DEGREE PROJECT, IN CHEMICAL ENGINEERING FOR ENERGY AND THE , SECOND LEVEL
ENVIRONMENT
STOCKHOLM, SWEDEN 2015
Techno-economic Study for Full-scale
Production of Microalgal Biomass
Techno-economic Study for Full-scale Production of
Microalgal Biomass
August 5, 2015
Author: Maria Tengqvist
Abstract
Microalgae have received a surge in attention in the past decade as a source for re-newable energy. They are currently used to produce high-value products but have the potential to produce biofuels such as bioethanol, biodiesel and biohydrogen among others. The present work is an evaluation of the feasibility of a process producing microalgae as a wet biomass paste through modeling of a real process. The produc-tion process of microalgal-derived low-value products has yet to be realized due to the low productivity in current culture systems, the high cost of such systems and the high cost of harvesting the microalgal biomass. An accurate and efficient model of this process is key in allowing for scale up to where it can contribute sufficiently to a more sustainable society.
The model constructed evaluates the best alternative out of twelve configurations using data supplied by the user. The model is flexible in that it allows for modeling of different microalgae and different scales of production. Genetic engineering of the microalgae is modeled as three different cases: a reduction in the light-harvesting antennae, the expression of a fluorescent protein that by absorbing UV light emits photosynthetically active radiation and a combination of the two. The model is then run for the case relevant to the user. To evaluate the performance of the model and the viability of the modeled process, it was ran for the microalgae P. tricornutum and an annual production demand of 1000 ton wet biomass paste. The break-even price of the biomass was 8.79 Ä for the base case and 5.68 Ä with both cases of genetic engineering of the microalgal cell. The best configuration was found to be a tubular photobioreactor in the cultivation stage with flocculation-sedimentation followed by filtration in the harvesting stage.
Sammanfattning
Intresset för mikroalger som en förnyelsebar energikälla har ökat under det senaste decenniet. För närvarande används mikroalger enbart för produktion av specialpro-dukter men de har potential att användas vid produktion av bland annat bioetanol, biodiesel och vätgas. Detta arbete är en teknoekonomisk studie av produktion av våt biomassa från mikroalger genom modellering av en verklig process. En sådan process finns ännu inte i stor skala på grund av den låga produktiviteten i nuvarande odlingssystem och dess höga kostnader samt de höga kostnaderna kopplade till skörd-ning av biomassan. För att skala upp denna process krävs en noggrann och effektiv modell som simulerar processen samt hur den kan förbättras genom att genetiskt modifiera mikroalgerna.
Modellen som konstruerats tar in data från användaren och utvärderar den bästa pro-cessen av tolv konfigurationer. Modellen är flexibel och tillåter simulering av olika typer av mikroalger och olika produktionskrav. Genetisk modifiering av mikroalgerna modelleras för tre fall: en reducering av ljuskomplexens antennstorlekar, uttryckn-ing av ett fluorescerande protein som absorberar UV-ljus och emitterar fotosyntetiskt aktiv strålning och en kombination av båda. Modellen körs sedan för det fall som användaren finner relevant, ett basfall utan genetiska modifieringar och med dessa. För att utvärdera modellens prestation och den modellerade processens genomför-barhet kördes den för mikroalgen P. tricornutum och en årlig produktion på 1000 ton våt biomassa. För att uppnå ett nollresultat krävs ett försäljningspris på 8.79 Ä för basfallet och 5.68 Ä för fallet med båda de genetiska modifieringarna. Den bästa kon-figurationen var en tubreaktor i odlingssteget följt av flockulering och sedimentering följt av filtrering.
Acknowledgements
This master thesis was conducted as part of the master program Chemical Engineer-ing for Energy and the Environment at KTH, Royal Institute of Technology. The project was carried out at the Department of Chemical Technology between January 2015 and June 2015. The project was conceived by my two supervisors Lina Norberg Samuelsson, a PhD student at the Department of Chemical Technology, and Paul Hudson, an associate professor at the Department of Proteomics and Nanobiotech-nology at the school of BiotechNanobiotech-nology.
Foremost I would like to express my deepest gratitude to Lina for her constant support and encouragement throughout the project. She has dedicated her time and shown me patience as well as provided me with stimulating discussions and suggestions. I could not have asked for a better supervisor. I would also like to give a special thank you to Paul who has provided me with his expert knowledge in the field of Biology as well as fruitful discussions and guidance. It has been a pleasure to work with both of you and I would like to thank you for providing me with the opportunity to carry out this project.
Lastly I would like to thank my examiner Henrik Kusar for providing his time and to those who have taken their time to give me valuable inputs as well as encourage and support me throughout these five months.
Table of contents
1. Introduction 1
1.1 Background 1
1.2 Aim 2
1.3 Limitations and Delimitations 2
2. The Production Process: From Unicellular Microalgae to Biomass 4
2.1 What are Algae? 4
2.2 Cultivation for Large-scale Production of Biomass 5
2.2.1 Photosynthesis 5
2.2.2 The Effect of Light on Microalgal Growth 7
2.2.3 The Different Phases of Microalgal Growth 9
2.2.4 Nutrients 10
2.2.5 Annual and Diurnal Cycles 11
2.2.6 Culture Systems 11
2.2.7 Genetic Engineering for Higher Productivities 15
2.2.8 Modeling of Microalgal Growth 16
2.3 Alternatives for Harvesting of Biomass 17
2.3.1 Coagulation and Flocculation 18
2.3.2 Gravitational Separation Processes 19
2.3.3 Centrifugal Recovery 20
2.3.4 Filtration 21
3. The Model 22
3.1 Cultivation 23
3.1.1 Light Available for Photosynthesis 23
3.1.2 Temperature Dependence of Specific Growth Rate 26
3.1.3 Specific Growth Rate 26
3.1.5 From Batch to Annual Production 29
3.1.6 Mixing in the PBRs: Pump and Fan Requirements 30
3.1.7 Choice of Photobioreactors 32
3.1.7 Modeling of Process Improvement by Genetic Engineering 32
3.2 Harvesting of Biomass 32
3.2.1 The Configurations of the Harvest Process 33
3.1.2 Energy Consumption 34
3.3 Economic Analysis 34
3.3.1 Total and Annual Fixed Capital Investment 34
3.3.2 Other Costs 36
3.3.3 Total Costs 36
4. Results 37
5. Discussion 46
List of Figures
1 Conversion of light energy to chemical energy in a microalgal cell [11]. 6
2 Interaction between PS I and PS II to form energy carriers ATP and
NADPH. Q, pC, Fd and FNR are components not discussed here [11]. 6
3 Light response curve showing the relationship between net rate of
photosynthesis (net P) and irradiance (I). Rd is the dark respiration,
Ic is the compensation irradiance where the rate of photosynthesis
equals the rate of respiration, – is the linear relationship between P and I at low irradiance, Ik is the saturation irradiance and Pm is the light-saturated rate of photosynthesis, the highest attainable when
light is the limiting factor of photosynthesis [12]. . . 8
4 Phases of microalgal growth [17]. . . 9
5 A typical raceway pond for microalgal production [22]. . . 12
6 Two types of tubular PBRs: to the left a horizontal configuration with a large diameter and to the right a configuration with a smaller diameter where the tubes are arranged in a framework on top of each other [23, 24]. . . 13
7 Flat panel PBRs: To the left a rigid PBR used by the German com-pany Subitec GmbH and to the right a flexible PBR used by the American company Algenol [4, 25]. . . 14
8 Schematic of the modeled process. . . 22
9 Geometry of a flat panel reactor [47]. . . 25
10 Approximating the geometry of a tubular PBR as numerous paral-lelepipeds that the light travels through [47]. . . 25
