature distribution on an overcast day (April 20th, 2007).

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Figure 44 and Figure 45 show the temperature distribution for an indoor PBR operation

on a clear day and an overcast day, respectively, in a scaled-up view in order to have a

deeper insight and better understanding. Obviously, there was a much higher greenhouse,

floor and PBR temperature, compared to the outdoor PBR condition, where the

temperature followed the outside temperature air closely. Here, the greenhouse air was

used as a heat buffer and kept the surrounding air of the PBR at relatively higher

temperatures (what also can turn into a disadvantage on hot days if proper ventilation is

not provided, because the PBR temperature will rise accordingly). The floor temperature

was maintained at about 5 °C above the outside conditions. As typical for greenhouses,

the inside air temperature was mainly a function of the incoming solar radiation rather

than that of the outside air temperature, which also explains the temperature differences

between the outdoor and indoor PBR operations. The outdoor PBR was exposed to the

outside air and the indoor PBR was exposed to the greenhouse air.

The inside air temperature fluctuated more than the inside PBR temperature, and

the inside PBR temperature more than the floor temperature, due to relatively smaller heat

storage capacities. The PBR temperature responded to the greenhouse temperature with a

lag phase of 1 to 3 hours due to the greater thermal mass. The floor temperature followed

the PBR temperature by another 1 to 3 hours. The maximum air temperatures in the

greenhouse, especially at the end of the month when the solar radiation was much higher

(980 W/m2 instead of 820 W/m2), reached up to 50 °C and above. Even the PBR

temperature rose to the upper 40 °C, and the floor temperature to almost 30 °C. This

phenomenon was experienced during trial runs of a lab-scale PBR in a greenhouse with

no cooling, shading or ventilation on Cal Poly campus in Spring 2008. Greenhouse

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temperatures of up to 50 °C and PBR temperatures of far more than 40 °C were recorded

then. As a consequence, the algae died (also shown in the temperature experiments in the

previous section).

Not only too high temperatures, but also too low temperatures harmed algae

growth as shown in the temperature experiments section earlier. The theoretical yield

losses due to temperature fluctuations (or not maintaining the temperature at optimal

level) can be calculated with the data obtained from the experiments. The yield losses

were expressed as percent productivity where the productivity at optimal temperature was

100%. Temperatures above and below the optimum reduced the productivity.

Figure 46. Algae productivity with respect to the temperature in each hour in the outdoor

PBR operation.

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Detailed productivity rates per hour were presented in Figure 46 and Figure 47 for

outdoor and indoor operations, respectively. The average productivity for outdoor

operations was 23.4% (in Figure 46 it was shown as blue area, whereas the white area

under the 100% line was the productivity losses). The average productivity for the indoor

operation was 66.9% (in Figure 47 it was shown as orange area). The main difference

between the outdoor and indoor operations was the way productivity losses occurred. In

the outdoor operation, all productivity losses occurred due to low temperatures (the solar

radiation was not strong enough to heat up the system to optimal temperature), whereas in

the indoor operation, productivity losses occurred mainly due to overheating of the PBR.

Figure 47. Algae productivity with respect to the temperature in each hour in the

indoor PBR operation.

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For visualization purposes, it was now assumed that overheating would not cause

productivity losses. Figure 48 shows the impressive productivity rate averaging at 90%.

Consequently, two different strategies for controlling the temperature in outdoor and

indoor operations were considered: Cooling the greenhouse and PBR for indoor

operation; and heating the PBR for the outdoor operation.

Figure 48. The hypothetical algae productivity with respect to the temperature in each

hour for indoor PBR operation, when losses due to overheating were ignored.

As the next step, the actual amount of energy needed for heating and cooling was

determined. The heating and cooling loads were calculated and presented separately

because the technology and therefore the energy prices for heating and cooling are

different. Generally speaking, heating is cheaper than cooling a system. Heat is a

byproduct of many industrial processes, and can either be purchased for moderate prices

or produced easily with a burner. Therefore, reducing the cooling loads in the first place

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is always the major goal. Appendix A presents the heating and cooling loads for indoor

and outdoor operations for each day. The daily figures were the sums of the hourly

heating and cooling loads calculated. Average values per day and the total sum for the

period studied (here 21 days) were shown in Appendix A. As discussed previously, the

total cooling load for outdoor conditions (593 MJ for the period of 21 days) could be

neglected. However, an average heating load of 90,212 MJ per day and a total heating

load of 2,338,000 MJ for the entire period of 21 days was determined. Heating loads for

the indoor PBR operation of 14,091 MJ (average per day) and 411,580 MJ for the entire

period of 21 days were determined. However, in the case of indoor operation, the cooling

loads were very high (12,097 MJ average per day, and 266,320 MJ total for the entire

period). Figure 49 shows the heating and cooling loads for the indoor operation

graphically.