11 Logarithmic microalgal concentration as a function of cultivation time. 37 12 Productivities for the cheapest configuration as a function of cultiva-tion time for all cases. . . 39
13 Total costs by type for the base case. . . 40
14 Total fixed capital investment by type. . . 40
15 Major equipment costs by type. . . 41
17 Other costs by type. . . 42
18 Total costs and energy consumption for each configuration. . . 43
19 Sensitivity analysis with regard to three parameters: Irradiance (L), light path of PBR (T) and energy price (E). Each parameter was varied ± 50% and the bars represent the difference in selling price between the two levels for each parameter. . . 44
20 Variable costs per year as a function of final concentration. . . 45
21 Harvesting flow scheme flotation . . . 60
22 Harvesting flow scheme flocculation flotation . . . 60
List of Tables
1 Flocculation of P. tricornutum with PAC, AS and chitosan [41]. . . . 19
2 Total fixed capital investment. . . 35
3 Annual fixed capital investment. . . 35
4 Other costs. . . 36
5 Cheapest configuration: tubular PBR, flocculation followed by sedi-mentation and filtration. Selling price and energy demand for annual production of 1000 ton of biomass for the base case and three cases of improvement of the process via genetic engineering. . . 38
6 Most expensive configuration: flat panel PBR, flotation and centrifu-gation. Selling price and energy demand for annual production of 1000 ton of biomass for the base case and three cases of improvement of the process via genetic engineering. . . 38
7 Data that is hard-coded into the model . . . 58
8 User-supplied data for P. tricornutum. . . 59
9 CEPCI indices used in the model. . . 62
10 Equipment used in the cultivation stage and their prices. . . 62
11 Raw materials used in the cultivation stage and their prices. . . 63
12 Equipment used in the cultivation stage and their prices. . . 63
Nomenclature
P Pressure drop, page 31
÷harvest Total biomass recovery in harvesting stage, page 30
÷pump Pump efficiency, page 31
µ Specific growth rate, page 16
µmax Maximum specific growth rate, page 16
µopt Maximum specific growth rate at the optimal temperature for growth,
page 26
µvisc Viscosity of cultivation medium, page 31
fl Density of cultivation medium, page 31
a Experimental constant, page 26
b Experimental constant, page 26
c Experimental constant, page 26
Cb Biomass concentration, page 24
CCO2(aq) Concentration of CO2(aq), page 28
Cf inal Final concentration of cultivation, page 30
f Friction factor of tubular photobioreactor, page 31
H Henry constant, page 28
I Light intensity, page 24
I0 Incident light intensity, page 24
Ik Microalgal affinity for light, page 26
Iav Average light intensity, page 16
Ki Photoinhibition constant, page 26
Ks Half saturation constant, page 16
L Reactor light path, page 24
Ltube Length of tubular photobioreactor, page 30
MC Molar mass of carbon, page 29
Nbatches Number of batches per year, page 29
NP BR,f p Number of flat panel photobioreactors, page 30
P Pump power, page 31
PCO2 Pressure of CO2, page 28
Q Volumetric flow, page 31
qC Quota of carbon in the microalgal cell, page 29
R Radius of tubular photobioreactor, page 25
Re Reynold number, page 31
tbatch Time per batch, page 29
Tmax Maximum temperature for growth, page 26
Tmin Minimum temperature for growth, page 26
Topt Optimum temperature for growth, page 26
tprod Production time per year, page 29
u Fluid flow velocity in tubular photobioreactor, page 31
Vf p Volume of a flat panel photobioreactor, page 30
Vtot Total volume per batch, page 30
X Biomass concentration, page 16
Xyear Annual production demand, page 30
AS Aluminum sulfate, page 19
CF Concentration factor, page 17
DW Dry weight, page 3
FP Flat panel, page 30
NPQ Non-photochemical quenching, page 15
PAC Polyacrylamides, page 18
PBR Photobioreactor, page 11
ROS Reactive oxygen species, page 7
1 Introduction
1.1 Background
With a growing world population and an increase in life quality for people around the world, consumption of commodities is increasing at a fast rate. Growing economies spur an increase in transport, which puts a large stress on the environment through emissions of carbon dioxide and other gases harmful to the environment.
In the past 40 years, specifically following the oil crisis during the 1970’s, a great effort has been put into developing and producing so called first generation biofuels in order to reduce our dependency on oil [1]. Production of first generation biofuels such as bioethanol and biodiesel, that are produced from grains and food crops, are well developed and large quantities of these fuels are produced around the world. Between year 2000-2012, the use of biofuels increased by 604% [2]. Second generation biofuels, produced from lignocellulosic biomass, is gaining ground within the biofuels field with products such as bioethanol, biodiesel and syngas [3].
While first generation biofuels are an integrated part of most countries’ energy policy, their sustainability has been questioned. Biofuels produced on arable land and from edible crops compete with food supply and thereby affect the price and availability of certain foods, spurring the well-known debate of food vs. fuel [3].
Biofuels of the future will constitute many different types of biofuels and the search for new energy sources is constantly ongoing. Microalgae as a renewable feedstock for the production of third generation biofuels has gained interest [3]. The field is fairly young and has yet to develop viable processes for commercial mass production of microalgae and microalgae-derived biofuels. However, the American companies Algenol and Sapphire Energy show interesting developments [4, 5].
order to reduce costs; from genetic engineering through genetically modifying the microalgae, to developing cheaper and more efficient culture systems and dewatering processes [7].
1.2 Aim
The aim of this thesis is to develop a model in Python of the production of microalgal biomass, which simulates growth and harvest of the microalgal biomass. The model is to be used to perform a techno-economic study of the process as well as of im-provements made through genetic engineering. Furthermore, the model is intended to aid researchers in optimization of a future microalgal production process.
The model should include cultivation of microalgae and subsequent harvesting pro-cess and present the best propro-cess alternative to the user. It should be able to draw conclusions regarding which genetic modifications to a microalgal cell will have the greatest positive effect on large-scale production. Furthermore, the model should be flexible for use with different microalgal species and modes of production. It should be easily used and modified for specific purposes, should the user wish to do so.
1.3 Limitations and Delimitations (Har jag tolkat rätt att
de är två olika saker? Blir det en konstig rubrik?)
In order to set boundaries and better focus the goals of the project, certain de-limitations have been made. Furthermore, creating a model capable of accurately modeling a microalgal production process requires a large input of time. Since this project only spans 20 weeks, this has incurred further restrictions to the project. These limitations and delimitations are presented below.
After a literature study was performed, the choice was made to model the harvesting process in two stages, with three alternatives in the first stage and two alternatives in the second stage. Availability of data that could be used when modeling the harvesting stage was scarce, which limited the choice of raw materials and equipment for the different processes. Therefore the choices for each process were made based on what data was available, which cannot guarantee that that the chosen raw materials and/or equipment were optimal. Furthermore, such data was taken for laboratory scale, as data for pilot plant or full scale was not available.
A possible dewatering step after harvesting has been omitted from the model due to questions regarding its necessity. The dewatering step is costly, both in terms of energy and cost and since the model does not determine products and/or byproducts of the process, it is unknown whether a dewatering step will be necessary. Processes exist that use wet biomass (approximately 15% dry weight (DW)) as a feedstock for biofuel production e.g. hydrothermal liquefaction, which can be used to produce biocrude. Another possible use for wet biomass is integration with a pulp plant using black liquor gasification to produce syngas, which is further upgraded to biofuels. With regard to genetic engineering, the model will not include modeling of carbon partitioning since the model deals only with the production of biomass. However, secondary and tertiary products are important for a future microalgal production process and this research is therefore of great interest. The process is modeled for a specific species depending on the data given by the user as well as some data that are hard-coded into the model. These are easily replaced, given that all data required are available. The model is currently constructed for use for the microalgae species Phaeodactylum tricornutum.
2 The Production Process: From Unicellular
Mi-croalgae to Biomass
This section will provide background on the aspects of large-scale production of biomass from microalgae. The first subsection, What are Algae?, shortly describes what microalgae are; the second, Cultivation, provides theory behind and conditions for large-scale cultivation of microalgal biomass; the third, Alternatives for Harvest-ing of Biomass, describes how the biomass in the dilute culture can be harvested and presents challenges and possibilities of this step.
2.1 What are Algae?
Algae are a group of organisms that can be classified as either autotrophs or het-erotrophs, meaning that they use either carbon dioxide or organic carbon for growth [9]. Algae can be further classified in accordance with the energy source used to sustain life; phototrophs, which utilize light energy to sustain life; or chemotrophs, which utilize energy derived from the oxidation of organic or inorganic compounds [9]. Algae are either unicellular microalgae or multicellular macroalgae, such as seaweed [10]. In this thesis only photoautotrophic microalgae are considered, i.e. microalgae that utilize light in the process of photosynthesis to assimilate carbon dioxide. Microalgae can be classified as eukaryotic microalgae and prokaryotic cyanobacteria, the latter of which is sometimes regarded as microalgae and sometimes not, depend-ing on the definition [10]. This thesis will adopt the definition of microalgae that includes cyanobacteria, as they are of interest with regard to mass cultivation for renewable energy.
2.2 Cultivation for Large-scale Production of Microalgae
This subsection will deal with the theoretical and practical details of cultivation of microalgae. First, photosynthesis is explained briefly on a cellular level to show how it fuels the cell. This is followed by how irradiance will affect the cell and the rate of photosynthesis. After this, the nature of microalgal growth is described as well as the nutrients required for growth. The effect of annual and diurnal cycles on growth is described and lastly, modern culture systems for mass cultivation of microalgae are presented.2.2.1 Photosynthesis
Microalgal cells grow by assimilating carbon dioxide from the atmosphere and pro-duces biomass with the help of harvesting solar energy. This process is called pho-tosynthesis and can be summarized by equation 1.
6CO2+ 6H2O ≠æ Clight 6H12O6+ 6O2 (1)
In reality the process is much more complex, consisting of two main parts: the light reactions and the dark reactions.
473
from the excited chlorophyll special pair (Figure 14–32). This electron transfer lies at the heart of photosynthesis, because it converts the light energy that came into the special pair into chemical energy in the form of a transferable electron. As soon as the high-energy electron is handed off, the chlorophyll special pair becomes positively charged, and the elec-tron carrier that accepts the elecelec-tron becomes negatively charged. The rapid movement of this electron along a set of electron carriers in the reaction center then creates a charge separation that sets in motion the flow of electrons from the reaction center to an electron-transport chain
(Figure 14–33).
A Pair of Photosystems Cooperate to Generate Both ATP and NADPH
Photosynthesis is ultimately a biosynthetic process, and to build organic molecules from CO2, a plant cell requires a huge input of energy, in the
form of ATP, and a very large amount of reducing power, in the form of the activated carrier NADPH (see Figure 3–34). To generate both ATP and NADPH, plant cells—and free-living photosynthetic organisms such as cyanobacteria—use a pair of photosystems that are similar in structure, but that do different things with the high-energy electrons that leave their reaction center chlorophylls.
When the first photosystem (which, paradoxically, is called photosystem II for historical reasons) absorbs light energy, its reaction center passes electrons to a mobile electron carrier called plastoquinone, which is part of the photosynthetic electron-transport chain. This carrier transfers the high-energy electrons to a proton pump, which—like the proton pumps in the mitochondrial inner membrane—uses the movement of electrons to generate an electrochemical proton gradient. The electrochemical proton gradient then drives the production of ATP by an ATP synthase located in the thylakoid membrane (Figure 14–34).
At the same time, a second nearby photosystem—called photosystem I—has been also busy capturing the energy from sunlight. The reaction center of this photosystem passes its high-energy electrons to a different mobile electron carrier, which brings them to an enzyme that uses them to reduce NADP+ to NADPH (Figure 14–35). The combined action of these
thylakoid membrane chlorophyll
special pair light-harvesting
antenna complexes reaction center
energy transferred from one chlorophyll molecule to another
photosystem
ECB4 m14.323a/14.34 LIGHT
Figure 14–32 A photosystem consists of a reaction center surrounded by chlorophyll-containing antenna complexes. Once light energy has been captured by a chlorophyll molecule in an antenna complex, it will pass randomly from one chlorophyll molecule to another (red lines), until it gets trapped by a chlorophyll dimer called the special pair, located in the reaction center. The chlorophyll special pair holds its electrons at a lower energy than the antenna chlorophylls, so the energy transferred to it from the antenna gets trapped there. Note that in the antenna complex only energy moves from one chlorophyll molecule to another, not electrons.
Figure 14–33 In a reaction center, a high-energy electron is transferred from the special pair to a carrier that becomes part of an electron-transport chain. Not shown is a set of intermediary carriers embedded in the reaction center that provide the path from the special pair to this carrier (orange). As illustrated, the transfer of the high-energy electron from the excited chlorophyll special pair leaves behind a positive charge that creates a charge-separated state, thereby converting light energy to chemical energy. Once the electron in the special pair has been replaced (an event we will discuss in detail shortly), the carrier diffuses away from the reaction center, transferring the high-energy electron to the transport chain.
Chloroplasts and Photosynthesis
reaction
center electroncarrier
thylakoid membrane special pair e– TRANSFER OF HIGH-ENERGY ELECTRON FROM SPECIAL PAIR CREATES A CHARGE SEPARATION CARRIER PASSES HIGH-ENERGY ELECTRON TO TRANSPORT CHAIN charge-separated state SPECIAL PAIR ELECTRON REPLACED
Figure 1: Conversion of light energy to chemical energy in a microalgal cell [11].
The special pairs of both photosystems are now missing an electron. In PS II this is replenished by an associated protein complex that removes electrons from two water molecules, thus producing oxygen gas and four protons. PS I receives its electron from PS II; the electron travels from PS II through an electron-transport chain to the special pair in the reaction center of PS I, during which some of its energy is used to produce ATP. The electron remains there until the special pair receives energy yet again, after which it is used to produce NADPH. Both of these energy carriers are then used in the dark reactions to produce carbohydrates from carbon dioxide through carbon fixation [11].