The easiest way to reduce cooling loads is to reduce solar radiation. The simplest

way to reduce the solar gains is to provide shading with a shading cloth, curtain, or

whitening the greenhouse glazing. Simulations were performed with a curtain or

whitening having transmissivities of 60% and 80%, and findings were presented in

Appendices B and C, respectively. For a cover with 60% transmissivity, the cooling loads

were significantly reduced (1,228 MJ average per day, 25,790 MJ total for the entire

period). This was only about 10% of the cooling needed in a greenhouse without shading.

However, heating loads increased in this scenario to 30,990 MJ on a daily basis, and to

837,320 MJ in total for the entire period (about 203% more than the base scenario), which

was still small compared to outdoor operation.

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In a third scenario, the energy needs using a whitening or curtain with an 80%

transmissivity was simulated. The cooling loads decreased further compared to the first

scenario by 55% (5,420 MJ based on daily basis, 115,610 MJ total for the entire period).

The heating loads increased by 148% (20,902 MJ based on daily basis, 585,170 MJ total

for the entire period).

With the knowledge of heating and cooling costs, the best scenario could be

determined to minimize operational costs. Obviously, it would be different for each

analyzed project. The previous comparison of scenarios was done for the change of cover

transmissivities just to show the effect of a single variable on heating and cooling

requirements. In addition to that, many other variables, for instance, tube diameter,

number of tubes, number of PBRs, etc. could be examined as well. Dozens of parameters

could be optimized for energy consumption, which would be the topics for future studies.

Figure 49. Required heating and cooling loads for the indoor PBR operation.

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CHAPTER V

CONCLUSIONS

5.1 Temperature Experiments

A procedure was developed and used for

Chlorella

algae to determine the growth

dependency on temperature. The experimental data was needed to develop a

mathematical model for heat management purposes. Besides a literature review for

common strains, this was another method to provide the necessary data. For the

Chlorella

strain, the developed method resulted in a similar maximum growth rate as previously

presented in the literature; i.e. 1.44 doublings per day versus 1.0 to 2.0 doublings per day.

In this study, it was not required to reach the maximum growth rate, rather to monitor the

growth distribution as a function of temperature. The important outcome was the percent

losses and gains with respect to the observed maximum growth rate. This goal was

fulfilled, and the data was successfully incorporated into the simulation model.

Some weaknesses of the procedure included the measurement of the nutrient

content in the algae water. The multimeter operated based on the transmittance of a

specific wavelength. At higher densities (>25%), the green algae water caused

misreadings and errors. The accuracy of the measurements decreased subsequently.

However, for this study, an exact measurement was not essential. The nutrient availability

was critical and maintained at high nutrient levels. Even with a large tolerance band of the

nutrient measurement, the minimum requirements were always maintained. The nutrients

(fertilizer) in this study were chosen only based on the N-P-K ratio. For further

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experiments, micronutrients, vitamins and silicon additions should be considered at

proper concentrations.

The sensitivity of the spectrophotometer played an important role. Especially for

small transmittance readings (<20%), a slight difference of only 1% had an impact on the

calculated growth rate of up to 0.3 doublings per day. A more precise spectrophotometer

with digital readings and PC control would provide better accuracy and more reliable

data, as well as the possibility of long term data storage.

The room where the experiments took place was not fully darkened, so the

daylight probably had a small impact on the growth rate as well. Since the daily radiation

fluctuated during the experiments, it could have impacted the results slightly.

The density range of 5% to 85% transmittance was very large. Especially for high

densities, optimal algae growth could be harmed. For future research, it is

recommendable to keep the cell density low (transmittance >15%), which would lead to

better growth conditions, but the frequency of diluting the broth would decrease

consequently. A more frequent dilution would cause more lag (adaption) phases and

would extend the time of research.

The sample sizes were relatively small due to an enormous amount (>50%) of

void measurements. For future experiments, a longer period of time or more parallel

PBRs should be considered. With the experimental improvements mentioned above, the

amount of void measurements could be reduced.

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5.2 Heat Management Model

The developed heat management model delivered good results for the temperature

regime in greenhouses and PBRs, comparable to experiences made for the same location

at the same time of the year in the Cal Poly campus greenhouse. From the temperature

data, the heat management requirements for any specific location could be estimated.

Using the model could in advance (i.e. in a planning stage of a project) precisely estimate

its future heating or cooling loads, or estimate the productivity without heating or cooling.

This simulation model is a fundamental tool and guidance in the economical decision

making processes related to algae growth in photobioreactors.

Sensitivity analyses for outside air temperature, solar radiation, ground

reflectivity, PBR column distance, transmissivity of the shading material, and ventilation

rate were performed on the model. It took the system roughly two days to adjust to an

outside temperature step change of 15 °C. As expected, the storage components with

smaller thermal mass (i.e. greenhouse air) reacted faster to environmental influences than

components with larger thermal mass (i.e. ground). Therefore, the daily temperature

peaks of the greenhouse air temperature, PBR temperature, and ground temperature had a

gap of 1 to 4 hours. The sensitivity analysis for the ground reflectivity showed that the

energy requirements rose with higher reflectivity. The algae productivity dropped with

higher reflectivity. The sensitivity analysis for the PBR column distance showed a

dependency of energy requirement on the distance. The wider the PBR columns were

placed apart, the more energy was consumed. However, the algae productivity was the

highest at 0.75 m column distance. This led to the conclusion that there is an optimal

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distance between PBR columns for any specific PBR design, where the productivity rate

peaks. The transmissivity of the shading material had a major impact on the energy

requirements as well as the productivity rate. The heating needs increased by over 300%

when putting any kind of shading with a transmissivity of 20% on the greenhouse.

However, cooling requirements can be reduced to zero just by changing the shading. This

gives a huge optimization potential for photobioreactor operators. The ventilation rate had

hardly influence on the algae productivity, however, can reduce cooling loads of the

photobioreactor.

A simulation of a hypothetical tubular photobioreactor in San Luis Obispo,

California, U.S.A. with a volume of about 100,000 liter capacity showed the potential of

the model exemplary. Average algae productivity rates of 23% and 67% for outdoor and

indoor PBR operations, respectively, were obtained. Changing parameters (e.g. diameter,

distance, reflectivity, number of PBRs, etc.) in the model had direct impact on the algae

productivity rate and could be compared easily to the base case. Actual energy loads

(heating and cooling) needed to maintain the PBR at optimal temperature were

determined and compared, too. With the knowledge of the actual energy requirements,

photobioreactor operators will be able to estimate their operational costs in advance and

see what changes to their system would decrease their costs.

The developed model is only a mathematical estimation tool. An experimental

validation of the model is still to be performed in future studies, in order to see the

deviations to the real case. The validation could be carried out in the Cal Poly greenhouse

after the commercial PBR is installed.

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The model itself can be optimized as well. Instead of using one-hour time

intervals, the true interval could be reduced to minutes, which would provide better

estimates of energy consumptions.

In addition to the presented analyses, many other parameters could be examined.

Since all greenhouse and PBR dimensions are variable, heat requirements for different

greenhouse types or PBRs could be compared easily.

Later on, the model could be extended to estimate all energy needs; for example,

the pumping energy requirements for the specific PBR; the energy and productivity of

artificial lighting; or the energy required for harvesting (centrifuge, drying, ultrasonic,

pressing, etc.). All operational costs could be estimated and optimized accordingly.

Eventually, a complete production facility could be simulated with all inputs and

outputs. Entire economical studies could be performed using selling prices for algae cake,

algae oil or biodiesel directly in the model. Furthermore, doing a reverse analysis by

introducing the desired price of a liter or gallon of biodiesel/ethanol could also be

performed. The model would estimate the production plant size; suggest the location

based on its latitude and required solar radiation, and give out the operational costs.

An all-in-one application for the the planning and operation of photobioreactors is

the target.

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119

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Appendix A: Energy requirements per day for standard transmissivity.