Figure 2: Interaction between PS I and PS II to form energy carriers ATP and NADPH. Q, pC, Fd and FNR are components not discussed here [11].
Carbon dioxide is attached to ribulose 1,5-biphosphate, a sugar derivative, by the en-zyme ribulose biphosphate carboxylase, more commonly referred to as Rubisco. This produces an intermediate that enters the Calvin cycle, which uses three molecules of carbon dioxide, five molecules of water, nine molecules of ATP and six molecules of NADPH to produce one molecule of glyceraldehyde 3-phosphate. This molecule is a precursor of the various organic molecules that can be produced in the cell depending on what it requires at the time [11].
In addition to facilitating carbon dioxide fixation, Rubisco can also facilitate pho-torespiration, a process where organic carbon is converted to carbon dioxide with consumption of oxygen gas. This is favored when the O2/CO2 ratio is high, whereas a low ratio favors carbon dioxide fixation [11]. This means that it is important to remove oxygen from the photobioreactors to favor photosynthesis.
This subsection has given a brief description of how photosynthesis occurs in mi-croalgae and how solar energy and carbon dioxide is used to produce biomass on a cellular level. The next subsection will present how this process and the level of irradiance effects the growth of microalgae.
2.2.2 The Effect of Light on Microalgal Growth
As previously mentioned, microalgae harvest solar energy in order to sustain life. The chlorophyll molecules of the microalgae’s photosystems I and II absorb light from the visual spectra of sunlight, referred to as photosynthetic active radiation, PAR. This light spans radiation from 400-700 nm, with most of the light being absorbed around 450-475 nm (violet light) and 630-675 nm (red light), thus giving chlorophylls their characteristic green color. Furthermore, microalgae have accessory light-harvesting pigments that absorb light between 400-550 nm. These pigments can serve several different purposes, e.g. enhancing light absorption by transferring excited electrons to chlorophyll a but also protect the cell from excess irradiance and reactive oxygen species, referred to as ROS [12].
point is called the light compensation point. At a low irradiance, growth is light-limited and the rate of photosynthesis will depend on the rate of the light reactions, namely photon absorption. At higher irradiance, the culture transfers from light-limited to light-saturated, which is represented by the convex portion of the curve, and the dark reactions of photosynthesis now become limiting, given nutrient-replete conditions [14]. The saturation point, Ik, indicates when this shift occurs [12, 15].
Environmental Stress Physiology 91
Schematically, the sequence of events associated with the response of living cells to an environmental change may be described as follows:
Steady state → Environmental change → Sensing mechanism → Response mechanism adaptation → New steady state
Outdoor algal cultures are exposed to a variety of changes in environmental conditions. These changes take place in two different timescales. One is the diurnal cycle that includes variation in light and temperature in a 24-h cycle. The other is a seasonal cycle that varies according to the climatic and geographical location of the particular habi-tat in which the algae are growing. In dense algal cultures used in algal biotechnology, a third cycle is imposed by mixing and culture depth (optical path length of reactor), which mainly results in a light–dark cycle which fluctuates in terms of fraction of seconds or minutes as compared to the hours or months in the other two cycles.
Microalgae have indeed developed diverse mechanisms for sensing and acclimating to changes in their environ-ment (for reviews see Pfannschimdt et al., 2001; Li et al., 2009). Acclimation responses observed include the alter-ation of light-harvesting complex synthesis and degrada-tion in response to changes in light quality and intensity. Such alterations are aimed to help balance efficiently the absorption of excitation energy and the production of reduc-ing power (NADPH) and chemical energy (ATP) with their utilization for growth and reproduction. Inability to main-tain this balance due to excess excitation of the photosyn-thetic reaction centers may result in the production of toxic reactive oxygen species (ROS) that may lead to photoox-idative death. As implied, many of the stress responses and adaptive processes are associated with the photosyn-thetic apparatus. In recent years, it has become evident that photosynthesis itself contributes important signals to this light control of gene expression by means of changes in the reduction/oxidation state of signaling molecules which are induced by changes in quality and quantity of incident light. This provides a feedback-response loop in which the expression of photosynthesis genes is coupled to the func-tion of the photosynthetic process and highlight its dual role in energy fixation and the reception of environmen-tal information (Pfannschimdt, 2003). The great variety of these signaling mechanisms is summarized under the term “redox control.” The concept of photosynthesis as a sensor for environmental information was originally introduced as the “grand design of photosynthesis” by Arnon (1982) and further extended by Anderson et al. (1995) and Huner et al. (1998).
6.2 LIGHT AND PHOTOSYNTHESIS RATE 6.2.1 P versus I curve
The light response curve (P/I) of microalgae has been used as a tool in analyzing the response of photosyntheti-cally grown cells to the light environment and at the same time to analyze the response of the photosynthetic appa-ratus to environmental conditions. The P/I curve can be divided into three distinct regions: a light-limited region, in which photosynthesis increases with increasing irradi-ance; a light-saturated region, in which photosynthesis is independent of irradiance; and a photoinhibited region, in which photosynthesis decreases with further increase in irradiance. In addition, an intermediate region where there is either a gradual or abrupt transition from light-limited to light-saturated photosynthesis has been identified (Prioul & Chartier, 1977; Leverenz, 1987). A typical response of pho-tosynthesis (CO2assimilation or O2evolution) to increas-ing irradiance is shown in Figure 6.1. At low irradiance, photosynthesis rates are linearly proportional to irradiance. In this region of the P/I curve, the rate of photon absorption
Irradiance Photoinhibition α Ik Pm Ic Rd 0 Net P
Figure 6.1. A schematic diagram of photosynthesis (P) versus irradiance (I) curve, showing the typical photosynthetic parameters. The light-saturated rate is denotedPmax. At low irradiance, photosynthesis
rate is approximately a linear function of irradiance, and the ratio between photosynthesis and irradiance is often denoted by the symbol α. The saturation irradiance,Ik, is given as intercept between α and
Pmax. At irradiance above the optimum,
photosynthesis rates usually shows a decline from the light-saturate value. Dark respiration is denoted byRd. The compensation irradianceIc, where no net
oxygen evolution is observed.
Figure 3: Light response curve showing the relationship between net rate of photosynthesis (net P) and irradiance (I). Rd is the dark respiration, Ic is the compensation irradiance where the rate of
photosynthesis equals the rate of respiration, – is the linear relationship between P and I at low irradiance, Ik is the saturation irradiance and Pmis the light-saturated rate of photosynthesis, the
highest attainable when light is the limiting factor of photosynthesis [12].
Photoacclimation is a process by which microalgae adapt their photosynthetic appa-ratus to the light available. It is generally defined as the cell decreasing its chlorophyll A and accessory light-harvesting pigment contents at high irradiance [12]. The cell can acclimate in two ways, either by reducing the size of its light-harvesting com-plexes (mainly by reducing the antennae size) or the number of reaction centers [15].
Once the culture is fully light-saturated, an increase in irradiance will not incur an
increase in photosynthetic rate, which will have reached its maximum value Pmax.
considered photoinhibited if it shows a decrease in the rate of photosynthesis with an increase in irradiance [16].
Irrespective of irradiance, photodamage of PS II will occur, however the microalgae are able to repair the damage to an extent. Reactive oxygen species, which are pro-duced due to excess excitation of the reaction centers of PS I and II, are thought to inhibit the repair by suppressing synthesis of proteins required in the repair cy-cle. Photoinhibition will become more severe when the microalgae are exposed to environmental stresses, such as very low and high temperatures and high oxygen concentrations, as these factors also suppress the repair of photodamage to PS II [12]. This highlights the importance of process control of the cultivation system. How microalgal growth depends on light may change in reality, giving the P/I curve a different appearance. The shape will depend on conditions of growth, e.g. if the culture is photoinhibited or if the microalgae are subject to other physiological stresses the convexity of the curve will change [12]. Next the different phases of microalgal growth in a batch will be presented.
2.2.3 The Different Phases of Microalgal Growth
During a batch culture the microalgal growth goes through different phases, namely the lag phase, the exponential phase, the linear growth phase and the stationary phase, as shown in figure 4 (where marking of the lag phase is omitted). Cultivation starts with the lag phase, which is a short period of time right after inoculum. During this phase, the microalgae are adjusting to their new environment, whereby there is a short lag until net growth is observed [17].
After this follows the exponential growth phase, so called because the growth of the microalgae is an exponential function of time, given that there is not a depletion of the raw materials required for growth. The culture continues to grow in this fashion until all of the light reaching the reactor is absorbed by the culture. Once the culture reaches this point it enters the linear growth phase, where the culture is light-limited, and growth of the microalgae is a linear function of time. Eventually one of the raw materials required for growth is depleted and the growth enters the stationary phase where no net growth is observed, meaning that growth and cell death occurs in equal amounts [17].
2.2.4 Nutrients
Equation 1 in subsection 2.2.1 is a simplification of photosynthesis and it gives the impression that microalgal cells only consist of carbon, oxygen and hydrogen. In reality, the cells contain many elements in different amounts. Besides carbon, nitro-gen and phosphorus are the two most important nutrients for the microalgal cell. Nitrogen constitutes between 1-10 % of the cell and plays a major role in all of its functions [18]. Much of the nitrogen in the cell is used in the photosynthetic appa-ratus, making it important for photosynthesis. A limitation in nitrogen thus limits growth not only due to incorporation in the cell and its numerous maintenance and growth functions but also because of its importance in the photosystems. Nitrogen is usually supplied as nitrate1N O≠32, but ammonia1N H4+2and urea are also common sources of this important nutrient [18].
Phosphorus constitutes approximately 1% of the cell, but is vital to cell growth due to its prominent role in energy transfer. Nitrogen and phosphorus are considered macronutrients, meaning they are required in relatively large amounts. Microalgae require a variety of other nutrients in smaller amounts, referred to as micronutrients. Among these are sulphur, potassium, sodium, iron, magnesium and calcium as well as trace amounts of boron, copper, manganese and zinc [18].
2.2.5 Annual and Diurnal Cycles
For a microalgal culture, temperature and light varies throughout two natural cycles: an annual cycle with seasonal changes and a diurnal cycle with light and dark hours. The nature of these cycles will depend on the geographical location [20].
A third cycle occurs due to the fact that the photobioreactor has two regions, a light region and a dark region, and through the mixing that is applied in the culture system. The light region is near the surfaces of the reactor and the dark region is toward the middle of the reactor where no light reaches because it has been absorbed by the cells closer to the surface. How far the light reaches into the reactor will depend on the type of microalgae, the concentration of microalgae and the depth of the reactor. The third cycle is applied by mixing and is necessary in order for all cells to receive a moderate amount of light, i.e. for them to not be light-limited nor photoinhibited, and to achieve proper mass transfer [12]. Part of the research around microalgal production is to optimize this cycle, in order to make the process more efficient and less costly.
2.2.6 Culture Systems
Large-scale cultivation of microalgae is performed either in large, open ponds or in enclosed photobioreactors (PBRs). Common for all types is that they allow light to enter the reactor, and depending on the dimensions of the reactor or pond the light path through the reactor can be of different lengths [21]. As mentioned in subsection 2.2.5, one of the key characteristics of a culture system is the mixing. Sufficient mixing will ensure that the cells experience short cycles of both light and dark periods, that biomass gradients do not build up in the system, that carbon dioxide is supplied to the culture more efficiently and it is important for the removal of oxygen [12, 21].
There are three main types of PBRs: open ponds, tubular reactor (plug-flow reactor) and flat panels, but also less common reactors such as spiral, hybrid systems and biofilm reactors exist. Open ponds can come in different designs, with raceway ponds being the most common, and are usually very large pools of moderate depth (20-30 cm). Raceway ponds are long ponds arranged in a manner shown in figure 5, where the culture is circulated along the pond by a paddle wheel. The open nature of the system makes it difficult to control and it suffers from evaporation as well as rainfall, suboptimal temperatures and contamination of other species. Despite these issues it is the most common culture system for some microalgal species, most importantly because of its simple construction and low cost [21].
Figure 5: A typical raceway pond for microalgal production [22].
Figure 6: Two types of tubular PBRs: to the left a horizontal configuration with a large diameter and to the right a configuration with a smaller diameter where the tubes are arranged in a framework on top of each other [23, 24].
The tubular reactor is constructed of long, enclosed tubes of a relatively small di-ameter in which the culture is circulated, giving a turbulent flow in the reactor thus reducing fouling of the reactor. Mass transfer and nutrient supplement is conducted in a separate chamber where carbon dioxide is supplied and oxygen is stripped off. There exists several different configurations of tubular reactors. They can be of a large diameter and positioned horizontally in a serpentine or manifold manner on the ground or with a smaller diameter and arranged horizontally in a framework on top of each other as shown in figure 6. They can be constructed of rigid or flexible materials, most notably glass and polyethylene [21].
These are only a few of many possible designs for tubular photobioreactors. Com-pared to a raceway pond, the culture system costs are higher as well as the energy consumption due to the mixing requirements. However, they have a higher produc-tivity per area and are capable of producing microalgae at a higher biomass concen-tration than raceway ponds, a characteristic that is important because the higher the concentration, the lower the cost in the subsequent harvest step considering the smaller volume that needs to be handled and the the lower amount of water that needs to be removed.
Figure 7: Flat panel PBRs: To the left a rigid PBR used by the German company Subitec GmbH and to the right a flexible PBR used by the American company Algenol [4, 25].
of the culture during parts of the day. Mixing is accomplished by bubbling of the air and carbon dioxide gas mixture through the culture. This will ensure turbulence inside the reactor. A gas pocket is usually employed in the reactor that enables gas exchange whereby the culture does not need to pass through a degasser. However, for optimal cultivation the bubbling rates need to be high and this incurs a high energy consumption, one of the main drawbacks of this reactor type along with its generally high prices [21].
As with the tubular reactor, there are many different configurations of flat panel PBRs. They have different light paths, can be vertical or inclined towards the sun, made of rigid or flexible materials, have flat surfaces much like a window or a more corrugated surface in order to optimize light use. Figure 7 shows two configurations of flat panels used in pilot scale production of microalgal biomass.
2.2.7 Genetic Engineering for Higher Productivities
One of the reasons for the present unfeasibility of a large-scale microalgal production process for biofuels is the inability to reach the high, theoretical productivities in the current culture system. When a culture becomes dense the light impinging on the culture does not reach very far through the culture. Cells at the surface absorb much of the light and run the risk of becoming photoinhibited while the cells further in do not receive enough light; both cases decreases the productivity. According to [27], approximately 60% of the daily irradiance is dissipated by the photosynthetic apparatus as heat through the process of non-photochemical quenching (NPQ). It is a wasteful process and there is an abundance of research going into resolving this issue [12, 27].