120

---

ENERGY REQUIREMENTS

Standard conditions

Outdoor PBR

Outdoor PBR

Indoor PBR

Indoor PBR

Day

HEATING

COOLING

HEATING

COOLING

4/10/2007 79,589.92

-

7,597.61

12,851.42

4/11/2007 98,322.68

-

12,629.32 763.38

4/12/2007 96,634.68

-

21,271.53

5,719.14

4/13/2007 89,956.91

-

10,624.42

10,509.83

4/14/2007 102,787.00

-

24,379.18 450.80

4/15/2007 101,199.15

-

30,602.05 756.65

4/16/2007 85,740.59

-

15,004.92

9,751.53

4/17/2007 97,253.60

-

8,775.14 6,196.31

4/18/2007 99,619.53

-

10,506.93

9,976.65

4/19/2007 109,223.92

-

22,219.41 255.85

4/20/2007 100,427.18

-

44,149.25

-

4/21/2007 97,909.99

-

25,425.36

1,199.59

4/22/2007 95,193.49

-

27,498.19

-

4/23/2007 89,170.67

-

20,266.23

10,658.66

4/24/2007 82,469.53

-

4,757.31

19,913.38

4/25/2007 89,421.30

-

2,306.41

22,779.33

4/26/2007 85,181.94 593.36 2,766.19

21,630.42

4/27/2007 61,340.37

-

2,109.29

31,100.81

4/28/2007 67,170.55

-

-

39,278.31

4/29/2007 85,013.27

-

487.20 26,264.15

4/30/2007 80,819.91

-

2,545.04

23,979.76

SUM (total per

2,337,613.10 593.36 411,579.99

266,324.63

period) (MJ)

AVG per day (MJ)

90,211.72

28.26

14,091.48

12,096.95

121

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Appendix B: Energy requirements per day for 60% transmissivity.

122

---

ENERGY REQUIREMENTS

Curtain with 60% transmissivity

Outdoor PBR

Outdoor PBR

Indoor PBR

Indoor PBR

Day

HEATING

COOLING

HEATING

COOLING

4/10/2007 79,589.92

-

23,100.57 11.46

4/11/2007 98,322.68

-

34,451.33 -

4/12/2007 96,634.68

-

39,522.03 -

4/13/2007 89,956.91

-

29,693.19 -

4/14/2007 102,787.00

-

44,615.92

-

4/15/2007 101,199.15

-

50,984.23

-

4/16/2007 85,740.59

-

34,122.66 -

4/17/2007 97,253.60

-

30,166.12 -

4/18/2007 99,619.53

-

29,972.24 -

4/19/2007 109,223.92

-

45,082.24

-

4/20/2007 100,427.18

-

61,289.32

-

4/21/2007 97,909.99

-

48,762.33 -

4/22/2007 95,193.49

-

48,424.85 -

4/23/2007 89,170.67

-

36,670.19 -

4/24/2007 82,469.53

-

19,401.91

1,332.84

4/25/2007 89,421.30

-

15,180.09

1,425.13

4/26/2007 85,181.94 593.36 16,555.04

1,120.14

4/27/2007 61,340.37

-

13,686.10

7,161.18

4/28/2007 67,170.55

-

5,735.42 9,707.42

4/29/2007 85,013.27

-

9,046.35 2,573.50

4/30/2007 80,819.91

-

14,319.17

2,460.28

SUM (total per

2,337,613.10 593.36 837,316.94

25,791.96

period) (MJ)

AVG per day (MJ)

90,211.72

28.26

30,989.59

1,228.19

123

---

Appendix C: Energy requirements per day for 80% transmissivity.

124

---

ENERGY REQUIREMENTS

Curtain with 80% transmissivity.

Outdoor PBR

Outdoor PBR

Indoor PBR

Indoor PBR

Day

HEATING

COOLING

HEATING

COOLING

4/10/2007 79,589.92

-

13,607.92

5,072.29

4/11/2007 98,322.68

-

22,757.03

-

4/12/2007 96,634.68

-

27,743.44 476.61

4/13/2007 89,956.91

-

17,570.73

3,041.81

4/14/2007 102,787.00

-

33,826.55

-

4/15/2007 101,199.15

-

40,188.62

-

4/16/2007 85,740.59

-

21,849.34

2,499.91

4/17/2007 97,253.60

-

16,526.31 552.91

4/18/2007 99,619.53

-

17,409.52

2,496.19

4/19/2007 109,223.92

-

33,095.87

-

4/20/2007 100,427.18

-

52,453.63

-

4/21/2007 97,909.99

-

36,214.24

-

4/22/2007 95,193.49

-

37,625.74

-

4/23/2007 89,170.67

-

25,837.47

2,990.33

4/24/2007 82,469.53

-

10,644.48

9,645.41

4/25/2007 89,421.30

-

6,680.27

10,517.66

4/26/2007 85,181.94 593.36 7,548.84 9,749.04

4/27/2007 61,340.37

-

6,208.18

17,989.97

4/28/2007 67,170.55

-

1,251.18

23,452.51

4/29/2007 85,013.27

-

3,184.60

13,329.96

4/30/2007 80,819.91

-

6,718.56

11,979.40

SUM (total per

2,337,613.10 593.36 585,172.47

115,612.67

period) (MJ)

AVG per day (MJ)

90,211.72

28.26

20,902.02

5,418.76

125

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Appendix D: Effects of different Nitrogen concentrations on the

chemical composition of various algae strains.

126

---

127

---