Genetic engineering involves genetically altering the microalgal cell to improve the process and make it more economic. It could involve the regulation or deregulation of genes as well as inserting new genes from another organism. One of the major issues the field is trying resolve is to improve the photosynthetic apparatus of the cells. One way of doing this is to reduce the size of the light-harvesting antennae. This would increase the transmittance in the culture whereby the light distribution becomes more even and less energy is wasted through NPQ. This could improve the productivity of the culture by 300%, if the antennae are reduced to the minimum size required for photosynthesis [27]. This would also increase the light saturation of the photosynthetic apparatus, thus allowing for a more efficient use of the light impinging on the reactor surface.
Other aspects of light utilization are also studied; e.g. Gressel et al. [28] have found a fluorescent protein that absorbs UV light and emits PAR, thus increasing the light available for the culture locally, which increases the productivity globally [28]. A better light utilization in the reactor would allow for reaching higher biomass concentrations, which would reduce the costs for both cultivation and harvesting of the biomass.
2.2.8 Modeling of Microalgal Growth
Microalgal growth can be modeled in various ways. The most common and simple expression is that of the Monod equation for growth of microorganisms, which con-siders one factor the limiting factor of growth, e.g. availability of light, nutrients or carbon dioxide. Equation 2 shows this equation where light is the limiting factor, followed by a differential equation for cell growth, shown in equation 3.
µ= µmax· Iav Ks+ Iav
(2) dX
dt = f (t, X) = µX (3)
An alternative way to model microalgal growth is by using the Droop model. This model considers microalgal growth dependent on so called cell quotas of a limiting nutrient, while the cell’s uptake of said nutrient is dependent on the external nutrient concentration [31]. Such a modeling effort is proposed by [31], which considers nitro-gen the limiting nutrient and incorporates the light gradient in the photobioreactor as well as photoacclimation [31].
The Monod equation, where light is the limiting factor, has been modified by various researchers to better fit the equation to real growth by incorporating elements that account for e.g. photoinhibition and photoacclimation. An extensive review of such models, as well as other modeling aspects of microalgal growth, is performed by [32]. The review mainly covers models of the relationship between light and microalgal growth and divides such models into three categories [32].
Type I models determine microalgal growth as a function of incident light intensity on the reactor or the average light intensity inside the reactor. Type II models determine microalgal growth as a function of the light gradient in the reactor and thus model the conditions for each cell more accurately. Type III models are similar to type II models, only they also include modeling of the short light and dark cycles induced by mixing in the reactor. A type II model is deemed the best choice, as type I models are only valid for the operating conditions for which they were developed and type III models suffer from high complexity making their application difficult [32].
2.3 Alternatives for Harvesting of Biomass
When cultivation is finished and the biomass is to be harvested, a few challenges present themselves. The biomass concentration is very low and to ease product recovery, large amounts of water needs to be removed, which is costly both econom-ically and energeteconom-ically. It can surmount to approximately 20-30% of the total cost [35].
Irrespective of the size of the culture, the biomass concentration restrictions of cur-rent cultivation systems remain, meaning that large scale production of microalgal biomass will incur large harvesting volumes. The chosen harvesting process thus needs to be of low cost and have a low energy consumption while being easily scaled up under these premises. Choosing a harvesting process will depend on the species used, the culture conditions and the desired product. Due to the variety in size and shape of microalgae as well as in the constructed processes there is no universal method for a microalgal process and the costs and energy requirements for harvest-ing can be very different dependharvest-ing on the process [36]. Three factors determine the performance of a harvesting process: the efficiency of cell recovery, the concentration factor (CF) and the productivity of the process. The efficiency of the cell recovery is defined as how much biomass is lost during the process. The concentration factor is defined as the increase in biomass concentration before and after harvesting. The productivity of the process is defined as the rate of water removal [37].
2.3.1 Coagulation and Flocculation
Due to the small size of the microalgal cells they have a very low settling velocity. This can be improved by forming cell clusters, either via coagulation or flocculation, thus increasing the particle size. Coagulation is the process where an addition of electrolytes will cause the cells to aggregate and with flocculation this is performed by the addition of polymers [39]. The cells have a negative charge, causing them to repel each other and prevent aggregation. In order to reduce and/or neutralize this charge, a coagulant or flocculant is added, which allows van der Waals forces to aggregate the cells. The process is dependent on the temperature and especially the pH of the medium and requires intense mixing for a short period of time in order to disperse the coagulants/flocculants followed by moderate mixing to enhance aggregation [36, 40]. The selection of coagulant or flocculant as well as operating conditions will depend on the yield, which must be determined experimentally for any given process as this will vary depending on the species of microalgae. The pre-concentration step can be performed with a variety of chemicals but also with different biopolymers. Furthermore it can be performed with autoflocculation, which is performed through either a natural or chemically induced pH increase, whereby carbonates and hydroxides precipitate and flocculate the microalgae [37].
Coagulation is performed with multivalent metal salts of aluminum and iron, e.g. aluminum sulfate and ferric chloride [39]. [40] report that the use of metal salts can be problematic due to the process’ sensitivity to pH, the variability in success for different microalgal species and the fact that the harvested biomass will be contam-inated with the coagulant. [36] report yields of 60-82% for different species when using aluminum sulfate at concentrations varying from 30-1000 ppm.
and polyethyleneimine [36].
In order to reduce the contamination of the biomass after harvesting, natural poly-mers (also called bioflocculants) have been evaluated for use in the harvesting process. Chitosan, a derivative of chitin, and other microorganisms have received some at-tention, with chitosan showing cell recoveries of 85-95%. It creates larger flocs than polyelectrolytes, thus giving a faster separation, however an issue with the use of chitosan is that it can be very expensive depending on its origin; costs can be up to a hundred times the cost of PAC [36]. Table 1 shows a comparison of efficiencies and prices of the common coagulants/flocculants aluminum sulfate (AS) and PAC with that of chitosan.
Table 1: Flocculation of P. tricornutum with PAC, AS and chitosan [41].
Flocculant pH Recovery efficiency [%] CF Price [$/kg of dry reagent]
PAC 7.5 66.60 6.5 0.429-1.429
AS 5.9 82.60 7.2 0.976-2.073
Chitosan 9.9 91.80 8.9 2-1001
1Prices dependent on the cost of chitosan raw material
Lastly, autoflocculation occurs at elevated pH levels where carbonate and other hy-droxides precipitate, mainly calcium carbonate and magnesium hydroxide. The pre-cipitates attach to the microalgal cells and flocculation occurs. This autoflocculation happens naturally to a degree because of carbon dioxide consumption in photosyn-thesis but it can also be induced by addition of e.g. caustic soda or lime. The optimal pH will vary with the microalgal species; [41] showed that for P. tricornutum the recovery efficiency decreases when the pH is increased by more than 0.5-0.7 units from the pH of cultivation [36, 41].
2.3.2 Gravitational Separation Processes
viable; [36] provide a lower limit of 0.0001 m/s [36]. Sedimentation is a low cost method and it has a relatively low energy consumption of 0.1kWh/m3, but considering
the small size of microalgal cells it is questionable as a viable option. It could be viable with a precursor step such as coagulation or flocculation, but this needs to be shown effective at a large scale [37, 38].
Flotation is used when the density of a particle is lower than that of the medium. Air is either dispersed or dissolved in the medium whereby bubbles of varying size are created. Microalgal cells will attach to the bubbles that will surface after which the float is skimmed off [37]. The smaller the size of bubbles, the more efficient separation but also the more costly operation economically and energetically. In dispersed air flotation the air is injected into the fluid that then passes through a disperser, creating bubbles of size 700-1500 mm. In dissolved air flotation air is dissolved in a water stream at pressures higher than atmospheric. This stream, which is saturated with air, is then injected in the medium at atmospheric pressure through nozzles, which produce bubbles of sizes 10-100 mm. Flotation is considered more efficient than sedimentation and a proposed harvesting configuration is flocculation followed by dissolved air flotation [37]. The energy consumption of an optimized flotation process is reported as 0.3kWh/m3 [42].
2.3.3 Centrifugal Recovery
In centrifugation, solids or liquids of different densities are separated from each other by making use of the centrifugal force. In terms of time and cell recovery it is an efficient separation method that is well established for harvesting small cultures. The efficiency will depend on size and density of the particles as well as the force applied. Cell recovery can be well over 95% when using large acceleration factors, but this requires a high input of energy and unfortunately the cell recovery decreases markedly when operating with lower acceleration factors as shown in a study by [43]. The method requires high operating and investment costs, and despite it being time efficient and proven for smaller cultures, it could become time consuming and expensive for larger cultures [37].
The decanter centrifuge handles somewhat larger particles than the disc stack, rang-ing from 10 mm to well over 1 mm. It is also capable of producrang-ing biomass of a much higher concentration than the disc stack, up to 50% TSS. However, these capabilities come at a very high energy consumption of 8kWh/m3 [35].
2.3.4 Filtration
Filtration is a separation method that removes solids from a fluid by letting it pass through a porous media or a screen that retains the solids. The feed side is pressurized and as the slurry is fed to the filter, water passes through it and the particles are blocked and start to form a cake over the filter. The cake is an important part of the effective filter but it also causes the required pressure on the feed side to increase [44]. This will lead to high energy costs for prolonged filtration.
Depending on the pore size of the filter, the method is classified as macrofiltration (> 10 mm), microfiltration (10 ≠ 0.1 mm) and ultrafiltration (0.02 ≠ 0.2 mm). This suggests that macro- and microfiltration are applicable to harvesting of microalgae and cyanobacteria. Filter presses, rotary drum filters could be an interesting choice as a second harvesting step due to their flexibility of operation and simple design [38]. [35] have shown that a belt press can be used as a second harvesting step with a concentration factor of 180 for a large microalgal species and an energy consumption of 0.5 kWh/m3 [35].
Fouling can become an issue with filtration, which means that the filter gets clogged and performance drops rapidly. This would incur high maintenance and operating costs for cleaning and/or replacing the filter [38]. Another issue with using filtration for microalgal cultures is that the cells are fairly sensitive to shear stress, whereby the transmembrane pressure applied to the feed side of the filter should not exceed 4-5 kg/cm2 [35]. This, together with high energy costs, limits its use as a method
3 The Model
The model is constructed in Python version 3.4.1 and can be divided into four main parts: user-supplied data, cultivation, harvesting and economic evaluation. Each part of the model is placed in separate files that contain various functions that per-form the calculations. Each of these files are then run from a main file, which executes the program. The model is constructed using Object Oriented Programming (OOP), which involves creating classes that define a template for objects. The classes of the model are defined in the file Biomassclass. Objects pertaining to a class can then be created and are used to store and pass around parameters in the model. The files can be found in appendix E. A schematic of the modeled process is shown in figure 8 along with input parameters to the model and the twelve different configu-rations. The parameters that are hard-coded into the model can be found in table 7 in appendix A.
Flat panel PBR Flocculation & flotation Flotation Centrifugation Filtration Centrifugation Filtration Flocculation & sedimentation Centrifugation Filtration
Tubular PBR Flocculation & flotation Flotation Centrifugation Filtration Centrifugation Filtration Flocculation & sedimentation Centrifugation Filtration Cultivation Harvest step 1 Harvest step 2 • Microalgae type • Microalgae diameter
• Tmin for growth
• Tmax for growth
• Topt for growth
• pHopt for growth
• Production demand
• Irradiance data
• Temperature data
• Electricity price
General input data
• Final concentration • Total reactor volume • Batches/year • Volumetric flow to harvest stage • Reactor dimensions
• Reactor light path
Output Reactor specific 1 2 3 4 5 6 7 8 9 10 11 12
Various parts of the model require species-specific data and constants, meaning that the model can only be used for a specific species at a time; currently the species is P. tricornutum. The file Load retrieves user-supplied data from a text file as well as creates objects used in the different parts. The file Cultivation simulates cultivation based on the user-supplied data for two different reactors: a flat panel and a tubular PBR. Furthermore, it determines plant size depending on production demand and costs and energy consumption of the cultivation stage.
The file Harvest simulates harvesting of biomass from the medium after cultivation. Harvesting is modeled as two separate steps, a pre-concentration step and a second step that produces a wet biomass paste. The cost and energy consumption of each stage is calculated and provided to the last part of the model: the economic eval-uation. This is performed in the file Economy, which calculates total fixed capital investment, total costs and determines the cheapest and the most expensive config-uration, which are presented to the user along with the price in Ä/kg.
Furthermore, the model contains a file Plotter that illustrates results of the model by plotting the behavior of the cultivation stage and different plots evaluating different aspects of the costs of the process.
3.1 Cultivation
The literature study presented in section 2 shows that the cultivation of microalgae can be limited by certain factors. Of these, light attenuation is deemed the most significant because light is the only factor whose availability to the microalgae cannot be controlled through process control, given that the light source used is sunlight. Modeling of microalgal growth is thus performed using a Monod-type expression for the specific growth rate where light is the limiting factor, the Lambert-Beer law for light distribution in the culture and a differential equation for biomass growth. 3.1.1 Light Available for Photosynthesis
account. The irradiance comprises two different components: global irradiance and diffuse irradiance which are added together. Furthermore, irradiance data are taken for both the south and the north side of the PBR, which are added and assumed originating from the same direction. The irradiance data is read into the model from a text file and converted from W/m2 toµmol/m2,s, as well as converted to PAR, which
is assumed as 43% of incident irradiance in accordance with [46].
One of the major constraints of growth of microalgae is light utilization in the pho-tobioreactor. As described in subsection 2.2.5 the light may not reach all the cells and each cell will experience a different light intensity. This local light intensity can be calculated using the Lambert-Beer law for attenuation of light in a material or fluid. The law states that, for low to moderate concentrations, the light intensity decreases inside the material according to:
I = I0· e(≠L·Ka·Cb) (4)
where I0 is the incident irradiance on the reactor surface in PAR, L is the optical light path of the reactor, Ka is the extinction coefficient of the biomass and Cb is the concentration of biomass in the reactor [47]. With the geometry of a flat panel photobioreactor shown in figure 9, the average light intensity for the whole volume in the reactor can be calculated by integrating the Lambert-Beer law over the volume of the reactor: Iav = ´ vIp(x) · dV V = ´L 0 I0· e(≠Ka·Cb·x)· H · L · dx H· L2 (5)
Integration then gives the final expression of: Iav =
I0 L· Ka· Cb ·
1
1 ≠ e(≠Ka·Cb·L)2 (6)
L
x
H$
I0$
Figure 9: Geometry of a flat panel reactor [47]. ! ! ! I0# ϕ# x# R#
Figure 10: Approximating the geometry of a tubular PBR as numerous parallelepipeds that the light travels through [47].
The average light intensity can then be calculated as follows:
Iav = 2 · I0
R· Ka· Cb· fi ·
A
1 ≠ˆ cos(Ï) · e[≠2·R·Ka·Cb·cos(Ï)]· dÏ
B
3.1.2 Temperature Dependence of the Specific Growth Rate
As discussed in subsection 2.2.2, the ambient temperature will affect microalgal growth in different ways, with growth being optimal at a certain temperature. In order to account for this effect, the Monod-type equation as shown above is com-plemented by an expression where the maximum specific growth rate depends on temperature.
The temperature dependence of the maximum specific growth rate of microalgae,
µmax, is modeled according to [48], where it is modeled between the minimum and
maximum temperature for growth of a specific species, Tmin and Tmax respectively.
µmax = 0 for T < Tmin
µmax = µopt· „ (T ) for Tmin < T < Tmax
µmax = 0 for T > Tmax
where µopt is the maximum specific growth rate at the optimal temperature for
growth, Topt, and „ (T ) is given by equation 7:
„(T ) = (T ≠ Tmax) · (T ≠ Tmin)
2
(Topt≠ Tmin) · [(Topt≠ Tmin) · (T ≠ Topt) ≠ (Topt≠ Tmax) · (Topt+ Tmin≠ 2 · T )] (7) Temperature data is taken from the same source as the irradiance data for the same conditions [45].
3.1.3 Specific Growth Rate
Determination of the specific growth rate, µ, is based on the Monod equation, shown in equation 8:
µ= µmax· Iav Ks+ Iav
µ= µmax· I 1 b+c I0 2 av Ë Ik· 1 1 +1I0 Ki 2a2È 1 b+c I0 2 + I 1 b+c I0 2 av (9) where a, b and c are constants derived from experimental work by Molina Grima et al. [33]; Ik is microalgal affinity for light and Ki is a photoinhibition constant [33]. 3.1.4 Biomass Growth, Carbon Dioxide and Nutrients
Growth of microalgae is described by the differential equation: dX
dt = f (t, X) = µX (10)
where X is the biomass at time t. The differential equation is an initial value problem and X is solved for numerically using the Runge-Kutta fourth-order method:
Xn+1 = Xn+
h
6 (k1+ 2 · k2+ 2 · k3+ k4) (11)
tn+1 = tn+ h (12)
the Runge-Kutta calculations as a 10% decrease in biomass for each iteration given that the irradiance is not zero [34]. During the dark hours of a day, the microal-gae cease to grow, thus giving a final concentration at the end of each day. Dark respiration is modeled as a 10% decrease of that final concentration. The extent of dark respiration can vary largely depending on culture conditions and environmental factors; the value of 10% is chosen arbitrarily [13].
The supplement of carbon dioxide is modeled through a mass balance over each time interval, once ∆X is known, using Henry’s law (equation 17) for the dissolution of gases in liquids and the dissociation equilibria of carbon dioxide in water (equations 18 and 19).
PCO2 = H · CCO2(aq) (17)
where PCO2 is the partial pressure of carbon dioxide above the liquid, H is the Henry’s
constant and CCO2(aq) is the concentration of dissolved carbon dioxide in the liquid.
After the carbon dioxide has dissolved, it reacts with the water in the following equilibria:
CO2,aq+ 2H2O ⌦ H3O++ HCO3≠ HCO3≠+ H2O ⌦ H3O++ CO2≠3
The concentrations of the different species are then given by the following equations: k1 = [H3 O+]ËHCO3≠È [CO2]aq (18) k2 = [H3 O+]ËCO32≠È Ë HCO≠3È (19)
where k1 and k2 are the dissociation constants. Most microalgae species grow in wa-ters of neutral or close to neutral pH and since the speciation will depend on the pH, as given by a Bjerrum plot, a large portion of the carbon will be in the form of
car-bonate (HCO≠
and the remaining 20% is from dissolved carbon dioxide gas. No information was found regarding the amount of each carbon species used for photosynthesis, therefore
the ratio of 4:1 was assumed based on the excess of HCO≠
3. The ratio was chosen
arbitrarily and can easily be changed by the user.
The carbon dioxide consumption is calculated as shown in equation 20: CO2,consumption = ∆X · qC
MC
(20) where qC is the fraction of carbon in microalgae and MC is the molar mass of carbon. The consumption of carbonate and dissolved carbon dioxide at time t is given as:
[CO2]aq = CO2,consumption· 0.2 (21)
Ë
HCO≠3È= CO2,consumption· 0.8 (22)
Carbon dioxide supplement is then controlled depending on the carbonate concen-tration; if it goes below a certain value, carbon dioxide is supplied to the culture with air at 15 v/v%.
As previously described in section 2.2.5, microalgae require various nutrients to grow. The nutrient consumption is modeled in a simple manner in accordance with [26], where the production of 1 kg of biomass requires 1 kg of culture medium premix. 3.1.5 From Batch to Annual Production
The previous sections describe how the model is constructed to calculate biomass production on a batch basis. The length of a batch is determined by the final concentration of biomass, which is hard-coded into the model. This value is chosen by running the model for 41 linearly spaced final concentrations between 1-10 g/L and finding the final concentration that gives the lowest overall cost/kg.
The batch time is given by the cultivation stage. This time is reduced by a specified number of hours in order to account for the lag phase of growth in the PBRs as well as emptying and filling of the PBRs with medium. Once the batch time is known, the number of batches required per year can be calculated as follows:
Nbatches =
tprod
tbatch
where tprodis the production time/year, which as of now is set to 8760 hours, whereas some downtime during the summer would be plausible for a real plant. Given the number of batches and the annual production demand, the amount of biomass per PBR and batch and subsequently the number of PBRs required can be calculated for the flat panel PBR in equations 24 and 25 respectively:
Xbatch,f p = Cf inal· Vf p (24)
NP BR,f p =
Xyear
Xbatch,f p· Nbatches· ÷harvest
(25)
where X denotes the amount of biomass in g/m3 and ÷
harvest is the total biomass recovery in the harvesting stage, which needs to be included in order to correct for the biomass lost during harvesting.
For the tubular PBR, the parameter deciding the size of the reactor, namely its length, is calculated via the total reactor volume required per batch:
Vtot = Xyear Nbatches·÷harvest Cf inal (26) Ltube = Vtot fi· R2 (27)
The area of the plant will depend on the production demand in a linear relationship. The area is minimized when the rows of flat panel PBRs/number of tube bends are minimized, which is not plausible for economic reasons as well as cultivation efficiency. The plant is thus assumed to approach a square shape with regard to the cultivation section and an extra 20% of area is added to account for the harvesting section and other buildings.
3.1.6 Mixing in the PBRs: Pump and Fan Requirements
